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Title: Miscellanea Curiosa, Vol. 1

Editor: Edmond Halley

Contributor: M. de Fontenelle
George Garden
Clopton Havers
Richard Mead
Isaac Newton
Royal Society
John Wallis

Release date: August 27, 2015 [eBook #49791]
Most recently updated: October 24, 2024

Language: English

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*** START OF THE PROJECT GUTENBERG EBOOK MISCELLANEA
CURIOSA, VOL. 1 ***

Transcriber's Note.
Apparent errors in mathematical expressions have been retained,
although apparent typographical errors elsewhere in the text have
been corrected. Inconsistencies in hyphenation have been
retained.
The decimal point may be indicated by a "." or "," while
illustrations are referred to as a "Plate" or a "Tab."
The frontispiece probably depicts Charles II.
The Table of Discourses has been amended to include one
omitted title and to correct erroneous page numbers.
Fifth roots and "nth" roots are indicated by 5√ and n√
respectively.

M: Ver Gucht Sculp:

Miscellanea Curiosa.

CONTAINING A

COLLECTION
Of some of the Principal

PHÆNOMENA
IN

NATURE
Accounted for by the Greatest Philosophers of this Age;
BEING THE

Most Valuable Discourses, Read and Delivered to the Royal Society, for
the Advancement of Physical and Mathematical Knowledge.
As also a Collection of Curious Travels, Voyages, Antiquities, and Natural
Histories of Countries; Presented to the same Society.

In Three VOLUMES.

The Second Edition; To which is added, A Discourse of the Influence of the Sun and Moon on
Humane Bodies, &c. By R. MEAD, M. D. F. R. S. And also Fontenelle's Preface of the
Usefulness of Mathematical Learning.

VOL. I.

LONDON:
Printed by F. M. for R. Smith, at the Bible under the Piazza of the Royal Exchange in Cornhill. 1708.

TO THE

READER.
OME of the Principal Discoveries and Enquiries, both in Physical and
S Mathematical Learning, being register'd in the Voluminous Journals of
the Royal Society, are amongst a multitude of less useful Matters, so
Obscurely hid, that but very few inquisitive Gentlemen ever so much as
heard of them.
The Design therefore of the ensuing Collection, is to digest in a
convenient Method, all the most curious Philosophical and Mathematical
Discoveries, as they are to be met with, which may any way tend to the Use
of Life or Advancement of Arts and Sciences.
And on this Occasion, it will be convenient to intimate to the Reader;
First, That the Theories and Discourses here collected, have already past
the Censure of the Learned World: Who have acknowleg'd them the most
satisfactory Accounts of Nature's Proceedings, wherein some of her greatest
Depths are fathom'd, and a Foundation laid for Posterity to build an infinite
Superstructure.
Secondly, That they are related (Verbatim) just as they were delivered in,
or read before the Royal Society: For it has been the Opinion of the most
Judicious among those Honourable Members, that it is impossible so to
abridge them, (which are but Abridgments themselves) as not to render
them obscure and unintelligible.

ranslation of Part of Monsieur Fontenelle's Preface to the Memoirs
of the Royal Academy at Paris, in the Year 1699. treating of the

Usefulness of Mathematical Learning.

UT to what purpose should People become fond of the Mathematicks
B and Natural Philosophy. Of what use are the Transactions of the
Academy? These are common Questions, which most do not barely
propose as Questions; and it will not be improper to clear them.
People very readily call useless, what they do not understand. It is a sort
of Revenge; and as the Mathematicks and Natural Philosophy are known
but by few, they are generally look'd upon as useless. The reason of this is;
because they are crabbed and not easily learnt.
We have a Moon to light us in the Night; What is it to us, say they,
whether Jupiter hath four? Why so many laborious Observations, so many
tedious Calculations to know exactly their Course? They'll not afford us the
more Light for it; and Nature, which hath plac'd these little Planets without
the reach of our Eyes, doth not seem to have made them for us. According
to this plausible Argument they ought not to have been observ'd with a
Telescope, nor study'd. But it is certain, that we had been considerable
Loosers by it: For those who have some insight into the Principles of
Geography and Navigation know, that since these four Moons about Jupiter
have been discover'd, they have been more useful to those Sciences than our
own Moon; and that they serve, and shall more and more serve to make new
Sea-Charts, infinitely more exact than the Old; and are likely to save the
Lives of a vast many Seamen. Did we reap no other advantage from
Astronomy than this from these Satellites of Jupiter, that wou'd be
sufficient to justifie those prodigious Calculations, those assiduous and nice
Observations, this great number of elaborate Instruments, and this Noble
Edifice built only for this Science. However the greatest part of Mankind
know nothing of these Satellites of Jupiter, unless perhaps by hear-say, and
that too confusedly; or else they are ignorant of what Affinity they have
with Navigation, or of the great Improvements which have been lately made
in it.

This is the Fate of Sciences, which are study'd and improv'd by few. Most
People are not sensible of their Progress, and especially when made in some
mean Callings. But what doth it signifie, that we can now more easily direct
the Course of Rivers, cut out Canals, and settle new Navigations; because
our Method of taking the Level and making Sluces is infinitely better than
heretofore? Some Masons and Seamen have thereby found their Business
easier, but they themselves were not sensible of the Skill of the
Geometrician who directed them. They were mov'd, as the Body by a Soul,
it doth not know. Others are yet less sensible of the Genius that presided
over the Undertaking; and the World is the better for its succeeding well,
but not altogether free from Ingratitude.
Anatomy, which is some time since so carefully study'd, can't become
more exact, but Chyrurgical Operations must also be more sure. Surgeons
know this; but those who receive the Benefit of their Art know nothing of it.
And indeed how should they? They would be oblig'd to compare Old with
Modern Surgery; and this wou'd take too much Time, and go against the
Grain: So that since the Operation hath succeeded well, they do not think it
material to know whether it had succeeded as well in another Century.
It is strange that so many things are before our Eyes, and that we do not
see them. Your Handycraft Shops are full of ingenious Works; but yet we
hardly mind them: And very useful and well contriv'd Instruments and
Experiments want Spectators, who wou'd be wonderfully pleas'd, wou'd
they take the pains to admire them.
If a Learned Society have made some Improvements in Geometry,
Anatomy, Mechanicks, or any other useful Science, it must not be expected,
that the World will go back to so remote a Spring to thank and applaud them
for the Usefulness of their Productions: For it will be more easie to enjoy
the Benefit of their Discoveries and Improvements than to know them. The
Determination of Longitude by the Satellites, the Discovery of the Ductus

Thoracicus, a more convenient, and more exact Level, are not Novelties so
fit to make a noise as a pleasant Poem, or a handsome Piece of Oratory.
Altho' the Usefulness of Mathematicks and Natural Philosophy is
obscure, yet it is real. To consider Mankind in their Natural State, nothing is
more useful to them, than what may preserve their Lives, and produce those
Arts, which are both great Helps and Ornaments to Publick Societies.
As for what concerns the Preservation of Life, it peculiarly belongs to
Physick; which for that reason is divided in the Academy into three
Branches, which make three different sorts of Members of this Society,
Anatomy, Chymistry, and Botanicks. Every Body knows of what
Importance it is to have an exact Knowledge of Human Body, and of what
Medicines may be extracted from Minerals and Plants.
As for Arts, too tedious to be reckon'd, they depend some upon Natural
Philosophy, others upon Mathematicks.
One wou'd think at first, that if the Mathematicks were to be confin'd to
what is useful in them, they ought only to be improv'd in those things,
which have an immediate and sensible affinity with Arts, and the rest ought
to be neglected as a Vain Theory. But this wou'd be a very wrong Notion.
As for Instance, the Art of Navigation hath a necessary Connexion with
Astronomy, and Astronomy can never be too much improv'd for the Benefit
of Navigation. Astronomy cannot be without Opticks by reason of
Perspective Glasses; and both, as all other Parts of Mathematicks, are
grounded upon Geometry, and to go as far as you can, even upon Algebra.
Geometry, and especially Algebra, are the Keys of all the Inquiries, that
can be made concerning Magnitude. These Sciences which are only
conversant about abstruse Relations, and simple Ideas, may seem dry and
barren, whilst they keep within the Verge of the Intellectual World; but mixt
Mathematicks, which stoop to Matter, and consider the Motion of the Stars,
the Augmentation of moving Forces, the different Passages of the Rays of
Light through different Mediums; the different Effects of Sound by the

Vibration of Things; to conclude all those Sciences, which discover the
particular Relations of Sensible Magnitudes go on farther and more
securely, when the Art of discovering Relations in General is more perfect.
The Universal Instrument cannot be too extensive, too handy, or too easily
apply'd: It is useful to all the Sciences, and they cannot be without it: And
therefore among the Mathematicians of the Academy, who are design'd to
be useful to the Publick, the Geometricians and Algebrists make a Class, as
well as the Astronomers and Mechanicks.
However, it is certain, that Speculations purely of Geometry, or of
Algebra, are not about useful things: But it is certain too, that those that are
not, either lead or belong to those that are. It is in it self a very barren thing
to know, that in a Parabola a Subtangant is double the corresponding
Abscissæ; but yet it is a Degree of Knowledge necessary to the Art of
throwing Bombs, so exactly as they can do now. There are not by far so
many evident Uses as Propositions or Truths in the Mathematicks: Yet it is
enough if the Concourse of several Truths is generally of some use.
Farther, a Geometrical Speculation, which was not at first applicable to
any use, becomes so afterwards. When the greatest Geometricians in the
Seventeenth Century set about to study a new Curve, which they call'd a
Cycloide, they only engag'd themselves in a meer Speculation out of Vanity,
striving to outdo one another by the Discovery of difficult Theorems. They
did not even pretend that this was for the Publick Good; however by diving
into the Nature of the Cycloide it was found, that it was destin'd to make
Pendulums as perfect as may be, and carry the Measure of Time as far as it
can go.
It is the same thing with Natural Philosophy as with Geometry. The
Anatomy of Animals seems insignificant; and it only concerns us to know
that of Human Body. But yet some Parts of it, which are of so nice, or so
confus'd a Make, that they are invisible, are sensible and manifest in the
Body of an Animal. Hence it is, that Monsters themselves are not to be

neglected. The Mechanism conceal'd in a particular Kind or in a common
Make, is unfolded in another kind, or in an extraordinary Make; and one
wou'd be almost apt to say, that Nature by multiplying and varying so much
her Works, can't sometimes forbear betraying her Secrets. All that the
Antients knew of the Load-stone, was, that it attracts Iron. But whether they
did not value a Curiosity, which promis'd them nothing; or that their Genius
did not lead them to make Experiments, they have not examin'd this Stone
as carefully as they might. One Experiment taught them, that it turns of its
self towards the Poles of the World, and did put into their Hands the
inestimable Treasure of the Mariners Compass. They might easily have
made this Discovery important, and yet they did not do it; and if they had
spent a little more time upon a Curiosity which seem'd useless to them, the
Latent use of it had soon appear'd.
Let us always make a Collection of Mathematical and Physical Truths;
happen what it will we can't hazard much by it. It is certain, that they shall
be drawn from Springs, whence a great many useful ones have already been
drawn. We have reason to presume, that we shall draw from thence, some
that shall shine as soon as they are discover'd, and convince us of their
Usefulness. Other Truths shall stay some time till a piercing Meditation, or
some happy Accident discovers their Use. Some Truths being consider'd by
themselves shall be barren, till they are consider'd with reference to one
another. Lastly, let the worse come to the worse, some shall be eternally
useless.
I mean useless with reference to sensible and gross Uses; for otherwise
they shall not be so. An Object upon which alone you cast your Eyes is the
clearer and brighter, when the neighbouring Objects, which however you do
not look upon, are also enlighten'd; because it hath the Benefit of the Rays,
which are reflected from them. Thus those Discoveries, which are palpably
useful, and deserve our chiefest Attention, are in some measure enlighten'd
by those, which may be call'd useless. For all Truths make one another
more lucid.

It is always useful to have right Notions, even of useless Subjects. And
tho' we cou'd reap no benefit by the Knowledge of Numbers and Sines, yet
it wou'd still be the only certain Knowledge granted to our Natural Light,
and they wou'd serve to give our Reason the first Habit of and Inclination to
Truth. They wou'd teach us to operate upon Truths; to take the Thread of
them, which is generally very fine and almost imperceptible; and to follow
it as far as it reaches: In a word, they wou'd make Truth so familiar, that we
might on other Occasions know it at first sight, and almost by Instinct.
A Geometrical Genius is not so confin'd to Geometry, but that it may be
capable of learning other Sciences. A Tract of Morality, Politicks, or
Criticism, and even a Piece of Oratory, supposing the Author qualify'd
otherwise for those Performances, shall be the better for being compos'd by
a Geometrician. That Order, Perspicuity, Precision and Exactness, which
some time since are found in good Books, may originally proceed from that
Geometrical Genius, which is now more common than ever, and in some
manner is communicated by one Relation to another, nay even to those that
do not understand Geometry. Sometimes a Great Man draws all his
Cotemporaries after him; and he who hath the justest Claim to the Glory of
having settled a new Art of Arguing, was an Excellent Geometrician.
Lastly, whatever raises us to Great and Noble Reflexions, tho' they be
purely Speculative, afford a Spiritual and Philosophical Utility. The Wants
of the Mind are perhaps as many as those of the Body. She desires to extend
her Knowledge: All that can be known, is necessary to her, and there can be
no better Proof than this, that she is design'd for Truth. Nothing perhaps can
redound more to her Glory, than the Pleasure that is felt sometimes, in
spight of ones self, in the dry and crabbed Questions of Algebra.
But without running counter to the common Notions, and recurring to
Advantages which may seem too far fetch'd and refin'd, it may fairly be
own'd, that the Mathematicks and Natural Philosophy have some things

which are only subservient to Curiosity; and so have those Sciences which
are most generally acknowledg'd to be useful, as History, &c.
History doth not in every Part of it supply us with Examples of Vertue
and Rules for our Behaviour. For besides these, therein you have a View of
the perpetual Revolutions of Human Affairs, of the Beginning and Fall of
Empires, of Manners, Customs, and Opinions which continually succeed
one another; and in a word, of all that rapid, tho' insensible, Motion that
carries all before it, and incessantly alters the Face of the Earth.
Had we a mind to oppose Curiosity to Curiosity, we shou'd find that
instead of the Motion, which agitates Nations, and gives birth to, and
destroys States; Natural Philosophy considers that Great and Universal
Motion, which hath put the whole Frame of Nature in Order, and suspended
the Cœlestial Bodies in several Spheres, and which illuminates and
extinguishes some Stars; and by following always unalterable Laws,
diversifies its effects ad infinitum. If the surprising difference of Manners
and Opinions of Mankind is so entertaining; there is too a great deal of
Pleasure to study the prodigious diversity of the Structure of the different
Species of Animals, with reference to their different Functions, to the
Elements they live in, to the Climates they inhabit, and the Aliments they
are to take, &c. The most curious strokes of History shall hardly be more
curious than the Phosphorus, the cold Liquors which being mixt together,
break out into a flame; Silver Trees, the almost Magical Operations of the
Load-Stone, and a vast number of Secrets, which Art hath discover'd by a
near and diligent Scrutiny of Nature.
Lastly, Natural Philosophy doth as much as it is possible unravel the
Footsteps of that Infinite Intellect and Wisdom, who hath made all things:
Whereas the Object of History are the disorderly Effects of the Passion, and
of Humane Caprices; and so odd a Series of Events, that some formerly
fancy'd that a Blind and Senseless Deity had the Direction of them.

We must not look upon the Sublime Reflexions which Natural
Philosophy leads us to make concerning the Author of the Universe, as
meer Curiosities. For this stupendous Work, which appears always more
wonderful the more we know it, gives us such exalted Notions of its Maker,
that they fill our Minds with Admiration and Respect. But above all,
Astronomy and Anatomy are the two Sciences which more palpably lay
before us two grand Attributes of our Creator; one his Immensity by the
distance, Magnitude and Number of Cœlestial Bodies; the other his Infinite
Knowledge by the Mechanism of Animals. True Natural Philosophy is a
kind of Theology.
The different views of Humane Understanding are almost infinite; and
Nature is really so. So that we may every day expect some Discoveries,
either in Mathematicks or Natural Philosophy, which shall be of a new sort
of Utility or Curiosity. Make a Collection of all the different Advantages
which the Mathematicks afforded a Hundred Years ago, and you'll find
nothing to be compar'd to the Perspective Glasses they have furnish'd since
that time, and which are a new Organ to the Sight, and cou'd not be
expected from Art. How surpriz'd had the Ancients been, if they had been
told that their Posterity, by the help of some Instruments, shou'd one day see
a vast number of Objects which they did not see; a Heaven that was
unknown to them; and Plants and Animals they did not even suspect it was
possible to exist. Naturalists had already a great many curious Experiments;
but within about half a Century, the Air-Pump hath produced a prodigious
quantity of them wholly new, and which by shewing Bodies in a Space void
of Air, shews them as transported in a World different from ours, where they
undergo Alterations whereof we had no Notion. The Excellency of
Geometrical Methods, which are every day invented and improv'd, may
perhaps at last exhaust Geometry; that is, The Art of making Geometrical
Discoveries, and that is all: Whereas Natural Philosophy, which
contemplates an Object of an unlimited Variety, and Fæcundity, shall
always find room for new Observations, and opportunities to increase its

vast Stock, and shall have the Advantage of never being a compleat
Science.
There are so many things to be discover'd, whereof a great part, in all
likelyhood shall never be known; that they give an opportunity to those who
will not encounter with the Thorns and Difficulties of Natural Philosophy,
to affect a sort of Discouragement. A great many to vilify this Natural
Science, pretend a mighty veneration for the works of Nature, and that they
are absolutely incomprehensible. However, Nature is never so admirable,
nor so admir'd as when known. True it is, that what is known is
inconsiderable in comparison of what is not yet known. Nay, Sometimes
what is not known, is exactly what seems shou'd be the soonest known. As
for instance, it is not at least certainly known, why a Stone thrown up into
the Air falls down again; but we certainly know the cause of the Rainbow,
why it doth not exceed a certain height; why its breadth is always the same;
why when there are two Rainbows at the same time, the Colours of the one
are overset with reference to the Colours of the other; and yet the fall of a
Stone in the Air appears a more simple Phænomenon, than the Rainbow.
But in a word, altho' we do not know every thing, we are not neither
ignorant of every thing. And altho' we are ignorant of the most simple
Events, yet we have a knowledge of what seems the most Complex. So that
if we have on the one hand reason to fear, lest our Vanity shou'd flatter us
with the hopes of attaining to the knowledge of things above our reach; on
the other we ought to dread, lest our Slothfulness should also flatter us that
we are condemn'd to a greater degree of Ignorance than really we are.
People may think that the Sciences do not begin to exert themselves,
either because they cou'd be but imperfect among the Ancients; or because
we have almost lost the Footsteps of them during the gloomy Darkness of
Barbarity; or because a better method hath been taken about 100 Years ago.
Was the Progress Historically examin'd, they have already made in so short
a time, notwithstanding the strong, but false Prejudices they had long to
encounter with, even sometimes the foreign Obstacles they have met with

from Authority and Power; the want of Zeal for Sciences so remote from
common use, those few who apply'd themselves to this Work, and the weak
Motives which engag'd them in it; a Man would wonder at the Greatness
and Rapidity of the Progress of the Sciences, and even we might observe
some new ones to start out of nothing, and perhaps be tempted to have too
great hopes of future Improvements.
The greater reason we have of future Success, the greater we have to look
upon the Sciences as in their Cradles, at least Natural Philosophy. And
therefore the Academy is only now employ'd to make an ample Provision of
Observations, and Facts well attested, which may one day be the foundation
of a System. For before the Systematical Natural Philosophy can raise solid
Edifices; Experimental Natural Philosophy must be in a condition to supply
it with good Materials.
None but Societies, of those too countenanc'd and encourag'd by the
Prince, can successfully make and prepare this Collection of Materials. All
the Learning, Care, Life and Wealth of one Private Man can never answer
this Design. There are too many different Experiments to be made, which
are to be too much vary'd, and a long time prosecuted with the same Temper
and Mind. The Cause of the least Effect is so wrap'd up, that unless you
very carefully open all the various Foldings, you cannot come at it.
Hitherto the Academy of Sciences hath consider'd Nature but by parcels:
They have fix'd upon no general System, for fear of falling into the
inconveniency of hasty Systems, which are very grateful to the impatience
of Humane Understanding; and being once settled, are Obstacles to what
Truths are afterwards discover'd. This day we are sure of a Fact, to morrow
we shall be sure of another that hath no relation with the former. However
some Conjectures are ventur'd at upon Causes; but they are only
Conjectures. So that this Collection, which the Academy gives to the
Publick, is compos'd of separate Fragments, independant of one another;
whereof every one who is the Author, warrants the Facts and Experiments;

and whose Arguments are approv'd by the Academy, but with Restrictions
becoming Wise and Wary Scepticks.
Time perhaps will come, when these scatter'd Fragments shall be united
into one regular Body; and if they be such as they are wish'd, they may of
themselves Unite. A great many Truths, when their Numbers is
considerable, shew so near a Relation to, and so mutual a Dependance upon
one another, that it seems, that notwithstanding their violent Separation,
they have a natural Tendency to be re-united.

A

TABLE
OF THE

Discourses contain'd in this Volume.

PAGE
An Estimate of the Quantity of Vapours raised out of the Sea, as derived from Experiment:
Together with an Account of the Circulation of the wat'ry Vapours of the Sea, and of the
Cause of Springs. Presented to the Royal Society by Mr. E. Halley, F. R. S. 1
The True Theory of the Tides, extracted from that admired Treatise of Mr. Isaac Newton,
Intituled Philosophiæ Naturalis Principia Mathematica; being a Discourse presented
with that Book to the late King James, by Mr. E. Halley. 13
A Theory of the Variation of the Magnetical Compass, by Mr. E. Halley. 27
An Account of the Cause of the Change of the Variation of the Magnetical Needle, with an
Hypothesis of the Structure of the Internal Parts of the Earth; as it was presented to the
Royal Society in one of their late Meetings, by Mr. E. Halley. 43
An Historical Account of the Trade-Winds and Monsoons, observable in the Seas between
and near the Tropicks; with an Attempt to assign the Physical Cause of the said Winds,
by Mr. E. Halley. 61
A Discourse of the Rule of the Decrease of the Heighth of the Mercury in the Barometer,
according as Places are elevated above the Surface of the Earth; with an Attempt to
discover the true Reason of the rising and falling of the Mercury, upon Change of
Weather, by Mr. E. Halley. 81
A Letter from Mr. Isaac Newton, while Professor of the Mathematicks in the University of
Cambridge; containing his new Theory about Light and Colours: Sent from Cambridge,
Feb. 6. 1671/2. in order to be communicated to the Royal Society. 97
A farther Explanation of the same Theory. 114
A Demonstration concerning the Motion of Light, communicated from Paris. 118
An Introductory Essay to the Doctrine of Sounds, containing some Proposals for the
Improvement of Acousticks; as it was presented to the Dublin Society, by the Right
Reverend Father in God Narcissus, Lord Bishop of Ferns and Leighlin. 121
A Discourse concerning the Modern Theory of Generation, by Dr. Geo. Garden, of Aberdeen,
being part of a Letter to Dr. William Musgrave, L. L. D. Reg. Soc. S. and by him
communicated to the Royal Society. 142
A short Discourse concerning Concoction Read at a Meeting of the Royal Society, by
Clopton Havers, M. D. Fellow of the Royal Society. 153

A Discourse concerning some Influence of Respiration on the Motion of the Heart hitherto
unobserved. By J. Drake, M. D. F. R. S. 171
Some Thoughts and Experiments concerning Vegetation. By John Woodward, M. D. of the
College of Physicians and Royal Society, and Professor of Physick in Gresham-College. 203
An Account of the Measure of Gold upon Gilt Wire; together with a Demonstration of the
exceeding Minuteness of the Atoms, or constituent Parts of Gold; as it was read before
the Royal Society, by Mr. E. Halley. 243
An Account of the several Species of Infinite Quantity, and of the Proportions they bear one
to the other; as it was read before the Royal Society, by E. Halley. 246
An Account of Dr. Robert Hook's Invention of the Marine Barometer, with it's Description and
Uses. Published by Order of the Royal Society by Mr. E. Halley. 250
A Discourse concerning the Proportional Heat of the Sun in all Latitudes; with the Method of
collecting the same, as it was read before the Royal Society in one of their late Meetings,
by Mr. E. Halley. 256
Concerning the Distance of the Fixed Stars, by the Honourable Fran. Roberts, Esq; F. R. S. 265
Mr. Isaac Newton's Theory of the Moon. 268
An estimate of the Degrees of the Mortality of Mankind, drawn from Curious Tables of Births
and Funerals at the City of Breslaw; with an Attempt to ascertain the Price of Annuities
upon Lives, by Mr. E. Halley. 280
A Discourse concerning Gravity, and its Properties, wherein the Descent of Heavy Bodies,
and the Motion of Projects is briefly, but fully handled: Together with the Solution of a
Problem of great Use in Gunnery, by Mr. E. Halley. 302
A Proposition of General Use in the Art of Gunnery, shewing the Rule of laying a Mortar to
pass, in order to strike any Object above or below the Horizon, by Mr. E. Halley. 326
A Discourse concerning the Measure of the Air's Resistance to Bodies moved in it. By the
Learned John Wallis, S. T. D. and F. R. S. 332
An Instance of the Excellency of the Modern Algebra, in the Resolution of the Problem of
finding the Foci of Optick Glasses universally. By Mr. E. Halley, S. R. S. 348

Appendix
An Analytical Resolution of certain Equations of the 3d, 5th, 7th, 9th Powers, and so on ad
Infinitum, in finite Terms, after the manner of Cardan's Rules for Cubicks. By Mr. A.
Moivre, F. R. S. 365
A Discourse concerning the Action of the Sun and Moon on Animal Bodies; and the Influence
which this may have in many Diseases. By Richard Mead, M. D. F. R. S. 371

Miscellanea Curiosa.

Estimate of the Quantity of the Vapours raised out of the Sea derived
from Experiment: Together with an Account of the Circulation of
the watry Vapours of the Sea, and of the Cause of Springs,
presented to the Royal Society. By Mr. E. Halley, F. R. S.

HAT the Quantity of Aqueous Vapours contain'd in the Medium of the
T Air, is very considerable, seems most evident from the great Rains and
Snows which are sometimes observ'd to fall, to that degree, that the
Water thus discharg'd out of the Interstices of the Particles of Air, is in
weight a very sensible part of the incumbent Atmosphere: But in what
proportion these Vapours rise, which are the Sources not only of Rains, but
also of Springs or Fountains (as I design to prove) has not, that I know of,
been any where well examin'd, tho' it seem to be one of the most necessary
Ingredients of a Real and Philosophical Meteorology, and, as such; to
deserve the Consideration of this Honourable Society. I thought it might not
be unacceptable to attempt by Experiment to determine the Quantity of the
Evaporations of Water, as far as they arise from Heat, which upon Trial
succeeded as follows.
We took a Pan of Water, about 4 inches deep, and 7 Inches 9⁄10 Diameter,
in which we placed a Thermometer, and by means of a Pan of Coals, we
brought the Water to the same degree of Heat, which is observed to be that
of the Air in our hottest Summer; the Thermometer nicely shewing it: This
done, we affixed the Pan of Water, with the Thermometer in it, to one end
of the Beam of a Pair of Scales, and exactly counterpois'd it with weights in
the other Scale; and by the application or removal of the Pan of Coals, we

found it very easie to maintain the Water in the same degree of Heat
precisely. Doing thus we found the weight of the Water sensibly to
decrease; and at the end of two hours we observed that there wanted half an
Ounce Troy, all but 7 grains, or 233 grains of Water, which in that time had
gone off in Vapour; tho' one could hardly perceive it smoke, and the Water
were not sensibly warm. This Quantity in so short a time seem'd very
considerable, being little less than 6 ounces in 24 hours, from so small a
Surface as a Circle of 8 inches Diameter. To reduce this Experiment to an
exact Calculus, and determine the thickness of the Skin of Water that had so
evaporated, I assume the Experiment alledg'd by Dr. Edward Bernard to
have been made in the Oxford Society, viz. That the Cube-foot English of
Water weighs exactly 76 Pounds Troy; this divided by 1728, the number of
Inches in a Foot, will give 253⅓ grains, or ½ ounce 13⅓ grains for the
weight of a Cube-inch of Water; wherefore the weight of 233 grains is
233
⁄253 or 35 Parts of 38 of a Cube-inch of Water. Now the Area of the Circle
whose Diameter is 79⁄10 Inches, is 49 square Inches: by which dividing the
Quantity of Water evaporated, viz. 35⁄38 of an Inch, the Quote 35⁄1862 or 1⁄53
shews that the thickness of the Water evaporated was the 53d part of an
Inch; but we will suppose it only the 60th part, for the Facility of
Calculation. If therefore Water as warm as the Air in Summer, exhales the
thickness of a 60th part of an Inch in two hours from its whole Surface, in
12 hours it will exhale the ⅒ of an Inch; which Quantity will be found
abundantly sufficient to serve for all the Rains, Springs, and Dews; and
account for the Caspian Sea, being always at a stand, neither wasting nor
overflowing; as likewise for the Current said to set always in at the
Streights of Gibralter, tho' those Mediterranean Seas receive so many and
so considerable Rivers.
To estimate the Quantity of Water arising in Vapours out of the Sea, I
think I ought to consider it only for the time the Sun is up, for that the Dews
return in the Night, as much if not more Vapours than are then emitted; and
in Summer the Days being no longer than 12 hours, this Excess is ballanc'd

by the weaker Action of the Sun, especially when rising before the Water be
warmed: So that if I allow ⅒ of an Inch of the Surface of the Sea, to be
raised per diem in Vapours, it may not be an improbable Conjecture.
Upon this Supposition, every 10 square Inches of the Surface of the
Water, yields in Vapour per diem a Cube-inch of Water; and each square
Foot half a Wine-pint; every Space of 4 Foot square, a Gallon; a Mile
square, 6914 Tons; a square Degree suppose of 69 English Miles, will
evaporate 33 Millions of Tons: And if the Mediterranean be estimated at
forty degrees long and four broad, allowances being made for the Places
where it is broader, by those where it is narrower (and I am sure I guess at
the least) there will be 160 Square degrees of Sea; and consequently, the
whole Mediterranean must lose in Vapour, in a Summer's day, at least 5280
Millions of Tons. And this Quantity of Vapour, tho' very great, is as little as
can be concluded from the Experiment produced: And yet there remains
another Cause, which cannot be reduced to Rule, I mean the Winds,
whereby the Surface of the Water is licked up some times faster than it
exhales by the heat of the Sun; as is well known to those that have
consider'd those drying Winds which blow sometimes.
To estimate the Quantity of Water, the Mediterranean Sea receives from
the Rivers that fall into it, is a very hard Task, unless one had the
Opportunity to measure their Chanels and Velocity; and therefore we can
only do it by allowing more than enough; that is, by assuming these Rivers
greater than in all probability they be, and then comparing the Quantity of
Water voided by the Thames, with that of those Rivers, whose Waters we
desire to compute.
The Mediterranean receives these considerable Rivers; the Iberus, the
Rhone, the Tiber, the Po, the Danube, the Neister, the Borystenes, the
Tanais, and the Nile; all the rest being of no great Note, and their Quantity
of Water inconsiderable: These nine Rivers, we will suppose each of them
to bring down ten times as much Water as the River Thames; not that any of

them is great in reality, but to comprehend with them all the small Rivulets
that fall into the Sea, which otherwise I know not how to allow for.
To calculate the Water of the Thames, I assume that at Kingston Bridge
where the Flood never reaches, and the Water always runs down, the
breadth of the Chanel is 100 Yards, and its Depth 3, it being reduced to an
Equality (in both which Suppositions I am sure I take with the most) hence
the Profil of the Water in this Place is 300 square Yards: This multiplied by
48 Miles (which I allow the Water to run in 24 hours, at 2 Miles an hour) or
84480 Yards, gives 25344000 Cubick-yards of Water to be evacuated every
Day; that is, 20300000 Tons per diem; and I doubt not, but in the excess of
my Measures of the Chanel of the River, I have made more than sufficient
allowance for the Waters of the Brent, the Wandel, the Lea, and Darwent,
which are all worth notice, that fall into the Thames below Kingston.
Now if each of the aforesaid 9 Rivers yield 10 times as much Water as
the Thames doth, 'twill follow that each of them yields but 203 Millions of
Ton per diem, and the whole 9, but 1827 Millions of Tons in a day; which is
but little more than ⅓ of what is proved to be raised in vapour out of the
Mediterranean in 12 hours time. Now what becomes of this Vapour when
rais'd, and how it comes to pass that the Current always sets in at the
Mouth, of the Streights of Gibralter, shall immediately be shew'd: But first
it is necessary to advertise the Reader, that in making the Experiment herein
mention'd, the Water used had been salted to the same degree as is the
common Sea-water, by the Solution of about a 40th part of Salt.

Aving thus shew'd by Experiment the Quantity of Water raised in
H Vapour from the Surface of the Sea in a Days time, which was so far
approv'd of by some Honourable Members of this Society, that I
receiv'd their Commands to prosecute these Enquiries; and particularly, in
relation to the Method used by Nature, to return the said Vapours again into
the Sea; which is so justly perform'd, that in many hundred of Years we are

sufficiently assured that the Sea has not sensibly decreased by the loss in
Vapour; nor yet abounded by the immense Quantity of fresh it receives
continually from the Rivers. To demonstrate this Equilibre of Receipt and
Expence in the whole Sea, is a Task too hard for me to undertake, yet in
obedience to those whom I have the Honour to serve, I shall here offer,
what to me has hitherto seem'd the most satisfactory Account of this grand
Phænomenon: I have in another place attempted to explain the manner of
the rising of Vapour by Warmth, by shewing, that if an Atom of Water were
expanded into a Shell or Bubble, so as to be ten times as big in Diameter as
when it was Water; such an Atom would become specifically lighter than
Air, and rise so long as that Flatus or warm Spirit that first separated it from
the Mass of Water, shall continue to distend it to the same Degree; and that
Warmth declining, and the Air growing cooler and also specifically lighter,
the Vapours consequently shall stop at a certain Region of the Air, or else
descend, which may happen upon several accounts, as I shall by and by
endeavour to make out; yet I undertake not that this is the only principal of
the rise of Vapours, and that there may not be a certain sort of Matter,
whose Conatus may be contrary to that of Gravity; as is evident in
Vegetation, where in the Tendency of the Sprouts is directly upwards, or
against the Perpendicular. But what ever is the true Cause, it is in Fact
certain, that warmth does separate the Particles of Water, and emit them
with a greater and greater Velocity, as the heat is more and more intense; as
is evident in the Steam of a boiling Cauldron, wherein likewise the Velocity
of the ascent of the Vapours does visibly decrease till they disappear, being
dispersed into and assimulated with the Ambient Air. Vapours being thus
raised by warmth, let us for a first Supposition put, that the whole Surface
of the Globe were all Water very deep, or rather that the whole Body of the
Earth were Water, and that the Sun had its diurnal course about it: I take it,
that it would follow, that the Air of it self would imbibe a certain Quantity
of aqueous Vapours, and retain them like Salts dissolved in Water; that the
Sun warming the Air, and raising a more plentiful Vapour from the Water in
the day-time, the Air would sustain a greater proportion of Vapour, as warm

Water will hold more dissolved Salts, which upon the absence of the Sun in
the Nights would be all again discharged in Dews, analogous to the
Precipitation of Salts on the cooling of the Liquors; nor is it to be believed
that in such Case there would be any diversity of Weather, other than
periodically, every Year alike; the mixture of all terrestrious, saline,
heterogenious Vapours being taken away, which as they are variously
compounded and brought by the Winds, seem to be the Causes of those
various Seasons which we now find. In this case the Aiery Regions every
where, at the same height, would be equally replenished with the Proportion
of Water it could contain, regard being only to be had to the different degree
of warmth, from the nearness or distance of the Sun; and an eternal East-
wind would blow all round the Globe, inclining only to the same side of the
East, as the Latitude doth from the Equator; as is observed in the Ocean
between the Tropicks.
Next let us suppose this Ocean interspersed with wide and spacious
Tracts of Land, with high Ridges of Mountains, such as the Pyrenean, the
Alps, the Apennine, the Carpathian in Europe, Taurus, Caucasus, Imaus,
and several others in Asia; Atlas and the Montes Lunæ, with other unknown
Ridges in Africa, whence came the Nile, the Nigre, and the Zaire: And in
America, the Andes and the Apalatean Mountains; each of which far
surpass the usual height to which the Aqueous Vapours of themselves
ascend, and on the tops of which the Air is so cold and rarified, as to retain
but a small part of those Vapours, that shall be brought thither by Winds.
Those Vapours therefore that are raised copiously in the Sea, and by the
Wind, are carried over the low Land to those Ridges of Mountains, are there
compelled by the Stream of the Air to mount up with it to the tops of the
Mountains, where the Water presently precipitates, gleeting down by the
Crannies of the Stone; and part of the Vapour entering into the Caverns of
the Hills, the Water thereof gathers as in an Alembick into the Basons of
Stone it finds; which being once fill'd, all the overplus of Water that comes
thither runs over by the lowest place, and breaking out by the sides of the

Hills, forms single Springs. Many of these running down by the Valleys or
Guts between the Ridges of the Hills, and coming to unite, form little
Rivulets, or Brooks: Many of these again, meeting in one common Valley
and gaining the plain Ground, being grown less rapid, become a River; and
many of these being united in one common Channel, make such Streams as
the Rhine, the Rhone, the Danube; which latter, one would hardly think the
Collection of Water condensed out of Vapour, unless we consider how vast
a Tract of Ground that River drains, and that it is the Sum of all those
Springs which break out on the South side of the Carpathian Mountains,
and on the North side of the immense Ridge of the Alps, which is one
continued Chain of Mountains from Switzerland, to the Black-Sea. And it
may almost pass for a Rule, that the magnitude of a River, or the quantity of
Water it evacuates, is proportionable to the length and height of the Ridges
from whence its Fountains arise. Now this Theory of Springs is not a bare
Hypothesis, but founded on Experience, which it was my luck to gain in my
abode at St. Helena, where in the Night-time, on the tops of the Hills, about
800 Yards above the Sea, there was so strange a condensation, or rather
precipitation of the Vapours, that it was a great Impediment to my Cœlestial
Observations; for in the clear Sky, the Dew would fall so fast, as to cover,
each half quarter of an Hour, my Glasses with little drops; so that I was
necessitated to wipe them so often, and my Paper on which I wrote my
Observations would immediately be so wet with Dew, that it would not bear
Ink: By which it may be suppos'd how fast the Water gathers in those
mighty high Ridges I but now nam'd.
Thus is one part of the Vapours blown upon the Land return'd by the
Rivers into the Sea, from whence they came; another part by the cool of the
Night falls in Dews, or else in Rains, again into the Sea before it reaches the
Land, which is by much the greatest part of the whole Vapours, because of
the great extent of the Ocean, which the motion of the Wind does not
traverse in a very long space of Time; and this is the Reason why the Rivers
do not return so much into the Mediterranean, as is extracted into Vapour. A

third part falls on the Low-Lands, and is the Pabulum of Plants, where yet it
does not rest, but is again exhaled in Vapour by the action of the Sun, and is
either carried by the Winds to the Sea to fall in Rain or Dew there, or else to
the Mountains to be there turn'd into Springs; and tho' this does not
immediately come to pass, yet after several Vicissitudes of rising in Vapour,
and falling in Rain or Dews, each Particle of the Water is at length return'd
to the Sea from whence it came. Add to this, that the Rain-waters after the
Earth is fully sated with moisture, does, by the Vallies or lower parts of the
Earth, find its way into the Rivers, and so is compendiously sent back to the
Sea. After this manner is the Circulation perform'd, and I doubt not but this
Hypothesis is more reasonable than that of those who derive all Springs
from the Rain-waters, which yet are perpetual and without diminution, even
when no Rain falls for a long space of time; or that derive them from a
Filtration or Percolation of the Sea-waters, thro' certain imaginary Tubes or
Passages within the Earth wherein they lose their Saltness. This, besides
many others, labouring under this principal Absurdity, that the greatest
Rivers have their most copious Fountains farthest from the Sea, and
whether so great quantities of fresh Water cannot reasonably be deriv'd any
other way than in Vapour. This, if we may allow final Causes, seems to be
the design of the Hills, that their Ridges being plac'd thro' the midst of the
Continents, might serve, as it were, for Alembicks to distil fresh Water for
the use of Man and Beast, and their heights to give a descent to those
Streams to run gently, like so many Veins, of the Macrocosm to be the more
beneficial to the Creation. If the difference between Rain and Dew, and the
cause why sometimes 'tis Cloudy, at other times Serene, be inquir'd, I can
offer nothing like a proper Solution thereof, only with submission to
propose Conjectures, which are the best I can find, viz. That the Air being
heaped up by the meeting of two contrary Winds, when the Mercury is high,
the Vapours are the better sustain'd and kept from Co-agulating or
Condensing into Drops, whereby Clouds are not so easily generated, and
the Night the Vapours fall down single, as they rose in imperceptible Atoms
of Water: Whereas, when the Mercury is low, And the Air rarified by the

Exhaustion thereof, by two contrary Winds blowing from the place; the
Atoms of Air keep the Vapours not so well separated, and they coalesce into
visible Drops in the Clouds, and from thence are easily drawn into greater
Drops of Rain; to which 'tis possible and not improbable, that some sort of
Saline or Angular Particles of Terrestrial Vapour being immix'd with the
Aqueous, which I take to be Bubbles, may cut or break their Skins or Coats,
and so contribute to their more speedy Condensation into Rain.

True Theory of the Tides, extracted from that admired Treatise of
Mr. Isaac Newton, Intitled, Philosophiæ Naturalis Principia
Mathematica; Being a Discourse presented with that Book to the
late King James, by Mr. Edmund Halley.

T may, perhaps, seem strange, that this Paper, being no other than a
I particular Account of a Book long since published, should now appear
here; but the Desires of several honourable Persons, which could not be
withstood, have obliged us to insert it here, for the sake of such, who being
less knowing in Mathematical Matters, and therefore not daring to
adventure on the Author himself, are notwithstanding, very curious to be
inform'd of the Causes of Things; particularly of so general and
extraordinary Phænomena, as are those of the Tides. Now this Paper having
been drawn up for the late King James's Use, (in whose Reign the Book was
publish'd) and having given good Satisfaction to those that got Copies of it;
it is hoped the Savans of the higher Form will indulge us this Liberty we
take to gratifie their Inferiours in point of Science; and not be offended, that
we here insist more largely upon Mr. Newton's Theory of the Tides, which,
how plain and easie soever we find, is very little understood by the common
Reader.
HE sole Principle upon which this Author proceeds to explain most of
T the great and surprizing Appearances of Nature, is no other than that of
Gravity, whereby in the Earth all Bodies have a tendency towards its

Centre; as is most evident: And from undoubted Arguments it's proved, that
there is such a Gravitation towards the Centre of the Sun, Moon, and all the
Planets.
From this Principle, as a necessary Consequence, follows the Sphærical
Figure of the Earth and Sea, and of all the other Cœlestial Bodies: And tho'
the tenacity and firmness of the Solid Parts, support the Inequalities of the
Land above the Level; yet the Fluids, pressing equally and easily yielding to
each other, soon restore the Æquilibrium, if disturbed, and maintain the
exact Figure of the Globe.
Now this force of Descent of Bodies towards the Centre, is not in all
places alike, but is still less and less, as the distance from the Center
encreases: And in this Book it is demonstrated, that this Force decreases as
the Square of the distance increases; that is, the weight of Bodies, and the
Force of their Fall is less, in parts more removed from the Center, in the
proportion of the Squares of the Distance. So as for Example, a Ton weight
on the Surface of the Earth, if it were raised to the height of 4000 Miles,
which I suppose the Semidiameter of the Earth, would weigh but ¼ of a
Ton, or 5 Hundred weight: If to 12000 Miles, or 3 Semidiameters from the
Surface, that is 4 from the Center, it would weigh but 1⁄16 part of the Weight
on the Surface, or a Hundred and Quarter: So that it would be as easie for
the Strength of a Man at that height to carry a Ton weight, as here on the
Surface a 100¼. And in the same Proportion does the Velocities of the fall
of Bodies decrease: For whereas on the Surface of the Earth all things fall
16 Foot in a second; at one Semidiameter above, this fall is but four Foot;
and at three Semidiameters, or four from the Centre, it is but 1⁄16 of the Fall
at the Surface, or but one Foot in a second: And at greater Distances both
Weight and Fall become very small, but yet at all given Distances is still
some thing, tho' the Effect become insensible. At the distance of the Moon
(which I will suppose 60 Semidiameters of the Earth) 3600 Pounds weigh
but one Pound, and the fall of Bodies is but of 1⁄3600 a Foot in a second, or

16 Foot in a Minute; that is, a Body so far off descends in a Minute no more
than the same at the Surface of the Earth would do in a Second of Time.
As was said before, the same force decreasing after the same manner is
evidently found in the Sun, Moon, and all the Planets; but more especially
in the Sun, whose Force is prodigious; becoming sensible even in the
immense distance of Saturn: This gives room to suspect, that the force of
Gravity is in the Cœlestial Globes proportional to the quantity of Matter in
each of them: And the Sun being at least ten Thousand times as big as the
Earth, its Gravitation or attracting Force, is found to be at least ten
Thousand times as much as that of the Earth, acting on Bodies at the same
distance.
This Law of the decrease of Gravity being demonstratively proved, and
put past contradiction; the Author with great Sagacity, inquires into the
necessary Consequences of this Supposition; whereby he finds the genuine
Cause of the several Appearances in the Theory of the Moon and Planets,
and discovers the hitherto unknown Laws of the Motion of Comets, and of
the Ebbing and flowing of the Sea. Each of which are Subjects that have
hitherto taken up much larger Volumes; but Truth being uniform, and
always the same, it is admirable to observe how easily we are enabled to
make out very abstruse and difficult Matters, when once true and genuine
Principles are obtain'd: And on the other hand it may be wondred; that,
notwithstanding the great facility of truth, and the perplexity and
nonconsequences that always attend erroneous Suppositions, these great
Discoveries should have escaped the acute Disquisitions of the best
Philosophical Heads of all past Ages, and be reserv'd to these our Times.
But that wonder will soon cease, if it be consider'd how great improvements
Geometry has receiv'd in our Memory, and particularly from the profound
Discoveries of our incomparable Author.
The Theory of the Motion of the primary Planets is here shewn to be
nothing else, but the contemplation of the Curve Lines which Bodies cast

with a given Velocity, in a given Direction, and at the same time drawn
towards the Sun by its gravitating Power, would describe. Or, which is all
one, that the Orbs of the Planets are such Curve Lines as a Shot from a Gun
describes in the Air, being cast according to the direction of the Piece, but
bent in a crooked Line by the supervening Tendency towards the Earths
Centre: And the Planets being supposed to be projected with a given Force,
and attracted towards the Sun, after the aforesaid manner, are here proved to
describe such Figures, as answer punctually to all that the Industry of this
and the last Age has observed in the Planetary Motions. So that it appears,
that there is no need of solid Orbs and Intelligences, as the Antients
imagin'd, nor yet of Vortices or Whirlpools of the Cœlestial Matter, as Des
Cartes supposes; but the whole Affair is simply and mechanically
performed, upon the sole Supposition of a Gravitation towards the Sun;
which cannot be denied.
The Motion of Comets is here shewn to be compounded of the same
Elements, and not to differ from Planets, but in their greater swiftness,
whereby overpowering the Gravity that should hold them to the Sun, as it
doth the Planets, they flie off again, and distance themselves from the Sun
and Earth, so that they soon are out of our sight. And the imperfect
Accounts and Observations Antiquity has left us, are not sufficient to
determine whether the same Comet ever return again. But this Author has
shewn how Geometrically to determine the Orb of a Comet from
Observations, and to find his Distance from the Earth and Sun, which was
never before done.
The third thing here done is the Theory of the Moon, all the Inequalities
of whose Motion are proved to arise from the same Principles, only here the
effect of two Centers operating on, or attracting a projected Body, comes to
be considered; for the Moon, though principally attracted by the Earth, and
moving round it, does together with the Earth, move round the Sun once a
Year, and is, according as she is nearer or farther from the Sun, drawn by
him more or less than the Center of the Earth, about which she moves;

whence arise several Irregularities in her Motion, of all which, the Author in
this Book, with no less Subtility than Industry, has given a full account. And
though by reason of the great Complication of the Problem, he has not yet
been able to make it purely Geometrical, 'tis to be hoped, that in some
farther Essay he may surmount the difficulty: And having perfected the
Theory of the Moon, the long desir'd Discovery of the Longitude (which at
Sea is only practicable this way) may at length be brought to light, to the
great Honour of your Majesty, and Advantage of your Subjects.
All the surprising Phænomena of the Flux and Reflux of the Sea, are in
like manner shewn to proceed from the same Principle; which I design
more largely to insist on, since the Matter of Fact is in this Case much better
known to your Majesty than in the foregoing.
If the Earth were alone, that is to say, not affected by the Actions of the
Sun and Moon, it is not to be doubted, but the Ocean, being equally press'd
by the force of Gravity towards the Center, would continue in a perfect
Stagnation, always at the same height, without either Ebbing or Flowing;
but it being here demonstrated, that the Sun and Moon have a like Principle
of Gravitation towards their Centers, and that the Earth is within the
Activity of their Attractions, it will plainly follow, that the Equality of the
pressure of Gravity towards the Center will thereby be disturb'd; and though
the smallness of these Forces, in respect of the Gravitation towards the
Earth's Center, renders them altogether imperceptible by any Experiments
we can devise, yet the Ocean being fluid and yielding to the least force, by
its rising shews where it is less press'd, and where it is more press'd by its
sinking.
Now if we suppose the force of the Moon's Attaction to decrease as the
Square of the Distance from its Center increases (as in the Earth and other
Cœlestial Bodies) we shall find, that where the Moon is perpendicularly
either above or below the Horizon, either in Zenith or Nadir, there the force
of Gravity is most of all diminished, and consequently that there the Ocean

must necessarily swell by the coming in of the Water from those parts
where the Pressure is greatest, viz. in those places where the Moon is near
the Horizon: But that this may be the better understood, I thought it needful
to add the following Figure, (Vide Fig. 1. Plate 1.) where M is the Moon, E
the Earth, C its Center, and Z the place where the Moon is in the Zenith, N
where in the Nadir.
Now by the Hypothesis it is evident, that the Water in Z, being nearer, is
more drawn by the Moon, than the Center of the Earth C, and that again
more than the Water in N; wherefore the Water in Z hath a tendency towards
the Moon, contrary to that of Gravity, being equal to the excess of the
Gravitation in Z, above that in C: And in the other case, the Water in N,
tending less towards the Moon than the Center C, will be less pressed, by as
much as is the difference of the Gravitation towards the Moon in C and N.
This rightly understood, it follows plainly, that the Sea, which otherwise
would be Spherical, upon the Pressure of the Moon, must form it self into a
Spheroidal or Oval Figure, whose longest Diameter is where the Moon is
vertical, and shortest where she is in the Horizon; and that the Moon
shifting her Position as she turns round the Earth once a Day, this Oval of
Water shifts with her, occasioning thereby the two Floods and Ebbs
observable in each 25 Hours.
And this may suffice, as to the general Cause of the Tides; it remains now
to shew how naturally this Motion accounts for all the Particulars that have
been observ'd about them; so that there can be no room left to doubt, but
that this is the true cause thereof.
The Spring Tides upon the New and Full Moons, and Neap Tides on the
Quarters, are occasion'd by the attractive Force of the Sun in the New and
Full, conspiring with the Attraction of the Moon, and producing a Tide by
their united Forces: Whereas in the Quarters, the Sun raises the Water where
the Moon depresses it, and the contrary; so as the Tides are made only by
the difference of their Attractions. That the force of the Sun is no greater in

this Case, proceeds from the very small Proportion the Semi-diameter of the
Earth bears to the vast distance of the Sun.
It is also observ'd, that cæteris paribus, the Æquinoctial Spring Tides in
March and September, or near them, are the Highest, and the Neap Tides
the lowest; which proceeds from the greater Agitations of the Waters, when
the fluid Spheroid revolves about a great Circle of the Earth, than when it
turns about in a lesser Circle; it being plain that if the Moon were
constituted in the Pole, and there stood, that the Spheroid would have a fix'd
Position, and that it would be always high Water under the Poles, and low
Water every where under the Æquinoctial: And therefore the nearer the
Moon approaches the Poles, the less is the agitation of the Ocean, which is
of all the greatest, when the Moon is in the Æquinoctial, or farthest distant
from the Poles. Whence the Sun and Moon, being either conjoined or
opposite in the Æquinoctial, produce the greatest Spring Tides; and the
subsequent Neap Tides, being produc'd by the Tropical Moon in the
Quarters, are always the least Tides; whereas in June and December, the
Spring Tides are made by the Tropical Sun and Moon, and therefore less
vigorous; and the Neap Tides by the Æquinoctial Moon, which therefore are
the stronger: Hence it happens, that the difference between the Spring and
Neap Tides in these Months, is much less considerable than in March and
September. And the reason why the very highest Spring Tides are found to
be rather before the Vernal and after the Autumnal Equinox, viz. in
February and October, than precisely upon them, is, because the Sun is
nearer the Earth in the Winter Months, and so comes to have a greater effect
in producing the Tides.
Hitherto we have consider'd such Affections of the Tides as are
Universal, without relation to particular Cases; what follows from the
differing Latitudes of places, will be easily understood by the following Fig.
(Vide Fig. 2. Plate 1.)

Let ApEP be the Earth cover'd over with very deep Waters, C its Center,
P, p, its Poles, AE the Æquinoctial, F, f, the parallel of Latitude of a Place,
D, d, another Parallel at equal distance on the other side of the Æquinoctial,
H, h, the two Points where the Moon is vertical, and let K, k, be the great
Circle, wherein the Moon appears Horizontal. It is evident, that a Spheroid
describ'd upon Hh, and Kk, shall nearly represent the Figure of the Sea, and
Cf, CD, CF, Cd, shall be the heighths of the Sea in the places f, D, F, d, in
all which it is High-water: And seeing that in twelve Hours time, by the
diurnal Rotation of the Earth, the Point F is transferr'd to f, and d to D: The
height of the Sea CF will be that of the High-water when the Moon is
present, and Cf that of the other High-water, when the Moon is under the
Earth: Which in the case of this Figure is less than the former CF. And in
the opposite Parallel Dd, the contrary happens. The Rising of the Water
being always alternately greater and less in each place, when it is produc'd
by the Moon declining sensibly from the Æquinoctial; that being the
greatest of the two High-waters in each diurnal Revolution of the Moon,
wherein she approaches nearest either to the Zenith or Nadir of the place:
Whence it is, that the Moon in the Northern Signs, in this part of the World,
makes the greatest Tides when above the Earth, and in Southern Signs,
when under the Earth; the Effect being always the greatest where the Moon
is farthest from the Horizon, either above or below it. And this alternate
Increase and Decrease of the Tides has been observ'd to hold true on the
Coast of England, at Bristol by Captain Sturmy, and at Plymouth by Mr.
Colepresse.
But the Motions hitherto mentioned are somewhat alter'd by the Libration
of the Water, whereby, though the Action of the Luminaries should cease,
the Flux and Reflux of the Sea would for some time continue: This
Conservation of the impress'd Motion diminishes the differences that
otherwise would be between two consequent Tides, and is the reason why
the highest Spring-Tides are not precisely on the New and Full Moons, nor

the Neaps on the Quarters; but generally they are the third Tides after them,
and sometimes later.
All these things would regularly come to pass, if the whole Earth were
cover'd with Sea very deep; but by reason of the shoalness of some places,
and the narrowness of the Streights, by which the Tides are in many cases
propagated, there arises a great diversity in the Effect, and not to be
accounted for, without an exact Knowledge of all the Circumstances of the
Places, as of the Position of the Land, and the Breadth and Depth of the
Channels by which the Tide flows; for a very slow and imperceptible
Motion of the whole Body of the Water, where it is (for Example) 2 Miles
deep, will suffice to raise its Surface 10 or 12 Feet in a Tides time; whereas,
if the same quantity of Water were to be convey'd up a Channel of 40
Fathoms deep, it would require a very great Stream to effect it, in so large
Inlets as are the Channel of England, and the German Ocean; whence the
Tide is found to set strongest in those places where the Sea grows
narrowest; the same quantity of Water being to pass through a smaller
Passage: This is most evident in the Streights, between Portland and Cape
de Hague in Normandy, where the Tide runs like a Sluce; and would be yet
more between Dover and Calais, if the Tide coming about the Island from
the North did not check it. And this force being once impress'd upon the
Water, continues to carry it above the level of the ordinary height in the
Ocean, particularly where the Water meets a direct Obstacle, as it is at St.
Malo's; and where it enters into a long Channel, which running far into the
Land, grows very streight at its Extremity; as it is in the Severn-Sea at
Chepstow and Bristol.
This shoalness of the Sea, and the intercurrent Continents are the reason,
that in the open Ocean the time of High water is not at the Moons appulse
to the Meridian, but always some Hours after it; as it is observ'd upon all
the West Coast of Europe and Africa, from Ireland to the Cape of Good
Hope: In all which a S. W. Moon makes High-water, and the same is
reported to be on the West side of America. But it would be endless to

account all the particular Solutions, which are easie Corollaries of this
Hypothesis; as why the Lakes, such as the Caspian Sea, and Mediterranean
Seas, such as the Black Sea, the Streights and Baltick, have no sensible
Tides: For Lakes having no Communication with the Ocean, can neither
increase nor diminish their Water, whereby to rise and fall; and Seas that
communicate by such narrow Inlets, and are of so immense an Extent,
cannot in a few Hours time receive or empty Water enough to raise or sink
their Surface any thing sensibly.
Lastly, to demonstrate the Excellency of this Doctrine, the Example of
the Tides in the Port of Tunking in China, which are so extraordinary, and
differing from all others we have yet heard of, may suffice. In this Port
there is but one Flood and Ebb in 24 Hours; and twice in each Month, viz.
when the Moon is near the Æquinoctial there is no Tide at all, but the Water
is stagnant; but with the Moons Declination there begins a Tide, which is
greatest when she is in the Tropical Signs: Only with this difference, that
when the Moon is to the Northward of the Æquinoctial, it Flows when she
is above the Earth, and Ebbs when she is under, so as to make High-water at
Moons-setting, and Low-water at Moons-rising: But on the contrary, the
Moon being to the Southward, makes High-water at rising, and Low-water
at setting; it Ebbing all the time she is above the Horizon. As may be seen
more at large in the Philosophical Transactions, Numb. 162.
The Cause of this odd Appearance is propos'd by Mr. Newton, to be from
the concurrence of two Tides; the one propagated in six Hours out of the
great South-Sea along the Coast of China; the other out of the Indian-Sea,
from between the Islands in twelve Hours, along the Coast of Malacca and
Cambodia. The one of these Tides, being produc'd in North Latitude, is, as
has been said, greater, when the Moon being to the North of the Equator is
above the Earth, and less when she is under the Earth. The other of them,
which is propagated from the Indian Sea, being raised in South-Latitude, is
greater when the Moon declining to the South, is above the Earth, and less
when she is under the Earth: So that of these Tides alternately greater and

lesser, there comes always successively two of the greater and two of the
lesser together every Day; and the High-water falls always between the
times of the arrival of the two greater Floods; and the Low-water between
the arrival of the two lesser Floods. And the Moon coming to the
Æquinoctial, and the alternate Floods becoming equal, the Tide ceases, and
the Water stagnates: But when she has pass'd to the other side of the
Equator, those Floods which in the former Order were the least, now
becoming the greatest, that That before was the time of High-water, now
becomes the Low-water, and the Converse. So that the whole appearance of
these strange Tides, is without any forcing naturally deduc'd from these
Principles, and is a great Argument of the Certainty of the whole Theory.

Theory of the Variation of the Magnetical Compass. By Mr. Ed.
Halley, Fellow of the Royal Society.

HE Variation of the Compass (by which I mean the Deflection of the
T Magnetical Needle from the true Meridian) is of that great
Concernment in the Art of Navigation, that the neglect thereof, does
little less than render useless one of the noblest Inventions Mankind ever
yet attained to. And for this cause all Ships of Consequence (especially
those bound beyond the Equator) carry with them Instruments on purpose to
observe this Variation: That so the Course steer'd by the Compass, may be
reduc'd to the true Course in respect of the Meridian.
Now although the great utility that a perfect Knowledge of the Theory of
the Magnetical Direction would afford to Mankind in general, and
especially to those concern'd in Sea Affairs, seems as sufficient incitement
to all Philosophical and Mathematical Heads, to take under serious
Consideration the several Phænomena, and to endeavour to reconcile them
by some general Rule: Yet so it is; that almost all the Authors, from whom a
Discourse of this kind ought to have been expected, pass by in silence the
Difficulties they here Encounter. And those that mention this Variation: By

affirming it to proceed from Causes altogether uncertain (as are the casual
lying of Iron Mines and Loadstones in the Earth) put a stop to all further
Contemplation; and give discouragement to those that would otherwise
undertake this Enquiry. 'Tis true, that not long since one Mr. Bond, an old
Teacher of Navigation, put forth a small Treatise, wherein he pretends to
calculate the Variation: But he limits his Hypothesis to the City of London,
affirming himself (as he had a great deal of reason) that the same Calculus
is not sufficient for other Places; whereby it appears that this Rule is far
short of the so much desir'd general one.
Now although (through want of sufficient Observations, and some other
Difficulties, which I shall anon shew) I cannot pretend perfectly to establish
the Numbers and Rules of a Calculus, which shall precisely answer to the
Variations of all parts of the World: Yet I suppose it will not be unacceptable
to the Curious to propose something of a Light into this abstruse Mystery;
which, if no other, may have this good Effect, to stir up the Philosophical
Genii of the Age to apply themselves more attentively to this useful
Speculation. But before I proceed, 'twill be necessary to lay down the
Grounds upon which I raise my Conclusions; and at once to give a Synopsis
of those Variations, which I have reason to look upon as sure, being mostly
the Observations of Persons of good Skill and Integrity.

A
TABLE
OF
VARIATIONS.
Names of Longitude Anno Variation
Latitude
Places. from Lon. Dom. Observ'd.
d m d m d m
London 0 0 51 32 N 1580 11 15 E
1622 6 0 E
1634 4 5 E
1672 2 30 W

Paris 2 25 E 48 51 N 1683 4 30 W
1640 3 00 E
1666 0 0
1681 2 30 W
Uraniburg 13 0 E 55 54 N 1672 2 35 W
Copenhagen 12 53 E 55 41 N 1649 1 30 E
1672 3 35 W
Dantzick 19 0 E 54 23 N 1679 7 00 W
Mompelier 4 0 E 43 37 N 1674 1 10 W
Brest 4 25 W 48 23 N 1680 1 45 W
Rome 13 0 E 41 50 N 1681 5 0 W
Bayonne 1 20 W 43 30 N 1680 1 20 W
Hudson's Bay 79 40 W 51 00 N 1668 19 15 W
In Hud. Straights 57 00 W 61 00 N 1668 29 30 W
In Baffin's Bay at Sir
Thomas Smith's Sound 80 00 W 78 00 N 1616 57 00 W
At Sea 50 00 W 38 40 N 1682 7 30 W
At Sea 31 30 W 43 50 N 1682 5 30 W
At Sea 42 0 W 21 0 N 1678 0 40 E
Cape St. Aug. of Brazile 35 30 W 8 0 S 1670 5 30 E
Cape Frio 41 10 W 22 40 S 1670 12 10 E
At Sea off of the Mou.
of the River Plate 53 00 W 39 30 S 1670 20 33 E
At the East Entrance of
Magellan Straits 68 00 W 52 30 S 1670 17 00 E
At the W. Entrance of the
Magellan Straits 75 00 W 53 00 S 1670 14 10 E
Baldivia 73 00 W 40 00 S 1670 8 10 E
At Cape d'Agulbas 16 30 E 34 50 S 1622 2 99 W
1675 8 00 W
At Sea 1 0 E 34 30 S 1675 0 00
At Sea 20 0 W 34 0 S 1675 10 30 E
At Sea 32 0 W 24 0 S 1675 10 30 E
At St. Helena 6 30 W 16 00 S 1677 0 40 E
At Ascension 14 30 W 7 50 S 1678 1 00 E
At Johanna 44 00 E 12 15 S 1675 19 30 W
At Monbasa 40 00 E 4 00 S 1675 16 00 W
At Zocatra 56 00 E 12 30 N 1674 17 00 W
At Aden, at the Mo.
of the Red Sea 47 30 E 13 00 N 1674 15 00 W
At Diego Roiz 61 0 E 20 0 S 1676 20 30 W
At Sea 64 30 E 0 0 1676 15 30 W
At Sea 55 0 E 27 0 S 1676 24 00 W
At Bombay 72 30 E 19 0 N 1676 12 00 W
At Cape Comorin 76 00 E 8 15 N 1680 8 48 W
At Ballafore 87 00 E 21 30 N 1680 8 20 W
At Fort St. George 80 00 E 13 15 N 1680 8 10 W
At the W. Point of Java 104 00 E 6 40 S 1676 3 10 W
At Sea 58 00 39 0 S 1677 27 30 W
At the Isle of St. Paul 72 0 E 38 0 S 1677 23 30 W

At Van Dimen's Land 142 0 E 42 25 S 1642 0 0
At New Zealand 170 0 E 40 50 S 1642 9 0 E
At Three Kings Isle in
New Zealand. 169 30 E 34 35 S 1642 8 40 E
At the Isle Rotterdam
in the South Sea 184 00 E 20 15 S 1642 6 20 E
On the Coast of N. Guin. 149 00 E 4 30 S 1643 8 45 E
At the W. P. of N. Guin. 126 00 E 0 26 S 1643 5 30 E

Tho' I could wish we could obtain from the Spaniards what Variations
they find in their Voyages from the Manilhas towards Acapulco, through the
North part of the South Sea; as likewise what it is at Japan from the Dutch:
Yet (considering the number of these Observations I have collected, and
that they are made in parts of the World so remote from Europe, and from
one another) I suppose that the Theory that answers these will scarce fail in
those Regions from whence we have as yet no account. But first we must
make some Remarks upon the foregoing Table: And, First,
That in all Europe the Variation at this time is West, and more in the
Eastern Parts thereof than the Western: As likewise, that it seems
throughout to be upon the increase that way.
Secondly, That on the Coast of America, about Virginia, New-England
and New-Foundland, the Variation is likewise Westerly; and that it increases
all the way as you go Northerly along the Coast, so as to be above 20
Degrees at New-Found-Land, nearly 30 gr. in Hudson's Straights, and not
less than 57 Degrees in Baffin's Bay; also, that as you Sail Eastward from
this Coast, the Variation diminishes. From these two it is a Legitimate
Corollary: That Somewhere between Europe, and the North part of
America, there ought to be an Easterly Variation, or at least no Westerly.
And so I conjecture it is about the Eastermost of the Tercera Islands.
Thirdly, That on the Coast of Brasile there is East Variation, which
increases very notably as you go to the Southward, so as to be 12 Degrees
at Cape Frio, and over against the River of Plate 20½ Degrees: And from
thence Sailing South-Westerly to the Straits of Magellan it decreases 17
Degrees, and at the West Entrance but 14 Degrees.

Fourthly, That at the Eastward of Brasile, properly so call'd, this Easterly
Variation decreases, so as to be very little at St. Helena and Ascension, and
to be quite gone, and the Compass Point true about 18 Degrees of
Longitude West from the Cape of Good-hope.
Fifthly, That to the Eastward of the aforesaid Places a Westward Variation
begins, which Reigns in the whole Indian Sea, and arises to no less than
Eighteen Degrees under the Equator it self, about the Meridian of the
Northern part of Madagascar; and near the same Meridian, but in 39
Degrees South Latitude it is found full 27½ Degrees: From thence Easterly
the West Variation decreases, so as to be little more than eight Degrees at
Cape Comorin, and than three Degrees upon the Coast of Java; and to be
quite extinct about the Molucca Islands, as also a little to the Westwards of
Van Diemens Land found out by the Dutch in 1642.
Sixthly, That to the Eastward of the Molucca's and Van Diemens Land in
South Latitude there arises another Easterly Variation, which seems not so
great as the former, nor of so large Extent; for that at the Island Rotterdam it
is sensibly less than upon the East Coast of New Guinea; and, at the rate it
decreases, it may well be suppos'd, that about 20 Degrees farther East, or
225 Degrees East Longitude from London, in the Latitude of 20 Degrees
South, a Westerly Variation begins.
Seventhly, That the Variations observ'd by the Honourable Sir John
Norborough at Baldivia, and at the West Entrance of the Straights of
Magellan do plainly shew, that That East Variation, noted in our third
Remark, is decreasing apace; and that it cannot reasonably extend many
Degrees into the South Sea from the Coast of Peru and Chili, leaving room
for a small Westerly Variation, in that Tract of the unknown World that lies
in the mid-way between Chili and New-Zealand, and between Hounds-
Island and Peru.
Eighthly, That in Sailing North-West from St. Helena by Ascension, as
far as the Equator, the Variation continues very small East, and as it were

constantly the same: So that in this part of the World the Course, wherein
there is no Variation, is evidently no Meridian, but rather North-West.
Ninthly, That the Entrance of Hudson's Straights, and the Mouth of the
River of Plate, being nearly under the same Meridian, at the one place the
Needle varies 29½ Degrees to the West; at the other 20½ Degrees to the
East. This plainly demonstrates the impossibility of reconciling these
Variations by the Theory of Bond; which is by two Magnetical Poles and an
Axis, inclin'd to the Axis of the Earth; from whence it would follow, That
under the same Meridian the Variation should be in all places the same
way.

These things being premised may serve as a sure Foundation to raise the
Superstructure of a Theory upon. But first it would not be amiss to shew
hereby the mistake of Gilbert and Des Cartes: The first whereof supposes,
that the Earth it self being in all its parts Magnetical, and the Water not;
wheresoever the Land is, thither also should the Needle turn, as to the
greater quantity of Magnetical Matter. But this in many Instances is not
true; but most remarkably upon the Coast of Brazile, where the Needle is so
far from being attracted by the Land, that it turns the quite contrary way,
leaving the Meridian to lye N b E, which is just along the Coast. As to the
Position of Des Cartes, that the Iron and Loadstones hid in the Bowels of
the Earth and the Bottom of the Sea, may be the Causes that the Needle
varies; if we consider for how great a part of the Earths Surface, ex. gr. in
the whole Indian Sea, the Needle declines the same way, and that regularly,
'twill follow that the attracting Substance that occasions it, must be very far
distant. Now by Experience we find the little force that Iron Guns have
upon the Compass in Ships (their Vertue, though they be Demiculverin, or
greater Cannon, being not perceptible at four or five Yards distance) and the
Experiments now before the Royal Society do plainly shew, how little a
Magnetism there is in most crude Iron Oars: What quantity thereof must be
then suppos'd to make so powerful a Diversion at two or three Thousand

Miles distance? Yet I cannot deny that in some places near the Shoar, or in
Shoal-Water, the Needle may be irregularly directed from the aforesaid
Causes, and that not a little, as Gassendus gives a notable instance of the
Island Elba in the Mediterranean Sea: But these differences from the
general Direction are always signs of the nearness of those Magnetical
Substances, for the Production whereof that Island Elba has been famous
from all Antiquity. Besides, against both Des Cartes and Gilbert, the change
of the Variation, which has been within these Hundred Years last past more
than 15 gr. at London, is an entire Demonstration; tho' Des Cartes does not
stick to say, that the transportation of Iron from place to place, and the
growth of new Iron within the Earth, where there was none before, may be
the cause thereof. The same holds likewise against the Hypothesis of
Magnetical Fibres, which Kircher maintains.
Now to propose something that may answer the several appearances, and
introduce nothing strange in Philosophy, after a great many close Thoughts,
I can come to no other Conclusion than that, The whole Globe of the Earth
is one great Magnet, having four Magnetical Poles, or Points of Attraction,
near each Pole of the Equator. Two; and that, in those parts of the World
which lie near adjacent to any one of those Magnetical Poles, the Needle is
govern'd thereby, the nearest Pole being always predominant over the more
remote. The parts of the Earth wherein these Magnetical Poles lie, cannot as
yet be exactly determin'd for want of sufficient Data to proceed
Geometrically; but, as near as Conjecture can reach, I reckon that the Pole,
which is at present nearest to us, lies in or near the Meridian of the Lands-
end of England, and not above seven Degrees from the Pole Arctick; by this
Pole the Variations in all Europe and Tartary, and the North Sea are
principally govern'd, though with regard to the other Northern Pole, whose
situation is in a Meridian passing about the middle of California, and about
15 gr. from the North Pole of the World; to this the Needle has chiefly
respect in all the North America, and in the two Oceans on either side
thereof, from the Azores Westward to Japan, and farther. The two Southern

Poles are rather farther distant from the South Pole of the World: The one
about sixteen Degrees therefrom, is in a Meridian, some twenty Degrees to
the Westward of Magellan Straights, or ninety five Degrees West from
London: This commands the Needle in all the South-America, in the
Pacifick Sea, and the greatest part of the Ethiopick Ocean. The Fourth and
last Pole seems to have the greatest Power, and largest Dominions of all, as
it is the most remote from the Pole of the World, being little less than 20
Degrees distant therefrom in the Meridian, which passes through Hollandia
Nova, and the Island Celebes about one hundred and twenty Degrees East
from London; this Pole is predominant in the South part of Africa, in Arabia
and the Red Sea, in Persia, India, and its Islands, and all over the Indian
Sea, from the Cape of Good-Hope Eastwards to the middle of the great
South Sea, that divides Asia from America. This seems to be the present
Disposition of the Magnetical Vertue throughout the whole Globe of the
Earth; it remains to shew how this Hypothesis makes out all the Variations
that have been observ'd of late; and how it answers to our several Remarks
drawn from the Table. And first it is plain, that (our European North Pole
being in the Meridian of the Lands-end of England) all places more
Easterly than that will have it on the West side of their Meridian, and
consequently the Needle, respecting it with its Northern Point, will have a
Westerly Variation, which will still be greater as you go to the Eastwards,
till you come to some Meridian of Russia, where 'twill be greatest, and from
thence decrease again. Thus at Brest the Variation is but 1¾ Degrees, at
London 4½ Degrees; but at Dantzick seven Degrees West. To the Westward
of the Meridian of the Lands-end, the Needle ought to have an Easterly
Variation; were it not that (by approaching the American Northern Pole,
which lies on the West side of the Meridian, and seems to be of greater
force than this other) the Needle is drawn thereby Westwards, so as to
counterballance the Direction given by the European Pole, and to make a
small West Variation in the Meridian of the Lands-end it self. Yet I suppose
that about the Meridian of the Isle Tercera, our nearest Pole may so far
prevail as to give the Needle a little turn to the East, though but for a very

small space: The Counterballance of those two Poles permitting no
considerable Variation in all the Eastern Parts of the Atlantick Ocean; nor
upon the West Coasts of England and Ireland, France, Spain and Barbary.
But to the Westwards of the Azores the Power of the American Pole
overcoming that of the European, the Needle has chiefly respect thereto,
and turns still more and more towards it as you approach it. Whence it
comes to pass, that on the Coast of Virginia, New-England, New-found-
Land, and in Hudson's-Straights the Variation is Westward; that it decreases
as you go from thence towards Europe, and that it is less in Virginia and
New-England, than in New-found-Land, and Hudson's-Straights. This
Westerly Variation again decreases, as you pass over the North America;
and about the Meridian of the middle of California the Needle again points
due North; and from thence Westward to Yedzo and Japan, I make no doubt
but the Variation is Easterly, and half the Sea over no less than fifteen
Degrees, if there be any truth in this Hypothesis of mine. Therefore I
propose this as a Trial, that the whole may be scann'd thereby; and I
conceive it will not be hard to know of the Spaniards how it is, who so
frequently sail through that Ocean, in their return from the Manilha Isles.
This East Variation extends over Japan, Yedzo, East-Tartary, and part of
China, till it meet with the Westerly, which is govern'd by the European
North Pole, and which I said was greatest some where in Russia.
Towards the Southern Pole the effect is much the same, only that here the
South Point of the Needle is attracted. Hence it will follow, that the
Variation on the Coast of Brazile, at the River of Plate, and so on to the
Straights of Magellan, should be Easterly (as in our third Remark); if we
suppose a Magnetical Pole situate about twenty Degrees more Westerly
than the Straights of Magellan. And this Easterly Variation doth extend
Eastward over the greatest part of the Ethiopick Sea, till it be counterpoised
by the Vertue of the other Southern Pole; as it is about mid-way between the
Cape of Good-Hope, and the Isles of Tristan d' Acuntia. From thence
Eastwards, the Asian South Pole (as I must take the liberty to call it)

becoming prevalent, and the South point of the Needle being attracted
thereby, there arises a West Variation, very great in quantity and extent,
because of the great distance of this Magnetical Pole of the World. Hence it
is, that in all the Indian Sea as far as Hollandia Nova, and farther, there is
constantly West Variation; at that under the Equator it self it arises to no less
than eighteen Degrees, where 'tis most. About the Meridian of the Island
Celebes, being likewise that of this Pole, this Westerly Variation ceases, and
an Easterly begins; which reaches, according to my Hypothesis, to the
middle of the South-Sea, between Zelandia Nova, and Chili, leaving room
for a small West Variation govern'd by the American South Pole, which I
shew'd to be in the Pacifick Sea, in the sixth and seventh Remark.
What I have now said, does plainly shew the sufficiency of this
Hypothesis for solving the Variations that are at this time observ'd in the
temperate and frigid Zones, where the Direction of the Needle chiefly
depends upon the Counterpoise of the forces of two Magnetical Poles of the
same Nature; and I suppose I have shewn how it comes to pass, that under
the same Meridian the Variation should be in one place 29½ West, and
another 20½ East; as I have noted in my ninth Remark.
In the Torrid Zone, and particularly under the Equinoctial, respect must
be had to all four Poles, and their Positions well consider'd, otherwise it will
not be easie to determine what the Variations shall be; the nearest Pole
being always the strongest; yet not so, as not to be counterballanc'd
sometimes by the united forces of two more remote; a notable Instance
whereof is in our eighth Remark, where I took notice, that in sailing from
St. Helena by the Isle of Ascension, to the Equator, on a N. W. Course, the
Variation is very little Easterly, and in that whole Tract unalterable; for
which I give this Reason, That the South American Pole (which is
considerably the nearest in the aforesaid Places) requiring a great Easterly
Variation, is counterpoised by the contrary Attraction of the North-
American and the Asian-South-Pole; each whereof singly are in these Parts,
weaker than the American-South-Pole; and upon the North West Course, the

Distance from this latter is very little varied; and as you recede from the
Asian-South-Pole, the Ballance is still preserv'd by the access towards the
North-American-Pole. I mention not in this Case the European-North-Pole,
its Meridian being little remov'd from those of these places; and of it self
requiring the same Variations we here find. After the same manner we
might proceed to conclude the Variations in other places under and near the
Equator; but I purposely leave it for an Exercise to the Thoughts of the
serious Reader, who is desir'd to help his Imagination, by having before him
a Map or Globe of the Earth: And to mark thereon the Magnetical Poles in
the Longitudes and Latitudes I assign them. (Vide Plate 2.)
Thus, I hope, I have not lost my Pains and Study in this difficult Subject;
believing that I have put it past doubt, That there are in the Earth four such
Magnetical Points or Poles, which occasion the great variety and seeming
irregularity which is observed in the Variations of the Compass. But to
calculate exactly what it is, in any place assign'd, is what I dare not yet
pretend to, though I could wish it were my happiness to be able to oblige
the World with so useful a piece of Knowledge; there are Difficulties that
occur, that render the thing as yet not feasible; for first there are a great
many Observations requisite, which ought to be made at the same time; not
at Sea, but ashore, with greater Care and Attention than the generality of
Sailors apply. And besides, it remains undetermin'd in what proportion the
attractive Power decreases, as you remove from the Pole of a Magnet,
without which it were a vain attempt to go about to calculate. There is yet a
further Difficulty, which is the Change of the Variation, one of the
Discoveries of this last Century; which shews, that it will require some
hundreds of Years to establish a compleat Doctrine of the Magnetical
System. From the foregoing Table it should seem, that all the Magnetical
Poles had a motion Westward: But if it be so, 'tis evident, that it is not a
Rotation about the Axis of the Earth; for then the Variations would continue
the same, in the same parallel of Latitude (the Longitude only chang'd) as
much as is the motion of the Magnetical Poles, but the contrary is found by

Experience; for there is no where in the Latitude of 15½ North between
England and America, a Variation of eleven Degrees East at this time; as it
was once here at London; it seems therefore, that our European Pole is
grown nearer the Pole Arctick than it was heretofore, or else that it has lost
part of its Vertue. But whether these Magnetical Poles move altogether with
one motion, or with several; whether equally or unequally; whether Circular
or Libratory: If Circular, about what Center; if Libratory, after what manner;
are Secrets as yet utterly unknown to Mankind, and are reserv'd for the
Industry of future Ages.

Account of the Cause of the Change of the Variation of the
Magnetical Needle, with an Hypothesis of the Structure of the
Internal Parts of the Earth; as it was proposed to the Royal Society
in one of their late Meetings. By Mr. Edmund Halley.

Aving in the precedent Discourse delivered a Theory of the Variation
H of the Magnetical Compass, wherein I did collect as many
Observations as at that time I could procure, and having carefully
compar'd them together, I came at length to this general conclusion, That
the Globe of the Earth might be supposed to be one great Magnet, having
four Magnetical Poles or Points of Attraction, near each Pole of the
Equator two; and that in those parts of the World which lie near adjacent to
any one of those Magnetical Poles, the Needle is chiefly govern'd thereby;
the nearest Pole being always predominant ever the more remote. And I
there have endeavour'd to state and limit the present Position of those Poles
in the Surface of our Globe, which the Reader pleasing to consult, will save
us the pains of repeating. But after all, tho' that Discourse was favourably
receiv'd both at home and abroad, as seeming to render a tolerable account
of the observ'd Variations, yet I found two Difficulties not easie to
surmount; the one was, that no Magnet I had ever seen or heard of, had
more than two opposite Poles, whereas the Earth had visibly four, and

perhaps more. And secondly, it was plain that these Poles were not, at least
all of them, fixt in the Earth, but shifted from place to place, as appear'd by
the great Changes in the Needles Direction within this last Century of
Years, not only at London, (where this great Discovery was first made) but
almost all over the Globe of Earth; whereas it is not known or observ'd that
the Poles of a Load-stone ever shifted their place in the Stone, nor
(considering the compact hardness of that Substance) can it easily be
suppos'd; though the Matter of Fact be too notorious and universal, not to
be accounted for.
These Difficulties had wholly made me despond, and I had long since
given over an Inquiry I had so little hopes of, when in accidental Discourse,
and least expecting it, I stumbl'd on the following Hypothesis; in delivering
whereof, if I shall seem to advance any thing that looks like Extravagant or
Romantick, the Reader is desir'd to suspend his Censure, till he have
consider'd the force and number of the many Arguments which concur to
make good so new and so bold a Supposition.
Though it be sufficiently known and allow'd, that the Needles Variation
changes, it will be necessary however to give a few Instances, whereby it
may appear that this Change is gradual and universal, and the effect of a
great and permanent motion: For which take the following Examples.
At London, in the Year 1580, the Variation was observ'd by Mr. Burrows
to be 11° 15' East. In Anno 1622, the same was found by Mr. Gunter to be
but 6° 0' East. In the Year 1634, Mr. Gellibrand found it 4° 5' East. In 1657,
Mr. Bond observ'd that there was no Variation at London. Anno 1672, my
self observ'd it 2° 30' to the West; and in the Year 1692, I again found it 6°
00' West. So that in 112 Years the Direction of the Needle has chang'd no
less than seventeen Degrees.
At Paris, Orontius Finæus about the Year 1550, did account it about
eight or nine Degrees East Variation. Anno 1640, it was found three Degrees

East. Anno 1660, there was no Variation there, and Anno 1681, I found it to
be 2° 30' to the West.
At Cape d' Agulhas, the most Southerly Promontary of Africa, about the
Year 1600, the Needle pointed due North and South without Variation,
whence the Portugueze gave its name. Anno 1622, there was two Degrees
West Variation. Anno 1675, it was 8° 50' West; and in the Year 1691, it was
curiously observ'd not less than eleven Degrees West.
At St. Helena, about the Year 1600, the Needle declin'd eight Degrees to
the East. Anno 1623, it was but 6° 0' East. Anno 1677, when I was there, I
observ'd it accurately on Shoar to be 0° 40' East; and in 1692 it was found
about 1° to the Westward of the North.
At Cape Comorine in India, in the Year 1620, there was 14° 20' West
Variation. In the Year 1680, there was 8° 48', but now lately in the Year
1688, it was no more than 7° 30', so that here the Needle has return'd to the
East about seven Degrees in seventy Years.
In all the other Examples the Needle has gradually mov'd towards the
West, and the places are too far asunder to be influenc'd by the removal of
any Magnetical Matter, which may by accident be transplac'd within the
Bowels, or on the Surface of the Earth. If more Examples are desir'd, the
Reader may be furnished with them in the Portugueze Routier of Aleixo de
Motta (written about the Year 1600) and in the Voyage of Beaulieu, both
publish'd in Mr. Thevenot's first Collection of curious Voyages, Printed at
Paris, Anno 1663; which he is to compare with the Journals of our late East
India Voyagers, and I am assur'd, that it will be thereby evident, that the
Direction of the Needle is in no place fix'd and constant, tho' in some it
change faster than in others: And where for a long time it has continu'd as it
were unalter'd, it is there to be understood, that the Needle has its greatest
Deflection, and is become Stationary in order to return, like the Sun, in the
Tropick. This, at present, is in the Indian Sea, about the Island Mauritius,
where is the highest West Variation, and in a Tract tending from thence into

the N. N. W. towards the Red-Sea and Egypt. And in all Places to the
Westward of this Tract, all over Africa and the Seas adjoining, the West
Variation will be found to have encreas'd; and to the Eastwards thereof as in
the Example of Cape Comorine, to have decreased, viz. all over the East-
Indies, and the Islands near it.
After the like manner in that Space of East Variation, which, beginning
near St. Helena, is found all over the South America, and which at present
is highest about the Mouth of Rio de la Plata, it has been observ'd, that in
the Eastern Parts thereof, the Variation of the Needle gradually decreases;
but whether on the contrary it increases in those places which lie more
Westerly than that Tract wherein the highest East Variation is found; or how
it may be in the vast Pacifick Sea, we have not Experience enough to
ascertain, only we may by Analogy infer, that both the East and West
Variations therein do gradually increase and decrease after the same Rule.
These Phænomena being well understood and duly consider'd, do
sufficiently evince, That the whole Magnetical System is by one, or perhaps
more motions translated, whether Eastwards or Westwards, I shall anon
discuss; that this moving thing is very great, as extending its effects from
Pole to Pole, and that the motion thereof is not per saltum, but a gradual and
regular motion.
Now considering the Structure of our Terraqueous Globe, it cannot be
well suppos'd that a very great part thereof can move within it, without
notably changing its Center of Gravity and the Equilibre of its Parts, which
would produce very wonderful Effects in changing the Axis of diurnal
Rotation, and occasion strange alteration in the Seas Surface, by
Inundations and Recesses thereof, such as History never yet mention'd.
Besides, the solid parts of the Earth are not to be granted permeably by any
other than fluid Substances, of which we know none that are any ways
Magnetical. So that the only way to render this motion intelligible and
possible, is to suppose it to turn about the Center of the Globe, having its

Center of Gravity fix'd and immoveable in the same common Center of the
Earth: And there is yet requir'd, that this moving internal Substance be loose
and detached from the external Parts of the Earth whereon we live; for
otherwise, were it affix'd thereto, the whole must necessarily move together.
So then the External Parts of the Globe may well be reckon'd as the Shell,
and the Internal as a Nucleus or inner Globe, included within ours, with a
fluid Medium between, which having the same Common Center and Axis
of diurnal Rotation, may turn about with our Earth each twenty four Hours;
only this outer Sphere having its turbinating motion some small matter
either swifter or slower than the internal Ball: And a very minute Difference
in length of time, by many Repetitions becoming sensible, the Internal Parts
will by degrees recede from the External, and not keeping pace with one
another, will appear gradually to move either Eastwards or Westwards by
the difference of their motions.
Now supposing such an Internal Sphere having such a motion, we shall
solve the two great Difficulties we encounter'd in my former Hypothesis:
For if this exteriour Shell of Earth be a Magnet, having its Poles at a
distance from the Poles of diurnal Rotation; and if the Internal Nucleus be
likewise a Magnet, having its Poles in two other places, distant also from
the Axis; and these latter by a gradual and slow motion change their place
in respect of the External; we may then give a reasonable account of the
four Magnetical Poles I presume to have demonstrated before; as likewise
of the Changes of the Needles Variations, which till now hath been
unattempted.
The Period of this Motion being wonderful great, and there being hardly
an hundred Years since these Variations have been duly observ'd, it will be
very hard to bring this Hypothesis to a Calculus, especially since, though
the Variations do increase and decrease regularly in the same place, yet in
differing places, at no great distance, there are found such casual Changes
thereof as can no ways be accounted for by a regular Hypothesis; as

depending upon the unequal and irregular distribution of the Magnetical
Matter within the Substance of the External Shell or Coat of the Earth,
which deflect the Needle from the Position it would acquire from the effect
of the general Magnetism of the whole. Of this the Variations at London and
Paris give a notable Instance, for the Needle has been constantly about 1°½
more Easterly at Paris than at London; though it be certain that according to
the general effect, the Difference ought to be the contrary way:
Notwithstanding which, the Variations in both places do change alike.
Hence, and from some other of like Nature, I conclude, That the two
Poles of the External Globe are fixt in the Earth, and that if the Needle were
wholly govern'd by them, the Variations thereof would be always the same,
with some little Irregularities upon the account I but just now mention'd:
But the Internal Sphere having such a gradual translation of its Poles, does
influence the Needle, and direct it variously, according to the result of the
attractive or directive Power of each Pole; and consequently there must be a
Period of the Revolution of this Internal Ball, after which the Variations will
return again as before. But if it shall in future Ages be observ'd otherwise,
we must then conclude that there are more of these Internal Spheres, and
more Magnetical Poles than Four, which at present we have not a sufficient
number of Observations to determine, and particularly in that vast Mar del
Zur, which occupies so great a part of the whole Surface of the Earth.
If then two of the Poles be fixt and two moveable, it remains to ascertain
which they are that keep their place; and though I could wish we had the
Experience of another Century of Years to found our Conclusions upon, yet
I think we may safely determine, That our European North Pole (which in
the precedent Discourse I suppos'd near the Meridian of the Lands-end of
England, and about seven Degrees therefrom) is that That is moveable of
the two Northern Poles, and that That has chiefly influenc'd the Variations
in these parts of the World: For in Hudson's Bay, which is under the
Direction of the American Pole, the Change is not observ'd to be near so

fast as in these parts of Europe, though that Pole be much farther remov'd
from the Axis.
As to the South Poles, I take the Asian Pole, which I place about the
Meridian of the Island Celebes to be the fixt, and consequently the
American Pole to move; from the like Observation of the slow Decrease of
the Variation on the Coast of Java, and near the Meridian of the Asian Pole;
though I must confess to have no account of the effects of the other beyond
Magellan's Streights.
If this be allow'd me, 'tis plain that the fixt Poles are the Poles of this
External Shell or Cortex of the Earth, and the other two the Poles of a
Magnetical Nucleus included and moveable within the other. It likewise
follows, that this Motion is Westwards, and by consequence that the
aforesaid Nucleus has not precisely attained the same degree of Velocity
with the exteriour Parts in their diurnal Revolution; but so very nearly
equals it, that in 365 Revolves the difference is scarce sensible. This I
conceive to arise from the Impulse whereby this diurnal Motion was
imprest on the Earth, being given to the External Parts, and from thence in
time communicated to the Internal; but not so as perfectly to equal the
Velocity of the first Motion impress'd on, and still conserv'd by the
superficial Parts of the Globe.
As to the quantity of this Motion it is almost impossible to define it, both
from the Nature of this kind of Observation, which cannot be very
accurately perform'd, as also from the small time these Variations have been
observ'd, and their Change discover'd. It appears by all Circumstances, that
its Period is of many Centuries of Years, and as far as may be collected
from the Change of the Place, where there was no Variation, by reason of
the Equilibre of the two Southern Magnetical Poles, viz. from Cape d'
Agulhas to the Meridian of St. Helena (which is about 23 degr. in about
ninety Years) and of the place where the Westerly Variation is in its ἀκμὴ or
greatest Deflection, being about half so much, viz. from the Isle of Diego

Roiz to the South West Parts of Madagascar. We may with some Reason
conjecture, that the American Pole has mov'd Westwards forty six Degrees
in that time, and that the whole Period thereof is perform'd in seven hundred
Years, or thereabouts; so that the nice Determination of this, and of several
other Particulars in the Magnetick System is reserv'd for remote Posterity;
all that we can hope to do, is to leave behind us Observations that may be
confided in, and to propose an Hypothesis which after Ages may examine,
amend or refute. Only here I must take leave to recommend to all Masters
of Ships, and all others, Lovers of Natural Truths, that they use their utmost
Diligence to make, or procure to be made, Observations of these Variations
in all parts of the World, as well in the North as South Latitude (after the
laudable Custom of our East India Commanders) and that they please to
communicate them to the Royal Society, in order to leave as compleat a
History as may be to those that are hereafter to compare all together, and to
compleat and perfect this abstruse Theory.
And by the way it will not be amiss to amend a receiv'd Error in the
Practice of observing the Variation, which is, to take it by the Amplitude of
the Rising and Setting Sun, when his Center appears in the visible Horizon;
whereas he ought to be observ'd when his under Limb is still above the
Horizon about ⅔ of his Diameter, or twenty Minutes, upon the score of the
Refraction, and the height of the Eye of the Observer above the Surface of
the Sea: Or else they are to work the Amplitudes as they do the Azimuth,
reckoning the Suns Distance from the Zenith 90° 36': This, though it be of
little consequence near the Æquinoctial, will make a great Error in high
Latitudes, where the Sun rises and sets obliquely.
But to return to our Hypothesis, In order to explain the Change of the
Variations, we have adventur'd to make the Earth hollow, and to place
another Globe within it; and I doubt not but this will find Opposers enough.
I know 'twill be Objected, That there is no Instance in Nature of the like
thing; that if there was such a middle Globe it would not keep its place in
the Center, but be apt to deviate therefrom, and might possibly chock

against the Concave Shell, to the ruin, or at least endammaging thereof;
That the Water of the Sea would perpetually leak through, unless we
suppose the Cavity full of Water; That were it possible, yet it does not
appear of what use such an inward Sphere can be of, being shut up in
Eternal Darkness, and therefore unfit for the Production of Animals or
Plants; with many more Objections, according to the Fate of all such new
Propositions.
To these, and all other that I can foresee, I briefly Answer, That the Ring
environing the Globe of Saturn is a notable Instance of this kind, as having
the same common Center, and moving along with the Planet, without
sensibly approaching him on one side more than the other. And if this Ring
were turn'd on one of its Diameters, it would then describe such a Concave
Sphere as I suppose our External one to be. And since the Ring, in any
Position given, would, in the same manner, keep the Centre of Saturn in its
own, it follows, that such a Concave Sphere may move with another
included in it, having the same common Centre. Nor can it well be suppos'd
otherwise, considering the Nature of Gravity; for should these Globes be
adjusted once to the same common Centre, the Gravity of the parts of the
Concave would press equally towards the Centre of the inner Ball, which
equality must necessarily continue till some External Force disturb it, which
is not easie to imagine in our Case. This perhaps I might more intelligibly
express, by saying that the inner Globe being posited in the Centre of the
Exteriour, must necessarily ascend which way soever it move; that is, it
must overcome the force of Gravity pressing towards the common Centre,
by an impulse it must receive from some outward Agent; but all outward
Efforts being sufficiently fenc'd against by the Shell that surrounds it, it
follows, that this Nucleus being once fixt in the common Centre, must
always there remain.
As to the leaking of the Water through this Shell, when once a passage
shall be found for it to run through, I must confess it is an Objection
seemingly of weight; but when we consider how tightly great Beds of Chalk

or Clay, and much more Stone do hold Water, and even Caves arch'd with
Sand; no Man can doubt but the Wisdom of the Creator has provided for the
Macrocosm by many more ways than I can either imagine or express,
especially since we see the admirable and innumerable Contrivances
wherewith each worthless Individual is furnish'd both to defend it self, and
propagate its Species. What Curiosity in the Structure, what Accuracy in the
Mixture and Composition of the parts, ought not we to expect in the Fabrick
of this Globe, made to be the lasting Habitation of so many various Species
of Animals, in each of which there want not many Instances that manifest
the boundless Power and Goodness of their Divine Author; and can we then
think it a hard Supposition, that the Internal Parts of this Bubble of Earth
should be replete with such Saline and Vitriolick Particles as may contribute
to Petrefaction, and dispose the transuding Water to shoot and coagulate
into Stone, so as continually to fortifie, and, if need were, to consolidate any
breach or flaw in the Concave Surface of the Shell.
And this perhaps may not without Reason be suppos'd to be the final
Cause of the admixture of the Magnetical Matter in the Mass of the
Terrestrial parts of our Globe, viz. To make good and maintain the Concave
Arch of this Shell: For by what the Excellent Mr. Newton has shewn in his
Principia Philosophiæ, it will follow, that according to the general Principle
of Gravity, visible throughout the whole Universe, all those Particles that by
length of time, or otherwise, shall moulder away, or become loose on the
Concave Surface of the External Sphere, would fall in, and with great force
descend on the Internal, unless those Particles were of another sort of
Matter capable by their stronger tendency to each other, to suspend the
force of Gravity; but we know no other Substances capable of supporting
each other by their mutual Attraction but the Magnetical, and these we see
miraculously to perform that Office, even where the Power of Gravity has
its full effect, much more within the Globe where it is weaker. Why then
may we not suppose these said Arches to be lin'd throughout with a
Magnetical Matter, or rather to be one great Concave Magnet, whose two

Poles are the Poles we have before observ'd to be fixt in the Surface of our
Globe.
Another Argument, favouring this Hypothesis, is drawn from a
Proposition of the same Mr. Newton, where he determines the force
wherewith the Moon moves the Sea in producing the Tides: His Words are,
Densitas Lunæ est ad densitatem Terra ut 680 ad 387 seu 9 ad 5
quamproximé. Est igitur corpus Lunæ densius ac magis terrestre quam
Terra nostra, p. 466. Now if the Moon be more solid than the Earth, as 9 to
5, why may we not reasonably suppose the Moon, being a small Body, and
a secondary Planet, to be solid Earth, Water, Stone, and this Globe to
consist of the same Materials, only four Ninths thereof to be Cavity, within
and between the Internal Spheres; which I would render not improbable.
To those that shall enquire of what use these included Globes can be, it
must be allow'd, that they can be of very little service to the Inhabitants of
this outward World, nor can the Sun be serviceable to them, either with his
Light or Heat. But since it is now taken for granted, that the Earth is one of
the Planets, and they all are with Reason suppos'd Habitable, though we are
not able to define by what sort of Animals; and since we see all the parts of
the Creation abound with Animate Beings, as the Air with Birds and Flies,
the Water with the numerous varieties of Fish, and the very Earth with
Reptiles of so many sorts; all whose ways of Living would be to us
incredible did not daily Experience teach us. Why then should we think it
strange that the prodigious Mass of Matter, whereof this Globe does consist,
should be capable of some other improvement than barely to serve to
support its Surface? Why may not we rather suppose that the exceeding
small quantity of solid Matter, in respect of the fluid Æther, is so dispos'd
by the Almighty Wisdom, as to yield as great a Surface for the use of living
Creatures, as can consist with the conveniency and security of the whole?
We our selves, in Cities where we are pressed for Room, commonly build
many Stories one over the other, and thereby accommodate a much greater
multitude of Inhabitants.

But still it will be said, That without Light there can be no living, and
therefore all this apparatus of our inward Globes must be useless: To this I
Answer, That there are many ways of producing Light which we are wholly
ignorant of; the Medium it self may be always luminous after the manner of
our Ignes fatui. The Concave Arches may in several places shine with such
a Substance as invests the Surface of the Sun; nor can we, without a
boldness unbecoming a Philosopher, adventure to assert the impossibility of
peculiar Luminaries below, of which we have no sort of Idea. I am sure the
Poets Virgil and Claudian have gone before me in this Thought, inlightning
their Elysian Fields with Sun and Stars proper to those infernal, or rather
internal Regions. Virg. Æneid. 6.
Largior hic compos Æther & lumine vestit
Purpureo; Solemque suum sua Sidera norunt.
And Claudian lib 2. De Raptu Proserpinæ.
Amissum ne crede diem, sunt altera nobis
Sidera, sunt orbes alii, luménque videbis
Purius, Elysiumque magis mirabere Solem.
And though this be not to be esteem'd as an Argument, yet I may take the
liberty I see others do, to quote the Poets when it makes for my purpose.
Lastly, To explain yet farther what I mean, I have adventur'd to adjoin the
following Scheme, (Tab. 1. Fig. 3) wherein the Earth is represented by the
outward Circle, and the three inward Circles are made nearly proportionable
to the Magnitudes of the Planets Venus, Mars and Mercury, all which may
be included within the Globe of Earth, and all the Arches more than
sufficiently strong to bear their weight. The Concave of each Arch, which is
shaded differently from the rest, I suppose to be made up of Magnetical
Matter; and the whole to turn about the same common Axis pp, only with
this difference, that the Outer Sphere still moves somewhat faster than the
Inner. Thus the Diameter of the Earth being about eight thousand English
Miles, I allow five hundred Miles for the thickness of its Shell, and another

space of five hundred Miles for a Medium between, capable of an immense
Atmosphere for the use of the Globe of Venus: Venus again I give a Shell of
the same thickness, and leave as great a space between her Concave and
Mars; so likewise from Mars to Mercury, which latter Ball we will suppose
solid, and about two thousand Miles Diameter. Thus I have shew'd a
possibility of a much more ample Creation, than has hitherto been imagin'd;
and if this seem strange to those that are unacquainted with the Magnetical
System, it is hop'd that all such will endeavour, first, to inform themselves
of the Matter of Fact, and then try if they can find out a more simple
Hypothesis, at least a less absurd, even in their own Opinions. And whereas
I have adventur'd to make these Subterraneous Orbs capable of being
Inhabited, 'twas done designedly for the sake of those who will be apt to ask
cui bono, and with whom Arguments drawn from Final Causes prevail
much. If this short Essay shall find a kind Acceptance, I shall be encourag'd
to enquire farther, and to Polish this rough Draft of a Notion till hitherto not
so much as started in the World, and of which we could have no Intimation
from any other of the Phænomena of Nature.
Since this was written, a Discovery I have made in the Cœlestial
Motions, seems to render a farther Account of the Use of the Cavity of the
Earth, viz. To diminish the Specifick Gravity thereof, in respect of the
Moon; for I think I can demonstrate that the Opposition of the Æther to the
Motions of the Planets in long time becomes sensible; and consequently the
greater Body must receive a less Opposition than the smaller, unless the
Specifick Gravity of the smaller do proportionably exceed that of the
greater, in which case only they can move together; so that the Cavity I
assign in the Earth, may well serve to adjust its weight to that of the Moon,
for otherwise the Earth would leave the Moon behind it, and she become
another Primary Planet.

Historical Account of the Trade Winds and Monsoons, observable in
the Seas between and near the Tropicks, with an attempt to assign
the Physical Cause of the said Winds, by Mr. Ed. Halley.

N exact Relation of the constant and periodical Winds, observable in
A several Tracts of the Ocean, is a part of Natural History not less
desireable and useful, than it is difficult to obtain, and its Phænomena
hard to explicate: I am not ignorant that several Writers have undertaken
this Subject, and although Varenius (Lib. 1. Chap. 21. Geo. Gen.) seems to
have endeavour'd after the best information from Voyagers, yet cannot his
Accounts be admitted for accurate, by those that shall attentively consider
and compare them together, and some of them are most evident Mistakes;
which, as near as I can, I shall attempt to rectify, having had the opportunity
of conversing with Navigators, acquainted with all parts of India, and
having liv'd a considerable time between the Tropicks, and there made my
own Remarks.
The Substance of what I have collected is briefly as follows.
The Universal Ocean may most properly be divided into three Parts, viz.
1. The Atlantick and Æthiopick-Sea. 2. The Indian Ocean. 3. The Great
South Sea, or the Pacifick Ocean; and though these Seas do all
communicate by the South, yet as to our present purpose of the Trade
Winds, they are sufficiently separated by the interposition of great Tracts of
Land; the first lying between Africa and America, the second between
Africa and the Indian Islands, and Hollandia Nova; and the last between the
Phillipine Isles, China, Japan and Hollandia Nova on the West, and the
Coast of America on the East. Now following this natural division of the
Seas, so will we divide our History into three parts in the same order.

I. In the Atlantick and Æthiopick Seas between the Tropicks, there is a
general Easterly Wind all the Year long, without any considerable Variation,

excepting that it is subject to be deflected therefrom, some few Points of the
Compass towards the North or South, according to the Position of the place.
The Observations which have been made of these Deflections, are the
following.
1. That near the Coast of Africa, as soon as you have pass'd the Canary
Isles, you are sure to meet a fresh Gale of North East Wind, about the
Latitude of 28 Degrees North, which seldom comes to the Eastwards of the
East North-East, or passes the North North-East. This Wind accompanies
those bound to the Southward, to the Latitude of ten North, and about a
hundred Leagues from the Guinea Coast, where, till the fourth Degree of
North Latitude, they fall into the Calms and Tornadoes; of which more
hereafter.
2. That those bound to the Caribbee Isles, find, as they approach the
American side, that the aforesaid North-East Wind becomes still more and
more Easterly, so as sometimes to be East, sometimes East by South, but
yet most commonly to the Northward of the East a Point or two, seldom
more. 'Tis likewise observ'd, that the strength of these Winds does gradually
decrease, as you sail to the Westwards.
3. That the limits of the Trade and variable Winds, in this Ocean, are
farther extended on the American side than the African; for whereas you
meet not with this certain Wind till after you have pass'd the Latitude of
twenty eight Degrees on this side; on the American side it commonly holds
to thirty, thirty one, or thirty two Degrees of Latitude; and this is verified
likewise to the Southwards of the Æquinoctial, for near the Cape of Good-
Hope the limits of the Trade Winds, are three or four Degrees nearer the
Line, than on the Coast of Brazile.
4. That from the Latitude of four Degrees North, to the aforesaid Limits
on the South of the Æquator, the Winds are generally and perpetually
between the South and East, and most commonly between the South-East
and East, observing always this Rule, That on the African side they are

more Southerly, on the Brazilian more Easterly, so as to become almost due
East, the little deflection they have being still to the Southwards. In this part
of the Ocean it has been my fortune to pass a full Year, in an Employment
that oblig'd me to regard more than ordinary the Weather, and I found the
Winds constantly about the South-East, the most usual Point S E b E; when
it was Easterly, it generally blew hard, and was gloomy, dark, and
sometimes rainy Weather; if it came to the Southwards it was generally
Serene, and a small Gale next to a Calm, but this not very common. But I
never saw it to the Westwards of the South, or Northwards of the East.
5. That the Season of the Year has some small effect on these Trade
Winds, for that when the Sun is considerable to the Northwards of the
Æquator, the South-East Winds, especially in the Straight of this Ocean (if I
may so call it) between Brazile and the Coast of Guinea, do vary a Point or
two to the Southwards, and the North-East become more Easterly; and on
the contrary, when the Sun is towards the Tropick of Capricorn the South-
Easterly Winds become more Easterly, and the North-Easterly Winds on
this side the Line veere more to the Northwards.
6. That as there is no general Rule that admits not of some Exception, so
there is in this Ocean a Tract of Sea wherein the Southerly and South-West
Winds are perpetual, viz. all along the Coast of Guinea, for above five
hundred Leagues together, from Sierra Leona to the Isle of St. Thomas; for
the South-East Trade Wind having pass'd the Line, and approaching the
Coast of Guinea within eighty or 100 Leagues, inclines towards the Shore,
and becomes S. S. E. and by Degrees, as you come nearer, it veeres about to
South, S. S. W. and in with the Land South-West, and sometimes West
South-West; which Variation is better express'd in the Mapp hereto
annexed, (Vide Plate 2) than it can well be in Words. These are the Winds
which are observ'd on this Coast when it blows true, but there are frequent
Calms, violent sudden Gusts call'd Tornado's, from all Points of the
Compass, and sometimes unwholsome foggy Easterly Winds, call'd

Hermitaa by the Natives, which too often infest the Navigation of these
parts.
7. That to the Northwards of the Line, between four and ten Degrees of
Latitude, and between the Meridians of Cape Virde, and of the Eastermost
Islands that bear that Name, there is a Tract of Sea wherein it were improper
to say there is any Trade Wind, or yet a Variable; for it seems condemn'd to
perpetual Calms, attended with terrible Thunder and Lightning, and Rains
so frequent, that our Navigators from thence call this part of the Sea the
Rains; the little Winds that are, be only some sudden uncertain Gusts, of
very little Continuance and less Extent; so that sometimes each Hour you
shall have a different Gale, which dies away into a Calm before another
succeed, and in a Fleet of Ships in sight of one another, each shall have the
Wind from a several Point of the Compass; with these weak Breezes Ships
are oblig'd to make the best of their way to the Southward through the
aforesaid six Degrees, wherein 'tis reported some have been detain'd whole
Months for want of Wind.
From the three last Observables is shewn the Reason of two notable
Occurents in the East-India and Guinea Navigations: The one is, why,
notwithstanding the narrowest part of the Sea between Guinea and Brazile
be about five hundred Leagues over, yet Ships bound to the Southward,
sometimes, especially in the Months of July and August, find a great
difficulty to pass it. This happens because of the South-East Winds, at that
time of the Year commonly extending some Degrees beyond the ordinary
limit of four Degrees North Latitude, and withal they come so much
Southerly, as to be sometimes South, sometimes a Point or two to the West;
there remains then only to ply to Windward, and if on the one side they
stand away W. S. W. they gain the Wind still more and more Easterly; but
there is danger of not weathering the Brazilian Shoar, or at least the Shoals
upon that Coast. But if upon the other Tack they go away E. S. E. they fall
into the Neighbourhood of the Coast of Guinea, from which there is no
departing without running Easterly, as far as the Isle of St. Thomas, which

is the constant practice of all the Guinea Ships, and which may seem very
strange, without the consideration of the sixth Remark, which shews the
Reason of it: For being in with the Coast, the Wind blows generally at S. W.
and W. S. W. with which Winds they cannot go to the Northward for the
Land; and on the other Tack they can lie no nearer the Wind than S. S. E. or
South; with these Courses they run off the Shoar, but in so doing they
always find the Winds more and more contrary; so that when near the Shoar
they could lie South, at a greater distance they can make their way no better
than S. E. and afterwards E. S. E. with which Courses they fetch commonly
the Isle of St. Thomas and Cape Lopez, where finding the Winds to the
Eastward of the South, they keep them favourable, by running away to the
Westward in the South Latitude, of three or four Degrees, where the S. E.
Winds are perpetual.
For the sake of these general Winds, all those that use the West-Indian
Trade, even those bound to Virginia, count it their best Course to get as
soon as they can to the Southwards, that so they may be certain of a fair and
fresh Gale to run before it to the Westwards; and for the same Reason those
homewards bound from America, endeavour to gain the Latitude of thirty
Degrees, as soon as possible, where they first find the Winds begin to be
variable; tho' the most ordinary Winds in the Northern part of the Atlantick
Ocean come from between the South and West.
As to those furious Storms call'd Hurricanes, which are, as it were,
peculiar to the Caribbee Isles; and which so dreadfully afflict them in the
Month of August, or not much before or after, they do not so properly
belong to this place, both by Reason of their small continuance and extent,
as likewise because they are not Anniversary, some Years having more than
one, and sometimes for several Years together there being none at all. But
their Violence is so unconceivable, and their other Phænomena so
surprising, that they merit well to be consider'd apart.

What is here said, is to be understood of the Sea Winds at some distance
from the Land; for upon and near the Shoars, the Land and Sea Breezes are
almost every where sensible; and the great Variety which happens in their
Periods, Force and Direction, from the situation of the Mountains, Vallies
and Woods, and from the various Texture of the Soil, more or less capable
of retaining and reflecting Heat, and of exhaling or condensing Vapours, is
such, that it were an endless task, to endeavour to account for them.

II. In the Indian Ocean, the Winds are partly general, as in the Æthiopick
Ocean, partly Periodical; that is, half the Year they blow one way, and the
other half near upon the opposite Points; and these Points and Times of
shifting are different in different parts of this Ocean; the limits of each Tract
of Sea, subject to the same Change or Monsoon, are certainly very hard to
determine, but the diligence I have used to be rightly inform'd, and the care
I have taken therein, has, in a great measure, surmounted that Difficulty;
and I am perswaded that the following Particulars may be relied upon.
1. That between the Latitudes of ten Degrees and thirty Degrees South,
between Madagascar and Hollandia Nova, the general Trade Wind about
the S. E. by E. is found to blow all the Year long, to all Intents and Purposes
after the same manner as in the same Latitudes in the Æthiopick Ocean, as it
is describ'd in the fourth Remark aforegoing.
2. That the aforesaid S. E. Winds extend to within two Degrees of the
Æquator, during the Months of June, July, August, &c. to November; at
which time between the South Latitudes of three and ten Degrees, being
near the Meridian of the North end of Madagascar, and between two and
twelve South Latitude, being near Sumatra and Java, the contrary Winds
from the N. W. or between the North and West, set in and blow for half the
Year, viz. from the beginning of December till May; and this Monsoon is
observ'd as far as the Molucca Isles, of which more anon.

3. That to the Northward of three Degrees South Latitude, over the whole
Arabian or Indian-Sea and Gulph of Bengall, from Sumatra to the Coast of
Africa, there is another Monsoon, blowing from October to April upon the
North East Points; but in the other half Year, from April to October, upon
the opposite Points of S. W. and W. S. W. and that with rather more force
than the other, accompanied with dark rainy Weather, whereas the N. E.
blows clear; 'tis likewise to be noted, that the Winds are not so constant,
either in strength or point in the Gulph of Bengall, as they are in the Indian-
Sea, where a certain and steady Gale scarce ever fails. 'Tis also remarkable,
that the S. W. Winds in these Seas are generally more Southerly on the
African side, more Westerly on the Indian.
4. That as an Appendix to the last describ'd Monsoon, there is a Tract of
Sea to the Southwards of the Æquator, subject to the same Changes of the
Winds, viz. near the African Coast, between it and the Island Madagascar
or St. Lawrence, and from thence Northwards as far as the Line; wherein
from April to October there is found a constant fresh S. S. W. Wind, which,
as you go more Northerly, becomes still more and more Westerly, so as to
fall in with the W. S. W. Winds, mention'd before, in those Months of the
Year to be certain to the Northward of the Æquator: What Winds blow in
these Seas, for the other half Year, from October to April, I have not yet
been able to obtain to my full satisfaction, for that our Navigators always
return from India without Madagascar, and so are little acquainted in this
Matter; the Account that has been given me is only this, that the Winds are
much Easterly hereabouts, and as often to the North of the true East as to
the Southwards thereof.
5. That to the Eastward of Sumatra and Malacca, to the Northwards of
the Line, and along the Coast of Cambodia and China, the Monsoons blow
North and South, that is to say, the N. E. Winds are much Northerly, and the
S. W. much Southerly: This Constitution reaches to the Eastwards of the
Philippine Isles, and as far Northerly as Japan. The Northern Monsoon
setting in, in these Seas, in October or November, and the Southern in May,

blowing all the Summer Months: Here it is to be noted, That the Points of
the Compass, from whence the Wind comes in these Parts of the World, are
not so fixt as in those lately describ'd; for the Southerly will frequently pass
a Point or two to the Eastwards of the South, and the Northerly as much to
the Westwards of the North, which seems occasion'd by the great quantity
of Land, which is interspers'd in these Seas.
6. That in the same Meridians, but to the Southwards of the Æquator,
being that Tract lying between Sumatra and Java to the West, and New
Guinea to the East, the same Northerly Monsoons are observ'd, but with this
difference, that the inclination of the Northerly is towards the N. West, and
of the Southerly towards the S. E. but the plagæ venti are not more constant
here than in the former, viz. variable five or six Points; besides the times of
the Change of these Winds, are not the same as in the Chinese Seas, but
about a Month or six Weeks later.
7. That these contrary Winds do not shift all at once, but in some places
the time of the Change is attended with Calms, in others with variable
Winds; and it is particularly remarkable, that the end of the Westerly
Monsoon on the Coast of Coromandel, and the two last Months of the
Southerly Monsoon in the Seas of China, are very subject to be
tempestuous: The violence of these Storms is such, that they seem to be of
the Nature of the West-India Hurricanes, and render the Navigation of these
parts very unsafe about that time of the Year. These Tempests are by our
Seamen usually term'd, The breaking up of the Monsoons.
By reason of the shifting of these Winds, all those that sail in these Seas,
are oblig'd to observe the Seasons proper for their Voyages, and so doing
they fail not of a fair Wind and speedy Passage; but if so be they chance to
out-stay their time, till the contrary Monsoon sets in, as it frequently
happens, they are forc'd to give over the hopes of accomplishing their
intended Voyages, and either return to the Port from whence they came, or

else put in to some other Harbour, there to spend the time till the Winds
shall come favourable.

III. The third Ocean call'd Mare Pacificum, whose Extent is equal to that
of the other two (it being from the West Coast of America to the Philippine
Islands, not less than 150 Degrees of Longitude) is that which is least
known to our own or the Neighbour Nations; that Navigation that there is
on it, is by the Spaniards, who go Yearly from the Coast of New Spain to
the Manilha's, but that but by one beaten track; so that I cannot be so
particular here as in the other two. What the Spanish Authors say of the
Winds they find in their Courses, and what is confirm'd by the old Accounts
of Drake and Cavendish; and since by Schooten, who sail'd the whole
breadth of this Sea in the Southern Latitude of fifteen or sixteen Degrees, is,
that there is a great conformity between the Winds of this Sea, and those of
the Atlantick and Æthiopick; that is to say, that to the Northwards of the
Æquator, the predominant Wind is between the East and North-East; and to
the Southwards thereof there is a constant steady Gale between the East and
South-East, and that on both sides the Line with so much constancy, that
they scarce ever need to attend the Sails, and Strength, that it is rare to fail
of crossing this vast Ocean in ten Weeks time, which is about 130 Miles per
diem; besides, 'tis said that Storms and Tempests are never known in these
parts: So that here is the very best of Sailing; no want of a fresh fair Wind,
and yet no danger of having too much: Wherefore some have thought it
might be as short a Voyage to Japan and China, to go by the Streights of
Magellan, as by the Cape of Good Hope.
The Limits of these general Winds are also much the same as in the
Atlantick Sea, viz. about the thirtieth Degree of Latitude on both sides; for
the Spaniards homewards bound from the Manilha's, always take the
advantage of the Southerly Monsoon, blowing there in the Summer Months,
and run up to the Northwards of that Latitude, as high as Japan, before they
meet with variable Winds, to shape their Course to the Eastwards. And

Schooten and others that have gone about by the Magellan Streights, have
found the Limits of S. E. Winds, much about the same Latitude to the
Southwards; besides a farther Analogy between the Winds of this Ocean,
and the Æthiopick, appears in that, upon the Coast of Peru, they are always
much Southerly, like as they are found near the Shoars of Angola.

Thus far Matter of Fact, wherein if the information I have receiv'd be not
in all parts Accurate, it has not been for want of inquiry from those I
conceiv'd best able to instruct me; and I shall take it for a very great
Kindness if any Master of a Ship, or other Person, well inform'd of the
Nature of the Winds, in any of the aforemention'd parts of the World, shall
please to communicate their Observations thereupon; so that what I have
here Collected may be either confirm'd or amended, or by the addition of
some material Circumstances enlarg'd. It is not the work of one, nor of few,
but of a multitude of Observers, to bring together the Experience requisite
to compose a perfect and compleat History of these Winds; however I am
not much doubtful that I have err'd in, or omitted any of the principal
Observables, whatever lesser Particulars may have escaped my Knowledge.
To help the Conception of the Reader in a manner of so much difficulty, I
believ'd it necessary to adjoin a Scheme, (Plate 2.) shewing at one view all
the various Tracts and Courses of these Winds; whereby 'tis possible the
thing may be better understood, than by any verbal Description whatsoever.
The Limits of these several Tracts are design'd every where by prickt
Lines, as well in the Atlantick and Æthiopick, where they are the boundaries
of the Trade and variable Winds, as in the Indian Ocean, where they also
shew the Extent of the several Monsoons. I could think of no better way to
design the Course of the Winds on the Map, than by drawing rows of
stroaks in the same Line that a Ship would move going always before it; the
sharp end of each little stroak pointing out that part of the Horizon, from
whence the Wind continually comes; and where there are Monsoons, the

rows of the stroaks run alternately backwards and forwards, by which
means they are thicker there than elsewhere. As to the great South Sea,
considering its vast Extent, and the little Variety there is in its Winds, and
the great Analogy between them, and those of the Atlantick and Æthiopick
Oceans; besides, that the greatest part thereof is wholly unknown to us; I
thought it unnecessary to lengthen the Map therewith.
In the foregoing History are contained several Problems, that merit well
the Consideration of our acutest Naturalists, both by reason of the
constancy of the Effect, and of the immense Extent thereof; near half the
Surface of the Globe being concerned. The chief of these Problems are,
1. Why these Winds are perpetually from the East in the Atlantic and
Æthiopick; as likewise in the Pacifick Ocean, between the Latitudes of 30
North and South? 2. Why the said Winds extend no farther with constancy
than to the Latitude of 30 Degrees? 3. Why there should be a constant
South-Westerly Wind upon and near the Coast of Guinea? 4. Why in the
North part of the Indian Ocean, the Winds, which for one half Year do agree
with those of the other two Oceans, should change in other half Year, and
blow from the opposite Points; whilst the Southern part of that Ocean
follows the General Rule, and has perpetual Winds about S. E? 5. Why in
these General Trade-Winds it should be always true, that to the Northward
of the Æquator it is inclin'd to the Northwards of the East; and in South
Latitudes, to the Southward thereof? 6. Why in these Seas of China there
should be so great an Inclination from the East to the North, more than
elsewhere? with many more, which it would be much easier to propose than
answer.
But lest I should seem to propose to others, Difficulties which I have not
thought worth my own Time and Pains, take here the result of an earnest
Endeavour after the true reason of the aforesaid Phænomena; wherein if I
am not able to account for all Particulars, yet 'tis hoped the Thoughts I have
spent thereon, will not be judged wholly lost, by the Curious in Natural
Enquiries.

Wind is most properly defined to be the Stream or Current of the Air, and
where such a Current is perpetual and fixt in its Course, 'tis necessary that it
proceed from a permanent un-intermitting Cause. Wherefore some have
been inclin'd to propose the diurnal Rotation of the Earth upon its Axis, by
which, as the Globe turns Eastwards, the loose and fluid Particles of the Air,
being so exceeding light as they be, are left behind, so that in respect of the
Earths Surface they move Westwards, and become a constant Easterly
Wind. This Opinion seems confirm'd, for that these Winds are found only
near the Æquinoctial, in those Parallels of Latitude where the diurnal
Motion is swiftest; and I should readily assent to it, if the constant Calms in
the Atlantick Sea, near the Æquator, the Westerly Winds near the Coast of
Guinea; and the Periodical Westerly Monsoons under the Æquator in the
Indian Seas, did not declare the insufficency of that Hypothesis. Besides the
Air being kept to the Earth by the Principle of Gravity, would acquire the
same degree of Velocity that the Earths Surface moves with, as well in
respect of the diurnal Rotation, as of the Annual about the Sun, which is
about thirty times swifter.
It remains therefore to substitute some other Cause, capable of producing
a like constant Effect, not liable to the same Objections, but agreeable to the
known Properties of the Elements of Air and Water, and the Laws of the
Motion of fluid Bodies. Such an one is, I conceive, the Action of the Sun
Beams upon the Air and Water, as he passes every Day over the Oceans,
consider'd together with the Nature of the Soil, and Situation of the
adjoining Continents: I say therefore, first, that according to the Laws of
Staticks, the Air which is less rarified or expanded by heat, and
consequently more ponderous, must have a Motion towards those parts
thereof, which are more rarified, and less ponderous, to bring it to an
Æquilibrium; and secondly, That the Presence of the Sun continually
shifting to the Westwards, that part towards which the Air tends, by reason
of the Rarifaction made by his greatest Meridian Heat, is with him carried

Westward, and consequently the tendency of the whole Body of the lower
Air is that way.
Thus a general Easterly Wind is formed, which being impressed upon all
the Air of a vast Ocean, the Parts impel one the other, and so keep moving
till the next return of the Sun, whereby so much of the Motion as was lost,
is again restored, and thus the Westerly Wind is made perpetual.
From the same Principle it follows, that this Easterly Wind should on the
North side of the Æquator, be to the Northwards of the East, and in South
Latitudes to the Southwards thereof; for near the Line, the Air is much more
rarified, than at a greater distance from it; because of the Sun twice in a
Year Vertical, and at no time distant above 23 Degr. and a half; at which
distance the Heat, being as the Sine of the Angle of Incidence, is but little
short of that of the perpendicular Ray. Whereas under the Tropicks, though
the Sun stay long Vertical, yet he is as long 47 Degr. off; which is a kind of
Winter, wherein the Air so cools, as that the Summer-heat cannot warm it to
the same degree with that under the Æquator. Wherefore the Air to the
Northwards and Southwards, being less rarified than that in the middle, it
follows, that from both sides it ought to tend towards the Æquator: This
Motion compounded with the former Easterly Wind, answers all the
Phænomena of the general Trade-winds; which, if the whole Surface of the
Globe were Sea, would undoubtedly blow all round the World, as they are
found to do in the Atlantick, and Æthiopick Oceans.
But seeing that so great Continents do interpose, and break the continuity
of the Oceans, regard must be had to the Nature of the Soil, and the Position
of the high Mountains, which I suppose the two principal Causes of the
several Variations of the Winds, from the former general Rule: For if a
Country lying near the Sun, prove to be flat, sandy, low Land, such as the
Desarts of Lybia are usually reported to be, the Heat occasion'd by the
Reflection of the Suns Beams, and the retention thereof in the Sand, is
incredible to those that have not felt it; whereby the Air being exceedingly

rarified, it is necessary that the cooler and more dense Air should run
thitherwards to restore the Æquilibrium: This I take to be the cause, why
near the Coast of Guinea the Wind always sets in upon the Land, blowing
Westerly instead of Easterly, there being sufficient Reason to believe, that
the Inland Parts of Africa are prodigiously hot, since the Northern Borders
thereof were so intemperate, as to give the Ancients cause to conclude, that
all beyond the Tropick, was made uninhabitable by excess of Heat: From
the same Cause it happens, that there are so constant Calms in that part of
the Ocean, called the Rains, (described in the 7th Remark on the Atlantick
Sea) for this Tract being placed in the middle, between the Westerly Winds
blowing on the Coast of Guinea, and the Easterly Trade-winds, blowing to
the Westwards thereof, the tendency of the Air here, is indifferent to either,
and so stands in Æquilibrio between both; and the weight of the incumbent
Atmosphere being diminished by the continual contrary Winds blowing
from hence, is the reason that the Air here holds not the copious Vapour it
receives, but lets it fall into frequent Rains.
But as the cool and dense Air, by reason of its greater Gravity, presses
upon the hot and rarified, 'tis demonstrative that this latter must ascend in a
continued Stream as fast it rarifies; and that being ascended, it must
disperse it self to preserve the Æquilibrium: that is, by a contrary Current,
the upper Air must move from those Parts where the greatest Heat is: So by
a kind of Circulation, the North-East Trade-Wind below, will be attended
with a South-Westerly above, and the South-Easterly with a North-West
Wind above; that this is more than a bare Conjecture, the almost
instantaneous Change of the Wind to the opposite Point, which is frequently
found in passing the limits of the Trade-winds, seems to assure us; but that
which above all confirms this Hypothesis is the Phænomenon of the
Monsoons, by this means most easily solved, and without it hardly
explicable.
Supposing therefore such a Circulation, as above, 'tis to be considered
that to the Northward of the Indian Ocean there is every where Land within

the usual limit of the Latitude of 30, viz. Arabia, Persia, India, &c. which
for the same reason as the Mediterranean Parts of Africa, are subject to
unsufferable Heats when the Sun is to the North, passing nearly Vertical;
but yet are temperate enough when the Sun is removed towards the other
Tropick; because of a ridge of Mountains at some distance within the Land,
said to be frequently in Winter cover'd with Snow, over which the Air, as it
passes, must needs be much chill'd. Hence it comes to pass, that the Air
coming according to the general Rule, out of the N. E. in the Indian Seas, is
sometimes hotter, sometimes colder, than that which by this Circulation is
return'd out of the S. W. and by consequence, sometimes the under Current
or Wind, is from the N. E. sometimes from the S. W.
That this has no other Cause, is clear from the times wherein these Winds
set in, viz. in April, when the Sun begins to warm those Countries to the
North, the S. W. Monsoon begins, and blows during the Heats till October;
when the Sun being retir'd, and all things growing cooler Northward, and
the Heat increasing to the South, the North-East Winds enter and blow all
the Winter till April again. And it is undoubtedly from the same Principle
that to the Southwards of the Æquator, in part of the Indian Ocean, the
North-West Winds succeed to the South-East, when the Sun draws near the
Tropick of Capricorn; but I must confess, that in this latter occurs a
difficulty, not well to be accounted for, which is, why this Change of the
Monsoons should be any more in this Ocean, than in the same Latitudes in
the Æthopick, where there is nothing more certain than a S. E. Wind all the
Year.
'Tis likewise very hard to conceive why the limits of the Trade-wind
should be fixt, about the thirtieth Degree of Latitude all round the Globe;
and that they should so seldom transgress or fall short of those bounds; as
also that in the Indian Sea, only the Northern Part should be subject to the
changeable Monsoons, and in the Southern there be a constant S. E.

These are Particulars that merit to be consider'd more at large, and
furnish a sufficient Subject for a just Volume, which will be a very
commendable Task for such, who being us'd to Philosophick
Contemplation, shall have leisure to apply their serious Thoughts about it.

Plate 2 pag. 80
A new & Correct Sea chart of the whole World
Shewing the Variations of ye COMPASS as they
were found Año 1700 with a View of the Generall
and Coasting Trade Winds and Monsoons or
shifting Trade Winds by the Direction of Capt.
Edm. Halley.

iscourse of the Rule of the Decrease of the height of the Mercury in
the Barometer, according as Places are elevated above the Surface
of the Earth; with an Attempt to discover the true Reason of the
Rising and Falling of the Mercury, upon Change of Weather. By
Edm. Halley.

HE Elastick Property of the Air has been long since made out, by
T Experiments before the Royal Society, and elsewhere; and the
Resistance of its Spring is found to be nearly equal to the Weight or
Force that compresses it; as also, that the Spaces the same Air occupies,
under differing Pressures, are reciprocally as those Pressures: It has been
shewn likewise by undoubted Experiment, that the specifick Gravity of the
Air, near the Earth's Surface to that of Water, was once as 1 to 840; again as

1 to 852; and a third time, in a very large Vessel holding 10 Gallons, as 1 to
860; all which, considering the Difficulty of the Experiment, agree well
enough, the Mercury standing at all those times about 29 Inches ¾: But by
Reason 'twas Summer-weather, and consequently the Air rarified, when all
these were tried, we may without sensible Error say in round numbers, that
the Barometer standing at 30 Inches, and in a mean State of Heat and Cold,
the specifick Gravity of the Air to Water, is as 1 to 800. By the like Trials
the weight of Mercury to Water, is as 13½ to 1, or very near it; so that the
weight of Mercury to Air, is as 10800 to 1; and a Cylinder of Air of 10800
Inches or 900 Feet, is equal to an Inch of Mercury; and were the Air of an
equal density like Water, the whole Atmosphere would be no more than 5,1
Miles high, and in the Ascent of every 900 Feet the Barometer would sink
an Inch. But the Expansion of the Air increasing in the same proportion as
the incumbent weight of the Atmosphere decreases; that is, as the Mercury
in the Barometer sinks; the upper Parts of the Air are much more rarified
than the lower, and each Space answering to an Inch of Quicksilver, grows
greater and greater; so that the Atmosphere must be extended to a much
greater height. Now, upon these Principles, to determine the height of the
Mercury at any assigned height in the Air; and è contra, having the height
of the Mercury given, to find the height of the Place where the Barometer
stands, are Problems not more difficult than curious; and which I thus
resolve.
The Expansions of the Air being reciprocally as the heights of the
Mercury, it is evident, that by the help of the Curve of the Hyperbola and its
Asymptotes, the said Expansions may be expounded to any given height of
the Mercury: For by the 65th Prop. lib. 2. Conic. Mydorgii, the Rectangles,
ABCE, AKGE, ALDE, &c. (in Plate 1. Fig. 4.) are always equal, and
consequently the sides, CB, GK, LD, &c. are reciprocally as the sides AB,
AK, AL, &c. If then the Lines AB, AK, AL, be supposed equal to the heights
of the Mercury, or the pressures of the Atmosphere, the Lines CB, GK, LD,
answering thereto, will be as the Expansions of the Air under those

Pressures, or the Bulks that the same quantity of Air will occupy; which
Expansions being taken infinitely many, and infinitely little, (according to
the Method of Indivisibles) their Summ will give the Spaces of Air between
the several heights of the Barometer; that is to say, the Summ of all the
Lines between CB and KG, or the Area CBKG, will be proportioned to the
Distance or Space intercepted between the Levels of two Places in the Air,
where the Mercury would stand at the heights represented by the Lines AB,
AK; so then the Spaces of Air answering to equal Parts of Mercury in the
Barometer, are as the Area's CBKG, GKLD, DLFM, &c. These Area's again
are, by the Demonstration of Gregory of St. Vincent, proportionate to the
Logarithms of the Numbers expressing the Rationes of AK to AB, of AL to
AK, of AM to AL, &c. So then by the common Table of Logarithms, the
height of any Place in the Atmosphere, having any assign'd height of the
Mercury, may most easily be found: For the Line CB in the Hyperbola,
whereof the Area's design the Tabular Logarithms, being 0,0144765; 'twill
be, as 0,0144765, to the difference of the Logarithms of 30, or any other
lesser Number, for 900 Feet, or the Space answering to an Inch of Mercury,
if the Air were equally prest with 30 Inches of Mercury, and every where
alike, to the height of the Barometer in the Air, where it will stand at that
lesser number of Inches: And by the Converse of this Proportion may the
height of the Mercury be found, having the Altitude of the Place given.
From these Rules I deriv'd the following Tables.

A Table shewing the
Altitude, to given heights
of the Mercury.
Inch. Feet.
30 0
29 915
28 1862
27 2844
26 3863

25 10947
15 18715
10 29662
5 48378
1 91831
0.5 110547
0.25 129262
0.1 29 m. or 154000
0.01 41 m. or 216169
0.001 53 m. or 278338

A Table shewing the
heights of the Mercury,
at given Altitudes.
Feet. Inch.
0 30 00
1000 28 91
2000 27 86
3000 26 85
4000 35 87
5000 feet 24 93
1 mile 24 67
2 20 29
3 16 68
4 13 72
5 11 28
10 4 24
15 1 60
20 0 95
25 0 23
30 0 08
40 0 012

PON these Suppositions it appears, that at the height of 41 Miles the
U Air is so rarified, as to take up 3000 times the Space it occupies here,
and at 53 Miles high it would be expanded above 30000 times; but it's
probable that the utmost Power of its Spring cannot exert it self, to so great
an Extension, and that no part of the Atmosphere reaches above 45 Miles
from the Surface of the Earth.
This seems confirm'd from the Observations of the Crepusculum, which
is observ'd commonly to begin and end when the Sun is about 18 Degrees
below the Horizon; for supposing the Air to reflect light from its most
rarified Parts, and that as long as the Sun illuminates any of its Atoms, they
are visible to an Eye not intercepted by the Curvity of the Earth, it will
follow from Fig. 5. Plate 1. that the proportion of the height of the whole
Air, to the Semi-diameter of the Earth, is much about, as 1 to 90, or as the
excess of the Secant of about 8½ Degrees to the Radius. For if E be the Eye
of the Observer, S a Place where the Sun sets at the end of Twilight in E,
and the Arch ECS, or TCA, be found 18 Degrees, the excess of the Secant of
half thereof ECH, would be the height of the Air, viz. GH: But the Beam of
the Sun ASH, and the Visual Ray EH, do each of them suffer a Refraction of
about 32 or 33 Minutes, whereby being bent inwards from H towards G, the
height of the Air need not be so great as if they went streight; and having
from the Angle ECS taken the double Refraction of the Horizontal Ray, the
half of the Remainder will be 8½ Degrees circiter, whose Secant being
10,111, it follows, that as 10000 to 111, so the Semi-diameter of the Earth
supposed 4000 Miles, to 44,4 Miles; which will be the height of the whole
Air, if the Places E, S, whose visible Portions of the Atmosphere ERZH, and
SHKB, just touch one the other, be 18 Degrees asunder.
At this height the Air is expanded into above 3000 times the space it
occupies here, and we have seen the Experience of condensing it into the
60th part of the same Space, so that it should seem, that the Air is a
Substance capable of being compressed into the 180000th part of the Space
it would naturally take up, when free from pressure. Now what Texture or

Composition of Parts shall be capable of this great Expansion and
Contraction, seems a very hard Question; and which, I suppose, is scarce
sufficiently accounted for, by comparing it to Wool, Cotten, and the like
springy Bodies.
Hitherto I have only consider'd the Air and Atmosphere, as one unalter'd
Body, as having constantly at the Earth's Surface the 800th part of the
weight of Water, and being capable of Rarifaction and Condensation in
infinitum; neither of which Hypotheses are rigidly true: For here in England
it is notoriously known, that the weight of the whole Atmosphere is various,
being counterpoised sometimes by 28½ Inches of Mercury, and at other
times by no less than 30½; so that the under parts being pressed by about a
15th part, less weight, the specifick Gravity of the Air upon that score will
sometimes be a 15th part lighter than another; besides Heat and Cold, does
very considerably dilate and contract the Air, and consequently alter its
Gravity; to which add the mixture of Effluvia, or steams arising from almost
all Bodies, which assimulating into the Form of Air, are kept suspended
therein, as Salts dissolv'd in Liquors, or Metals in corroding Menstrua;
which Bodies being all of them very much heavier than Air, their Particles
by their Admixture must needs encrease the weight of that Air they lie
incorporated withal, after the same manner as melted Salts do augment the
specifick Gravity of Water. The other Consideration is, that the Rarifaction
and Condensation of the Air is not precisely according to the proportion
here laid down; for the Experiment very nearly agrees thereto, as may be
seen in the 58th Chapter of Mr. Hook's Micrography; yet are the
Condensations not possible beyond certain degrees: For being compressed
into an 800th part of the Space it takes up here, its consistence would be
equally dense with that of Water; which yields not to any force whatsoever,
as hath been found by several Experiments tried here, and at Florence, by
the Academia del Cimento. Nor can the Rarifaction proceed in infinitum; for
supposing the Spring whereby it dilates it self, occasion'd by what Texture
of Parts you please, yet must there be a determinate Magnitude of the

natural State of each Particle, as we see it is in Wool, and the like, whose
Bodies being compressable into a very small Space, have yet a determinate
bulk which they cannot exceed, when free'd from all manner of Pressure.
These Objections being true, do disturb the Geometrical Accuracy of
these Conclusions, drawn from the specifick Gravity of the Air observ'd at
any time; but the Method here shewn will compute by a like Calculation,
the heights of the Quick-silver, and the Rarifactions of the Air from any
assign'd height of the Barometer at the Earth's Surface, and any specifick
Gravity given. As to the Condensation and Rarifaction by Heat and Cold,
and the various mixture of Aqueous and other Vapours, these two
Objections seem generally to compensate each other; for when the Air is
rarified by Heat, they are raised most copiously; so that though the Air
properly so call'd, be expanded, and consequently lighter, yet the Interstices
thereof being crouded full of Vapours of much heavier Matters, bulk for
bulk, the weight of the Compositum may continue much the same, at least a
most curious Experiment made by the Ingenious Mr. John Caswell, of
Oxford, upon the top of Snowdon Hill, in Carnarvanshire, seems to prove,
that the first Inches of Mercury have their Portions of Air near enough to
what I now determine: For the height of the Hill being 1240 Yards, or very
near it, he found the Mercury to have subsided to 25,6 Inches, or 4 inches
below the mean Altitude thereof at the Level of the Sea, (which is a greater
difference than has been found in any of our former Experiments,) and the
Space answering to 4 Inches, by my Calculation, should be 1288 Yards; and
it agrees as well with the Observations in the Appendix to Mr. Pascall's
Book, del Equilibre des Liqueurs, made on the high Hill in Auvergne, call'd
le puy de Domme. So that the Rarifaction and Vapours seem not to have
alter'd considerably, the Gravity of the under Parts of the Air; and much
above the height where these Experiments were made, do few Vapours
ascend, and the Cold is such that the Snow lies continually, so that for the
more elevated Parts of the Sphere of Air, there is much less Reason to
doubt.

But now we have had occasion to mention the difference there is between
the height of the Mercury at one time, from the height thereof at another, it
may not be unacceptable to offer at some Reasons for the said difference;
which, at least to my self, seem to have some appearance of Truth. First,
Then it's undoubtedly demonstrable, that the height of the Cylinder of
Mercury is equal to the weight of the whole incumbent Air, and
consequently that that whole is sometimes a fifteenth more than at other
times; which cannot otherwise be, but by the access of new Matter when 'tis
heavy, and its diminution when 'tis light; that Hypothesis therefore that
shews how the Air shall be encreased or diminished, in any particular place,
will give a Reason for the greater and lesser height of the Mercury in the
Baroscope: But to direct us in the choice of the several Causes, which may
be assign'd for the Increase and Decrease of the Air, 'twill not be
unnecessary to enumerate some of the principal Observations made upon
the Barometer, most whereof are sufficiently known already to all those that
are curious in these Matters.
The First is, That in calm Weather, when the Air is inclin'd to Rain, the
Mercury is commonly low.
2. That in serene good settled Weather, the Mercury is generally high.
3. That upon very great Winds, though they be not accompanied with
Rain, the Mercury sinks lowest of all, with relation to the Point of the
Compass the Wind blows upon.
4. That cæteris paribus the greatest heights of the Mercury are found
upon Easterly and North-Easterly Winds.
5. That in calm frosty Weather the Mercury generally stands high.
6. That after very great Storms of Wind, when the Quicksilver has been
low, it generally rises again very fast.
7. That the more Northerly places have greater Alterations of the
Baroscope, than the more Southerly.

8. That within the Tropicks and near them, those Accounts I have had
from others, and my own Observation at St. Helena, make very little or no
Variation of the height of the Mercury in all Weathers.

Now that Theory that can well account for all these appearances, will, in
all probability, approach nearer the true cause of the Barometers Variations,
than any thing hitherto afforded; and such an one I am bound to believe, is
that which I here lay down with submission to better Judgments.
I conceive that the principal Cause of the rise and fall of the Mercury, is
from the variable Winds, which are found in the Temperate Zones, and
whose great unconstancy here in England is most notorious. I shall not at
present inquire into the Cause of its uncertainty, but the Matter of Fact
being most undoubted, the Legitimate Consequences thereof must be
allow'd me, let it proceed from what it will.
A second Cause is the uncertain Exhalation and Præcipitation of the
Vapours lodging in the Air, whereby it comes to be at one time much more
crowded than at another, and consequently heavier; but this latter in a great
measure depends upon the former. Now from these Principles I shall
endeavour to explicate the several Phænomena of the Barometer, taking
them in the same order I laid them down.
1. Why in calm Weather the Air being inclin'd to Rain, the Mercury is
commonly low? I Answer, That the Mercury's being low, inclines it to Rain;
for the Air being light, the Vapours are no longer supported thereby, being
become specifically heavier than the Medium wherein they floated; so that
they descend towards the Earth, and in their fall meeting with other aqueous
Particles, they incorporate together, and form little drops of Rain; but the
Mercury's being at one time lower than another, is the effect of two contrary
Winds blowing from the place whence the Barometer stands; whereby the
Air of that place is carried both ways from it, and consequently the
incumbent Cylinder of Air is diminished, and accordingly the Mercury

sinks; as for Instance, if in the German Ocean it should blow a Gale of
Westerly Wind, and at the same time an Easterly Wind in the Irish Sea; or if
in France it should blow a Southerly Wind, and in Scotland a Northern; it
must be granted me, that That part of the Atmosphere impendent over
England, would thereby be exhausted and attenuated, and the Mercury
would subside, and the Vapours which before floated in those parts of the
Air of equal Gravity with themselves, would sink to the Earth.
2. Why in serene good settled weather the Mercury is generally high? To
this I Answer, That the greater height of the Barometer, is occasion'd by two
contrary Winds blowing towards the place of Observation, whereby the Air
of other places is brought thither and accumulated; so that the incumbent
Cylinder of Air being encreas'd both in height and weight, the Mercury
press'd thereby must needs rise and stand high, as long as the Winds
continue so to blow; and then the Air being specifically heavier, the Vapours
are better kept suspended, so that they have no inclination to Præcipitate
and fall down in Drops, which is the reason of the serene good Weather,
which attends the greater heights of the Mercury.
3. Why upon very great Winds or Storms, tho' accompanied with no Rain,
the Mercury sinks lowest of all, with relation to the Point of the Compass
upon which the Wind blows? This is caus'd by the very rapid Motion of the
Air in these Storms; for the Tract or Region of the Earths Surface, wherein
these Winds rage, not extending all round the Globe, that stagnant Air
which is left behind, as likewise that on the sides, cannot come in so fast as
to supply the Evacuation made by so swift a Current; so that the Air must
necessarily be attenuated, when and where the said Winds continue to blow,
and that more or less, according to their Violence; add to which, that the
Horizontal Motion of the Air being so quick as it is, may in all probability
take off some part of the perpendicular pressure thereof; and the great
Agitation of its Particles, is the Reason why the Vapours are dissipated, and
do not condense into Drops, so as to form Rain, otherwise the natural
Consequence of the Airs Rarifaction.

4. Why cæteris paribus the Mercury stands highest upon an Easterly or
North-Easterly Wind? This happens because that in the great Atlantick
Ocean, on this side the thirty fifth Degree of North Latitude, the Westerly
and South-Westerly Trade-Winds blow almost always; so that whenever
here the Wind comes up at East and North-East, 'tis sure to be checked by a
contrary Gale, as soon as it reaches the Ocean; wherefore, according to
what is made out in our second Remark, the Air must needs be heaped over
this Island; and consequently the Mercury must stand high, as often as these
Winds blow. This holds true in this Country, but is not a general Rule for
others, where the Winds are under different Circumstances; and I have
sometimes seen the Mercury here as low as twenty nine Inches, upon an
Easterly Wind, but then it blows exceeding hard, and so comes to be
accounted for by what was observ'd upon the third Remark.
5. Why in calm Weather the Mercury generally stands high? The cause
hereof is, as I conceive, that it seldom freezes but when the Winds come out
of the Northern and North-Eastern Quarters, or at least unless those Winds
blow at no great distance off; for the Northern Parts of Germany, Denmark,
Sweden, Norway, and all that Tract from whence North-Eastern Winds
come, are subject to almost continual Frost all the Winter; and thereby the
lower Air is very much condens'd, and in that State is brought hitherwards
by these Winds, and being accumulated by the opposition of the Westerly
Wind blowing in the Ocean, the Mercury must needs be prest to a more than
ordinary height, and as a concurring Cause, the shrinking of the lower parts
of the Air into lesser room by cold, must needs cause a descent of the upper
parts of the Atmosphere, to reduce the Cavity made by this contraction to an
Æquilibrium.
6. Why after very great Storms of Wind, when the Mercury has been very
low, it generally rises again very fast? This I have frequently observed, and
once found it risen an Inch and a half in less than six Hours, after a long
continu'd Storm of South-West Wind. This seems to be occasion'd by the
sudden Accession of new Air to supply the great Evacuation which such

continu'd Storms make thereof, in those places whence they happen (as in
the third Remark) and by the Recoile of the Air, after the force ceases that
impelled it; and the Reason why the Mercury rises so fast, is because the
Air being very much rarify'd beyond its mean density, the Neighbouring Air
runs in the more swiftly to bring it to an Æquilibration, as we see Water
runs the faster for having a great declivity.
7. Why in more Northerly places the Variations of the Baroscope are
greater than in the Southerly? The truth of the Matter of Fact is prov'd from
Observations made at Clermont and Paris, compar'd with others, made at
Stockholm, as may be seen in the Appendix to Mr. Pascal's Book before-
cited. The Reason I conjecture to be, that the more Northerly Parts have
usually greater Storms of Wind than the more Southerly, whereby the
Mercury should sink lower in that Extream; and then the Northerly Winds
bringing the condens'd and ponderous Air from the Neighbourhood of the
Pole, and that again being check'd by a Southerly Wind, at no great
distance, and so heaped, must of necessity make the Mercury in such case
stand higher in the other Extream.
8. And Lastly, Why near the Æquinoctial, as at Barbadoes and St.
Helena, there is very little or no Variation of the height of the Barometer?
This Remark, above all others, confirms the Hypothesis of the variable
Winds, being the cause of these Variations of the height of the Mercury; for
in the Places above-named, there is always an easie Gale of Wind blowing
nearly upon the same Point, viz. E. N. E. at Barbadoes, and E. S. E. at St.
Helena; so that there being no contrary Currents of the Air, to exhaust or
accumulate it, the Atmosphere continues much in the same State. However,
upon Hurricanes, the most violent of Storms, the Mercury has been observ'd
very low, but this is but for once in two or three Years, and it soon recovers
its settled state of about 29½ Inches. I doubt not but the same thing is in the
East Coast of Africa, and in India, where the Monsoons or Trade-Winds are
for half the Year one way, and half the Year another; only it's probable, that
there may something worth noting happen, about the times of the change or

shifting of the Winds, which might be obtain'd, if any Body had the
Curiosity to keep the Barometer at our Factories in India.

I doubt not but this Doctrine will find some Opposers, and that one
principal Objection will be, that I suppose the Air sometimes to move from
those Parts where it is already evacuated below the Æquilibrium, and
sometimes again towards those parts, where it is condens'd and crouded
above the mean State, which may be thought contradictory to the Laws of
Staticks and the Rules of the Æquilibrium of Fluids. But those that shall
consider how, when once an impetus is given to a Fluid Body, it is capable
of mounting above its Level, and checking others that have a contrary
tendency to descent by their own Gravity, will no longer regard this as a
material Obstacle, but will rather conclude, that the great Analogy there is
between the rising and falling of the Water upon the Flux and Reflux of the
Sea, and this of the accumulating and extenuating the Air, is a great
Argument for the Truth of this Hypothesis: For as the Sea over against the
Coast of Essex, rises and swells by the meeting of the two contrary Tides of
Flood, (whereof the one comes from the S. W. along the Channel of
England, and the other from the North); and on the contrary sinks below its
Level upon the retreat of the Water both ways in the Tide of Ebb; so it is
very probable that the Air may Ebb and Flow, after the same manner; but by
reason of the diversity of Causes, whereby the Air may be set in moving,
the times of these Fluxes and Refluxes thereof, are purely Casual, and not
reducible to any Rule, as are the Motions of the Sea, depending wholly
upon the regular Course of the Moon.

Plate 1. pag. 97

etter of Mr. Isaac Newton, Professor of the Mathematicks in the
University of Cambridge; containing his New Theory about Light
and Colours: Sent by the Author to the Publisher from Cambridge,
Feb. 6. 1671/2; in order to be communicated to the Royal Society.

S I R,
O perform my late promise to you, I shall without further Ceremony
T acquaint you, That in the beginning of the Year 1666 (at which time I
apply'd my self to the grinding of Optick-glasses of other Figures than
Spherical,) I procur'd me a Triangular Glass-Prism, to try therewith the
celebrated Phænomena of Colours. And in order thereto, having darken'd
my Chamber, and made a small hole in my Window-shuts, to let in a
convenient quantity of the Sun's Light, I plac'd my Prism at his entrance,
that it might be thereby refracted to the opposite Wall. It was at first a very
pleasing Divertisement, to view the vivid and intense Colours produced
thereby; but after a while applying my self to consider them more
circumspectly, I became surpriz'd to see them in an oblong Form; which,
according to the received Laws of Rarefraction, I expected should have
been Circular.
They were terminated at the sides with streight Lines, but at the ends, the
decay of Light was so gradual, that it was difficult to determine justly, what
was their Figure; yet they seem'd Semicircular.
Comparing the length of this colour'd Spectrum with its breadth, I found
it about five times greater; a disproportion so extravagant, that it excited me
to a more than ordinary Curiosity of examining, from whence it might
proceed. I could scarce think, that the various thickness of the Glass, or the
termination with shadow or darkness, could have any Influence on Light to
produce such an effect; yet I thought it not amiss, first to examine those
Circumstances, and so try'd what would happen by transmitting Light
through parts of the Glass of divers thicknesses, or through holes in the
Window of divers bignesses, or by setting the Prism without, so that the
Light might pass through it, and be refracted before it was terminated by the
hole: But I found none of those Circumstances material. The fashion of the
Colours was, in all these Cases, the same.

Then I suspected, whether by any unevenness in the Glass, or other
contingent Irregularity, these Colours might be thus dilated. And to try this,
I took another Prism like the former, and so plac'd it, that the Light passing
through them both, might be refracted contrary ways, and so by the latter
return'd into that Course, from which the former had diverted it. For, by this
means, I thought the regular effects of the first Prism would be destroy'd by
the second Prism, but the irregular ones more augmented by the
multiplicity of Refractions. The Event was, that the Light, which by the first
Prism was diffused into an oblong Form, was, by the second, reduc'd into
an orbicular one, with as much regularity, as when it did not at all pass
through them. So that whatever was the cause of that length, 'twas not any
contingent Irregularity.
I then proceeded to examine more critically, what might be effected by
the difference of the incidence of Rays coming from divers parts of the Sun;
and to that end, measur'd the several Lines and Angles belonging to the
Image. Its distance from the Hole or Prism was twenty two Foot; its utmost
length 13¼ Inches; its breadth 2⅝; the Diameter of the Hole ¼ of an Inch;
the Angle, with the Rays, tending towards the middle of the Image, made
with those Lines, in which they would have proceeded without Refraction,
was 44° 56'. And the Vertical Angle of the Prism, 63° 12'. Also the
Refractions on both sides the Prism, that is, of the Incident, and Emergent
Rays, were as near, as I could make them, equal, and consequently about
54° 4'. And the Rays fell perpendicularly upon the Wall. Now subducting
the Diameter of the Hole from the length and breadth of the Image, there
remains 13 Inches the length, and 2⅜ the breadth, comprehended by those
Rays, which passed thro' the Center of the said Hole, and consequently the
Angle of the Hole, which that breadth subtended, was about 31', answerable
to the Sun's Diameter; but the Angle, which its length subtended, was more
than five such Diameters, namely 2° 49'.
Having made these Observations, I first computed from them the
refractive Power of that Glass, and found it measur'd by the ratio of the

Sines, twenty to thirty one. And then, by that ratio, I computed the
Refractions of two Rays flowing from opposite parts of the Sun's discus, so
as to differ 31' in their obliquity of Incidence, and found that the emergent
Rays should have comprehended an Angle of about 31', as they did, before
they were incident.
But because this Computation was founded on the Hypothesis of the
proportionality of the Sines of Incidence and Refraction, which, tho' by my
own Experience I could not imagine to be so erroneous as to make that
Angle but 31', which in reality was 2° 49'; yet my Curiosity caus'd me again
to take my Prism. And having plac'd it at my Window, as before, I observ'd,
that by turning it a little about its Axis to and fro, so as to vary its obliquity
to the light, more than an Angle of four or five Degrees, the Colours were
not thereby sensibly translated from their place on the Wall, and
consequently by that Variation of Incidence, the quantity of Refraction was
not sensibly varied. By this Experiment therefore, as well as by the former
Computation, it was evident, that the difference of the Incidence of Rays,
flowing from divers parts of the Sun could not make them, after
decussation, diverge at a sensibly greater Angle, than that at which they
before converged; which being, at most, but about thirty one or thirty two
Minutes, there still remain'd some other cause to be found out, from whence
it could be two Deg. 49 Min.
Then I began to suspect, whether the Rays, after their Trajection through
the Prism, did not move in curve Lines, and according to their more or less
Curvity, tend to divers parts of the Wall. And it increas'd my suspicion,
when I remember'd that I had often seen a Tennis-Ball, struck with an
oblique Racket, describe such a curve Line. For a Circular as well as a
Progressive Motion being communicated to it by that stroak, its parts on
that side, where the Motions conspire, must press and beat the contiguous
Air more violently than on the other, and there excite a Reluctancy and
Reaction of the Air proportionably greater. And for the same Reason, if the
Rays of Light should possibly be globular Bodies, and by their oblique

Passage out of one Medium into another, acquire a circulating Motion, they
ought to feel the greater resistance from the ambient Æther, on that side,
where this Motion conspires, and thence be continually bowed to the other.
But notwithstanding this plausible ground of suspicion, when I came to
examine it, I could observe no such Curvity in them. And besides (which
was enough for my purpose) I observ'd, that the difference 'twixt the length
of the Image, and Diameter of the Hole, through which the Light was
transmitted, was proportionable to their distance.
The gradual removal of these suspicions, at length led me to the
Experimentum Crucis, which was this; I took two Boards, and plac'd one of
them close behind the Prism at the Window, so that the light might pass
through a small hole, made in it for the purpose, and fall on the other Board,
which I plac'd at about twelve Feet distance, having first made a small hole
in it also, for some of that incident Light to pass through. Then I plac'd
another Prism behind this second Board, so that the Light, trajected through
both the Boards, might pass thro' that also, and be again refracted before it
arrived at the Wall. This done, I took the first Prism in my Hand, and turn'd
it to and fro slowly about its Axis, so much as to make the several parts of
the Image, cast on the second Board, successively pass through the hole in
it, that I might observe to what places on the Wall the second Prism would
refract them. And I saw by the Variation of those places, that the Light,
tending to that end of the Image, towards which the Refraction of the first
Prism was made, did, in the second Prism, suffer a Refraction considerably
greater than the Light tending to the other end. And so the true cause of the
length of that Image was detected to be no other, than that Light consists of
Rays differently refrangible, which, without any respect to a difference in
their incidence, were, according to their degrees of Refrangibility,
transmitted towards divers parts of the Wall.
When I understood this, I left off my aforesaid Glass Works; for I saw,
that the perfection of Telescopes was hitherto limited, not so much for want
of Glasses truly figur'd, according to the prescriptions of Optick Authors

(which all Men have hitherto imagin'd), as because that Light it self is a
Heterogeneous mixture of differently refrangible Rays. So that, were a Glass
so exactly figur'd, so as to collect any one sort of Rays into one Point, it
could not collect those also into the same Point, which having the same
Incidence upon the same Medium, are apt to suffer a different Refraction.
Nay, I wonder'd, that seeing the difference of Refrangibility was so great, as
I found it, Telescopes should arrive to that perfection they are now at. For,
measuring the Refractions in one of my Prisms, I found, that, supposing the
common Sine of Incidence upon one of its plains, was forty four Parts, the
Sine of Refraction of the utmost Rays on the red end of the Colours, made
out of the Glass into the Air, would be sixty eight parts, and the Sine of
Refraction of the utmost Rays on the other end, sixty nine parts; so that the
difference is about a twenty fourth or twenty fifth part of the whole
Refraction. And consequently the Object glass of any Telescope cannot
collect all the Rays, which come from one point of an Object, so as to make
them convene at its Focus in less room than in a Circular space, whose
Diameter is the fiftieth part of the Diameter of its Aperture; which is an
irregularity, some hundred of times greater, than a circularly figur'd Lens, of
so small a section as the Object-glasses of long Telescopes are, would cause
by the unfitness of its Figure, were Light uniform.
This made me take Reflections into Consideration, and finding them
regular, so that the Angle of Reflection of all sorts of Rays was equal to
their Angle of Incidence; I understood, that by their mediation, Optick
Instruments might be brought to any degree of Perfection imaginable,
provided a Reflecting Substance could be found, which would polish as
finely as Glass, and reflect as much Light as Glass transmits; and the art of
communicating to it a Parabolick Figure be also attain'd. But there seem'd
very great Difficulties, and I have almost thought them insuperable, when I
further consider'd, that every Irregularity in a reflecting Superficies makes
the Rays stray five or six times more out of their due course, than the like

Irregularities in a refracting one; So that a much greater Curiosity would be
here requisite, than in Figuring Glasses for Refraction.
Amidst these Thoughts I was forc'd from Cambridge by the Intervening
Plague, and it was more than two Years before I proceeded further. But then
having thought on a tender way of polishing, proper for Metal, whereby, as
I imagin'd, the Figure also would be corrected to the last; I began to try
what might be effected in this kind, and by degrees so far perfected an
Instrument (in the essential parts of it like that I sent to London,) by which I
could discern Jupiter's four Concomitants, and shew'd them divers times to
two others of my Acquaintance. I could also discern the Moon-like Phase of
Venus, but not very distinctly, nor without some niceness in disposing the
Instrument.
From that time I was interrupted, till this last Autumn, when I made the
other. And as that was sensibly better than the first (especially for Day-
Objects,) so I doubt not but they will be still brought to a much greater
perfection by their Endeavours, who, as you inform me, are taking care
about it at London.
I have sometimes thought to make a Microscope, which in like manner
should have, instead of an Object-glass, a reflecting piece of Metal. And
this I hope they will also take into Consideration: For those Instruments
seem as capable of improvement as Telescopes, and perhaps more, because
but one reflective piece of Metal is requisite in them, as you may perceive
in Plate 3. Fig. 1. where AB representeth the Object Metal, CD the Eye-
glass, F their common Focus, and O the other Focus of the Metal, in which
the Object is placed.
But to return from this digression, I told you, that Light is not similar, or
homogeneal, but consists of difform Rays, some of which are more
refrangible than others: So that of those, which are alike incident on the
same Medium, some shall be more refracted than others, and that not by

any virtue of the Glass, or other external Cause, but from a predisposition,
which every particular Ray hath to suffer a particular degree of Refraction.
I shall now proceed to acquaint you with another more notable deformity
in its Rays, wherein the Origin of Colours is unfolded: Concerning which I
shall lay down the Doctrine first, and then, for its Examination, give you an
Instance or two of the Experiments, as a Specimen of the rest.
The Doctrine you will find comprehended and illustrated in the following
Propositions.
1. As the Rays of Light differ in degrees of Refrangibility, so they also
differ in their disposition to exhibit this or that particular Colour. Colours
are not Qualifications of Light, derived from Refractions, or Reflections of
natural Bodies, (as 'tis generally believed) but Original and connate
Properties, which in divers Rays are divers. Some Rays are disposed to
exhibit a red Colour and no other; some a yellow and no other, some a
green and no other, and so of the rest. Nor are there only Rays proper and
particular to the more eminent Colours, but even to all their intermediate
Gradations.
2. To the same degree of Refrangibility ever belongs the same Colour,
and to the same Colour ever belongs the same degree of Refrangibility. The
least Refrangible Rays are all disposed to exhibit a Red Colour, and
contrarily those Rays, which are disposed to exhibit a Red Colour, are all
the least Refrangible: So the most Refrangible Rays are all disposed to
exhibit a deep Violet Colour, and contrarily those which are apt to exhibit
such a Violet Colour, are all the most Refrangible. And so to all the
intermediate Colours in a continued Series belong intermediate degrees of
Refrangibility. And this Analogy 'twixt Colours, and Refrangibility, is very
precise and strict; the Rays always either exactly agreeing in both, or
proportionally disagreeing in both.
3. The Species of Colour, and Degree of Refrangibility proper to any
particular sort of Rays, is not mutable by Refraction, nor by Reflection from

Natural Bodies, nor by any other Cause, that I could yet observe. When any
one sort of Rays hath been well parted from those of other kinds, it hath
afterwards obstinately retain'd its Colour, notwithstanding my utmost
Endeavours to change it. I have refracted it with Prisms, and reflected it
with Bodies, which in Day-light were of other Colours; I have intercepted it
with the colour'd Film of Air interceding two compressed Plates of Glass;
transmitted it through colour'd Mediums, and through Mediums irradiated
with other sorts of Rays, and diversly terminated it, and yet could never
produce any new Colour out of it. It would by contracting and dilating
become more brisk, or faint, and by the loss of many Rays in some Cases
very obscure and dark; but I could never see it chang'd in specie.
4. Yet seeming Transmutations of Colours may be made, where there is
any mixture of divers sorts of Rays. For in such mixtures, the component
Colours appear not, but by their mutual allaying each other, constitute a
midling Colour. And therefore, if by Refraction, or any other of the
aforesaid Causes, the difform Rays, latent in such a mixture, be separated,
there shall emerge Colours different from the colour of the Composition.
Which Colours are not new generated, but only made apparent by being
parted; for if they be again intirely mix'd and blended together, they will
again compose that Colour, which they did before separation. And for the
same reason, Transmutations made by the convening of divers Colours are
not real; for when the difform Rays are again severed, they will exhibit the
very same Colours, which they did before they entered the Composition; as
you see, Blue and Yellow Powders, when finely mixed, appear to the naked
Eye Green, and yet the Colours of the component Corpuscles are not
thereby really transmuted, but only blended. For, when viewed with a good
Microscope, they still appear Blue and Yellow interspersedly.
5. There are therefore two sorts of Colours. The one Original and Simple,
the other compounded of these. The Original or Primary Colours are, Red,
Yellow, Green, Blue, and a Violet-purple, together with Orange, Indico, and
an indefinite variety of intermediate Gradations.

6. The same Colours in Specie with these primary Ones, may be also
produced by Composition: For, a mixture of Yellow and Blue makes Green;
of Red and Yellow, makes Orange; of Orange and Yellowish Green, makes
Yellow. And in general, if any two Colours be mix'd, which in the Series of
those, generated by the Prism, are not too far distant one from another, they
by their mutual Alloy compound that Colour, which in the said Series
appeareth in the mid-way between them. But those, which are situated at
too great a distance, do not so. Orange and Indico produce not the
intermediate Green, nor Scarlet and Green the intermediate Yellow.
7. But the most surprizing and wonderful Composition was that of
Whiteness. There is no one sort of Rays which alone can exhibit this. 'Tis
ever compounded, and to its Composition are requisite all the aforesaid
primary Colours, mix'd in a due proportion. I have often with admiration
beheld, that all the Colours of the Prism being made to converge, and
thereby to be again mixed as they were in the light before it was incident
upon the Prism, reproduced light, intirely and perfectly white, and not at all
sensibly differing from a direct light of the Sun, unless when the Glasses, I
used, were not sufficiently clear; for then they would a little incline it to
their Colour.
8. Hence therefore it comes to pass, that Whiteness is the usual Colour of
Light; for Light is a confused aggregate of Rays, indued with all sorts of
Colours, as they are promiscuously darted from the various parts of
luminous Bodies. And of such a confused aggregate, as I said, is generated
Whiteness, if there be a due proportion of the Ingredients; but if any one
predominate, the Light must incline to that Colour; as it happens in the blue
Flame of Brimstone, the yellow Flame of a Candle, and the various Colours
of the fixed Stars.
9. These things consider'd, the manner, how Colours are produced by the
Prism, is evident. For, of the Rays, constituting the incident Light, since
those which differ in Colour proportionally differ in Refrangibility, they by

their unequal Refractions must be severed and dispersed into an oblong
Form, in an orderly succession, from the least refracted Scarlet to the most
refracted Violet. And for the same reason it is, that Objects, when look'd
upon through a Prism, appear coloured. For the difform Rays, by their
unequal Refractions, are made to diverge towards several parts of the
Retina, and there express the Images of things coloured, as in the former
case they did the Sun's Image upon a Wall. And by this inequality of
Refractions, they become not only coloured, but also very confused and
indistinct.
10. Why the Colours of the Rainbow appear in falling drops of Rain, is
also from hence evident. For those drops, which refract the Rays, disposed
to appear Purple, in greatest quantity to the Spectator's Eye, refract the Rays
of other sorts so much less, as to make them pass beside it; and such are the
drops on the inside of the Primary Bow, and on the outside of the
Secondary or Exteriour one. So those drops, which refract in greatest plenty
the Rays, apt to appear red, toward the Spectator's Eye, refract those of
other sorts so much more, as to make them pass beside it; and such are the
drops on the Exteriour part of the Primary, and Interiour part of the
Secondary Bow.
11. The odd Phænomena of an infusion of Lignum Nephriticum, Leaf-
gold, Fragments of colour'd Glass, and some other transparently coloured
Bodies, appearing in one Position of one Colour, and of another in another,
are on these grounds no longer Riddles. For those are Substances apt to
reflect one sort of Light, and transmit another; as may be seen in a dark
Room, by illuminating them with similar or uncompounded Light. For then
they appear of that Colour only, with which they are illuminated; but yet in
one Position more vivid and luminous than in another, accordingly as they
are disposed more or less to reflect or transmit the incident Colour.
12. From hence also is manifest the reason of an unexpected Experiment,
which Mr. Hook, somewhere in his Micrography, relates to have made with

two wedge-like transparent Vessels fill'd, the one with a red, the other with
a blue Liquor; namely, that though they were severally transparent enough,
yet both together became opake: For, if one transmitted only red, and the
other only blue, no Rays could pass through both.
13. I might add more Instances of this Nature; but I shall conclude with
this general one, that the Colours of all natural Bodies have no other Origin
than this, that they are variously qualified to reflect one sort of Light in
greater plenty than another. And this I have experimented in a dark Room,
by illuminating those Bodies with uncompounded Light of divers Colours.
For by that means any body may be made to appear of any Colour. They
have there no appropriate Colour, but ever appear of the Colour of the Light
cast upon them; but yet with this difference, that they are most brisk and
vivid in the Light of their own day-light-colour. Minium appeareth there of
any Colour indifferently, with which 'tis illustrated, but yet most luminous
in red; and so Bise appeareth indifferently of any Colour with which 'tis
illustrated, but yet most luminous in blue. And therefore Minium reflecteth
Rays of any Colour, but most copiously those endu'd with red, and
consequently when illustrated with day-light, that is, with all sorts of Rays
promiscuously blended, those qualified with red, shall abound most in the
reflected Light, and by their prevalence cause it to appear of that Colour.
And for the same reason Bise, reflecting blue most copiously, shall appear
blue by the excess of those Rays in its reflected Light; and the like of other
Bodies. And that this is the intire and adequate cause of their Colours, is
manifest, because they have no power to change or alter the Colours of any
sort of Rays incident apart, but put on all Colours indifferently, with which
they are enlightned.
These things being so, it can be no longer disputed, whether there be
Colours in the dark, nor whether they be the Qualities of the Objects we
see, no nor perhaps, whether Light be a Body. For, since Colours are the
Qualities of Light, having its Rays for their intire and immediate Subject,
how can we think those Rays Qualities also, unless one Quality may be the

Subject of and sustain another; which in effect is to call it Substance? We
should not know Bodies for Substances, were it not for their sensible
Qualities; and the principal of those being now found due to something else,
we have as good reason to believe that to be a Substance also.
Besides, whoever thought any Quality to be a heterogeneous Aggregate,
such as Light is discovered to be? But to determine more absolutely, what
Light is, after what manner refracted, and by what Modes or Actions it
produceth in our Minds the Phantasms of Colours, is not so easie. And I
shall not mingle Conjectures with Certainties.
Reviewing what I have written, I see the Discourse it self will lead to
divers Experiments sufficient for its Examination; and therefore I shall not
trouble you farther, than to describe one of those, which I have already
insinuated.
In a darkned Room, make a hole in the shut of a Window, whose
Diameter may conveniently be about a third part of an Inch, to admit a
convenient quantity of the Sun's Light. And there place a clear and
colourless Prism, to refract the entring Light towards the farther part of the
Room; which, as I said, will thereby be diffused into an oblong coloured
Image. Then place a Lens of about three Foot Radius (suppose a broad
Object-glass of a three Foot Telescope,) at the distance of about four or five
Foot from thence, through which all those Colours may at once be
transmitted, and made by its Refraction to convene at a farther distance of
about ten or twelve Feet. If at that distance you intercept this Light with a
Sheet of white Paper, you will see the Colours converted into whiteness
again by being mingled. But it is requisite, that the Prism and Lens be
placed steady, and that the Paper, on which the Colours are cast, be moved
to and fro; for, by such motion, you will not only find at what distance the
whiteness is most perfect, but also see how the Colours gradually convene,
and vanish into whiteness; and afterwards, having crossed one another in
that place where they compound whiteness, are again dissipated and

severed, and in an inverted order retain the same Colours, which they had
before they entred the Composition. You may also see, that, if any of the
Colours at the Lens be intercepted, the whiteness will be changed into the
other Colours. And therefore, that the Composition of whiteness be perfect,
care must be taken that none of the Colours fall besides the Lens.
In the annexed Design, Tab. 3. Fig. 2. of this Experiment, ABC
expresseth the Prism set end-wise to sight, close by the hole F of the
Window EG. Its vertical Angle ABC may conveniently be about 60
Degrees: MN designeth the Lens. Its breadth 2½ or 3 Inches. SF one of the
streight Lines, in which difform Rays may be conceived to flow
successively from the Sun. FP, and FR two of those Rays unequally
refracted, which the Lens makes to converge towards Q, and after
decussation to diverge again. And HI the Paper, at divers distances, on
which the Colours are projected, which in Q constitute Whiteness, but are
Red and Yellow in R, r, and ρ, and Blue and Purple in P, p, and π.
If you proceed further to try the impossibility of changing any
uncompounded Colour (which I have asserted in the third and thirteenth
Propositions,) 'tis requisite that the Room may be very dark, lest any
scattering light, mixing with the Colour, disturb and allay it, and render it
compound, contrary to the design of the Experiment. 'Tis also requisite, that
there be a perfecter separation of the Colours, than, after the manner above
described, can be made by the Refraction of one single Prism; and how to
make such farther separations, will scarce be difficult to them, that consider
the discovered Laws of Refractions. But if trial shall be made with Colours
not throughly separated, there must be allowed changes proportionable to
the mixture. Thus if compound Yellow Light fall upon blue Bise, the Bise
will not appear perfectly yellow, but rather green, because there are in the
yellow mixture many Rays indued with green, and green being less remote
from the usual blue Colour of Bise than yellow, is the more copiously
reflected by it.

In like manner, if any one of the Prismatick Colours, suppose red, be
intercepted, on design to try the asserted impossibility of reproducing that
Colour out of the others which are pretermitted; 'tis necessary, either that
the Colours be very well parted before the red be intercepted; or that,
together with the red, the neighbouring Colours, into which any red is
secretly dispersed, (that is, the yellow, and perhaps green too) be
intercepted; or else, that allowance be made for the emerging of so much
red out of the yellow green, as may possibly have been diffused, and
scatteringly blended in those Colours. And if these things be observed, the
new Production of red, or any intercepted Colour, will be found impossible.
This, I conceive, is enough for an Introduction to Experiments of this
kind; which if any of the Royal Society shall be so curious as to prosecute, I
should be very glad to be informed with what success: That, if any thing
seem to be defective, or to thwart this Relation, I may have an opportunity
of giving farther Direction about it, or of acknowledging my Errors, if I
have committed any.

Since the Publication of this Theory, some Misunderstandings happening
between a French Philosopher at Paris and Mr. Newton, he has
endeavour'd to explain himself a little further in these Things,
according to the following Method.
A farther Explanation of the same Theory.
DEFINITIONS.
1. I call that Light Homogeneal, Similar, or Uniform, whose Rays are
equally refrangible.
2. And that Heterogeneal, whose Rays are unequally refrangible.
Note, There are but three Affections of Light in which I have observ'd its
Rays to differ; viz. Refrangibility, Reflexibility, and Colour; and those Rays
which agree in Refrangibility, agree also in the other two, and therefore may

well be defined Homogeneal; especially since Men usually call those things
Homogeneal, which are so in all Qualities that come under their
Knowledge, tho' in other Qualities, that their Knowledge extends not to,
there may possibly be some Heterogeneity.
3. Those Colours I call Simple or Homogeneal, which are exhibited by
Homogeneal Light.
4. And those Compound or Heterogeneal, which are exhibited by
Heterogeneal Light.
5. Different Colours, I call, not only the more eminent Species, Red,
Yellow, Green, Blue, Purple, but all other the minutest Gradations; much
after the same manner, that not only the more eminent Degrees in Musick,
but all the lead Gradations, are esteem'd different Sounds.
PROPOSITIONS.
1. The Sun's Light consists of Rays differing by indefinite Degrees of
Refrangibility.
2. Rays which differ in Refrangibility, when parted from one another, do
proportionally differ in the Colours which they exhibit. These Two
Propositions are Matter of Fact.
3. There are as many Simple or Homogeneal Colours, as Degrees of
Refrangibility. For to every Degree of Refrangibility belongs a different
Colour, by Prop. 2. and that Colour is Simple, by Def. 1, and 3.
4. Whiteness, in all respects like that of the Sun's immediate Light, and of
all the usual Objects of our Senses, cannot be compounded of two Simple
Colours alone. For such a Composition must be made by Rays that have
only two Degrees of Refrangibility, by Def. 1 and 3. and therefore it cannot
be like that of the Sun's Light. by Prop. 1. nor, for the same Reason, like
that of ordinary white Objects.

5. Whiteness, in all respects, like that of the Sun's immediate Light,
cannot be compounded of Simple Colours without an indefinite Variety of
them. For to such a Composition, there are requisite Rays endu'd with all
the indefinite Degrees of Refrangibility, by Prop. 1. And those infer as
many Simple Colours, by Def. 1 and 3. and Prop. 2 and 3.
To make these a little plainer, I have added also the Propositions that
follow.
6. The Rays of Light do not act on one another, in passing through the
same Medium.
7. The Rays of Light suffer not any change of their Qualities from
Refraction.
8. Nor afterwards from the adjacent quiet Medium: These two
Propositions are manifest de Facto in Homogeneal Light, whose Colour and
Refrangibility is not at all changeable, either by Refraction, or by the
Contermination of a quiet Medium. And as for Heterogeneal Light, it is but
an Aggregate of several sorts of Homogeneal Light, no one sort of which
suffers any more alteration than if it were alone; because the Rays act not
on one another, by Prop. 6. and therefore the Aggregate can suffer none.
These two Propositions also might be further proved apart, by Experiments
too long to be here described.
9. There can no Homogeneal Colours be reduced out of Light by
Refraction, which were not commixt in it before. Because by Prop. 7. and
8. Refraction changeth not the Qualities of the Rays, but only separates
those which have divers Qualities, by means of their different
Refrangibility.
10. The Sun's Light is an Aggregate of an indefinite variety of
Homogeneal Colours, by Prop. 1, 3, and 9. And hence it is, that I call
Homogeneal Colours also Primitive or Original. And thus much concerning
Colours.

For a further Illustration of this Doctrine, Mr. Newton, in his Book of
Opticks lately published, has by undeniable Experiments explained
most of the Principal Phænomena of Light and Colours: To which we
refer the Reader.

emonstration concerning the Motion of Light, communicated from
Paris.

Hilosophers have been labouring for many Years to decide by some
P Experiment, whether the Action of Light be conveyed in an instant to
distant Places, or whether it requireth time. M. Romer, of the Royal
Academy of Sciences, hath devised a way taken from the Observations of
the first Satellit of Jupiter, by which he demonstrates, that for the distance
of about 3000 Leagues, such as is very near the bigness of the Diameter of
the Earth, Light needs not one Second of Time.
Let (in Fig. 3. Plate 3.) A be the Sun, B Jupiter, C the first Satellit of
Jupiter, which enters into the shadow of Jupiter, to come out at D, and let
EFGHKL be the Earth, placed at divers distances from Jupiter.
Now suppose the Earth, being in L, towards the second Quadrature of
Jupiter, hath seen the first Satellit, at the time of its emersion, or issuing out
of the shadow at D, and that about 42½ Hours after (viz. after one
Revolution of this Satellit) the Earth being in K, do see it return'd in D: It is
manifest, that if the Light require time to traverse the Interval LK, the
Satellit will be seen return'd later in D, than it would have been if the Earth
had remained in L. So that the Revolution of the Satellit being thus observ'd
by the Emersions, will be retarded by so much time, as the Light shall have
taken in passing from L to K; and that on the contrary, in the other
Quadrature FG, where the Earth by approaching goes to meet the Light, the
Revolutions of the Emersions will appear to be shortned, by so much as
those of the Emersions had appear'd to be lengthned. And because 42½

Hours, which this Satellit very near takes to make one Revolution, the
distance between the Earth and Jupiter, in both the Quadratures, varies at
least 210 Diameters of the Earth: It follows, that if for the Account of every
Diameter of the Earth there were required a Second of Time, the Light
would take 3½ Minutes for each of the Intervals GF, KL; which would
cause near half a quarter of an Hour between two Revolutions of the first
Satellit, one observ'd in FG, and the other in KL, whereas there is not
observed any sensible difference.
Yet doth it not follow hence, that Light demands no time. For after M.
Romer had examin'd the thing more nearly, he found that what was not
sensible in two Revolutions, became very considerable in many being taken
together; and that, for Example, forty Revolutions observed on the side F,
might be sensibly shorter, than forty others observ'd in any place of the
Zodiack where Jupiter may be met with; and that in proportion of Twenty
two for the whole Interval of HE, which is the double of the Interval that is
from hence to the Sun.
The necessity of this new Equation of the Retardment of Light, is
establish'd by all the Observations that have been made in the Royal
Academy, and in the Observatory, for the space of eight Years; and it hath
been lately confirmed by the Emersion of the first Satellit observ'd at Paris,
the 9th of November last, at 5 a-clock 35' 45" at Night, 10 Minutes later
than it was to be expected, by deducting it from those that had been
observ'd in the Month of August, when the Earth was much nearer to
Jupiter; which M. Romer had predicted to the said Academy from the
beginning of September.
But to remove all doubt, that this Inequality is caused by the Retardment
of the Light, he demonstrates, that it cannot come from any Excentricity, or
other Cause of those that are commonly alledged to explicate the
Irregularities of the Moon, and the other Planets; though he be well aware,
that the first Satellit of Jupiter was Excentrick; and that, besides his

Revolutions were advanced or retarded, according as Jupiter did approach
to or recede from the Sun; as also, that the Revolutions of the Primum
Mobile were unequal: Yet, saith he, these three last Causes of Inequality do
not hinder the first from being manifest.

introductory Essay to the Doctrine of Sounds, containing some
Proposals for the improvement of Acousticks; As it was presented
to the Dublin Society, Nov. 12. 1683, by the Right Reverend Father
in God Narcissus Lord Bishop of Ferns and Leighlin.

Eing to treat of the Doctrine of Sounds, I hold it convenient to premise
B something in the general, concerning this Theory; which may serve at
once to ingage your Attention, and excuse my Pains, when I shall have
recommended them, as bestow'd on a Subject not altogether useless and
unfruitful.
And for this purpose I shall omit to speak any thing of the Excellency of
the Matter in Hand; though it might be celebrated by Arguments drawn
from several Topicks, and particularly from this, that new Discoveries and
Improvements may be made, both as to the Generation, Propagation and
Reception of Sounds into the Sense; which, in a peculiar manner agrees to
this, above the Object of any other Sense whatsoever. I shall, I say, omit
these things, and apply my self wholly to the Usefulness of the Theory, that
we are now falling upon, which I think cannot better be discovered, than by
making a comparison 'twixt the Senses of Seeing and Hearing, as to their
Improvements. I mean, by shewing, that this latter of Hearing is capable of
all those improvements which the Sense of Seeing has receiv'd from Art,
besides many more advantages that the Ear may enjoy, by the help of our
Doctrine, above the Eye; all which moreover will be of as great benefit to
Mankind, as any thing that Opticks have yet discover'd, if not of greater;
which, with some other pre-eminencies that it has upon another Score, will
happily render Acousticks the nobler Science of the two.

In order to the making good what I but now premised of the Comparison
of these two Faculties of Seeing and Hearing, as to their Improvements, I
observe;
That Vision is threefold, Direct, Refracted, and Reflex'd; answerable
whereunto we have Opticks, Dioptricks, and Catoptricks.
In like manner Hearing may be divided into Direct, Refracted and
Reflex'd; whereto answer three parts of our Doctrine of Acousticks, which
are yet nameless, unless we call them Acousticks, Diacousticks, and
Catacousticks, or (in another Sense, but to as good Purpose) Phonicks,
Diaphonicks, and Cataphonicks.

I. Direct Vision has been improv'd two ways, ex parte Objecti, and ex
parte Organi vel Medii.
1. Ex parte Objecti, Direct Vision has receiv'd advantages by the Arts of
Producing, Conserving and Imitating Light and Colours, which are the
Objects of Vision.
1. For the Art of Producing Light, we have the Frication of all hard
Bodies that beget Fire; especially of the Flint and Steel; and instead of the
Flint, most hard Stones (as well as the Cane) may be us'd to the same effect,
as upon trial I have found. Add hereto the lately invented Phosphorus,
which is a new and admirable way of producing a Lucid Substance by Art,
out of a Body in itself not Lucid; and therefore may not unfitly be term'd an
Artificial production of Light.
And then of the Art of Conserving Light, the Lapis Bononiensis is a
notable Instance; and so happily were the Sepulchral Lamps of the
Ancients.
2. As to Colours, 'tis the greatest part of the Art of Dying to be able to
make and fix (that is preserve) them; and the Painters and Limners will own

it to be no small part of their Skill to be able well to Mix (that is, in effect,
to Generate) Colours.
3. For Imitation of Light and Colours, 'tis well known how far
Perspective with the Art of Limning and Shadowing have gone therein,
which all tend some way to the Advance or Improvement of Direct Vision.
Add to all these, That a due Application of Light to the Object renders it
Visible, if it were not so before; as appears from a dark Room illuminated;
or else makes it better and more truly discernable by the Sense of Seeing, if
before it might have been discern'd.
Hence the same Colour, in a diverse Light, will appear different, and no
Picture can well be discern'd or judg'd of but by its true Light. Besides, the
Limner will assure you, that he can hardly make true Work, or hit the Air of
a Face exactly, unless he draw by a North-Light, by reason of the steadiness
of that, and the uncertainty of all other Lights whatsoever. Which things
shew, that the Art of duly applying Light to the Object does very much help
and improve Vision. So also does the due placing of the Object, as to Height
and Distance. But to enumerate all things that help Direct Vision, would be
infinite.
2. Ex parte Organi vel Medii, Direct Vision has been improv'd by making
use of a Tube, without Glasses, or a Man's clos'd Hand, to look thro'; which
admitting into the Eye only the principal Rays, that come directly from the
Object, do very much strengthen and clear the Sight, by excluding all the
Collateral Rays, that crouding into the Eye, together with the direct ones,
would confound and disturb it, partly by mixing and interfering with the
direct Rays, and partly (or rather chiefly) by too much enlightning the fund
of the Eye, wherein Vision is truly (tho' then imperfectly) made.
On this is founded the Art of making Spectacles without Glasses; (as well
as Tubes) which is done by putting into the Glass-holes (instead of Glasses)
two short Tubes of between three and four Inches long (for their length is to
be vary'd according to the Age or Eye of the Beholder, and so also is the

Diameter of the extream ends) which Tubes being made of Spanish Leather
(or Past-board, or some such like Matter) and black'd on the inside, are so to
be placed, as that the visual Rays, receiv'd thro' them, may meet in one
point (or rather issue out from one Point) of the Object standing at such a
due distance, as the Person may clearly and distinctly see it, or according to
his length of Sight (as ABC, in the 4th Fig. Tab. 3.)
And these Spectacles may be suppos'd better for preserving the Sight,
than the ordinary ones with Glasses, because they represent the Object more
naturally, and withal more clearly and distinctly to the Eye, than the other,
whose refracted Rays being collected together with the right ones in the
Glasses, do somewhat confound good Vision, as before: Especially if the
visive Power be strong enough to be sufficiently determin'd by the right
Rays alone.
For I speak now of preserving a good Eye by these Spectacles, which
holds in proportion true also of a bad one. Because those Rays (both right
and refracted) being collected and brought so near the Eye (whether good or
bad) as the Spectacles are usually plac'd, do too much affect it, both by their
own brightness, and also by the brightness of the Colours of the Object
(when they are bright) which is brought very near also; whereby the Eye is
dazl'd and confounded, unless there be a strong attention and conatus of the
Spirits, whereto the bright Rays do certainly engage them, which of
necessity weakens Vision, especially if these Glass-spectacles be much us'd.
Wherefore the now describ'd new Tube-spectacles, contributing so much
to the help and preservation of Sight, may well be counted an improvement
of Direct Vision, because they convey the Rays to the Eye without any kind
of Refraction whatsoever. Seeing the same Object also through various
holes, plac'd at certain distances, does somewhat alter Vision; but of this
perhaps more hereafter.
Now as Direct Vision has thus been improved, so likewise Direct
Hearing partly has already receiv'd, and partly may by the Doctrine

whereof we are treating, (if well cultivated) farther receive as great and
notable Improvements, both ex parte Objecti, and ex parte Organi vel
Medii.
1. As to the Object of Hearing, which is Sound, improvement has been
and may be made, both as to the Begetting, and as to the Conveying and
Propagating (which is a kind of Conserving) of Sounds.
1. As to the Begetting of Sounds. The Art of imitating any Sound,
whether by Speaking (that is pronouncing) any kind of Language, (which
really is an Art, and the Art of Speaking, perhaps one of the greatest) or by
Whistling, or by Singing (which are allow'd Arts) or by Hollowing or Luring
(which the Huntsman or Faulkner would have to be an Art also) or by
imitating with the Mouth (or otherwise) the Voice of any Animal, as of
Quails, Cats, and the like; or by representing any Sound begotten by the
Collision of Solid Bodies, or after any other manner; these are all
Improvements of Direct Hearing, and may be improv'd.
Moreover the Skill to make all sorts of Musical Instruments, both
Ancient and Modern, whether Wind Instruments or String'd, or of any other
sort, whereof there are very many (as Drums, Bells, the Systrum of the
Egyptians, and the like) that beget (and not only propagate) Sounds; the
Skill of making these, I say, is an Art, that has as much improv'd Direct
Hearing, as an Harmonious Sound exceeds a single and rude one, that is, an
immusical Tone; which Art is yet capable of farther improvement. And I do
hope, that by the Rules, which may happily be laid down concerning the
Nature, Propagation and Proportion, or Adapting of Sounds, a way may be
found out, both to improve Musical Instruments already in use, and to
invent new ones, that shall be more sweet and luscious, than any yet known.
Besides that, by the same means Instruments may be made, that shall
imitate any Sound in Nature, that is not Articulate, be it of Bird, Beast, or
what thing else soever.

2. The Conveying and Propagating (which is a kind of Conserving) of
Sounds, is much help'd by duly placing the Sonorous Body, and also by the
Medium.
For if the Medium be Thin and Quiescent, and the Sounding Body plac'd
conveniently, the Sound will be easily and regularly propagated, and
mightily conserv'd. I say,
1. If the Medium be Thin and Quiescent, because it otherwise causes a
Refracted Sound, of which afterwards. Hence in a still Evening, or the dead
of the Night (when the Wind ceases) a Sound is better sent out, and to a
greater distance than otherwise, tho' much of this may be ascrib'd to its
Refraction also.
2. I say, that the Sonorous Body must be plac'd conveniently, near a
Smooth Wall, near Water, or a Plain, whose Surface is even.
1. Near a Smooth Wall, either Plain or Arch'd (Cycloidically or
Elliptically, rather than otherwise, tho' a Circular or any Arch will do, but
not so well.)
Hence in a Church, the nearer the Preacher stands to the Wall (and
certainly 'tis much the best way to place Pulpits near the Wall) the better is
he heard, especially by those who stand near the Wall also, though at a
greater distance from the Pulpit; those at the remotest end of the Church, by
laying their Ears somewhat close to the Wall, may hear him easier than
those in the middle.
Hence also do arise Whispering Places. For the Voice being apply'd to
one end of an Arch, easily rowls to the other. And indeed were the Motion
and Propagation of Sounds but rightly understood, 'twould be no hard
matter to contrive Whispering Places of infinite variety and use. And
perhaps there could be no better or more pleasant hearing a Consort of
Musick than at such a place as this, where the Sounds rowling along
together, before they come to the Ear, must needs consolidate and imbody

into one; which becomes a true composition of Sounds, and is the very Life
and Soul of Consort.
2. If the Sonorous Body be plac'd near Water, the Sound will easily be
convey'd, yet mollified; as Experience teacheth us from a Ring of Bells near
a River, and a great Gun shot off at Sea, which yet differ much in the
strength, and softness and continuance, or propagation of their Sounds,
from the same at Land, where the Sound is more harsh and more perishing,
or much sooner decays.
3. In a Plain a Voice may be heard at a far greater distance than in uneven
Ground.
The Reason of all which last nam'd Phænomena is the same; because the
Sonorous Air meeting with little or no resistance upon a Plane (much less
upon an Arch'd) smooth Superficies, easily rowls along it, without being let
or hinder'd in its Motion, and consequently without having its parts
disfigured, and put into another kind of Revolution, than what they had at
the first begetting of the Sound. Which is the true cause of its Preservation
or Progression, and fails much when the Air passes over an uneven Surface,
according to the degrees of its inequality, and somewhat also, when it
passes over the plain Superficies of a Body that is hard and resisting.
Wherefore the smooth Top of the Water (by reason of its yielding to the
Arch'd Air, and gently arising again with a kind of Resurge, like to
Elasticity, tho' it be not so, by which Resurge it quickens and hastens the
motion of the Air rowling over it, and by its yielding preserves it in its
Arch'd Cycloidical or Elliptical Figure) the smooth Top of the Water, I say,
for these Reasons, and by these Means, conveys a Sound more entire, and
to a greater distance than the plain Surface of a piece of Ground, a Wall, or
any other Solid Body whatever, can do.
As for the Speaking Trumpet, by which a Voice may be convey'd to a
considerable distance, I refer its consideration to that of Refracted Sounds,
or Refracted Audition.

Thus much of the Improvements of Hearing, that respect its Object,
which is Sound.
2. The Organ and Medium are to be consider'd. And, 1. The Organ,
which is the Ear, is helpt much by placing it near a Wall (especially at one
end of an Arch, the Sound being begotten at the other) or near the Surface
of Water, or of the Earth, along which the Sounds are most easily and
naturally convey'd, as was before declar'd. And 'tis incredible how far a
Sound made upon the Earth (by the trampling of a Troop of Horses, for
Example) may be heard in a still Night, if a Man lays his Ear close to the
Ground in a large Plain.
Otacousticks here come in for helping the Ear; which may be so contriv'd
(by a right understanding the Progression of Sounds, which is the principal
thing to be known for the due regulating all such kinds of Instruments) as
that the Sound might enter the Ear without any Refraction, but as now they
are generally made I refer them to Refracted Audition.
2. As to the Medium, I know not how that, by any contrivance of Art, can
advantage Direct Hearing, otherwise than I have declar'd already in the
propagation or conveyance of Sounds, though to the Refracting or
Reflecting of them it may very much conduce; of which presently.
And so I have done with the first part of my present undertaking, which
is the Comparison of Direct Vision and Audition, as to their Improvements
from Art. The rest follow. Wherefore,

II. Concerning Refracted Vision and its Comparison, I observe, That
Refracted Vision is always made Ex parte Medii, as Reflected is ex parte
Objecti. And therefore, though Direct Vision may be help'd ex parte Objecti,
Medii vel Organi, yet Refracted can be improv'd only ex parte Medii, and
Reflected ex parte Corporis oppositi alone. Unless it be in a mixt or
compound Vision, that is Refracto-Reflext, when the reflext Rays pass to the
Eye through a refracting Medium, such as the Medium Internum, contain'd

in the Body of the Eye, always is. So that in truth, all Vision is Refracted by
an internal Refraction made in ipso Oculo.
And all that I have spoken of Vision holds true of Hearing also, both
Refracted and Reflext, and therefore need not be repeated.
Refracted Vision arises from the different Density, Figure, and Magnitude
of the Medium, which is somewhat alter'd also by the diverse incidence of
the visible Rays. And so it is in Refracted Hearing, all these Causes concur
to its Production, and some others to be hereafter consider'd.
Now as any Object (a Man for example) seen through a thicken'd Air, by
Refraction appears greater than really he is: So likewise a Sound, heard
through the same thicken'd part of the Atmosphere, will be considerably
vary'd from what it would seem to be, if heard through a thinner Medium.
And this I call a Refracted Sound: But what this Refraction of Sound is,
and how caus'd, may hereafter be discuss'd, when the Nature, and Motion,
or Progression of Sounds are well stated.
For the Improvement of Refracted Vision artificial Instruments have been
made, by grinding or blowing Glasses, into a certain Figure, and placing
them at due distances, whereby the Object may be (as 'twere) enabled to
send forth its Rays more vigorously, and the Visive Faculty impower'd the
better to receive them. And thus also Instruments may be contriv'd for the
assisting both the Sonorous Body, to send forth its Sound more strongly, and
the Acoustick Faculty, to receive and discern it more easily and clearly. For,
1. As a fine Glass Bubble, fill'd with clear Water, and placed before a
burning Candle or Lamp, does help it to dart forth its Rays to a prodigious
Length and Brightness: So an Instrument may be invented, that apply'd to
the Mouth (or any Sonorous Body) shall send forth the Voice distinctly to as
prodigious a Distance and Loudness.
For if the Stentoro-phonecon (which is but a rude and unartificial
Instrument) does such great feats, what might be done with one compos'd

according to the Rules of Art? whose make should comply with the Laws of
Sonorous Motion (which that does not) and therefore not so much Refract,
as to alter and confound the Tone of the Voice and Words (as that somewhat
does.)
Now of what use such an Instrument might be for speaking clearly and
articulately at a distance (and that without altering the Tone of the Voice)
whether it be at Sea or at Land (but especially at Sea in tempestuous
Weather and in the Night) is obvious to any Man to conceive.
2. As Instruments have been invented to help the Eye, So likewise are
there some, and more such there may be, for the Ear.
For,
1. As Spectacles and other Glasses are made to help the Purblind and
weak Eyes, to see at any competent distance: So there are Otacousticks (and
better may be made) to help weak Ears to hear at a reasonable distance also.
Which would be as great a help to the infirmity of Old Age, as the other
invention of Spectacles is, and perhaps greater; forasmuch as the Hearing
what's spoken is of more daily use and concern to such Men, then to be able
to read Books or to view Pictures.
2. As Perspective-Glasses and Telescopes help the Eye to see Objects at a
very great distance, which otherwise would not be discernable; in like
manner may a sort of Otacousticks be so contriv'd, as that they shall receive
in Sounds made at a very great distance also, but with so much advantage,
that the Ear shall be able to hear them, which otherwise would have been
inaudible.
And these Otacousticks in some respects would be of greater use than
Perspectives. For whereas at Land Perspectives are many times render'd
almost useless, by the interposition of Woods and Mountains, which hinder
the Sight from reaching very far: Our Otacousticks would, notwithstanding
these Obstacles, take in a Sound made some Leagues off. Which might be

of notable use in the time of War, for discovering the Enemy at a good
distance, when he marches or lyes incamp'd behind a Mountain or Wood, or
any such place of shelter.
Yea, even at Sea also, where Perspectives are of most use, by reason of
the plainess of the Surface of the Water; yet sometimes there Otacousticks
may be of more benefit, when in dark hazy Weather the Air is too thick, or
in Stormy Tempestuous Weather the Waves arise too high for the
Perspective to be made use of.
But, whether at Sea or Land, Perspectives become altogether
insignificant in the Night-time (unless it be for viewing the Stars) which is
the chief time for using Otacousticks; as it is generally, for Soldiers to take
their March, when they would surprise their Enemies.
And therefore this sort of Otacousticks have then their chief use, when
Perspectives are of no use at all; besides that they may be imploy'd in the
Day-time, as well as Perspectives, whence they may (not unfitly) be term'd
the most useful Instrument of the two.
3. As Microscopes or Magnifying-Glasses help the Eye to see near
Objects, that by reason of their smallness were Invisible before; which
Objects they Magnify to a strange greatness: So Microphones or
Micracousticks, that is Magnifying Ear Instruments, may be contriv'd after
that manner, that they shall render the most minute Sound in nature
distinctly audible, by Magnifying it to an unconceivable loudness.
By the help hereof we may hear the different Cries and Tones, as well as
by Microscopes see the divers Shapes and Figures of the smallest Animals.
4. As by Polyscopes or Multiplying-Glasses, one thing is represented to
the Eye as many, whether in the same or different Shapes (for so
Multiplying-Glasses may be contriv'd:) So by a Polyphone or Polyacoustick
well order'd, one Sound may be heard as many, either of the same or a
different Note. Insomuch, that who uses this Instrument, he shall, at the

Sound of a single Viol, seem to hear a whole Consort and all true Harmony.
By which means this Instrument has much the advantage of the Polyscope.
And thus much may suffice for comparing the Improvements made upon
Refracted Seeing and Hearing; I call it Refracted Hearing, because made
through a Medium, viz. thick Air, or an Instrument, through which the
Sound passing is broken or refracted.

III. Reflected Vision has been improv'd by the Invention of Looking-
glasses and Polished Metals, whether Plane, Concave, or Convex; and these
two last, either Spherical, Oval, Cylindrical, Conical, Hyperbolical, or of
several other shapes; all which cause a different Reflection, and vary the
Phænomena.
Thus also Reflext Audition, made by Ecchoes, may be improv'd, by
contriving several sorts of Artificial Ecchoes; as 'tis no hard matter to do in
almost any place.
For (speaking in the general) Any Sound, falling directly or obliquely
upon any dense Body, of a smooth (whether Plane or Arch'd) Superficies, is
beat back again and reflected, or does eccho more or less.
I say (1.) falling directly or obliquely; because, if the Sound be sent out
and propagated parallel to the Surface of the Dense Body, or be made so far
off and so weak, that it cannot reach it, there will be no Reflection of Sound,
no Eccho.
I say (2.) upon a Body of a smooth Superficies; because if the Surface of
the Corpus Obstans be uneven, the Air by reverberation will be put out of
its regular Motion, and the Sound thereby broken and extinguish'd: So that
tho' in this case also the Air be beaten back again, yet Sound is not
reflected, nor is there any Eccho.
I say (3.) it does eccho more or less, to shew, that when all things are, as
is before describ'd, there is still an Ecchoing, though it be not always heard;

either because the direct Sound is too weak to be beaten quite back again to
him that made it; or that it does return home to him, but so weak, that
without the help of a good Otacoustick, it cannot be discern'd; or that he
stands in a wrong place, to receive the reflected Sound, which passes over
his head, under his Feet, or to one side of him; which therefore may be
heard by a Man standing in that place, where the reflected Sound will come,
provided no interpos'd Body does intercept it; but not by him, that first
made it.
I shall further make out the comparison 'twixt Reflex'd Vision and
Audition, by these following Propositions.
1. As a Plain Speculum reflects the Object in its due Dimensions and
Colours; allowing for their difference of appearance, according to their
distance: So a Plane Corpus Obstans reflects the Sound back in its due Tone
and Loudness; if allowance be likewise made for the proportionable
decrease of the Sound, according to its distance.
2. As a Convex Speculum reflects the Object less, but somewhat brighter
or clearer: So a Convex Corpus Obstans repels the Sound (insensibly)
smaller; but somewhat quicker (though weaker) than otherwise it would be.
3. As a Concave Speculum reflects the Object bigger, more obscure and
Inverted: So a Concave Corpus Obstans ecchoes back the Sound
(insensibly) bigger, slower (though stronger) and also inverted; but never
according to the order of Words. Nor do I think it possible for the Art of
Man to contrive a Single Eccho, that shall invert the Sound, and repeat
backwards; because then the Words last spoken, that is, which do last occur
to the Corpus Obstans, must first be repell'd; which cannot be: For where,
in the mean time, should the first Words hang, and be conceal'd, or lie
dormant? Or how, after such a pause, be reviv'd and animated again into
Motion? Yet in complicated or Compound Ecchoes, where many receive
from one another, I know not whether something that way may not be done.

From the determinate Concavity or Archedness of these reflecting
Bodies, it comes to pass, that some of them, from a certain distance or
posture, will eccho back but one determinate Note, and from no other place
will they reverberate any; because of the undue Position of the sounding
Body. Such an one (as I remember) is the Vault in Merton College in
Oxford.
4. As a Speculum takes in and reflects more of its Object, when plac'd at a
great distance from it, than when nearer; because it reflects according to the
apparent Magnitude of the Body at such a distance, which is less: So also
the Ecchoing Body, being remov'd farther off, reflects more of the Sound,
than when nearer. And this is the reason, why some Ecchoes repeat but one
Syllable, some one Word, and some many.
5. As Specula's may be so plac'd, that reflecting one upon or into the
other, either directly or obliquely, one Object shall appear many; as in Sir
Samuel Moreland's Glass-room: After the same manner Ecchoing Bodies
may be so contriv'd and plac'd, as that reflecting the Sound from one to the
other, either directly and mutually, or obliquely and by Succession, out of
one Sound shall many Ecchoes be begotten; which in the first case will be
all together, and somewhat involv'd or swallow'd up of each other, and
thereby confus'd (as a Face in Looking-glasses obverted) in the other they
will be distinct, separate, and succeeding one another; as most multiple
Ecchoes do.
Moreover a Multiple-Eccho may be made, by so placing the Ecchoing
Bodies, at unequal distances, that they reflect all one way, and not one on
the other; by which means a manifold successive Sound will be heard (not
without astonishment) one Clap of the hands like many, one Ha, like a
laughter, one single Word like many of the same Tone and Accent, and so
one Viol like many of the same kind imitating each other.
Furthermore, as Specula's may be so order'd, that by Reflection they shall
make one single thing appear many different things; as one single Man to

seem many Men, differing as to Shape and Complexion (or a company of
Men) which I think Sir Samuel Moreland's Contrivance does not: So may
Ecchoing Bodies also be order'd, that from any one Sound given, they shall
produce many Ecchoes, different both as to their Tone and Intension. (The
ground whereof has elsewhere been laid down in a Treatise concerning the
Sympathy of Lute-strings.)
By this means a Musical Room may be so contriv'd, that not only one
Instrument, play'd on in it shall seem many of the same sort and size; but
even a Consort of (somewhat) different ones; only by placing certain
Ecchoing Bodies so, as that any Note (play'd) shall be return'd by them in
3ds, 5ths, and 8ths, which is possible to be done otherwise than was
mention'd before in Refracted Audition.
I have now done with my Comparison of the two Noblest Senses, and
Sciences, as to their Improvements; wherein I have been thus large, that I
might give you a little prospect into the Excellency and Usefulness of
Acousticks; and that thereby I might excite all that hear me, to bend their
Thoughts towards the making of Experiments for the compleating this (yet
very imperfect, tho' noble) Science; a Specimen whereof I will give you in
three Problems, and then present you with the Semiplane of an Acoustick or
Phonical Sphere, as an Attempt to explicate the great Principle in this
Science, which is The Progression of Sounds.

The Problems are these:
1. Sonum intendere quousque velis; or, Datum sonum ad datum gradum
intendere.
2. Sonum extendere quousque velis; or, Datum sonum ad datum
distantiam extendere seu propagare.
3. Sonum transire ab extremo ad extremum & non per Medium.

1. The first is, To make the least Sound (by the help of Instruments) as
loud as the greatest; a whisper to become as loud as the shot of a Cannon.
By the help of this Problem, the most minute Sounds in Nature may be
clearly and distinctly heard.
2. The second is, To propagate any (the least) Sound to the greatest
distance.
By the help hereof any Sound may be convey'd to any, and therefore
heard at any distance, (I must add, within a certain, tho' very large Sphere.)
Moreover, by this means, a Weather-cock may be so contriv'd, as that
with an ordinary blast of Wind it shall cry (or whistle) loud enough to be
heard many Leagues: Which happily may be found of some use, not only
for Pilots in mighty tempestuous Weather, when light Houses are render'd
almost useless, but also for the measuring the strength of Winds, if
allowance be made for their different moisture. For I conceive, that the
more dry any Wind is, the louder it will whistle cæteris paribus; I say,
cæteris paribus, because, besides the strength and dryness of Winds or
Breath, there are a great many other things (hereafter to be considered) that
concur to the increase or magnifying of Sounds, begotten by them in an
Instrument exposed to their Violence, or blown into.
3. The third Problem, is, That a Sound may be convey'd from one extreme
to the other (or from one distant place to another) so as not to be heard in
the middle.
By the help of this Problem a Man may talk to his Friend at a very
considerable distance, so that those in the middle space shall hear nothing
of what passed betwixt them.
FIG. V. TAB. III.
Semiplanum Sphæræ Phonicæ seu Acousticæ.

You are to conceive that (rude) Semiplane, as parallel to the Horizon: For
if it be perpendicular thereunto, I suppose the upper extremity will be no
longer Circular, but Hyperbolical, and the lower part of it suited to a
greater Circle of the Earth. So that the whole Phonical Sphere (if I may so
call it) will be a solid Hyperbola, standing upon a Concave Spherical Base.
I speak this concerning Sounds made (as usually they are) nigh the Earth,
and whose Sonorous Medium has a free passage every way. For if they are
generated high in the Air, or directed one way, the case will be different;
which is partly design'd in the inequality of that Draught.

Discourse concerning the Modern Theory of Generation, by Dr.
George Garden of Aberdeen, being part of a Letter to Dr. William
Musgrave, L. L. D. Reg. Soc. S. and by him communicated the
Royal Society.

HE Subject I pitch upon, is that of the Formation of Animals. You
T know how wide and unsatisfying Men's Conjectures were upon this
Head, until this Age, in which first the deservedly Famous Dr. Harvey
discovered the proper place of the Formation of the Chick in the Cicatricula
of the Egg, and the Formation of the Parts so far as was discernable by the
naked Eye; and after him Malpighius, by the help of exact Glasses, observ'd
the first Rudiments of it there, both before and after Incubation: And R. de
Graef, and others, having upon many Observations concluded, that the
Testes Fœminei were the Ovaries of Females, and consequently that all
Animals were ex ovo; they began from hence to infer, that the Rudiments of
each Animal were originally in the respective Females, and that the Male
contributed only to give a new Ferment to the Mass of the Blood and
Spirits, by which means a spirituous Liquor (which the Blood in its ordinary
Ferment could not produce) did insinuate it self into the same Ducts and
Pores of the Rudiments of those Animals, which were in greatest
forwardness in the Ovary, and so extend and enlarge all their Parts, and at

last bring them to perfection, as Mr. Perrault does ingeniously discourse in
the third Part of his Essais de Physique; till now at last Leowenhoek has
discover'd an infinite number of Animalcula in semine marium of all kinds,
which has made him condemn the former Opinions about the Propagation
of all Animals ex Ovo.
Now upon comparing the Observations and Discoveries which have been
made with one another, these three things seem to me very probable. 1. That
Animals are ex Animalculo. 2. That these Animalcles are originally in
semine Marium & non in Fœminis. 3. That they can never come forward,
nor be formed into Animals of the respective kind, without the Ova in
Fœminis.
The first of these seems probable from these three Observations. 1. That
some such thing has been so often observ'd by Malpighius, in the
Cicatricula of an Egg before Incubation, as the Rudiments of an Animal in
the shape of a Tadpole, as may be seen in his first, and in his repeated
Observations de formatione Pulli in Ovo. 2. The sudden appearance and
displaying of all the Parts after Incubation, makes it probable, that they are
not then actually formed out of a fluid, but that the Stamina of them have
been formerly there existent, and are now expanded. The first Part of the
Chick which is discovered with the naked Eye, is, you know, the Punctum
saliens, and that not till three days and nights of Incubation be past; and
then, on the fifth day, the Rudiments of the Head and Body do appear. This
made Dr. Harvey conclude, that the Blood had a being before any other Part
of the Body; and that from it, all the Organs of the Fœtus were both form'd
and nourished: But by Malpighius's Observations we find that the Parts are
then only so far extended, as to be made visible to the naked Eye, and that
they were actually existent before, and discernable by Glasses. After an
Incubation of thirty hours, are to be seen the Head, the Eyes, and the Carina
with the Vertebræ, distinct, and the Heart. After forty hours its Pulse is
visible, and all the other Parts more distinct, which cannot be discerned by
the naked Eye before the beginning of the fifth day; from whence it seems

probable, that even the so early discovery of those Parts of the Fœtus by the
Microscope, is not the discerning of Parts newly formed, but only more
dilated and extended by receiving of Nutriment from the Colliquamentum;
so that they seem all to have been actually existent before the Incubation of
the Hen. And what Swammerdam has discovered in the transformation of
Insects, gives no small light to this; whilst he makes appear in the
Explanation of the 13th Table of the General History of Insects, that in
those large Eruca's which feed upon Cabbage, if they be taken about the
time they retire to be transformed into Aurelia's, and plung'd often in warm
Water to make a Rupture of the outer Skin, you will discern through the
transparency of their second Membrane, all the Parts of the Butterfly, the
Trunk, Wings, Feelers, &c. folded up. But that after the Eruca is chang'd
into an Aurelia, none of these Parts can be discern'd, they are so drencht
with moisture, tho' they be there actually form'd. Another Consideration is
from the Analogy, which we may suppose between Plants and Animals. All
Vegetables we do see proceed ex Plantula, the Seeds of Vegetables being
nothing else but little Plants of the same kind folded up in Coats and
Membranes; and from hence we may probably conjecture, that so curiously
an organized Creature as an Animal, is not the sudden Product of a Fluid or
Colliquamentum, but does much rather proceed from an Animalcle of the
same kind, and has all its little Members folded up according to their
several Joints and Plicatures, which are afterwards enlarged and distended,
as we see in Plants. Now tho' this Consideration alone may seem not to bear
much weight; yet being join'd to the two former, they do mutually
strengthen each other. And indeed all the Laws of Motion, which are as yet
discovered, can give but a very lame account of the forming of a Plant or
Animal. We see how wretchedly Des Cartes came off when he began to
apply them to this Subject; they are formed by Laws yet unknown to
Mankind; and it seems most probable, that the Stamina of all the Plants and
Animals that have been, or ever shall be in the World, have been form'd, ab
Origine Mundi, by the Almighty Creator within the first of each respective
kind. And he who considers the Nature of Vision, that it does not give us the

true magnitude, but the proportion of things; and that what seems to our
naked Eye but a Point, may truly be made up of as many Parts as seem to us
to be in the whole visible World, will not think this an absurd or impossible
thing.
But the second thing which later Discoveries have made probable, is, that
these Animalcles are originally in Semine Marium & non in Fœminis. And
this I collect from these Considerations: 1. That there are innumerable
Animalcula discover'd in Semine Masculo omnium Animalium. Mr.
Leewenhoeck has made this so evident by so many Observations, that I do
not in the least question the truth of the thing. The reason of their Multitude,
and some of the Difficulties which arise thereupon, he has cleared to very
good Purpose, so that I shall not repeat them. 2. The observing the
Rudiments of the Fœtus in Eggs, which have been fecundated by the Male,
and the seeing no such thing in those which are not fecundated, as appears
from Malpighius his Observations, make it very probable that these
Rudiments proceed originally from the Male, and not from the Female. 3.
The resemblance between the Rudiments of the Fœtus in Ovo, both before
and after Incubation, and the Animalcle, makes it very probable, that they
are one and the same. The same Shape and Figure which Mr. Leewenhoeck
gives us of the Animalcle, Malpighius likewise gives of the Rudiments of
the Fœtus, both before and after Incubation; yea, and even the Fœtus's of
Animals do appear so at first to the naked Eye, so that Dr. Harvey does
acknowledge that all Animals, even the most perfect, are begotten of a
Worm, De Gen. Anim. Ex. 18. 4. This gives a rational account of many
Fœtus's at one Birth, especially that of the Countess of Holland, and how at
least a whole Cluster of Eggs in a Hen are fecundated by one Coition of the
Male. 5. This gives a new light, as it were, to the first Prophecy concerning
the Messiah, that the Seed of the Woman shall bruise the Head of the
Serpent, all the rest of Mankind being thus most properly and truly the Seed
of the Man. 6. The Analogy I have already mentioned, which we may
rationally suppose between the manner of the propagation of Plants and

Animals, does likewise make this probable. Every Herb and Tree bears its
Seed after its kind; which Seed is nothing else but a little Plant of the same
kind, which being thrown into the Earth, as into its Uterus, spreads forth its
Roots, and receives its Nourishment, but has its form within its self, and we
may rationally conjecture some such Analogy in the Propagation of
Animals.
The third Particular which later Discoveries make probable, is, that
Animals cannot be formed of these Animalcula without the Ova in fœminis,
which are necessary for supplying of them with proper Nutriment: And this
these Considerations seem to evince. 1. It is probable that an Animalcle
cannot come forward, if it do not fall into a proper Nidus. This we see is the
Cicatricula in Eggs; and tho' a Million of them should fall into an Egg,
none of them would come forward, but what were in the Center of the
Cicatricula; and perhaps the Nidus necessary for their formation is so
proportion'd to their bulk, that it can hardly contain more than one
Animalcle; and this may be the reason why there are so few Monsters. This
we see is absolutely necessary in Oviparis; and the only difference which
seems to be between them and the Vivipara, in this matter, is in this, that in
the latter the Ova are properly nothing more but the Cicatricula, with its
Colliquamentum, so that the Fœtus must spread forth its Roots into the
Uterus to receive its nourishment; but the Eggs in Oviparis may be properly
term'd an Uterus, in relation to the Fœtus; for they contain not only the
Cicatricula, with its Amnion and the Colliquamentum, which is the
immediate nourishment of the Fœtus, but also the materials which are to be
converted into that Colliquamentum; so that the Fœtus spreads forth its
Roots no farther than into the White and Yolk of the Egg, from whence it
derives all its nourishment. Now that an Animalcle cannot come forward
without some such proper Nidus, Mr. Leewenhoeck will not readily deny;
for if there were nothing needful, but their being thrown into the Uterus, I
do not see why many hundreds of them should not come forward at once;
for as to what Mr. Leewenhoeck says, that one of them would be-dwarf and

choak the rest; this might fall out in process of time: But at first I do not see
why many of them should not grow together, whilst scatter'd in so large a
Field (and yet no such thing is observed) if there were not an absolute
necessity of a Cicatricula for their growth and thriving. Now, 2. That this
Cicatricula is not originally in Utero, seems evident from the frequent
Conceptions which have been found extra Uterum: Such as the Child which
continued Twenty six Years in the Woman of Tholouse's Belly, mention'd
Numb. 139. of the Philos. Trans. And the little Fœtus found in the Abdomen
de St. Mere, together with the Testicle torn and full of clotted Blood,
recorded Numb. 150. both taken out of the Journals des Savans: Such also
seem to be the Fœtus in the Abdomen of the Woman of Copenhagen,
mention'd in the Nouvelles des Lettres, for Sept. 85. pag. 996. all the
Members of which were easily to be felt through the Skin of the Belly, and
which she had carried in her Belly for four Years; and the seven Years
Gravidation, related by Dr. Cole, Numb. 172. of the Transact. That these
two were undoubtedly extra Uterum, is uncertain, because the last was not
open'd after her death, and the former may be yet still alive. Now granting
once the necessity of a proper Nidus, for the formation of an Animalcle into
the Animal of its respective kind; these Observations make it probable, that
the Testes are the Ovaria appropriated for this use; for tho' the Animalcles
coming thither in such Cases may seem to be extraordinary, and that usually
the Impregnation is in Utero; yet it may be collected from hence, that the
Cicatriculæ or Ova to be impregnated, are in Testibus fœmineis; for if it
were not so, the accidental coming of Animalcles thither could not make
them come forward more than in any other part of the Body, since they
cannot be formed and nourished without a proper Nidus. But 3. It is
acknowledg'd by all, that the Fœtus in Utero, for some considerable time
after Conception, has no connexion with the Womb, that it sits wholly loose
to it, and is perfectly a little round Egg with the Fœtus in the midst, which
sends forth its Umbilical Vessels by degrees, and at last lays hold on the
Uterus. Now from hence it seems evident, that the Cicatricula, which is the
Fountain of the Animalcles nourishment, does not sprout from the Uterus,

but has its Origin elsewhere, and falls in thither as into a fit Soil, from
whence it may draw Nutriment for the growth of the Fœtus, else it cannot
be easily imagin'd, how it should not have an immediate Connexion with
the Uterus from the time of Conception. If you join all these three
Considerations together, viz. that an Animalcle cannot come forward
without a proper Nidus or Cicatricula; that there have been frequent Fœtus's
extra Uterum; and that they have no Adhæsion to the Uterus, for a
considerable time after Conception, they seem to make it evident, that
Animals cannot be form'd ex Animalculis without the Ova in Fœminis. To
all these I shall subjoin the Proposal of an Experimentum Crucis, which
may seem to determine, whether the Testes Fœmineæ be truly the Ovaria,
viz. Open the Abdomen of the Females of some kinds, and cut out these
Testicles, and this will determine, whether they be absolutely necessary for
the formation of Animals.
There are some Difficulties proposed against this Conjecture, which I
think may be easily resolved. Some object the distance between the Tubæ or
Cornua Uteri, and the Testicles; but to this is opposed by Swammerdam,
and others, the like distance between the Infundibulum, in Hens and Frogs,
and the Ovary; and yet it cannot be denied that the Eggs are transmitted
thro' this into the Uterus: And besides R. de Graef, and others, have by
repeated Observations found that the Cornua Uteri do at certain times after
Conception, embrace the Testes on both sides the Uterus. They object in the
second place the great disproportion between the pretended Eggs in the
Ovary, and the Aperture of the Tubæ or Cornua Uteri, the former being a
great deal bigger than the latter: But both R. de Graef and Malpighius have
clear'd that Matter, by making appear, that these Bladders in the Ovary are
not the Ova, but serve to form the Glandules within which the Ova are
formed, which break through a small Papilla opening in the Glandule,
which bears a proportion to the Aperture of the Tube. They object 3, The
difficulty to conceive how these Eggs should be impregnated per semen
Maris, both because there is no Connexion between the Tubæ and the Ovary

for its transmission, and for that Dr. Harvey could never discover any thing
of it in Utero. As to the last, Mr. Leewenhoeck has cleared that difficulty, by
the discovery of innumerable Animalcula Seminis Maris in Cornubus Uteri,
and those living a considerable time after Coition. Numb. 174. of the
Transact. And as to the former, we may either suppose that there is such an
Inflation of the Tubæ or Cornua Uteri tempore Coitionis, as makes them
embrace the Ovaria, and such an approach of the Uterus and its Cornua, as
that I may easily transmit the Seed into the Ovary; or else, that the Ova are
impregnated by the Animalcles after they descend into the Uterus, and not
in the Ovary; the former seems probable for this Reason, that at least a
whole Cluster of Eggs in a Hen will be fecundated by one Tread of the
Cock: Now this Fecundation seems to be in the Vitellary, and not in the
Uterus, as the Eggs pass along from day to day; for it can hardly be
supposed that the Animalcles should subsist so long, being scattered loosely
in the Uterus, as to wait there for many days for the Fecundation of the
Eggs as they pass along. The latter Conjecture has this to strengthen it, that
the Animalcles are found to live a considerable time in the Uterus; and that
if they should impregnate the Ova in the Ovary it self, the Fœtus would
increase so fast, that the Ova could not pass through the Tubæ Uteri, but
would either burst the Ovary, or fall down into the Abdomen from the
Orifices of the Tubæ; and that from hence proceed those extraordinary
Conceptions in Abdomine extra Uterum. But, 4. Mr. Leewehoeck, Numb.
147. of the Transact. to weaken the third Consideration about the
Conceptions, being like unto an Ovum in the Womb, proposes a Parallel
between these Animalcles and Insects; and insinuates, that as the latter cast
their Skins, and appear of another Shape, so the other which at first seem
like Tadpoles, may cast their outer Skin, and then be round; and that this
may be the occasion of the round Figure of the Conception in the Womb. To
this it may be replied, that according to Mr. Leewenhoeck's own Sentiment,
the Animalcles cannot come forward, if they do not find the Punctum or
proper place for their Nourishment, to which it seems they must have some
Adhæsion. Now the Conception in Viviparis is not fastned unto the Womb

for many days, nor does adhere to any point of it; so that it seems this
roundish Body is not the Animalcle thus chang'd after having cast an outer
Skin, but is rather the Cicatricula or little Egg, into which the Animalcle
has entred as its Punctum or place of nourishment; else I do not see why
they should not be adhering to the Womb from the first Conception, or why
(as I have said) many hundreds of them are not conceiv'd and formed
together, &c.

hort Discourse concerning Concoction: Read at a Meeting of the
Royal Society, May ... 1699, by Clopton Havers, M. D. Fellow of
the Royal Society.

HE manner in which the Digestion of the Aliment is performed, is a
T thing not very easie to be understood and explained. However, it has
not escap'd the Conjectures of some Philosophical Men, who having
curiously observ'd the Phænomena of Nature, and enquired into their
Causes, have, amongst other things, endeavour'd to account for this. But
their Sentiments about it have been various, and the Hypothesis, by which
they have studied to explain it, very different. Some have thought the
Concoction of the Food to be a kind of Elixation; and that the grosser and
more solid Parts being, as it were, boil'd in the Liquid by the Heat of the
Stomach, and the Parts adjacent to it, as the Liver, Spleen, and Omentum,
are by a long and continued Elixation, first render'd more tender, and then
colliquated, and dissolved into minuter Particles, so as to mix more equally
with the Fluid, and with that to make one Pulpament, or chylous Mass. And
Hippocrates, tho' he does not plainly call it an Elixation, yet seems to
attribute the Concoction of the Food to the Heat of the Stomach, as the
Cause of it, Sect. 4. Libro de salubri victus ratione. So where he takes
notice of the voiding of such Fæces, as appear to be like the Food that has
been eaten; he adds, Constat enim, sane ventriculum, ciborum copiam, ut
concoquat, calefacere non posse. And there are other Passages in the same

Book, from which we may conclude, that he suppos'd the Heat of the
Stomach to be the great Cause of the Digestion of the Food.
There are others that make the Stomach itself to be the great Instrument
of Digestion, but in a different manner: And they suppose it to be perform'd
by an Attrition, as if the Stomach, by those repeated Motions, which are the
necessary Effects of Respiration, when it is distended by the Aliment, did
both rub or grind off some minuter Particles from the grosser Parts; and by
continually agitating the Mass of Food, make those Parts, which are not
contiguous to the Stomach, strike one against another, and break one
another in pieces, until they are all attenuated. It is evident enough, that the
sides of the Stomach do in Expiration press upon the Contenta, so as to
oblige, at least some Parts of them, every time the Muscles of the Abdomen
are contracted, to move and shift their places. So in Inspiration, when the
Diaphragm and Liver press upon the upper part of the Stomach, the Aliment
must be moved again. So that by these reciprocal Motions, that part of the
Food which is contiguous to the Stomach, and moves in a Line parallel to it,
must rub against it; and all the other Parts being moved by such a
Compression, as gives them a different Tendency, it is certain they must be
continually striking one against another. And for Bread, and such things as
are made of Flower, that will be softned and dissolv'd with any common
Liquid, that Agitation of the Stomach which moves them in Respiration,
might seem sufficient to break and dissolve them, when they are sufficiently
moisten'd with a Fluid. Yet this cannot be thought enough to break and
digest Flesh-meat, Fruits, or any other thing that will not be softned and
dissolv'd in Water, or some such Liquid. But although this Motion of the
Aliment, caused by Respiration, does not actually digest it, yet it has a great
and necessary Use in Concoction, and makes all the grosser Parts, as they
are attenuated, mix equally with the Fluid.
Some think that the Bilious Juice; others, that the Spirits are chiefly
concern'd in this Affair. Galen, in his Book de Neutralibus Facultatibus,
makes it to be the Effect, not of one, but of several Causes; as a pituitous

Juice in the Stomach, the Bile, &c. which appears from what he has said,
and the Translator thus render'd: 'Verum quanto ii (cibi) qui mansi sunt, iis,
qui inhæserunt, magis sunt alterati; tanto etiam his magis ii, qui devorati
sunt. Siquidem incomparabilis erit horum alterationis excessus, si & quæ in
ventre est Pituita & Bilis, & Spiritus, & Calor, & tota Ventris substantia,
æstimentur.'
Some there are that will have the Food to be dissolv'd by a Menstruum,
which is supply'd from the Glands of the Stomach, or some other way: But
those that do so far agree in the General, as to think Concoction is perform'd
by a Dissolvent, do differ in their Notions of the Nature of the Menstruum:
For there are some that suppose it to be an Acid, which does erode the
grosser parts of the Food, and dissolves them in the same manner as
Vinegar, Spirit of Vitriol, or any such-like Acid, will dissolve even so solid
a Body as Iron. And it cannot be deny'd, but that Oil of Vitriol will dissolve
Flesh-meat, and reduce it to a Pulp; but it is not to be suppos'd, that the
Fibres of the Stomach can admit any such strong and corroding Acid,
without something to correct it, but it must be injur'd in its Tone, and labour
under great and extraordinary Pains. Neither does such a Menstruum, tho' it
will digest some things, seem capable of dissolving so great a Variety of
Things as we eat, especially when a great many of them are of a contrary
Nature. Some will have the Menstruum to be a nitro-aerius Spirit, that is,
quick, and very penetrating, and included in its proper Vehicle; which,
being in its own Nature apt to penetrate the Mass of the Aliment, does
diffuse it self through the Whole, and breaking the Vinculum of the more
solid Parts, does dissolve their Compages. By others, it is thought to be
some saline Juice in the Stomach, by which the Parts of the Aliment are
divided and dissolved, and those which are fit for Nourishment, are
volatiliz'd.
Lastly, There are some others who reject the Opinions I have already
mention'd, and suppose the Digestion of the Food to be perform'd by the
Benefit of a Ferment; which, when it is mixed with the Aliment, excites in

the Mass an intestine motion; and the different and contrary motions and
tendency of the Parts, making some kind of Collision, gradually break off
Particles from the grosser, and more solid Parts, till they are so attenuated as
to be apt to mix more equally with the Fluid, and with them to make one
soft or chylous Substance. But yet there is not amongst them an universal
Consent, either about the Nature of this Ferment, or the manner how it is
supply'd. For first, some think it to be the Remains of the Food that was last
digested; which having lain some time in the Stomach, after the rest is
carried down into the Intestines, contracts an Acid, or some other Quality,
and is so alter'd, as to partake of the Nature of a Leaven. And this Leaven
being a part of the Food, which has been already digested, is so soft and
liquid as to be capable of mixing with the Aliment, which is next taken into
the Stomach; and being agitated with it by the repeated Pressures of the
Diaphragm, Liver, and Abdominal Muscles upon the Stomach in
Respiration, does diffuse it self through the whole Mass; and being mixed
with it, like Leaven, or Yest added to new Wort, &c. puts it into a State of
Fermentation; and by this Fermentation, or the Expansion of the Ferment,
and the more tenuious Parts, which are first put into motion by it, those
which are more solid, and with which they are intermixed, are rent, and
divided, and so attenuated, as to become a soft and pulpous matter. And
altho' the greatest part of the Food, that is thus broken and concocted, is by
the Contraction of the Fibres of the Stomach press'd into the Duodenum; yet
they do not contract themselves so as to force out all the Aliment, but leave
between the Rugæ or Folds, on the inside of the Stomach, a sufficient
Quantity to be a Leaven to the next Meal; and so from time to time.
Some have a Notion, That this Ferment, or Principle of Fermentation, is
in the Aliment it self; which being a Congeries of Matter, consisting of
various Parts of a different Nature, is no sooner enclosed in the Stomach,
and digested in the Heat of that, and the adjacent Parts, but the more
spirituous and subtil Particles are put into motion both from that Warmth,
and the difference of their Natures, and enter upon a Fermentation. And so

by their intestine Commotion, and the Violence they offer to those Parts
which oppose the tendency of any of them, they break and dissolve what is
more solid.
Again: Some suppose, that this Ferment is supply'd from the Glands of
the Stomach.
And Lastly, Others, and perhaps with much better Reason, contend for
the Saliva, and make that to be the Ferment, which serves principally for the
Digestion of the Food; which in Mastication being mix'd with our Aliment,
is with that carried down into the Stomach, where the Parts of it being put
into motion by a kindly and agreeable Heat, they do ferment with, and
exagitate first those Parts of the Food which are most apt to ferment with it,
and then both conspire to break and dissolve the grosser and more stubborn
Parts. And Galen, in the Book I have before-mention'd, plainly allows that
the Saliva is concern'd in the business of Concoction, tho' he supposes the
Alteration, which is produc'd by this Juice, to be made in the Mouth, as
appears from these Words: Quæ (alteratio) in ore agitur mutat quidem id
(nutrimentum) in alteram speciem manifestè, non tamen ad perfectionem
transmutat--Qui mansi sunt cibi primum quidem hac Pituita (oris)
imbuunter, & cum ea miscentur----Itaque majorem mutationem consecuti
sunt, quam ii, qui in vacuis dentium intervallis fuere impacti.
Now I have given this short Account of the various Opinions of some
Ingenious Men, concerning the manner how Concoction is perform'd; I
come now to propose my own Hypothesis, by which I shall endeavour to
explain it.

In order to the more easie and effectual Digestion of the Food, Nature has
appointed some Parts for the breaking our Aliment, and reducing whatever
is gross into smaller Parts, before it is put upon Digestion: Others to supply
the Ferment, by which it is to be dissolv'd and concocted, and which, before
it comes to be included in the Stomach, does moisten, and make it more

soft, that it may more easily be penetrated, and broken by those Parts which
serve to divide every Morsel into smaller Pieces, and prevents the
Inconvenience and Trouble which would arise from the Nourishment
sticking about or between them, when it is dry or viscous.
For the breaking of that part of our Food, which is not liquid, Nature has
furnish'd us with Teeth, and those of two sorts: For some are ordain'd to
divide and break off smaller Morsels from a larger Mass; others are made
for the grinding those Morsels into much smaller parts. The Teeth, which
serve to break off Pieces of a convenient Magnitude from a larger Mass, are
of two sorts, accommodated to the Nature of the Substance which we eat.
These are the Incisores, and the Dentes Canini. If the Substance, which we
have to eat, be not hard, but more easily penetrated and divided, then the
Incisores are capable of making an Impression upon it, and fix'd firmly
enough in the Jaws to break off that part which they take hold of. But if it
be more solid, and not easily penetrated, nor any Piece without difficulty to
be separated from that Body, whereof it is a part; then we apply the Dentes
Canini, or Eye-Teeth, to it, which are not spread, nor have such an edge as
the Incisores, but are sharp and pointed like an Awl, and so do more readily
penetrate a Substance that is hard, and which the Incisores can scarcely
make any Impression upon. And as the Parts of a more solid Body are
commonly with more difficulty separated, and there must be a greater stress
put upon those Teeth which pull it into pieces; so these Teeth are much
more firmly fixed in the Jaws than the Incisores, tho' they have but one
single Root. Besides, the Position of all these Teeth is accommodated to
their use, as being planted opposite to the Aperture of the Mouth; so that
they may be conveniently apply'd to the Substance which we have to eat,
before it is broken, and when it is too large to be admitted within the
Mouth.
The Teeth which do by a Compression and Attrition reduce the little
Morsels to smaller Parts, are from the manner in which they break the
Aliment, called Dentes Molares, because they do, like so many Mill-stones,

grind the Food between them. And that they might be render'd fit for this
purpose, they are made broad at that Extremity, which stands out of the
Gums, by which means they retain some Quantity of the Food between
them every time the lower Jaw is pulled up and forc'd against the Maxilla
superior. And as they are broad, so they are formed with Inequalities and
Protuberances; and by the motion of the lower Jaw, from one side towards
the other, they grind what they have between them into pieces. The Position
of these Teeth too is as convenient as that of the Incisores, and the Dentes
Canini: For being design'd to break those pieces of our solid Food, which
are taken into the Mouth, and these pieces, when they are compress'd, and
mov'd by the Dentes Molares, being apt to fly out of the Mouth, if there
were no Contrivance to prevent it, they are placed beyond the Aperture of
the Mouth, and opposite to the Cheeks, which keep the Food within that
Cavity, and not only so, but press it in between the Dentes Molares on one
side, as the Tongue does on the other, until they have sufficiently broken
and divided it.
At the same time, whilst the Dentes Molares are breaking the Food, there
flows into the Mouth a Salival Juice, which mixes with it, and not only
serves to moisten it, and to render it more apt and easie to be divided, but
seems to be the Ferment, by the Benefit of which the Food is dissolved and
digested. And therefore it is intimately mixed with it, by the Teeth agitating
or stirring them together in Mastication.
This Liquor, which we commonly call the Saliva, or Spittle, seems to be
a Composition made of two several Juices, very different in their Nature:
And therefore the several Parts of it are separated by their proper Glands,
and Nature has planted no fewer than four Pair about the Mouth, which
supply the Juices that make the Saliva; to wit, the Parotides, and the
Glandulæ Nuckianæ, the Glandulæ Maxillares internæ, and Sublinguales.
Whereas if the Saliva were but one more simple Liquor, a less number of
Glands might have been sufficient. At least there appears no Reason why
one of every Pair should disembogue itself into the Mouth so very near to

the Orifice, by which a Gland of some other Pair throws in its Juice; and
they are not rather all planted at more equal distances from one another, so
to flow in upon every part of the Aliment at the same time.
Not that I suppose, as there are four Pair of salivatory Glands, so there
are four sorts of Juices supply'd from them, to make the Saliva; but, as I
hinted before, that there are only two different Juices that constitute it. And
these are not only sufficient, but more proper to excite and secure that
Fermentation, which is necessary to Concoction. For we find that most of
those Fermentations, which arise upon Mixtures made for Experiments, are
produced from the mixture of two things; and it is not so easie to find out
three or four such Liquors of a different Nature, as will, upon the mixtion of
them all, produce a Fermentation, and from the omission of any one of them
discover no Discord or Disposition to ferment: Besides, it is certain that two
do better secure the End, which Nature designs. For, if there were three or
four different Juices, of which the Saliva naturally consists, these must all
have their proper Qualities preserved to them, or else the Fermentation,
which should arise between them, will not necessarily follow upon their
mixture; and it is certain, that there would be more Danger, that one of three
or four should be deprived of its Natural Quality, than one of two.
What Nature these two Juices are of, I do not pretend positively to
determine; but so far as I have been able to make my Conjectures about it
from Experiments, I do think one of them to be an acid Juice; the other an
oleaginous Liquor, something like Oil of Turpentine. For amongst the many
Experiments I have made, there was no one that gave me so much
Satisfaction, as that which I made with Oil of Turpentine, and Oil of Vitriol,
though I try'd several other things, that will produce a Fermentation upon
their Mixture. And it was for this Reason, that I made the Experiment with
Oil of Turpentine and the other Oil.
I took a piece of raw Flesh, and having cut it into pieces, but much larger
than what our more solid Food is reduc'd to by due Mastication, I mix'd

some Crums of Bread with it, then I pour'd in the Oil of Turpentine to them,
and upon that the Oil of Vitriol; and having shak'd them together, I digested
them about four Hours in Balneo Mariæ, and then shaking them again in
the Glass, I found the Meat dissolv'd, and they all became a thickish Pulp. I
could not but take notice, that Oil of Camphire (though it does not
otherwise seem much different in its Nature from Oil of Turpentine) and Oil
of Vitriol, which upon mixture will produce an Effervescence as well as the
Oil of Turpentine and Oil of Vitriol, yet did not touch the Meat, upon which
I poured them, so as in the least to dissolve them. I cannot deny but that an
Acid, and a Solution of Salt of Tartar, did dissolve some part of the Flesh-
meat, which I mix'd them with, but yet neither so soon, nor so perfectly as
the two forementioned Oils. And I do the rather think one of those Juices,
which constitute the Saliva, to be of the Nature of Oil of Turpentine, than of
a fix'd Salt, because it will correct and temper even Oil of Vitriol, so as to
render it more tolerable to the Fibres of the Stomach. Not that I suppose the
acid part of the Saliva to come near to the Acidity of Oil of Vitriol. For
though, when they are mix'd, they will make a Liquor that may not be
injurious to the Stomach; yet the acid Juice, if it were so corrosive as Oil of
Vitriol, would certainly be injurious and painful to the Salivatory Ducts,
which convey it to the Mouth before it is mix'd with the oleaginous Liquor.
But I only say it is an Acid, and in some degree approaches to the Nature of
that Oil. And Nature, which can much better adapt several Causes for the
Production of such an Effect than Art, may attain her End by a more
temperate Acid; though, at the same time, we may be able to make some
probable and true Conjectures about the Nature of those Causes from
Experiments.
It being most reasonable to suppose, that there are but two sorts of Juices,
of a different Quality, that make the Saliva, I do conceive, that four of the
eight Salivatory Glands, or two Pair of the four, do supply one of these
Juices, and the other four Glands the other. And this seems to be a very
good Reason, why they are so planted, and the Orifice of their Ducts so

order'd, that the Juice, which is supply'd by one Gland, is discharg'd into the
Mouth, very near to the Orifice, by which the Juice of a different Nature is
transmitted from another, so that they must necessarily meet and mix
together. Thus the Glandulæ Nuckianæ, and Parotides, throw in two
different Juices by Orifices, which open into the Mouth very near to one
another; and the Glandulæ Maxillares internæ, and Sublinguales, do below
supply the same kind of Juices by Orifices, that open so near to one another
as to secure the mixture of the two different Juices.
These Glands, I say, do between them afford two divers sorts of Liquors,
of such a Nature as are apt to ferment upon their first Mixture, but perhaps
more considerably when they come to be digested by the Heat of the
Stomach. So that the Colluctation, or Fermentation, which attenuates and
concocts the Food in the Stomach, does not ordinarily arise between the
Aliment and the Saliva, but between the several Parts of the Saliva it self.
And indeed, if the Saliva did not consist of two Juices, whose Nature is in
such a manner different, as to render them apt to ferment upon their
mixture, it would be very hard to conceive how it should so readily and
indifferently serve for the Digestion of all Eatables; how it should ferment
with, and dissolve so great a variety of Things, not only of a different, but
of a contrary Nature; how it should ferment with Acids as well as Alkalies,
digest things that are cold, as well as hot or temperate; some things that are
salt, others that are insipid, bitter and sweet, mucilaginous, oily, &c. But if
we suppose, that the Fermentation, which serves for the Digestion of the
Food, arises from a peculiar difference in the Nature of two Juices, which
constitute the Saliva, it will be easie to give a rational Account of our
Concoction of innumerable things of a different Nature. And this seems to
be as effectual, and a more certain way to attenuate and dissolve the grosser
Parts of our Food, than if the Fermentation were made only between the
Saliva and the Aliment: Besides, the Saliva seems to discover a
Fermentation upon the mixture of its constituent Juices, even at those times
when we do not actually eat; for it is always attended with Bubbles, and a

Froth, when it has not been at all agitated in the Mouth, and many of those
Bubbles will remain for some considerable time after we have spit it out.
Nature therefore having appointed the Saliva for the digestion of the
Food, has taken care that it shall be thrown in upon the Aliment on every
side. Thus the Glandulæ Nuckianæ, and the Parotides, supply their Juices to
that part of the Food, which lies on the outside of the Gums, between the
Cheeks and the Teeth, and the Glandulæ Maxillares internæ, and
Sublinguales, do bestow their Liquor upon the Meat, which is within the
Teeth and Gums. Neither has she had a Regard only to that Supply, which is
due to all the parts of our Food, but likewise to the mixture of the two
different Juices of the Saliva, which is necessary to its Fermentation. And
therefore, as I have already observ'd, the Orifices of the Ducts, which
belong to one sort of Glands, are placed near the Aperture of a Duct, which
conveys a Juice from one of the other Glands. So the Ducts of the Glandulæ
Nuckianæ, and the Ductus Stenoniani, do on each side open into the Mouth,
near one another; and the salivatory Ducts of the Glandulæ Sublinguales,
and the Maxillares internæ, though they have distinct Orifices, empty
themselves under the same Papillæ, and the Juices, which are supply'd by
them, meet there, and flow into the Mouth together.
The several Parts of the Saliva being discharg'd into the Mouth in such a
manner as to meet and begin a Fermentation, the Saliva does, partly as it is
agitated, with the Food by the Teeth, and some other parts of the Mouth;
partly by its own Fluidity, insinuate it self into, and mixes with the Food,
and not only moistens and softens it, but excites the Fermentation, which is
to dissolve it. And when the Aliment is thus mix'd with the Saliva, which
serves to ferment the whole Mass, it is then to be convey'd into the
Stomach, that great digestive Vessel of the Body, where the Fermentation is
not only continued, but improved.
The Nourishment being convey'd into the Cavity of the Stomach, is there
kept for some time in a digestive Heat, all which time it is under a

Fermentation, produc'd by the different Parts or Juices of the Saliva, which
are mix'd with it; which Fermentation does first agitate the more tenuious or
subtil parts of the Food, and puts them into motion, and so with the
Fermentation of its own, and those Alimentary Parts, which it first
communicates a Motion to, improved by the Heat of the Stomach, the
Saliva must necessarily act upon the grosser Parts. For the intestine Motion,
which is excited in the Mass, does not give the Particles, which are
fermented, the same Tendency, but what is so various and confus'd, that
they must inevitably strike not only one against another, but against those
which are more gross, so as to attenuate them, sometimes by a Collision,
which strikes off smaller Particles from the larger Parts; sometimes by a
Compression, when the Particles which are in Motion, happen to strike
directly against any grosser Part, on every side of it, sometimes by a kind of
Explosion. For without doubt the Saliva, which is fluid, insinuates it self
into the Interstices of the more crass Parts of the Aliment, and whatever is
agitated and expanded in those Interstices, requiring a larger space for the
Freedom of its Motion, and offering a Violence to every thing that opposes
its Tendency, will, like Gun-powder included in a Shell, force its way out,
and tear to pieces that Matter, which does endeavour to confine it.
Thus the grosser Parts are broken and divided, until they are at last so far
attenuated as to mix more equally with the Fluid, and with them to make
one Pulp or Chylous Mass. And although I do not apprehend how the
Stomach should by its reciprocal Motions in Inspiration and Expiration, be
able to break and attenuate any Matter, that will not be softned and
dissolved by Agitation in a Liquid; yet it is certain that these Motions,
caused by the Diaphragm and Abdominal Muscles in Respiration, do make
those Parts, which are broken off, as they are dissolv'd, mix intimately with
the more Liquid; as the Meat which I digested with Oil of Turpentine, and
Oil of Vitriol, did by Agitation mix more equally with the Oils, and became
a Pulpament.

As the Juices, which constitute the Saliva, do ferment upon their mixture,
so it is probable, that from their Mixture and Fermentation there results
such a Tertium quid, as is apt to ferment with the Bile. And therefore, when
the Aliment has been under the Fermentation, excited by the Saliva, a
sufficient time, it is then thrown into the Duodenum, where it meets with
the bilious Juice, which flows into that Intestine from the Liver, from which
a new Fermentation seems to begin; and the Commotion of the Parts of the
Aliment being still continued, does carry on the Business of Digestion until
the Food is perfectly concocted: Though it is probable, that this new
Fermentation serves not only for the more perfect Digestion of the Food,
but likewise for the Separation of the Chyle from the feculent Parts.
Neither do I by a random Guess, and an ungrounded Conjecture, suppose
that from the Mixture and Fermentation of the two Juices, which constitute
the Saliva, there results a Matter, which is apt to ferment with the Bile. But
to me the Notion seem'd to be confirmed by an Experiment that I made. For
considering with my self, that the Bile is generally allow'd to have much of
a saponary Nature, I made a Solution of Soap in fair Water, and mix'd it
with the Oils of Turpentine and Vitriol first put together, and from their
Mixture I observ'd a very easie and gentle Fermentation, which continued
for a considerable time.

iscourse concerning some Influence of Respiration on the Motion of
the Heart, hitherto unobserved. By J. Drake, M. D. F. R. S.

HO' divers accurate Treatises of the Heart, and its Action, have been
T written by Learned Men of several Nations, especially by two of our
own Country; the Great Dr. Harvey, to whose happy Sagacity this
Nation owes the Glory of the Invention of the Circulation of the Blood; and
the incomparable Dr. Lower, to whom we are beholden for a compleat
Display of the Mechanical Structure of the Heart, and a most ingenious
Rationale of its Action. Yet there remain several Doubts and Difficulties

about it (in my Opinion) not sufficiently accounted for; towards the
resolving some of which, I shall offer what my own Thoughts have
suggested to me, and leave it to the Consideration of the Reader.
The Learned Dr. Lower (whose accurate Piece on this Argument will
insure his Reputation so long as Physical Knowledge shall last in esteem)
has so well accounted for the Systole, or Contraction of the Heart, from the
Mechanical Structure of it, that he seems almost to have exhausted the
Subject; and had he been as happy in discovering the true cause of the
Diastole, he had left little room for the Industry and Sagacity of others
about this Viscus.
But having judiciously and solidly explain'd the Systole, he contents
himself to ascribe the Diastole to a motion of Restitution, which account
gives me no Satisfaction: Because the Systole being the proper, and (as
himself confesses) the only motion of the Heart, a State of Contraction
seems to be the natural State, and consequently without External Violence,
it shou'd have no Diastole at all.
This will appear more plain, if we consider the Circumstances of it, and
its Motion, as a Muscle, with respect to other Muscles. That Contraction is
the proper Action, and State of all Muscles, is evident from Experience of
Fact, as well as Reason. For, if any Muscle be freed from the power of its
Antagonist, it is immediately contracted, and is not by any Action of the
Will, or Spirits, to be reduced to a State of Dilatation. Thus, if the Musculi
Flexores of any Joint be divided, the Extensores of that Joint being by that
means free'd from the contrary Action of their Antagonists, that Joint is
immediately extended without any consent of the Will, and in that State it
remains; and so Vice versa, if the Extensores be divided. From whence it is
plain, that the Muscles have no restitutive Motion, but what they derive
from the Action of their Antagonists, by which they are balanc'd. Thus
likewise the Sphincters of the Gula, Anus and Vesica, having no proper
Antagonists, are always in a State of Contraction, and suffer nothing to pass

them, but what is forced through them by the contrary Action of some
stronger Muscles, which, though not properly to be call'd Antagonists, yet
on all necessary Occasions perform the Office of such.
That the Heart is a Muscle, furnish'd and instructed for Motion like other
Muscles, is (in my Opinion at least) demonstrated beyond Contradiction by
Dr. Lower and others. And, as it is a Solitary Muscle without any proper
Antagonist, and not directly under the power of the Will, nor exercising
Voluntary Motion, it approaches nearest to the Sphincter kind, which only
has these Conditions in common with it. But in constant and regular
Alternations of Contraction and Dilatation, it differs exceedingly from all
the Muscles of the Body.
This reciprocal Æstus of the Heart has given the Learned abundance of
trouble; who, finding nothing peculiar in the Structure, which shou'd
necessarily occasion it, nor any Antagonist, whose re-action should produce
it, have been extreamly perplex'd to find out the cause of it.
But passing over the various Opinions of Authors, to avoid being tedious,
I shall take notice here only of the very Learned Dr. Lower's, in whose
Account of the Systole, however solid and ingenious, I observe something
deficient, and whose Hypothesis of the Diastole I think to be precarious and
false.
This Excellent Author, having by sound Arguments drawn from the
Structure and Mechanism of the Heart, establish'd the Certainty of its
Muscular Motion, rests satisfied, without taking notice of any Assistance,
that the Heart receives from any other Part, except from the Brain, by the
means of the eight pair of Nerves.

Part 2d.
The Accurate Borellus, in his Oeconomia Animalis, computes
Prop. 67. the Motive Power of the Machine of the Heart to be equal to, or
Prop. 73. to surmount that of a Weight of 3000l. The Obstacles to the
Prop. 76.
Motion of the Blood thro' the Arteries he esteems equivalent to
180,000l. which is 60 times as much as he rates the Force of the Heart at.
Then deducting 45,000l. for the adventitious Help of the Muscular Elastic
Coat of the Arteries, he leaves the Heart with a Force of 3,000l. to
overcome a resistance of 135,000l. that is, with 1, to remove 45.
This stupendous Effect he contents himself to ascribe to the Energy of
Percussion. But, had he proceeded in his Calculation to the Veins, which he
allows to contain constantly a quantity of Blood, quadruple to the Contents
of the Arteries, and to which this Energy of Percussion does either not reach
at all, or but very languidly, he might probably have seen a necessity for
some other Expedient to remove so insuperable a Difficulty.
But not to insist rigorously on the Exactness of this Calculation, (though
the great Abilities of the Author in this way, and his Ingenuity and Modesty,
are a sufficient Warrant for the Accuracy of his Computations, and the
Fidelity of his Accounts) we may allow a much greater Deduction, than
would be justifiable, without lessening the Difficulty. But this Account I
have taken notice of purely for the sake of the Calculation, which may be of
use in the Sequel; the account it self being in other respects more defective
than Dr. Lower's, to which we will return.
The Doctor, notwithstanding his great Sagacity, appears (to me) to have
overlook'd something of very great moment, and importance in the
explication of the Action of the Heart. For, tho' it should be granted, that the
Muscular Fibres of the Heart acted by the Nerves, are the immediate
Instruments of its Constriction or Systole, yet it must not be denied, that the
Intercostal Muscles and Diaphragm are of great service to aid and facilitate
this Contraction, by opening a Passage for the Blood through the Lungs,
which denied would be an invincible Obstacle.

Neither do they promote it that way only. The manner how they farther
assist the Heart in its Contraction, will appear manifestly, if we consider the
different Posture, Situation, and Capacity of the Blood-Vessels of the Lungs
in the several times of Elevation and Depression of the Costæ.
The Pulmonary Artery rises from the right Ventricle of the Heart, and
runs in one Trunk, till it comes to the Aspera Arteria, where it is divided,
and sends a Branch along with each Division of the Aspera Arteria,
according to all the minutest Subdivisions, of which it is likewise
subdivided, accompanying all the Bronchi, in their whole progress through
the Lungs.
The Pulmonary Vein, which empties itself into the Left Ventricle of the
Heart, spreads it self on the Aspera Arteria and Bronchi, in the same
manner that the Artery does.
The necessary confluence of this Disposition if, that this Artery and Vein
being co-extended with, and fasten'd to the Bronchi, must needs suffer such
alteration of Superficial Dimensions, as the Bronchi do in the Elevation or
Depression of the Costæ.
While the Ribs are in a State of Depression (whether before Commerce
with the External Air or after) the Annular Cartilages of the Bronchi shrink
one into another, and by that means their Dimensions are exceedingly
contracted. In conformity to this condition of the Bronchi, the Pulmonary
Artery and Vein must likewise, either by means of their Muscular Coats,
contract themselves to the same Dimensions, or lye in Folds or
Corrugations, which is less probable.
On the other hand, when the Ribs are elevated, and the Diaphragm bears
downward, the Air rushing into the Lungs, shoots out the Cartilaginous
Rings, and divaricates the Branches of the Trachea, and by them extends
and divaricates the several Divisions of the Pulmonary Artery and Veins,
and thereby lengthens and enlarges their Cavities.

This enlargement of their Cavities is very considerable, not only upon the
score of the addition, which they receive in length thereby, but also upon
the account of their Divarication. For whereas, when the Ribs are depress'd,
and the Lungs subside, the Blood-vessels are not only contracted, (as I have
already observ'd) but their Branches, which are exceeding numerous,
approach one another, and lie in juxta-position, by which their Cavities are
very much compress'd and streighten'd: When the Ribs are elevated, and the
Lungs turgid with Air, not only the Fibres, by which their Coats in the
opposite state were contracted, are extended; but those innumerable Vessels,
which lying before in lines almost parallel upon one another, compress'd
one another, making an acute Angle at their Junctures, are divaricated and
separated from each other, and make an obtuse, whereby their Channels are
widened.
Thus a passage is open'd to the Blood, from the Right Ventricle of the
Heart to the Left, through the Lungs, to which it could not otherwise pass;
and the opposition, which the Blood contain'd in that Ventricle, must
otherwise necessarily have made to its Constriction, is taken off, and the
Systole thereby facilitated.
Nor is that all. For the Diastole being caus'd (as I shall in the Sequel
shew) by the force of the Blood rushing into the Ventricles, this Ampliation
and Extension of the Pulmonary Artery is a sort of Check or Counterpoise
to it, and prevents an endeavour towards two contrary Actions at once,
which must necessarily frustrate both. For the Heart being a Springy,
Compressible Body, whose proper Action, which is Contraction, depends on
the influx of certain Fluids into its Fibers, or Substance; and containing
besides a Fluid in its Ventricles, or great Cavities, in one of which is the
Mouth of this Artery, the action of this Vessel must in great measure
resemble that of a Syringe, whose extremity is immers'd in Water, the
Enlargement or Expansion of the Chanels of the Artery answering the
drawing of the Embolum, as the constrictive motion of the Muscle of the
Heart does the pressure of the Atmosphere upon the Surface of the Water,

the one making way for the fluid, and the other forcing it to follow, where
the resistance is least. In this Sense we may allow a sort of Attraction to the
Pulmonary-Artery, depending wholly upon the Action of the Intercostal
Muscles and Diaphragm, which we must therefore confess to be very
serviceable and instrumental in promoting the Systole of the Heart.
But if the Learned Author be deficient in his Account of the Systole; that
is, if he has not observ'd all the Mechanism and Contrivance of Nature for
the Contraction of the Heart; much less sufficiently has he accounted for the
Diastole, or Dilatation of it, which he ascribes to a motion of Restitution of
the over-strain'd Fibres, which yet he confesses are made for Constriction
only. 'Tis true, he immediately after joins the Influx of the Blood as a
concurrent Cause; but from the slight notice that he takes of it, 'tis plain,
that he did not so much as dream of any great share it had in that Action.
His Words are these:

De Corde,
Quin & (ut obiter hoc moneam) omnis motus contractione
Pag. 75. perficiatur, & Cordis Fibræ ad constrictionem solum factæ sint,
apparet quoque Cordis motum totum in Systole positum esse;
cumque Fibræ ultra tonum suum in omni constrictione eius tendantur,
idcirco ubi nixus iste absolvitur, motu quasi restitutionis Cor iterum
relaxatur, & sanguine à Venis influente rursus distenditur; à nullo enim
cordis motu, nisi tensionem suam remittente, & ab irruente sanguine
Diastole ejus libratis adeo viribus succedit.
I have transcrib'd the intire Paragraph, because it contains his whole
Hypothesis of the Diastole, and all the notice that he takes of it through his
whole Work. But how slender soever this may prove, it is the most
substantial that I have any where met with, except a late one of Mr. Cowper,
which is properly an Improvement of this, and shall be consider'd in the
Sequel.
But if Contraction be the sole Action of these Fibres (as this Great Man
confesses it to be) and as indeed it is of all Muscular Fibres, I wonder how

so judicious a Writer came to slip into such an Absurdity, as to call their
Distention (vulgarly but improperly call'd Relaxation) a Motion of
Restitution. For from the Nature of those Fibres, and their disposition in the
Structure of the Heart, the natural State of the Heart appears manifestly to
be Tonical, and its Dilatation a State of Violence; and consequently, the
Constriction is the true motion of Restitution, and the State to which it will
spontaneously return, when the Force is taken off, which is the work of the
Intercostal Muscles and Diaphragm.
Thus we are left still to seek for the true Cause of the Diastole, which
seems to me to be the main and most difficult Phænomenon, relating to the
Heart and the Circulation of the Blood. But in Mr. Cowper's ingenious
Introduction to his Anatomy of Humane Bodies, I find the Share which Dr.
Lower hints the Blood to have in that Action, further prosecuted, and
improved into the main Instrument of the Dilatation of the Heart, wherein I
agree intirely with him. But as to the manner, and reasons of its being so
very instrumental, I can't be so perfectly of his mind.
The Heart (says this accurate Anatomist) of an Animal bears a great
Analogy to the Pendulums of those Artificial Automata, Clocks and
Watches, whilst its motion is performed like that of other Muscles, the Blood
doing the Office of a Pondus.
This Explication, being but a Simile without a distinct application to
Particulars, is beside so very short, that I can at best but give a conjecture at
the meaning; which if I mistake, I shall deserve to be excused, and expect to
be better inform'd.
By the Bloods doing the Office of a Pondus, I suppose he means, that the
Blood contributes in the same manner to the motion of the Heart, as the
Weights do to that of the Pendulum of a Clock. If so, the Blood, according
to him, must be the Instrument of Constriction; and Dilatation must be the
Natural State, or Spontaneous Motion, to which it wou'd, when under no

violence, return; the contrary of which, I presume, will appear e're I have
done.
But if he means, that the Blood in its reflux, by gravitating on the
Auricles and Ventricles, dilates and expands 'em, acting therein as a
Counterpoise to its contractions as a Muscle, I cou'd wish his Design had
not bound him up to so narrow a compass, and that he had given us an
explication at large of so abstruse and so important a Phænomenon:
Because the Specifick Gravity of the Blood seems to me a cause by no
means alone adequate to the effect, which it is here suppos'd to produce.
For, if the Blood acts only as a weight by meer gravitation, then that part
of it only which descends from the Parts above the Heart can be employ'd in
that Action. This at the largest computation can't amount to Five pound
weight, and must, according to the computation of Borellus, force a
Machine, that is able to overcome a resistance of 135,000l. I leave every
Man to deduct what he shall upon examination find reasonably to be
deducted, and yet shall rest secure, that it is not to be effected in the least
with so small a Weight.
But neither does the Refluent Blood gravitate in any such proportion, as I
have here assign'd. For to make a true estimate of its Gravitation, we must
consider the Circumstances of the Liquor suppos'd to gravitate; in which it
very much resembles Water inclos'd in a recurve Tube, of which, if the
length of the two Legs be equal, it may be suspended in the Air full of
Water, with the Extremities downwards, without losing a drop, although the
Diameter of those Legs should be very unequal. The Case of the Arteries
and Veins is pretty near a parallel to a Tube, so fill'd and inverted. For, if the
Arteries and Veins be continued Tubes, (as by the Microscope they are
made to appear) then supposing their contents to have no other
determination of motion, than their own weight wou'd give them, the
contain'd Fluids must be Counterpoises to each other. For the Veins and
Arteries being join'd at the smaller Extremities, and the larger of both

terminating in the same parallel Line, it is impossible, according to the
Laws of Hydrostaticks, that the contents of either shou'd overbalance
t'other. How far then must it fall short of forcing the natural Power and
Resistance of so strong a Muscle as the Heart, by meer Gravitation?
The Blood indeed has a Progressive Motion through its Vessels, wherein
it differs from Water, in a recurve Tube, in the Experiment above-stated.
But, if the natural Gravitation of the Blood contributes nothing to the
Dilatation of the Heart, this progressive Motion will not be found much
more sufficient. For, as this Motion is deriv'd intirely from the Heart's
Constriction (as all Accounts hitherto derive it) cou'd the Blood be suppos'd
to re-act upon it by the Heart, with all the force first impress'd upon it by the
Heart, it would be insufficient, unless we will suppose the Force
communicated to be superiour to the Power Communicant, which is absurd.
But when the just and necessary Deductions for the Impediments, which
the Blood meets with in its Progress through the Vessels, shall be made, the
remaining Force will be found so exceeding weak, that to prop the Blood
through the Veins may be a task alone too great for so small a Power,
without charging it with the additional difficulty of forcing the Muscle of
the Heart.
Alphonsus Borellus, after a great deal of solemn pains taken to shew his
Care and Exactness, and to possess his Reader of the Truth of his
Calculations, casts up the force of the Heart, and the Muscular Coat of the
Arteries, to be together equal to a weight of 3,750l. and allots them a
Resistance equal to 180,000l. to overcome which is 45 to 1. To make up for
a disproportion, by his own confession, incredible to those who have not
consider'd the Matter as he had done, he flings into the Scale the additional
Force of Percussion, which he leaves indefinite, and thinks sufficient to
force any quiescent finite Resistance whatsoever.
But as this Account and Hypothesis are part of a Posthumous Work (if a
liberty of Conjecture may be allow'd in so uncertain a Matter,) I shou'd

suspect, that these Papers were left unfinish'd by Borellus; or at least, that in
many places the last Hand was never put to them. For neither in this Place,
nor any other of this Work, does he account for any more than the Systole of
the Heart, and the resistance which is made to the progressive motion of the
Blood in the Arteries only. This alone he found to exceed the Power of the
Heart so prodigiously, that he seems to shuffle it off his Hands with a
general and precarious Solution, as a difficulty that he was desirous to be
rid of. For, having ascrib'd this stupendous (as he himself calls it) effect to
the Energy of Percussion, he takes no care to satisfie his Reader any farther
about it, or to refer him, or give him the expectation of Satisfaction any
where else; although he has an express Treatise on the Force of Percussion,
which was written preparatory to this, and to which he frequently refers in
other Places of this Work. But what confirms my suspicion, that this part
was intended for a farther Revise by the Author, is, that he has left the
Progress of the Blood through the Veins, and the Diastole of the Heart,
absolutely untouch'd, tho' they are Difficulties of a much greater magnitude
than this, which he has attempted to account so slightly for: For, in these he
is excluded the benefit of Percussion, and has yet a greater resistance to
overcome without it. Omissions of this kind are so unusual with this Author,
where-ever he knows himself to go upon sure grounds, that it is to me an
Argument, that he doubted the sufficience of his Percussion, and reserv'd
these important Phænomena for farther Consideration, without plunging
himself into such an Absurdity, as to ascribe to Percussion any such Energy
as to be able (so broken as it returns to the Heart) by its re-action to force
that Power, from whence only it was at first deriv'd.
Dr. Lower, and Mr. Cowper, deliver their Opinions of the Cause of the
Dilatation of the Heart so very short, and without any Arguments to support
them, that by exposing them naked, they seem rather to discourse of it
transiently, as Men oblig'd by the Nature of their Subjects to say something
of it, than solicitous to give any full or satisfactory Account; and therefore I
shall proceed no farther upon them here.

But though the Hypothesis of Borellus may, in this Case, be found
precarious or insufficient (a Misfortune that has befallen him in divers other
Particulars) his Theory holds still good. At least it ought to be allow'd, in
justice to his great Abilities and Exactness, till some Body convicts him of
some material Error in his Calculations, which has not as yet been done by
any Body, that I know of.
Supposing then the force of the Heart, and of the Muscular Coat of the
Arteries, as likewise of the resistance, which they must overcome, to be
computed with any degree of accuracy, there remains yet such a prodigious
disproportion to be accounted for, as requires some more powerful Agent,
than any yet assign'd, to make up the deficiency.
What assistance the Heart receives from the action of the Thorax towards
the facilitating its Contraction, without which assistance there cou'd have
been no Systole, has been already shewn. But neither the Intercostal
Muscles, or Diaphragm, which are so instrumental in that part of its action,
can contribute any thing to the Diastole; because they serve only to enlarge
the Cavity of the Thorax, and thereby to open a passage to the Blood from
the Heart, and promote its Constriction.
Whatever therefore the force is, that dilates the Heart, and is the cause of
the Diastole, it must be equal to that of the Heart, the Intercostal Muscles
and Diaphragm; to all which it acts as an Antagonist. I take no notice of the
Serratus Major Anticus, and other Muscles; which have an obscure share in
the Elevation of the Costæ, because as much may reasonably be deducted
upon the account of the Obliquus externus Abdominis, and other Muscles;
which having their Insertions on some of the lower Ribs are as instrumental
towards the Depression of them, and so balance the Account. But the chief
use of these is in violent Respiration: In ordinary Respiration their share is
small.
Such a real Power (which may in the least be suspected of any share in
this Action) is hard, perhaps impossible to be found in the Machine of any

Animal Body; and yet without some such Antagonist, it is as impossible the
Circulation of the Blood should be maintain'd. All the Engines yet
discover'd within the Body, conspire towards the Constriction of the Heart,
which is the State of Quiescence, to which it naturally tends. Yet we find it
alternately in a State of Violence, that is, of Dilatation; and this upon
necessity, because upon this Alternation depends all Animal Life.
Some sufficient Cause External must therefore be found, to produce this
great Phænomenon; which Cause must be either in the Air, or Atmosphere,
because we have no constant and immediate Commerce with any other
Mediums.
Some great Physicians observing this, and that depriv'd by whatsoever
means of Communication with the external Air, we became instantly
extinct, have imagin'd, that in the Act of Inspiration certain purer parts of
the Air, mixed with the Blood in the Lungs, and was convey'd with it to the
Heart, where it nourish'd a sort of Vital Flame, which was the Cause of this
reciprocal Æstus of the Heart. Others not quite so gross, rejecting an Actual
Flame, have fancied, that these fine Parts of Air mixing with the Blood in
the Ventricles of the Heart, produc'd an Effervescence which dilated it. But
these Fancies have been long since exploded and condemn'd upon ample
Conviction; and 'tis a Point yet undetermin'd, whether any Air does mix
with the Blood at all in the Lungs, or not.
But supposing, that some Air may insinuate it self into the Pulmonary
Vein, it can no other way dilate the Heart than by an Effervescence in the
Left Ventricle, which wou'd not dilate the Right. But this Opinion is
contradicted by Autopsie, and too laboriously confuted by others, to be
brought upon the Stage again here.
There remains therefore only the gross Body of the Atmosphere to be
considered, which is undoubtedly the true Antagonist to all those Muscles,
which serve for ordinary Inspiration, and the Constriction of the Heart. This
will appear more evidently, if we consider not only the Power, but the

Necessity of its Action upon Animal Bodies, as well as the want of other
sufficient Agents.
The Heart is a Solitary Muscle of very great strength, and the Intercostal
Muscles and Diaphragm, which likewise have no Antagonists, are a vast
additional Force, which must be balanc'd by the contrary Action of some
equivalent Power or other. For, tho' the Action of the Intercostal Muscles be
voluntary, that does not exempt them from the condition of all other
Muscles serving for voluntary motion, which wou'd be in a State of
perpetual Contraction, notwithstanding any Influence of the Will, were it
not for the Libration of Antagonist Muscles. This Libration between other
Muscles, is answer'd by the Weight of the incumbent Atmosphere, which
presses upon the Thorax and other parts of the Body. And, as in all other
voluntary Motions the influence of the Will only gives a prevalence to one
of its two Powers before equilibrated, so here it serves to enable those
Muscles to lift up a weight too ponderous for their strength not so assisted;
and therefore as soon as that assistance is withdrawn, the Costæ are again
depress'd by the meer Gravitation of the Atmosphere, which wou'd
otherwise remain elevated through the natural Tendency of those Muscles to
Contraction.
This is evidently prov'd from the Torricellian Experiments, and those
made upon Animals in Mr. Boyle's Engine; where, as soon as the Air is
withdrawn, and the pressure thereby taken off, the Intercostal Muscles and
Diaphragm are contracted, and the Ribs elevated in an instant, and can't by
any Power of the Will be made to subside, till the Air is again let in to bear
them forcibly down.
It were scarce worth while to take notice here of a Mistake of the
Learned Dr. Willis, were it not for the great Authority of the Man, which is
De Respirationis
almost sufficient to keep Error in countenance. The Doctor
Organis & Usu. having observ'd, that the Fibres of the External and Internal
Intercostal Muscles ran in a contrary order, as it were,

decussating each other, takes occasion from thence to fansie, that there was
an opposition in their Office; and that as the External serv'd to raise up the
Ribs, the Internal drew them down again, forgetting at that time, That,
when a contractile Body is fasten'd at the several ends to Points unequally
moveable, let the Contraction happen in what part or manner soever, the
more moveable Point must be drawn towards the less moveable: By which
Rule, whether External or Internal Intercostals be contracted, the lower
Ribs will be forc'd to approach the upper, that is, be rais'd up.
As in the Elevation of the Costæ, the Blood, by the passage that is open'd
for it, is in a manner solicited into the Lungs; so in the Depression of them,
by the subsidence of the Lungs, and the Contraction of the Blood-Vessels,
both which are consequent thereof, the Blood is forcibly driven, as it were
with an Embolum, through the Pulmonary Vein into the Left Ventricle of the
Heart. And this, together with the general Compression of the Body by the
weight of the Atmosphere, which surrounds and presses upon the whole
Surface of it, is that Power which causes the Blood to mount in the Veins,
after the force impress'd upon it by the Heart is broken and spent, and which
is sufficient to force the Heart from its natural State to Dilatation.
He that is able to compute the weight of a Column of Air, equal to the
Surface of the whole Body, will readily grant it a power sufficient for the
Effects, which are here ascrib'd to it. And when he considers, that the
Bodies of Animals are compressible Machines, he will find that it must of
necessity affect them in the manner here laid down. But though our Bodies
be entirely compos'd of Tubuli, or Vessels fill'd with Fluids; yet this
pressure, how great soever, being equal, cou'd have no effect upon them, if
the superficial Dimensions were not easily variable; because being
compress'd on all parts with the same degree of Force, the contain'd Fluids
cou'd not any where begin to recede, and make way for the rest to follow,
but wou'd remain as fix'd and immoveable as if they were actually solid.
But by the Dilatation of the Thorax, room is made for the Fluids to move,

and by the Coarctation of it, fresh motion is imprest, which is the main
Spring whereby the Circulation is set and kept going.
This reciprocal Dilatation and Contraction of the superficial Dimensions
of the Body, seems so necessary to Animal Life, that there is not any
Animal so imperfect as to want it, at least none to the inward Structure, of
which our Anatomical Discoveries have yet reach'd. For, tho' most kinds of
Fish and Insects, want both moveable Ribs and Lungs, and consequently
have no dilatable Thorax, yet that want is made up to 'em by an Analogous
Mechanism, answering sufficiently the Necessities of their Life.
Those Fishes which have no Lungs, have Gills, which do the Office of
Lungs, receiving and expelling alternately the Water, whereby the Blood-
Vessels suffer the same alteration of Dimensions, that they do in the Lungs
of more perfect Animals.
The Lungs or Air-Vessels of Insects, are yet exceedingly more different in
Structure, Distribution, and Situation from those of perfect Animals, than
those of Fishes are, and yet in their Use and Action agree perfectly with
both; that is, receiving and expelling the Air, and varying the Dimensions
and Capacities of the Blood-Vessels. These having no Thorax, or separate
Cavity for the Heart and Air-Vessels, have the latter distributed through the
whole Trunk of their Bodies, by which they communicate with the External
Air through several Spiracula or Vent-holes, to which are fasten'd so many
little Tracheæ, or Wind-pipes, which thence send their Branches to all the
Muscles and Viscera, and seem to accompany the Blood-Vessels all over the
Body, as they do in the Lungs only of perfect Animals. By this disposition
in every Inspiration, the whole Body of these little Animals is inflated, and
in every Expiration compress'd; and consequently the Blood-Vessels must
suffer a Vicissitude of Extension and Contraction, and a greater motion must
thereby be impress'd upon the Fluids contain'd in them, than the Heart,
which does not in those Creatures appear to be Muscular, seems capable of
giving.

The only Animal that is exempted from this necessary condition of
Breathing, or receiving and expelling alternately some Fluid into and out of
the Body, is a Fœtus. But this, while included in the Womb, has little more
than a vegetative Life, and ought scarce to be reckon'd among the number
of Animals. For, were it not for that small share of Muscular Motion, which
it exercises in the Womb, it might without absurdity be accounted for as a
Graft upon, or Branch of the Mother.
Concerning the immediate Matter, and Means of Life, and Nutrition,
Authors are not agreed, nor is it the business of this place to reconcile, or
decide their Differences, but to account for the Motion of the Blood through
the Vessels only. In order to this, it will be necessary to observe, that the
Pulsation of the Heart in a Fœtus is so very weak and obscure, and the
Motion of the Blood so extream slow and languid, as to be scarce, if at all
perceivable, as has been experienced in the Dissection of Puppies before
Boyle of the
Respiration had. To produce such a feeble Palpitation,
Elasticity of Air. and creeping Motion, no greater force seems to be
Pechlinus de Aeris required, than may be deriv'd from the Communication
& Alimenti defectu.
between the Vessels of the Mother and Fœtus in the
Placenta. I am not ignorant, that divers very Learned Anatomists (whom the
Crowd have implicitly follow'd) have absolutely rejected all
Communication between these Vessels. But, with submission to Great
Authorities, I think they have acted arbitrarily, and without sufficient
Warrant from Reason or Experiment: For neither are the Arguments which
they bring against it conclusive, nor the Office which they assign to the
Umbilical Vessels in lieu of it, proper, or natural to those Vessels, or the
reality of the Fact made out by any substantial Reasons. Those that reject
this Communication usually do it in favour of one or both of these
Opinions, that the Arteries of the Uterus do deposite a Nutritive Juice, or a
Juice impregnate with Air in the Placenta, which is suck'd in by the
Umbilical Vein, and convey'd to the Fœtus, for the necessary Uses of
Nutrition and Life. Now those that patronize either of these Opinions, lead

Nature an unnecessary Dance. For if the Maternal Blood does really
contain any such Nutritious, or any such necessary Aerial Particles, why
shou'd they be separated and extravasated, to be with difficulty receiv'd into
the Umbilical Vein, and again mixt with the Blood, when they might more
easily have been imparted by the plain simple way of Transfusion from the
Arteries of the Mother to the Veins of the Fœtus. And, that this is the course
which Nature takes in this Case, I am perswaded from the easiness and
simplicity of the Method, which readily performs what might be perhaps in
vain expected from the other, and wou'd over and above find them, what
they seem to grope so blindly about for, a first Mover of the Blood in a
Fœtus.
Those that contend for the conveyance of the Nutricious Juice, through
the Umbilical Vein from the Placenta, are forc'd upon two Difficulties next
to Absurdities. For first they are oblig'd to make this Vein, which, as all
other Veins, seems dedicated to the Re-conveyance of Blood only, the
proper and immediate Chanel, thro' which a very different Liquour is to be
carried; and next, to give a Power of Attraction or Suction to it; because the
Nutricious Juice, which it is thus destin'd to carry, is both viscous and
stagnant, and has neither force to drive, nor subtilty to penetrate, or
insinuate it self into the Capillary Veins; and therefore must be drawn or
suck'd as Milk is from the Breast, to which the Placenta and its Nutricious
Juice are by the Favourers of them expresly compar'd. But if this were the
sole use of the Placenta, and Umbilical Vessels, why were the Umbilical
Arteries sent along with the Vein? Their business is not to bring any thing
back to the Fœtus, nor can they contribute any thing to the benefit of the
Mother; for the Uterine Arteries bring all to the Placenta, the Umbilical
Vein carries it to the Fœtus, and the Uterine Veins convey back again the
Surcharge of the Mother's Blood; the Umbilical Arteries only, have nothing
to do, and are superfluous and impertinent, which is contrary to the constant
Practice of Nature. Yet if Autopsie did in the least countenance this
Hypothesis, some Defence might still be made; but we find in the Umbilical

Vein of a Fœtus nothing but Florid Blood, such as in all probability it
received immediately from the Arteries of the Mother without any mixture.
And therefore I can't help concluding, that this Opinion engages its
Favourers in some Absurdity, without Necessity and without Proof.
They that from the Placenta supply the Body of the Fœtus with Air, are
as much distress'd as t'other; for they are forc'd to beg the Question twice,
which, even when granted, will not answer their Ends. First, they suppose,
that an intimate mixture or confusion of Air with the Blood, is necessary for
the support of Animal Life, a Postulatum, which perhaps the former part of
this Discourse may have render'd unnecessary; and next, that the Fœtus is
supply'd with Air from, and its Blood mix'd with it in the Placenta.
But here again they fetch a Compass without necessity or proof. For if a
mixture of Air were necessary to a Fœtus, why should it be separated from
the Mother's Blood, and not rather both communicated together, since it is
so much more easie and commodious? But neither does the Placenta seem
to be instructed and provided for the separation of Air, but of a much
grosser Fluid, destin'd to some other use, which Autopsie confirms: Yet,
were both these Opinions true, they are however defective, and the Circular
Motion of the Blood unprovided for.
By the way of Transfusion, this great Phænomenon is naturally accounted
for, and the Ends, for which the other two Hypotheses were devis'd, might
both be answer'd with more ease. For the Hysterick Arteries transmitting
their Blood immediately to the Umbilical Vein, may very easily transmit
such Nutricious Juices or Aerìal Particles, as are contain'd in the Blood,
along with it, without depositing them by the way. By this means so much
of the Impulse of the Mother's Blood is preserv'd, as suffices to maintain
that languid Circulation which a Fœtus enjoys. For the Blood being driven
through the Arteries of the Uterus into the Umbilical Vein, is convey'd
directly to the Sinus of the Porta, and thence by a short and direct Passage
through the Cava to the Heart; where passing through the Foramen Ovale

to the Left Ventricle, and through the Canalis Arteriosus from the Right and
Pulmonary Artery, it is all deliver'd without coming at the Lungs to the
Aorta, and from thence again by the Umbilical Arteries to the Veins of the
Uterus, making a sort of Epicycle to the main Circulation in the Mother.
As this Opinion is Favour'd by the Structure and Disposition of the
Blood-Vessels on both Parts, so there is nothing in it difficult to be
conceiv'd, or repugnant to Experience. Late Discoveries have made it
appear, that the Arteries and Veins are continu'd Tubes, and that the latter
contain nothing but what they receive from the former, and no Reason
appears why we shou'd think this Method to be varied in the Placenta. On
the other hand, if the Arteries of the Uterus were continued to the Veins of
the same part, and those of the Fœtus in like manner, without
communicating with each other, their Confluence in the Placenta seems to
be altogether impertinent, and of no use, and the Umbilical Arteries and
Vein fram'd for no other Service or Purpose, than to give the Blood room
for an idle Sally.
Thus the Reasonableness of this old Opinion may be vindicated, but the
Certainty of it rests upon stronger Proof. Mr. Cowper, to whose happy
Industry we owe the Confirmation of many ancient Discoveries, and the
Benefit of some new ones, has the Honour to re-establish this old, but long
exploded Truth. For by pouring Mercury into a Branch of the Uterine
Arterie of a Cow, that went into one of the Cotyledones of the Uterus, he
fill'd those Branches of the Umbilical Veins, which went from that
Cotyledon to the Navel of the Fœtus; which, with a part of the Uterus, he
keeps prepared by him.
It would be a weak Objection, to alledge, That the Observation and
Experiment being made on the Uterus of a Cow, the Inference would not
hold from thence to a Woman, the one being Glanduliferous, and the other
Placentiferous; since every one of these Cotyledones, or Uterine Glandules,
is in all respects a little Placenta, and all the difference between them is in

number, name, and magnitude. Why Ruminants differ in this Particular
from other Viviparous Animals, is beside the Subject of our present Enquiry.
But the great Flux of Blood, which constantly follows upon drawing the
Placenta from Women (which is frequently so great as to cost them their
Lives) is as plain a demonstration to Reason of the Continuity of the
Vessels, as Mr. Cowper's Experiments is to the Eye.
I have heard it objected by very Learned Men, that if there were such a
Continuity of Vessels, and such Transfusion of Blood, the Fœtus must
necessarily perish through loss of Blood, upon the separation of the
Placenta from the Uterus; but that, on the contrary, no visible Flux of Blood
does follow while the Fœtus continues wrapt in the Membrane, in which
Condition it may be kept alive some Hours. To this it may be answer'd, that
the Circulation in the Fœtus, being deriv'd from the Mother, may be
suppos'd wholly to cease upon the cutting off the Communication between
them, till it is again renew'd more forcibly by Respiration. But if we allow
the motion already impress'd upon the Blood to be sufficient to keep it
going a little while; yet it must needs be so exceeding languid, that the meer
resistance of the External Air must be more than enough to hinder any
Efflux of Blood from a Fœtus before Respiration. How long Life may be
preserv'd without an actual Circulation of the Blood, is a Question not of
this place. But we have been convinc'd by many and notorious Observations
and Experiments, that Life has been recover'd a long time after all tokens of
Respiration, Circulation, or even Life it self, have disappear'd; so that we
can't think the first Solution either impossible or improbable.
I expect to be told, that in the early Days of Gestation in Viviparous
Animals, there is no Placenta, or any Adhesion of the Umbilical Vessels to
any part of the Mother, and consequently no such Transfusion; and that in
Oviparous there is no continuity, or communication of Vessels of any kind,
during the whole time of Incubation.

But these Objections carry neither the Weight nor Difficulty along with
them, that they may be suppos'd to do; for in those Days there is neither
Blood or Blood-Vessels, and consequently there can be no Circulation of the
Blood; and the Embryo, of what Species soever, is no more than a Vegetable
at that time; nor does the Fœtus of any Viviparous Creature enjoy any
Circulation, or shew any signs of Animal Life, till after those Vessels, as
well as others requisite to the Circulation, are compleated.
It must be confess'd, that Oviparous Animals are denied the benefit of
this Communication; but that want is sufficiently compensated by a peculiar
Mechanism, which directly answers the ends of Respiration, and the
pressure of the Atmosphere upon the Fœtus. There is at the obtuse end of an
Egg a small Cavity fill'd with Air, which is the succedaneous Instrument to
the Respiratory Organs. For as soon as the Contents begin to be warm'd by
the Incubation of the Hen, or any analogous Heat of Furnace or Dunghill,
the several Humours of the Egg require a fermentative motion, and the Air
contain'd in the Cavity or Vesicle, at the obtuse end of the Egg, is rarefied,
and the Vesicle extended and enlarg'd, and consequently the other Contents
are comprest; to which the fermentative motion naturally resists. But both
Bodies being as well compressible as dilatable, and both having an
expansive motion imprest upon them by Incubation, the Compression and
Renitency will be mutual, but varied in degree, according as either, through
the variation of Circumstances, shall prevail. By this means, an Alternation
of Compression and Dilatation will be produc'd in both, answering the
respiratory motion, by which a motion will be communicated, which, as
soon as the Organs by which it should be regulated are compleated, will in
the Body of the Pullus be regular and circulatory.
Fabricius ab Aquapendente, and after him, our Great Dr. Harvey, have
assign'd divers Uses to this Cavity or Air Vesicle, the Extravagance of
which have perhaps deterr'd others from enquiring so much into the Use, as
the Importance of it requir'd. But though I can't agree to that Perspiration,
Refrigeration, and Respiration, which they make it the Instrument of; yet

perhaps the Air, that was inclos'd in that Cavity, may through the
Augmentation of the Body of the Pullus, and its own Rarefaction (which is
at last so great as to occupy half the Shell) break the Membrane, which
separated it from the Pullus, and thereby give so much Respiration as to
form the chirping Voice, which is often heard before the breaking of the
Shell, and with it give an addition of Strength to enable it to break the Shell.
But how it should respire sooner, is to me inconceivable.
There are many Problems of great seeming Difficulty, the Solutions of
which flow naturally from what has been laid down here: But intending to
prosecute this Subject farther, and to treat of the Impediments of
Respiration, and the Consequences of Respiration obstructed or intermitted,
I shall reserve them for that Opportunity, and content my self here to
attempt the Harveyan Problem only, which has given abundance of Authors
so much perplexity.
That incomparable Philosopher enquires, Why a Fœtus, taken out of the
Uterus with the Membranes intire, shall live in Water some Hours without
communication with the External Air; whereas if it be taken out and suffer'd
once to breath, it can't afterwards survive a Moment without the benefit of
Respiration.
Granting the Fact to be as he has deliver'd it, which yet is not so in all
Cases, the main Difficulty is grounded on a Mistake, which from the stating
of the Question I find this Great Man to have slipt into. For he thinks, that a
Fœtus is sooner suffocated after having once breath'd, than if it had not
breath'd at all, and that by breathing it had contracted something which
render'd it more perishable. Idem tamen secundis exutus, (says he) si semel
aerem intra Pulmones attraxerit, postea ne momentum quidem temporis
absque eo durare possit, sed confestim moriatur. And presently after,
Siquidem constat, fœtum, postquam eum semel hauserit, citius suffocari;
quam cum ab illo prorsus accebatur. The Doctor observing a Fœtus to live
longer without Respiration, and to dispence better with the want of Air

while included in the Membranes intire, than it cou'd afterwards; infers
thence, that the Air does in the first Act of Inspiration impress upon the
Lungs some quality, which renders it ever after more indispensably
necessary. But allowing his Observation, I must yet deny his Inference to be
good: For deprive a Fœtus of means of respiring, and then take it out of the
Membranes, and it shall be as soon suffocated, as if it had respired before.
This proves, that this necessity of intercourse with the Air, by way of the
Lungs, is not the Offspring, but the Parent of Respiration, and that, that
Learned Man was drawn into a Fallacy of Non causa pro causa.
The Reason of this Necessity is the pressure of the External Air upon the
Surface of the Body, from which it was defended by the Interposition of the
Membranes, and the Humours contain'd, which are not so compressible as
the Body of the Fœtus it self. So soon therefore as the Fœtus is excluded,
and expos'd to the immediate contact of the ambient Atmosphere, the
Vessels and all the Cavities of the Body must necessarily be so compress'd,
that the Fluids can't have room for motion, and consequently the Fœtus
could have no Life, if Nature had not contriv'd by the motion of the Thorax
to remove and admit that pressure alternately, and thereby to impress a
motion on the Fluids, which is the Spring of Life. But this motion of the
Thorax being any way suppress'd, the equal pressure of the Atmosphere on
all parts, occasions a total Cessation of motion, which is Death.
I shall prosecute this Subject no farther now, nor trouble the Reader with
any Apology, for dissenting from those Great Men herein named; because, I
hope, I have done it with Modesty, and all the Respect due to so great
Authorities, and have assign'd nothing which is not Matter of Fact
uncontroverted, or deduc'd from it by plain Mechanical Necessity.

e Thoughts and Experiments concerning Vegetation. By John
Woodward, M. D. of the College of Physicians, and R. S. and
Professor of Physick in Gresham College.

HE Ancients generally intitled the Earth to the Production of the
T Animals, Vegetables, and other Bodies upon and about it; and that for
that Reason 'twas, that they gave it so frequently the Epithets of Parent
and Mother[1]. They were of opinion, that it furnished forth the Matter
whereof those Bodies consist; and receiv'd it all back again at their
Dissolution for the Composure of others. Even those who asserted four
Elements, supposed that the Earth was the Matter that constituted those
Bodies; and that Water and the rest, serv'd only for the Conveyance and
Distribution of that Matter, in order to the forming and composition of
them. 'Tis true, Thales, a Philosopher of the first Rank in those early Ages,
has been thought to have Sentiments very different from these; but that
without just Grounds, as I think I have sufficiently prov'd in another Paper,
which I am ready to produce.
But though Antiquity thus gave its Vote for Terrestrial Matter, several of
the Moderns, and some of very great Name too, both here and abroad, have
gone quite counter, and given theirs in behalf of Water. The Dignity of the
Persons that have espoused it, as well as their Numbers, renders this
Doctrine very considerable, and well worth our enquiring into. The great
Restorer of Philosophy in this last Age, my Lord Bacon, is of Opinion, That
for Nourishment of Vegetables, the Water is almost all in all; and that the
Earth doth but keep the Plant upright, and save it from over-heat, and over-
cold[2]. Others there are who are still more express; and assert Water to be
the only Principle or Ingredient of all Natural Things. They suppose that, I
cannot tell by what Process of Nature, Water is transmuted into Stones, into
Plants, and in brief, all other Substances whatever. Helmont,[3] particularly,
and his Followers, are very positive in this; and offer some Experiments to
render it credible. Nay, a very Extraordinary Person of our own Nation[4]
tries those Experiments over again; and discovers a great Propensity to the
same Thoughts and Opinion they had; declaring for this Transmutation of
Water into Plants and other Bodies, though with great Modesty and
Deference, which was his usual manner.

The Experiments they insist upon are chiefly two; the first is, that Mint,
and several other Plants prosper and thrive very greatly in Water. The other
is this; they take a certain quantity of Earth, and bake it in an Oven; then
they weigh it, and put it into an Earthen Pot. Having well water'd this
Earth, they make choice of some fit Plant, which, being first carefully
weigh'd, they set in it. There they let it grow, continuing to water it for some
time, till 'tis much advanced in bigness: Then they take it up; and though the
Bulk and Weight of the Plant be much greater than when first set, yet upon
baking the Earth, and weighing it, as at first, they find it little or not at all
diminished in weight; and therefore conclude, 'tis not the Earth but Water,
that nourishes and is turn'd into the Substance of the Plant.
I must confess I cannot see how this Experiment can ever be made with
the nicety and justness that is requisite, in order to build upon it so much as
these Gentlemen do. 'Tis hard to weigh Earth in that quantity, or Plants of
the size of those they mention, with any great exactness; or to bake the
Earth with that accuracy, as to reduce it twice to just the same Driness. But
I may wave all this; for though the Experiment be never so easily
practicable, and all the Accidents of it exactly as they set forth, yet nothing
like what they infer can possibly be concluded from it; unless Water, which
they so plentifully bestow upon the Plant in this Experiment, be pure,
homogeneous, and not charged with any terrestrial Mixture; for if it be, the
Plant after all may owe its Growth and Encrease intirely to that.
Some Waters are indeed so very clear and transparent, that one would
not easily suspect any terrestrial Matter were latent in them; but they may
be highly saturated with such Matter, though the Eye be not presently able
to descry or discern it. 'Tis true, Earth is an Opake Body; but it may be so
far dissolved, reduced to so extreme small Particles, and these so diffused
through the watry Mass, as not sensibly to impede Vision, or render the
Water much the less diaphanous. Silver is an Opake, and indeed a very
dense Body; and yet, if perfectly dissolved in Spirit of Nitre, or Aqua Fortis,
that is rectified and thorowly fine, it does not darken the Menstruum, or

render it less pellucid than before[5]. And other Instances there are, that
oftentimes great quantities of Opake Matter are sustain'd in Fluids, without
considerably striking the Eye, or being perceiv'd by it. So that were there
Water any where found so pure, that the quickest Eye could discover in it
no terrestrial Intermixture; that would be far short of a Proof, that in reality
there was none.
But after all, even the clearest Water is very far from being pure and
wholly defecate, in any part of the World that I can learn. For ours here, I
have had an Opportunity of examining it over a good part of England; and
cannot say I ever met with any, that, however fresh and newly taken out of
the Spring, did not exhibit, even to the naked Eye, great numbers of
exceeding small terrestrial Particles disseminated through all parts of it.
Thicker and crasser Water exhibits them in still greater Plenty.
These are of two general kinds. The one a vegetable terrestrial Matter,
consisting of very different Corpuscles; some whereof are proper for the
formation and increment of one sort of Plant, and some of another; as also
some for the Nourishment of one part of the same Plant, and some of
another. The other kind of Particles sustain'd in Water are of a Mineral
Nature. These likewise are of different sorts. In some Springs we find
common Salt, in others Vitriol, in others Alum, Nitre, Sparr, Ochre, &c. nay,
frequently several of these, or other Minerals, all in the same Spring; the
Water as it drains and passes thorough the Strata of Stone, Earth, and the
like, taking up and bearing along such loose Mineral Corpuscles, as it meets
with in the Pores and Interstices of those Strata, and bringing them on with
it quite to the Spring. All Water whatever is much charg'd with the
Vegetable Matter, this being fine, light, and easily moveable. For the
Mineral, the Water of Springs contains more of it than that of Rivers,
especially when at distance from their Sources; and that of Rivers more
than the Water that falls in Rain. This I have learn'd from several Trials,
which I must not give Account of here; my Drift in this place being only to
evince the Existence of Terrestrial Matter in Water.

Any one who desires farther Satisfaction in this, may easily obtain it, if
he only put Water into a clear Glass Viol, stopping it close, to keep Dust and
other exterior Matter out, and letting it stand, without stirring it for some
Days: He will then find a considerable Quantity of terrestrial Matter in the
Water, however pure and free it might appear when first put into the Viol.
He will in a very short time observe, as I have frequently done, the
Corpuscles that were at first, while the Water was agitated and kept in
motion, separate, and hardly visible[6], by degrees, as the Water permits, by
its becoming more still and at rest, assembling and combining together; by
that means forming somewhat larger and more conspicuous Moleculæ.
Afterwards he may behold these joining and fixing each to other, by that
means forming large thin Masses, appearing like Nubeculæ, or Clouds in
the Water; which grow more thick and opake, by the continual appulse and
accretion of fresh Matter. If the said Matter be chiefly of the Vegetable kind,
it will be sustain'd in the Water; and discover at length a green Colour,
becoming still more and more of that Colour, I mean an higher and more
saturate Green, as the Matter thickens and encreases. That this Matter
inclines so much to that Colour, is the less strange, since we see so large a
share of it, when constituting Vegetables wearing the same Colour in them.
But if there be any considerable quantity of meer Mineral Matter in the
Water, this, being of a greater specifick Gravity than the Vegetable, as the
Particles of it unite and combine in such Number, till they form a Molecula,
the Impetus of whose Gravity surpasses that of the Resistance of the Water,
subsides a great deal of it to the bottom. Nor does it only fall down it self,
but frequently entangling with the Vegetable Nubeculæ, forces them down
along with it.
The Reason why Bodies, when dissolved and reduced to extreme small
Parts, are sustain'd in Liquors that are of less specifick Gravity than those
Bodies are, hath been pointed at by a late ingenious Member of this
Society[7]. He is indeed far from having adjusted all the Momenta of this
Affair; however it must be admitted, that, in the dividing or solution of

Bodies, their Surfaces do not decrease in the same Proportion that their
Bulk does. Now the Gravity of a Body, which is the Cause of its sinking or
tendency downwards, is commensurate to its Bulk; but the resistance that
the Liquor makes, is proportion'd, not to the Bulk, but to the Extent of the
Surface of the Body immersed in it. Whence 'tis plain, a Body may be so far
divided, that its Parts may be sustain'd in a Fluid, whose specifick Gravity
is less than that of the said Body. Nay, 'tis Matter of Fact, that they
frequently are so; and we daily see Menstrua supporting the Parts of Metals,
and other Bodies, that are of six, ten, nay, almost twenty times the specifick
Gravity of those Menstrua. And as the Parts of Bodies when divided, are
thus supported in a Fluid; so when they occur and unite again, they must
sink of course, and fall to the Bottom.
Upon the whole, 'tis palpable and beyond reasonable Contest, that Water
contains in it a very considerable Quantity of terrestrial Matter. Now the
Question is, to which of these, the Water, or the Earthly Matter sustain'd in
it, Vegetables owe their Growth and Augment: For deciding of which, I
conceive the following Experiments may afford some Light; and I can
safely say, they were made with due Care and Exactness.
Anno 1691.
I chose several Glass Vials, that were all, as near as possible, of the same
shape and bigness. After I had put what Water I thought fit into every one of
them, and taken an Account of the weight of it, I strain'd and ty'd over the
Orifice of each Vial, a Piece of Parchment, having an hole in the middle of
it, large enough to admit the Stem of the Plant I design'd to set in the Vial,
without confining or streightning it, so as to impede its Growth. My
Intention in this, was to prevent the inclosed Water from evaporating, or
ascending any other way than only through the Plant to be set therein. Then
I made choice of several Sprigs of Mint, and other Plants, that were, as near
as I could possibly judge, alike fresh, sound, and lively. Having taken the
weight of each, I placed it in a Vial, order'd as above; and as the Plant

imbib'd and drew off the Water, I took care to add more of the same from
time to time, keeping an Account of the weight of all I added. Each of the
Glasses were, for better distinction, and the more easie keeping a Register
of all Circumstances, noted with a different Mark or Letter, A, B, C, &c. and
all set in a Row in the same Window, in such manner that all might partake
alike of Air, Light, and Sun. Thus they continued from July the Twentieth,
to October the Fifth, which was just Seventy Seven Days. Then I took them
out, weigh'd the Water in each Vial, and the Plant likewise, adding to its
weight that of all the Leaves that had fallen off during the time it stood thus.
And Lastly, I computed how much each Plant had gain'd; and how much
Water was spent upon it. The Particulars are as follow.

(A.) Common Spear-Mint, set in Spring-Water. The Planted
weighed when put in, July 20. just 27 Grains; when taken forth,
October 5. 42 Grains: So that in this space of 77 Days, it had gained
in weight 15 Grains.
The whole Quantity of Water expended, during these 77 Days,
amounted to 2558 Grains. Consequently the weight of the Water
taken up, was 1708⁄15 times as much as the Plant had got in weight.

(B.) Common Spear-Mint, Rain-Water. The Mint weigh'd, when
put in, Gr. 28¼; when taken out Gr. 45¾, having gain'd in 77 Days
Gr. 17½.
The Dispendium of the Water Gr. 3004, which was 17122⁄35 times
as much as the Plant had received in weight.

(C.) Common Spear-Mint, Thames-water. The Plant when put in,
Gr. 28, when taken forth, Gr. 54. So that in 77 Days it had gained
Gr. 26.

The Water expended, amounted to Gr. 2493. which was 9523⁄26
times as much as the additional weight of the Mint.

(D.) Common Solanum, or Night-shade: Spring-water. The Plant
weigh'd, when put in, Gr. 49; when taken out, 106; having gain'd in
77 Days 57 Gr.
The Water expended during the said time, was 3708 Gr. which
was 653⁄57 times as much as the Augment of the Plant.
This Specimen had several Buds upon it, when first set in the
Water. These in some Days became fair Flowers, which were at
length succeeded by Berries.

(E.) Lathyris seu Cataputia Gerh. Spring-Water. It weigh'd, when
put in, Gr. 98. when taken forth, Gr. 101½. The additional weight
for the whole 77 Days, being but Gr. 3½.
The Quantity of Water spent upon it during that time, Gr. 2501.
which is 7144⁄7 times as much as the Plant was augmented.
Several other Plants were try'd, that did not thrive in Water, or succeed any
better than the Cataputia foregoing: But 'tis besides my purpose to give
a particular Account of them here.

(F, G.) These Two Vials were fill'd, the former (F) with Rain, the
other with Spring-water, at the same time as those above-mention'd
were; and stood as long as they did. But they had neither of them
any Plant; my Design in these being only to inform my self, whether
any Water exhaled out of the Glasses, otherwise than thorow the
Bodies of the Plants. The Orifices of these two Glasses were cover'd
with Parchment; each piece of it being perforated with an hole of

the same bigness with those of the Vials above. In this I suspended a
bit of Stick, about the thickness of the Stem of one of the aforesaid
Plants, but not reaching down to the Surface of the included Water. I
put them in thus, that the Water in these might not have more Scope
to evaporate than that in the other Vials. Thus they stood the whole
77 Days in the same Window with the rest; when, upon
Examination, I found none of the Water in these wasted or gone off.
Tho' I observed both in these, and the rest, especially after hot
Weather, small Drops of Water, not unlike Dew, adhering to the
Insides of the Glasses, that Part of them, I mean, that was above the
Surface of the enclosed Water.
The Water in these two Glasses that had no Plants in them, at the
end of the Experiment, exhibited a larger Quantity of Terrestrial
Matter than that in any of those that had the Plants in them did. The
Sediment at the bottom of the Vials was greater; and the Nubeculæ,
diffus'd through the Body of the Water, thicker. And of that which
was in the others, some of it proceeded from certain small Leaves
that had fallen from that part of the Stems of the Plants that was
within the Water, wherein they rotted and dissolved. The Terrestrial
Matter in the Rain-water was finer than that in the Spring-water.
Anno 1692.
The Glasses made use of in this, were of the same sort with those in the
former Experiment; and cover'd over with Parchment in like manner. The
Plants here were all Spear-Mint; the most kindly, fresh, sprightly Shoots I
could chuse. The Water, and the Plants were weigh'd as above; and the Vials
set in a Line, in a South Window: where they stood from June the 2d to July
28. which was just 56 Days.

(H.) Hyde-Park Conduit Water, alone. The Mint weighed, when
put in, 127 Gr. when taken out, 255 Gr. The whole Quantity of

Water expended upon this Plant, amounted to 14190 Gr.
This was all along a very kindly Plant; and had run up to above
two Foot in height. It had shot but one considerable collateral
Branch; but had sent forth many and long Roots, from which sprung
very numerous, though small and short, lesser Fibres. These lesser
Roots came out of the larger on two opposite sides, for the most
part; so that each Root, with its Fibrillæ, appear'd not unlike a small
Feather. To these Fibrillæ adher'd pretty must Terrestrial Matter. In
the Water, which was at last thick and turbid, was a green
Substance, resembling a fine thin Conserva.

(I.) The same Water, alone. The Mint weigh'd, when put in, 110
Gr. when taken out, 249. Water expended, 13140 Gr.
This Plant was as kindly as the former, but had shot no collateral
Branches. Its Roots, the Water, and the green Substance, all much as
in the former.

(K.) Hyde-Park Conduit-water, in which was dissolved an Ounce
and half of Common Garden-earth. The Mint weigh'd, when put in,
76 Gr. when taken out, 244 Gr. Water expended, Gr. 10731.
This Plant, though it had the Misfortune to be annoy'd with many
small Insects that hapn'd to fix upon it; yet had shot very
considerable collateral Branches; and at least as many Roots as
either that in H or I; which had a much greater Quantity of
Terrestrial Matter adhering to the Extremities of them. The same
green Substance here, that was in the two preceding.

(L.) Hyde-Park Water, with the same Quantity of Garden-mould
as in the former. The Mint weigh'd, when put in, 92 Gr. when taken

out, 376 Gr. The Water expended 14950 Gr.
This Plant was far more flourishing than any of the precedent;
had several very considerable collateral Branches, and very
numerous Roots, to which Terrestrial Matter adhered very
copiously.
The Earth in both these Glasses was very sensibly and
considerably wasted, and less than when first put in. The same sort
of green Substance here as in those above.

(M.) Hyde-Park Water, distilled off with a gentle Still. The Mint
weigh'd, when put in, 114 Gr. when taken out 155. The Water
expended, 8803 Gr.
This Plant was pretty kindly; had two small collateral Branches,
and several Roots, though not so many as that in H or I, but as much
Terrestrial Matter adhering to them as those had. The Water was
pretty thick; having very numerous small Terrestrial Particles
swimming in it, and some Sediment at the bottom of the Glass. This
Glass had none of the green Matter above mentioned, in it.

(N.) The Residue of the Water, which remain'd in the Still after
that in M, was distill'd off. It was very turbid, and as high-colour'd
(reddish) as ordinary Beer. The Mint weigh'd, when put in, 81 Gr.
when taken out, 175 Gr. Water expended, 4344 Gr. This Plant was
very lively; and had sent out six collateral Branches, and several
Roots.

(O.) Hyde-Park Conduit-water, in which was dissolved a Drachm
of Nitre. The Mint set in this suddenly began to wither and decay;
and died in a few Days: As likewise did two more Sprigs, that were

set in it, successively. In another Glass I dissolv'd an Ounce of good
Garden-mould, and a Drachm of Nitre, and in a third, half an Ounce
of Wood ashes, and a Drachm of Nitre; but the Plants in these
succeeded no better than in the former. In other Glasses I dissolved
several other sorts of Earths, Clays, Marles, and variety of Manures,
&c. I set Mint in distill'd Mint-water; and other Experiments I made,
of several kinds, in order to get Light and Information, what
hastened or retarded, promoted or impeded Vegetation; but these do
not belong to the Head I am now upon.

(P.) Hyde-Park Conduit-water. In this I fix'd a Glass-Tube about
ten Inches long, the Bore about one sixth of an Inch in Diameter,
fill'd with very fine and white Sand, which I kept from falling down
out of the Tube into the Vial, by tying a thin piece of Silk over that
end of the Tube that was downwards. Upon Immersion of the lower
end of it into the Water, this by little and little ascended quite to the
upper Orifice of the Tube. And yet, in all the fifty six Days which it
stood thus, a very inconsiderable Quantity of Water had gone off,
viz. scarce twenty Grains; though the Sand continued moist up to the
top till the very last. The Water had imparted a green Tincture to the
Sand, quite to the very top of the Tube. And, in the Vial, it had
precipitated a greenish Sediment, mix'd with black. To the bottom
and sides of the Tube, as far as 'twas immers'd in the Water, adher'd
pretty much of the green Substance describ'd above. Other like
Tubes I fill'd with Cotton, Lint, Pith of Elder, and several other
porous Vegetable Substances; setting some of them in clear Water;
others in Water tinged with Saffron, Cochinele, &c. And several
other Trials were made, in order to give a mechanical
Representation of the motion and distribution of the Juices in Plants;
and of some other Phænomena observable in Vegetation, which I

shall not give the Particulars of here, as being not of use to my
present design.

(Q, R, S, &c.) Several Plants set in Vials, ordered in like manner
as those above, in October, and the following colder Months. These
throve not near so much; nor did the Water ascend in nigh the
quantity it did in the better Seasons, in which the before recited
Trials were made.
Some Reflections upon the foregoing Experiments.
1. In Plants of the same kind, the less they are in Bulk, the smaller the
Quantity of the fluid Mass, in which they are set, is drawn off; the
Dispendium of it, where the Mass is of equal thickness, being pretty nearly
proportion'd to the Bulk, of the Plant. Thus that in the Glass mark'd A,
which weigh'd only 27 Grains, drew off but 2558 Grains of the Fluid; and
that in B, which weigh'd only 28¼, took up but 3004 Grains; whereas that
in H, which weigh'd 127 Grains, spent 14190 Grains of the Liquid Mass.
The Water seems to ascend up the Vessels of Plants, in much the same
manner as up a Filtre; and 'tis no great wonder that a larger Filtre should
draw off more Water than a lesser; or that a Plant that has more and larger
Vessels, should take up a greater share of the Fluid in which it is set, than
one that has fewer and smaller ones can. Nor do I note this as a thing very
considerable in it self, but chiefly in regard to what I am about to offer
beneath; and that it may be seen that, in my other Collations of Things, I
made due Allowance for this Difference.

2. The much greatest part of the fluid Mass, that is thus drawn off and
convey'd into the Plants, does not settle or abide there; but passes through
the pores of them, and exhales up into the Atmosphere. That the Water in
these Experiments ascended only through the Vessel of the Plants, is

certain. The Glasses F and G, that had no Plants in them, though disposed
of in like manner as the rest, remain'd at the End of the Experiment, as at
first; and none of the Water was gone off. And that the greatest part of it
flies off from the Plant into the Atmosphere, is as certain. The least
Proportion of the Water expended, was to the Augment of the Plant, as 46 or
50 to 1. And in some the weight of the Water drawn off, was 100, 200, nay,
in one above 700 times as much as the Plant had received of Addition.
This so continual an Emission and Detachment of Water, in so great
Plenty from the Parts of Plants, affords us a manifest Reason why Countries
that abound with Trees, and the larger Vegetables especially, should be very
obnoxious to Damps, great Humidity in the Air, and more frequent Rains,
than others that are more open and free. The great Moisture in the Air, was a
mighty inconvenience and annoyance to those who first settled in America;
which at that time was much overgrown with Woods and Groves. But as
these were burnt and destroy'd, to make way for Habitation and Culture of
the Earth, the Air mended and clear'd up apace, changing into a Temper
much more dry and serene than before.
Nor does this Humidity go off pure and alone; but usually bears forth
with it many Parts of the same Nature with those whereof the Plant, through
which it passes, consists. The Crasser indeed are not so easily born up into
the Atmosphere; but are usually deposited on the Surface of the Flowers,
Leaves, and other Parts of the Plants: Hence comes our Manna's, our
Honeys, and other Gummous Exsudations of Vegetables. But the finer and
lighter Parts are with greater ease sent up into the Atmosphere. Thence they
are conveyed to our Organs of Smell, by the Air we draw in Respiration;
and are pleasant or offensive, beneficent or injurious to us, according to the
Nature of the Plants from whence they arise. And since these owe their Rise
to the Water, that ascends out of the Earth through the Bodies of Plants, we
cannot be far to seek for the Cause why they are more numerous in the Air,
and we find a greater quantity of Odors exhaling from Vegetables, in warm,
humid Seasons, than in any other whatever.

3. A great part of the Terrestrial Matter that is mix'd with the Water,
ascends up into the Plant as well as the Water. There was much more
Terrestrial Matter at the end of the Experiment, in the Water of the Glasses
F and G, that had no Plants in them, than in those that had Plants. The
Garden-mould dissolved in the Glasses K and L, was considerably
diminished, and carried off. Nay, the Terrestrial and Vegetable Matter was
born up in the Tubes fill'd with Sand, Cotton, &c. in that Quantity, as to be
evident even to Sense. And the Bodies in the Cavities of the other Tubes,
that had their lower Ends immers'd in Water, wherein Saffron, Cochinele,
&c. had been infused, were tinged with Yellow, Purple, &c.
If I may be permitted to look abroad a while, towards our Shores and
Parts within the Verge of the Sea, these will present us with a large Scene of
Plants, that, along with the Vegetable, take up into them meer mineral
Matter also in great abundance. Such are our Sea-Purslains, the several sorts
of Alga's, of Sampires, and other marine Plants. These contain common
Sea-salt, which is all one with the Fossil, in such plenty, as not only to be
plainly distinguish'd on the Palate, but may be drawn forth of them in
considerable Quantity. Nay, there want not those who affirm, there are
Plants found that will yield Nitre, and other mineral Salts; of which indeed I
am not so far satisfied, that I can depend on the Thing, and therefore give
this only as an hint for Enquiry.
To go on with the Vegetable Matter, how apt and how much disposed
this, being so very fine and light, is to attend Water in all its Motions, and
follow it into each of its Recesses, is manifest, not only from the Instances
above alledg'd, but many others. Percolate it withal the Care imaginable:
Filter it with never so many Filtrations, yet some Terrestrial Matter will
remain. 'Tis true, the Fluid will be thinner every time than other, and more
disingaged of the said Matter; but never wholly free and clear. I have filtred
Water thorough several wholly free and clear Sheets of thick Paper; and,
after that, through very close fine Cloth twelve times doubled. Nay, I have
done this over and over; and yet a considerable quantity of this Matter

discover'd it self in the Water after all. Now if it thus pass Interstices, that
are so very small and fine along with the Water, 'tis the less strange it should
attend it in its passage through the Ducts and Vessels of Plants. 'Tis true,
filtering and distilling of Water intercepts and makes it quit some of the
Earthy Matter it was before impregnated withal: But then that which
continues with the Water after this, is fine and light; and such consequently,
as is in a peculiar manner fit for the Growth and Nourishment of
Vegetables. And this is the Case of Rain-water. The Quantity of Terrestrial
Matter it bears up into the Atmosphere, is not great. But that which it does
bear up, is mainly of that light kind of Vegetable Matter; and that too
perfectly dissolved, and reduced to single Corpuscles, all fit to enter the
Tubules and Vessels of Plants: On which Account 'tis, that this Water is so
very fertile and prolifick.
The Reason, why in this Proposition, I say, only a great part of the
Terrestrial Matter that is mix'd with the Water, ascends up with it into the
Plant, is, because all of it cannot. The Mineral Matter is a great deal of it,
not only gross and ponderous, but scabrous and inflexible; and so not
disposed to enter the Pores of the Roots. And a great many of the simple
Vegetable Particles by degrees unite, and form some of them small Clods or
Moleculæ; such as those mention'd in H, K, and L, sticking to the
Extremities of the Roots of those Plants. Others of them intangle in a looser
manner; and form the Nubeculæ, and green Bodies, so commonly observ'd
in stagnant Water. These, when thus conjoin'd, are too big to enter the Pores,
or ascend up the Vessels of Plants, which singly they might have done.
They who are conversant in Agriculture, will easily subscribe to this. They
are well aware that, be their Earth never so rich, so good, and so fit for the
production of Corn or other Vegetables, little will come of it, unless the
Parts of it be separated and loose. 'Tis on this Account they bestow the
Pains they do in Culture of it, in Digging, Plowing, Harrowing, and
Breaking of the Clodded Lumps of Earth. 'Tis the same way that Sea-salt,
Nitre, and other Salts, promote Vegetation. I am sorry I cannot subscribe to

the Opinion of those Learned Gentlemen, who imagine Nitre to be essential
to Plants; and that nothing in the Vegetable Kingdom is transacted without
it. By all the Trials I have been able to make, the thing is quite otherwise;
and when contiguous to the Plant, it rather destroys than nourishes it. But
this Nitre and other Salts certainly do; they loosen the Earth, and separate
the concreted Parts of it; by that means fitting and disposing them to be
assumed by the Water, and carried up into the Seed or Plant, for its
Formation and Augment. There's no Man but must observe, how apt all
sorts of Salts are to be wrought upon by Moisture; how easily they liquate
and run with it; and when these are drawn off, and have deserted the Lumps
wherewith they were incorporated, those must moulder immediately, and
fall asunder of Course. The hardest Stone we meet with, if it happen, as
frequently it does, to have any sort of Salt intermix'd with the Sand, of
which it consists, upon being expos'd to an humid Air, in a short time
dissolves and crumbles all to pieces; and much more will clodded Earth or
Clay, which is not of near so compact and solid a Constitution as Stone is.
The same way likewise is Lime serviceable in this Affair. The Husbandmen
say of it, that it does not fatten, but only mellows the Ground: By which
they mean, that it does not contain any thing in it self that is of the same
Nature with the Vegetable Mould, or afford any Matter fit for the Formation
of Plants; but meerly softens and relaxes the Earth; by that means rendering
it more capable of entering the Seeds and Vegetables set in it, in order to
their Nourishment, than otherwise it would have been. The Properties of
Lime are well known; and how apt 'tis to be put into Ferment and
Commotion by Water. Nor can such Commotion ever happen when Lime is
mix'd with Earth, however hard and clodded that may be, without opening
and loosening of it.

4. The Plant is more or less nourish'd and augmented, in Proportion as
the Water, in which it stands, contains a greater or smaller Quantity of
proper terrestrial Matter in it. The Truth of this Proportion is so eminently

discernable through the whole Process of these Trials, that I think no doubt
can be made of it. The Mint in the Glass C, was of much the same Bulk and
Weight with those in A and B. But the Water, in which that was, being
River-water, which was apparently stored more copiously with terrestrial
Matter, than the Spring or Rain-water, wherein they stood, were; it had
thriven to almost double the Bulk that either of them had, and with a less
Expence of Water too. So likewise the Mint in L, in whose Water was
dissolved a small quantity of good Garden-mould, though it had the
disadvantage[8] to be less, when first set, than either of the Mints in H or I,
whose Water was the very same with this in L, but had none of that Earth
mix'd with it; yet, in a short time the Plant not only overtook, but much out-
strip'd those and at the end of the Experiment was very considerably bigger
and heavier than either of them. In like manner the Mint in N, though less at
the beginning than that in M, being set in that thick, turbid, feculent Water,
that remained behind, after that wherein M was placed, was still'd off, had
in fine more than double its original weight and bulk; and receiv'd above
twice the additional Encrease, than that in M, which stood in the thinner
distill'd Water, had done. And, which is not less considerable, had not drawn
off half the Quantity of Water that that had.
Why, in the beginning of this Article, I limit the Proportion of the
Augment of the Plant to the Quantity of proper Terrestrial Matter in the
Water, is, because all, even the Vegetable Matter, to say nothing of the
Mineral, is not proper for the Nourishment of every Plant. There may be,
and doubtless are, some Parts in different Species of Plants, that may be
much alike, and so owe their Supply to the same common Matter; but 'tis
plain all cannot. And there are other Parts so differing, that 'tis no ways
credible they should be formed all out of the same sort of Corpuscles. So far
from it, that there want not good Indications, as we shall see by and by, that
every kind of Vegetable requires a peculiar and specifick Matter for its
Formation and Nourishment. Yea, each Part of the same Vegetable does so;
and there are very many and different Ingredients go to the Composition of

the same individual Plant. If therefore the Soil, wherein any Vegetable or
Seed is planted, contains all or most of these ingredients, and those in due
quantity, it will grow and thrive there; otherwise 'twill not. If there be not as
many sorts of Corpuscles as are requisite for the Constitution of the main
and more essential Parts of the Plant, 'twill not prosper at all. If there be
these, and not in sufficient Plenty, 'twill starve, and never arrive to its
natural Stature: Or if there be any the less necessary and essential
Corpuscles wanting, there will be some failure in the Plant; 'twill be
defective in Taste, in Smell, in Colour, or some other way. But though a
Tract of Land may happen not to contain Matter proper for the Constitution
of some one peculiar kind of Plant; yet it may for several others, and those
much differing among themselves. The Vegetative Particles are commix'd
and blended in the Earth, with all the diversity and variety, as well as all the
uncertainty, conceivable. I have given some intimations of this elsewhere[9],
and shall not repeat them here, but hope in due time to put them into a much
better Light than that they there stand in.
It is not possible to imagine, how one uniform, homogeneous Matter,
having its Principles or Original Parts all of the same Substance,
Constitution, Magnitude, Figure, and Gravity, should ever constitute Bodies
so egregiously unlike, in all those respects, as Vegetables of different kinds
are; nay, even as the different Parts of the same Vegetable. That one should
carry a resinous, another a milky, a third a yellow, a fourth a red Juice, in its
Veins; one afford a fragrant, another an offensive Smell; one be sweet to the
Taste, another bitter, acid, acerbe, austere, &c. that one should be
nourishing, another poisonous, one purging, another astringent: In brief,
that there should be that vast difference in them, in their several
Constitutions, Makes, Properties, and Effects, and yet all arise from the
very same sort of Matter, would be very strange. And, to note by the by, this
Argument makes equally strong against those, who suppose meer Water the
Matter, out of which all Bodies are form'd.

The Cataputia in the Glass E, received but very little Encrease, only
three Grains and an half all the while it stood, though 2501 Grains of Water
were spent upon it. I will not say the Reason was, because that Water did
not contain in it Matter fit and proper for the Nourishment of that peculiar
and remarkable Plant. No, it may be the Water was not a proper Medium for
it to grow in; and we know there are very many Plants that will not thrive in
it. Too much of that Liquor, in some Plants, may probably hurry the
Terrestrial Matter thorough their Vessels too fast for them to arrest and lay
hold of it. Be that as it will, 'tis most certain there are peculiar Soils that suit
particular Plants. In England, Cherries are observ'd to succeed best in Kent;
Apples in Herefordshire; Saffron in Cambridgeshire; Wood in two or three
of our Midland Counties; and Teazles in Somersetshire. This is an
Observation that hath held in all Parts, and indeed in all Ages of the World.
The most ancient Writers of Husbandry[10] took notice of it; and are not
wanting in their Rules for making choice of Soils suited to the Nature of
each kind of Vegetable they thought valuable, or worth propagating.
But, which is a further Proof of what I am here endeavouring to advance,
that Soil that is once proper and fit for the Production of some one sort of
Vegetable, does not ever continue to be so. No, in Tract of time it loses that
Property; but sooner in some Lands, and later in others: This is what all
who are conversant in these things know very well. If Wheat, for Example,
be sown upon a Tract of Land that is proper for that Grain, the first Crop
will succeed very well; and perhaps the second, and the third, as long as the
Ground is in Heart, as the Farmers speak; but in a few Years 'twill produce
no more, if sowed with that Corn: Some other Grain indeed it may, as
Barley. And after this has been sown so often, that the Land can bring forth
no more of the same, it may afterwards yield good Oats; and, perhaps,
Pease after them. At length 'twill become barren; the Vegetative Matter, that
at first it abounded withal, being educed forth of it by those successive
Crops, and most of it born off. Each sort of Grain takes forth that peculiar
Matter that is proper for its own Nourishment. First, the Wheat draws off

those Particles that suit the Body of that Plant; the rest lying all quiet and
undisturbed the while. And when the Earth has yielded up all them, those
that are proper for Barley, a different Grain, remain still behind, till the
successive Crops of that Corn fetch them forth too. And so the Oats and
Pease, in their Turn; till in fine all is carried off, and the Earth in great
measure drain'd of that sort of Matter.
After all which, that very Tract of Land may be brought to produce
another Series of the same Vegetables; but never till 'tis supplied with a new
Fund of Matter, of like sort with that it at first contain'd. This Supply is
made several ways: By the Grounds lying fallow for some time, till the
Rain has pour'd down a fresh Stock upon it: Or, by the Tiller's Care in
manuring of it. And for farther Evidence that this Supply is in reality of like
sort, we need only reflect a while upon those Manures that are found by
constant Experience best to promote Vegetation, and the Fruitfulness of the
Earth. These are chiefly either parts of Vegetables, or of Animals; which
indeed either derive their own Nourishment immediately from Vegetable
Bodies, or from other Animals that do so. In particular, the Blood, Urine,
and Excrements of Animals; Shavings of Horns, and of Hoofs; Hair, Wool,
Feathers; calcin'd Shells; Lees of Wine, and of Beer; Ashes of all sorts of
Vegetable Bodies; Leaves, Straw, Roots, and Stubble, turn'd into the Earth
by Plowing or otherwise to rot and dissolve there: These, I say, are our best
Manures; and, being Vegetable Substances, when refunded back again into
the Earth, serve for the Formation of other like Bodies.
Not wholly to confine our Thoughts to the Fields, let us look a while into
our Gardens; where we shall meet with still further Confirmations of the
same thing. The Trees, Shrubs, and Herbs cultivated in these, after they
have continued in one Station, till they have derived thence the greater part
of the Matter fit for their Augment, will decay and degenerate, unless either
fresh Earth, or some fit Manure, be applied unto them. 'Tis true, they may
maintain themselves there for some time, by sending forth Roots further
and further to a great Extent all round, to fetch in more remote Provision;

but at last all will fail; and they must either have a fresh Supply brought to
them, or they themselves be removed and transplanted to some Place better
furnished with Matter for their Subsistence. And accordingly Gardiners
observe, that Plants that have stood a great while in a Place, have longer
Roots than usual; part of which they cut off, when they transplant them to a
fresh Soil, as now not of any further use to them. All these Instances, to
pass over a great many others that might be alledg'd, point forth a particular
Terrestrial Matter, and not Water, for the Subject to which Plants owe their
Increase. Were it Water only, there would be no need of Manures; or of
transplanting them from place to place. The Rain falls in all Places alike; in
this Field and in that indifferently; in one side of an Orchard or Garden, as
well as another. Nor could there be any Reason, why a Tract of Land should
yield Wheat one Year, and not the next; since the Rain showers down alike
in each. But I am sensible I have carried on this Article to too great a length;
which yet on so ample and extensive a Subject, 'twas not easie to avoid.

5. Vegetables are not form'd of Water; but of a certain peculiar
Terrestrial Matter. It hath been shewn, that there is a considerable Quantity
of this Matter contain'd both in Rain, Spring, and River-water: That the
much greatest part of the fluid Mass that ascends up into Plants, does not
settle or abide there, but passes through the Pores of them, and exhales up
into the Atmosphere; That a great part of the Terrestrial Matter, mix'd with
the Water, passes up into the Plant along with it; and that the Plant is more
or less augmented in proportion, as the Water contains a greater or smaller
Quantity of that Matter. From all which we may very reasonably infer, that
Earth, and not Water, is the Matter that constitutes Vegetables. The Plant in
E, drew up into it 2501 Grains of the fluid Mass; and yet had received but
Grains 3 and a half of Increase from all that. The Mint in L, though it had at
first the disadvantage to be much less than that in I; yet being set in Water
wherewith Earth was plentifully mix'd, and that in I, only in Water without
any such additional Earth, it had vastly outgrown the other, weighing at last

145 Grains more than that did, and so having gain'd about twice as much as
that had. In like manner that in K, though 'twas a great deal less when put in
than that in I, and also was impair'd and offended by Insects; yet being
planted in Water wherein Earth was dissolved, whereas the Water in which
it stood had none, it not only over-took, but considerably surpass'd the
other; weighing at last 29 Grains more than that in I, and yet had not
expended so much Water as that, by above 2400 Grains. The Plant in N, tho'
at first a great deal less than that in M; yet being set in the foul crass Water
that was left in the Still, after that, in which M was set, was drawn off, in
Conclusion had gain'd in weight above double what that in the finer and
thinner Water had. The Proportion of the Augment of that Plant that throve
most was, to the fluid Mass spent upon it, but as 1 to 46. In others, 'twas but
as 1 to 60, 100, 200; nay, in the Cataputia, 'twas but as 1 to 714. The Mint
in B took up 39 Grains of Water a-day, one day with another; which was
much more than the whole weight of the Plant originally; and yet, with all
this, it gain'd not one fourth of a Grain a-day in weight. Nay, that in H took
up 253 Grains a day of the Fluid: Which was near twice as much as its
original Weight, it weighing, when first set in the Water, but 127 Grains.
And, after all, the daily Encrease of the Plant was no more than Grains
215⁄56.

6. Spring, and Rain-water, contain pretty near an equal Charge of
Vegetable Matter; River-water more than either of them. The Plants in the
Glasses A, B, and C, were at first of much the same size and weight. At the
End of the Experiment, the Mint in A had gain'd 15 Grains out of 2558
Grains of Spring-water; that in B, Grains 17 and an half, out of 3004 Grains
of Rain-water; but that in C had got 26 Grains out of only 2493 Grains of
River-water. I do not found this Proposition solely upon these Trials; having
made some more, which I do not relate here, that agree well enough with
these. So that the Proportions here deliver'd, will hold for the main; but a
strict and just Comparison is hardly to be expected. So far from it, that I

make no doubt, but the Water that falls in Rain, at some times, contains a
greater share of Terrestrial Matter than that which falls at others. A more
powerful and intense Heat must needs hurry up a larger quantity of that
Matter along with the humid Vapours that form Rain, than one more feeble
and remiss ever possibly can. The Water of one Spring may flow forth with
an higher Charge of this Matter, than that of another; this depending partly
upon the quickness of the Ebullition of the Water, and partly upon the
Quantity of that Matter latent in the Strata, through which the Fluid passes,
and the greater or less laxity of those Strata. For the same Reason, the
Water of one River may abound with it more than that of another. Nay, the
same River, when much agitated, and in commotion, must bear up more of
it, than when it moves with less rapidity and violence. That there is a great
Quantity of this Matter in Rivers; and that it contributes vastly to the
ordinary Fertility of the Earth, we have an illustrious Instance in the Nile,
the Ganges, and other Rivers that yearly overflow the neighbouring Plains.
Their Banks shew the fairest and largest Crops of any in the whole World.
They are even loaded with the multitude of their Productions; and those
who have not seen them, will hardly be induced to believe the mighty
Returns those Tracts make in comparison of others, that have not the
Benefit of like Inundations.

7. Water serves only for a Vehicle to the Terrestrial Matter, which forms
Vegetables; and does not it self make any addition unto them. Where the
proper Terrestrial Matter is wanting, the Plant is not augmented, though
never so much Water ascend into it. The Cataputia in E, took up more
Water than the Mint in C, and yet had grown but very little, having received
only three Grains and an half of additional weight; whereas the other had
received no less than twenty six Grains. The Mint in I, was planted in the
same sort of Water as that in K, was; only the latter had Earth dissolved in
the Water; and yet that drew off 13140 Grains of the Water, gaining it self
no more than 139 Grains in weight; whereas the other took up but 10731

Grains of the Water, and was augmented 168 Grains in weight.
Consequently that spent 2409 Grains more of the Water than this in K, did,
and yet was not so much encreased in weight as this by 29 Grains. The Mint
in M, stood in the very same kind of Water as that in N, did. But the Water
in M, having much less Terrestrial Matter in it than that in N had, the Plant
bore up 8803 Grains of it, gaining it self only 41 Grains the while; whereas
that in N drew off no more than 4344 Grains, and yet was augmented 94
Grains. So that it spent 4459 Grains of Water more than that did; and yet
was not it self so much increased in weight, as that was, by 53 Grains. This
is both a very fair, and a very conclusive Instance; on which Account 'tis
that I make oftner use of it. Indeed they are all so; and to add any thing
further on this Head, will not be needful.
'Tis evident therefore Water is not the Matter that composes Vegetable
Bodies. 'Tis only the Agent that conveys that Matter to them; that introduces
and distributes it to their several Parts for their Nourishment. That Matter is
sluggish and unactive, and would lie eternally confin'd to its Beds of Earth,
without ever advancing up into Plants, did not Water, or some like
Instrument, fetch it forth and carry it unto them. That therefore there is that
plentiful Provision, and vast Abundance of it supplied to all Parts of the
Earth, is a mark of a natural Providence superintending over the Globe we
inhabit; and ordaining a due Dispensation of that Fluid, without the
Ministry of which the Noble Succession of Bodies we behold, Animals,
Vegetables, and Minerals, would be all at a stand[11]. But to keep to Plants,
'tis manifest Water, as well on this, as upon the other Hypothesis, is
absolutely necessary in the Affair of Vegetation; and it will not succeed
without it: Which indeed gave occasion to the Opinion, that Water it self
nourished, and was changed into Vegetable Bodies. They saw, though these
were planted in a Soil never so rich, so happy, so advantageous, nothing
came of it unless there was Water too in a considerable quantity. And it
must be allow'd Vegetables will not come on or prosper where that is

wanting: But yet what those Gentlemen inferr'd thence, was not, we see,
well grounded.
This Fluid is capacitated for the Office here assign'd it several ways: By
the Figure of its Parts, which, as appears from many Experiments, is exactly
and mathematically Spherical; their Surfaces being perfectly polite, and
without any the least Inequalities. 'Tis evident, Corpuscles of such a Figure
are easily susceptible of Motion, yea, far above any others whatever; and
consequently the most capable of moving and conveying other Matter, that
is not so active and voluble. Then the Intervals of Bodies of that Figure are,
with respect to their Bulk, of all others the largest; and so the most fitted to
receive and entertain foreign Matter in them. Besides, as far as the Trials
hitherto made inform us, the constituent Corpuscles of Water are, each
singly consider'd, absolutely solid; and do not yield to the greatest External
Force. This secures their Figure against any Alteration; and the Intervals of
the Corpuscles must be always alike. By the latter, 'twill be ever disposed to
receive Matter into it; and by the former, when once received, to bear it on
along with it. Water is further capacitated to be a Vehicle to this Matter, by
the tenuity and fineness of the Corpuscles of which it consists. We hardly
know any Fluid in all Nature, except Fire, whose constituent Parts are so
exceeding subtle and small as those of Water are. They'll pass Pores and
Interstices, that neither Air nor any other Fluid will. This enables them to
enter the finest Tubes and Vessels of Plants, and to introduce the Terrestrial
Matter, conveying it to all Parts of them; whilst each, by means of Organs
'tis endowed with for the Purpose, intercepts and assumes into it self such
Particles as are suitable to its own Nature, letting the rest pass on through
the common Ducts. Nay, we have almost every where Mechanical Instances
of much the same Tenor. 'Tis obvious to every one, how easily and suddenly
Humidity, or the Corpuscles of Water sustained in the Air, pervade and
insinuate themselves into Cords, however tightly twisted, into Leather,
Parchment, Vegetable Bodies, Wood, and the like. This it is that fits them
for Hygrometers; and to measure and determine the different quantities of

Moisture in the Air, in different Places and Seasons. How freely Water
passes and carries with it Terrestrial Matter, through Filtres, Colatures,
Distillations, &c. hath been intimated already.

8. Water is not capable of performing this Office to Plants, unless
assisted by a due Quantity of Heat; and this must concur, or Vegetation will
not succeed. The Plants that were set in the Glasses Q, R, S, &c. in October,
and the following colder Months, had not near the quantity of Water sent up
into them, or so great an additional Encrease by much, as those that were
set in June, July, and the hotter. 'Tis plain Water has no power of moving it
self; or rising to the vast height it does in the more tall and lofty Plants. So
far from this, that it does not appear from any Discovery yet made, that
even its own Fluidity consists in the intestine Motion of its Parts; whatever
some, otherwise very learned and knowing, Persons may have thought.
There is no need of any thing more, for solving all the Phænomena of
Fluidity, than such a Figure and Disposition of the Parts, as Water has.
Corpuscles of that make, and that are all absolutely Spherical, must stand so
very tickle and nicely upon each other, as to be susceptible of every
Impression; and though not perpetually in Motion, yet must be ever ready
and liable to be put into it, by any the slightest Force imaginable. It is true,
the Parts of Fire or Heat are not capable of moving themselves any more
than those of Water; but they are more subtil, light, and active, than those
are, and so more easily put into Motion. In fine, 'tis evident and matter of
Fact, that Heat does operate upon, and move the Water, in order to its
carrying on the Work of Vegetation: But how 'tis agitated it self, and where
the Motion first begins, this is no fit Place to enquire.
That the Concourse of Heat in this Work is really necessary, appears, not
only from the Experiments before us, but from all Nature; from our Fields
and Forests, our Gardens and our Orchards. We see in Autumn, as the Sun's
Power grows gradually less and less, so its Effects on Plants is remitted, and
their Vegetation slackens by little and little. Its Failure is first discernible in

Trees. These are raised highest above the Earth; and require a more intense
Heat to elevate the Water, charged with their Nourishment, to the Tops and
Extremities of them. So that for want of fresh Support and Nutriment, they
shed their Leaves, unless secur'd by a very firm and hardy Constitution
indeed, as our ever-Greens are. Next the Shrubs part with theirs; and then
the Herbs and lower Tribes; the Heat being at length not sufficient to supply
even these, though so near the Earth, the Fund of their Nourishment. As the
Heat returns the succeeding Spring, they all recruit again; and are furnish'd
with fresh Supplies and Verdure: But first, those which are lowest and
nearest the Earth, Herbs, and they that require a lesser degree of Heat to
raise the Water with its Earthy Charge into them: Then the Shrubs and
higher Vegetables in their Turns; and lastly, the Trees. As the Heat
increases, it grows too powerful, and hurries the Matter with too great
Rapidity thorough the finer and more tender Plants: These therefore go off,
and decay; and others that are more hardy and vigorous, and require a
greater share of Heat, succeed in their Order. By which Mechanism,
provident Nature furnishes us with a very various and differing
Entertainment; and what is best suited to each Season, all the Year round.
As the Heat of the several Seasons affords us a different Face of Things;
so the several distant Climates shew different Scenes of Nature, and
Productions of the Earth[12]. The Hotter Countries yield ordinarily the largest
and tallest Trees; and those in too much greater variety than the colder ever
do. Even those Plants which are common to both, attain to a much greater
Bulk in the Southern than in the Northern Climes. Nay, there are some
Regions so bleak and chill, that they raise no Vegetables at all to any
considerable Size. This we learn from Greenland, from Iseland, and other
Places of like cold Site and Condition. In these no Tree ever appears; and
the very Shrubs they afford, are few, little, and low.
Again, in the warmer Climates, and such as do furnish forth Trees and the
larger Vegetables, if there happen a remission or diminution of the usual
Heat, their Productions will be impeded and diminished in proportion. Our

late Colder Summers have given us proof enough of this. For though the
Heat we have had, was sufficient to raise the Vegetative Matter into the
lower Plants, into our Corns, our Wheat, Barley, Pease and the like; and we
have had plenty of Straw-berries, Ras-berries, Currans, Goosberries, and the
Fruits of such other Vegetables as are low and near the Earth: Yea, and a
moderate store of Cherries, Mulberries, Plumbs, Filberts, and some others
that grow somewhat at a greater Height; yet our Apples, our Pears, Walnuts,
and the Productions of the taller[13] Trees have been fewer, and those not so
kindly, so thoroughly ripen'd, and brought to that Perfection they were in
the former more benign and their warm Seasons. Nay, even the lower Fruits
and Grains have had some share in the common Calamity; and fallen short
both in Number and Goodness of what the hotter and kinder Seasons were
wont to shew us. As to our Grapes, Abricots, Peaches, Nectarens, and Figs,
being transplanted hither out of hotter Climes, 'tis the less wonder we have
of late had so general a Failure of them.
Nor is it the Sun, or the ordinary emission of the Subterranean Heat only,
that promotes Vegetation; but any other indifferently, according to its Power
and Degree: This we are taught by our Stoves, hot Beds, and the like. All
Heat is of like kind; and where-ever is the same Cause, there will be
constantly the same Effect. There's a Procedure in every part of Nature, that
is perfectly regular and geometrical, if we can but find it out; and the further
our Searches carry us, the more shall we have occasion to admire this, and
the better 'twill compensate our Industry.
[1] Terra Parens. Γῆ μὴτηρ πάντων. Terra Matter.
[2] Nat. History, Cent. 5. §. 411.
[3] Complexionum atque Mistion. Element. Figm.
[4] Mr. Boyle, Scept. Chym. par. 2.
[5] Provided the Silver be pure and absolutely refin'd: For the least admixture of Copper will
produce a blue Tincture in the Menstruum; as that of some other Bodies, one different.
[6] To say nothing of those that were not discernible.
[7] Mr. W. Molineux, Philosophical Trans. No. 181.

[8] Confer. Prop. 1. supra.
[9] Nat. Hist. Earth, p. 228. & seq.
[10] Vid. Varronem, Columellam, & reliquos Rei Rusticæ Scriptores.
[11] Conf. Nat. Hist. Earth, p. 47. & seq. uti & p. 128, &c.
[12] Conf. Nat. Hist. Earth, Pag. 267. & seq.
[13] The Dwarf Apple and Pear trees have succeeded better. And indeed in Trees of the same
kind, those that keep closest to the Earth always produce the most and best Fruit. For which
Reason 'tis that the Gardiners check and restrain the Growth of better Fruit-trees, and prevent
their running up to too great a Height.

Account of the Measure of the thickness of Gold upon Gilt Wire;
together with Demonstration of the exceeding Minuteness of the
Atoms or constituent Particles of Gold; as it was read before the
Royal Society, by E. Halley.

HAT are the constituent Parts of Matter, and how there comes to be
W so great a diversity in the weight of Bodies, to all appearance equally
solid and dense, such as are Gold and Glass, (whose specifick
Gravities are nearly as 7 to 1) seems a very hard Question to those that shall
rightly consider it: For from undoubted Experiment, Gravity is in all Bodies
proportionable to the Quantity of Matter in each; and there is no such thing
as a Propension of some more, others less, towards the Earth's Center; since
the Impediment of the Air being removed, all Bodies descend, be they never
so loose or compact in Texture, with equal Velocity. It follows therefore,
That there is 7 times as much Matter in Gold, as in a piece of Glass of the
same Magnitude; and consequently, that at least six parts of seven in the
Bulk of Glass, must be Pore or Vacuity: This some Favourers of the
Atomical Philosophy have endeavoured to solve, by supposing the primary
or constituent Atoms of Gold to be much larger than those of other Bodies,
and consequently the Pores fewer; whereas in other Bodies, the great
multitude of the interspersed Vacuities does diminish their Weights.

Being desirous to examine this Notion of the Magnitude of Atoms of
Gold, I bethought my self of the extreme Ductility of that Metal, which is
seen in the beating of it into Leaf, and above all in the drawing fine Gilt-
wire, by means whereof, I believed I might most exactly obtain the true
thickness of the Coat of Gold, that appears, even with the Microscope, so
well to represent Gold it self, that not the least point of Silver appears
through it. In order to this, I inform'd my self among the Wire-drawers,
what Gold they us'd to their Silver; and they told me, That the very best
double Gilt Wire was made out of Cylindrick Ingots, 4 Inches in
Circumference, and 28 Inches long, which weigh 16 Pounds Troy; on these
they bestow 4 Ounces of Gold, that is, to every 48 Ounces of Silver one of
Gold; and that two Yards of the super-fine Wire weighs a Grain. Hence at
first sight it appear'd, that the length of 98 Yards is in weight 49 Grains, and
that a single Grain of Gold covers the said 98 Yards, and that the 10000th
part of a Grain is above ⅓ of an Inch long; which yet may be actually
divided into 10, and so the 100000th part of a Grain of Gold be visible
without a Microscope. But being desirous to compute the thickness of the
Skin of Gold, by means of the specifick Gravities of the Metals, viz. Silver
10⅓, and Gold 18⅔, I found the Diameter of such Wire the 1⁄386 part of an
Inch, and its Circumference the 1⁄123 part; but the Gold in thickness not to
exceed the 1⁄134500 part of an Inch; whence it may be concluded, that the
Cube of the hundredth part of an Inch would contain above 2433000000,
(or the Cube of 1345) of such Atoms. And it may likewise be marvelled at,
that Gold being stretcht to so great a degree, as is here demonstrated, should
yet shew it self of so even and united a Texture, as not to let the white
Colour of the Silver under it appear through any the least Pores; which
argues, that even in this exceeding thinness very many of those Atoms may
still lie one over the other: Which is a Consideration may merit the
Thoughts of this Honourable Society, as tending to examine that renowned
Atomical Doctrine, which has of late much obtain'd among the Learned.

Account of the several Species of Infinite Quantity, and of the
Proportions they bear one to the other; as it was read before the
Royal Society, by E. Halley.

HAT all Magnitudes infinitely great, or such as exceed any assignable
T Quantity, are equal among themselves, though it be vulgarly received
for a Maxim, is not yet so common as it is erroneous; and the Reason
of the mistake seems to be, That the Mind of Man, coming to contemplate
the Extensions of what exceeds the bounds of its Capacity, and of which the
very Idea does include a Negation of Limits; it comes to pass that we
acquiesce generally, and it suffices to say such a Quantity is infinite.
But if we come more nearly to examine this Notion, we shall find, that
there are really besides infinite Length and infinite Area, no less than three
several sorts of infinite Solidity; all of which are Quantitates sui generis,
having no more relation or proportion the one to the other, than a Line to a
Plane, or a Plane to a Solid, or a Finite to an Infinite. But that among
themselves, each of those Species of Infinites are in given Proportions, is
what I now intend to make plain, if possible.
But first, infinite Length, or a Line infinitely long, is to be considered
either as beginning at a Point, and so infinitely extended one way, or else
both ways from the same Point; in which case the one, which is a beginning
infinity, is the one half of the whole, which is the Summ of the beginning
and ceasing Infinity; or, as I may say, of Infinity, à parte ante, and à parte
post: Which is analogous to Eternity in Time or Duration, in which there is
always as much to follow as is past, from any point or moment of Time:
Nor doth the Addition or Subduction of finite Length or Space of time alter
the case either in Infinity or Eternity, since both the one or the other cannot
be any part of the whole.
As to infinite Surface or Area, any right Line, infinitely extended both
ways on an infinite Plane, does divide that infinite Plane into equal Parts;
the one to the right, and the other to the left of the said Line: But if from

any Point in such a Plane, two right Lines be infinitely extended, so as to
make an Angle, the infinite Area, intercepted between those infinite right
Lines, is to the whole infinite Plane, as the Arch of a Circle, on the Point of
Concourse of those Lines, as a Centre, intercepted between the said Lines,
is to the Circumference of the Circle; or as the Degrees of the Angle to the
360 Degrees of a Circle. For Example, two right Lines meeting at a right
Angle do include, on an infinite Plane, a quarter part of the whole infinite
Area of such a Plane.
But if so be, two parallel infinite Lines be supposed drawn on such an
infinite Plane, the Area intercepted between them will be likewise infinite;
but at the same time will be infinitely less, than that Space which is
intercepted between two infinite Lines that are inclined, though with never
so small an Angle; for that in the one Case, the given finite distance of the
parallel Lines diminishes the Infinity in one Degree of Dimension; whereas
in a Sector, there is Infinity in both Dimensions; and consequently, the
Quantities are the one infinitely greater than the other, and there is no
proportion between them.
From the same Consideration arise the Three several Species of infinite
Space or Solidity, as has been said; for a Parallelepipede, or a Cylinder,
infinitely long, is greater than any finite Magnitude how great soever; and
all such Solids, supposed to be formed on given Bases, are as those Bases,
in proportion to one another. But if two of these three Dimensions are
wanting, as in the Space intercepted between two parallel Planes infinitely
extended, and at a finite distance; or with infinite Length and Breadth, with
a finite Thickness; All such Solids shall be as the given finite distances one
to another: But these Quantities, though infinitely greater than the other, are
yet infinitely less than any of those, wherein all the three Dimensions are
infinite. Such are the Spaces intercepted between two inclined Planes
infinitely extended; the Space intercepted by the Surface of a Cone, or the
sides of a Pyramid likewise infinitely continued, &c. of all which
notwithstanding, the Proportions one to another, and to the τὸ πᾶν, or vast

Abyss of infinite Space (wherein is the Locus of all things that are or can
be; or to the Solid of infinite Length, Breadth, and Thickness, taken all
manner of ways) are easily assignable. For the Space between two Planes,
is to the whole, as the Angle of those Planes to the 360 Degrees of the
Circle. As for Cones and Pyramids, they are as the Spherical Surface,
intercepted by them, is to the Surface of the Sphere; and therefore Cones
are as the versed Sines of half their Angles, to the Diameter of the Circle:
These three sorts of infinite Quantity are analogous to a Line, Surface and
Solid, and after the same manner cannot be compared, or have any
proportion the one to the other.
Besides these, there are several other Species of infinite Quantity, arising
from the Contemplation of Curves, and their Asymptotes; which, by reason
of the difficulty of the Subject, cannot be made so plain to most Readers:
But what has been already said, may be sufficient to evince what we
undertook to explain.

Account of Dr. Robert Hook's Invention of the Marine Barometer,
with its Description and Uses; published by order of the Royal
Society, by E. Halley, R. S. S.

Ince it was found that the Torricellian Tube, commonly call'd the
S Mercurial Barometer, by the rising and falling of the Quick-silver
therein, doth presage the Changes of the Air, in relation to fair and foul
Weather; upon several Years Observation of it, it has been proved and
adjusted for that purpose by Dr. Robert Hook; and there have been by him
many attempts to improve the Instrument, and render the Minute Divisions
on the Scale thereof more sensible. He also judging that it might be of great
use at Sea, contrived several ways to make it serviceable on Board of Ship;
one of which he explain'd to the Royal Society at their Weekly Meeting in
Gresham College, January 2. 1667/8. Since which time he hath further
cultivated the Invention, and some Years ago produced before the said

Society, the Instrument I am now to describe, which for its subtilty and
usefulness, seemeth to surpass all other performances of the like Nature.
'Till such time as the Author's present Indisposition will give him leave to
bestow freely his Thoughts on this Subject upon the Publick, it is the
Opinion of the Society, that such an Account be given of this Contrivance,
as may render it known, and recommend it to the Mariners use, for which it
was principally intended.
The Mercurial Barometer requiring a perpendicular Posture, and the
Quick-silver vibrating therein with great Violence upon any Agitation, is
therefore uncapable of being used at Sea (tho' it hath lately been contrived
to be made portable), so it remain'd to find out some other Principle,
wherein the Position of the Instrument was not so indispensably necessary:
For this, all those that use the Sea are obliged to the great facility Dr. Hook
has always shewn, in applying Philosophical Experiments to their proper
uses.
It is about forty Years since, that the Thermometers of Robert de
Fluctibus, depending on the Dilatation and Contraction of included Air by
Heat and Cold, have been disused, upon discovery that the Airs pressure is
unequal; that inequality mixing it self with the Effects of the warmth of the
Air in that Instrument. And instead thereof was substituted the seal'd
Thermometer, including Spirit of Wine (first brought into England, out of
Italy, by Sir Robert Southwell) as a proper Standard of the temper of the
Air, in relation to Heat and Cold; that Ætherial Spirit being of all the known
Liquors the most susceptible of Dilatation and Contraction, especially with
a moderate degree of either Heat or Cold. Now this being allow'd as a
Standard, and the other Thermometer that includes Air, being graduated
with the same Divisions, so as at the time when the Air was included, to
agree with the Spirit-Thermometer in all the degrees of Heat and Cold,
noting at the same time the precise height of the Mercury in the common
Barometers: It will readily be understood, that whensoever these two

Thermometers shall agree, the pressure of the Air is the same it was, when
the Air was included, and the Instrument graduated: That if in the Air-
Thermometer the Liquor stand higher than the Division marked thereon,
corresponding with that on the Spirit-glass, it is an indication that there is a
greater pressure of the Air at that time, than when the Instrument was
graduated. And the contrary is to be concluded, when the Air-glass stands
lower than the Spirit, viz. that then the Air is so much lighter, and the Quick
silver, in the ordinary Barometer lower than at the said time of Graduation.
And the Spaces answering to an Inch of Mercury, will be more or less,
according to the quantity of Air so included, and the smallness of the Glass
Cane, in which the Liquor rises and falls, and may be augmented almost in
any proportion, under that of the Specifick Gravity of the Liquor of the
Thermometer to Mercury. So as to have a Foot or more for an Inch of
Mercury, which is another great convenience.
It has been observed by some, that in long keeping this Instrument, the
Air included either finds a means to escape, or deposites some Vapours mixt
with it, or else for some other cause becomes less Elastick, whereby, in
process of time, it gives the height of the Mercury somewhat greater than it
ought; but this, if it should happen in some of them, hinders not the
usefulness thereof, for that it may at any time very easily be corrected by
Experiment, and the rising and falling thereof are the things chiefly
remarkable in it, the just height being barely a Curiosity.
In these Parts of the World, long Experience has told us, that the rising of
the Mercury forebodes fair Weather after foul, and an Easterly or Northerly
Wind; and that the falling thereof, on the contrary, signifies Southerly or
Westerly Winds, with Rain, or stormy Winds, or both; which latter it is of
much more consequence to provide against at Sea than at Land; and in a
Storm, the Mercury beginning to rise is a sure sign that it begins to abate, as
has been experienced in high Latitudes, both to the Northwards and
Southwards of the Æquator.

The Form of this Instrument is shown in the Cut, by Tab. 4. Fig. 1.
wherein,
AB represents the Spirit-Thermometer, graduated from 0, or the freezing
Point, through all the possible degrees of the Heat or Cold of the Air, at
least in these Climates.
CD, is the Air-Thermometer, graduated after the same manner with the
like Degrees.
EF, is a Plate applied to the side of the Thermometer CD, graduated into
Spaces answering to Inches and parts of an Inch of Mercury, in the common
Barometers.
G, a Hand standing on the Plate at the height of the Mercury thereon, as it
was when the Instrument was graduated, as suppose here at 29½ Inches.
LM, a Wire on which the Plate EF, slips up and down, parallel to the
Cane of the Thermometer CD.
K, any Point at which the Spirit stands at the time of Observation;
suppose at 38 on the Spirit-Thermometer; Slide the Plate EF till the Hand G
stand at 38 on the Air-Thermometer, and if the Liquor therein stand at 38
likewise, then is the pressure of the Air the same as at the time of
Graduation, viz. 29,5; but if it stand higher, as at 30, at I; then is the
pressure of the Air greater; and the division on the sliding Plate against the
Liquor, shews the present height of the Mercury to be twenty nine Inches
seven Tenths. And this may suffice as to the manner of using it.
I had one of these Barometers with me in my late Southern Voyage, and
it never failed to prognostick and give early notice of all the bad Weather
we had, so that I depended thereon, and made provision accordingly; and
from my own Experience I conclude that a more useful Contrivance hath
not for this long time been offer for the benefit of Navigation.
These Instruments are made according to the Direction of Dr. Hook, by
Mr. Henry Hunt, Operator to the Royal Society, who will furnish any

Gentlemen with them, and give them Directions how to use them.

Discourse concerning the Proportional Heat of the Sun in all
Latitudes, with the Method of collecting the same; as it was read
before the Royal Society, in one of their late Meetings. By E.
Halley.

Here having lately arisen some Discourse about that part of the Heat of
T Weather, simply produced by the Action of the Sun; and I having
affirmed, that if that were considered, as the only Cause of the Heat of
the Weather, I saw no Reason, but that under the Pole the solstitical Day
ought to be as hot as it is under the Æquinoctial, when the Sun comes
vertical, or over the Zenith: For this Reason, that for all the 24 Hours of that
Day under the Pole, the Sun's Beams are inclined to the Horizon, with an
Angle of 23½ Degrees; and under the Æquinoctial, though he come
vertical, yet he shines no more than 12 Hours, and is again 12 Hours absent;
and that for 3 Hours 8 Minutes of that 12 Hours, he is not so much elevated
as under the Pole; so that he is not 9 of the whole 24, higher than 'tis there,
and is 15 Hours lower. Now the simple Action of the Sun is, as all other
Impulses or Stroaks, more or less forceable, according to the Sinus of the
Angle of Incidence, or to the Perpendicular let fall on the Plain, whence the
vertical Ray (being that of the greatest Heat,) being put Radius, the force of
the Sun on the Horizontal Surface of the Earth will be to that, as the Sinus
of the Sun's Altitude at any other time. This being allow'd for true, it will
then follow, that the time of the continuance of the Sun's shining being
taken for a Basis, and the Sines of the Sun's Altitudes erected thereon as
Perpendiculars, and a Curve drawn through the Extremities of those
Perpendiculars, the Area comprehended shall be proportionate to the
Collection of the Heat of all the Beams of the Sun in that space of time.
Hence it will follow, that under the Pole the Collection of all the Heat of a
tropical Day, is proportionate to a Rectangle of the Sine of 23½ gr. into 24

Hours, or the Circumference of a Circle; that is, the Sine of 23½ gr. being
nearly 4 Tenths of Radius; as 3⁄10 into 12 Hours. Or the Polar Heat is equal
to that of the Sun containing 12 Hours above the Horizon, at 53 gr. height,
than which the Sun is not 5 Hours more elevated under the Æquinoctial.
But that this Matter may the better be understood, I have exemplified it
by a Scheme, (Tab. 4. Fig. 2) wherein the Area ZGHH, is equal to the Area
of all the Sines of the Sun's Altitude under the Æquinoctial, erected on the
respective Hours from Sun-rise to the Zenith; and the Area ♋HH♋ is in the
same proportion to the Heat of the same 6 Hours under the Pole on the
Topical Day; and ⨀HHQ, is proportional to the collected Heat of 12 Hours,
or half a Day under the Pole, which space ⨀HHQ, is visibly greater than
the other Area HZGH, by as much as the Area HGQ is greater than the Area
ZG⨀; which, that it is so, is visible to sight, by a great excess; and so much
in proportion does the Heat of the 24 Hours Sun-shine under the Pole,
exceed that of the 12 Hours under the Æquinoctial: Whence, Cæteris
paribus, it is reasonable to conclude, that were the Sun perpetually under
the Tropick, the Pole would be at least as warm, as it is now under the Line
it self.
But whereas the Nature of Heat is to remain in the Subject, after the
Cause that heated is removed, and particularly in the Air; under the
Æquinoctial, the 12 Hours absence of the Sun does very little still the
Motion impressed by the part Action of his Rays, wherein Heat consists,
before he arise again: But under the Pole the long absence of the Sun for 6
Months, wherein the extremity of Cold does obtain, has so chill'd the Air,
that it is as it were frozen, and cannot, before the Sun has got far towards it,
be any way sensible of his presence, his Beams being obstructed by thick
Clouds, and perpetual Fogs and Mists, and by that Atmosphere of Cold, as
the late Honourable Mr. Boyle was pleased to term it, proceeding from the
everlasting Ice, which in immense Quantities does chill the Neighbouring
Air, and which the too soon retreat of the Sun leaves unthawed, to encrease
again, during the long Winter that follows this short interval of Summer.

But the differing Degrees of Heat and Cold, in differing Places, depend in
great measure upon the Accidents of the Neighbourhood of high Mountains,
whose height exceedingly chills the Air brought by the Winds over them;
and of the Nature of the Soil, which variously retains the Heat, particularly
the Sandy, which in Africa, Arabia, and generally where such Sandy
Desarts are found, do make the Heat of the Summer incredible to those that
have not felt it.
In the prosecution of this first Thought, I have solved the Problem
generally, viz. to give the proportional Degree of Heat, or the Sum of all the
Sines of the Sun's Altitude, while he is above the Horizon in any oblique
Sphere, by reducing it to the finding of the Curve Surface of a Cylindrick
Hoof, or of a given part thereof.
Now this Problem is not of that difficulty as appears at first sight, for in
Tab. 4. Fig. 3. let the Cylinder ABCD be cut obliquely with the Ellipse
BKDI, and by the Center thereof H, describe the Circle IKLM; I say, the
Curve Surface IKLB is equal to the Rectangle of IK and BL, or of HK and
2 BL or BC: And if there be supposed another Circle, as NQPO, cutting the
said Ellipse in the Points P, Q; draw PS, QR, parallel to the Cylinders Axe,
till they meet with the aforesaid Circle IKLM in the Points R, S, and draw
the Lines RTS, QVP bisected in T and V. I say again, that the Curve Surface
RMSQDP is equal to the Rectangle of BL or MD and RS, or of 2 BL or AD
and ST or VP; and the Curve Surface QNPD is equal to RS × MD----the
Arch RMS × SP, or the Arch MS × 2 SP: Or it is equal to the Surface
RMSQDP, substracting the Surface RMSQNP. So likewise the Curve
Surface QBPO is equal to the Sum of the Surface RMSQDP, or RS × MD,
and of the Surface RLSQOP, or the Arch LS × 2 SP.
This is the most easily demonstrated from the Consideration, That the
Cylindrick Surface IKLB is to the inscrib'd Spherical Surface IKLE, either
in the whole, or in its Analogous Parts, as the tangent BL is to the Arch EL,
and from the Demonstrations of Archimedes de Sphæra & Cylindro, Lib. I.

Prop. XXX, and XXXVII, XXXIIX. which I shall not repeat here, but leave the
Reader the pleasure of examining it himself; nor will it be amiss to consult
Dr. Barrow's Learned Lectures on that Book, Publish'd at London, Anno
1684, viz. Probl. IX. and the Corollaries thereof.
Now to reduce our Case of the Sum of all the Sines of the Sun's Altitude
in a given Declination and Latitude to the aforesaid Problem, let us consider
(Tab. 4. Fig. 4.) which is the Analemma projected on the Plain of the
Meridian, Z the Zenith, P the Pole, HH the Horizon, ææ the Æquinoctial,
♋♋, ♑♑ the two Tropicks, ♋1 the Sine of the Meridian Altitude in ♋; and
equal thereto, but perpendicular to the Tropick, erect ♋I, and draw the Line
TI intersecting the Horizon in T, and the Hour Circle of 6, in the Point 4,
and 64 shall be equal to 6R, or to the Sine of the Altitude at 6: And the like
for any other Point in the Tropick, erecting a Perpendicular thereat,
terminated by the Line T I: Through the Point 4 draw the Line 4, 5, 7
parallel to the Tropick, and representing a Circle equal thereto; then shall
the Tropick ♋♋ in Fig. 4. answer to the Circle NOPQ, in Fig. 3. the Circle
457 shall answer the Circle IKLM, T4I shall answer to the Elliptick
Segment QIBKP, 6R or 64 shall answer to SP, and 5I to BL, and the Arch
♋ T, to the Arch LS, being the semidiurnal Arch in that Latitude and
Declination; the Sine whereof, tho' not expressible in Fig. 4. must be
conceived as Analogous to the Line TS or UP in Fig. 3.
The Relation between these two Figures being well understood, it will
follow from what precedes, That, the sum of the Sines of the Meridian
Altitudes of the Sun in the two Tropicks, (and the like for any two opposite
Parallels) being multiplied by the Sine of the semidiurnal Arch, will give an
Area Analogous to the Curve Surface RIMSQDP; and thereto adding in
Summer, or substracting in Winter, the Product of the length of the
semidiurnal Arch, (taken according to Van Ceulen's Numbers) into the
difference of the above-said Sines of the Meridian Altitude: The sum in one
case, and difference in another, shall be as the Aggregate of all the Sines of
the Sun's Altitude, during his appearance above the Horizon; and

consequently of all his Heat and Action on the Plain of the Horizon in the
proposed Day. And this may also be extended to the parts of the same Day;
for if the aforesaid Sum of the Sines of the Meridian Altitudes, be
multiplied by half the Sum of the Sines of the Sun's Horary distance from
Noon, when the Times are before and after Noon; or by half their
difference, when both are on the same side of the Meridian; and thereto in
Summer, or therefrom in Winter, be added or substracted the Product of half
the Arch answerable to the proposed interval of Time, into the difference of
the Sines of Meridian Altitudes, the Sum in one case and Difference in the
other, shall be proportional to all the Action of the Sun during that space of
time.
I fore-see it will be Objected, that I take the Radius of my Circle on
which I erect my Perpendiculars always the same, whereas the Parallels of
Declination are unequal; but to this I answer, That our said Circular Bases
ought not to be Analogous to the Parallels, but to the Times of Revolution,
which are equal in all of them.
It may perhaps be useful to give an Example of the Computation of this
Rule, which may seem difficult to some. Let the Solstitical Heat in ♋ and
♑ be required at London, Lat. 51° 32'.

380- 2'28 Co-Lat
23-30 Decl. ⨀
61-58 Sinus = ,8826 4
14-58 Sinus = ,258257
Summa 1,140931
Diff. ,624417

Diff. Ascen. 3300-1'1.
Arch. Semid. æstiv. 123-11.
Ar. Sem. hyb. 56-49. S. 638923
Arch. æstiv. mensura 2,149955
Arc. hyb. mensura 991683

Then 1,140931 in ,836923 + 624417 in 2,149955 = 2,29734. And 1,140931
in 836929 - ,624417 in ,991638 = 33895.
So that 2,29734 will be as the Tropical Summers Day Heat, and 0,33895
as the Action of the Sun in the Day of the Winter Solstice.
After this manner I computed the following Table for every tenth Degree
of Latitude, to the Æquinoctial and Tropical Sun, by which an Estimate may
be made of the intermediate Degrees.

Sun in Sun in Sun in
Lat.
♈♎ ♋ ♑

0 20000 18341 18341
10 19696 20290 15834
20 18794 21737 13166
30 17321 22651 10124
40 15321 23048 6944
50 12855 22991 3798
60 10000 22773 1075
70 6840 23543 000
80 3473 24673 000
90 0000 25055 000

Those that desire more of the Nature of this Problem, as to the Geometry
thereof, would do well to compare the XIII. Prop. Cap. V. of the Learned
Treatise, De Calculo Centri Gravitatis, by the Reverend Dr. Wallis,
Published Anno 1670.
From this Rule there follow several Corollaries worth Note: As I. That
the Æquinoctial Heat, when the Sun comes Vertical, is as twice the Square
of Radius, which may be proposed as a Standard to compare with, in all
other Cases. II. That under the Æquinoctial, the Heat is as the Sine of the
Sun's Declination. III. That in the Frigid Zones when the Sun sets not, the

Heat is as the Circumference of a Circle into the Sine of the Altitude at 6.
And consequently, that in the same Latitude these Aggregates of Warmth,
are as the Sines of the Sun's Declinations; and in the same Declination of
Sol, they are as the Sines of the Latitude, and generally they are as the Sines
of the Latitude into the Sines of Declination. IV. That the Æquinoctial Days
Heat is every where as the Co-sine of the Latitude. V. In all places where
the Sun sets, the difference between the Summer and Winter Heats, when
the Declinations are contrary, is equal to a Circle into the Sine of the
Altitude at six in the Summer Parallel, and consequently those differences
are as the Sines of Latitude into, or multiplied by the Sines of Declination.
VI. From the Table I have added, it appears, that the Tropical Sun under the
Æquinoctial, has, of all others, the least Force. Under the Pole it is greater
than any other Days Heat whatsoever, being to that of the Æquinoctial as 5
to 4.
From the Table and these Corollaries may a general Idea be conceived of
the Sum of all the Actions of the Sun in the whole Year, and that part of the
Heat that arises simply from the Presence of the Sun be brought to a
Geometrical Certainty: And if the like could be performed for Cold; which
is something else than the bare Absence of the Sun, as appears by many
Instances, we might hope to bring what relates to this part of Meteorology
to a perfect Theory.

cerning the Distance of the Fix'd Stars. By the Honourable Francis
Roberts, Esq; S. R. S.

HE Ancient Astronomers, who had no other way of computing the
T Distances of the Heavenly Bodies, but by their Parallax to the Semi-
diameter of the Earth; and being never able to discover any in the fix'd
Stars, did from thence rightly enough infer, that their Distance was very
great, and much exceeding that of the Planets, but could go no farther
otherwise than by uncertain guess.

Since the Pythagorean System of the World has been reviv'd by
Copernicus, (and now by all Mathematicians accepted for the true one)
there seem'd Ground to imagine that the Diameter of the Earth's Annual
Course (which, according to our best Astronomers, is at least 40000 times
bigger than the Semi-diameter of the Earth) might give a sensible Parallax
to the fix'd Stars, though the other could not, and thereby determine their
Distance more precisely.
But though we have a Foundation to build on so vastly exceeding that of
the Ancients, there are some Considerations may make us suspect that even
this is not large enough for our purpose.
Monsieur Hugens (who is very exact in his Astronomical Observations)
tells us, he could never discover any visible Magnitude in the fix'd Stars,
though he used Glasses which magnified the apparent Diameter above 100
times.
Now, since in all likelyhood the fix'd Stars are Suns, (perhaps of a
different Magnitude) we may as a reasonable Medium presume they are
generally about the bigness of the Sun.
Let us then (for Example) suppose the Dog-Star to be so. The Distance
from us to the Sun being about 100 times the Sun's Diameter (as is
demonstrable from the Sun's Diameter being 32 Minutes) it is evident, that
the Angle under which the Dog-Star is seen in Mr. Hugens's Telescope,
must be near the same with the Angle of its Parallax to the Sun's Distance,
or Semi-diameter of the Earth's Annual Course; so that the Parallax to the
whole Diameter, can be but double such a quantity, as even to Mr. Hugens's
nice Observation is altogether insensible.
The Distance therefore of the fix'd Stars seems hardly within the reach of
any of our Methods to determine; but from what has been laid down, we
may draw some Conclusions that will much illustrate the prodigious
vastness of it.

1. That the Diameter of the Earth's Annual Orb (which contains at least
160 Millions of Miles) is but as a Point in comparison of it; at least it must
be above 6000 times the Distance of the Sun. For if a Star should appear
thro' the aforesaid Telescope half a Minute broad (which is a pretty sensible
Magnitude) the true apparent Diameter would not exceed 18 3d Minutes,
which is less than the 6000th part of the apparent Diameter of the Sun, and
consequently the Sun's Distance not the 6000th part of the Distance of the
Star.
2. That could we advance towards the Stars 99 Parts of the whole
Distance, and have only 1⁄100 Part remaining, the Stars would appear little
bigger to us than they do here; for they would shew no otherwise than they
do through a Telescope, which magnifies an Hundred-fold.
3. That at least Nine Parts in Ten of the Space between us and the fix'd
Stars, can receive no greater Light from the Sun, or any of the Stars, than
what we have from the Stars in a clear Night.
4. That Light takes up more time in travelling from the Stars to us, than
we in making a West-India Voyage (which is ordinarily perform'd in six
Weeks.) That a Sound would not arrive to us from thence in 50000 Years,
nor a Cannon-bullet in a much longer time. This is easily computed, by
allowing (according to Mr. Newton) Ten Minutes for the Journey of Light
from the Sun hither, and that a Sound moves about 1300 Foot in a Second.

Famous Mr. Isaac Newton's Theory of the Moon.

HIS Theory which hath been long expected by all the true Lovers of
T Astronomy, was communicated from Mr. Newton to Dr. Gregory,
Astronomy Professor at Oxford, and by him published in his Astron.
Elem. Philos. and Geomet. p. 336. From whence, as it was lately translated
into English, I thought fit to insert it here.

By this Theory, what by all Astronomers was thought most difficult and
almost impossible to be done, the Excellent Mr. Newton hath now effected;
viz. to determine the Moon's Place even in her Quadratures, and all other
Parts of her Orbit, besides the Syzygys, so accurately by Calculation, that
the Difference between that and her true Place in the Heavens, shall scarce
be above two minutes in her Syzygys, or above three in her Quadratures,
and is usually so small, that it may well enough be reckon'd only as a
Defect in the Observation. And this Mr. Newton experienced, by comparing
it with very many Places of the Moon, observ'd by Mr. Flamsteed, and
communicated to him.
The Royal Observatory at Greenwich, is to the West of the Meridian of
Paris, 2 degrees, 19 minutes. Of Uraniburgh, 12 degrees, 51 minutes, 30
seconds. And of Gedanum, 18 degrees, 48 minutes.
The mean Motions of the Sun and Moon, accounted from the Vernal
Æquinox at the Meridian of Greenwich, I make to be as followeth.
The last Day of December 1680, at Noon (Old Stile) the mean Motion of
the Sun was 9 Signs, 20 degrees, 34 minutes, 46 seconds. Of the Sun's
Apogæum, was 3 S. 7 deg. 23 min. 30 seconds.
That the mean Motion of the Moon at that time, was 6 S. 1 degree, 45
minutes, 45 seconds. And of her Apogee, 8 S. 4 degrees, 28 minutes, 5
seconds. Of the ascending Node of the Moon's Orbit, 5 S. 24 deg. 14 min.
35 seconds, &c.
And on the last Day of December, 1700, at Noon, the mean Motion of the
Sun was 9 S. 20 degrees, 43 minutes, 50 seconds. Of the Sun's Apogee, 3 S.
7 degrees, 44 minutes, 30 seconds. The mean Motion of the Moon was
10 S. 15 degrees, 19 minutes, 50 seconds. Of the Moon's Apogee, 11 S. 8
degrees, 18 minutes, 20 seconds. And of her ascending Node, 4 S. 27
degrees, 24 minutes, 20 seconds. For in 20 Julian Years, or 7305 Days, the
Sun's Motion is 20 Revol. 0 S. 0 degrees, 9 minutes, 4 seconds. And the
Motion of the Sun's Apogee, 21 minutes, 0 seconds.

The Motion of the Moon in the same time, is 267 Revol. 4 S. 13 degrees,
34 minutes, 5 seconds. And the Motion of the Lunar Apogee, is 2 Revol.
3 S. 3 degrees, 50 minutes, 15 seconds. And the Motion of her Node, 1
Revol. 0 S, 26 degrees, 50 minutes, 15 seconds.
All which Motions are accounted from the Vernal Æquinox: Wherefore if
from them there be subtracted the Recession or Motion of the Æquinoctial
Point, in Antecedentia, during that space, which is 16 minutes, 40 seconds,
there will remain the Motions in reference to the fix'd Stars in 20 Julian
Years; viz. the Sun's 19 Revol. 11 S. 29 degrees, 52 minutes, 24 seconds. Of
his Apogee, 4 minutes, 20 seconds. And the Moon's 267 Revol. 4 S. 13
degrees, 17 minutes, 25 seconds. Of her Apogee, 2 Revol. 3 S. 3 degrees, 33
minutes, 35 seconds. And of the Node of the Moon, 1 Revol. 0 S. 27
degrees, 6 minutes, 55 seconds.
According to this Computation, the Tropical Year is 365 Days, 5 Hours,
48 Minutes, 57 Seconds. And the Sydereal Year is 365 Days, 6 Hours, 9
Minutes, 14 Seconds.
These mean Motions of the Luminaries are affected with various
Inequalities: Of which,
1. There are the Annual Equations of the aforesaid mean Motions of the
Sun and Moon, and of the Apogee and Node of the Moon.
The Annual Equation of the mean Motion of the Sun, depends on the
Eccentricity of the Earth's Orbit round the Sun, which is 1611⁄12 of such
Parts, as that the Earth's mean Distance from the Sun shall be 1000:
Whence 'tis call'd the Equation of the Centre; and is, when greatest, 1
degree, 56 minutes, 20 seconds.
The greatest Annual Equation of the Moon's mean Motion, is 11 degrees,
49 seconds; of her Apogee, 20 minutes, and of her Node, 9 minutes, 30
seconds.

And these four Annual Equations are always mutually proportional one
to another: Wherefore when any of them is at the greatest, the other three
will also be greatest; and when any one lessens, the other three will also be
diminished in the same Ratio.
The Annual Equation of the Sun's Centre being given, the three other
corresponding Annual Equations will be also given; and therefore a Table of
that will serve for all. For if the Annual Equation of the Sun's Centre be
taken from thence, for any Time, and be call'd P, and let ⅒P = Q, Q + 1⁄60Q
= R, ⅙ P = D, D + 1⁄30D = E, and D - 1⁄50D = 2F; then shall the Annual
Equation of the Moon's mean Motion for that time be R, that of the Apogee
of the Moon will be E, and that of the Node F.
Only observe here, That if the Equation of the Sun's Centre be required to
be added; then the Equation of the Moon's mean Motion must be subtracted,
that of her Apogee must be added, and that of the Node subducted, And on
the contrary, if the Equation of the Sun's Centre were to be subducted, the
Moon's Equation must be added, the Equation of her Apogee subducted,
and that of her Node added.
There is also an Equation of the Moon's mean Motion, depending on the
situation of her Apogee, in respect of the Sun; which is greatest when the
Moon's Apogee is in an Octant with the Sun, and is nothing at all when it is
in the Quadratures or Syzygys. This Equation, when greatest, and the Sun in
Perigæo, is 3 Minutes, 56 Seconds. But if the Sun be in Apogæo, it will
never be above 3 Minutes, 34 Seconds. At other Distances of the Sun from
the Earth, this Equation, when greatest, is reciprocally as the Cube of such
Distance. But when the Moon's Apogee is any where but in the Octants, this
Equation grows less, and is mostly at the same distance between the Earth
and Sun, as the Sine of the double Distance of the Moon's Apogee, from the
next Quadrature or Syzygy, to the Radius.
This is to be added to the Moon's Motion, while her Apogee passes from
a Quadrature with the Sun to a Syzygy; but this is to be subtracted from it,

while the Apogee moves from the Syzygy to the Quadrature.
There is moreover another Equation of the Moon's Motion, which
depends on the Aspect of the Nodes of the Moon's Orbit with the Sun: And
this is greatest, when her Nodes are in Octants to the Sun, and vanishes
quite, when they come to their Quadratures or Syzygys. This Equation is
proportional to the Sine of the double Distance of the Node from the next
Syzygy, or Quadrature; and at greatest, is but 47 seconds. This must be
added to the Moon's mean Motion, while the Nodes are passing from their
Syzygys with the Sun, to their Quadratures with him; but subtracted while
they pass from the Quadratures to the Syzygys.
From the Sun's true Place, take the equated mean Motion of the Lunar
Apogee, as was above shew'd, the Remainder will be the Annual Argument
of the said Apogee. From whence the Eccentricity of the Moon, and the
second Equation of her Apogee may be computed after the manner of the
following (which takes place also in the Computation of any other
intermediate Equations).
Tab. 3. Fig. 6. Let T represent the Earth, TS, a Right Line joining the
Earth and Sun, TACB, a Right Line drawn from the Earth to the middle or
mean Place of the Moon's Apogee, equated, as above: Let the Angle STA be
the Annual Argument of the aforesaid Apogee, TA the least Eccentricity of
the Moon's Orbit, TB the greatest. Bissect AB in G; and on the Centre C,
with the Distance AC describe a Circle AFB, and make the Angle BCF = to
the double of the Annual Argument. Draw the Right Line TF, that shall be
the Eccentricity of the Moon's Orbit; and the Angle BTF, is the second
Equation of the Moon's Apogee required.
In order to whose Determination, let the mean Distance of the Earth from
the Moon, or the Semi-diameter of the Moon's Orbit, be 100000; then shall
its greatest Eccentricity TB be 66782 such Parts; and the least TA, 43319.
So that the greatest Equation of the Orbit, viz. when the Apogee is in the
Syzygys, will be 7 degrees, 39 minutes, 30 seconds, or perhaps 7 degrees,

40 minutes, (for I suspect there will be some Alteration, according to the
Position of the Apogee in Cancer and Capricorn.) But when it is Quadrate
to the Sun, the greatest Equation aforesaid will be 4 degrees, 57 minutes, 56
seconds; and the greatest Equation of the Apogee, 12 degrees, 15 minutes, 4
seconds.
Having from these Principles made a Table of the Equation of the Moon's
Apogee, and of the Eccentricities of her Orbit to each degree of the Annual
Argument, from whence the Eccentricity TF, and the Angle BTF (viz. the
second and the principal Equation of the Apogee) may easily be had for any
Time required; let the Equation thus found be added to the first Equated
Place of the Moon's Apogee, if the Annual Argument be less than 90
degrees, or greater than 180 degrees, and less than 270; otherwise it must be
subducted from it; and the Sum or Difference shall be the Place of the
Lunar Apogee secondarily equated; which being taken from the Moon's
Place equated a third time, shall leave the mean Anomaly of the Moon
corresponding to any given Time. Moreover, from this mean Anomaly of
the Moon, and the before-found Eccentricity of her Orbit, may be found (by
means of a Table of Equations of the Moon's Centre made to every degree
of the mean Anomaly, and some Eccentricities, viz. 45000, 50000, 55000,
60000, and 65000) the Prostaphæresis, or Equation of the Moon's Centre,
as in the common way: And this being taken from the former Semi-circle of
the middle Anomaly, and added in the latter to the Moon's Place thus thrice
equated, will produce the Place of the Moon a fourth time equated.
The greatest Variation of the Moon (viz. that which happens when the
Moon is in an Octant with the Sun) is nearly, reciprocally as the Cube of the
Distance of the Sun from the Earth. Let that be taken 37 minutes, 25
seconds, when the Sun is in Perigæo, and 33 minutes, 40 seconds, when he
is in Apogæo: And let the Differences of this Variation in the Octants be
made reciprocally, as the Cubes of the Distances of the Sun from the Earth;
and so let a Table be made of the aforesaid Variation of the Moon in her
Octants (or its Logarithms) to every Tenth, Sixth, or Fifth Degree of the

mean Anomaly: And for the Variation out of the Octants, make, as Radius to
the Sine of the double Distance of the Moon from the next Syzygy, or
Quadrature :: so let the afore-found Variation in the Octant be to the
Variation congruous to any other Aspect; and this added to the Moon's Place
before found in the first and third Quadrant (accounting from the Sun) or
subducted from it in the second and fourth, will give the Moon's Place
equated a fifth time.
Again, as Radius to the Sine of the Summ of the Distances of the Moon
from the Sun, and of her Apogee from the Sun's Apogee (or the Sine of the
Excess of that Summ above 360 degrees,) :: so is 2 minutes, 10 seconds, to
a sixth Equation of the Moon's Place, which must be subtracted, if the
aforesaid Summ or Excess be less than a Semi-circle; but added, if it be
greater. Let it be made also, as Radius to the Sine of the Moon's distance
from the Sun :: so 2 degrees, 20 secants, to a seventh Equation; which when
the Moon's Light is increasing, add; but when decreasing, subtract; and the
Moon's Place will be equated a seventh time, and this is her Place in her
proper Orbit.
Note here, the Equation thus produced by the mean Quantity 2 degrees,
20 seconds, is not always of the same magnitude; but is increased and
diminished, according to the Position of the Lunar Apogee. For if the
Moon's Apogee be in Conjunction with the Sun's, the aforesaid Equation is
about 54 seconds greater: But when the Apogees are in Opposition, 'tis
about as much less; and it librates between its greatest Quantity 3 minutes,
14 seconds, and its least, 1 minute, 26 seconds. And this is, when the Lunar
Apogee is in Conjunction, or Opposition with the Sun's: But in the
Quadratures, the aforesaid Equation is to be lessen'd about 50 seconds, or 1
minute, when the Apogees of the Sun and Moon are in Conjunction; but if
they are in Opposition, for want of a sufficient number of Observations, I
cannot determine, whether it is to be lessen'd or increas'd. And even as to
the Argument or Decrement of the Equation, 2 minutes, 20 seconds, above

mentioned, I dare determine nothing certain, for the same Reason, viz. the
want of Observations accurately made.
If the sixth and seventh Equations are augmented or diminished in a
reciprocal Ratio of the distance of the Moon from the Earth; i. e. in a direct
Ratio of the Moon's Horizontal Parallax, they will become more accurate:
And this may be readily done, if Tables are first made to each minute of the
said Parallax, and to every sixth or fifth degree of the Argument of the sixth
Equation for the Sixth, as of the distance of the Moon from the Sun, for the
Seventh Equation.
From the Sun's Place, take the mean motion of the Moon's ascending
Node, equated as above; the Remainder shall be the Annual Argument of
the Node, whence its second Equation may be computed after the following
manner in the preceding Figure.
Let T, as before, represent the Earth; TS a Right Line, conjoining the
Earth and Sun: Let also the Line TACB, be drawn to the Place of the
ascending Node of the Moon, as above equated; and let STA be the Annual
Argument of the Node. Take TA from a Scale, and let it be to AB :: as 56 to
3, or as 11⅔ to 1. Then bissect BA in C, and on C as a Centre, with the
Distance CA, describe a Circle, as AFB, and make the Angle BCF, equal to
double the Annual Argument of the Node before-found: So shall the Angle
BTF, be the second Equation of the ascending Node; which must be added,
when the Node is passing from the Quadrature to a Syzygy with the Sun;
and subducted, when the Node moves from a Syzygy towards a Quadrature.
By which means, the true Place of the Node of the Lunar Orbit will be
gained: Whence from Tables made after the common way, the Moon's
Latitude, and the Reduction of her Orbit to the Ecliptick, may be computed,
supposing the Inclination of the Moon's Orbit to the Ecliptick, to be 4
degrees, 59 minutes, 35 seconds, when the Nodes are in Quadrature with
the Sun; and 5 degrees, 17 minutes, 20 seconds, when they are in the
Syzygys.

And from the Longitude and Latitude thus found, and the given Obliquity
of the Ecliptick, 23 degrees, 29 minutes, the Right Ascension and
Declination of the Moon will be found.
The Horizontal Parallax of the Moon, when she is in the Syzygys, at a
mean distance from the Earth, I make to be 57 minutes, 30 seconds; and her
Horary Motion, 33 minutes, 32 seconds, 32 thirds; and her apparent
Diameter 31 minutes, 30 seconds. But in her Quadratures at a mean
Distance from the Earth, I make the Horizontal Parallax of the Moon to be
59 minutes, 40 seconds, her Horary Motion 32 minutes, 12 seconds, 2
thirds, and her apparent Diameter, 31 minutes, 3 seconds. The Moon in an
Octant to the Sun, and at a mean distance, hath her Centre distant from the
Centre of the Earth about 602⁄9 of the Earth's Semi-diameters.
The Sun's Horizontal Parallax I make to be 10 seconds, and its apparent
Diameter at a mean distance from the Earth, I make 32 minutes, 15 seconds.
The Atmosphere of the Earth, by dispersing and refracting the Sun's
Light, casts a Shadow, as if it were an Opake Body, at least to the height of
40 or 50 Geographical Miles (by a Geographical Mile, I mean the sixtieth
part of a Degree of a great Circle, on the Earth's Surface.) This Shadow
falling upon the Moon in a Lunar Eclipse, makes the Earth's Shadow be the
larger or broader. And to each Mile of the Earth's Atmosphere, is
correspondent a Second in the Moon's Disk, so that the Semi-diameter of
the Earth's shadow projected upon the Disk of the Moon, is to be increased
about 50 seconds: Or, which is all one, in a Lunar Eclipse, the Horizontal
Parallax of the Moon is to be increased in the Ratio of about 70 to 69.
Thus far the Theory of this Incomparable Mathematician. And if we had
many Places of the Moon accurately observ'd, especially about her
Quadratures, and these well compar'd with her Places, at the same time
calculated according to this Theory; it would then appear, whether there yet
remain any other sensible Equations; which when accounted for, might
serve to improve and enlarge this Theory.

Plate 3. pag. 280.

Estimate of the Degrees of the Mortality of Mankind, drawn from
curious Tables of the Births and Funerals at the City of Breslaw;
with an Attempt to ascertain the Price of Annuities upon Lives. By
Mr. E. Halley, R. S. S.

HE Contemplation of the Mortality of Mankind, has besides the Moral,
T its Physical and Political Uses, both which have been some Years since
most judiciously consider'd by the Curious Sir William Petty, in his
Natural and Political Observations on the Bills of Mortality of London,
own'd by Captain John Graunt: And since in a like Treatise on the Bills of
Mortality of Dublin. But the Deduction from those Bills of Mortality
seemed even to their Authors to be defective: First, In that the Number of
the People was wanting. Secondly, That the Ages of the People dying was
not to be had. And Lastly, That both London and Dublin, by reason of the
great and casual Accession of Strangers who die therein, (as appeared in
both, by the great Excess of the Funerals above the Births) rendred them
incapable of being Standards for this purpose; which requires, if it were
possible, that the People we treat of, should not at all be changed, but die
where they were born, without any adventitious Increase from Abroad, or
Decay by Migration elsewhere.
This Defect seems in a great measure to be satisfied by the late curious
Tables of the Bills of Mortality at the City of Breslaw, lately communicated
to this Honourable Society by Mr. Justell, wherein both the Ages and Sexes
of all that die, are Monthly delivered, and compared with the number of the
Births, for Five Years last past, viz. 1687, 88, 89, 90, 91, seeming to be done
with all the Exactness and Sincerity possible.
This City of Breslaw is the Capital City of the Province of Silesia; or, as
the Germans call it, Schlesia, and is situated on the Western Bank of the
River Oder, anciently call'd Viadrus, near the Confines of Germany and
Poland, and very nigh the Latitude of London. It is very far from the Sea,
and as much a Mediterranean Place as can be desired, whence the

Confluence of Strangers is but small, and the Manufacture of Linnen
employs chiefly the poor People of the Place, as well as of the Country
round about; whence comes that sort of Linnen we usually call your Sclesiæ
Linnen; which is the chief, if not the only Merchandize of the Place. For
these Reasons, the People of this City seem most proper for a Standard; and
the rather, for that the Births do a small matter exceed the Funerals. The
only thing wanting, is the Number of the whole People, which in some
measure I have endeavour'd to supply, by the comparison of the Mortality
of the People of all Ages, which I shall from the said Bills trace out with all
the Accuracy possible.
It appears that in the Five Years mentioned, viz. from 87 to 91 inclusive,
there were born 6193 Persons, and buried 5869; that is, born per Annum
1238, and buried 1174; whence an Increase of the People may be argued of
64 per Annum, or of about a 20th part, which may perhaps be balanc'd by
the Levies for the Emperor's Service in his Wars. But this being contingent,
and the Births certain, I will suppose the People of Breslaw to be increased
by 1238 Births annually. Of these it appears by the same Tables, that 348 do
die yearly in the first Year of their Age, and that but 890 do arrive at a full
Year's Age; and likewise, that 198 do die in the Five Years between 1 and 6
compleat, taken at a Medium; so that but 692 of the Persons born do survive
Six whole Years. From this Age the Infants being arrived at some degree of
Firmness, grow less and less Mortal; and it appears, that of the whole
People of Breslaw there die yearly, as in the following Table, wherein the
upper Line shews the Age, and the next under it, the Number of Persons of
that Age dying yearly.

7 8 9 14 18 21 27 28 35
11 11 6 5½ 2 3½ 5 6 4½ 6½ 9 8 7 7
36 42 45 49 54 55 56 63 70
8 9½ 8 9 7 7 10 11 9 9 10 12 9½ 14
71 72 77 81 84 90 91 98 99 100

9 11 9½ 6 7 3 4 2 1 1 1 0 ⅕ ⅗

And where no Figure is placed over, it is to be understood of those that
die between the Ages of the precedent and consequent Column.
From this Table it is evident, that from the Age of 9 to about 25, there
does not die above 6 per Annum of each Age, which is much about 1 per
Cent. of those that are of those Ages: And whereas in the 14, 15, 16, 17
Years, there appear to die much fewer, as 2 and 3½; yet that seems rather to
be attributed to Chance, as are the other Irregularities in the Series of Ages,
which would rectifie themselves, were the number of Years much more
considerable, as 20 instead of 5. And by our own Experience in Christ-
Church Hospital, I am inform'd there die of the Young Lads, much about 1
per Cent. per Annum, they being of the aforesaid Ages. From 25 to 50, there
seem to die from 7 to 8 and 9 per Annum of each Age; and after that to 70,
they growing more crasie, though the number be much diminished, yet the
Mortality increases, and there are found to die 10 or 11 of each Age per
Annum: From thence the number of the Living being grown very small,
they gradually decline till there be none left to die; as may be seen at one
View in the Table.
From these Considerations I have form'd the adjoined Table, whose Uses
are manifold, and give a more just Idea of the State and Condition of
Mankind, than any thing yet extant that I know of. It exhibits the Number of
People in the City of Breslaw of all Ages, from the Birth to extreme Old
Age, and thereby shews the Chances of Mortality at all Ages, and likewise
how to make a certain Estimate of the Value of Annuities for Lives, which
hitherto has been only done by an imaginary Valuation: Also the Chances
that there are that a Person of any Age proposed does live to any other Age
given; with many more, as I shall hereafter shew. This Table does shew the
Number of Persons that are living in the Age current annexed thereto, as
follows:

Age. Age. Age. Age.
Persons. Persons. Persons. Persons.
Curt. Curt. Curt. Curt.
1 1000 8 680 15 628 22 586
2 855 9 670 16 622 23 579
3 798 10 661 17 616 24 573
4 760 11 653 18 610 25 567
5 732 12 646 19 604 26 560
6 710 13 640 20 598 27 553
7 692 14 634 21 592 28 546
29 539 36 481 43 417 50 346
30 531 37 472 44 407 51 335
31 523 38 463 45 397 52 324
32 515 39 454 46 387 53 313
33 507 40 445 47 377 54 302
34 499 41 436 48 367 55 292
35 490 42 427 49 357 56 282
57 272 64 202 71 131 78 58
58 262 65 192 72 120 79 49
59 252 66 182 73 109 80 41
60 242 67 172 74 98 81 34
61 232 68 162 75 88 82 28
62 222 69 152 76 78 83 23
63 212 79 142 77 68 84 20

Age. Persons.
7 5547
14 4584
21 4270
28 3964
35 3604
42 3708
49 2709
56 2194
63 1694

70 1204
77 692
84 253
100 107
34000
Sum Total.

Thus it appears, that the whole People of Breslaw does consist of 34000
Souls, being the Sum Total of the Persons of all Ages in the Table: The first
use hereof is to shew the Proportion of Men able to bear Arms in any
Multitude, which are those between 18 and 56, rather than 16 and 60; the
one being generally too weak to bear the Fatigues of War, and the Weight
of Arms; and the other too crasie and infirm from Age, notwithstanding
particular Instances to the contrary. Under 18 from the Table, are found in
this City 11997 Persons, 3950 above 56, which together make 15947, so
that the Residue to 34000 being 18053, are Persons between those Ages. At
least one half thereof are Males, or 9027: So that the whole Force this City
can raise of Fencible Men, as the Scotch call them, is about 9000, or 9⁄34, or
somewhat more than a quarter of the Number of Souls; which may parhaps
pass for a Rule for all other places.
The Second Use of this Table, is, to shew the differing degrees of
Mortality, or rather Vitality, in all Ages; for if the Number of Persons of any
Age remaining after one Year, be divided by the difference between that and
the number of the Age proposed, it shews the Odds that there is, that a
Person of that Age does not die in a Year. As for Instance, a Person of 25
Years of Age has the Odds of 560 to 7, or 80 to 1, that he does not die in a
Year: Because that of 567, living of 25 Years of Age, there do die no more
than 7 in a Year, leaving 560 of 26 Years old.
So likewise for the Odds, that any Person does not die before he attain
any proposed Age: Take the number of the remaining Persons of the Age
proposed, and divide it by the difference between it and the number of those

of the Age of the Party proposed; and that shews the Odds there is between
the Chances of the Party's living or dying. As for Instance; What is the Odds
that a Man of 40 lives 7 Years: Take the number of Persons of 47 Years,
which in the Table is 377, and subtract it from the number of Persons of 40
Years, which is 445, and the difference is 68: Which shews that the Persons
dying in that 7 Years, are 68, and that it is 377 to 68, or 5½ to 1, that a Man
of 40 does live 7 Years. And the like for any other number of Years.
Use III. But if it be enquired at what number of Years, it is an even Lay
that a Person of any Age shall die, this Table readily performs it; For if the
number of Persons living of the Age proposed, be halfed, it will be found by
the Table at what Year the said Number is reduced to half by Mortality; and
that is the Age, to which it is an even Wager, that a Person of the Age
proposed shall arrive before he die. As for Instance; A Person of 30 Years of
Age is proposed, the number of that Age is 531, the half thereof is 265,
which number I find to be between 57 and 58 Years; so that a Man of 30
may reasonably expect to live between 27 and 28 Years.
Use IV. By what has been said, the Price of Insurance upon Lives ought
to be regulated, and the difference is discovered between the Price of
insuring the Life of a Man of 20 and 50. For Example; It being 100 to 1, that
a Man of 20 dies not in a Year, and but 38 to 1, for a Man of 50 Years of
Age.
Use V. On this depends the Valuation of Annuities upon Lives; for it is
plain, that the Purchaser ought to pay for only such a part of the Value of
the Annuity, as he has Chances that he is living; and this ought to be
computed yearly, and the Sum of all those yearly Values being added
together, will amount to the Value of the Annuity for the Life of the Person
proposed. Now the present Value of Money payable after a Term of Years,
at any given Rate of Interest, either may be had from Tables already
computed; or almost as compendiously, by the Table of Logarithms: For the
Arithmetical Complement of the Logarithm of Unity, and its yearly Interest,

(that is, of 1,06 for Six per Cent. being 9,974694.) being multiplied by the
number of Years proposed, gives the present Value of One Pound payable
after the end of so many Years. Then by the foregoing Proposition, it will be
as the number of Persons living after that Term of Years, to the number
dead; so are the Odds that any one Person is alive or dead. And by
consequence, as the Sum of both, or the number of Persons living of the
Age first proposed, to the number remaining after so many Years, (both
given by the Table) so the present Value of the yearly Sum payable after the
Term proposed, to the Sum which ought to be paid for the Chance the
Person has to enjoy such an Annuity after so many Years. And this being
repeated for every Year of the Person's Life, the Sum of all the present
Values of those Chances is the true Value of the Annuity. This will without
doubt appear to be a most laborious Calculation; but it being one of the
principal Uses of this Speculation, and having found some Compendia for
the Work, I took the pains to compute the following Table, being the short
Result of a not ordinary number of Arithmetical Operations: It shews the
Value of Annuities for every Fifth Year of Age, to the Seventieth, as
follows.

Age. Years Pur. Age. Years Pur. Age. Years Pur.
1 10,28 25 12,27 50 9,21
5 13,40 30 11,72 55 8,51
10 13,44 35 11,12 60 7,60
15 13,33 40 10,57 65 6,54
20 12,78 45 9,91 70 5,32

This shews the great Advantage of putting Money into the present Fund
lately granted to Their Majesties, giving 14 per Cent. per Annum, or at the
Rate of 7 Years Purchase for a Life; when young Lives, at the usual Rate of
Interest, are worth above 13 Years Purchase. It shews likewise the
Advantage of young Lives over those in Years; a Life of Ten Years being
almost worth 13½ Years Purchase, whereas one of 36 is worth but 11.

Use VI. Two Lives are likewise valuable by the same Rule; for the
number of Chances of each single Life, found in the Table, being multiplied
together, become the Chances of the Two Lives. And after any certain Term
of Years, the Product of the two remaining Sums is the Chances that both
the Persons are living. The Product of the two Differences, being the
numbers of the Dead of both Ages, are the Chances that both the Persons
are dead. And the two Products of the remaining Sums of the one Age
multiplied by those dead of the other, shew the Chances that there are, that
each Party survives the other: Whence is derived the Rule to estimate the
Value of the Remainder of one Life after another. Now as the Product of the
Two Numbers in the Table for the Two Ages proposed, is to the difference
between that Product, and the Product of the two numbers of Persons
deceased in any space of time; so is the Value of a Sum of Money to be paid
after so much time, to the Value thereof under the Contingency of Mortality.
And as the aforesaid Product of the two Numbers answering to the Ages
proposed, to the Product of the Deceased of one Age multiplied by those
remaining alive of the other; so the Value of a Sum of Money to be paid
after any time proposed, to the Value of the Chances, that the one Party has
that he survives the other, whose number of Deceased you made use of, in
the second Term of the Proportion. This perhaps may be better understood,
by putting N for the number of the younger Age, and n for that of the Elder;
Y, y the Deceased of both Ages respectively, and R, r for the Remainders;
and R + Y = N, and r + y = n. Then shall Nn be the whole Number of
Chances; Nn - Yy be the Chances that one of the two Persons is living, Yy
the Chances that they are both dead; Ry the Chances that the elder Person is
dead, and the younger living; and rY the Chances, that the elder is living,
and the younger dead. Thus two Persons of 18 and 35 are proposed, and
after 8 Years these Chances are required. The Numbers for 18 and 35, are
610 and 490; and there are 50 of the First Age dead in 8 Years, and 73 of the
Elder Age. There are in all 610 × 490, or 298900 Chances; of these there are
50 × 73, or 3650, that they are both dead. And as 298900, to 298900 - 3650,
or 295250: So is the present Value of a Sum of Money to be paid after 8

Years, to the present Value of a Sum to be paid, if either of the two live.
And as 560 × 73, so are the Chances that the Elder is dead, leaving the
Younger; and as 417 × 50, so are the Chances that the Younger is dead,
leaving the Elder. Wherefore as 610 × 490 to 560 × 73, so is the present
Value of a Sum to be paid at 8 Years end, to the Sum to be paid for the
Chance of the Younger's Survivance; and as 610 × 490 to 417 × 50, so is the
same present Value to the Sum to be paid for the Chance of the Elder's
Survivance.
This possibly may be yet better explained, by expounding these Products
by Rectangular Parallelograms, as in Fig. 7. wherein AB or CD represents
the number of Persons of the younger Age, and DE, BH those remaining
alive after a certain Term of Years; whence CE will answer the number of
those dead in that time: So AC, BD may represent the number of the elder
Age; AF, BI the Survivors after the same Term; and CF, DI, those of that
Age that are dead at that time. Then shall the whole Parallelogram ABCD be
Nn, or the Product of the two Numbers of Persons, representing such a
number of Persons of the two Ages given; and by what was said before,
after the Term proposed, the Rectangle HD shall be as the number of
Persons of the younger Age that survive, and the Rectangle AE as the
number of those that die. So likewise the Rectangles AI, FD shall be as the
Numbers, living and dead, of the other Age. Hence the Rectangle HI shall
be as an equal number of both Ages surviving. The Rectangle FE being the
Product of the Deceased, or Yy, an equal number of both dead. The
Rectangle GD or Ry, a number living of the younger Age, and dead of the
elder: And the Rectangle AG or rY a number living of the elder Age, but
dead of the younger. This being understood, it is obvious, that as the whole
Rectangle AD or Nn is to the Gnomon FABDEG or Nn - Yy, so is the whole
number of Persons or Chances, to the number of Chances that one of the
two Persons is living: And as AD or Nn is to FE or Yy, so are all the
Chances, to the Chances that both are dead; whereby may be computed the
Value of the Reversion after both Lives. And as AD to GD or Ry, so the

whole number of Chances, to the Chances that the younger is living, and the
other dead; whereby may be cast up what Value ought to be paid for the
Reversion of one Life after another, as in the Case of providing for Clergy-
men's Widows, and others, by such Reversions. And as AD to AG, or rY, so
are all the Chances, to those that the elder survives the younger. I have been
the more particular, and perhaps tedious, in this Matter, because it is the
Key to the Case of Three Lives, which of it self would not have been so
easie to comprehend.
VII. If Three Lives are proposed, to find the Value of an Annuity during
the continuance of any of those three Lives; the Rule is, As the Product of
the continual Multiplication of the Three Numbers, in the Table, answering
to the Ages proposed, is to the difference of that Product, and of the Product
of the Three Numbers of the Deceased of those Ages, in any given Term of
Years: So is the present Value of a Sum of Money, to be paid certainly after
so many Years, to the present Value of the same Sum to be paid, provided
one of those Three Persons be living at the Expiration of that Term. Which
Proportion being yearly repeated, the Sum of all those present Values will
be the Value of an Annuity granted for three such Lives. But to explain this,
together with all the Cases of Survivance in Three Lives: Let N be the
Number in the Table for the younger Age, n for the second, and ν for the
elder Age; let Y be those dead of the younger Age in the Term proposed, y
those dead of the second Age, and υ those of the elder Age; and let R be the
Remainder of the younger Age, r that of the middle Age, and ρ the
Remainder of the elder Age. Then shall R + Y be equal to N, r + y to n, and
ρ + υ to ν, and the continual Product of the three Numbers N, n, ν, shall be
equal to the continual Product of R + Y × r + y × ρ + υ, which being the
whole Number of Chances for three Lives, is compounded of the eight
Products following. (1) Rrρ, which is the Number of Chances that all three
of the Persons are living. (2) rρY, which is the Number of Chances that the
two elder Persons are living, and the younger dead. (3) Rρy the Number of
Chances that the middle Age is dead, and the younger and elder living. (4)

Rrυ being the Chances that the two younger are living, and the elder dead.
(5) ρYy the Chances that the two younger are dead, and the elder living. (6)
rYυ the Chances that the younger and elder are dead, and the middle Age
living. (7) Ryυ, which are the Chances that the younger is living, and the
two other dead. And Lastly and Eighthly, Yyυ, which are the Chances that
all three are dead. Which latter subtracted from the whole Number of
Chances Nnν, leaves Nnν - Yyυ the Sum of all the other seven Products; in
all of which one or more of the three Persons are surviving.
To make this yet more evident, I have added Fig. 8. wherein these eight
several Products are at one view exhibited. Let the rectangled
Parallelepipedon ABCDEFGH be constituted of the sides AB, GH, &c.
proportional to N the Number of the younger Age; AC, BD, &c.
proportional to n; and AG, CE, &c. proportional to the Number of the elder,
or ν. And the whole Parallelepipedon shall be as the Product Nnν, or our
whole Number of Chances. Let BP be as R, and AP as Y; let CL be as r, and
Ln as y; and GN as ρ, and NA as υ; and let the Plain PRea be made parallel
to the Plain ACGE; the Plain NVbY parallel to ABCD; and the Plain LXTQ
parallel to the Plain ABGH. And our first Product Rrρ shall be as the Solid
STWIFZeb. The Second, or rρY will be as the Solid EYZeQSMI. The Third,
Rρy, as the Solid RHOVWIST. And the Fourth, Rrυ, as the Solid
ZabDWXIK. Fifthly, ρYy, as the Solid GQRSIMNO. Sixthly, rYυ, as
IKLMGYZA. Seventhly, Ryυ, as the Solid IKPOBXVW. And Lastly,
AIKLMNOP will be as the Product of the 3 Numbers of Persons dead, or
Yyυ. I shall not apply this in all the Cases thereof, for brevity sake; only to
shew in one how all the rest may be performed, let it be demanded what is
the Value of the Reversion of the younger Life after the two elder proposed.
The proportion is as the whole Number of Chances, or Nnν to the Product
Ryυ; so is the certain present Value of the Sum payable after any Term
proposed, to the Value due to such Chances as the younger Person has to
bury both the elder, by the Term proposed; which therefore he is to pay for.
Here it is to be noted, that the first Term of all these Proportions is the same

throughout, viz. Nnν. The second changing yearly according to the Decrease
of R, r, ρ, and Increase of Y, y, υ. And the third are successively the present
Values of Money payable after one, two, three, &c. years, according to the
Rate of Interest agreed on. These Numbers, which are in all Cases of
Annuities of necessary Use, I have put into the following Table, they being
Decimal Values of one Pound payable after the Number of Years in the
Margent, at the Rate of 6 per Cent.

Pres. Value Pres. Value Pres. Value
Years. Years. Years.
of 1 l. of 1 l. of 1 l.
1 0,9434 19 0,3305 37 0,1158
2 0,8900 20 0,3118 38 0,1092
3 0,8396 21 0,2941 39 0,1031
4 0,7921 22 0,2775 40 0,0972
5 0,7473 23 0,2618 45 0,0726
6 0,7050 24 0,2470 50 0,0543
7 0,6650 25 0,2330 55 0,0406
8 0,6274 26 0,2198 60 0,0303
9 0,5919 27 0,2074 65 0,0227
10 0,5584 28 0,1956 70 0,0169
11 0,5268 29 0,1845 75 0,0126
12 0,4970 30 0,1741 80 0,0094
13 0,4688 31 0,1643 85 0,0071
14 0,4423 32 0,1550 90 0,0053
15 0,4173 33 0,1462 95 0,0039
16 0,3936 34 0,1379 100 0,0029
17 0,3714 35 0,1301
18 0,3503 36 0,1227

It were needless to advertise, that the great trouble of working so many
Proportions will be very much alleviated by using Logarithms; and that
instead of using Nnν - Yyυ for the second Term of the Proportion in finding
the Value of Three Lives, it may suffice to use only Yyυ, and then deducting

the fourth Term so found out of the third, the Remainder shall be the present
Value sought; or all these fourth Terms being added together, and deducted
out of the Value of the certain Annuity for so many Years, will leave the
Value of the contingent Annuity upon the Chance of Mortality of all those
Three Lives. For Example; Let there be Three Lives of 10, 30, and 40 Years
of Age proposed, and the Proportions will be thus;
As 661 in 531 in 445 or 156190995, or Nnν to 8 in 8 in 9, or 576, or Yyυ
for the first Year, so 0,9434. to 0,00000348.
To 15 in 16 in 18, or 4320, for the second Year, so 0,8900. to 0,00002462.
To 21 in 24 in 28, or 14112 for the third Year, so 0,8396. to 0,00008128.
To 27 in 32 in 38, for the fourth Year, so 0,7921. to 0,00016650.
To 33 in 41 in 48, for the fifth Year, so 0,7473. to 0,00031071.
To 39 in 50 in 58, for the sixth Year, so 0,7050. to 0,00051051.
And so forth to the 60th Year, when we suppose the elder Life of Forty
certainly to be expired; from whence till Seventy we must compute for the
First and Second only, and from thence to Ninety for the single youngest
Life. Then the Sum Total of all these Fourth Proportionals being taken out
of the Value of a certain Annuity for 90 Years, being 16,58 Years Purchase,
shall leave the just Value to be paid for an Annuity during the whole Term
of the Lives of Three Persons of the Ages proposed. And note, that it will
not be necessary to compute for every Year singly; but that in most Cases
every 4th or 5th Year may suffice, interpoling for the intermediate Years
seceundum artem.
It may be objected, that the different Salubrity of Places does hinder this
Proposal from being universal; nor can it be denied. But by the Number that
die, being 1174. per Annum in 34000, it does appear that about a 30th part
die yearly, as Sir William Petty has computed for London; and the Number
that die in Infancy, is a good Argument that the Air is but indifferently
salubrious. So that by what I can learn, there cannot perhaps be one better
Place proposed for a Standard. At least 'tis desired, that in Imitation hereof

the Curious in other Cities would attempt something of the same Nature,
than which nothing perhaps can be more useful.
Were this Calculus founded on the Experience of a very great number of
Years, it would be very well worth the while to think of Methods for
facilitating the Computation of the Value of two, three, or more Lives;
which, as proposed in my former, seems (as I am inform'd) a Work of too
much Difficulty for the ordinary Arithmetician to undertake.
I have sought, If it were possible, to find a Theorem that might be more
concise than the Rules there laid down, but in vain; for all that can be done
to expedite it, is, by Tables of Logarithms ready computed, to exhibit the
Rationes of N to Y in each single Life, for every third, fourth, or fifth Year
of Age, as occasion shall require; and these Logarithms being added to the
Logarithms of the present Value of Money payable after so many Years, will
give a Series of Numbers, the Sum of which will shew the Value of the
Annuity sought. However, for each Number of this Series, two Logarithms
for a single Life, three for two Lives, and four for three Lives, must
necessarily be added together. If you think the Matter, under the
Uncertainties I have mentioned, to deserve it, I shall shortly give you such a
Table of Logarithms, as I speak of, and an Example or two of the use
thereof: But by Vulgar Arithmetick, the Labour of these Numbers were
immense; and nothing will more recommend the useful Invention of
Logarithms to all Lovers of Numbers, than the advantage of Dispatch in this
and such like Computations.
Besides the Uses mentioned, it may perhaps not be an unacceptable thing
to infer from the same Tables, how unjustly we repine at the shortness of
our Lives, and think our selves wronged if we attain not old Age; whereas it
appears hereby, that the one half of those that are born are dead in
Seventeen Years time, 1238 being in that time reduced to 616. So that
instead of murmuring at what we call an untimely Death, we ought with
Patience and Unconcern to submit to that Dissolution which is the

necessary Condition of our perishable Materials, and of our nice and frail
Structure and Composition: And to account it as a Blessing that we have
survived, perhaps by many Years, that Period of Life, whereat the one half
of the whole Race of Mankind does not arrive.
A second Observation I make upon the said Table, is that the Growth and
Increase of Mankind is not so much stinted by any thing in the Nature of the
Species, as it is from the cautious difficulty most People make to adventure
on the State of Marriage, from the Prospect of the Trouble and Charge of
providing for a Family. Nor are the poorer sort of People herein to be
blamed, since their difficulty of subsisting is occasion'd by the unequal
Distribution of Possessions, all being necessarily fed from the Earth, of
which yet so few are Masters. So that besides themselves and Families, they
are yet to work for those who own the Ground that feeds them: And of such
does by very much the greater part of Mankind consist; otherwise it is plain,
that there might well be four times as many Births as we now find. For by
Computation from the Table, I find that there are nearly 15000 Persons
above 16, and under 45, of which at least 7000 are Women capable to bear
Children. Of these notwithstanding there are but 1238 born yearly, which is
but little more than a sixth part: So that about one in six of these Women do
breed yearly; whereas were they all married, it would not appear strange or
unlikely, that four of six should bring a Child every Year. The Political
Consequences hereof I shall not insist on; only the Strength and Glory of a
King being in the multitude of his Subjects, I shall only hint, that above all
things, Celibacy ought to be discouraged, as, by extraordinary Taxing and
Military Service: And those who have numerous Families of Children to be
countenanced and encouraged by such Laws as the Jus trium Liberorum
among the Romans. But especially, by an effectual Care to provide for the
Subsistence of the Poor, by finding them Employments, whereby they may
earn their Bread, without being chargeable to the Publick.

Discourse concerning Gravity, and its Properties, wherein the
Descent of Heavy Bodies, and the Motion of Projects is briefly, but
fully handled: Together with the Solution of a Problem of great Use
in Gunnery. By E. Halley.

ATURE, amidst the great Variety of Problems, wherewith She
N exercises the Wits of Philosophical Men, scarce affords any one
wherein the Effect is more visible, and the Cause more concealed, than
in those of the Phænomena of Gravity. Before we can go alone, we must
learn to defend our selves from the Violence of its Impulse, by not trusting
the Center of Gravity of our Bodies beyond our reach; and yet the acutest
Philosophers, and the subtilest Enquirers into the Original of this Motion,
have been so far from satisfying their Readers, that they themselves seem
little to have understood the Consequences of their own Hypotheses.
Des Cartes his Notion, I must needs confess to be to me
incomprehensible, while he will have the Particles of his Cœlestial Matter,
by being reflected on the Surface of the Earth, and so ascending therefrom,
to drive down into their Places those Terrestrial Bodies they find above
them: This is, as near as I can gather, the Scope of the 20, 21, 22, and 23
Sections of the last Book of his Principia Philosophiæ; yet neither he, nor
any of his Followers, can shew how a Body suspended in Libero Æthere,
shall be carried downwards by a continual Impulse tending upwards, and
acting upon all its Parts equally: And besides the Obscurity wherewith he
expresses himself, particularly, Sect. 23. does sufficiently argue according
to his own Rules, the confused Idea he had of the thing he wrote.
Others, and among them Dr. Vossius, assert the Cause of the Descent of
heavy Bodies, to be the Diurnal Rotation of the Earth upon its Axis, without
considering, that according to the Doctrine of Motion fortified with
Demonstration, all Bodies moved in Circulo, would recede from the Center
of their Motion; whereby the contrary to Gravity would follow, and all
loose Bodies would be cast into the Air in a Tangent to the Parallel of

Latitude, without the intervention of some other Principle to keep them fast,
such as is that of Gravity. Besides, the Effect of this Principle is throughout
the whole Surface of the Globe found nearly equal; and certain Experiments
have proved it rather less near the Æquinoctial, than towards the Poles;
which could not be by any means, if the Diurnal Rotation of the Earth upon
its Axis were the Cause of Gravity; for where the Motion was swiftest, the
Effect would be most considerable.
Others assign the Pressure of the Atmosphere, to be the Cause of this
Tendency towards the Center of the Earth; but unhappily they have
mistaken the Cause for the Effect; it being from undoubted Principles plain,
that the Atmosphere has no other Pressure but what it derives from its
Gravity; and that the Weight of the upper Parts of the Air, pressing on the
lower Parts thereof, do so far bend the Springs of that Elastick Body, as to
give it a Force equal to the Weight that compress'd it, having of it self no
force at all: And supposing it had, it will be very hard to explain the Modus,
how that Pressure should occasion the Descent of a Body circumscribed by
it, and pressed equally above and below, without some other Force to draw,
or thrust it downwards. But to demonstrate the contrary of this Opinion, an
Experiment was long since shewn before the Royal Society, whereby it
appeared, that the Atmosphere was so far from being the Cause of Gravity,
that the Effects thereof were much more vigorous, where the Pressure of the
Atmosphere was taken off; for a long Glass-Receiver having a light Down-
feather included, being evacuated of Air, the Feather, which in the Air
would hardly sink, did in vacuo descend with nearly the same Velocity, as if
it had been a Stone.
Some think to illustrate this Descent of Heavy Bodies, by comparing it
with the Vertue of the Loadstone; but setting aside the difference there is in
the manner of their Attractions, the Loadstone drawing only in and about its
Poles, and the Earth near equally in all Parts of its Surface, this Comparison
avails no more than to explain ignotum per æque ignotum.

Others assign a certain Sympæthetical Attraction between the Earth and
its Parts, whereby they have, as it were, a desire to be united, to be the
Cause we enquire after: But this is so far from explaining the Modus, that it
is little more, than to tell us in other Terms, that Heavy Bodies descend,
because they descend.
This, I say, not that I can pretend to substitute any Solution of this
Important Philosophical Problem, that shall more happily explicate the
Appearances of Gravity; only it may be serviceable to those with whom the
Credit of great Authors sways much, and who too readily assent in Verba
Magistri, to let them see that their Books are not always infallible: Besides,
the detection of Errors is the first and surest Step towards the discovery of
Truth.
Though the efficient Cause of Gravity be so obscure, yet the final Cause
thereof is clear enough; for it is by this single Principle, that the Earth and
all the Cœlestial Bodies are kept from Dissolution; the least of their
Particles not being suffer'd to recede far from their Surfaces, without being
immediately brought down again by Virtue of this Natural Tendency;
which, for their Preservation, the Infinite Wisdom of their Creator has
ordained to be towards each of their Centers; nor can the Globes of the Sun
and Planets otherwise be destroy'd, but by taking from them this Power of
keeping their Parts united.
The Affections or Properties of Gravity, and its manner of acting upon
Bodies falling, have been in a great measure discovered, and most of them
made out by Mathematical Demonstration in this our Century, by the
accurate diligence of Galilæus, Torricellius, Hugenius, and others, and now
lately by our worthy Countryman, Mr. Isaac Newton, which Properties it
may be very material here to enumerate, that they may serve for a
Foundation to all those that shall be willing to spend their Thoughts in
search of the true Cause of this Descent of Bodies.

The first Property is, That by this Principle of Gravitation, all Bodies do
descend towards a Point, which either is, or else is very near to the Center
of Magnitude of the Earth and Sea, about which the Sea forms it self
exactly into a Spherical Surface, and the Prominences of the Land,
considering the Bulk of the whole, differ but insensibly therefrom.
Secondly, That this Point or Center of Gravitation, is fix'd within the
Earth, or at least has been so, ever since we have any Authentick History:
For a Consequence of its Change, though never so little, would be the over-
flowing of the low Lands on that side of the Globe towards which it
approached, and the leaving new Islands bare on the opposite side, from
which it receded; but for this Two Thousand Years it appears, that the low
Islands of the Mediterranean Sea (near to which the ancientest Writers
liv'd) have continued much at the same height above the Water, as they now
are found; and no Inundations or Recesses of the Sea arguing any such
Change, are recorded in History; excepting the Universal Deluge, which
can no better way be accounted for, than by supposing this Center of
Gravitation removed for a time, towards the middle of the then inhabited
Parts of the World; and a change of its Place, but the Two Thousandth Part
of the Radius of this Globe, were sufficient to bury the Tops of the highest
Hills under Water.
Thirdly, That in all Parts of the Surface of the Earth, or rather in all
Points equidistant from its Center, the Force of Gravity is nearly equal; so
that the length of the Pendulum vibrating Seconds of Time, is found in all
Parts of the World to be very near the same. 'Tis true at St. Helena, in the
Latitude of 16 Degrees South, I found that the Pendulum of my Clock,
which vibrated Seconds, needed to be made shorter than it had been in
England, by a very sensible Space (but which at that time I neglected to
observe accurately) before it would keep time; and since the like
Observations have been made by the French Observers, near the
Æquinoctial: Yet I dare not affirm, that in mine it proceeded from any other
Cause, than the great Height of my Place of Observation above the Surface

of the Sea, whereby the Gravity being diminished, the length of the
Pendulum vibrating Seconds, is proportionably short'ned.
Fourthly, That Gravity does equally affect all Bodies, without regard
either to their Matter, Bulk, or Figure; so that the Impediment of the
Medium being removed, the most compact and most loose, the greatest and
smallest Bodies would descend the same Spaces in equal Times; the Truth
thereof will appear from the Experiment I before-cited. In these two last
Particulars, is shewn the great difference between Gravity and Magnetism,
the one affecting only Iron, and that towards its Poles, the other all Bodies
alike in every part. As a Corollary, from hence it will follow, that there is no
such thing as positive Levity, those things that appear light, being only
comparatively so; and whereas several things rise and swim in Fluids, 'tis
because, Bulk for Bulk, they are not so heavy as those Fluids; nor is there
any Reason why Cork, for Instance, should be said to be light, because it
swims on Water, any more than Iron, because it swims on Mercury.
Fifthly, That this Power increases as you descend, and decreases as you
ascend from the Center, and that in the Proportion of the Squares of the
Distances therefrom reciprocally, so as at a double Distance to have but a
quarter of the Force; this Property is the Principle on which Mr. Newton has
made out all the Phænomena of the Cœlestial Motions, so easily and
naturally, that its Truth is past Dispute. Besides that, it is highly rational,
that the attractive or gravitating Power should exert it self more vigorously
in a small Sphere, and weaker in a greater, in proportion as it is contracted
or expanded; and if so, seeing that the Surfaces of Spheres are as the
Squares of their Radii, this Power, at several Distances, will be as the
Squares of those Distances reciprocally; and then its whole Action upon
each Spherical Surface, be it great or small, will be always equal. And this
is evidently the Rule of Gravitation towards the Centers of the Sun, Jupiter,
Saturn and the Earth, and thence is reasonably inferred, to be the general
Principle observed by Nature, in all the rest of the Cœlestial Bodies.

These are the principal Affections of Gravity, from which the Rules of
the Fall of Bodies, and the Motion of Projects are Mathematically
deducible. Mr. Isaac Newton has shew'd how to define the Spaces of the
Descent of a Body, let fall from any given height, down to the Center,
supposing the Gravitation to increase, as in the fifth Property; but
considering the smallness of heighth, to which any Project can be made
ascend, and over how little an Arch of the Globe it can be cast by any of our
Engines, we may well enough suppose the Gravity equal throughout, and
the Descents of Projects in parallel Lines, which in Truth are towards the
Center, the difference being so small as by no means to be discovered in
Practice. The Opposition of the Air, 'tis true, is considerable against all light
Bodies moving through it, as likewise against small ones (of which more
hereafter) but in great and ponderous Shot, this Impediment is found by
Experience but very small, and may safely be neglected.

Propositions concerning the Descent of Heavy Bodies, and the Motion of
Projects.
Prop. I. The Velocities of Falling Bodies, are proportionate to the Times
from the beginning of their Falls.
This follows, for that the Action of Gravity being continual, in every
Space of Time, the falling Body receives a new Impulse, equal to what it
had before, in the same Space of Time, received from the same Power: For
Instance, in the first Second of Time, the falling Body has acquired a
Velocity, which in that time would carry it to a certain Distance, suppose 32
Foot, and were there no new Force, would descend at that rate with an
equable Motion: But in the next Second of Time, the same Power of
Gravity continually acting thereon, superadds a new Velocity equal to the
former; so that at the end of two Seconds, the Velocity is double to what it
was at the end of the first, and after the same manner may it be proved to be

triple, at the end of the third Second, and so on. Wherefore the Velocities of
falling Bodies, are proportionate to the Time of their Falls, Q. E. D.

Plate 4. pag. 310.

Prop. II. The Spaces described by the Fall of a Body, are as the Squares
of the Times, from the beginning of the Fall.
Demonstration. Let AB (Fig. 9. Tab. 4.) represent the Time of the Fall of
a Body, BC perpendicular to AB, the Velocity acquired at the end of the
Fall, and draw the Line AC; then divide the Line AB representing the Time,
into as many equal Parts as you please, as b, b, b, b, &c. and through these
Points draw the Lines bc, bc, bc, bc, &c. parallel to BC, 'tis manifest that
the several Lines, bc, represent the several Velocities of the falling Body, in
such Parts of the Time as Ab is of AB, by the former Proposition. It is
evident likewise, that the Area ABC is the Sum of all the Lines bc being
taken, according to the Method of Indivisibles, infinitely many; so that the
Area ABC represents the Sum of all the Velocities, between none and BC
supposed infinitely many; which Sum is as the Space descended in the Time
represented by AB. And by the same Reason the Areas Abc, will represent
the Spaces descended in the Times Ab; so then the Spaces descended in the
Times AB, Ab, are as the Areas of the Triangles ABC, Abc, which by the
20th of the 6 of Euclid, are as the Squares of their Homologous Sides AB,
Ab, that is to say, of the Times: Wherefore the Descents of falling Bodies,
are as the Squares of the Times of their Fall, Q. E. D.

Prop. III. The Velocity which a falling Body acquires in any Space of
time, is double to that, wherewith it would have moved the Space,
descended by an equable Motion, in the same time.
Demonstration. Draw the Line EC parallel to AB, and AE parallel to BC
in the same Fig. 9. and compleat the Parallelogram ABCE, it is evident that
the Area thereof may represent the Space, a Body moved equably with the
Velocity BC would describe in the Time AB, and the Triangle ABC
represents the Space describ'd by the Fall of a Body, in the same Time AB,
by the second Proposition. Now the Triangle ABC is half of the
Parallelogram ABCE, and consequently the Space described by the Fall, is

half what would have been described by an equable Motion with the
Velocity BC, in the same Time; wherefore the Velocity BC at the end of the
Fall, is double to that Velocity, which in the Time AB, would have
described the Space fallen, represented by the Triangle ABC with an
equable Motion, Q. E. D.

Prop. IV. All Bodies on or near the Surface of the Earth, in their Fall,
descend so, as at the end of the first Second of Time, they have described 16
Feet, 1 Inch, London Measure, and acquired the Velocity of 32 Feet, 2
Inches, in a Second.
This is made out from the 25th Proposition of the second Part of that
excellent Treatise of Mr. Hugenius de Horologio Oscillatorio; wherein he
demonstrates the time of the least Vibrations of a Pendulum, to be to the
Time of the Fall of a Body, from the heighth of half the length of the
Pendulum, as the Circumference of a Circle to its Diameter; whence, as a
Corollary, it follows, That as the Square of the Diameter to the Square of
the Circumference, so half the length of the Pendulum vibrating Seconds, to
the Space described by the Fall of a Body in a Second of Time: And the
Length of the Pendulum vibrating Seconds, being found 39, 125, or ⅛
Inches, the Descent in a Second will be found by the aforesaid Analogy 16
Foot and 1 Inch; and, by the third Proposition, the Velocity will be double
thereto; and near to this it hath been found by several Experiments, which
by reason of the swiftness of the Fall, cannot so exactly determine its
Quantity. The Demonstration of Hugenius being the Conclusion of a long
Train of Consequences, I shall for brevity sake omit; and refer you to his
Book, where these things are more amply treated of.
From these Four Propositions, all Questions concerning the
Perpendicular Fall of Bodies, are easily solved, and either Time, Height, or
Velocity being assign'd, one may readily find the other two. From them
likewise is the Doctrine of Projects deducible, assuming the two following

Axioms; viz. That a Body set a moving, will move on continually in a right
Line with an equable Motion, unless some other Force or Impediment
intervene, whereby it is accelerated, or retarded, or deflected.
Secondly, That a Body being agitated by two Motions at a time, does by
their compounded Forces pass through the same Points, as it would do,
were the two Motions divided and acted successively. As for Instance,
Suppose a Body moved in the Line GF, (Fig. 1. Tab. 5.) from G to R, and
there stopping, by another Impulse, suppose it moved in a Space of Time
equal to the former, from R towards K, to V. I say, the Body shall pass
through the Point to V, though these two several Forces acted both in the
same time.

Prop. V. The Motion of all Projects is in the Curve of a Parabola: Let the
Line GRF (in Fig. 1.) be the Line in which the Project is directed, and in
which by the first Axiom it would move equal Spaces in equal Times, were
it not deflected downwards by the Force of Gravity. Let GB be the
Horizontal Line, and GC a Perpendicular thereto. Then the Line GRF being
divided into equal Parts, answering to equal Spaces of Time, let the
Descents of the Project be laid down in Lines parallel to GC, proportioned
as the Squares of the Lines GS, GR, GL, GF, or as the Squares of the Times,
from S to T, from R to V, from L to X, and from F to B, and draw the Lines
TH, VD, XY, BC parallel to GF; I say, the Points T, V, X, B, are Points in
the Curve described by the Project, and that that Curve is a Parabola. By
the second Axiom, they are Points in the Curve; and the Parts of the Descent
GH, GD, GY, GC, = to ST, RV, LX, FB, being as the Squares of the Times
(by the Second Proposition) that is, as the Squares of the Ordinates, HT,
DU, YX, BC, equal to GS, GR, GL, GF, the Spaces measured in those
Times; and there being no other Curve but the Parabola, whose Parts of the
Diameter are as the Squares of the Ordinates, it follows that the Curve
describ'd by a Project, can be no other than a Parabola: And saying, as RU
the Descent in any time, to GR or UD the direct Motion in the same time, so

is UD to a third proportional; that third will be the Line call'd by all Writers
of Conicks, the Parameter of the Parabola to the Diameter GC, which is
always the same in Projects cast with the same Velocity: And the Velocity
being defined by the Number of Feet moved in a Second of Time, the
Parameter will be found by dividing the Square of the Velocity, by 16 Feet,
1 Inch, the Fall of a Body in the same Time.
Lemma.
The Sine of the double of any Arch, is equal to twice the Sine of that Arch
into its Co-sine, divided by Radius; and the versed Sine of the double of any
Arch is equal to twice the Square of the Sine thereof divided by Radius.
Let the Arch BC (in Fig. 2. Tab. 5.) be double the Arch BF, and A the
Center; draw the Radii AB, AF, AC, and the Chord BDC, and let fall BE
perpendicular to AC, and the Angle EBC, will be equal to the Angle ABD,
and the Triangle BCE, will be like to the Triangle BDA; wherefore it will
be as AB to AD, so BC or twice BD, to BE; that is, as Radius to Co-sine, so
twice Sine to Sine of the double Arch. And as AB to BD, so twice BD or BC
to EC, that is, as Radius to Sine, so twice that Sine, to the Versed Sine of the
double Arch; which two Analogies resolved into Equations, are the
Propositions contained in the Lemma to be proved.

Prop. VI. The Horizontal Distances of Projections made with the same
Velocity, at several Elevations of the Line of Direction, are as the Sines of
the doubled Angles of Elevation.
Let GB (Fig. 1) the Horizontal Distance be = z, the Sine of the Angle of
Elevation, FGB, be = s, its Co-sine = c, Radius = r, and the Parameter = p.
It will be as c to s; so z to sz⁄c = FB = GC, and by reason of the Parabola
psz
⁄c = to the Square of CB, or GF; Now as c to r, so is z to zr⁄c = GF, and its
Square zzrr⁄cc will be therefore = to psz⁄c: Which Equation reduced will be
psc
⁄rr = z. But by the former Lemma 2sc⁄r is equal to the Sine of the double

Angle, whereof s is the Sine: Wherefore 'twill be as Radius to Sine of double
the Angle FGB, so is half the Parameter, to the Horizontal Range or
Distance sought; and at the several Elevations, the Ranges are as the Sines
of the double Angles of Elevation, Q. E. D.
Corollary.
Hence it follows, that half the Parameter is the greatest Randon, and that
that happens at the Elevation of 45 Degrees, the Sine of whose double is
Radius. Likewise that the Ranges equally distant above and below 45 are
equal, as are the Sines of all double Arches, to the Sines of their doubled
Complements.

Prop. VII. The Altitudes of Projections made with the same Velocity, at
several Elevations, are as the versed Sines of the doubled Angles of
Elevation: As c is to s; so is psc⁄rr = GB to pss⁄rr = BF: and UK = RU = BF/4,
the Altitude of the Projection = psc⁄4rr. Now by the foregoing Lemma 2ss⁄r =
to the versed Sine of the double Angle, and therefore it will be as Radius, to
versed Sine of double the Angle FGB, so an 8th of the Parameter to the
height of the Projection VK; and so these heights at several Elevations, are
as the said versed Sines, Q. E. D.
Corollary.
From hence it is plain, that the greatest Altitude of the perpendicular
Projection is a 4th of Parameter, or half the greatest Horizontal Range; the
versed Sine of 180 Degrees being = 2r.

Prop. VIII. The Lines GF, or Times of the Flight of a Project cast with the
same Degree of Velocity at different Elevations, are as the Sines of the
Elevations.

As c is to r; so is psc⁄rr = GB by the 6 Prop. to ps⁄r GF; that is, as Radius to
Sine of Elevation, so the Parameter to the Line GF; so the Lines GF are as
the Sines of Elevation, and the Times are proportional to those Lines;
wherefore the Times are as the Sines of Elevation: Ergo constat propositio.

Prop. IX. Problem. A Projection being made as you please, having the
Distance and Altitude, or Descent, of an Object, through which the Project
passes, together with the Angle of Elevation of the Line of Direction; to find
the Parameter and Velocity, that is (in Fig. 1.) having the Angle FGB, GM,
and MX.
Solution. As Radius to Secant of FGB, so GM the Distance given to GL;
and as Radius to Tangent of FGB, so GM to LM. Then LM - MX in
Heights, or + MX in Descents; or else MX - ML, if the Direction be below
the Horizontal Line, is the Fall in the Time that the direct Impulse given in
G would have carried the Project from G to L = LX = GY; then by Reason
of the Parabola, as LX or GY, is to GL or YX, so is GL to the Parameter
sought. To find the Velocity of the Impulse: by Prop. 2, and 4, find the Time
in Seconds that a Body would fall the Space LX; and by that dividing the
Line GL, the Quote will be the Velocity, or Space moved in a Second
sought, which is always a mean Proportional between the Parameter, and
16 Feet, 1 Inch.

Prop. X. Problem 2. Having the Parameter, Horizontal Distance, and
Height or Descent of an Object, to find the Elevations of the Line of
Direction necessary to hit the given Object; that is, having GM, MX, and
the greatest Randon equal to half the Parameter; to find the Angles FGB.
Let the Tangent of the Angle sought be = t, the Horizontal Distance GM
= b, the Altitude of the Object MX = h, the Parameter = p, and Radius = r,
and it will be,

As r to t, so b to tb⁄r = ML and tb⁄r ∓ h { in ascents } = LX, and
{in descents}
ptb
⁄r ∓ ph = GL quad. = XY quad. ratione Parabolæ; but
bb ∓ ttbb⁄rr = GL quad. 47. 1. Euclid. Wherefore
ptb
⁄r ∓ ph = bb ∓ ttbb⁄rr which Equation transposed, is
ttbb
⁄rr = ptb⁄r ∓ ph - bb, divided by bb is tt⁄rr = pt⁄br ∓ ph⁄bb - 1.
this Equation shews the Question to have 2 Answers, and the Roots thereof
pp ∓ 4ph
are t⁄r = p⁄2b ∓ √ ‍ 4bb
- 1; from which I derive the following Rule.

Divide half the Parameter by the Horizontal distance, and keep the
Quote; viz. p⁄2b then say, as square of the distance given to the half
Parameter, so half Parameter ∓ double height to the square of a Secant =
descent
pp ∓ 4ph pp ∓ 4ph
4bb
. The Tangent answering to that Secant, will be ‍ √
- 1 or
4bb
Square of Radius, so then the sum and difference of the afore-found Quote,
and this Tangent will be the Roots of the Equation, and the Tangents of the
Elevations sought.
Note here, that in Descents, if the Tangent exceed the Quote, as it does
when ph is more than bb, the direction of the lower Elevation will be below
the Horizon, and if ph = bb, it must be directed Horizontal, and the Tangent
of the upper Elevation will be pr⁄b: Note likewise, that if 4bb + 4ph in
Ascents, or 4bb - 4ph in Descents, be equal to pp, there is but one Elevation
that can hit the Object, and its Tangent is pr⁄2b. And if 4bb + 4ph in Ascents,
or 4bb - 4ph in descents, do exceed pp, the Object is without the reach of a
Project cast with that Velocity, and so the thing impossible.
From this Equation 4bb ∓ 4ph = pp are determined the utmost limits of
the reach of any Project, and the Figure assigned, wherein are all the
heights upon each Horizontal distance beyond which it cannot pass; for by
reduction of that Equation, h will be found = ¼p - bb⁄p in heights, and bb⁄p -
¼p in descents; from whence it follows, that all the Points h are in the

Curve of the Parabola, whose Focus is the Point from whence the Project
is cast, and whose Latus rectum, or Parameter ad Axem is = p. Likewise
from the same Equation may the least Parameter or Velocity be found
capable to reach the Object proposed; for bb = ¼pp ∓ ph being reduced, ½p
will be = √‍ bb + hh ± h { in ascents } which is the Horizontal Range at 45
{in descents}
degrees, of a Project cast with the least Velocity that would just reach the
Object, and the Elevation requisite will be easily had; for dividing the so
found Semi-parameter by the Horizontal distance given b, the Quote into
Radius will be the Tangent of the Elevation sought. This Rule may be of
good use to all Bombardiers and Gunners, not only that they may use no
more Powder than is necessary, to cast their Bombs into the place assigned,
but that they may shoot with much more certainty, for that a small Error
committed in the Elevation of the Piece, will produce no sensible
Difference in the fall of the Shot: For which Reasons the French Engineers
in their late Sieges have used Mortar-pieces inclin'd constantly to the
Elevation of 45, proportioning their Charge of Pouder according to the
distance of the Object they intend to strike on the Horizon.
And this is all that need to be said concerning this Problem of shooting
upon Heights and Descents. But if a Geometrical Construction thereof be
required; I think I have one that is as easy as can be expected, which I
¼pp ± ph - bb
deduce from the foregoing Analytical Solution, viz. t⁄r = p⁄2b ± √‍ bb
, and 'tis this, having made the right Angle GDF, (Tab. 5. Fig. 3.) make DF
= ½p, or greatest Range, and GD = b the Horizontal Distance, and DB = h
the perpendicular heighth of the Object; to be laid upwards from D, if the
Object be above the Horizon, or downwards if below it. Parallel to GD
draw FA, and make it equal to GB the Hypothenusal Distance of the Object;
and with the Center A and Radius FB = ½p ± h, sweep an Arch, which shall
if the thing be possible, intersect the indeterminate Perpendicular DF in two
Points K and L, to which draw the Lines, GL, GK; I say, the Angles DGK,
DGL, are the Elevations requisite to strike the Object B.