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Title: Pioneers of Science

Author: Sir Oliver Lodge

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Language: English

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PIONEERS OF SCIENCE

NEWTON
From the picture by Kneller, 1689, now at Cambridge

PIONEERS OF SCIENCE

BY
OLIVER LODGE, F.R.S.
PROFESSOR OF PHYSICS IN VICTORIA UNIVERSITY COLLEGE, LIVERPOOL

WITH PORTRAITS AND OTHER ILLUSTRATIONS

London

MACMILLAN AND CO.
AND NEW YORK
1893

Richard Clay and Sons, Limited,
LONDON AND BUNGAY.

P R E FA C E
This book takes its origin in a course of lectures on the history and
progress of Astronomy arranged for me in the year 1887 by three of my
colleagues (A.C.B., J.M., G.H.R.), one of whom gave the course its name.

The lectures having been found interesting, it was natural to write them
out in full and publish.

If I may claim for them any merit, I should say it consists in their simple
statement and explanation of scientific facts and laws. The biographical
details are compiled from all readily available sources, there is no novelty
or originality about them; though it is hoped that there may be some
vividness. I have simply tried to present a living figure of each Pioneer in
turn, and to trace his influence on the progress of thought.

I am indebted to many biographers and writers, among others to Mr.
E.J.C. Morton, whose excellent set of lives published by the S.P.C.K. saved
me much trouble in the early part of the course.

As we approach recent times the subject grows more complex, and the
men more nearly contemporaries; hence the biographical aspect diminishes
and the scientific treatment becomes fuller, but in no case has it been
allowed to become technical and generally unreadable.

To the friends (C.C.C., F.W.H.M., E.F.R.) who with great kindness have
revised the proofs, and have indicated places where the facts could be made
more readily intelligible by a clearer statement, I express my genuine
gratitude.

University College, Liverpool,
November, 1892.

CONTENTS
PART I

LECTURE I
PAGE
COPERNICUS AND THE MOTION OF THE EARTH 2

LECTURE II
TYCHO BRAHÉ AND THE EARLIEST OBSERVATORY 32

LECTURE III
KEPLER AND THE LAWS OF PLANETARY MOTION 56

LECTURE IV
GALILEO AND THE INVENTION OF THE TELESCOPE 80

LECTURE V
GALILEO AND THE INQUISITION 108

LECTURE VI
DESCARTES AND HIS THEORY OF VORTICES 136

LECTURE VII
SIR ISAAC NEWTON 159

LECTURE VIII
NEWTON AND THE LAW OF GRAVITATION 180

LECTURE IX
NEWTON'S "PRINCIPIA" 203

PART II

LECTURE X
ROEMER AND BRADLEY AND THE VELOCITY OF LIGHT 232

LECTURE XI
LAGRANGE AND LAPLACE—THE STABILITY OF THE SOLAR SYSTEM, AND THE 254
NEBULAR HYPOTHESIS

LECTURE XII
HERSCHEL AND THE MOTION OF THE FIXED STARS 273

LECTURE XIII
THE DISCOVERY OF THE ASTEROIDS 294

LECTURE XIV
BESSEL—THE DISTANCES OF THE STARS, AND THE DISCOVERY OF STELLAR 304
PLANETS

LECTURE XV
THE DISCOVERY OF NEPTUNE 317

LECTURE XVI
COMETS AND METEORS 331

LECTURE XVII
THE TIDES 353

LECTURE XVIII
THE TIDES, AND PLANETARY EVOLUTION 379

I L L U S T R AT I O N S
FIG. PAGE
1. Archimedes 8
2. Leonardo da Vinci 10
3. Copernicus 12
4. Homeric Cosmogony 15
5. Egyptian Symbol of the Universe 16
6. Hindoo Earth 17
7. Order of ancient Planets corresponding to the Days of 19
the Week
8. Ptolemaic System 20
9. Specimens of Apparent Paths of Venus and of Mars among 21
the stars
10. Apparent Epicyclic Orbits of Jupiter and Saturn 22
11. Egyptian System 24
12. True Orbits of Earth and Jupiter 25
13. Orbits of Mercury and Earth 25
14. Copernican System as frequently represented 26
15. Slow Movement of the North Pole in a Circle among the 29
Stars
16. Tychonic system, showing the Sun with all the Planets 38
revolving round the Earth
17. Portrait of Tycho 41
18. Early out-door Quadrant of Tycho 43
19. Map of Denmark, showing the Island of Huen 45
20. Uraniburg 46
21. Astrolabe 47
22. Tycho's large Sextant 48
23. The Quadrant in Uraniburg 49

24. Tycho's Form of Transit Circle 50
25. A Modern Transit Circle 51
26. Orbits of some of the Planets drawn to scale 60
27. Many-sided Polygon or Approximate Circle enveloped by 61
Straight Lines
28. Kepler's Idea of the Regular Solids 62
29. Diagram of Equant 67
30. Excentric Circle supposed to be divided into equal Areas 68
31. Mode of drawing an Ellipse 70
32. Kepler's Diagram proving Equable Description of Areas 71
for an Ellipse
33. Diagram of a Planet's Velocity in Different Parts of its 72
Orbit
34. Portrait of Kepler 76
35. Curve described by a Projectile 82
36. Two Forms of Pulsilogy 87
37. Tower of Pisa 91
38. View of the Half-Moon in small Telescope 97
39. Portion of the Lunar Surface more highly magnified 98
40. Another Portion of the Lunar Surface 99
41. Lunar Landscape showing Earth 100
42. Galileo's Method of estimating the Height of Lunar 101
Mountain
43. Some Clusters and Nebulæ 102
44. Stages of the Discovery of Jupiter's Satellites 103
45. Eclipses of Jupiter's Satellites 105
46. Old Drawings of Saturn by Different Observers, with 111
the imperfect Instruments of that day
47. Phases of Venus 112
48. Sunspots as seen with Low Power 113
49. A Portion of the Sun's Disk as seen in a powerful modern 114
Telescope
50. Saturn and his Rings 115
51. Map of Italy 118
52. Portrait of Galileo 126

53. Portrait of Descartes 148
54. Descartes's Eye Diagram 151
55. Descartes's Diagram of Vortices from his "Principia" 152
56. Manor-house of Woolsthorpe 162
57. Projectile Diagram 170
58. 171
Diagrams illustrative of those near the Beginning of
59. 174
Newton's "Principia"
60. } { 175
61-
175
2.
63. Prismatic Dispersion 182
64. A single Constituent of White Light is capable of no 183
more Dispersion
65. Parallel Beam passing through a Lens 184
66. Newton's Telescope 186
67. The Sextant, as now made 187
68. Newton when young 196
69. Sir Isaac Newton 200
70. Another "Principia" Diagram 207
71. Well-known Model exhibiting the Oblate Spheroidal 219
Form as a Consequence of spinning about a Central Axis
72. Jupiter 221
73. Diagram of Eye looking at a Light reflected in a Distant 238
Mirror through the Teeth of a revolving Wheel
74. Fizeau's Wheel, showing the appearance of distant Image 239
seen through its Teeth
75. Eclipses of one of Jupiter's Satellites 241
76. A Transit instrument for the British Astronomical 243
Expedition, 1874
77. Diagram of equatorially mounted Telescope 245
78. Aberration Diagram 250
79. Showing the three Conjunction Places in the Orbits of 259
Jupiter and Saturn

80. Lord Rosse's Drawing of the Spiral Nebula in Canes 269
Venatici
81. Saturn 271
82. Principle of Newtonian Reflector 278
83. Herschel's 40-foot telescope 283
84. William Herschel 285
85. Caroline Herschel 287
86. Double Stars 288
87. Old Drawing of the Cluster in Hercules 290
88. Old Drawing of the Andromeda Nebula 291
89. The Great Nebula in Orion 292
90. Planetary Orbits to scale 297
91. Diagram illustrating Parallax 307
92. The Königsberg Heliometer 312
93. Perturbations of Uranus 320
94. Uranus' and Neptune's Relative Positions 325
95. Meteorite 333
96. Meteor Stream crossing Field of Telescope 334
97. Diagram of Direction of Earth's Orbital Motion 335
98. Parabolic and Elliptic Orbits 340
99. Orbit of Halley's Comet 341
100. Various Appearances of Halley's Comet when last seen 342
101. Head of Donati's Comet of 1858 343
102. Comet 344
103. Encke's Comet 345
104. Biela's Comet as last seen in two Portions 346
105. Radiant Point Perspective 348
106. Present Orbit of November Meteors 349
107. Orbit of November Meteors before and after Encounter 351
with Uranus
108. The Mersey 355
109. Co-tidal Lines, showing the way the Tidal Wave reaches 359
the British Isles from the Atlantic
110. Whirling Earth Model 364

111. Earth and Moon Model 365
112. Earth and Moon (Earth's Rotation Neglected) 366
113. Maps showing how comparatively Free from Land 369
Obstruction the Ocean in the Southern Hemisphere Is
114. Spring and Neap Tides 370
115. Tidal Clock 371
116. Sir William Thomson (Lord Kelvin) 373
117. Tide-gauge for recording Local Tides 375
118. Harmonic Analyzer 375
119. Tide-predicter 376
120. Weekly Sheet of Curves 377

PIONEERS OF SCIENCE

PART I

FROM DUSK TO DAYLIGHT

DAT E S AND S UM M ARY OF FACT S F OR L E CT URE
I

Physical Science of the Ancients. Thales 640 b.c., Anaximander 610 b.c.,
Pythagoras 600 b.c., Anaxagoras 500 b.c., Eudoxus 400 b.c., Aristotle
384 b.c., Aristarchus 300 b.c., Archimedes 287 b.c., Eratosthenes 276 b.c.,
Hipparchus 160 b.c., Ptolemy 100 a.d.

Science of the Middle Ages. Cultivated only among the Arabs; largely in
the forms of astrology, alchemy, and algebra.

Return of Science to Europe. Roger Bacon 1240, Leonardo da Vinci
1480, (Printing 1455), Columbus 1492, Copernicus 1543.

A sketch of Copernik's life and work. Born 1473 at Thorn in Poland.
Studied mathematics at Bologna. Became an ecclesiastic. Lived at
Frauenburg near mouth of Vistula. Substituted for the apparent motion of
the heavens the real motion of the earth. Published tables of planetary
motions. Motion still supposed to be in epicycles. Worked out his ideas for
36 years, and finally dedicated his work to the Pope. Died just as his book
was printed, aged 72, a century before the birth of Newton. A colossal
statue by Thorwaldsen erected at Warsaw in 1830.

PIONEERS OF SCIENCE

LECTURE I

COPERNICUS AND THE MOTION OF THE EARTH

The ordinary run of men live among phenomena of which they know
nothing and care less. They see bodies fall to the earth, they hear sounds,
they kindle fires, they see the heavens roll above them, but of the causes
and inner working of the whole they are ignorant, and with their ignorance
they are content.

"Understand the structure of a soap-bubble?" said a cultivated literary
man whom I know; "I wouldn't cross the street to know it!"

And if this is a prevalent attitude now, what must have been the attitude
in ancient times, when mankind was emerging from savagery, and when
history seems composed of harassments by wars abroad and revolutions at
home? In the most violently disturbed times indeed, those with which
ordinary history is mainly occupied, science is quite impossible. It needs as
its condition, in order to flourish, a fairly quiet, untroubled state, or else a
cloister or university removed from the din and bustle of the political and
commercial world. In such places it has taken its rise, and in such peaceful
places and quiet times true science will continue to be cultivated.

The great bulk of mankind must always remain, I suppose, more or less
careless of scientific research and scientific result, except in so far as it

affects their modes of locomotion, their health and pleasure, or their purse.

But among a people hurried and busy and preoccupied, some in the
pursuit of riches, some in the pursuit of pleasure, and some, the majority, in
the struggle for existence, there arise in every generation, here and there,
one or two great souls—men who seem of another age and country, who
look upon the bustle and feverish activity and are not infected by it, who
watch others achieving prizes of riches and pleasure and are not disturbed,
who look on the world and the universe they are born in with quite other
eyes. To them it appears not as a bazaar to buy and to sell in; not as a ladder
to scramble up (or down) helter-skelter without knowing whither or why;
but as a fact—a great and mysterious fact—to be pondered over, studied,
and perchance in some small measure understood. By the multitude these
men were sneered at as eccentric or feared as supernatural. Their calm,
clear, contemplative attitude seemed either insane or diabolic; and
accordingly they have been pitied as enthusiasts or killed as blasphemers.
One of these great souls may have been a prophet or preacher, and have
called to his generation to bethink them of why and what they were, to
struggle less and meditate more, to search for things of true value and not
for dross. Another has been a poet or musician, and has uttered in words or
in song thoughts dimly possible to many men, but by them unutterable and
left inarticulate. Another has been influenced still more directly by the
universe around him, has felt at times overpowered by the mystery and
solemnity of it all, and has been impelled by a force stronger than himself to
study it, patiently, slowly, diligently; content if he could gather a few
crumbs of the great harvest of knowledge, happy if he could grasp some
great generalization or wide-embracing law, and so in some small measure
enter into the mind and thought of the Designer of all this wondrous frame
of things.

These last have been the men of science, the great and heaven-born men
of science; and they are few. In our own day, amid the throng of inventions,
there are a multitude of small men using the name of science but working
for their own ends, jostling and scrambling just as they would jostle and

scramble in any other trade or profession. These may be workers, they may
and do advance knowledge, but they are never pioneers. Not to them is it
given to open out great tracts of unexplored territory, or to view the
promised land as from a mountain-top. Of them we shall not speak; we will
concern ourselves only with the greatest, the epoch-making men, to whose
life and work we and all who come after them owe so much. Such a man
was Thales. Such was Archimedes, Hipparchus, Copernicus. Such pre-
eminently was Newton.

Now I am not going to attempt a history of science. Such a work in ten
lectures would be absurd. I intend to pick out a few salient names here and
there, and to study these in some detail, rather than by attempting to deal
with too many to lose individuality and distinctness.

We know so little of the great names of antiquity, that they are for this
purpose scarcely suitable. In some departments the science of the Greeks
was remarkable, though it is completely overshadowed by their philosophy;
yet it was largely based on what has proved to be a wrong method of
procedure, viz the introspective and conjectural, rather than the inductive
and experimental methods. They investigated Nature by studying their own
minds, by considering the meanings of words, rather than by studying
things and recording phenomena. This wrong (though by no means, on the
face of it, absurd) method was not pursued exclusively, else would their
science have been valueless, but the influence it had was such as materially
to detract from the value of their speculations and discoveries. For when
truth and falsehood are inextricably woven into a statement, the truth is as
hopelessly hidden as if it had never been stated, for we have no criterion to
distinguish the false from the true.

Fig. 1.—Archimedes.

Besides this, however, many of their discoveries were ultimately lost to
the world, some, as at Alexandria, by fire—the bigoted work of a
Mohammedan conqueror—some by irruption of barbarians; and all were
buried so long and so completely by the night of the dark ages, that they
had to be rediscovered almost as absolutely and completely as though they
had never been. Some of the names of antiquity we shall have occasion to
refer to; so I have arranged some of them in chronological order on page 4,
and as a representative one I may specially emphasize Archimedes, one of
the greatest men of science there has ever been, and the father of physics.

The only effective link between the old and the new science is afforded
by the Arabs. The dark ages come as an utter gap in the scientific history of
Europe, and for more than a thousand years there was not a scientific man
of note except in Arabia; and with the Arabs knowledge was so mixed up
with magic and enchantment that one cannot contemplate it with any degree
of satisfaction, and little real progress was made. In some of the Waverley

Novels you can realize the state of matters in these times; and you know
how the only approach to science is through some Arab sorcerer or
astrologer, maintained usually by a monarch, and consulted upon all great
occasions, as the oracles were of old.

In the thirteenth century, however, a really great scientific man appeared,
who may be said to herald the dawn of modern science in Europe. This man
was Roger Bacon. He cannot be said to do more than herald it, however, for
we must wait two hundred years for the next name of great magnitude;
moreover he was isolated, and so far in advance of his time that he left no
followers. His own work suffered from the prevailing ignorance, for he was
persecuted and imprisoned, not for the commonplace and natural reason
that he frightened the Church, but merely because he was eccentric in his
habits and knew too much.

The man I spoke of as coming two hundred years later is Leonardo da
Vinci. True he is best known as an artist, but if you read his works you will
come to the conclusion that he was the most scientific artist who ever lived.
He teaches the laws of perspective (then new), of light and shade, of colour,
of the equilibrium of bodies, and of a multitude of other matters where
science touches on art—not always quite correctly according to modern
ideas, but in beautiful and precise language. For clear and conscious power,
for wide-embracing knowledge and skill, Leonardo is one of the most
remarkable men that ever lived.

About this time the tremendous invention of printing was achieved, and
Columbus unwittingly discovered the New World. The middle of the next
century must be taken as the real dawn of modern science; for the year 1543
marks the publication of the life-work of Copernicus.

Fig. 2.—Leonardo da Vinci.

Nicolas Copernik was his proper name. Copernicus is merely the
Latinized form of it, according to the then prevailing fashion. He was born
at Thorn, in Polish Prussia, in 1473. His father is believed to have been a
German. He graduated at Cracow as doctor in arts and medicine, and was
destined for the ecclesiastical profession. The details of his life are few; it
seems to have been quiet and uneventful, and we know very little about it.
He was instructed in astronomy at Cracow, and learnt mathematics at
Bologna. Thence he went to Rome, where he was made Professor of
Mathematics; and soon afterwards he went into orders. On his return home,
he took charge of the principal church in his native place, and became a
canon. At Frauenburg, near the mouth of the Vistula, he lived the remainder
of his life. We find him reporting on coinage for the Government, but
otherwise he does not appear as having entered into the life of the times.

He was a quiet, scholarly monk of studious habits, and with a reputation
which drew to him several earnest students, who received vivâ voce

instruction from him; so, in study and meditation, his life passed.

He compiled tables of the planetary motions which were far more
correct than any which had hitherto appeared, and which remained
serviceable for long afterwards. The Ptolemaic system of the heavens,
which had been the orthodox system all through the Christian era, he
endeavoured to improve and simplify by the hypothesis that the sun was the
centre of the system instead of the earth; and the first consequences of this
change he worked out for many years, producing in the end a great book:
his one life-work. This famous work, "De Revolutionibus Orbium
Cœlestium," embodied all his painstaking calculations, applied his new
system to each of the bodies in the solar system in succession, and treated
besides of much other recondite matter. Towards the close of his life it was
put into type. He can scarcely be said to have lived to see it appear, for he
was stricken with paralysis before its completion; but a printed copy was
brought to his bedside and put into his hands, so that he might just feel it
before he died.

Fig. 3.—Copernicus.

That Copernicus was a giant in intellect or power—such as had lived in
the past, and were destined to live in the near future—I see no reason
whatever to believe. He was just a quiet, earnest, patient, and God-fearing
man, a deep student, an unbiassed thinker, although with no specially
brilliant or striking gifts; yet to him it was given to effect such a revolution
in the whole course of man's thoughts as is difficult to parallel.

You know what the outcome of his work was. It proved—he did not
merely speculate, he proved—that the earth is a planet like the others, and
that it revolves round the sun.

Yes, it can be summed up in a sentence, but what a revelation it contains.
If you have never made an effort to grasp the full significance of this
discovery you will not appreciate it. The doctrine is very familiar to us now,

we have heard it, I suppose, since we were four years old, but can you
realize it? I know it was a long time before I could. Think of the solid earth,
with trees and houses, cities and countries, mountains and seas—think of
the vast tracts of land in Asia, Africa, and America—and then picture the
whole mass spinning like a top, and rushing along its annual course round
the sun at the rate of nineteen miles every second.

Were we not accustomed to it, the idea would be staggering. No wonder
it was received with incredulity. But the difficulties of the conception are
not only physical, they are still more felt from the speculative and
theological points of view. With this last, indeed, the reconcilement cannot
be considered complete even yet. Theologians do not, indeed, now deny the
fact of the earth's subordination in the scheme of the universe, but many of
them ignore it and pass it by. So soon as the Church awoke to a perception
of the tremendous and revolutionary import of the new doctrines, it was
bound to resist them or be false to its traditions. For the whole tenor of
men's thought must have been changed had they accepted it. If the earth
were not the central and all-important body in the universe, if the sun and
planets and stars were not attendant and subsidiary lights, but were other
worlds larger and perhaps superior to ours, where was man's place in the
universe? and where were the doctrines they had maintained as
irrefragable? I by no means assert that the new doctrines were really utterly
irreconcilable with the more essential parts of the old dogmas, if only
theologians had had patience and genius enough to consider the matter
calmly. I suppose that in that case they might have reached the amount of
reconciliation at present attained, and not only have left scientific truth in
peace to spread as it could, but might perhaps themselves have joined the
band of earnest students and workers, as so many of the higher Catholic
clergy do at the present day.

But this was too much to expect. Such a revelation was not to be
accepted in a day or in a century—the easiest plan was to treat it as a
heresy, and try to crush it out.

Not in Copernik's life, however, did they perceive the dangerous
tendency of the doctrine—partly because it was buried in a ponderous and
learned treatise not likely to be easily understood; partly, perhaps, because
its propounder was himself an ecclesiastic; mainly because he was a patient
and judicious man, not given to loud or intolerant assertion, but content to
state his views in quiet conversation, and to let them gently spread for thirty
years before he published them. And, when he did publish them, he used the
happy device of dedicating his great book to the Pope, and a cardinal bore
the expense of printing it. Thus did the Roman Church stand sponsor to a
system of truth against which it was destined in the next century to hurl its
anathemas, and to inflict on its conspicuous adherents torture,
imprisonment, and death.

To realize the change of thought, the utterly new view of the universe,
which the Copernican theory introduced, we must go back to preceding
ages, and try to recall the views which had been held as probable
concerning the form of the earth and the motion of the heavenly bodies.

Fig. 4.—Homeric Cosmogony.

The earliest recorded notion of the earth is the very natural one that it is
a flat area floating in an illimitable ocean. The sun was a god who drove his
chariot across the heavens once a day; and Anaxagoras was threatened with
death and punished with banishment for teaching that the sun was only a
ball of fire, and that it might perhaps be as big as the country of Greece. The
obvious difficulty as to how the sun got back to the east again every
morning was got over—not by the conjecture that he went back in the dark,
nor by the idea that there was a fresh sun every day; though, indeed, it was
once believed that the moon was created once a month, and periodically cut
up into stars—but by the doctrine that in the northern part of the earth was a
high range of mountains, and that the sun travelled round on the surface of
the sea behind these. Sometimes, indeed, you find a representation of the
sun being rowed round in a boat. Later on it was perceived to be necessary
that the sun should be able to travel beneath the earth, and so the earth was
supposed to be supported on pillars or on roots, or to be a dome-shaped
body floating in air—much like Dean Swift's island of Laputa. The elephant
and tortoise of the Hindu earth are, no doubt, emblematic or typical, not
literal.

Fig. 5.—Egyptian Symbol of the Universe.
The earth a figure with leaves, the heaven a figure with stars, the principle of equilibrium and
support, the boats of the rising and setting sun.

Aristotle, however, taught that the earth must be a sphere, and used all
the orthodox arguments of the present children's geography-books about the
way you see ships at sea, and about lunar eclipses.

To imagine a possible antipodes must, however, have been a tremendous
difficulty in the way of this conception of a sphere, and I scarcely suppose
that any one can at that time have contemplated the possibility of such
upside-down regions being inhabited. I find that intelligent children
invariably feel the greatest difficulty in realizing the existence of inhabitants
on the opposite side of the earth. Stupid children, like stupid persons in
general, will of course believe anything they are told, and much good may
the belief do them; but the kind of difficulties felt by intelligent and
thoughtful children are most instructive, since it is quite certain that the
early philosophers must have encountered and overcome those very same
difficulties by their own genius.

Fig. 6.—Hindoo Earth.

However, somehow or other the conception of a spherical earth was
gradually grasped, and the heavenly bodies were perceived all to revolve
round it: some moving regularly, as the stars, all fixed together into one
spherical shell or firmament; some moving irregularly and apparently
anomalously—these irregular bodies were therefore called planets [or
wanderers]. Seven of them were known, viz. Moon, Mercury, Venus, Sun,

Mars, Jupiter, Saturn, and there is little doubt that this number seven, so
suggested, is the origin of the seven days of the week.
The above order of the ancient planets is that of their supposed distance from the
earth. Not always, however, are they thus quoted by the ancients: sometimes the sun is
supposed nearer than Mercury or Venus. It has always been known that the moon was
the nearest of the heavenly bodies; and some rough notion of its distance was current.
Mars, Jupiter, and Saturn were placed in that order because that is the order of their
apparent motions, and it was natural to suppose that the slowest moving bodies were
the furthest off.

The order of the days of the week shows what astrologers considered to be the
order of the planets; on their system of each successive hour of the day being ruled
over by the successive planets taken in order. The diagram (fig. 7) shows that if the
Sun rule the first hour of a certain day (thereby giving its name to the day) Venus will
rule the second hour, Mercury the third, and so on; the Sun will thus be found to rule
the eighth, fifteenth, and twenty-second hour of that day, Venus the twenty-third, and
Mercury the twenty-fourth hour; so the Moon will rule the first hour of the next day,
which will therefore be Monday. On the same principle (numbering round the hours
successively, with the arrows) the first hour of the next day will be found to be ruled
by Mars, or by the Saxon deity corresponding thereto; the first hour of the day after,
by Mercury (Mercredi), and so on (following the straight lines of the pattern).

The order of the planets round the circle counter-clockwise, i.e. the direction of
their proper motions, is that quoted above in the text.

To explain the motion of the planets and reduce them to any sort of law
was a work of tremendous difficulty. The greatest astronomer of ancient
times was Hipparchus, and to him the system known as the Ptolemaic
system is no doubt largely due. But it was delivered to the world mainly by
Ptolemy, and goes by his name. This was a fine piece of work, and a great
advance on anything that had gone before; for although it is of course
saturated with error, still it is based on a large substratum of truth. Its
superiority to all the previously mentioned systems is obvious. And it really
did in its more developed form describe the observed motions of the
planets.

Each planet was, in the early stages of this system, as taught, say, by
Eudoxus, supposed to be set in a crystal sphere, which revolved so as to
carry the planet with it. The sphere had to be of crystal to account for the

visibility of other planets and the stars through it. Outside the seven
planetary spheres, arranged one inside the other, was a still larger one in
which were set the stars. This was believed to turn all the others, and was
called the primum mobile. The whole system was supposed to produce, in
its revolution, for the few privileged to hear the music of the spheres, a
sound as of some magnificent harmony.

Fig. 7.—Order of ancient planets corresponding to the days of the
week.

The enthusiastic disciples of Pythagoras believed that their master was
privileged to hear this noble chant; and far be it from us to doubt that the
rapt and absorbing pleasure of contemplating the harmony of nature, to a
man so eminently great as Pythagoras, must be truly and adequately
represented by some such poetic conception.

Fig. 8.—Ptolemaic system.

The precise kind of motion supposed to be communicated from the
primum mobile to the other spheres so as to produce the observed motions
of the planets was modified and improved by various philosophers until it
developed into the epicyclic train of Hipparchus and of Ptolemy.

It is very instructive to observe a planet (say Mars or Jupiter) night after
night and plot down its place with reference to the fixed stars on a celestial
globe or star-map. Or, instead of direct observation by alignment with
known stars, it is easier to look out its right ascension and declination in
Whitaker's Almanac, and plot those down. If this be done for a year or two,
it will be found that the motion of the planet is by no means regular, but that
though on the whole it advances it sometimes is stationary and sometimes
goes back.[1]

Fig. 9.—Specimens of Apparent paths of Venus and of Mars
among the stars.

Fig. 10.—Apparent epicyclic orbits of Jupiter and Saturn; the
Earth being supposed fixed at the centre, with the Sun
revolving in a small circle. A loop is made by each planet
every year.

These "stations" and "retrogressions" of the planets were well known to
the ancients. It was not to be supposed for a moment that the crystal spheres
were subject to any irregularity, neither was uniform circular motion to be
readily abandoned; so it was surmised that the main sphere carried, not the
planet itself, but the centre or axis of a subordinate sphere, and that the
planet was carried by this. The minor sphere could be allowed to revolve at
a different uniform pace from the main sphere, and so a curve of some
complexity could be obtained.

A curve described in space by a point of a circle or sphere, which itself is
carried along at the same time, is some kind of cycloid; if the centre of the
tracing circle travels along a straight line, we get the ordinary cycloid, the
curve traced in air by a nail on a coach-wheel; but if the centre of the
tracing circle be carried round another circle the curve described is called
an epicycloid. By such curves the planetary stations and retrogressions
could be explained. A large sphere would have to revolve once for a "year"
of the particular planet, carrying with it a subsidiary sphere in which the
planet was fixed; this latter sphere revolving once for a "year" of the earth.
The actual looped curve thus described is depicted for Jupiter and Saturn in
the annexed diagram (fig. 10.)
It was long ago perceived that real material spheres were unnecessary; such
spheres indeed, though possibly transparent to light, would be impermeable to
comets: any other epicyclic gearing would serve, and as a mere description of the
motion it is simpler to think of a system of jointed bars, one long arm carrying a
shorter arm, the two revolving at different rates, and the end of the short one carrying
the planet. This does all that is needful for the first approximation to a planet's motion.
In so far as the motion cannot be thus truly stated, the short arm may be supposed to
carry another, and that another, and so on, so that the resultant motion of the planet is
compounded of a large number of circular motions of different periods; by this device
any required amount of complexity could be attained. We shall return to this at greater
length in Lecture III.

The main features of the motion, as shown in the diagram, required only two arms
for their expression; one arm revolving with the average motion of the planet, and the
other revolving with the apparent motion of the sun, and always pointing in the same
direction as the single arm supposed to carry the sun. This last fact is of course
because the motion to be represented does not really belong to the planet at all, but to
the earth, and so all the main epicyclic motions for the superior planets were the same.
As for the inferior planets (Mercury and Venus) they only appear to oscillate like the
bob of a pendulum about the sun, and so it is very obvious that they must be really
revolving round it. An ancient Egyptian system perceived this truth; but the Ptolemaic
system imagined them to revolve round the earth like the rest, with an artificial
system of epicycles to prevent their ever getting far away from the neighbourhood of
the sun.

It is easy now to see how the Copernican system explains the main features of
planetary motion, the stations and retrogressions, quite naturally and without any
complexity.

Fig. 11.—Egyptian system.
Let the outer circle represent the orbit of Jupiter, and the inner circle the orbit of
the earth, which is moving faster than Jupiter (since Jupiter takes 4332 days to make
one revolution); then remember that the apparent position of Jupiter is referred to the
infinitely distant fixed stars and refer to fig. 12.

Let E1, E2, &c., be successive positions of the earth; J1, J2, &c., corresponding
positions of Jupiter. Produce the lines E1 J1, E2 J2, &c., to an enormously greater
circle outside, and it will be seen that the termination of these lines, representing
apparent positions of Jupiter among the stars, advances while the earth goes from E1
to E3; is almost stationary from somewhere about E3 to E4; and recedes from E4 to
E5; so that evidently the recessions of Jupiter are only apparent, and are due to the
orbital motion of the earth. The apparent complications in the path of Jupiter, shown
in Fig. 10, are seen to be caused simply by the motion of the earth, and to be thus
completely and easily explained.

Fig. 12.—True orbits of Earth and Jupiter.
The same thing for an inferior planet, say Mercury, is even still more easily seen
(vide figure 13).

The motion of Mercury is direct from M'' to M''', retrograde from M''' to M'', and
stationary at M'' and M'''. It appears to oscillate, taking 72·5 days for its direct swing,
and 43·5 for its return swing.

Fig. 13.—Orbit of Mercury and Earth.
On this system no artificiality is required to prevent Mercury's ever getting far
from the sun: the radius of its orbit limits its real and apparent excursions. Even if the
earth were stationary, the motions of Mercury and Venus would not be essentially
modified, but the stations and retrogressions of the superior planets, Mars, Jupiter,
&c., would wholly cease.

The complexity of the old mode of regarding apparent motion may be illustrated
by the case of a traveller in a railway train unaware of his own motion. It is as though
trees, hedges, distant objects, were all flying past him and contorting themselves as
you may see the furrows of a ploughed field do when travelling, while you yourself
seem stationary amidst it all. How great a simplicity would be introduced by the
hypothesis that, after all, these things might be stationary and one's self moving.

Fig. 14.—Copernican system as frequently represented. But the
cometary orbit is a much later addition, and no attempt is
made to show the relative distances of the planets.

Now you are not to suppose that the system of Copernicus swept away
the entire doctrine of epicycles; that doctrine can hardly be said to be swept
away even now. As a description of a planet's motion it is not incorrect,
though it is geometrically cumbrous. If you describe the motion of a railway
train by stating that every point on the rim of each wheel describes a
cycloid with reference to the earth, and a circle with reference to the train,
and that the motion of the train is compounded of these cycloidal and
circular motions, you will not be saying what is false, only what is
cumbrous.

The Ptolemaic system demanded large epicycles, depending on the
motion of the earth, these are what Copernicus overthrew; but to express the
minuter details of the motion smaller epicycles remained, and grew more
and more complex as observations increased in accuracy, until a greater

man than either Copernicus or Ptolemy, viz. Kepler, replaced them all by a
simple ellipse.

One point I must not omit from this brief notice of the work of
Copernicus. Hipparchus had, by most sagacious interpretation of certain
observations of his, discovered a remarkable phenomenon called the
precession of the equinoxes. It was a discovery of the first magnitude, and
such as would raise to great fame the man who should have made it in any
period of the world's history, even the present. It is scarcely expressible in
popular language, and without some technical terms; but I can try.

The plane of the earth's orbit produced into the sky gives the apparent
path of the sun throughout a year. This path is known as the ecliptic,
because eclipses only happen when the moon is in it. The sun keeps to it
accurately, but the planets wander somewhat above and below it (fig. 9),
and the moon wanders a good deal. It is manifest, however, in order that
there may be an eclipse of any kind, that a straight line must be able to be
drawn through earth and moon and sun (not necessarily through their
centres of course), and this is impossible unless some parts of the three
bodies are in one plane, viz. the ecliptic, or something very near it. The
ecliptic is a great circle of the sphere, and is usually drawn on both celestial
and terrestrial globes.

The earth's equator also produced into the sky, where it may still be
called the equator (sometimes it is awkwardly called "the equinoctial"),
gives another great circle inclined to the ecliptic and cutting it at two
opposite points, labelled respectively ♈ and ♎ , and together called "the
equinoxes." The reason for the name is that when the sun is in that part of
the ecliptic it is temporarily also on the equator, and hence is symmetrically
situated with respect to the earth's axis of rotation, and consequently day
and night are equal all over the earth.

Well, Hipparchus found, by plotting the position of the sun for a long
time,[2] that these points of intersection, or equinoxes, were not stationary

from century to century, but slowly moved among the stars, moving as it
were to meet the sun, so that he gets back to one of these points again 20
minutes 23¼ seconds before it has really completed a revolution, i.e. before
the true year is fairly over. This slow movement forward of the goal-post is
called precession—the precession of the equinoxes. (One result of it is to
shorten our years by about 20 minutes each; for the shortened period has to
be called a year, because it is on the position of the sun with respect to the
earth's axis that our seasons depend.) Copernicus perceived that, assuming
the motion of the earth, a clearer account of this motion could be given. The
ordinary approximate statement concerning the earth's axis is that it remains
parallel to itself, i.e. has a fixed direction as the earth moves round the sun.
But if, instead of being thus fixed, it be supposed to have a slow movement
of revolution, so that it traces out a cone in the course of about 26,000
years, then, since the equator of course goes with it, the motion of its
intersection with the fixed ecliptic is so far accounted for. That is to say, the
precession of the equinoxes is seen to be dependent on, and caused by, a
slow conical movement of the earth's axis.

The prolongation of each end of the earth's axis into the sky, or the
celestial north and south poles, will thus slowly trace out an approximate
circle among the stars; and the course of the north pole during historic time
is exhibited in the annexed diagram.

It is now situated near one of the stars of the Lesser Bear, which we
therefore call the Pole star; but not always was it so, nor will it be so in the
future. The position of the north pole 4000 years ago is shown in the figure;
and a revolution will be completed in something like 26,000 years.[3]

Fig. 15.—Slow movement of the north pole in a circle among the stars.
(Copied from Sir R. Ball.)

This perception of the conical motion of the earth's axis was a beautiful
generalization of Copernik's, whereby a multitude of facts were grouped
into a single phenomenon. Of course he did not explain the motion of the
axis itself. He stated the fact that it so moved, and I do not suppose it ever
struck him to seek for an explanation.

An explanation was given later, and that a most complete one; but the
idea even of seeking for it is a brilliant and striking one: the achievement of
the explanation by a single individual in the way it actually was
accomplished is one of the most astounding things in the history of science;
and were it not that the same individual accomplished a dozen other things,
equally and some still more extraordinary, we should rank that man as one
of the greatest astronomers that ever lived.

As it is, he is Sir Isaac Newton.

We are to remember, then, as the life-work of Copernicus, that he placed
the sun in its true place as the centre of the solar system, instead of the
earth; that he greatly simplified the theory of planetary motion by this step,

and also by the simpler epicyclic chain which now sufficed, and which he
worked out mathematically; that he exhibited the precession of the
equinoxes (discovered by Hipparchus) as due to a conical motion of the
earth's axis; and that, by means of his simpler theory and more exact
planetary tables, he reduced to some sort of order the confused chaos of the
Ptolemaic system, whose accumulation of complexity and of outstanding
errors threatened to render astronomy impossible by the mere burden of its
detail.

There are many imperfections in his system, it is true; but his great merit
is that he dared to look at the facts of Nature with his own eyes,
unhampered by the prejudice of centuries. A system venerable with age, and
supported by great names, was universally believed, and had been believed
for centuries. To doubt this system, and to seek after another and better one,
at a time when all men's minds were governed by tradition and authority,
and when to doubt was sin—this required a great mind and a high character.
Such a mind and such a character had this monk of Frauenburg. And it is
interesting to notice that the so-called religious scruples of smaller and less
truly religious men did not affect Copernicus; it was no dread of
consequences to one form of truth that led him to delay the publication of
the other form of truth specially revealed to him. In his dedication he says:
—

"If there be some babblers who, though ignorant of all mathematics, take
upon them to judge of these things, and dare to blame and cavil at my work,
because of some passage of Scripture which they have wrested to their own
purpose, I regard them not, and will not scruple to hold their judgment in
contempt."

I will conclude with the words of one of his biographers (Mr. E.J.C.
Morton):—

"Copernicus cannot be said to have flooded with light the dark places of
nature—in the way that one stupendous mind subsequently did—but still, as

we look back through the long vista of the history of science, the dim
Titanic figure of the old monk seems to rear itself out of the dull flats
around it, pierces with its head the mists that overshadow them, and catches
the first gleam of the rising sun,
"'... like some iron peak, by the Creator
Fired with the red glow of the rushing morn.'"

DAT E S AND S UM M ARY OF FACT S F OR L E CT URE
II

Copernicus lived from 1473 to 1543, and was contemporary with
Paracelsus and Raphael.

Tycho Brahé from 1546 to 1601.
Kepler from 1571 to 1630.
Galileo from 1564 to 1642.
Gilbert from 1540 to 1603.
Francis Bacon from 1561 to 1626.
Descartes from 1596 to 1650.

A sketch of Tycho Brahé's life and work. Tycho was a Danish noble, born
on his ancestral estate at Knudstorp, near Helsinborg, in 1546. Adopted by
his uncle, and sent to the University of Copenhagen to study law. Attracted
to astronomy by the occurrence of an eclipse on its predicted day, August
21st, 1560. Began to construct astronomical instruments, especially a
quadrant and a sextant. Observed at Augsburg and Wittenberg. Studied
alchemy, but was recalled to astronomy by the appearance of a new star.
Overcame his aristocratic prejudices, and delivered a course of lectures at
Copenhagen, at the request of the king. After this he married a peasant girl.
Again travelled and observed in Germany. In 1576 was sent for to Denmark
by Frederick II., and established in the island of Huen, with an endowment

enabling him to devote his life to astronomy. Built Uraniburg, furnished it
with splendid instruments, and became the founder of accurate instrumental
astronomy. His theories were poor, but his observations were admirable. In
1592 Frederick died, and five years later, Tycho was impoverished and
practically banished. After wandering till 1599, he was invited to Prague by
the Emperor Rudolf, and there received John Kepler among other pupils.
But the sentence of exile was too severe, and he died in 1601, aged 54
years.

A man of strong character, untiring energy, and devotion to accuracy, his
influence on astronomy has been immense.

LECTURE II

TYCHO BRAHÉ AND THE EARLIEST OBSERVATORY

We have seen how Copernicus placed the earth in its true position in the
solar system, making it merely one of a number of other worlds revolving
about a central luminary. And observe that there are two phenomena to be
thus accounted for and explained: first, the diurnal revolution of the
heavens; second, the annual motion of the sun among the stars.

The effect of the diurnal motion is conspicuous to every one, and
explains the rising, southing, and setting of the whole visible firmament.
The effect of the annual motion, i.e. of the apparent annual motion, of the
sun among the stars, is less obvious, but it may be followed easily enough
by observing the stars visible at any given time of evening at different
seasons of the year. At midnight, for instance, the position of the sun is
definite, viz. due north always, but the constellation which at that time is
due south or is rising or setting varies with the time of year; an interval of
one month producing just the same effect on the appearance of the

constellations as an interval of two hours does (because the day contains
twice as many hours as the year contains months), e.g. the sky looks the
same at midnight on the 1st of October as it does at 10 p.m. on the 1st of
November.

All these simple consequences of the geocentric as opposed to the
heliocentric point of view were pointed out by Copernicus, in addition to
his greater work of constructing improved planetary tables on the basis of
his theory. But it must be admitted that he himself felt the hypothesis of the
motion of the earth to be a difficulty. Its acceptance is by no means such an
easy and childish matter as we are apt now to regard it, and the hostility to it
is not at all surprising. The human race, after having ridiculed and resisted
the truth for a long time, is apt to end in accepting it so blindly and
unimaginatively as to fail to recognize the real achievement of its first
propounders, or the difficulties which they had to overcome. The majority
of men at the present day have grown accustomed to hear the motion of the
earth spoken of: their acceptance of it means nothing: the attitude of the
paradoxer who denies it is more intelligent.

It is not to be supposed that the idea of thus explaining some of the
phenomena of the heavens, especially the daily motion of the entire
firmament, by a diurnal rotation of the earth had not struck any one. It was
often at this time referred to as the Pythagorean theory, and it had been
taught, I believe, by Aristarchus. But it was new to the modern world, and it
had the great weight of Aristotle against it. Consequently, for long after
Copernicus, only a few leading spirits could be found to support it, and the
long-established venerable Ptolemaic system continued to be taught in all
Universities.

The main objections to the motion of the earth were such as the
following:—

1. The motion is unfelt and difficult to imagine.

That it is unfelt is due to its uniformity, and can be explained mechanically. That it
is difficult to imagine is and remains true, but a most important lesson we have to
learn is that difficulty of conception is no valid argument against reality.

2. That the stars do not alter their relative positions according to the
season of the year, but the constellations preserve always the same aspect
precisely, even to careful measurement.
This is indeed a difficulty, and a great one. In June the earth is 184 million miles
away from where it was in December: how can we see precisely the same fixed stars?
It is not possible, unless they are at a practically infinite distance. That is the only
answer that can be given. It was the tentative answer given by Copernicus. It is the
correct answer. Not only from every position of the earth, but from every planet of the
solar system, the same constellations are visible, and the stars have the same aspect.
The whole immensity of the solar system shrinks to practically a point when
confronted with the distance of the stars.

Not, however, so entirely a speck as to resist the terrific accuracy of the present
century, and their microscopic relative displacement with the season of the year has
now at length been detected, and the distance of many thereby measured.

3. That, if the earth revolved round the sun, Mercury and Venus ought to
show phases like the moon.
So they ought. Any globe must show phases if it live nearer the sun than we do and
if we go round it, for we shall see varying amounts of its illuminated half. The only
answer that Copernicus could give to this was that they might be difficult to see
without extra powers of sight, but he ventured to predict that the phases would be seen
if ever our powers of vision should be enhanced.

4. That if the earth moved, or even revolved on its own axis, a stone or
other dropped body ought to be left far behind.
This difficulty is not a real one, like the two last, and it is based on an ignorance of
the laws of mechanics, which had not at that time been formulated. We know now that
a ball dropped from a high tower, so far from lagging, drops a minute trifle in front of
the foot of a perpendicular, because the top of the tower is moving a trace faster than
the bottom, by reason of the diurnal rotation. But, ignoring this, a stone dropped from
the lamp of a railway carriage drops in the centre of the floor, whether the carriage be
moving steadily or standing still; a slant direction of fall could only be detected if the
carriage were being accelerated or if the brake were applied. A body dropped from a
moving carriage shares the motion of the carriage, and starts with that as its initial
velocity. A ball dropped from a moving balloon does not simply drop, but starts off in

whatever direction the car was moving, its motion being immediately modified by
gravity, precisely in the same way as that of a thrown ball is modified. This is, indeed,
the whole philosophy of throwing—to drop a ball from a moving carriage. The
carriage is the hand, and, to throw far, a run is taken and the body is jerked forward;
the arm is also moved as rapidly as possible on the shoulder as pivot. The fore-arm
can be moved still faster, and the wrist-joint gives yet another motion: the art of
throwing is to bring all these to bear at the same instant, and then just as they have all
attained their maximum velocity to let the ball go. It starts off with the initial velocity
thus imparted, and is abandoned to gravity. If the vehicle were able to continue its
motion steadily, as a balloon does, the ball when let go from it would appear to the
occupant simply to drop; and it would strike the ground at a spot vertically under the
moving vehicle, though by no means vertically below the place where it started. The
resistance of the air makes observations of this kind inaccurate, except when
performed inside a carriage so that the air shares in the motion. Otherwise a person
could toss and catch a ball out of a train window just as well as if he were stationary;
though to a spectator outside he would seem to be using great skill to throw the ball in
the parabola adapted to bring it back to his hand.

The same circumstance enhances the apparent difficulty of the circus rider's
jumping feats. All he has to do is to jump up and down on the horse; the forward
motion which carries him through hoops belongs to him by virtue of the motion of the
horse, without effort on his part.

Thus, then, it happens that a stone dropped sixteen feet on the earth appears to fall
straight down, although its real path in space is a very flat trajectory of nineteen miles
base and sixteen feet height; nineteen miles being the distance traversed by the earth
every second in the course of its annual journey round the sun.

No wonder that it was thought that bodies must be left behind if the earth was
subject to such terrific speed as this. All that Copernicus could suggest on this head
was that perhaps the atmosphere might help to carry things forward, and enable them
to keep pace with the earth.

There were thus several outstanding physical difficulties in the way of
the acceptance of the Copernican theory, besides the Biblical difficulty.

It was quite natural that the idea of the earth's motion should be
repugnant, and take a long time to sink into the minds of men; and as
scientific progress was vastly slower then than it is now, we find not only
all priests but even some astronomers one hundred years afterwards still
imagining the earth to be at rest. And among them was a very eminent one,
Tycho Brahé.

It is interesting to note, moreover, that the argument about the motion of
the earth being contrary to Scripture appealed not only to ecclesiastics in
those days, but to scientific men also; and Tycho Brahé, being a man of
great piety, and highly superstitious also, was so much influenced by it, that
he endeavoured to devise some scheme by which the chief practical
advantages of the Copernican system could be retained, and yet the earth be
kept still at the centre of the whole. This was done by making all the
celestial sphere, with stars and everything, rotate round the earth once a day,
as in the Ptolemaic scheme; and then besides this making all the planets
revolve round the sun, and this to revolve round the earth. Such is the
Tychonic system.

So far as relative motion is concerned it comes to the same thing; just as
when you drop a book you may say either that the earth rises to meet the
book, or that the book falls to meet the earth. Or when a fly buzzes round
your head, you may say that you are revolving round the fly. But the
absurdity of making the whole gigantic system of sun and planets and stars
revolve round our insignificant earth was too great to be swallowed by
other astronomers after they had once had a taste of the Copernican theory;
and accordingly the Tychonic system died a speedy and an easy death at the
same time as its inventor.

Wherein then lay the magnitude of the man?—not in his theories, which
were puerile, but in his observations, which were magnificent. He was the
first observational astronomer, the founder of the splendid system of
practical astronomy which has culminated in the present Greenwich
Observatory.

Fig. 16.—Tychonic system showing the sun with all the planets
revolving round the earth.

Up to Tycho the only astronomical measurements had been of the rudest
kind. Copernicus even improved upon what had gone before, with
measuring rules made with his own hands. Ptolemy's observations could
never be trusted to half a degree. Tycho introduced accuracy before
undreamed of, and though his measurements, reckoned by modern ideas,
are of course almost ludicrously rough (remember no such thing as a
telescope or microscope was then dreamed of), yet, estimated by the era in
which they were made, they are marvels of accuracy, and not a single
mistake due to carelessness has ever been detected in them. In fact they
may be depended on almost to minutes of arc, i.e. to sixtieths of a degree.

For certain purposes connected with the proper motion of stars they are
still appealed to, and they served as the certain and trustworthy data for
succeeding generations of theorists to work upon. It was long, indeed, after
Tycho's death before observations approaching in accuracy to his were
again made.

In every sense, therefore, he was a pioneer: let us proceed to trace his
history.

Born the eldest son of a noble family—"as noble and ignorant as sixteen
undisputed quarterings could make them," as one of his biographers says—
in a period when, even more than at present, killing and hunting were the
only natural aristocratic pursuits, when all study was regarded as something
only fit for monks, and when science was looked at askance as something
unsavoury, useless, and semi-diabolic, there was little in his introduction to
the world urging him in the direction where his genius lay. Of course he
was destined for a soldier; but fortunately his uncle, George Brahé, a more
educated man than his father, having no son of his own, was anxious to
adopt him, and though not permitted to do so for a time, succeeded in
getting his way on the birth of a second son, Steno—who, by the way,
ultimately became Privy Councillor to the King of Denmark.

Tycho's uncle gave him what he would never have got at home—a good
education; and ultimately put him to study law. At the age of thirteen he
entered the University of Copenhagen, and while there occurred the
determining influence of his life.

An eclipse of the sun in those days was not regarded with the cold-
blooded inquisitiveness or matter-of-fact apathy, according as there is or is
not anything to be learnt from it, with which such an event is now regarded.
Every occurrence in the heavens was then believed to carry with it the
destiny of nations and the fate of individuals, and accordingly was of
surpassing interest. Ever since the time of Hipparchus it had been possible
for some capable man here and there to predict the occurrence of eclipses
pretty closely. The thing is not difficult. The prediction was not, indeed, to
the minute and second, as it is now; but the day could usually be hit upon
pretty accurately some time ahead, much as we now manage to hit upon the
return of a comet—barring accidents; and the hour could be predicted as the
event approached.

Well, the boy Tycho, among others, watched for this eclipse on August
21st, 1560; and when it appeared at its appointed time, every instinct for the
marvellous, dormant in his strong nature, awoke to strenuous life, and he
determined to understand for himself a science permitting such wonderful
possibilities of prediction. He was sent to Leipzig with a tutor to go on with
his study of law, but he seems to have done as little law as possible: he
spent all his money on books and instruments, and sat up half the night
studying and watching the stars.

In 1563 he observed a conjunction of Jupiter and Saturn, the precursor,
and cause as he thought it, of the great plague. He found that the old
planetary tables were as much as a month in error in fixing this event, and
even the Copernican tables were several days out; so he formed the resolve
to devote his life to improving astronomical tables. This resolve he executed
with a vengeance. His first instrument was a jointed ruler with sights for
fixing the position of planets with respect to the stars, and observing their
stations and retrogressions. By thus measuring the angles between a planet
and two fixed stars, its position can be plotted down on a celestial map or
globe.

Fig. 17.—Portrait of Tycho.

In 1565 his uncle George died, and made Tycho his heir. He returned to
Denmark, but met with nothing but ridicule and contempt for his absurd
drivelling away of time over useless pursuits. So he went back to Germany
—first to Wittenberg, thence, driven by the plague, to Rostock.

Here his fiery nature led him into an absurd though somewhat dangerous
adventure. A quarrel at some feast, on a mathematical point, with a
countryman, Manderupius, led to the fixing of a duel, and it was fought
with swords at 7 p.m. at the end of December, when, if there was any light
at all, it must have been of a flickering and unsatisfactory nature. The result
of this insane performance was that Tycho got his nose cut clean off.

He managed however to construct an artificial one, some say of gold and
silver, some say of putty and brass; but whatever it was made of there is no
doubt that he wore it for the rest of his life, and it is a most famous feature.
It excited generally far more interest than his astronomical researches. It is
said, moreover, to have very fairly resembled the original, but whether this
remark was made by a friend or by an enemy I cannot say. One account
says that he used to carry about with him a box of cement to apply
whenever his nose came off, which it periodically did.

About this time he visited Augsburg, met with some kindred and
enlightened spirits in that town, and with much enthusiasm and spirit
constructed a great quadrant. These early instruments were tremendous
affairs. A great number of workmen were employed upon this quadrant, and
it took twenty men to carry it to its place and erect it. It stood in the open air
for five years, and then was destroyed by a storm. With it he made many
observations.

Fig. 18.—Early out-door quadrant of Tycho; for observing
altitudes by help of the sights D, L and the plumb line.

On his return to Denmark in 1571, his fame preceded him, and he was
much better received; and in order to increase his power of constructing
instruments he took up the study of alchemy, and like the rest of the
persuasion tried to make gold. The precious metals were by many old
philosophers considered to be related in some way to the heavenly bodies:
silver to the moon, for instance—as we still see by the name lunar caustic
applied to nitrate of silver; gold to the sun, copper to Mars, lead to Saturn.
Hence astronomy and alchemy often went together. Tycho all his life

combined a little alchemy with his astronomical labours, and he constructed
a wonderful patent medicine to cure all disorders, which had as wide a
circulation in Europe in its time as Holloway's pills; he gives a tremendous
receipt for it, with liquid gold and all manner of ingredients in it; among
them, however, occurs a little antimony—a well-known sudorific—and to
this, no doubt, whatever efficacy the medicine possessed was due.

So he might have gone on wasting his time, were it not that in
November, 1572, a new star made its appearance, as they have done
occasionally before and since. On the average one may say that about every
fifty years a new star of fair magnitude makes its temporary appearance.
They are now known to be the result of some catastrophe or collision,
whereby immense masses of incandescent gas are produced. This one seen
by Tycho became as bright as Jupiter, and then died away in about a year
and a half. Tycho observed all its changes, and endeavoured to measure its
distance from the earth, with the result that it was proved to belong to the
region of the fixed stars, at an immeasurable distance, and was not some
nearer and more trivial phenomenon.

He was asked by the University of Copenhagen to give a course of
lectures on astronomy; but this was a step he felt some aristocratic aversion
to, until a little friendly pressure was brought to bear upon him by a request
from the king, and delivered they were.

He now seems to have finally thrown off his aristocratic prejudices, and
to have indulged himself in treading on the corns of nearly all the high and
mighty people he came into contact with. In short, he became what we
might now call a violent Radical; but he was a good-hearted man,
nevertheless, and many are the tales told of his visits to sick peasants, of his
consulting the stars as to their fate—all in perfect good faith—and of the
medicines which he concocted and prescribed for them.

The daughter of one of these peasants he married, and very happy the
marriage seems to have been.

Fig. 19.—Map of Denmark, showing the island of Huen.
Walker & Boutallse.

Now comes the crowning episode in Tycho's life. Frederick II., realizing
how eminent a man they had among them, and how much he could do if
only he had the means—for we must understand that Tycho, though of good
family and well off, was by no means what we would call a wealthy man—
Frederick II. made him a splendid and enlightened offer. The offer was this:
that if Tycho would agree to settle down and make his astronomical
observations in Denmark, he should have an estate in Norway settled upon
him, a pension of £400 a year for life, a site for a large observatory, and
£20,000 to build it with.

Fig. 20.—Uraniburg.

Fig. 21.—Astrolabe. An old instrument with sights for marking the
positions of the celestial bodies roughly. A sort of skeleton celestial globe.

Fig. 22.—Tycho's large sextant; for measuring the angular
distance between two bodies by direct sighting.

Well, if ever money was well spent, this was. By its means Denmark
before long headed the nations of Europe in the matter of science—a thing
it has not done before or since. The site granted was the island of Huen,
between Copenhagen and Elsinore; and here the most magnificent
observatory ever built was raised, and called Uraniburg—the castle of the
heavens. It was built on a hill in the centre of the island, and included
gardens, printing shops, laboratory, dwelling-houses, and four observatories
—all furnished with the most splendid instruments that Tycho could devise,
and that could then be constructed. It was decorated with pictures and

sculptures of eminent men, and altogether was a most gorgeous place.
£20,000 no doubt went far in those days, but the original grant was
supplemented by Tycho himself, who is said to have spent another equal
sum out of his own pocket on the place.

Fig. 23.—The Quadrant in Uraniburg; or altitude and
azimuth instrument.

For twenty years this great temple of science was continually worked in
by him, and he soon became the foremost scientific man in Europe.
Philosophers, statesmen, and occasionally kings, came to visit the great
astronomer, and to inspect his curiosities.

Fig. 24.—Tycho's form of transit circle.

The method of utilising the extremely uniform rotation of the earth by watching the
planets and stars as they cross the meridian, and recording their times of transit; observing
also at the same time their meridian altitudes (see observer F), was the invention of Tycho,
and constitutes his greatest achievement. His method is followed to this day in all
observatories.

Fig. 25.—A modern transit circle, showing essentially the same
parts as in Tycho's instrument, viz. the observer watching the
transit, the clock, the recorder of the observation, and the
graduated circle; the latter to be read by a second observer.

And very wholesome for some of these great personages must have been
the treatment they met with. For Tycho was no respecter of persons. His
humbly-born wife sat at the head of the table, whoever was there; and he
would snub and contradict a chancellor just as soon as he would a serf.
Whatever form his pride may have taken when a youth, in his maturity it
impelled him to ignore differences of rank not substantially justified, and he
seemed to take a delight in exposing the ignorance of shallow titled persons,
to whom contradiction and exposure were most unusual experiences.

For sick peasants he would take no end of trouble, and went about
doctoring them for nothing, till he set all the professional doctors against
him; so that when his day of misfortune came, as come it did, their
influence was not wanting to help to ruin one who spoilt their practice, and
whom they derided as a quack.

But some of the great ignorant folk who came to visit his temple of
science, and to inspect its curiosities, felt themselves insulted—not always
without reason. He kept a tame maniac in the house, named Lep, and he
used to regard the sayings of this personage as oracular, presaging future
events, and far better worth listening to than ordinary conversation.
Consequently he used to have him at his banquets and feed him himself;
and whenever Lep opened his mouth to speak, every one else was
peremptorily ordered to hold his tongue, so that Lep's words might be
written down. In fact it was something like an exaggerated edition of Betsy
Trotwood and Mr. Dick.

"It must have been an odd dinner party" (says Prof. Stuart), "with this
strange, wild, terribly clever man, with his red hair and brazen nose,
sometimes flashing with wit and knowledge, sometimes making the whole
company, princes and servants alike, hold their peace and listen humbly to
the ravings of a poor imbecile."

To people he despised he did not show his serious instruments. He had
other attractions, in the shape of a lot of toy machinery, little windmills, and
queer doors, and golden globes, and all manner of ingenious tricks and
automata, many of which he had made himself, and these he used to show
them instead; and no doubt they were well enough pleased with them.
Those of the visitors, however, who really cared to see and understand his
instruments, went away enchanted with his genius and hospitality.

I may, perhaps, be producing an unfair impression of imperiousness and
insolence. Tycho was fiery, no doubt, but I think we should wrong him if
we considered him insolent. Most of the nobles of his day were haughty
persons, accustomed to deal with serfs, and very likely to sneer at and
trample on any meek man of science whom they could easily despise. So
Tycho was not meek; he stood up for the honour of his science, and paid
them back in their own coin, with perhaps a little interest. That this
behaviour was not worldly-wise is true enough, but I know of no
commandment enjoining us to be worldly-wise.

If we knew more about his so-called imbecile protégé we should
probably find some reason for the interest which Tycho took in him.
Whether he was what is now called a "clairvoyant" or not, Tycho evidently
regarded his utterances as oracular, and of course when one is receiving
what may be a revelation from heaven it is natural to suppress ordinary
conversation.

Among the noble visitors whom he received and entertained, it is
interesting to notice James I. of England, who spent eight days at Uraniburg
on the occasion of his marriage with Anne of Denmark in 1590, and seems
to have been deeply impressed by his visit.

Among other gifts, James presented Tycho with a dog (depicted in Fig.
24), and this same animal was subsequently the cause of trouble. For it
seems that one day the Chancellor of Denmark, Walchendorf, brutally
kicked the poor beast; and Tycho, who was very fond of animals, gave him
a piece of his mind in no measured language. Walchendorf went home
determined to ruin him. King Frederick, however, remained his true friend,
doubtless partly influenced thereto by his Queen Sophia, an enlightened
woman who paid many visits to Uraniburg, and knew Tycho well. But
unfortunately Frederick died; and his son, a mere boy, came to the throne.

Now was the time for the people whom Tycho had offended, for those
who were jealous of his great fame and importance, as well as for those
who cast longing eyes on his estate and endowments. The boy-king, too,
unfortunately paid a visit to Tycho, and, venturing upon a decided opinion
on some recondite subject, received a quiet setting down which he ill
relished.

Letters written by Tycho about this time are full of foreboding. He
greatly dreads having to leave Uraniburg, with which his whole life has for
twenty years been bound up. He tries to comfort himself with the thought
that, wherever he is sent, he will have the same heavens and the same stars
over his head.

Gradually his Norwegian estate and his pension were taken away, and in
five years poverty compelled him to abandon his magnificent temple, and to
take a small house in Copenhagen.

Not content with this, Walchendorf got a Royal Commission appointed
to inquire into the value of his astronomical labours. This sapient body
reported that his work was not only useless, but noxious; and soon after he
was attacked by the populace in the public street.

Nothing was left for him now but to leave the country, and he went into
Germany, leaving his wife and instruments to follow him whenever he
could find a home for them.

His wanderings in this dark time—some two years—are not quite clear;
but at last the enlightened Emperor of Bohemia, Rudolph II., invited him to
settle in Prague. Thither he repaired, a castle was given him as an
observatory, a house in the city, and 3000 crowns a year for life. So his
instruments were set up once more, students flocked to hear him and to
receive work at his hands—among them a poor youth, John Kepler, to
whom he was very kind, and who became, as you know, a still greater man
than his master.

But the spirit of Tycho was broken, and though some good work was
done at Prague—more observations made, and the Rudolphine tables begun
—yet the hand of death was upon him. A painful disease seized him,
attended with sleeplessness and temporary delirium, during the paroxysms
of which he frequently exclaimed, Ne frustra vixisse videar. ("Oh that it
may not appear that I have lived in vain!")

Quietly, however, at last, and surrounded by his friends and relatives,
this fierce, passionate soul passed away, on the 24th of October, 1601.

His beloved instruments, which were almost a part of himself, were
stored by Rudolph in a museum with scrupulous care, until the taking of
Prague by the Elector Palatine's troops. In this disturbed time they got

smashed, dispersed, and converted to other purposes. One thing only was
saved—the great brass globe, which some thirty years after was recognized
by a later king of Denmark as having belonged to Tycho, and deposited in
the Library of the Academy of Sciences at Copenhagen, where I believe it is
to this day.

The island of Huen was overrun by the Danish nobility, and nothing now
remains of Uraniburg but a mound of earth and two pits.

As to the real work of Tycho, that has become immortal enough,—
chiefly through the labours of his friend and scholar whose life we shall
consider in the next lecture.

S UM M ARY OF FACT S F OR L E CT URE I I I

Life and work of Kepler. Kepler was born in December, 1571, at Weil in
Würtemberg. Father an officer in the duke's army, mother something of a
virago, both very poor. Kepler was utilized as a tavern pot-boy, but
ultimately sent to a charity school, and thence to the University of
Tübingen. Health extremely delicate; he was liable to violent attacks all his
life. Studied mathematics, and accepted an astronomical lectureship at Graz
as the first post which offered. Endeavoured to discover some connection
between the number of the planets, their times of revolution, and their
distances from the sun. Ultimately hit upon his fanciful regular-solid
hypothesis, and published his first book in 1597. In 1599 was invited by
Tycho to Prague, and there appointed Imperial mathematician, at a
handsome but seldom paid salary. Observed the new star of 1604.
Endeavoured to find the law of refraction of light from Vitellio's
measurements, but failed. Analyzed Tycho's observations to find the true
law of motion of Mars. After incredible labour, through innumerable wrong
guesses, and six years of almost incessant calculation, he at length emerged

in his two "laws"—discoveries which swept away all epicycles, deferents,
equants, and other remnants of the Greek system, and ushered in the dawn
of modern astronomy.

Law I. Planets move in ellipses, with the Sun in one focus.

Law II. The radius vector (or line joining sun and planet) sweeps out
equal areas in equal times.

Published his second book containing these laws in 1609. Death of
Rudolph in 1612, and subsequent increased misery and misfortune of
Kepler. Ultimately discovered the connection between the times and
distances of the planets for which he had been groping all his mature life,
and announced it in 1618:—

Law III. The square of the time of revolution (or year) of each planet is
proportional to the cube of its mean distance from the sun.

The book in which this law was published ("On Celestial Harmonies")
was dedicated to James of England. In 1620 had to intervene to protect his
mother from being tortured for witchcraft. Accepted a professorship at Linz.
Published the Rudolphine tables in 1627, embodying Tycho's observations
and his own theory. Made a last effort to overcome his poverty by getting
the arrears of his salary paid at Prague, but was unsuccessful, and,
contracting brain fever on the journey, died in November, 1630, aged 59.

A man of keen imagination, indomitable perseverance, and
uncompromising love of truth, Kepler overcame ill-health, poverty, and
misfortune, and placed himself in the very highest rank of scientific men.
His laws, so extraordinarily discovered, introduced order and simplicity into
what else would have been a chaos of detailed observations; and they
served as a secure basis for the splendid erection made on them by Newton.
Seven planets of the Ptolemaic system—
Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.
Six planets of the Copernican system—
Mercury, Venus, Earth, Mars, Jupiter, Saturn.

The five regular solids, in appropriate order—
Octahedron, Icosahedron, Dodecahedron, Tetrahedron, Cube.

Table illustrating Kepler's third law.
Mean distance Length Cube of the Square of the
Planet. from Sun. of Year. Distance. Time.
3
D T D T2

Mercury ·3871 ·24084 ·05801 ·05801
Venus ·7233 ·61519 ·37845 ·37846
Earth 1·0000 1·0000 1·0000 1·0000
Mars 1·5237 1·8808 3·5375 3·5375
Jupiter 5·2028 11·862 140·83 140·70
Saturn 9·5388 29·457 867·92 867·70

The length of the earth's year is 365·256 days; its mean distance from the
sun, taken above as unity, is 92,000,000 miles.

LECTURE III

KEPLER AND THE LAWS OF PLANETARY MOTION

It is difficult to imagine a stronger contrast between two men engaged in the
same branch of science than exists between Tycho Brahé, the subject of last
lecture, and Kepler, our subject on the present occasion.

The one, rich, noble, vigorous, passionate, strong in mechanical ingenuity
and experimental skill, but not above the average in theoretical and
mathematical power.

The other, poor, sickly, devoid of experimental gifts, and unfitted by nature
for accurate observation, but strong almost beyond competition in speculative
subtlety and innate mathematical perception.

The one is the complement of the other; and from the fact of their following
each other so closely arose the most surprising benefits to science.

The outward life of Kepler is to a large extent a mere record of poverty and
misfortune. I shall only sketch in its broad features, so that we may have more
time to attend to his work.

He was born (so his biographer assures us) in longitude 29° 7', latitude 48°
54', on the 21st of December, 1571. His parents seem to have been of fair
condition, but by reason, it is said, of his becoming surety for a friend, the
father lost all his slender income, and was reduced to keeping a tavern. Young
John Kepler was thereupon taken from school, and employed as pot-boy
between the ages of nine and twelve. He was a sickly lad, subject to violent
illnesses from the cradle, so that his life was frequently despaired of. Ultimately
he was sent to a monastic school and thence to the University of Tübingen,
where he graduated second on the list. Meanwhile home affairs had gone to
rack and ruin. His father abandoned the home, and later died abroad. The
mother quarrelled with all her relations, including her son John; who was
therefore glad to get away as soon as possible.

All his connection with astronomy up to this time had been the hearing the
Copernican theory expounded in University lectures, and defending it in a
college debating society.

An astronomical lectureship at Graz happening to offer itself, he was urged
to take it, and agreed to do so, though stipulating that it should not debar him
from some more brilliant profession when there was a chance.

For astronomy in those days seems to have ranked as a minor science, like
mineralogy or meteorology now. It had little of the special dignity with which
the labours of Kepler himself were destined so greatly to aid in endowing it.

Well, he speedily became a thorough Copernican, and as he had a most
singularly restless and inquisitive mind, full of appreciation of everything
relating to number and magnitude—was a born speculator and thinker just as
Mozart was a born musician, or Bidder a born calculator—he was agitated by
questions such as these: Why are there exactly six planets? Is there any

connection between their orbital distances, or between their orbits and the times
of describing them? These things tormented him, and he thought about them
day and night. It is characteristic of the spirit of the times—this questioning
why there should be six planets. Nowadays, we should simply record the fact
and look out for a seventh. Then, some occult property of the number six was
groped for, such as that it was equal to 1 + 2 + 3 and likewise equal to 1 × 2 × 3,
and so on. Many fine reasons had been given for the seven planets of the
Ptolemaic system (see, for instance, p. 106), but for the six planets of the
Copernican system the reasons were not so cogent.

Again, with respect to their successive distances from the sun, some law
would seem to regulate their distance, but it was not known. (Parenthetically I
may remark that it is not known even now: a crude empirical statement known
as Bode's law—see page 294—is all that has been discovered.)

Once more, the further the planet the slower it moved; there seemed to be
some law connecting speed and distance. This also Kepler made continual
attempts to discover.

Fig. 26.—Orbits of some of the planets drawn to scale:
showing the gap between Mars and Jupiter.

One of his ideas concerning the law of the successive distances was based on
the inscription of a triangle in a circle. If you inscribe in a circle a large number
of equilateral triangles, they envelop another circle bearing a definite ratio to the
first: these might do for the orbits of two planets (see Fig. 27). Then try

inscribing and circumscribing squares, hexagons, and other figures, and see if
the circles thus defined would correspond to the several planetary orbits. But
they would not give any satisfactory result. Brooding over this disappointment,
the idea of trying solid figures suddenly strikes him. "What have plane figures
to do with the celestial orbits?" he cries out; "inscribe the regular solids." And
then—brilliant idea—he remembers that there are but five. Euclid had shown
that there could be only five regular solids.[4] The number evidently corresponds
to the gaps between the six planets. The reason of there being only six seems to
be attained. This coincidence assures him he is on the right track, and with great
enthusiasm and hope he "represents the earth's orbit by a sphere as the norm and
measure of all"; round it he circumscribes a dodecahedron, and puts another
sphere round that, which is approximately the orbit of Mars; round that, again, a
tetrahedron, the corners of which mark the sphere of the orbit of Jupiter; round
that sphere, again, he places a cube, which roughly gives the orbit of Saturn.

Fig. 27.—Many-sided polygon or approximate circle enveloped
by straight lines, as for instance by a number of equilateral
triangles.

On the other hand, he inscribes in the sphere of the earth's orbit an
icosahedron; and inside the sphere determined by that, an octahedron; which

figures he takes to inclose the spheres of Venus and of Mercury respectively.

The imagined discovery is purely fictitious and accidental. First of all, eight
planets are now known; and secondly, their real distances agree only very
approximately with Kepler's hypothesis.

Fig. 28.—Frameworks with inscribed and circumscribed spheres, representing the
five regular solids distributed as Kepler supposed them to be among the
planetary orbits. (See "Summary" at beginning of this lecture, p. 57.)

Nevertheless, the idea gave him great delight. He says:—"The intense
pleasure I have received from this discovery can never be told in words. I
regretted no more the time wasted; I tired of no labour; I shunned no toil of
reckoning, days and nights spent in calculation, until I could see whether my
hypothesis would agree with the orbits of Copernicus, or whether my joy was to
vanish into air."

He then went on to speculate as to the cause of the planets' motion. The old
idea was that they were carried round by angels or celestial intelligences. Kepler
tried to establish some propelling force emanating from the sun, like the spokes
of a windmill.

This first book of his brought him into notice, and served as an introduction
to Tycho and to Galileo.

Tycho Brahé was at this time at Prague under the patronage of the Emperor
Rudolph; and as he was known to have by far the best planetary observations of
any man living, Kepler wrote to him to know if he might come and examine
them so as to perfect his theory.

Tycho immediately replied, "Come, not as a stranger, but as a very welcome
friend; come and share in my observations with such instruments as I have with
me, and as a dearly beloved associate." After this visit, Tycho wrote again,
offering him the post of mathematical assistant, which after hesitation was
accepted. Part of the hesitation Kepler expresses by saying that "for
observations his sight was dull, and for mechanical operations his hand was
awkward. He suffered much from weak eyes, and dare not expose himself to
night air." In all this he was, of course, the antipodes of Tycho, but in
mathematical skill he was greatly his superior.

On his way to Prague he was seized with one of his periodical illnesses, and
all his means were exhausted by the time he could set forward again, so that he
had to apply for help to Tycho.

It is clear, indeed, that for some time now he subsisted entirely on the bounty
of Tycho, and he expresses himself most deeply grateful for all the kindness he
received from that noble and distinguished man, the head of the scientific world
at that date.

To illustrate Tycho's kindness and generosity, I must read you a letter written
to him by Kepler. It seems that Kepler, on one of his absences from Prague,
driven half mad with poverty and trouble, fell foul of Tycho, whom he thought
to be behaving badly in money matters to him and his family, and wrote him a
violent letter full of reproaches and insults. Tycho's secretary replied quietly
enough, pointing out the groundlessness and ingratitude of the accusation.

Kepler repents instantly, and replies:—
"Most Noble Tycho," (these are the words of his letter), "how shall I enumerate or
rightly estimate your benefits conferred on me? For two months you have liberally and

gratuitously maintained me, and my whole family; you have provided for all my wishes;
you have done me every possible kindness; you have communicated to me everything you
hold most dear; no one, by word or deed, has intentionally injured me in anything; in short,
not to your children, your wife, or yourself have you shown more indulgence than to me.
This being so, as I am anxious to put on record, I cannot reflect without consternation that
I should have been so given up by God to my own intemperance as to shut my eyes on all
these benefits; that, instead of modest and respectful gratitude, I should indulge for three
weeks in continual moroseness towards all your family, in headlong passion and the
utmost insolence towards yourself, who possess so many claims on my veneration, from
your noble family, your extraordinary learning, and distinguished reputation. Whatever I
have said or written against the person, the fame, the honour, and the learning of your
excellency; or whatever, in any other way, I have injuriously spoken or written (if they
admit no other more favourable interpretation), as, to my grief, I have spoken and written
many things, and more than I can remember; all and everything I recant, and freely and
honestly declare and profess to be groundless, false, and incapable of proof."

Tycho accepted the apology thus heartily rendered, and the temporary breach
was permanently healed.

In 1601, Kepler was appointed "Imperial mathematician," to assist Tycho in
his calculations.

The Emperor Rudolph did a good piece of work in thus maintaining these
two eminent men, but it is quite clear that it was as astrologers that he valued
them; and all he cared for in the planetary motions was limited to their supposed
effect on his own and his kingdom's destiny. He seems to have been politically a
weak and superstitious prince, who was letting his kingdom get into hopeless
confusion, and entangling himself in all manner of political complications.
While Bohemia suffered, however, the world has benefited at his hands; and the
tables upon which Tycho was now engaged are well called the Rudolphine
tables.

These tables of planetary motion Tycho had always regarded as the main
work of his life; but he died before they were finished, and on his death-bed he
intrusted the completion of them to Kepler, who loyally undertook their charge.

The Imperial funds were by this time, however, so taxed by wars and other
difficulties that the tables could only be proceeded with very slowly, a staff of
calculators being out of the question. In fact, Kepler could not get even his own
salary paid: he got orders, and promises, and drafts on estates for it; but when

the time came for them to be honoured they were worthless, and he had no
power to enforce his claims.

So everything but brooding had to be abandoned as too expensive, and he
proceeded to study optics. He gave a very accurate explanation of the action of
the human eye, and made many hypotheses, some of them shrewd and close to
the mark, concerning the law of refraction of light in dense media: but though
several minor points of interest turned up, nothing of the first magnitude came
out of this long research.

The true law of refraction was discovered some years after by a Dutch
professor, Willebrod Snell.

We must now devote a little time to the main work of Kepler's life. All the
time he had been at Prague he had been making a severe study of the motion of
the planet Mars, analyzing minutely Tycho's books of observations, in order to
find out, if possible, the true theory of his motion. Aristotle had taught that
circular motion was the only perfect and natural motion, and that the heavenly
bodies therefore necessarily moved in circles.

So firmly had this idea become rooted in men's minds, that no one ever
seems to have contemplated the possibility of its being false or meaningless.

When Hipparchus and others found that, as a matter of fact, the planets did
not revolve in simple circles, they did not try other curves, as we should at once
do now, but they tried combinations of circles, as we saw in Lecture I. The
small circle carried by a bigger one was called an Epicycle. The carrying circle
was called the Deferent. If for any reason the earth had to be placed out of the
centre, the main planetary orbit was called an Excentric, and so on.

But although the planetary paths might be roughly represented by a
combination of circles, their speeds could not, on the hypothesis of uniform
motion in each circle round the earth as a fixed body. Hence was introduced the
idea of an Equant, i.e. an arbitrary point, not the earth, about which the speed
might be uniform. Copernicus, by making the sun the centre, had been able to
simplify a good deal of this, and to abolish the equant.

But now that Kepler had the accurate observations of Tycho to refer to, he
found immense difficulty in obtaining the true positions of the planets for long
together on any such theory.

He specially attacked the motion of the planet Mars, because that was
sufficiently rapid in its changes for a considerable collection of data to have
accumulated with respect to it. He tried all manner of circular orbits for the
earth and for Mars, placing them in all sorts of aspects with respect to the sun.
The problem to be solved was to choose such an orbit and such a law of speed,
for both the earth and Mars, that a line joining them, produced out to the stars,
should always mark correctly the apparent position of Mars as seen from the
earth. He had to arrange the size of the orbits that suited best, then the positions
of their centres, both being supposed excentric with respect to the sun; but he
could not get any such arrangement to work with uniform motion about the sun.
So he reintroduced the equant, and thus had another variable at his disposal—in
fact, two, for he had an equant for the earth and another for Mars, getting a
pattern of the kind suggested in Fig. 29.

The equants might divide the line in any arbitrary ratio. All sorts of
combinations had to be tried, the relative positions of the earth and Mars to be
worked out for each, and compared with Tycho's recorded observations. It was
easy to get them to agree for a short time, but sooner or later a discrepancy
showed itself.

Fig. 29.—S represents the sun; EC, the centre of the earth's orbit, to be placed as best
suited; MC, the same for Mars; EE, the earth's equant, or point about which the earth
uniformly revolved (i.e. the point determining the law of speed about the sun),
likewise to be placed anywhere, but supposed to be in the line joining S to EC; ME,
the same thing for Mars; with ?ME for an alternative hypothesis that perhaps Mars'
equant was on line joining EC with MC.

I need not say that all these attempts and gropings, thus briefly summarized,
entailed enormous labour, and required not only great pertinacity, but a most
singularly constituted mind, that could thus continue groping in the dark
without a possible ray of theory to illuminate its search. Grope he did, however,
with unexampled diligence.

At length he hit upon a point that seemed nearly right. He thought he had
found the truth; but no, before long the position of the planet, as calculated, and
as recorded by Tycho, differed by eight minutes of arc, or about one-eighth of a
degree. Could the observation be wrong by this small amount? No, he had
known Tycho, and knew that he was never wrong eight minutes in an
observation.

So he set out the whole weary way again, and said that with those eight
minutes he would yet find out the law of the universe. He proceeded to see if by
making the planet librate, or the plane of its orbit tilt up and down, anything
could be done. He was rewarded by finding that at any rate the plane of the orbit
did not tilt up and down: it was fixed, and this was a simplification on
Copernicus's theory. It is not an absolute fixture, but the changes are very small
(see Laplace, page 266).

Fig. 30.—Excentric circle supposed to be divided into equal areas. The sun, S,
being placed at a selected point, it was possible to represent the varying speed

of a planet by saying that it moved from A to B, from B to C, and so on, in
equal times.

At last he thought of giving up the idea of uniform circular motion, and of
trying varying circular motion, say inversely as its distance from the sun. To
simplify calculation, he divided the orbit into triangles, and tried if making the
triangles equal would do. A great piece of luck, they did beautifully: the rate of
description of areas (not arcs) is uniform. Over this discovery he greatly
rejoices. He feels as though he had been carrying on a war against the planet
and had triumphed; but his gratulation was premature. Before long fresh little
errors appeared, and grew in importance. Thus he announces it himself:—

"While thus triumphing over Mars, and preparing for him, as for one already
vanquished, tabular prisons and equated excentric fetters, it is buzzed here and
there that the victory is vain, and that the war is raging anew as violently as
before. For the enemy left at home a despised captive has burst all the chains of
the equations, and broken forth from the prisons of the tables."

Still, a part of the truth had been gained, and was not to be abandoned any
more. The law of speed was fixed: that which is now known as his second law.
But what about the shape of the orbit—Was it after all possible that Aristotle,
and every philosopher since Aristotle, had been wrong? that circular motion was
not the perfect and natural motion, but that planets might move in some other
closed curve?

Suppose he tried an oval. Well, there are a great variety of ovals, and several
were tried: with the result that they could be made to answer better than a circle,
but still were not right.

Now, however, the geometrical and mathematical difficulties of calculation,
which before had been tedious and oppressive, threatened to become
overwhelming; and it is with a rising sense of despondency that Kepler sees his
six years' unremitting labour leading deeper and deeper into complication.

One most disheartening circumstance appeared, viz. that when he made the
circuit oval his law of equable description of areas broke down. That seemed to
require the circular orbit, and yet no circular orbit was quite accurate.

While thinking and pondering for weeks and months over this new dilemma
and complication of difficulties, till his brain reeled, an accidental ray of light
broke upon him in a way not now intelligible, or barely intelligible. Half the
extreme breadth intercepted between the circle and oval was 429⁄100,000 of the
radius, and he remembered that the "optical inequality" of Mars was also about
429⁄100,000. This coincidence, in his own words, woke him out of sleep; and for

some reason or other impelled him instantly to try making the planet oscillate in
the diameter of its epicycle instead of revolve round it—a singular idea, but
Copernicus had had a similar one to explain the motions of Mercury.

Fig. 31.—Mode of drawing an ellipse. The two pins F are
the foci.

Away he started through his calculations again. A long course of work night
and day was rewarded by finding that he was now able to hit off the motions
better than before; but what a singularly complicated motion it was. Could it be
expressed no more simply? Yes, the curve so described by the planet is a
comparatively simple one: it is a special kind of oval—the ellipse. Strange that
he had not thought of it before. It was a famous curve, for the Greek geometers
had studied it as one of the sections of a cone, but it was not so well known in
Kepler's time. The fact that the planets move in it has raised it to the first
importance, and it is familiar enough to us now. But did it satisfy the law of
speed? Could the rate of description of areas be uniform with it? Well, he tried
the ellipse, and to his inexpressible delight he found that it did satisfy the
condition of equable description of areas, if the sun was in one focus. So,
moving the planet in a selected ellipse, with the sun in one focus, at a speed
given by the equable area description, its position agreed with Tycho's

observations within the limits of the error of experiment. Mars was finally
conquered, and remains in his prison-house to this day. The orbit was found.

Fig. 32.

In a paroxysm of delight Kepler celebrates his victory by a triumphant
figure, sketched actually on his geometrical diagram—the diagram which
proves that the law of equable description of areas can hold good with an
ellipse. The above is a tracing of it.

Such is a crude and bald sketch of the steps by which Kepler rose to his great
generalizations—the two laws which have immortalized his name.

All the complications of epicycle, equant, deferent, excentric, and the like,
were swept at once away, and an orbit of striking and beautiful properties
substituted. Well might he be called, as he was, "the legislator," or law
interpreter, "of the heavens."

Fig. 33.—If S is the sun, a planet or comet moves from P to P1,
from P2 to P3, and from P4 to P5 in the same time; if the shaded
areas are equal.

He concludes his book on the motions of Mars with a half comic appeal to
the Emperor to provide him with the sinews of war for an attack on Mars's
relations—father Jupiter, brother Mercury, and the rest—but the death of his
unhappy patron in 1612 put an end to all these schemes, and reduced Kepler to
the utmost misery. While at Prague his salary was in continual arrear, and it was
with difficulty that he could provide sustenance for his family. He had been
there eleven years, but they had been hard years of poverty, and he could leave
without regret were it not that he should have to leave Tycho's instruments and
observations behind him. While he was hesitating what best to do, and reduced
to the verge of despair, his wife, who had long been suffering from low spirits
and despondency, and his three children, were taken ill; one of the sons died of
small-pox, and the wife eleven days after of low fever and epilepsy. No money
could be got at Prague, so after a short time he accepted a professorship at Linz,
and withdrew with his two quite young remaining children.

He provided for himself now partly by publishing a prophesying almanack, a
sort of Zadkiel arrangement—a thing which he despised, but the support of
which he could not afford to do without. He is continually attacking and
throwing sarcasm at astrology, but it was the only thing for which people would
pay him, and on it after a fashion he lived. We do not find that his circumstances

were ever prosperous, and though 8,000 crowns were due to him from Bohemia
he could not manage to get them paid.

About this time occurred a singular interruption to his work. His old mother,
of whose fierce temper something has already been indicated, had been engaged
in a law-suit for some years near their old home in Würtemberg. A change of
judge having in process of time occurred, the defendant saw his way to turn the
tables on the old lady by accusing her of sorcery. She was sent to prison, and
condemned to the torture, with the usual intelligent idea of extracting a
"voluntary" confession. Kepler had to hurry from Linz to interpose. He
succeeded in saving her from the torture, but she remained in prison for a year
or so. Her spirit, however, was unbroken, for no sooner was she released than
she commenced a fresh action against her accuser. But fresh trouble was averted
by the death of the poor old dame at the age of nearly eighty.

This narration renders the unflagging energy shown by her son in his
mathematical wrestlings less surprising.

Interspersed with these domestic troubles, and with harassing and
unsuccessful attempts to get his rights, he still brooded over his old problem of
some possible connection between the distances of the planets from the sun and
their times of revolution, i.e. the length of their years.

It might well have been that there was no connection, that it was purely
imaginary, like his old idea of the law of the successive distances of the planets,
and like so many others of the guesses and fancies which he entertained and
spent his energies in probing. But fortunately this time there was a connection,
and he lived to have the joy of discovering it.

The connection is this, that if one compares the distance of the different
planets from the sun with the length of time they take to go round him, the cube
of the respective distances is proportional to the square of the corresponding
times. In other words, the ratio of r3 to T2 for every planet is the same. Or,
again, the length of a planet's year depends on the 3⁄2th power of its distance
from the sun. Or, once more, the speed of each planet in its orbit is as the

inverse square-root of its distance from the sun. The product of the distance into
the square of the speed is the same for each planet.

This (however stated) is called Kepler's third law. It welds the planets
together, and shows them to be one system. His rapture on detecting the law
was unbounded, and he breaks out into an exulting rhapsody:—

"What I prophesied two-and-twenty years ago, as soon as I discovered the
five solids among the heavenly orbits—what I firmly believed long before I had
seen Ptolemy's Harmonies—what I had promised my friends in the title of this
book, which I named before I was sure of my discovery—what sixteen years
ago, I urged as a thing to be sought—that for which I joined Tycho Brahé, for
which I settled in Prague, for which I have devoted the best part of my life to
astronomical contemplations, at length I have brought to light, and recognized
its truth beyond my most sanguine expectations. It is not eighteen months since
I got the first glimpse of light, three months since the dawn, very few days since
the unveiled sun, most admirable to gaze upon, burst upon me. Nothing holds
me; I will indulge my sacred fury; I will triumph over mankind by the honest
confession that I have stolen the golden vases of the Egyptians to build up a
tabernacle for my God far away from the confines of Egypt. If you forgive me, I
rejoice; if you are angry, I can bear it; the die is cast, the book is written, to be
read either now or by posterity, I care not which; it may well wait a century for
a reader, as God has waited six thousand years for an observer."

Soon after this great work his third book appeared: it was an epitome of the
Copernican theory, a clear and fairly popular exposition of it, which had the
honour of being at once suppressed and placed on the list of books prohibited
by the Church, side by side with the work of Copernicus himself, De
Revolutionibus Orbium Cœlestium.

This honour, however, gave Kepler no satisfaction—it rather occasioned him
dismay, especially as it deprived him of all pecuniary benefit, and made it
almost impossible for him to get a publisher to undertake another book.

Still he worked on at the Rudolphine tables of Tycho, and ultimately, with
some small help from Vienna, completed them; but he could not get the means
to print them. He applied to the Court till he was sick of applying: they lay idle

four years. At last he determined to pay for the type himself. What he paid it
with, God knows, but he did pay it, and he did bring out the tables, and so was
faithful to the behest of his friend.

This great publication marks an era in astronomy. They were the first really
accurate tables which navigators ever possessed; they were the precursors of our
present Nautical Almanack.

After this, the Grand Duke of Tuscany sent Kepler a golden chain, which is
interesting inasmuch as it must really have come from Galileo, who was in high
favour at the Italian Court at this time.

Once more Kepler made a determined attempt to get his arrears of salary
paid, and rescue himself and family from their bitter poverty. He travelled to
Prague on purpose, attended the imperial meeting, and pleaded his own cause,
but it was all fruitless; and exhausted by the journey, weakened by over-study,
and disheartened by the failure, he caught a fever, and died in his fifty-ninth
year. His body was buried at Ratisbon, and a century ago a proposal was made
to erect a marble monument to his memory, but nothing was done. It matters
little one way or the other whether Germany, having almost refused him bread
during his life, should, a century and a half after his death, offer him a stone.

Fig. 34.—Portrait of Kepler, older.

The contiguity of the lives of Kepler and Tycho furnishes a moral too
obvious to need pointing out. What Kepler might have achieved had he been
relieved of those ghastly struggles for subsistence one cannot tell, but this much
is clear, that had Tycho been subjected to the same misfortune, instead of being
born rich and being assisted by generous and enlightened patrons, he could have
accomplished very little. His instruments, his observatory—the tools by which
he did his work—would have been impossible for him. Frederick and Sophia of
Denmark, and Rudolph of Bohemia, are therefore to be remembered as co-
workers with him.

Kepler, with his ill-health and inferior physical energy, was unable to
command the like advantages. Much, nevertheless, he did; more one cannot but
feel he might have done had he been properly helped. Besides, the world would
have been free from the reproach of accepting the fruits of his bright genius
while condemning the worker to a life of misery, relieved only by the beauty of

his own thoughts and the ecstasy awakened in him by the harmony and
precision of Nature.

Concerning the method of Kepler, the mode by which he made his
discoveries, we must remember that he gives us an account of all the steps,
unsuccessful as well as successful, by which he travelled. He maps out his route
like a traveller. In fact he compares himself to Columbus or Magellan, voyaging
into unknown lands, and recording his wandering route. This being
remembered, it will be found that his methods do not differ so utterly from
those used by other philosophers in like case. His imagination was perhaps
more luxuriant and was allowed freer play than most men's, but it was
nevertheless always controlled by rigid examination and comparison of
hypotheses with fact.

Brewster says of him:—"Ardent, restless, burning to distinguish himself by
discovery, he attempted everything; and once having obtained a glimpse of a
clue, no labour was too hard in following or verifying it. A few of his attempts
succeeded—a multitude failed. Those which failed seem to us now fanciful,
those which succeeded appear to us sublime. But his methods were the same.
When in search of what really existed he sometimes found it; when in pursuit of
a chimæra he could not but fail; but in either case he displayed the same great
qualities, and that obstinate perseverance which must conquer all difficulties
except those really insurmountable."

To realize what he did for astronomy, it is necessary for us now to consider
some science still in its infancy. Astronomy is so clear and so thoroughly
explored now, that it is difficult to put oneself into a contemporary attitude. But
take some other science still barely developed: meteorology, for instance. The
science of the weather, the succession of winds and rain, sunshine and frost,
clouds and fog, is now very much in the condition of astronomy before Kepler.

We have passed through the stage of ascribing atmospheric disturbances—
thunderstorms, cyclones, earthquakes, and the like—to supernatural agency; we
have had our Copernican era: not perhaps brought about by a single individual,
but still achieved. Something of the laws of cyclone and anticyclone are known,
and rude weather predictions across the Atlantic are roughly possible.

Barometers and thermometers and anemometers, and all their tribe, represent
the astronomical instruments in the island of Huen; and our numerous
meteorological observatories, with their continual record of events, represent
the work of Tycho Brahé.

Observation is heaped on observation; tables are compiled; volumes are
filled with data; the hours of sunshine are recorded, the fall of rain, the moisture
in the air, the kind of clouds, the temperature—millions of facts; but where is
the Kepler to study and brood over them? Where is the man to spend his life in
evolving the beginnings of law and order from the midst of all this chaos?

Perhaps as a man he may not come, but his era will come. Through this stage
the science must pass, ere it is ready for the commanding intellect of a Newton.

But what a work it will be for the man, whoever he be that undertakes it—a
fearful monotonous grind of calculation, hypothesis, hypothesis, calculation, a
desperate and groping endeavour to reconcile theories with facts.

A life of such labour, crowned by three brilliant discoveries, the world owes
(and too late recognizes its obligation) to the harshly treated German genius,
Kepler.

S UM M ARY OF FACT S F OR L E CT URE S I V AND V

In 1564, Michael Angelo died and Galileo was born; in 1642, Galileo died
and Newton was born. Milton lived from 1608 to 1674.

For teaching the plurality of worlds, with other heterodox doctrines, and
refusing to recant, Bruno, after six years' imprisonment in Rome, was burnt at
the stake on the 16th of February, 1600 a.d. A "natural" death in the dungeons
of the Inquisition saved Antonio de Dominis, the explainer of the rainbow, from
the same fate, but his body and books were publicly burned at Rome in 1624.

The persecution of Galileo began in 1615, became intense in 1632, and so
lasted till his death and after.

Galileo Galilei, eldest son of Vincenzo de Bonajuti de Galilei, a noble
Florentine, was born at Pisa, 18th of February, 1564. At the age of 17 was sent
to the University of Pisa to study medicine. Observed the swing of a pendulum
and applied it to count pulse-beats. Read Euclid and Archimedes, and could be
kept at medicine no more. At 26 was appointed Lecturer in Mathematics at Pisa.
Read Bruno and became smitten with the Copernican theory. Controverted the
Aristotelians concerning falling bodies, at Pisa. Hence became unpopular and
accepted a chair at Padua, 1592. Invented a thermometer. Wrote on astronomy,
adopting the Ptolemaic system provisionally, and so opened up a
correspondence with Kepler, with whom he formed a friendship. Lectured on
the new star of 1604, and publicly renounced the old systems of astronomy.
Invented a calculating compass or "Gunter's scale." In 1609 invented a
telescope, after hearing of a Dutch optician's discovery. Invented the
microscope soon after. Rapidly completed a better telescope and began a survey
of the heavens. On the 8th of January, 1610, discovered Jupiter's satellites.
Observed the mountains in the moon, and roughly measured their height.
Explained the visibility of the new moon by earth-shine. Was invited to the
Grand Ducal Court of Tuscany by Cosmo de Medici, and appointed philosopher
to that personage. Discovered innumerable new stars, and the nebulæ. Observed
a triple appearance of Saturn. Discovered the phases of Venus predicted by
Copernicus, and spots on the sun. Wrote on floating bodies. Tried to get his
satellites utilized for determining longitude at sea.

Went to Rome to defend the Copernican system, then under official
discussion, and as a result was formally forbidden ever to teach it. On the
accession of Pope Urban VIII. in 1623, Galileo again visited Rome to pay his
respects, and was well received. In 1632 appeared his "Dialogues" on the
Ptolemaic and Copernican systems. Summoned to Rome, practically
imprisoned, and "rigorously questioned." Was made to recant 22nd of June,
1633. Forbidden evermore to publish anything, or to teach, or receive friends.
Retired to Arcetri in broken down health. Death of his favourite daughter, Sister
Maria Celeste. Wrote and meditated on the laws of motion. Discovered the
moon's libration. In 1637 he became blind. The rigour was then slightly relaxed

and many visited him: among them John Milton. Died 8th of January, 1642,
aged 78. As a prisoner of the Inquisition his right to make a will or to be buried
in consecrated ground was disputed. Many of his manuscripts were destroyed.

Galileo, besides being a singularly clear-headed thinker and experimental
genius, was also something of a musician, a poet, and an artist. He was full of
humour as well as of solid common-sense, and his literary style is brilliant. Of
his scientific achievements those now reckoned most weighty, are the discovery
of the Laws of Motion, and the laying of the foundations of Mechanics.

Particulars of Jupiter's Satellites,
Illustrating their obedience to Kepler's third law.
Distance
T2
Time of from
d3
Diameter revolution Jupiter, in
Satellite. T2 d3 which is
in miles. in hours. Jovian
practically
(T) radii.
constant.
(d)

No. 1. 2437 42·47 6·049 1803·7 221·44 8·149
No. 2. 2188 85·23 9·623 7264·1 891·11 8·152
No. 3. 3575 177·72 15·350 29488· 3916·8 8·153
No. 4. 3059 400·53 26·998 160426· 19679· 8·152
The diameter of Jupiter is 85,823 miles.

Falling Bodies.

Since all bodies fall at the same rate, except for the disturbing effect of the
resistance of the air, a statement of their rates of fall is of interest. In one second
a freely falling body near the earth is found to drop 16 feet. In two seconds it
drops 64 feet altogether, viz. 16 feet in the first, and 48 feet in the next second;
because at the beginning of every second after the first it has the accumulated
velocity of preceding seconds. The height fallen by a dropped body is not
proportional to the time simply, but to what is rather absurdly called the square
of the time, i.e. the time multiplied by itself.

For instance, in 3 seconds it drops 9 × 16 = 144 feet; in 4 seconds 16 × 16, or
256 feet, and so on. The distances travelled in 1, 2, 3, 4, &c., seconds by a body
dropped from rest and not appreciably resisted by the air, are 1, 4, 9, 16, 25,
&c., respectively, each multiplied by the constant 16 feet.

Another way of stating the law is to say that the heights travelled in
successive seconds proceed in the proportion 1, 3, 5, 7, 9, &c.; again multiplied
by 16 feet in each case.

Fig. 35.—Curve described by a projectile, showing how it drops
from the line of fire, O D, in successive seconds, the same
distances AP, BQ, CR, &c., as are stated above for a dropped
body.

All this was experimentally established by Galileo.

A body takes half a second to drop 4 feet; and a quarter of a second to drop 1
foot. The easiest way of estimating a quarter of a second with some accuracy is
to drop a bullet one foot.

A bullet thrown or shot in any direction falls just as much as if merely
dropped; but instead of falling from the starting-point it drops vertically from
the line of fire. (See fig. 35).

The rate of fall depends on the intensity of gravity; if it could be doubled, a
body would fall twice as far in the same time; but to make it fall a given
distance in half the time the intensity of gravity would have to be quadrupled.
At a place where the intensity of gravity is 1⁄3600 of what it is here, a body
would fall as far in a minute as it now falls in a second. Such a place occurs at
about the distance of the moon (cf. page 177).

The fact that the height fallen through is proportional to the square of the
time proves that the attraction of the earth or the intensity of gravity is sensibly
constant throughout ordinary small ranges. Over great distances of fall, gravity
cannot be considered constant; so for things falling through great spaces the
Galilean law of the square of the time does not hold.

The fact that things near the earth fall 16 feet in the first second proves that
the intensity of ordinary terrestrial gravity is 32 British units of force per pound
of matter.

The fact that all bodies fall at the same rate (when the resistance of the air is
eliminated), proves that weight is proportional to mass; or more explicitly, that
the gravitative attraction of the earth on matter near its surface depends on the
amount of that matter, as estimated by its inertia, and on nothing else.

LECTURE IV

GALILEO AND THE INVENTION OF THE TELESCOPE

Contemporary with the life of Kepler, but overlapping it at both ends, comes
the great and eventful life of Galileo Galilei,[5] a man whose influence on the
development of human thought has been greater than that of any man whom we
have yet considered, and upon whom, therefore, it is necessary for us, in order
to carry out the plan of these lectures, to bestow much time. A man of great and
wide culture, a so-called universal genius, it is as an experimental philosopher
that he takes the first rank. In this capacity he must be placed alongside of
Archimedes, and it is pretty certain that between the two there was no man of
magnitude equal to either in experimental philosophy. It is perhaps too bold a
speculation, but I venture to doubt whether in succeeding generations we find
his equal in the domain of purely experimental science until we come to
Faraday. Faraday was no doubt his superior, but I know of no other of whom the
like can unhesitatingly be said. In mathematical and deductive science, of

course, it is quite otherwise. Kepler, for instance, and many men before and
since, have far excelled Galileo in mathematical skill and power, though at the
same time his achievements in this department are by no means to be despised.

Born at Pisa three centuries ago, on the very day that Michael Angelo lay
dying in Rome, he inherited from his father a noble name, cultivated tastes, a
keen love of truth, and an impoverished patrimony. Vincenzo de Galilei, a
descendant of the important Bonajuti family, was himself a mathematician and a
musician, and in a book of his still extant he declares himself in favour of free
and open inquiry into scientific matters, unrestrained by the weight of authority
and tradition.

In all probability the son imbibed these precepts: certainly he acted on them.

Vincenzo, having himself experienced the unremunerative character of
scientific work, had a horror of his son's taking to it, especially as in his
boyhood he was always constructing ingenious mechanical toys, and exhibiting
other marks of precocity. So the son was destined for business—to be, in fact, a
cloth-dealer. But he was to receive a good education first, and was sent to an
excellent convent school.

Here he made rapid progress, and soon excelled in all branches of classics
and literature. He delighted in poetry, and in later years wrote several essays on
Dante, Tasso, and Ariosto, besides composing some tolerable poems himself.
He played skilfully on several musical instruments, especially on the lute, of
which indeed he became a master, and on which he solaced himself when quite
an old man. Besides this he seems to have had some skill as an artist, which was
useful afterwards in illustrating his discoveries, and to have had a fine
sensibility as an art critic, for we find several eminent painters of that day
acknowledging the value of the opinion of the young Galileo.

Perceiving all this display of ability, the father wisely came to the conclusion
that the selling of woollen stuffs would hardly satisfy his aspirations for long,
and that it was worth a sacrifice to send him to the University. So to the
University of his native town he went, with the avowed object of studying
medicine, that career seeming the most likely to be profitable. Old Vincenzo's
horror of mathematics or science as a means of obtaining a livelihood is

justified by the fact that while the University Professor of Medicine received
2,000 scudi a year, the Professor of Mathematics had only 60, that is £13 a year,
or 7½d. a day.

So the son had been kept properly ignorant of such poverty-stricken subjects,
and to study medicine he went.

But his natural bent showed itself even here. For praying one day in the
Cathedral, like a good Catholic as he was all his life, his attention was arrested
by the great lamp which, after lighting it, the verger had left swinging to and
fro. Galileo proceeded to time its swings by the only watch he possessed—viz.,
his own pulse. He noticed that the time of swing remained as near as he could
tell the same, notwithstanding the fact that the swings were getting smaller and
smaller.

By subsequent experiment he verified the law, and the isochronism of the
pendulum was discovered. An immensely important practical discovery this, for
upon it all modern clocks are based; and Huyghens soon applied it to the
astronomical clock, which up to that time had been a crude and quite
untrustworthy instrument.

The best clock which Tycho Brahé could get for his observatory was inferior
to one that may now be purchased for a few shillings; and this change is owing
to the discovery of the pendulum by Galileo. Not that he applied it to clocks; he
was not thinking of astronomy, he was thinking of medicine, and wanted to
count people's pulses. The pendulum served; and "pulsilogies," as they were
called, were thus introduced to and used by medical practitioners.

The Tuscan Court came to Pisa for the summer months, for it was then a
seaside place, and among the suite was Ostillio Ricci, a distinguished
mathematician and old friend of the Galileo family. The youth visited him, and
one day, it is said, heard a lesson in Euclid being given by Ricci to the pages
while he stood outside the door entranced. Anyhow he implored Ricci to help
him into some knowledge of mathematics, and the old man willingly consented.
So he mastered Euclid and passed on to Archimedes, for whom he acquired a
great veneration.

His father soon heard of this obnoxious proclivity, and did what he could to
divert him back to medicine again. But it was no use. Underneath his Galen and
Hippocrates were secreted copies of Euclid and Archimedes, to be studied at
every available opportunity. Old Vincenzo perceived the bent of genius to be
too strong for him, and at last gave way.

Fig. 36.—Two forms of pulsilogy. The string is wound up till the
swinging weight keeps time with the pulse, and the position
of a bead or of an index connected with the string is then
read on a scale or dial.

With prodigious rapidity the released philosopher now assimilated the
elements of mathematics and physics, and at twenty-six we find him appointed
for three years to the University Chair of Mathematics, and enjoying the
paternally dreaded stipend of 7½d. a day.

Now it was that he pondered over the laws of falling bodies. He verified, by
experiment, the fact that the velocity acquired by falling down any slope of
given height was independent of the angle of slope. Also, that the height fallen
through was proportional to the square of the time.

Another thing he found experimentally was that all bodies, heavy and light,
fell at the same rate, striking the ground at the same time.[6]

Now this was clean contrary to what he had been taught. The physics of
those days were a simple reproduction of statements in old books. Aristotle had
asserted certain things to be true, and these were universally believed. No one
thought of trying the thing to see if it really were so. The idea of making an
experiment would have savoured of impiety, because it seemed to tend towards
scepticism, and cast a doubt on a reverend authority.

Young Galileo, with all the energy and imprudence of youth (what a blessing
that youth has a little imprudence and disregard of consequences in pursuing a
high ideal!), as soon as he perceived that his instructors were wrong on the
subject of falling bodies, instantly informed them of the fact. Whether he
expected them to be pleased or not is a question. Anyhow, they were not
pleased, but were much annoyed by his impertinent arrogance.

It is, perhaps, difficult for us now to appreciate precisely their position.
These doctrines of antiquity, which had come down hoary with age, and the
discovery of which had reawakened learning and quickened intellectual life,
were accepted less as a science or a philosophy, than as a religion. Had they
regarded Aristotle as a verbally inspired writer, they could not have received his
statements with more unhesitating conviction. In any dispute as to a question of
fact, such as the one before us concerning the laws of falling bodies, their
method was not to make an experiment, but to turn over the pages of Aristotle;
and he who could quote chapter and verse of this great writer was held to settle
the question and raise it above the reach of controversy.

It is very necessary for us to realize this state of things clearly, because
otherwise the attitude of the learned of those days towards every new discovery
seems stupid and almost insane. They had a crystallized system of truth, perfect,
symmetrical—it wanted no novelty, no additions; every addition or growth was
an imperfection, an excrescence, a deformity. Progress was unnecessary and
undesired. The Church had a rigid system of dogma, which must be accepted in
its entirety on pain of being treated as a heretic. Philosophers had a cast-iron
system of truth to match—a system founded upon Aristotle—and so interwoven

with the great theological dogmas that to question one was almost equivalent to
casting doubt upon the other.

In such an atmosphere true science was impossible. The life-blood of science
is growth, expansion, freedom, development. Before it could appear it must
throw off these old shackles of centuries. It must burst its old skin, and emerge,
worn with the struggle, weakly and unprotected, but free and able to grow and
to expand. The conflict was inevitable, and it was severe. Is it over yet? I fear
not quite, though so nearly as to disturb science hardly at all. Then it was
different; it was terrible. Honour to the men who bore the first shock of the
battle!

Now Aristotle had said that bodies fell at rates depending on their weight.

A 5 lb. weight would fall five times as quick as a 1 lb. weight; a 50 lb.
weight fifty times as quick, and so on.

Why he said so nobody knows. He cannot have tried. He was not above
trying experiments, like his smaller disciples; but probably it never occurred to
him to doubt the fact. It seems so natural that a heavy body should fall quicker
than a light one; and perhaps he thought of a stone and a feather, and was
satisfied.

Galileo, however, asserted that the weight did not matter a bit, that
everything fell at the same rate (even a stone and a feather, but for the resistance
of the air), and would reach the ground in the same time.

And he was not content to be pooh-poohed and snubbed. He knew he was
right, and he was determined to make every one see the facts as he saw them.
So one morning, before the assembled University, he ascended the famous
leaning tower, taking with him a 100 lb. shot and a 1 lb. shot. He balanced them
on the edge of the tower, and let them drop together. Together they fell, and
together they struck the ground.

The simultaneous clang of those two weights sounded the death-knell of the
old system of philosophy, and heralded the birth of the new.

But was the change sudden? Were his opponents convinced? Not a jot.
Though they had seen with their eyes, and heard with their ears, the full light of
heaven shining upon them, they went back muttering and discontented to their
musty old volumes and their garrets, there to invent occult reasons for denying
the validity of the observation, and for referring it to some unknown disturbing
cause.

They saw that if they gave way on this one point they would be letting go
their anchorage, and henceforward would be liable to drift along with the tide,
not knowing whither. They dared not do this. No; they must cling to the old
traditions; they could not cast away their rotting ropes and sail out on to the free
ocean of God's truth in a spirit of fearless faith.

Fig. 37.—Tower of Pisa.

Yet they had received a shock: as by a breath of fresh salt breeze and a dash
of spray in their faces, they had been awakened out of their comfortable
lethargy. They felt the approach of a new era.

Yes, it was a shock; and they hated the young Galileo for giving it them—
hated him with the sullen hatred of men who fight for a lost and dying cause.

We need scarcely blame these men; at least we need not blame them
overmuch. To say that they acted as they did is to say that they were human,
were narrow-minded, and were the apostles of a lost cause. But they could not

know this; they had no experience of the past to guide them; the conditions
under which they found themselves were novel, and had to be met for the first
time. Conduct which was excusable then would be unpardonable now, in the
light of all this experience to guide us. Are there any now who practically repeat
their error, and resist new truth? who cling to any old anchorage of dogma, and
refuse to rise with the tide of advancing knowledge? There may be some even
now.

Well, the unpopularity of Galileo smouldered for a time, until, by another
noble imprudence, he managed to offend a semi-royal personage, Giovanni de
Medici, by giving his real opinion, when consulted, about a machine which de
Medici had invented for cleaning out the harbour of Leghorn. He said it was as
useless as it in fact turned out to be. Through the influence of the mortified
inventor he lost favour at Court; and his enemies took advantage of the fact to
render his chair untenable. He resigned before his three years were up, and
retired to Florence.

His father at this time died, and the family were left in narrow
circumstances. He had a brother and three sisters to provide for.

He was offered a professorship at Padua for six years by the Senate of
Venice, and willingly accepted it.

Now began a very successful career. His introductory address was marked by
brilliant eloquence, and his lectures soon acquired fame. He wrote for his pupils
on the laws of motion, on fortifications, on sundials, on mechanics, and on the
celestial globe: some of these papers are now lost, others have been printed
during the present century.

Kepler sent him a copy of his new book, Mysterium Cosmographicum, and
Galileo in thanking him for it writes him the following letter:—[7]
"I count myself happy, in the search after truth, to have so great an ally as yourself, and
one who is so great a friend of the truth itself. It is really pitiful that there are so few who
seek truth, and who do not pursue a perverse method of philosophising. But this is not the
place to mourn over the miseries of our times, but to congratulate you on your splendid
discoveries in confirmation of truth. I shall read your book to the end, sure of finding
much that is excellent in it. I shall do so with the more pleasure, because I have been for
many years an adherent of the Copernican system, and it explains to me the causes of

many of the appearances of nature which are quite unintelligible on the commonly
accepted hypothesis. I have collected many arguments for the purpose of refuting the
latter; but I do not venture to bring them to the light of publicity, for fear of sharing the
fate of our master, Copernicus, who, although he has earned immortal fame with some, yet
with very many (so great is the number of fools) has become an object of ridicule and
scorn. I should certainly venture to publish my speculations if there were more people like
you. But this not being the case, I refrain from such an undertaking."

Kepler urged him to publish his arguments in favour of the Copernican
theory, but he hesitated for the present, knowing that his declaration would be
received with ridicule and opposition, and thinking it wiser to get rather more
firmly seated in his chair before encountering the storm of controversy.

The six years passed away, and the Venetian Senate, anxious not to lose so
bright an ornament, renewed his appointment for another six years at a largely
increased salary.

Soon after this appeared a new star, the stella nova of 1604, not the one
Tycho had seen—that was in 1572—but the same that Kepler was so much
interested in.

Galileo gave a course of three lectures upon it to a great audience. At the first
the theatre was over-crowded, so he had to adjourn to a hall holding 1000
persons. At the next he had to lecture in the open air.

He took occasion to rebuke his hearers for thronging to hear about an
ephemeral novelty, while for the much more wonderful and important truths
about the permanent stars and facts of nature they had but deaf ears.

But the main point he brought out concerning the new star was that it upset
the received Aristotelian doctrine of the immutability of the heavens. According
to that doctrine the heavens were unchangeable, perfect, subject neither to
growth nor to decay. Here was a body, not a meteor but a real distant star, which
had not been visible and which would shortly fade away again, but which
meanwhile was brighter than Jupiter.

The staff of petrified professorial wisdom were annoyed at the appearance of
the star, still more at Galileo's calling public attention to it; and controversy
began at Padua. However, he accepted it; and now boldly threw down the

gauntlet in favour of the Copernican theory, utterly repudiating the old
Ptolemaic system which up to that time he had taught in the schools according
to established custom.

The earth no longer the only world to which all else in the firmament were
obsequious attendants, but a mere insignificant speck among the host of heaven!
Man no longer the centre and cynosure of creation, but, as it were, an insect
crawling on the surface of this little speck! All this not set down in crabbed
Latin in dry folios for a few learned monks, as in Copernicus's time, but
promulgated and argued in rich Italian, illustrated by analogy, by experiment,
and with cultured wit; taught not to a few scholars here and there in musty
libraries, but proclaimed in the vernacular to the whole populace with all the
energy and enthusiasm of a recent convert and a master of language! Had a
bombshell been exploded among the fossilized professors it had been less
disturbing.

But there was worse in store for them.

A Dutch optician, Hans Lippershey by name, of Middleburg, had in his shop
a curious toy, rigged up, it is said, by an apprentice, and made out of a couple of
spectacle lenses, whereby, if one looked through it, the weather-cock of a
neighbouring church spire was seen nearer and upside down.

The tale goes that the Marquis Spinola, happening to call at the shop, was
struck with the toy and bought it. He showed it to Prince Maurice of Nassau,
who thought of using it for military reconnoitring. All this is trivial. What is
important is that some faint and inaccurate echo of this news found its way to
Padua, and into the ears of Galileo.

The seed fell on good soil. All that night he sat up and pondered. He knew
about lenses and magnifying glasses. He had read Kepler's theory of the eye,
and had himself lectured on optics. Could he not hit on the device and make an
instrument capable of bringing the heavenly bodies nearer? Who knew what
marvels he might not so perceive! By morning he had some schemes ready to
try, and one of them was successful. Singularly enough it was not the same plan
as the Dutch optician's, it was another mode of achieving the same end.

He took an old small organ pipe, jammed a suitably chosen spectacle glass
into either end, one convex the other concave, and behold, he had the half of a
wretchedly bad opera glass capable of magnifying three times. It was better than
the Dutchman's, however; it did not invert.
It is easy to understand the general principle of a telescope. A general knowledge of the
common magnifying glass may be assumed. Roger Bacon knew about lenses; and the
ancients often refer to them, though usually as burning glasses. The magnifying power of
globes of water must have been noticed soon after the discovery of glass and the art of
working it.

A magnifying glass is most simply thought of as an additional lens to the eye. The eye
has a lens by which ordinary vision is accomplished, an extra glass lens strengthens it and
enables objects to be seen nearer and therefore apparently bigger. But to apply a
magnifying glass to distant objects is impossible. In order to magnify distant objects,
another function of lenses has also to be employed, viz., their power of forming real
images, the power on which their use as burning-glasses depends: for the best focus is an
image of the sun. Although the object itself is inaccessible, the image of it is by no means
so, and to the image a magnifier can be applied. This is exactly what is done in the
telescope; the object glass or large lens forms an image, which is then looked at through a
magnifying glass or eye-piece.

Of course the image is nothing like so big as the object. For astronomical objects it is
almost infinitely less; still it is an exact representation at an accessible place, and no one
expects a telescope to show distant bodies as big as they really are. All it does is to show
them bigger than they could be seen without it.
But if the objects are not distant, the same principle may still be applied, and two lenses
may be used, one to form an image, the other to magnify it; only if the object can be put
where we please, we can easily place it so that its image is already much bigger than the
object even before magnification by the eye lens. This is the compound microscope, the
invention of which soon followed the telescope. In fact the two instruments shade off into
one another, so that the reading telescope or reading microscope of a laboratory (for
reading thermometers, and small divisions generally) goes by either name at random.

The arrangement so far described depicts things on the retina the unaccustomed way
up. By using a concave glass instead of a convex, and placing it so as to prevent any image
being formed, except on the retina direct, this inconvenience is avoided.

Fig. 38.—View of the half-moon in small telescope. The darker regions, or plains,
used to be called "seas."

Such a thing as Galileo made may now be bought at a toy-shop for I suppose
half a crown, and yet what a potentiality lay in that "glazed optic tube," as
Milton called it. Away he went with it to Venice and showed it to the Signoria,
to their great astonishment. "Many noblemen and senators," says Galileo,
"though of advanced age, mounted to the top of one of the highest towers to
watch the ships, which were visible through my glass two hours before they
were seen entering the harbour, for it makes a thing fifty miles off as near and
clear as if it were only five." Among the people too the instrument excited the
greatest astonishment and interest, so that he was nearly mobbed. The Senate
hinted to him that a present of the instrument would not be unacceptable, so
Galileo took the hint and made another for them.

Fig. 39.—Portion of the lunar surface more highly magnified, showing the shadows of a
mountain range, deep pits, and other details.

They immediately doubled his salary at Padua, making it 1000 florins, and
confirmed him in the enjoyment of it for life.

He now eagerly began the construction of a larger and better instrument.
Grinding the lenses with his own hands with consummate skill, he succeeded in
making a telescope magnifying thirty times. Thus equipped he was ready to
begin a survey of the heavens.

Fig. 40.—Another portion of the lunar surface, showing a so-called crater or vast
lava pool and other evidences of ancient heat unmodified by water.

The first object he carefully examined was naturally the moon. He found
there everything at first sight very like the earth, mountains and valleys, craters
and plains, rocks, and apparently seas. You may imagine the hostility excited
among the Aristotelian philosophers, especially no doubt those he had left
behind at Pisa, on the ground of his spoiling the pure, smooth, crystalline,
celestial face of the moon as they had thought it, and making it harsh and
rugged and like so vile and ignoble a body as the earth.

Fig. 41.—Lunar landscape showing earth. The earth would be a
stationary object in the moon's sky: its only apparent motion
being a slow oscillation as of a pendulum (the result of the
moon's libration).

He went further, however, into heterodoxy than this—he not only made the
moon like the earth, but he made the earth shine like the moon. The visibility of
"the old moon in the new moon's arms" he explained by earth-shine. Leonardo
had given the same explanation a century before. Now one of the many stock
arguments against Copernican theory of the earth being a planet like the rest
was that the earth was dull and dark and did not shine. Galileo argued that it

shone just as much as the moon does, and in fact rather more—especially if it
be covered with clouds. One reason of the peculiar brilliancy of Venus is that
she is a very cloudy planet.[8] Seen from the moon the earth would look exactly
as the moon does to us, only a little brighter and sixteen times as big (four times
the diameter).

Fig. 42.—Galileo's method of estimating the height of lunar mountain.
AB'BC is the illuminated half of the moon. SA is a solar ray just catching the peak of the mountain M.
Then by geometry, as MN is to MA, so is MA to MB'; whence the height of the mountain, MN, can be
determined. The earth and spectator are supposed to be somewhere in the direction BA produced, i.e.
towards the top of the page.
Galileo made a very good estimate of the height of lunar mountains, of which many are
five miles high and some as much as seven. He did this simply by measuring from the
half-moon's straight edge the distance at which their peaks caught the rising or setting sun.
The above simple diagram shows that as this distance is to the diameter of the moon, so is
the height of the sun-tipped mountain to the aforesaid distance.

Wherever Galileo turned his telescope new stars appeared. The Milky Way,
which had so puzzled the ancients, was found to be composed of stars. Stars
that appeared single to the eye were some of them found to be double; and at
intervals were found hazy nebulous wisps, some of which seemed to be star
clusters, while others seemed only a fleecy cloud.

Fig. 43.—Some clusters and nebulæ.

Fig. 44.—Jupiter's satellites, showing the stages of their discovery.

Now we come to his most brilliant, at least his most sensational, discovery.
Examining Jupiter minutely on January 7, 1610, he noticed three little stars near
it, which he noted down as fixing its then position. On the following night
Jupiter had moved to the other side of the three stars. This was natural enough,
but was it moving the right way? On examination it appeared not. Was it
possible the tables were wrong? The next evening was cloudy, and he had to
curb his feverish impatience. On the 10th there were only two, and those on the
other side. On the 11th two again, but one bigger than the other. On the 12th the
three re-appeared, and on the 13th there were four. No more appeared.

Jupiter then had moons like the earth, four of them in fact, and they revolved
round him in periods which were soon determined.
The reason why they were not all visible at first, and why their visibility so rapidly
changes, is because they revolve round him almost in the plane of our vision, so that
sometimes they are in front and sometimes behind him, while again at other times they
plunge into his shadow and are thus eclipsed from the light of the sun which enables us to
see them. A large modern telescope will show the moons when in front of Jupiter, but
small telescopes will only show them when clear of the disk and shadow. Often all four
can be thus seen, but three or two is a very common amount of visibility. Quite a small

telescope, such as a ship's telescope, if held steadily, suffices to show the satellites of
Jupiter, and very interesting objects they are. They are of habitable size, and may be
important worlds for all we know to the contrary.

The news of the discovery soon spread and excited the greatest interest and
astonishment. Many of course refused to believe it. Some there were who
having been shown them refused to believe their eyes, and asserted that
although the telescope acted well enough for terrestrial objects, it was altogether
false and illusory when applied to the heavens. Others took the safer ground of
refusing to look through the glass. One of these who would not look at the
satellites happened to die soon afterwards. "I hope," says Galileo, "that he saw
them on his way to heaven."

The way in which Kepler received the news is characteristic, though by
adding four to the supposed number of planets it might have seemed to upset his
notions about the five regular solids.
He says,[9] "I was sitting idle at home thinking of you, most excellent Galileo, and
your letters, when the news was brought me of the discovery of four planets by the help of
the double eye-glass. Wachenfels stopped his carriage at my door to tell me, when such a
fit of wonder seized me at a report which seemed so very absurd, and I was thrown into
such agitation at seeing an old dispute between us decided in this way, that between his
joy, my colouring, and the laughter of us both, confounded as we were by such a novelty,
we were hardly capable, he of speaking, or I of listening....
"On our separating, I immediately fell to thinking how there could be any addition to
the number of planets without overturning my Mysterium Cosmographicon, published
thirteen years ago, according to which Euclid's five regular solids do not allow more than
six planets round the sun.

"But I am so far from disbelieving the existence of the four circumjovial planets that I
long for a telescope to anticipate you if possible in discovering two round Mars (as the
proportion seems to me to require) six or eight round Saturn, and one each round Mercury
and Venus."

Fig. 45.—Eclipses of Jupiter's satellites. The diagram shows the first (i.e. the
nearest) moon in Jupiter's shadow, the second as passing between earth and
Jupiter, and appearing to transit his disk, the third as on the verge of entering
his shadow, and the fourth quite plainly and separately visible.

As an illustration of the opposite school, I will take the following extract
from Francesco Sizzi, a Florentine astronomer, who argues against the
discovery thus:—
"There are seven windows in the head, two nostrils, two eyes, two ears, and a mouth; so
in the heavens there are two favourable stars, two unpropitious, two luminaries, and
Mercury alone undecided and indifferent. From which and many other similar phenomena
of nature, such as the seven metals, &c., which it were tedious to enumerate, we gather
that the number of planets is necessarily seven.

"Moreover, the satellites are invisible to the naked eye, and therefore can have no
influence on the earth, and therefore would be useless, and therefore do not exist.

"Besides, the Jews and other ancient nations as well as modern Europeans have adopted
the division of the week into seven days, and have named them from the seven planets:
now if we increase the number of the planets this whole system falls to the ground."

To these arguments Galileo replied that whatever their force might be as a
reason for believing beforehand that no more than seven planets would be

discovered, they hardly seemed of sufficient weight to destroy the new ones
when actually seen.

Writing to Kepler at this time, Galileo ejaculates:
"Oh, my dear Kepler, how I wish that we could have one hearty laugh together! Here, at
Padua, is the principal professor of philosophy whom I have repeatedly and urgently
requested to look at the moon and planets through my glass, which he pertinaciously
refuses to do. Why are you not here? What shouts of laughter we should have at this
glorious folly! And to hear the professor of philosophy at Pisa labouring before the grand
duke with logical arguments, as if with magical incantations, to charm the new planets out
of the sky."

A young German protégé of Kepler, Martin Horkey, was travelling in Italy,
and meeting Galileo at Bologna was favoured with a view through his
telescope. But supposing that Kepler must necessarily be jealous of such great
discoveries, and thinking to please him, he writes, "I cannot tell what to think
about these observations. They are stupendous, they are wonderful, but whether
they are true or false I cannot tell." He concludes, "I will never concede his four
new planets to that Italian from Padua though I die for it." So he published a
pamphlet asserting that reflected rays and optical illusions were the sole cause
of the appearance, and that the only use of the imaginary planets was to gratify
Galileo's thirst for gold and notoriety.

When after this performance he paid a visit to his old instructor Kepler, he
got a reception which astonished him. However, he pleaded so hard to be
forgiven that Kepler restored him to partial favour, on this condition, that he
was to look again at the satellites, and this time to see them and own that they
were there.

By degrees the enemies of Galileo were compelled to confess to the truth of
the discovery, and the next step was to outdo him. Scheiner counted five,
Rheiter nine, and others went as high as twelve. Some of these were imaginary,
some were fixed stars, and four satellites only are known to this day.[10]

Here, close to the summit of his greatness, we must leave him for a time. A
few steps more and he will be on the brow of the hill; a short piece of table-
land, and then the descent begins.

LECTURE V

GALILEO AND THE INQUISITION

One sinister event occurred while Galileo was at Padua, some time before
the era we have now arrived at, before the invention of the telescope—two
years indeed after he had first gone to Padua; an event not directly concerning
Galileo, but which I must mention because it must have shadowed his life both
at the time and long afterwards. It was the execution of Giordano Bruno for
heresy. This eminent philosopher had travelled largely, had lived some time in
England, had acquired new and heterodox views on a variety of subjects, and
did not hesitate to propound them even after he had returned to Italy.

The Copernican doctrine of the motion of the earth was one of his obnoxious
heresies. Being persecuted to some extent by the Church, Bruno took refuge in
Venice—a free republic almost independent of the Papacy—where he felt
himself safe. Galileo was at Padua hard by: the University of Padua was under
the government of the Senate of Venice: the two men must in all probability
have met.

Well, the Inquisition at Rome sent messengers to Venice with a demand for
the extradition of Bruno—they wanted him at Rome to try him for heresy.

In a moment of miserable weakness the Venetian republic gave him up, and
Bruno was taken to Rome. There he was tried, and cast into the dungeons for
six years, and because he entirely refused to recant, was at length delivered over
to the secular arm and burned at the stake on 16th February, Anno Domini 1600.

This event could not but have cast a gloom over the mind of lovers and
expounders of truth, and the lesson probably sank deep into Galileo's soul.

In dealing with these historic events will you allow me to repudiate once for
all the slightest sectarian bias or meaning. I have nothing to do with Catholic or
Protestant as such. I have nothing to do with the Church of Rome as such. I am

dealing with the history of science. But historically at one period science and
the Church came into conflict. It was not specially one Church rather than
another—it was the Church in general, the only one that then existed in those
countries. Historically, I say, they came into conflict, and historically the
Church was the conqueror. It got its way; and science, in the persons of Bruno,
Galileo, and several others, was vanquished.

Such being the facts, there is no help but to mention them in dealing with the
history of science.

Doubtless now the Church regards it as an unhappy victory, and gladly
would ignore this painful struggle. This, however, is impossible. With their
creed the Churchmen of that day could act in no other way. They were bound to
prosecute heresy, and they were bound to conquer in the struggle or be
themselves shattered.

But let me insist on the fact that no one accuses the ecclesiastical courts of
crime or evil motives. They attacked heresy after their manner, as the civil
courts attacked witchcraft after their manner. Both erred grievously, but both
acted with the best intentions.

We must remember, moreover, that his doctrines were scientifically
heterodox, and the University Professors of that day were probably quite as
ready to condemn them as the Church was. To realise the position we must
think of some subjects which to-day are scientifically heterodox, and of the
customary attitude adopted towards them by persons of widely differing creeds.

If it be contended now, as it is, that the ecclesiastics treated Galileo well, I
admit it freely: they treated him as well as they possibly could. They overcame
him, and he recanted; but if he had not recanted, if he had persisted in his
heresy, they would—well, they would still have treated his soul well, but they
would have set fire to his body. Their mistake consisted not in cruelty, but in
supposing themselves the arbiters of eternal truth; and by no amount of slurring
and glossing over facts can they evade the responsibility assumed by them on
account of this mistaken attitude.

I am not here attacking the dogma of Papal Infallibility: it is historically, I
believe, quite unaffected by the controversy respecting the motion of the earth,
no Papal edict ex cathedrâ having been promulgated on the subject.

We left Galileo standing at his telescope and beginning his survey of the
heavens. We followed him indeed through a few of his first great discoveries—
the discovery of the mountains and other variety of surface in the moon, of the
nebulæ and a multitude of faint stars, and lastly of the four satellites of Jupiter.

This latter discovery made an immense sensation, and contributed its share
to his removal from Padua, which quickly followed it, as I shall shortly narrate;
but first I think it will be best to continue our survey of his astronomical
discoveries without regard to the place whence they were made.

Before the end of the year Galileo had made another discovery—this time on
Saturn. But to guard against the host of plagiarists and impostors, he published
it in the form of an anagram, which, at the request of the Emperor Rudolph (a
request probably inspired by Kepler), he interpreted; it ran thus: The furthest
planet is triple.

Very soon after he found that Venus was changing from a full moon to a half
moon appearance. He announced this also by an anagram, and waited till it
should become a crescent, which it did.

This was a dreadful blow to the anti-Copernicans, for it removed the last
lingering difficulty to the reception of the Copernican doctrine.

Fig. 46.—Old drawings of Saturn by different observers, with the
imperfect instruments of that day. The first is Galileo's idea of
what he saw.

Copernicus had predicted, indeed, a hundred years before, that, if ever our
powers of sight were sufficiently enhanced, Venus and Mercury would be seen
to have phases like the moon. And now Galileo with his telescope verifies the
prediction to the letter.

Here was a triumph for the grand old monk, and a bitter morsel for his
opponents.
Castelli writes: "This must now convince the most obstinate." But Galileo, with more
experience, replies:—"You almost make me laugh by saying that these clear observations
are sufficient to convince the most obstinate; it seems you have yet to learn that long ago
the observations were enough to convince those who are capable of reasoning, and those
who wish to learn the truth; but that to convince the obstinate, and those who care for
nothing beyond the vain applause of the senseless vulgar, not even the testimony of the
stars would suffice, were they to descend on earth to speak for themselves. Let us, then,
endeavour to procure some knowledge for ourselves, and rest contented with this sole
satisfaction; but of advancing in popular opinion, or of gaining the assent of the book-
philosophers, let us abandon both the hope and the desire."

Fig. 47.—Phases of Venus. Showing also its apparent variations in size by reason of its
varying distance from the earth. When fully illuminated it is necessarily most distant.
It looks brightest to us when a broad crescent.

What a year's work it had been!

In twelve months observational astronomy had made such a bound as it has
never made before or since.

Why did not others make any of these observations? Because no one could
make telescopes like Galileo.

He gathered pupils round him however, and taught them how to work the
lenses, so that gradually these instruments penetrated Europe, and astronomers
everywhere verified his splendid discoveries.

But still he worked on, and by March in the very next year, he saw
something still more hateful to the Aristotelian philosophers, viz. spots on the
sun.

Fig. 48.

If anything was pure and perfect it was the sun, they said. Was this impostor
going to blacken its face too?

Well, there they were. They slowly formed and changed, and by moving all
together showed him that the sun rotated about once a month.

Before taking leave of Galileo's astronomical researches, I must mention an
observation made at the end of 1612, that the apparent triplicity of Saturn (Fig.
46) had vanished.

Fig. 49.—A portion of the sun's disk as seen in a powerful modern
telescope.
"Looking on Saturn within these few days, I found it solitary, without the assistance of
its accustomed stars, and in short perfectly round and defined, like Jupiter, and such it still
remains. Now what can be said of so strange a metamorphosis? Are perhaps the two
smaller stars consumed like spots on the sun? Have they suddenly vanished and fled? Or
has Saturn devoured his own children? Or was the appearance indeed fraud and illusion,
with which the glasses have so long time mocked me and so many others who have so
often observed with me? Now perhaps the time is come to revive the withering hopes of
those, who, guided by more profound contemplations, have fathomed all the fallacies of
the new observations and recognized their impossibility! I cannot resolve what to say in a
chance so strange, so new, so unexpected. The shortness of time, the unexampled
occurrence, the weakness of my intellect, the terror of being mistaken, have greatly
confounded me."

However, he plucked up courage, and conjectured that the two attendants
would reappear, by revolving round the planet.

Fig. 50.—Saturn and his rings, as seen under the most favourable
circumstances.

The real reason of their disappearance is well known to us now. The plane of
Saturn's rings oscillates slowly about our line of sight, and so we sometimes see
them edgeways and sometimes with a moderate amount of obliquity. The rings
are so thin that, when turned precisely edgeways, they become invisible. The
two imaginary attendants were the most conspicuous portions of the ring,
subsequently called ansæ.

I have thought it better not to interrupt this catalogue of brilliant discoveries
by any biographical details; but we must now retrace our steps to the years 1609
and 1610, the era of the invention of the telescope.

By this time Galileo had been eighteen years at Padua, and like many
another man in like case, was getting rather tired of continual lecturing.
Moreover, he felt so full of ideas that he longed to have a better opportunity of
following them up, and more time for thinking them out.

Now in the holidays he had been accustomed to return to his family home at
Pisa, and there to come a good deal into contact with the Grand-Ducal House of
Tuscany. Young Cosmo di Medici became in fact his pupil, and arrived at man's
estate with the highest opinion of the philosopher. This young man had now
come to the throne as Cosmo II., and to him Galileo wrote saying how much he
should like more time and leisure, how full he was of discoveries if he only had
the chance of a reasonable income without the necessity of consuming so large
a portion of his time in elementary teaching, and practically asking to be
removed to some position in the Court. Nothing was done for a time, but
negotiations proceeded, and soon after the discovery of Jupiter's satellites
Cosmo wrote making a generous offer, which Galileo gladly and
enthusiastically accepted, and at once left Padua for Florence. All his
subsequent discoveries date from Florence.

Thus closed his brilliant and happy career as a professor at the University of
Padua. He had been treated well: his pay had become larger than that of any
Professor of Mathematics up to that time; and, as you know, immediately after
his invention of the telescope the Venetian Senate, in a fit of enthusiasm, had
doubled it and secured it to him for life wherever he was. To throw up his chair
and leave the place the very next year scarcely seems a strictly honourable
procedure. It was legal enough no doubt, and it is easy for small men to criticize
a great one, but nevertheless I think we must admit that it is a step such as a
man with a keen sense of honour would hardly have taken.

One quite feels and sympathizes with the temptation. Not emolument, but
leisure; freedom from harassing engagements and constant teaching, and liberty

to prosecute his studies day and night without interference: this was the golden
prospect before him. He yielded, but one cannot help wishing he had not.

As it turned out it was a false step—the first false step of his public career.
When made it was irretrievable, and it led to great misery.

At first it seemed brilliant enough. The great philosopher of the Tuscan
Court was courted and flattered by princes and nobles, he enjoyed a world-wide
reputation, lived as luxuriously as he cared for, had his time all to himself, and
lectured but very seldom, on great occasions or to a few crowned heads.

His position was in fact analogous to that of Tycho Brahé in his island of
Huen.

Misfortune overtook both. In Tycho's case it arose mainly from the death of
his patron. In Galileo's it was due to a more insidious cause, to understand
which cause aright we must remember the political divisions of Italy at that
date.

Tuscany was a Papal State, and thought there was by no means free. Venice
was a free republic, and was even hostile to the Papacy. In 1606 the Pope had
placed it under an interdict. In reply it had ejected every Jesuit.

Out of this atmosphere of comparative enlightenment and freedom into that
hotbed of mediævalism and superstition went Galileo with his eyes open. Keen
was the regret of his Paduan and Venetian friends; bitter were their
remonstrances and exhortations. But he was determined to go, and, not without
turning some of his old friends into enemies, he went.

Seldom has such a man made so great a mistake: never, I suppose, has one
been so cruelly punished for it.

Fig. 51.—Map of Italy.

We must remember, however, that Galileo, though by no means a saint, was
yet a really religious man, a devout Catholic and thorough adherent of the
Church, so that he would have no dislike to place himself under her sway.
Moreover, he had been born a Tuscan, his family had lived at Florence or Pisa,
and it felt like going home. His theological attitude is worthy of notice, for he
was not in the least a sceptic. He quite acquiesces in the authority of the Bible,
especially in all matters concerning faith and conduct; as to its statements in
scientific matters, he argues that we are so liable to misinterpret their meaning
that it is really easier to examine Nature for truth in scientific matters, and that
when direct observation and Scripture seem to clash, it is because of our
fallacious interpretation of one or both of them. He is, in fact, what one now
calls a "reconciler."

It is curious to find such a man prosecuted for heresy, when to-day his
opinions are those of the orthodox among the orthodox. But so it ever is, and
the heresy of one generation becomes the commonplace of the next.

He accepts Joshua's miracle, for instance, not as a striking poem, but as a
literal fact; and he points out how much more simply it could be done on the
Copernican system by stopping the earth's rotation for a short time, than by
stopping the sun and moon and all the host of heaven as on the old Ptolemaic
system, or again by stopping only the sun and not any of the other bodies, and
so throwing astronomy all wrong.

This reads to us like satire, but no doubt it was his genuine opinion.

These Scriptural reconciliations of his, however, angered the religious
authorities still more. They said it was bad enough for this heretic to try and
upset old scientific beliefs, and to spoil the face of Nature with his infidel
discoveries, but at least he might leave the Bible alone; and they addressed an
indignant remonstrance to Rome, to protect it from the hands of ignorant
laymen.

Thus, wherever he turned he encountered hostility. Of course he had many
friends—some of them powerful like Cosmo, all of them faithful and sincere.
But against the power of Rome what could they do? Cosmo dared no more than
remonstrate, and ultimately his successor had to refrain from even this, so
enchained and bound was the spirit of the rulers of those days; and so when his
day of tribulation came he stood alone and helpless in the midst of his enemies.

You may wonder, perhaps, why this man should excite so much more
hostility than many another man who was suffered to believe and teach much
the same doctrines unmolested. But no other man had made such brilliant and
exciting discoveries. No man stood so prominently forward in the eyes of all
Christendom as the champion of the new doctrines. No other man stated them
so clearly and forcibly, nor drove them home with such brilliant and telling
illustrations.

And again, there was the memory of his early conflict with the Aristotelians
at Pisa, of his scornful and successful refutation of their absurdities. All this
made him specially obnoxious to the Aristotelian Jesuits in their double
capacity both of priests and of philosophers, and they singled him out for
relentless official persecution.

Not yet, however, is he much troubled by them. The chief men at Rome have
not yet moved. Messages, however, keep going up from Tuscany to Rome
respecting the teachings of this man, and of the harm he is doing by his
pertinacious preaching of the Copernican doctrine that the earth moves.

At length, in 1615, Pope Paul V. wrote requesting him to come to Rome to
explain his views. He went, was well received, made a special friend of
Cardinal Barberino—an accomplished man in high position, who became in
fact the next Pope. Galileo showed cardinals and others his telescope, and to as
many as would look through it he showed Jupiter's satellites and his other
discoveries. He had a most successful visit. He talked, he harangued, he held
forth in the midst of fifteen or twenty disputants at once, confounding his
opponents and putting them to shame.

His method was to let the opposite arguments be stated as fully and
completely as possible, himself aiding, and often adducing the most forcible
and plausible arguments against his own views; and then, all having been well
stated, he would proceed to utterly undermine and demolish the whole fabric,
and bring out the truth in such a way as to convince all honest minds. It was this
habit that made him such a formidable antagonist. He never shrank from
meeting an opposing argument, never sought to ignore it, or cloak it in a cloud
of words. Every hostile argument he seemed to delight in, as a foe to be
crushed, and the better and stronger they sounded the more he liked them. He
knew many of them well, he invented a number more, and had he chosen could
have out-argued the stoutest Aristotelian on his own grounds. Thus did he lead
his adversaries on, almost like Socrates, only to ultimately overwhelm them in a
more hopeless rout. All this in Rome too, in the heart of the Catholic world. Had
he been worldly-wise, he would certainly have kept silent and unobtrusive till
he had leave to go away again. But he felt like an apostle of the new doctrines,
whose mission it was to proclaim them even in this centre of the world and of
the Church.

Well, he had an audience with the Pope—a chat an hour long—and the two
parted good friends, mutually pleased with each other.

He writes that he is all right now, and might return home when he liked. But
the question began to be agitated whether the whole system of Copernicus
ought not to be condemned as impious and heretical. This view was persistently
urged upon the Pope and College of Cardinals, and it was soon to be decided
upon.

Had Galileo been unfaithful to the Church he could have left them to stultify
themselves in any way they thought proper, and himself have gone; but he felt
supremely interested in the result, and he stayed. He writes:—
"So far as concerns the clearing of my own character, I might return home immediately;
but although this new question regards me no more than all those who for the last eighty
years have supported those opinions both in public and private, yet, as perhaps I may be of
some assistance in that part of the discussion which depends on the knowledge of truths
ascertained by means of the sciences which I profess, I, as a zealous and Catholic
Christian, neither can nor ought to withhold that assistance which my knowledge affords,
and this business keeps me sufficiently employed."

It is possible that his stay was the worst thing for the cause he had at heart.
Anyhow, the result was that the system was condemned, and both the book of
Copernicus and the epitome of it by Kepler were placed on the forbidden list,[11]
and Galileo himself was formally ordered never to teach or to believe the
motion of the earth.

He quitted Rome in disgust, which before long broke out in satire. The only
way in which he could safely speak of these views now was as if they were
hypothetical and uncertain, and so we find him writing to the Archduke
Leopold, with a presentation copy of his book on the tides, the following:—
"This theory occurred to me when in Rome whilst the theologians were debating on the
prohibition of Copernicus's book, and of the opinion maintained in it of the motion of the
earth, which I at that time believed: until it pleased those gentlemen to suspend the book,
and declare the opinion false and repugnant to the Holy Scriptures. Now, as I know how
well it becomes me to obey and believe the decisions of my superiors, which proceed out
of more knowledge than the weakness of my intellect can attain to, this theory which I
send you, which is founded on the motion of the earth, I now look upon as a fiction and a
dream, and beg your highness to receive it as such. But as poets often learn to prize the
creations of their fancy, so in like manner do I set some value on this absurdity of mine. It
is true that when I sketched this little work I did hope that Copernicus would not, after
eighty years, be convicted of error; and I had intended to develop and amplify it further,
but a voice from heaven suddenly awakened me, and at once annihilated all my confused
and entangled fancies."

This sarcasm, if it had been in print, would probably have been dangerous. It
was safe in a private letter, but it shows us his real feelings.

However, he was left comparatively quiet for a time. He was getting an old
man now, and passed the time studiously enough, partly at his house in
Florence, partly at his villa in Arcetri, a mile or so out of the town.

Here was a convent, and in it his two daughters were nuns. One of them,
who passed under the name of Sister Maria Celeste, seems to have been a
woman of considerable capacity—certainly she was of a most affectionate
disposition—and loved and honoured her father in the most dutiful way.

This was a quiet period of his life, spoiled only by occasional fits of illness
and severe rheumatic pains, to which the old man was always liable. Many little
circumstances are known of this peaceful time. For instance, the convent clock
won't go, and Galileo mends it for them. He is always doing little things for
them, and sending presents to the Lady Superior and his two daughters.

He was occupied now with problems in hydrostatics, and on other matters
unconnected with astronomy: a large piece of work which I must pass over.
Most interesting and acute it is, however.

In 1623, when the old Pope died, there was elected to the Papal throne, as
Urban VIII., Cardinal Barberino, a man of very considerable enlightenment, and
a personal friend of Galileo's, so that both he and his daughters rejoice greatly,
and hope that things will come all right, and the forbidding edict be withdrawn.

The year after this election he manages to make another journey to Rome to
compliment his friend on his elevation to the Pontifical chair. He had many
talks with Urban, and made himself very agreeable.

Urban wrote to the Grand Duke Ferdinand, son of Cosmo:—
"For We find in him not only literary distinction but also love of piety, and he is strong
in those qualities by which Pontifical good will is easily obtainable. And now, when he has
been brought to this city to congratulate Us on Our elevation, We have very lovingly
embraced him; nor can We suffer him to return to the country whither your liberality
recalls him without an ample provision of Pontifical love. And that you may know how
dear he is to Us, We have willed to give him this honourable testimonial of virtue and

piety. And We further signify that every benefit which you shall confer upon him, imitating
or even surpassing your father's liberality, will conduce to Our gratification."

Encouraged, doubtless, by these marks of approbation, and reposing too
much confidence in the individual good will of the Pope, without heeding the
crowd of half-declared enemies who were seeking to undermine his reputation,
he set about, after his return to Florence, his greatest literary and most popular
work, Dialogues on the Ptolemaic and Copernican Systems. This purports to be
a series of four conversations between three characters: Salviati, a Copernican
philosopher; Sagredo, a wit and scholar, not specially learned, but keen and
critical, and who lightens the talk with chaff; Simplicio, an Aristotelian
philosopher, who propounds the stock absurdities which served instead of
arguments to the majority of men.

The conversations are something between Plato's Dialogues and Sir Arthur
Helps's Friends in Council. The whole is conducted with great good temper and
fairness; and, discreetly enough, no definite conclusion is arrived at, the whole
being left in abeyance as if for a fifth and decisive dialogue, which, however,
was never written, and perhaps was only intended in case the reception was
favourable.

The preface also sets forth that the object of the writer is to show that the
Roman edict forbidding the Copernican doctrine was not issued in ignorance of
the facts of the case, as had been maliciously reported, and that he wishes to
show how well and clearly it was all known beforehand. So he says the
dialogue on the Copernican side takes up the question purely as a mathematical
hypothesis or speculative figment, and gives it every artificial advantage of
which the theory is capable.

This piece of caution was insufficient to blind the eyes of the Cardinals; for
in it the arguments in favour of the earth's motion are so cogent and
unanswerable, and are so popularly stated, as to do more in a few years to
undermine the old system than all that he had written and spoken before. He
could not get it printed for two years after he had written it, and then only got
consent through a piece of carelessness or laziness on the part of the
ecclesiastical censor through whose hands the manuscript passed—for which he
was afterwards dismissed.

However, it did appear, and was eagerly read; the more, perhaps, as the
Church at once sought to suppress it.

The Aristotelians were furious, and represented to the Pope that he himself
was the character intended by Simplicio, the philosopher whose opinions get
alternately refuted and ridiculed by the other two, till he is reduced to an abject
state of impotence.

The idea that Galileo had thus cast ridicule upon his friend and patron is no
doubt a gratuitous and insulting libel: there is no telling whether or not Urban
believed it, but certainly his countenance changed to Galileo henceforward, and
whether overruled by his Cardinals, or actuated by some other motive, his
favour was completely withdrawn.

The infirm old man was instantly summoned to Rome. His friends pleaded
his age—he was now seventy—his ill-health, the time of year, the state of the
roads, the quarantine existing on account of the plague. It was all of no avail, to
Rome he must go, and on the 14th of February he arrived.

Fig. 52.—Portrait of Galileo.

His daughter at Arcetri was in despair; and anxiety and fastings and penances
self-inflicted on his account, dangerously reduced her health.

At Rome he was not imprisoned, but he was told to keep indoors, and show
himself as little as possible. He was allowed, however, to stay at the house of
the Tuscan Ambassador instead of in gaol.

By April he was removed to the chambers of the Inquisition, and examined
several times. Here, however, the anxiety was too much, and his health began to
give way seriously; so, before long, he was allowed to return to the
Ambassador's house; and, after application had been made, was allowed to
drive in the public garden in a half-closed carriage. Thus in every way the
Inquisition dealt with him as leniently as they could. He was now their prisoner,
and they might have cast him into their dungeons, as many another had been

cast. By whatever they were influenced—perhaps the Pope's old friendship,
perhaps his advanced age and infirmities—he was not so cruelly used.

Still, they had their rules; he must be made to recant and abjure his heresy;
and, if necessary, torture must be applied. This he knew well enough, and his
daughter knew it, and her distress may be imagined. Moreover, it is not as if
they had really been heretics, as if they hated or despised the Church of Rome.
On the contrary, they loved and honoured the Church. They were sincere and
devout worshippers, and only on a few scientific matters did Galileo presume to
differ from his ecclesiastical superiors: his disagreement with them occasioned
him real sorrow; and his dearest hope was that they could be brought to his way
of thinking and embrace the truth.

Every time he was sent for by the Inquisition he was in danger of torture
unless he recanted. All his friends urged him repeatedly to submit. They said
resistance was hopeless and fatal. Within the memory of men still young,
Giordano Bruno had been burnt alive for a similar heresy. This had happened
while Galileo was at Padua. Venice was full of it. And since that, only eight
years ago indeed, Antonio de Dominis, Archbishop of Salpetria, had been
sentenced to the same fate: "to be handed over to the secular arm to be dealt
with as mercifully as possible without the shedding of blood." So ran the
hideous formula condemning a man to the stake. After his sentence, this
unfortunate man died in the dungeons in which he had been incarcerated six
years—died what is called a "natural" death; but the sentence was carried out,
notwithstanding, on his lifeless body and his writings. His writings for which he
had been willing to die!

These were the tender mercies of the Inquisition; and this was the kind of
meaning lurking behind many of their well-sounding and merciful phrases. For
instance, what they call "rigorous examination," we call "torture." Let us,
however, remember in our horror at this mode of compelling a prisoner to say
anything they wished, that they were a legally constituted tribunal; that they
acted with well established rules, and not in passion; and that torture was a
recognized mode of extracting evidence, not only in ecclesiastical but in civil
courts, at that date.

All this, however, was but poor solace to the pitiable old philosopher, thus
ruthlessly haled up and down, questioned and threatened, threatened and
questioned, receiving agonizing letters from his daughter week by week, and
trying to keep up a little spirit to reply as happily and hopefully as he could.

This condition of things could not go on. From February to June the
suspense lasted. On the 20th of June he was summoned again, and told he
would be wanted all next day for a rigorous examination. Early in the morning
of the 21st he repaired thither, and the doors were shut. Out of those chambers
of horror he did not reappear till the 24th. What went on all those three days no
one knows. He himself was bound to secrecy. No outsider was present. The
records of the Inquisition are jealously guarded. That he was technically
tortured is certain; that he actually underwent the torment of the rack is
doubtful. Much learning has been expended upon the question, especially in
Germany. Several eminent scholars have held the fact of actual torture to be
indisputable (geometrically certain, one says), and they confirm it by the hernia
from which he afterwards suffered, this being a well-known and frequent
consequence.

Other equally learned commentators, however, deny that the last stage was
reached. For there are five stages all laid down in the rules of the Inquisition,
and steadily adhered to in a rigorous examination, at each stage an opportunity
being given for recantation, every utterance, groan, or sigh being strictly
recorded. The recantation so given has to be confirmed a day or two later, under
pain of a precisely similar ordeal.

The five stages are:—1st. The official threat in the court. 2nd. The taking to
the door of the torture chamber and renewing the official threat. 3rd. The taking
inside and showing the instruments. 4th. Undressing and binding upon the rack.
5th. Territio realis.

Through how many of these ghastly acts Galileo passed I do not know. I
hope and believe not the last.

There are those who lament that he did not hold out, and accept the crown of
martyrdom thus offered to him. Had he done so we know his fate—a few years'
languishing in the dungeons, and then the flames.

Whatever he ought to have done, he did not hold out—he gave way. At one
stage or another of the dread ordeal he said: "I am in your hands. I will say
whatever you wish." Then was he removed to a cell while his special form of
perjury was drawn up.

The next day, clothed as a penitent, the venerable old man was taken to the
Convent of Minerva, where the Cardinals and prelates were assembled for the
purpose of passing judgment upon him.

The text of the judgment I have here, but it is too long to read. It sentences
him—1st. To the abjuration. 2nd. To formal imprisonment for life. 3rd. To recite
the seven penitential psalms every week.

Ten Cardinals were present; but, to their honour be it said, three refused to
sign; and this blasphemous record of intolerance and bigoted folly goes down
the ages with the names of seven Cardinals immortalized upon it.

This having been read, he next had to read word for word the abjuration
which had been drawn up for him, and then sign it.

The Abjuration of Galileo.

"I, Galileo Galilei, son of the late Vincenzo Galilei, of Florence, aged seventy
years, being brought personally to judgment, and kneeling before you Most Eminent
and Most Reverend Lords Cardinals, General Inquisitors of the universal Christian
republic against heretical depravity, having before my eyes the Holy Gospels, which I
touch with my own hands, swear that I have always believed, and now believe, and
with the help of God will in future believe, every article which the Holy Catholic and
Apostolic Church of Rome holds, teaches, and preaches. But because I have been
enjoined by this Holy Office altogether to abandon the false opinion which maintains
that the sun is the centre and immovable, and forbidden to hold, defend, or teach the
said false doctrine in any manner, and after it hath been signified to me that the said
doctrine is repugnant with the Holy Scripture, I have written and printed a book, in
which I treat of the same doctrine now condemned, and adduce reasons with great
force in support of the same, without giving any solution, and therefore have been
judged grievously suspected of heresy; that is to say, that I held and believed that the
sun is the centre of the universe and is immovable, and that the earth is not the centre
and is movable; willing, therefore, to remove from the minds of your Eminences, and
of every Catholic Christian, this vehement suspicion rightfully entertained towards
me, with a sincere heart and unfeigned faith, I abjure, curse, and detest the said errors
and heresies, and generally every other error and sect contrary to Holy Church; and I
swear that I will never more in future say or assert anything verbally, or in writing,
which may give rise to a similar suspicion of me; but if I shall know any heretic, or
any one suspected of heresy, that I will denounce him to this Holy Office, or to the
Inquisitor or Ordinary of the place where I may be; I swear, moreover, and promise,
that I will fulfil and observe fully, all the penances which have been or shall be laid on
me by this Holy Office. But if it shall happen that I violate any of my said promises,
oaths, and protestations (which God avert!), I subject myself to all the pains and
punishments which have been decreed and promulgated by the sacred canons, and
other general and particular constitutions, against delinquents of this description. So
may God help me, and his Holy Gospels which I touch with my own hands. I, the
above-named Galileo Galilei, have abjured, sworn, promised, and bound myself as
above, and in witness thereof with my own hand have subscribed this present writing
of my abjuration, which I have recited word for word. At Rome, in the Convent of
Minerva, 22nd June, 1633. I, Galileo Galilei, have abjured as above with my own
hand."

Those who believe the story about his muttering to a friend, as he rose
from his knees, "e pur si muove," do not realize the scene.

1st. There was no friend in the place.

2nd. It would have been fatally dangerous to mutter anything before
such an assemblage.

3rd. He was by this time an utterly broken and disgraced old man;
wishful, of all things, to get away and hide himself and his miseries from
the public gaze; probably with his senses deadened and stupefied by the
mental sufferings he had undergone, and no longer able to think or care
about anything—except perhaps his daughter,—certainly not about any
motion of this wretched earth.

Far and wide the news of the recantation spread. Copies of the abjuration
were immediately sent to all Universities, with instructions to the professors
to read it publicly.

At Florence, his home, it was read out in the Cathedral church, all his
friends and adherents being specially summoned to hear it.

For a short time more he was imprisoned in Rome; but at length was
permitted to depart, never more of his own will to return.

He was allowed to go to Siena. Here his daughter wrote consolingly,
rejoicing at his escape, and saying how joyfully she already recited the
penitential psalms for him, and so relieved him of that part of his sentence.

But the poor girl was herself, by this time, ill—thoroughly worn out with
anxiety and terror; she lay, in fact, on what proved to be her death-bed. Her
one wish was to see her dearest lord and father, so she calls him, once more.
The wish was granted. His prison was changed, by orders from Rome, from
Siena to Arcetri, and once more father and daughter embraced. Six days
after this she died.

The broken-hearted old man now asks for permission to go to live in
Florence, but is met with the stern answer that he is to stay at Arcetri, is not
to go out of the house, is not to receive visitors, and that if he asks for more
favours, or transgresses the commands laid upon him, he is liable to be
haled back to Rome and cast into a dungeon. These harsh measures were
dictated, not by cruelty, but by the fear of his still spreading heresy by
conversation, and so he was to be kept isolated.

Idle, however, he was not and could not be. He often complains that his
head is too busy for his body. In the enforced solitude of Arcetri he was
composing those dialogues on motion which are now reckoned his greatest
and most solid achievement. In these the true laws of motion are set forth
for the first time (see page 167). One more astronomical discovery also he
was to make—that of the moon's libration.

And then there came one more crushing blow. His eyes became inflamed
and painful—the sight of one of them failed, the other soon went; he
became totally blind. But this, being a heaven-sent infliction, he could bear
with resignation, though it must have been keenly painful to a solitary man
of his activity. "Alas!" says he, in one of his letters, "your dear friend and
servant is totally blind. Henceforth this heaven, this universe, which by
wonderful observations I had enlarged a hundred and a thousand times
beyond the conception of former ages, is shrunk for me into the narrow
space which I myself fill in it. So it pleases God; it shall therefore please me
also."

He was now allowed an amanuensis, and the help of his pupils Torricelli,
Castelli, and Viviani, all devotedly attached to him, and Torricelli very
famous after him. Visitors also were permitted, after approval by a Jesuit
supervisor; and under these circumstances many visited him, among them a
man as immortal as himself—John Milton, then only twenty-nine, travelling
in Italy. Surely a pathetic incident, this meeting of these two great men—the
one already blind, the other destined to become so. No wonder that, as in
his old age he dictated his masterpiece, the thoughts of the English poet
should run on the blind sage of Tuscany, and the reminiscence of their
conversation should lend colour to the poem.

Well, it were tedious to follow the petty annoyances and troubles to
which Galileo was still subject—how his own son was set to see that no
unauthorized procedure took place, and that no heretic visitors were
admitted; how it was impossible to get his new book printed till long
afterwards; and how one form of illness after another took possession of

him. The merciful end came at last, and at the age of seventy-eight he was
released from the Inquisition.

They wanted to deny him burial—they did deny him a monument; they
threatened to cart his bones away from Florence if his friends attempted
one. And so they hoped that he and his work might be forgotten.

Poor schemers! Before the year was out an infant was born in
Lincolnshire, whose destiny it was to round and complete and carry forward
the work of their victim, so that, until man shall cease from the planet,
neither the work nor its author shall have need of a monument.

Here might I end, were it not that the same kind of struggle as went on
fiercely in the seventeenth century is still smouldering even now. Not in
astronomy indeed, as then; nor yet in geology, as some fifty years ago; but
in biology mainly—perhaps in other subjects. I myself have heard Charles
Darwin spoken of as an atheist and an infidel, the theory of evolution
assailed as unscriptural, and the doctrine of the ascent of man from a lower
state of being, as opposed to the fall of man from some higher condition,
denied as impious and un-Christian.

Men will not learn by the past; still they brandish their feeble weapons
against the truths of Nature, as if assertions one way or another could alter
fact, or make the thing other than it really is. As Galileo said before his
spirit was broken, "In these and other positions certainly no man doubts but
His Holiness the Pope hath always an absolute power of admitting or
condemning them; but it is not in the power of any creature to make them to
be true or false, or otherwise than of their own nature and in fact they are."

I know nothing of the views of any here present; but I have met educated
persons who, while they might laugh at the men who refused to look
through a telescope lest they should learn something they did not like, yet

also themselves commit the very same folly. I have met persons who utterly
refuse to listen to any view concerning the origin of man other than that of a
perfect primæval pair in a garden, and I am constrained to say this much:
Take heed lest some prophet, after having excited your indignation at the
follies and bigotry of a bygone generation, does not turn upon you with the
sentence, "Thou art the man."

S UM M ARY OF FACT S F OR L E CT URE VI

Science before Newton

Dr. Gilbert, of Colchester, Physician to Queen Elizabeth, was an
excellent experimenter, and made many discoveries in magnetism and
electricity. He was contemporary with Tycho Brahé, and lived from 1540 to
1603.

Francis Bacon, Lord Verulam, 1561–1626, though a brilliant writer, is
not specially important as regards science. He was not a scientific man, and
his rules for making discoveries, or methods of induction, have never been
consciously, nor often indeed unconsciously, followed by discoverers. They
are not in fact practical rules at all, though they were so intended. His really
strong doctrines are that phenomena must be studied direct, and that
variations in the ordinary course of nature must be induced by aid of
experiment; but he lacked the scientific instinct for pursuing these great
truths into detail and special cases. He sneered at the work and methods of
both Gilbert and Galileo, and rejected the Copernican theory as absurd. His
literary gifts have conferred on him an artificially high scientific reputation,
especially in England; at the same time his writings undoubtedly helped to
make popular the idea of there being new methods for investigating Nature,
and, by insisting on the necessity for freedom from preconceived ideas and

opinions, they did much to release men from the bondage of Aristotelian
authority and scholastic tradition.

The greatest name between Galileo and Newton is that of Descartes.

René Descartes was born at La Haye in Touraine, 1596, and died at
Stockholm in 1650. He did important work in mathematics, physics,
anatomy, and philosophy. Was greatest as a philosopher and mathematician.
At the age of twenty-one he served as a volunteer under Prince Maurice of
Nassau, but spent most of his later life in Holland. His famous Discourse on
Method appeared at Leyden in 1637, and his Principia at Amsterdam in
1644; great pains being taken to avoid the condemnation of the Church.

Descartes's main scientific achievement was the application of algebra to
geometry; his most famous speculation was the "theory of vortices,"
invented to account for the motion of planets. He also made many
discoveries in optics and physiology. His best known immediate pupils
were the Princess Elizabeth of Bohemia, and Christina, Queen of Sweden.

He founded a distinct school of thought (the Cartesian), and was the
precursor of the modern mathematical method of investigating science, just
as Galileo and Gilbert were the originators of the modern experimental
method.

LECTURE VI

DESCARTES AND HIS THEORY OF VORTICES

After the dramatic life we have been considering in the last two
lectures, it is well to have a breathing space, to look round on what has been
accomplished, and to review the state of scientific thought, before

proceeding to the next great era. For we are still in the early morning of
scientific discovery: the dawn of the modern period, faintly heralded by
Copernicus, brought nearer by the work of Tycho and Kepler, and
introduced by the discoveries of Galileo—the dawn has occurred, but the
sun is not yet visible. It is hidden by the clouds and mists of the long night
of ignorance and prejudice. The light is sufficient, indeed, to render these
earth-born vapours more visible: it is not sufficient to dispel them. A
generation of slow and doubtful progress must pass, before the first ray of
sunlight can break through the eastern clouds and the full orb of day itself
appear.

It is this period of hesitating progress and slow leavening of men's ideas
that we have to pass through in this week's lecture. It always happens thus:
the assimilation of great and new ideas is always a slow and gradual
process: there is no haste either here or in any other department of Nature.
Die Zeit ist unendlich lang. Steadily the forces work, sometimes seeming to
accomplish nothing; sometimes even the motion appears retrograde; but in
the long run the destined end is reached, and the course, whether of a planet
or of men's thoughts about the universe, is permanently altered. Then, the
controversy was about the earth's place in the universe; now, if there be any
controversy of the same kind, it is about man's place in the universe; but the
process is the same: a startling statement by a great genius or prophet,
general disbelief, and, it may be, an attitude of hostility, gradual acceptance
by a few, slow spreading among the many, ending in universal acceptance
and faith often as unquestioning and unreasoning as the old state of unfaith
had been. Now the process is comparatively speedy: twenty years
accomplishes a great deal: then it was tediously slow, and a century seemed
to accomplish very little. Periodical literature may be responsible for some
waste of time, but it certainly assists the rapid spread of ideas. The rate with
which ideas are assimilated by the general public cannot even now be
considered excessive, but how much faster it is than it was a few centuries
ago may be illustrated by the attitude of the public to Darwinism now,
twenty-five years after The Origin of Species, as compared with their

attitude to the Copernican system a century after De Revolutionibus. By the
way, it is, I know, presumptuous for me to have an opinion, but I cannot
hear Darwin compared to or mentioned along with Newton without a
shudder. The stage in which he found biology seems to me far more
comparable with the Ptolemaic era in astronomy, and he himself to be quite
fairly comparable to Copernicus.

Let us proceed to summarize the stage at which the human race had
arrived at the epoch with which we are now dealing.

The Copernican view of the solar system had been stated, restated,
fought, and insisted on; a chain of brilliant telescopic discoveries had made
it popular and accessible to all men of any intelligence: henceforth it must
be left to slowly percolate and sink into the minds of the people. For the
nations were waking up now, and were accessible to new ideas. England
especially was, in some sort, at the zenith of its glory; or, if not at the
zenith, was in that full flush of youth and expectation and hope which is
stronger and more prolific of great deeds and thoughts than a maturer
period.

A common cause against a common and detested enemy had roused in
the hearts of Englishmen a passion of enthusiasm and patriotism; so that the
mean elements of trade, their cheating yard-wands, were forgotten for a
time; the Armada was defeated, and the nation's true and conscious adult
life began. Commerce was now no mere struggle for profit and hard
bargains; it was full of the spirit of adventure and discovery; a new world
had been opened up; who could tell what more remained unexplored? Men
awoke to the splendour of their inheritance, and away sailed Drake and
Frobisher and Raleigh into the lands of the West.

For literature, you know what a time it was. The author of Hamlet and
Othello was alive: it is needless to say more. And what about science? The
atmosphere of science is a more quiet and less stirring one; it thrives best
when the fever of excitement is allayed; it is necessarily a later growth than

literature. Already, however, our second great man of science was at work
in a quiet country town—second in point of time, I mean, Roger Bacon
being the first. Dr. Gilbert, of Colchester, was the second in point of time,
and the age was ripening for the time when England was to be honoured
with such a galaxy of scientific luminaries—Hooke and Boyle and Newton
—as the world had not yet known.

Yes, the nations were awake. "In all directions," as Draper says, "Nature
was investigated: in all directions new methods of examination were
yielding unexpected and beautiful results. On the ruins of its ivy-grown
cathedrals Ecclesiasticism [or Scholasticism], surprised and blinded by the
breaking day, sat solemnly blinking at the light and life about it, absorbed in
the recollection of the night that had passed, dreaming of new phantoms and
delusions in its wished-for return, and vindictively striking its talons at any
derisive assailant who incautiously approached too near."

Of the work of Gilbert there is much to say; so there is also of Roger
Bacon, whose life I am by no means sure I did right in omitting. But neither
of them had much to do with astronomy, and since it is in astronomy that
the most startling progress was during these centuries being made, I have
judged it wiser to adhere mainly to the pioneers in this particular
department.

Only for this reason do I pass Gilbert with but slight mention. He knew
of the Copernican theory and thoroughly accepted it (it is convenient to
speak of it as the Copernican theory, though you know that it had been
considerably improved in detail since the first crude statement by
Copernicus), but he made in it no changes. He was a cultivated scientific
man, and an acute experimental philosopher; his main work lay in the
domain of magnetism and electricity. The phenomena connected with the
mariner's compass had been studied somewhat by Roger Bacon; and they
were now examined still more thoroughly by Gilbert, whose treatise De
Magnete, marks the beginning of the science of magnetism.

As an appendix to that work he studied the phenomenon of amber, which
had been mentioned by Thales. He resuscitated this little fact after its burial
of 2,200 years, and greatly extended it. He it was who invented the name
electricity—I wish it had been a shorter one. Mankind invents names much
better than do philosophers. What can be better than "heat," "light,"
"sound"? How favourably they compare with electricity, magnetism,
galvanism, electro-magnetism, and magneto-electricity! The only long-
established monosyllabic name I know invented by a philosopher is "gas"—
an excellent attempt, which ought to be imitated.[12]

Of Lord Bacon, who flourished about the same time (a little later), it is
necessary to say something, because many persons are under the impression
that to him and his Novum Organon the reawakening of the world, and the
overthrow of Aristotelian tradition, are mainly due. His influence, however,
has been exaggerated. I am not going to enter into a discussion of the
Novum Organon, and the mechanical methods which he propounded as
certain to evolve truth if patiently pursued; for this is what he thought he
was doing—giving to the world an infallible recipe for discovering truth,
with which any ordinarily industrious man could make discoveries by
means of collection and discrimination of instances. You will take my
statement for what it is worth, but I assert this: that many of the methods
which Bacon lays down are not those which the experience of mankind has
found to be serviceable; nor are they such as a scientific man would have
thought of devising.

True it is that a real love and faculty for science are born in a man, and
that to the man of scientific capacity rules of procedure are unnecessary; his
own intuition is sufficient, or he has mistaken his vocation,—but that is not
my point. It is not that Bacon's methods are useless because the best men do
not need them; if they had been founded on a careful study of the methods
actually employed, though it might be unconsciously employed, by
scientific men—as the methods of induction, stated long after by John
Stuart Mill, were founded—then, no doubt, their statement would have been
a valuable service and a great thing to accomplish. But they were not this.

They are the ideas of a brilliant man of letters, writing in an age when
scientific research was almost unknown, about a subject in which he was an
amateur. I confess I do not see how he, or John Stuart Mill, or any one else,
writing in that age, could have formulated the true rules of philosophizing;
because the materials and information were scarcely to hand. Science and
its methods were only beginning to grow. No doubt it was a brilliant
attempt. No doubt also there are many good and true points in the
statement, especially in his insistence on the attitude of free and open
candour with which the investigation of Nature should be approached. No
doubt there was much beauty in his allegories of the errors into which men
were apt to fall—the idola of the market-place, of the tribe, of the theatre,
and of the den; but all this is literature, and on the solid progress of science
may be said to have had little or no effect. Descartes's Discourse on Method
was a much more solid production.

You will understand that I speak of Bacon purely as a scientific man. As
a man of letters, as a lawyer, a man of the world, and a statesman, he is
beyond any criticism of mine. I speak only of the purely scientific aspect of
the Novum Organon. The Essays and The Advancement of Learning are
masterly productions; and as a literary man he takes high rank.

The over-praise which, in the British Isles, has been lavished upon his
scientific importance is being followed abroad by what may be an
unnecessary amount of detraction. This is always the worst of setting up a
man on too high a pinnacle; some one has to undertake the ungrateful task
of pulling him down again. Justus von Liebig addressed himself to this task
with some vigour in his Reden und Abhandlung (Leipzig, 1874), where he
quotes from Bacon a number of suggestions for absurd experimentation.[13]

The next paragraph I read, not because I endorse it, but because it is
always well to hear both sides of a question. You have probably been long
accustomed to read over-estimates of Bacon's importance, and extravagant
laudation of his writings as making an epoch in science; hear what Draper
says on the opposite side:—[14]

"The more closely we examine the writings of Lord Bacon, the more unworthy
does he seem to have been of the great reputation which has been awarded to him.
The popular delusion to which he owes so much originated at a time when the history
of science was unknown. They who first brought him into notice knew nothing of the
old school of Alexandria. This boasted founder of a new philosophy could not
comprehend, and would not accept, the greatest of all scientific doctrines when it was
plainly set before his eyes.

"It has been represented that the invention of the true method of physical science
was an amusement of Bacon's hours of relaxation from the more laborious studies of
law, and duties of a Court.

"His chief admirers have been persons of a literary turn, who have an idea that
scientific discoveries are accomplished by a mechanico-mental operation. Bacon
never produced any great practical result himself, no great physicist has ever made
any use of his method. He has had the same to do with the development of modern
science that the inventor of the orrery has had to do with the discovery of the
mechanism of the world. Of all the important physical discoveries, there is not one
which shows that its author made it by the Baconian instrument.

"Newton never seems to have been aware that he was under any obligation to
Bacon. Archimedes, and the Alexandrians, and the Arabians, and Leonardo da Vinci
did very well before he was born; the discovery of America by Columbus and the
circumnavigation by Magellan can hardly be attributed to him, yet they were the
consequences of a truly philosophical reasoning. But the investigation of Nature is an
affair of genius, not of rules. No man can invent an organon for writing tragedies and
epic poems. Bacon's system is, in its own terms, an idol of the theatre. It would
scarcely guide a man to a solution of the riddle of Ælia Lælia Crispis, or to that of the
charade of Sir Hilary.

"Few scientific pretenders have made more mistakes than Lord Bacon. He rejected
the Copernican system, and spoke insolently of its great author; he undertook to
criticize adversely Gilbert's treatise De Magnete; he was occupied in the
condemnation of any investigation of final causes, while Harvey was deducing the
circulation of the blood from Aquapendente's discovery of the valves in the veins; he
was doubtful whether instruments were of any advantage, while Galileo was
investigating the heavens with the telescope. Ignorant himself of every branch of
mathematics, he presumed that they were useless in science but a few years before
Newton achieved by their aid his immortal discoveries.

"It is time that the sacred name of philosophy should be severed from its long
connection with that of one who was a pretender in science, a time-serving politician,
an insidious lawyer, a corrupt judge, a treacherous friend, a bad man."

This seems to me a depreciation as excessive as are the eulogies
commonly current. The truth probably lies somewhere between the two
extremes. It is unfair to judge Bacon's methods by thinking of physical
science in its present stage. To realise his position we must think of a
subject still in its very early infancy, one in which the advisability of
applying experimental methods is still doubted; one which has been studied
by means of books and words and discussion of normal instances, instead of
by collection and observation of the unusual and irregular, and by
experimental production of variety. If we think of a subject still in this
infantile and almost pre-scientific stage, Bacon's words and formulæ are far
from inapplicable; they are, within their limitations, quite necessary and
wholesome. A subject in this stage, strange to say, exists,—psychology;
now hesitatingly beginning to assume its experimental weapons amid a
stifling atmosphere of distrust and suspicion. Bacon's lack of the modern
scientific instinct must be admitted, but he rendered humanity a powerful
service in directing it from books to nature herself, and his genius is
indubitable. A judicious account of his life and work is given by Prof.
Adamson, in the Encyclopædia Britannica, and to this article I now refer
you.

Who, then, was the man of first magnitude filling up the gap in scientific
history between the death of Galileo and the maturity of Newton? Unknown
and mysterious are the laws regulating the appearance of genius. We have
passed in review a Pole, a Dane, a German, and an Italian,—the great man
is now a Frenchman, René Descartes, born in Touraine, on the 31st of
March, 1596.

His mother died at his birth; the father was of no importance, save as the
owner of some landed property. The boy was reared luxuriously, and
inherited a fair fortune. Nearly all the men of first rank, you notice, were
born well off. Genius born to poverty might, indeed, even then achieve

name and fame—as we see in the case of Kepler—but it was terribly
handicapped. Handicapped it is still, but far less than of old; and we may
hope it will become gradually still less so as enlightenment proceeds, and
the tremendous moment of great men to a nation is more clearly and
actively perceived.

It is possible for genius, when combined with strong character, to
overcome all obstacles, and reach the highest eminence, but the struggle
must be severe; and the absence of early training and refinement during the
receptive years of youth must be a lifelong drawback.

Descartes had none of these drawbacks; life came easily to him, and, as
a consequence perhaps, he never seems to have taken it quite seriously.
Great movements and stirring events were to him opportunities for the
study of men and manners; he was not the man to court persecution, nor to
show enthusiasm for a losing or struggling cause.

In this, as in many other things, he was imbued with a very modern
spirit, a cynical and sceptical spirit, which, to an outside and superficial
observer like myself, seems rather rife just now.

He was also imbued with a phase of scientific spirit which you
sometimes still meet with, though I believe it is passing away, viz. an
uncultured absorption in his own pursuits, and some feeling of contempt for
classical and literary and æsthetic studies.

In politics, art, and history he seems to have had no interest. He was a
spectator rather than an actor on the stage of the world; and though he
joined the army of that great military commander Prince Maurice of
Nassau, he did it not as a man with a cause at heart worth fighting for, but
precisely in the spirit in which one of our own gilded youths would
volunteer in a similar case, as a good opportunity for frolic and for seeing
life.

He soon tired of it and withdrew—at first to gay society in Paris. Here
he might naturally have sunk into the gutter with his companions, but for a
great mental shock which became the main epoch and turning-point of his
life, the crisis which diverted him from frivolity to seriousness. It was a
purely intellectual emotion, not excited by anything in the visible or
tangible world; nor could it be called conversion in the common acceptation
of that term. He tells us that on the 10th of November, 1619, at the age of
twenty-four, a brilliant idea flashed upon him—the first idea, namely, of his
great and powerful mathematical method, of which I will speak directly;
and in the flush of it he foresaw that just as geometers, starting with a few
simple and evident propositions or axioms, ascend by a long and intricate
ladder of reasoning to propositions more and more abstruse, so it might be
possible to ascend from a few data, to all the secrets and facts of the
universe, by a process of mathematical reasoning.

"Comparing the mysteries of Nature with the laws of mathematics, he
dared to hope that the secrets of both could be unlocked with the same key."

That night he lapsed gradually into a state of enthusiasm, in which he
saw three dreams or visions, which he interpreted at the time, even before
waking, to be revelations from the Spirit of Truth to direct his future course,
as well as to warn him from the sins he had already committed.

His account of the dreams is on record, but is not very easy to follow;
nor is it likely that a man should be able to convey to others any adequate
idea of the deepest spiritual or mental agitation which has shaken him to his
foundations.

His associates in Paris were now abandoned, and he withdrew, after
some wanderings, to Holland, where he abode the best part of his life and
did his real work.

Even now, however, he took life easily. He recommends idleness as
necessary to the production of good mental work. He worked and meditated
but a few hours a day: and most of those in bed. He used to think best in

bed, he said. The afternoon he devoted to society and recreation. After
supper he wrote letters to various persons, all plainly intended for
publication, and scrupulously preserved. He kept himself free from care,
and was most cautious about his health, regarding himself, no doubt, as a
subject of experiment, and wishful to see how long he could prolong his
life. At one time he writes to a friend that he shall be seriously disappointed
if he does not manage to see 100 years.

Fig. 53.—Descartes.

This plan of not over-working himself, and limiting the hours devoted to
serious thought, is one that might perhaps advantageously be followed by
some over-laborious students of the present day. At any rate it conveys a

lesson; for the amount of ground covered by Descartes, in a life not very
long, is extraordinary. He must, however, have had a singular aptitude for
scientific work; and the judicious leaven of selfishness whereby he was able
to keep himself free from care and embarrassments must have been a great
help to him.

And what did his versatile genius accomplish during his fifty-four years
of life?

In philosophy, using the term as meaning mental or moral philosophy
and metaphysics, as opposed to natural philosophy or physics, he takes a
very high rank, and it is on this that perhaps his greatest fame rests. (He is
the author, you may remember, of the famous aphorism, "Cogito, ergo
sum.")

In biology I believe he may be considered almost equally great: certainly
he spent a great deal of time in dissecting, and he made out a good deal of
what is now known of the structure of the body, and of the theory of vision.
He eagerly accepted the doctrine of the circulation of the blood, then being
taught by Harvey, and was an excellent anatomist.

You doubtless know Professor Huxley's article on Descartes in the Lay
Sermons, and you perceive in what high estimation he is there held.

He originated the hypothesis that animals are automata, for which indeed
there is much to be said from some points of view; but he unfortunately
believed that they were unconscious and non-sentient automata, and this
belief led his disciples into acts of abominable cruelty. Professor Huxley
lectured on this hypothesis and partially upheld it not many years since. The
article is included in his volume called Science and Culture.

Concerning his work in mathematics and physics I can speak with more
confidence. He is the author of the Cartesian system of algebraic or analytic
geometry, which has been so powerful an engine of research, far easier to
wield than the old synthetic geometry. Without it Newton could never have

written the Principia, or made his greatest discoveries. He might indeed
have invented it for himself, but it would have consumed some of his life to
have brought it to the necessary perfection.
The principle of it is the specification of the position of a point in a plane by two
numbers, indicating say its distance from two lines of reference in the plane; like the
latitude and longitude of a place on the globe. For instance, the two lines of reference
might be the bottom edge and the left-hand vertical edge of a wall; then a point on the
wall, stated as being for instance 6 feet along and 2 feet up, is precisely determined.
These two distances are called co-ordinates; horizontal ones are usually denoted by x,
and vertical ones by y.

If, instead of specifying two things, only one statement is made, such as y = 2, it is
satisfied by a whole row of points, all the points in a horizontal line 2 feet above the
ground. Hence y = 2 may be said to represent that straight line, and is called the
equation to that straight line. Similarly x = 6 represents a vertical straight line 6 feet
(or inches or some other unit) from the left-hand edge. If it is asserted that x = 6 and y
= 2, only one point can be found to satisfy both conditions, viz. the crossing point of
the above two straight lines.

Suppose an equation such as x = y to be given. This also is satisfied by a row of
points, viz. by all those that are equidistant from bottom and left-hand edges. In other
words, x = y represents a straight line slanting upwards at 45°. The equation x = 2y
represents another straight line with a different angle of slope, and so on. The
equation x2 + y2 = 36 represents a circle of radius 6. The equation 3x2 + 4y2 = 25
represents an ellipse; and in general every algebraic equation that can be written
down, provided it involve only two variables, x and y, represents some curve in a
plane; a curve moreover that can be drawn, or its properties completely investigated
without drawing, from the equation. Thus algebra is wedded to geometry, and the
investigation of geometric relations by means of algebraic equations is called
analytical geometry, as opposed to the old Euclidian or synthetic mode of treating the
subject by reasoning consciously directed to the subject by help of figures.

If there be three variables—x, y, and z,—instead of only two, an equation among
them represents not a curve in a plane but a surface in space; the three variables
corresponding to the three dimensions of space: length, breadth, and thickness.

An equation with four variables usually requires space of four dimensions for its
geometrical interpretation, and so on.

Thus geometry can not only be reasoned about in a more mechanical and therefore
much easier, manner, but it can be extended into regions of which we have and can
have no direct conception, because we are deficient in sense organs for accumulating
any kind of experience in connexion with such ideas.

Fig. 54.—The eye diagram. [From Descartes' Principia.] Three external points
are shown depicted on the retina: the image being appreciated by a
representation of the brain.

In physics proper Descartes' tract on optics is of considerable historical
interest. He treats all the subjects he takes up in an able and original
manner.

In Astronomy he is the author of that famous and long upheld theory, the
doctrine of vortices.

He regarded space as a plenum full of an all-pervading fluid. Certain
portions of this fluid were in a state of whirling motion, as in a whirlpool or
eddy of water; and each planet had its own eddy, in which it was whirled
round and round, as a straw is caught and whirled in a common whirlpool.
This idea he works out and elaborates very fully, applying it to the system
of the world, and to the explanation of all the motions of the planets.

Fig. 55.—Descartes's diagram of vortices, from his
Principia.

This system evidently supplied a void in men's minds, left vacant by the
overthrow of the Ptolemaic system, and it was rapidly accepted. In the

English Universities it held for a long time almost undisputed sway; it was
in this faith that Newton was brought up.

Something was felt to be necessary to keep the planets moving on their
endless round; the primum mobile of Ptolemy had been stopped; an angel
was sometimes assigned to each planet to carry it round, but though a
widely diffused belief, this was a fantastic and not a serious scientific one.
Descartes's vortices seemed to do exactly what was wanted.

It is true they had no connexion with the laws of Kepler. I doubt whether
he knew about the laws of Kepler; he had not much opinion of other
people's work; he read very little—found it easier to think. (He travelled
through Florence once when Galileo was at the height of his renown
without calling upon or seeing him.) In so far as the motion of a planet was
not circular, it had to be accounted for by the jostling and crowding and
distortion of the vortices.

Gravitation he explained by a settling down of bodies toward the centre
of each vortex; and cohesion by an absence of relative motion tending to
separate particles of matter. He "can imagine no stronger cement."

The vortices, as Descartes imagined them, are not now believed in. Are
we then to regard the system as absurd and wholly false? I do not see how
we can do this, when to this day philosophers are agreed in believing space
to be completely full of fluid, which fluid is certainly capable of vortex
motion, and perhaps everywhere does possess that motion. True, the now
imagined vortices are not the large whirls of planetary size, they are rather
infinitesimal whirls of less than atomic dimensions; still a whirling fluid is
believed in to this day, and many are seeking to deduce all the properties of
matter (rigidity, elasticity, cohesion gravitation, and the rest) from it.

Further, although we talk glibly about gravitation and magnetism, and so
on, we do not really know what they are. Progress is being made, but we do
not yet properly know. Much, overwhelmingly much, remains to be
discovered, and it ill-behoves us to reject any well-founded and long-held

theory as utterly and intrinsically false and absurd. The more one gets to
know, the more one perceives a kernel of truth even in the most singular
statements; and scientific men have learned by experience to be very careful
how they lop off any branch of the tree of knowledge, lest as they cut away
the dead wood they lose also some green shoot, some healthy bud of
unperceived truth.

However, it may be admitted that the idea of a Cartesian vortex in
connexion with the solar system applies, if at all, rather to an earlier—its
nebulous—stage, when the whole thing was one great whirl, ready to split
or shrink off planetary rings at their appropriate distances.

Soon after he had written his great work, the Principia Mathematica,
and before he printed it, news reached him of the persecution and
recantation of Galileo. "He seems to have been quite thunderstruck at the
tidings," says Mr. Mahaffy, in his Life of Descartes.[15] "He had started on
his scientific journeys with the firm determination to enter into no conflict
with the Church, and to carry out his system of pure mathematics and
physics without ever meddling with matters of faith. He was rudely
disillusioned as to the possibility of this severance. He wrote at once—
apparently, November 20th, 1633—to Mersenne to say he would on no
account publish his work—nay, that he had at first resolved to burn all his
papers, for that he would never prosecute philosophy at the risk of being
censured by his Church. 'I could hardly have believed,' he says, 'that an
Italian, and in favour with the Pope as I hear, could be considered criminal
for nothing else than for seeking to establish the earth's motion; though I
know it has formerly been censured by some Cardinals. But I thought I had
heard that since then it was constantly being taught, even at Rome; and I
confess that if the opinion of the earth's movement is false, all the
foundations of my philosophy are so also, because it is demonstrated clearly
by them. It is so bound up with every part of my treatise that I could not
sever it without making the remainder faulty; and although I consider all
my conclusions based on very certain and clear demonstrations, I would not
for all the world sustain them against the authority of the Church.'"

Ten years later, however, he did publish the book, for he had by this time
hit on an ingenious compromise. He formally denied that the earth moved,
and only asserted that it was carried along with its water and air in one of
those larger motions of the celestial ether which produce the diurnal and
annual revolutions of the solar system. So, just as a passenger on the deck
of a ship might be called stationary, so was the earth. He gives himself out
therefore as a follower of Tycho rather than of Copernicus, and says if the
Church won't accept this compromise he must return to the Ptolemaic
system; but he hopes they won't compel him to do that, seeing that it is
manifestly untrue.

This elaborate deference to the powers that be did not indeed save the
work from being ultimately placed upon the forbidden list by the Church,
but it saved himself, at any rate, from annoying persecution. He was not,
indeed, at all willing to be persecuted, and would no doubt have at once
withdrawn anything they wished. I should be sorry to call him a time-
server, but he certainly had plenty of that worldly wisdom in which some of
his predecessors had been so lamentably deficient. Moreover, he was really
a sceptic, and cared nothing at all about the Church or its dogmas. He knew
the Church's power, however, and the advisability of standing well with it:
he therefore professed himself a Catholic, and studiously kept his science
and his Christianity distinct.

In saying that he was a sceptic you must not understand that he was in
the least an atheist. Very few men are; certainly Descartes never thought of
being one. The term is indeed ludicrously inapplicable to him, for a great
part of his philosophy is occupied with what he considers a rigorous proof
of the existence of the Deity.

At the age of fifty-three he was sent for to Stockholm by Christina,
Queen of Sweden, a young lady enthusiastically devoted to study of all
kinds and determined to surround her Court with all that was most famous
in literature and science. Thither, after hesitation, Descartes went. He
greatly liked royalty, but he dreaded the cold climate. Born in Touraine, a

Swedish winter was peculiarly trying to him, especially as the energetic
Queen would have lessons given her at five o'clock in the morning. She
intended to treat him well, and was immensely taken with him; but this
getting up at five o'clock on a November morning, to a man accustomed all
his life to lie in bed till eleven, was a cruel hardship. He was too much of a
courtier, however, to murmur, and the early morning audience continued.
His health began to break down: he thought of retreating, but suddenly he
gave way and became delirious. The Queen's physician attended him, and
of course wanted to bleed him. This, knowing all he knew of physiology,
sent him furious, and they could do nothing with him. After some days he
became quiet, was bled twice, and gradually sank, discoursing with great
calmness on his approaching death, and duly fortified with all the rites of
the Catholic Church.

His general method of research was as nearly as possible a purely
deductive one:—i.e., after the manner of Euclid he starts with a few simple
principles, and then, by a chain of reasoning, endeavours to deduce from
them their consequences, and so to build up bit by bit an edifice of
connected knowledge. In this he was the precursor of Newton. This method,
when rigorously pursued, is the most powerful and satisfactory of all, and
results in an ordered province of science far superior to the fragmentary
conquests of experiment. But few indeed are the men who can handle it
safely and satisfactorily: and none without continual appeals to experiment
for verification. It was through not perceiving the necessity for verification
that he erred. His importance to science lies not so much in what he actually
discovered as in his anticipation of the right conditions for the solution of
problems in physical science. He in fact made the discovery that Nature
could after all be interrogated mathematically—a fact that was in great
danger of remaining unknown. For, observe, that the mathematical study of
Nature, the discovery of truth with a piece of paper and a pen, has a perilous
similarity at first sight to the straw-thrashing subtleties of the Greeks,
whose methods of investigating nature by discussing the meaning of words

and the usage of language and the necessities of thought, had proved to be
so futile and unproductive.

A reaction had set in, led by Galileo, Gilbert, and the whole modern
school of experimental philosophers, lasting down to the present day:—men
who teach that the only right way of investigating Nature is by experiment
and observation.

It is indeed a very right and an absolutely necessary way; but it is not the
only way. A foundation of experimental fact there must be; but upon this a
great structure of theoretical deduction can be based, all rigidly connected
together by pure reasoning, and all necessarily as true as the premises,
provided no mistake is made. To guard against the possibility of mistake
and oversight, especially oversight, all conclusions must sooner or later be
brought to the test of experiment; and if disagreeing therewith, the theory
itself must be re-examined, and the flaw discovered, or else the theory must
be abandoned.

Of this grand method, quite different from the gropings in the dark of
Kepler—this method, which, in combination with experiment, has made
science what it now is—this which in the hands of Newton was to lead to
such stupendous results, we owe the beginning and early stages to René
Descartes.

S UM M ARY OF FACT S F OR L E CT URE S VI I AND
VI I I

Otto Guericke 1602–1686
Hon. Robert Boyle 1626–1691
Huyghens 1629–1695
Christopher Wren 1632–1723
Robert Hooke 1635–1702

Newton 1642–1727
Edmund Halley 1656–1742
James Bradley 1692–1762

Chronology of Newton's Life.

Isaac Newton was born at Woolsthorpe, near Grantham, Lincolnshire, on
Christmas Day, 1642. His father, a small freehold farmer, also named Isaac,
died before his birth. His mother, née Hannah Ayscough, in two years
married a Mr. Smith, rector of North Witham, but was again left a widow in
1656. His uncle, W. Ayscough, was rector of a near parish and a graduate of
Trinity College, Cambridge. At the age of fifteen Isaac was removed from
school at Grantham to be made a farmer of, but as it seemed he would not
make a good one his uncle arranged for him to return to school and thence
to Cambridge, where he entered Trinity College as a sub-sizar in 1661.
Studied Descartes's geometry. Found out a method of infinite series in 1665,
and began the invention of Fluxions. In the same year and the next he was
driven from Cambridge by the plague. In 1666, at Woolsthorpe, the apple
fell. In 1667 he was elected a fellow of his college, and in 1669 was
specially noted as possessing an unparalleled genius by Dr. Barrow, first
Lucasian Professor of Mathematics. The same year Dr. Barrow retired from
his chair in favour of Newton, who was thus elected at the age of twenty-
six. He lectured first on optics with great success. Early in 1672 he was
elected a Fellow of the Royal Society, and communicated his researches in
optics, his reflecting telescope, and his discovery of the compound nature of
white light. Annoying controversies arose; but he nevertheless contributed a
good many other most important papers in optics, including observations in
diffraction, and colours of thin plates. He also invented the modern sextant.
In 1672 a letter from Paris was read at the Royal Society concerning a new
and accurate determination of the size of the earth by Picard. When Newton
heard of it he began the Principia, working in silence. In 1684 arose a
discussion between Wren, Hooke, and Halley concerning the law of inverse
square as applied to gravity and the path it would cause the planets to
describe. Hooke asserted that he had a solution, but he would not produce

it. After waiting some time for it Halley went to Cambridge to consult
Newton on the subject, and thus discovered the existence of the first part of
the Principia, wherein all this and much more was thoroughly worked out.
On his representations to the Royal Society the manuscript was asked for,
and when complete was printed and published in 1687 at Halley's expense.
While it was being completed Newton and seven others were sent to uphold
the dignity of the University, before the Court of High Commission and
Judge Jeffreys, against a high-handed action of James II. In 1682 he was
sent to Parliament, and was present at the coronation of William and Mary.
Made friends with Locke. In 1694 Montague, Lord Halifax, made him
Warden, and in 1697 Master, of the Mint. Whiston succeeded him as
Lucasian Professor. In 1693 the method of fluxions was published. In 1703
Newton was made President of the Royal Society, and held the office to the
end of his life. In 1705 he was knighted by Anne. In 1713 Cotes helped him
to bring out a new edition of the Principia, completed as we now have it.
On the 20th of March 1727, he died: having lived from Charles I. to George
II.

The Laws of Motion, discovered by Galileo, stated by Newton.

Law 1.—If no force acts on a body in motion, it continues to move
uniformly in a straight line.

Law 2.—If force acts on a body, it produces a change of motion
proportional to the force and in the same direction.

Law 3.—When one body exerts force on another, that other reacts with
equal force upon the one.

LECTURE VII

SIR ISAAC NEWTON

The little hamlet of Woolsthorpe lies close to the village of Colsterworth,
about six miles south of Grantham, in the county of Lincoln. In the manor
house of Woolsthorpe, on Christmas Day, 1642, was born to a widowed
mother a sickly infant who seemed not long for this world. Two women
who were sent to North Witham to get some medicine for him scarcely
expected to find him alive on their return. However, the child lived, became
fairly robust, and was named Isaac, after his father. What sort of a man this
father was we do not know. He was what we may call a yeoman, that most
wholesome and natural of all classes. He owned the soil he tilled, and his
little estate had already been in the family for some hundred years. He was
thirty-six when he died, and had only been married a few months.

Of the mother, unfortunately, we know almost as little. We hear that she
was recommended by a parishioner to the Rev. Barnabas Smith, an old
bachelor in search of a wife, as "the widow Newton—an extraordinary good
woman:" and so I expect she was, a thoroughly sensible, practical, homely,
industrious, middle-class, Mill-on-the-Floss sort of woman. However, on
her second marriage she went to live at North Witham, and her mother, old
Mrs. Ayscough, came to superintend the farm at Woolsthorpe, and take care
of young Isaac.

By her second marriage his mother acquired another piece of land,
which she settled on her first son; so Isaac found himself heir to two little
properties, bringing in a rental of about £80 a year.

Fig. 56.—Manor-house of Woolsthorpe.

He had been sent to a couple of village schools to acquire the ordinary
accomplishments taught at those places, and for three years to the grammar
school at Grantham, then conducted by an old gentleman named Mr.
Stokes. He had not been very industrious at school, nor did he feel keenly
the fascinations of the Latin Grammar, for he tells us that he was the last
boy in the lowest class but one. He used to pay much more attention to the
construction of kites and windmills and waterwheels, all of which he made
to work very well. He also used to tie paper lanterns to the tail of his kite, so
as to make the country folk fancy they saw a comet, and in general to
disport himself as a boy should.

It so happened, however, that he succeeded in thrashing, in fair fight, a
bigger boy who was higher in the school, and who had given him a kick.
His success awakened a spirit of emulation in other things than boxing, and
young Newton speedily rose to be top of the school.

Under these circumstances, at the age of fifteen, his mother, who had
now returned to Woolsthorpe, which had been rebuilt, thought it was time to
train him for the management of his land, and to make a farmer and grazier
of him. The boy was doubtless glad to get away from school, but he did not
take kindly to the farm—especially not to the marketing at Grantham. He

and an old servant were sent to Grantham every week to buy and sell
produce, but young Isaac used to leave his old mentor to do all the business,
and himself retire to an attic in the house he had lodged in when at school,
and there bury himself in books.

After a time he didn't even go through the farce of visiting Grantham at
all; but stopped on the road and sat under a hedge, reading or making some
model, until his companion returned.

We hear of him now in the great storm of 1658, the storm on the day
Cromwell died, measuring the force of the wind by seeing how far he could
jump with it and against it. He also made a water-clock and set it up in the
house at Grantham, where it kept fairly good time so long as he was in the
neighbourhood to look after it occasionally.

At his own home he made a couple of sundials on the side of the wall
(he began by marking the position of the sun by the shadow of a peg driven
into the wall, but this gradually developed into a regular dial) one of which
remained of use for some time; and was still to be seen in the same place
during the first half of the present century, only with the gnomon gone. In
1844 the stone on which it was carved was carefully extracted and
presented to the Royal Society, who preserve it in their library. The letters
WTON roughly carved on it are barely visible.

All these pursuits must have been rather trying to his poor mother, and
she probably complained to her brother, the rector of Burton Coggles: at
any rate this gentleman found master Newton one morning under a hedge
when he ought to have been farming. But as he found him working away at
mathematics, like a wise man he persuaded his sister to send the boy back
to school for a short time, and then to Cambridge. On the day of his finally
leaving school old Mr. Stokes assembled the boys, made them a speech in
praise of Newton's character and ability, and then dismissed him to
Cambridge.

At Trinity College a new world opened out before the country-bred lad.
He knew his classics passably, but of mathematics and science he was
ignorant, except through the smatterings he had picked up for himself. He
devoured a book on logic, and another on Kepler's Optics, so fast that his
attendance at lectures on these subjects became unnecessary. He also got
hold of a Euclid and of Descartes's Geometry. The Euclid seemed childishly
easy, and was thrown aside, but the Descartes baffled him for a time.
However, he set to it again and again and before long mastered it. He threw
himself heart and soul into mathematics, and very soon made some
remarkable discoveries. First he discovered the binomial theorem: familiar
now to all who have done any algebra, unintelligible to others, and
therefore I say nothing about it. By the age of twenty-one or two he had
begun his great mathematical discovery of infinite series and fluxions—
now known by the name of the Differential Calculus. He wrote these things
out and must have been quite absorbed in them, but it never seems to have
occurred to him to publish them or tell any one about them.

In 1664 he noticed some halos round the moon, and, as his manner was,
he measured their angles—the small ones 3 and 5 degrees each, the larger
one 22°·35. Later he gave their theory.
Small coloured halos round the moon are often seen, and are said to be a sign of
rain. They are produced by the action of minute globules of water or cloud particles
upon light, and are brightest when the particles are nearly equal in size. They are not
like the rainbow, every part of which is due to light that has entered a raindrop, and
been refracted and reflected with prismatic separation of colours; a halo is caused by
particles so small as to be almost comparable with the size of waves of light, in a way
which is explained in optics under the head "diffraction." It may be easily imitated by
dusting an ordinary piece of window-glass over with lycopodium, placing a candle
near it, and then looking at the candle-flame through the dusty glass from a fair
distance. Or you may look at the image of a candle in a dusted looking-glass.
Lycopodium dust is specially suitable, for its granules are remarkably equal in size.
The large halo, more rarely seen, of angular radius 22°·35, is due to another cause
again, and is a prismatic effect, although it exhibits hardly any colour. The angle 22½°
is characteristic of refraction in crystals with angles of 60° and refractive index about
the same as water; in other words this halo is caused by ice crystals in the higher
regions of the atmosphere.

He also the same year observed a comet, and sat up so late watching it
that he made himself ill. By the end of the year he was elected to a
scholarship and took his B.A. degree. The order of merit for that year never
existed or has not been kept. It would have been interesting, not as a
testimony to Newton, but to the sense or non-sense of the examiners. The
oldest Professorship of Mathematics at the University of Cambridge, the
Lucasian, had not then been long founded, and its first occupant was Dr.
Isaac Barrow, an eminent mathematician, and a kind old man. With him
Newton made good friends, and was helpful in preparing a treatise on optics
for the press. His help is acknowledged by Dr. Barrow in the preface, which
states that he had corrected several errors and made some capital additions
of his own. Thus we see that, although the chief part of his time was
devoted to mathematics, his attention was already directed to both optics
and astronomy. (Kepler, Descartes, Galileo, all combined some optics with
astronomy. Tycho and the old ones combined alchemy; Newton dabbled in
this also.)

Newton reached the age of twenty-three in 1665, the year of the Great
Plague. The plague broke out in Cambridge as well as in London, and the
whole college was sent down. Newton went back to Woolsthorpe, his mind
teeming with ideas, and spent the rest of this year and part of the next in
quiet pondering. Somehow or other he had got hold of the notion of
centrifugal force. It was six years before Huyghens discovered and
published the laws of centrifugal force, but in some quiet way of his own
Newton knew about it and applied the idea to the motion of the planets.

We can almost follow the course of his thoughts as he brooded and
meditated on the great problem which had taxed so many previous thinkers,
—What makes the planets move round the sun? Kepler had discovered how
they moved, but why did they so move, what urged them?

Even the "how" took a long time—all the time of the Greeks, through
Ptolemy, the Arabs, Copernicus, Tycho: circular motion, epicycles, and
excentrics had been the prevailing theory. Kepler, with his marvellous

industry, had wrested from Tycho's observations the secret of their orbits.
They moved in ellipses with the sun in one focus. Their rate of description
of area, not their speed, was uniform and proportional to time.

Yes, and a third law, a mysterious law of unintelligible import, had also
yielded itself to his penetrating industry—a law the discovery of which had
given him the keenest delight, and excited an outburst of rapture—viz. that
there was a relation between the distances and the periodic times of the
several planets. The cubes of the distances were proportional to the squares
of the times for the whole system. This law, first found true for the six
primary planets, he had also extended, after Galileo's discovery, to the four
secondary planets, or satellites of Jupiter (p. 81).

But all this was working in the dark—it was only the first step—this
empirical discovery of facts; the facts were so, but how came they so? What
made the planets move in this particular way? Descartes's vortices was an
attempt, a poor and imperfect attempt, at an explanation. It had been hailed
and adopted throughout Europe for want of a better, but it did not satisfy
Newton. No, it proceeded on a wrong tack, and Kepler had proceeded on a
wrong tack in imagining spokes or rays sticking out from the sun and
driving the planets round like a piece of mechanism or mill work. For, note
that all these theories are based on a wrong idea—the idea, viz., that some
force is necessary to maintain a body in motion. But this was contrary to the
laws of motion as discovered by Galileo. You know that during his last
years of blind helplessness at Arcetri, Galileo had pondered and written
much on the laws of motion, the foundation of mechanics. In his early
youth, at Pisa, he had been similarly occupied; he had discovered the
pendulum, he had refuted the Aristotelians by dropping weights from the
leaning tower (which we must rejoice that no earthquake has yet injured),
and he had returned to mechanics at intervals all his life; and now, when his
eyes were useless for astronomy, when the outer world has become to him
only a prison to be broken by death, he returns once more to the laws of
motion, and produces the most solid and substantial work of his life.

For this is Galileo's main glory—not his brilliant exposition of the
Copernican system, not his flashes of wit at the expense of a moribund
philosophy, not his experiments on floating bodies, not even his telescope
and astronomical discoveries—though these are the most taking and
dazzling at first sight. No; his main glory and title to immortality consists in
this, that he first laid the foundation of mechanics on a firm and secure basis
of experiment, reasoning, and observation. He first discovered the true
Laws of Motion.

I said little of this achievement in my lecture on him; for the work was
written towards the end of his life, and I had no time then. But I knew I
should have to return to it before we came to Newton, and here we are.

You may wonder how the work got published when so many of his
manuscripts were destroyed. Horrible to say, Galileo's own son destroyed a
great bundle of his father's manuscripts, thinking, no doubt, thereby to save
his own soul. This book on mechanics was not burnt, however. The fact is it
was rescued by one or other of his pupils, Toricelli or Viviani, who were
allowed to visit him in his last two or three years; it was kept by them for
some time, and then published surreptitiously in Holland. Not that there is
anything in it bearing in any visible way on any theological controversy;
but it is unlikely that the Inquisition would have suffered it to pass
notwithstanding.

I have appended to the summary preceding this lecture (p. 160) the three
axioms or laws of motion discovered by Galileo. They are stated by Newton
with unexampled clearness and accuracy, and are hence known as Newton's
laws, but they are based on Galileo's work. The first is the simplest; though
ignorance of it gave the ancients a deal of trouble. It is simply a statement
that force is needed to change the motion of a body; i.e. that if no force act
on a body it will continue to move uniformly both in speed and direction—
in other words, steadily, in a straight line. The old idea had been that some
force was needed to maintain motion. On the contrary, the first law asserts,
some force is needed to destroy it. Leave a body alone, free from all friction

or other retarding forces, and it will go on for ever. The planetary motion
through empty space therefore wants no keeping up; it is not the motion that
demands a force to maintain it, it is the curvature of the path that needs a
force to produce it continually. The motion of a planet is approximately
uniform so far as speed is concerned, but it is not constant in direction; it is
nearly a circle. The real force needed is not a propelling but a deflecting
force.

The second law asserts that when a force acts, the motion changes, either
in speed or in direction, or both, at a pace proportional to the magnitude of
the force, and in the same direction as that in which the force acts. Now
since it is almost solely in direction that planetary motion alters, a
deflecting force only is needed; a force at right angles to the direction of
motion, a force normal to the path. Considering the motion as circular, a
force along the radius, a radial or centripetal force, must be acting
continually. Whirl a weight round and round by a bit of elastic, the elastic is
stretched; whirl it faster, it is stretched more. The moving mass pulls at the
elastic—that is its centrifugal force; the hand at the centre pulls also—that
is centripetal force.

The third law asserts that these two forces are equal, and together
constitute the tension in the elastic. It is impossible to have one force alone,
there must be a pair. You can't push hard against a body that offers no
resistance. Whatever force you exert upon a body, with that same force the
body must react upon you. Action and reaction are always equal and
opposite.

Sometimes an absurd difficulty is felt with respect to this, even by
engineers. They say, "If the cart pulls against the horse with precisely the
same force as the horse pulls the cart, why should the cart move?" Why on
earth not? The cart moves because the horse pulls it, and because nothing
else is pulling it back. "Yes," they say, "the cart is pulling back." But what is
it pulling back? Not itself, surely? "No, the horse." Yes, certainly the cart is
pulling at the horse; if the cart offered no resistance what would be the good

of the horse? That is what he is for, to overcome the pull-back of the cart;
but nothing is pulling the cart back (except, of course, a little friction), and
the horse is pulling it forward, hence it goes forward. There is no puzzle at
all when once you realise that there are two bodies and two forces acting,
and that one force acts on each body.[16]

If, indeed, two balanced forces acted on one body that would be in
equilibrium, but the two equal forces contemplated in the third law act on
two different bodies, and neither is in equilibrium.

So much for the third law, which is extremely simple, though it has
extraordinarily far-reaching consequences, and when combined with a
denial of "action at a distance," is precisely the principle of the
Conservation of Energy. Attempts at perpetual motion may all be regarded
as attempts to get round this "third law."

Fig. 57.
On the subject of the second law a great deal more has to be said before it can be in
any proper sense even partially appreciated, but a complete discussion of it would
involve a treatise on mechanics. It is the law of mechanics. One aspect of it we must
attend to now in order to deal with the motion of the planets, and that is the fact that
the change of motion of a body depends solely and simply on the force acting, and not
at all upon what the body happens to be doing at the time it acts. It may be stationary,
or it may be moving in any direction; that makes no difference.

Thus, referring back to the summary preceding Lecture IV, it is there stated that a
dropped body falls 16 feet in the first second, that in two seconds it falls 64 feet, and
so on, in proportion to the square of the time. So also will it be the case with a thrown

body, but the drop must be reckoned from its line of motion—the straight line which,
but for gravity, it would describe.

Thus a stone thrown from O with the velocity OA would in one second find itself
at A, in two seconds at B, in three seconds at C, and so on, in accordance with the first
law of motion, if no force acted. But if gravity acts it will have fallen 16 feet by the
time it would have got to A, and so will find itself at P. In two seconds it will be at Q,
having fallen a vertical height of 64 feet; in three seconds it will be at R, 144 feet
below C; and so on. Its actual path will be a curve, which in this case is a parabola.
(Fig. 57.)

If a cannon is pointed horizontally over a level plain, the cannon ball will be just as
much affected by gravity as if it were dropped, and so will strike the plain at the same
instant as another which was simply dropped where it started. One ball may have
gone a mile and the other only dropped a hundred feet or so, but the time needed by
both for the vertical drop will be the same. The horizontal motion of one is an extra,
and is due to the powder.

As a matter of fact the path of a projectile in vacuo is only approximately a
parabola. It is instructive to remember that it is really an ellipse with one focus very
distant, but not at infinity. One of its foci is the centre of the earth. A projectile is
really a minute satellite of the earth's, and in vacuo it accurately obeys all Kepler's
laws. It happens not to be able to complete its orbit, because it was started
inconveniently close to the earth, whose bulk gets in its way; but in that respect the
earth is to be reckoned as a gratuitous obstruction, like a target, but a target that differs
from most targets in being hard to miss.

Fig. 58.

Now consider circular motion in the same way, say a ball whirled round by a
string. (Fig. 58.)

Attending to the body at O, it is for an instant moving towards A, and if no force
acted it would get to A in a time which for brevity we may call a second. But a force,
the pull of the string, is continually drawing it towards S, and so it really finds itself at
P, having described the circular arc OP, which may be considered to be compounded
of, and analyzable into the rectilinear motion OA and the drop AP. At P it is for an
instant moving towards B, and the same process therefore carries it to Q; in the third
second it gets to R; and so on: always falling, so to speak, from its natural rectilinear
path, towards the centre, but never getting any nearer to the centre.

The force with which it has thus to be constantly pulled in towards the centre, or,
which is the same thing, the force with which it is tugging at whatever constraint it is
that holds it in, is mv2/r; where m is the mass of the particle, v its velocity, and r the
radius of its circle of movement. This is the formula first given by Huyghens for
centrifugal force.

We shall find it convenient to express it in terms of the time of one revolution, say
T. It is easily done, since plainly T = circumference/speed = 2πr/v; so the above
expression for centrifugal force becomes 4π2mr/T2.

As to the fall of the body towards the centre every microscopic unit of time, it is
easily reckoned. For by Euclid III. 36, and Fig. 58, AP.AA' = AO2. Take A very near
O, then OA = vt, and AA' = 2r; so AP = v2t2/2r = 2π2r t2/T2; or the fall per second is
2π2r/T2, r being its distance from the centre, and T its time of going once round.

In the case of the moon for instance, r is 60 earth radii; more exactly 60·2; and T is
a lunar month, or more precisely 27 days, 7 hours, 43 minutes, and 11½ seconds.
Hence the moon's deflection from the tangential or rectilinear path every minute
comes out as very closely 16 feet (the true size of the earth being used).

Returning now to the case of a small body revolving round a big one,
and assuming a force directly proportional to the mass of both bodies, and
inversely proportional to the square of the distance between them: i.e.
assuming the known force of gravity, it is
V Mm
r2

where V is a constant, called the gravitation constant, to be determined by
experiment.

If this is the centripetal force pulling a planet or satellite in, it must be
equal to the centrifugal force of this latter, viz. (see above).

4π2mr
T2

Equate the two together, and at once we get

r3 V
= M;
T2 4π2

or, in words, the cube of the distance divided by the square of the periodic
time for every planet or satellite of the system under consideration, will be
constant and proportional to the mass of the central body.

This is Kepler's third law, with a notable addition. It is stated above for
circular motion only, so as to avoid geometrical difficulties, but even so it is
very instructive. The reason of the proportion between r3 and T2 is at once
manifest; and as soon as the constant V became known, the mass of the
central body, the sun in the case of a planet, the earth in the case of the
moon, Jupiter in the case of his satellites, was at once determined.

Newton's reasoning at this time might, however, be better displayed
perhaps by altering the order of the steps a little, as thus:—

The centrifugal force of a body is proportional to r3/T2, but by Kepler's
third law r3/T2 is constant for all the planets, reckoning r from the sun.
Hence the centripetal force needed to hold in all the planets will be a single
force emanating from the sun and varying inversely with the square of the
distance from that body.

Such a force is at once necessary and sufficient. Such a force would
explain the motion of the planets.

But then all this proceeds on a wrong assumption—that the planetary
motion is circular. Will it hold for elliptic orbits? Will an inverse square law

of force keep a body moving in an elliptic orbit about the sun in one focus?
This is a far more difficult question. Newton solved it, but I do not believe
that even he could have solved it, except that he had at his disposal two
mathematical engines of great power—the Cartesian method of treating
geometry, and his own method of Fluxions. One can explain the elliptic
motion now mathematically, but hardly otherwise; and I must be content to
state that the double fact is true—viz., that an inverse square law will move
the body in an ellipse or other conic section with the sun in one focus, and
that if a body so moves it must be acted on by an inverse square law.

Fig. 59.

This then is the meaning of the first and third laws of Kepler. What about
the second? What is the meaning of the equable description of areas? Well,
that rigorously proves that a planet is acted on by a force directed to the
centre about which the rate of description of areas is equable. It proves, in
fact, that the sun is the attracting body, and that no other force acts.
For first of all if the first law of motion is obeyed, i.e. if no force acts, and if the
path be equally subdivided to represent equal times, and straight lines be drawn from
the divisions to any point whatever, all these areas thus enclosed will be equal,
because they are triangles on equal base and of the same height (Euclid, I). See Fig.
59; S being any point whatever, and A, B, C, successive positions of a body.

Now at each of the successive instants let the body receive a sudden blow in the
direction of that same point S, sufficient to carry it from A to D in the same time as it

would have got to B if left alone. The result will be that there will be a compromise,
and it will really arrive at P, travelling along the diagonal of the parallelogram AP.
The area its radius vector sweeps out is therefore SAP, instead of what it would have
been, SAB. But then these two areas are equal, because they are triangles on the same
base AS, and between the same parallels BP, AS; for by the parallelogram law BP is
parallel to AD. Hence the area that would have been described is described, and as all
the areas were equal in the case of no force, they remain equal when the body receives
a blow at the end of every equal interval of time, provided that every blow is actually
directed to S, the point to which radii vectores are drawn.

Fig. 60.

Fig. 61.
It is instructive to see that it does not hold if the blow is any otherwise directed; for
instance, as in Fig. 61, when the blow is along AE, the body finds itself at P at the end
of the second interval, but the area SAP is by no means equal to SAB, and therefore
not equal to SOA, the area swept out in the first interval.

In order to modify Fig. 60 so as to represent continuous motion and steady forces,
we have to take the sides of the polygon OAPQ, &c., very numerous and very small;
in the limit, infinitely numerous and infinitely small. The path then becomes a curve,
and the series of blows becomes a steady force directed towards S. About whatever
point therefore the rate of description of areas is uniform, that point and no other must
be the centre of all the force there is. If there be no force, as in Fig. 59, well and good,
but if there be any force however small not directed towards S, then the rate of
description of areas about S cannot be uniform. Kepler, however, says that the rate of
description of areas of each planet about the sun is, by Tycho's observations, uniform;
hence the sun is the centre of all the force that acts on them, and there is no other
force, not even friction. That is the moral of Kepler's second law.

We may also see from it that gravity does not travel like light, so as to take time on
its journey from sun to planet; for, if it did, there would be a sort of aberration, and the
force on its arrival could no longer be accurately directed to the centre of the sun. (See
Nature, vol. xlvi., p. 497.) It is a matter for accuracy of observation, therefore, to
decide whether the minutest trace of such deviation can be detected, i.e. within what
limits of accuracy Kepler's second law is now known to be obeyed.

I will content myself by saying that the limits are extremely narrow. [Reference
may be made also to p. 208.]

Thus then it became clear to Newton that the whole solar system
depended on a central force emanating from the sun, and varying inversely
with the square of the distance from him: for by that hypothesis all the laws
of Kepler concerning these motions were completely accounted for; and, in
fact, the laws necessitated the hypothesis and established it as a theory.

Similarly the satellites of Jupiter were controlled by a force emanating
from Jupiter and varying according to the same law. And again our moon
must be controlled by a force from the earth, decreasing with the distance
according to the same law.

Grant this hypothetical attracting force pulling the planets towards the
sun, pulling the moon towards the earth, and the whole mechanism of the
solar system is beautifully explained.

If only one could be sure there was such a force! It was one thing to
calculate out what the effects of such a force would be: it was another to be
able to put one's finger upon it and say, this is the force that actually exists
and is known to exist. We must picture him meditating in his garden on this
want—an attractive force towards the earth.

If only such an attractive force pulling down bodies to the earth existed.
An apple falls from a tree. Why, it does exist! There is gravitation, common
gravity that makes bodies fall and gives them their weight.

Wanted, a force tending towards the centre of the earth. It is to hand!

It is common old gravity that had been known so long, that was perfectly
familiar to Galileo, and probably to Archimedes. Gravity that regulates the
motion of projectiles. Why should it only pull stones and apples? Why
should it not reach as high as the moon? Why should it not be the
gravitation of the sun that is the central force acting on all the planets?

Surely the secret of the universe is discovered! But, wait a bit; is it
discovered? Is this force of gravity sufficient for the purpose? It must vary
inversely with the square of the distance from the centre of the earth. How
far is the moon away? Sixty earth's radii. Hence the force of gravity at the
moon's distance can only be 1⁄3600 of what it is on the earth's surface. So,
instead of pulling it 16 ft. per second, it should pull it 16⁄3600 ft. per second,
or 16 ft. a minute.[17] How can one decide whether such a force is able to
pull the moon the actual amount required? To Newton this would seem only
like a sum in arithmetic. Out with a pencil and paper and reckon how much
the moon falls toward the earth in every second of its motion. Is it 16⁄3600?
That is what it ought to be: but is it? The size of the earth comes into the
calculation. Sixty miles make a degree, 360 degrees a circumference. This
gives as the earth's diameter 6,873 miles; work it out.

The answer is not 16 feet a minute, it is 13·9 feet.

Surely a mistake of calculation?

No, it is no mistake: there is something wrong in the theory, gravity is
too strong.

Instead of falling toward the earth 5⅓ hundredths of an inch every
second, as it would under gravity, the moon only falls 4⅔ hundredths of an
inch per second.

With such a discovery in his grasp at the age of twenty-three he is
disappointed—the figures do not agree, and he cannot make them agree.
Either gravity is not the force in action, or else something interferes with it.
Possibly, gravity does part of the work, and the vortices of Descartes
interfere with it.

He must abandon the fascinating idea for the time. In his own words, "he
laid aside at that time any further thought of the matter."

So far as is known, he never mentioned his disappointment to a soul. He
might, perhaps, if he had been at Cambridge, but he was a shy and solitary
youth, and just as likely he might not. Up in Lincolnshire, in the
seventeenth century, who was there for him to consult?

True, he might have rushed into premature publication, after our
nineteenth century fashion, but that was not his method. Publication never
seemed to have occurred to him.

His reticence now is noteworthy, but later on it is perfectly astonishing.
He is so absorbed in making discoveries that he actually has to be reminded
to tell any one about them, and some one else always has to see to the
printing and publishing for him.

I have entered thus fully into what I conjecture to be the stages of this
early discovery of the law of gravitation, as applicable to the heavenly
bodies, because it is frequently and commonly misunderstood. It is
sometimes thought that he discovered the force of gravity; I hope I have
made it clear that he did no such thing. Every educated man long before his
time, if asked why bodies fell, would reply just as glibly as they do now,
"Because the earth attracts them," or "because of the force of gravity."

His discovery was that the motions of the solar system were due to the
action of a central force, directed to the body at the centre of the system,
and varying inversely with the square of the distance from it. This discovery
was based upon Kepler's laws, and was clear and certain. It might have been
published had he so chosen.

But he did not like hypothetical and unknown forces; he tried to see
whether the known force of gravity would serve. This discovery at that time
he failed to make, owing to a wrong numerical datum. The size of the earth
he only knew from the common doctrine of sailors that 60 miles make a
degree; and that threw him out. Instead of falling 16 feet a minute, as it
ought under gravity, it only fell 13·9 feet, so he abandoned the idea. We do
not find that he returned to it for sixteen years.

LECTURE VIII

NEWTON AND THE LAW OF GRAVITATION

We left Newton at the age of twenty-three on the verge of discovering
the mechanism of the solar system, deterred therefrom only by an error in
the then imagined size of the earth. He had proved from Kepler's laws that a
centripetal force directed to the sun, and varying as the inverse square of the
distance from that body, would account for the observed planetary motions,
and that a similar force directed to the earth would account for the lunar
motion; and it had struck him that this force might be the very same as the
familiar force of gravitation which gave to bodies their weight: but in
attempting a numerical verification of this idea in the case of the moon he
was led by the then received notion that sixty miles made a degree on the
earth's surface into an erroneous estimate of the size of the moon's orbit.
Being thus baffled in obtaining such verification, he laid the matter aside
for a time.

The anecdote of the apple we learn from Voltaire, who had it from
Newton's favourite niece, who with her husband lived and kept house for
him all his later life. It is very like one of those anecdotes which are easily
invented and believed in, and very often turn out on scrutiny to have no
foundation. Fortunately this anecdote is well authenticated, and moreover is
intrinsically probable; I say fortunately, because it is always painful to have
to give up these child-learnt anecdotes, like Alfred and the cakes and so on.
This anecdote of the apple we need not resign. The tree was blown down in
1820 and part of its wood is preserved.

I have mentioned Voltaire in connection with Newton's philosophy. This
acute critic at a later stage did a good deal to popularise it throughout
Europe and to overturn that of his own countryman Descartes. Cambridge

rapidly became Newtonian, but Oxford remained Cartesian for fifty years or
more. It is curious what little hold science and mathematics have ever
secured in the older and more ecclesiastical University. The pride of
possessing Newton has however no doubt been the main stimulus to the
special pursuits of Cambridge.

He now began to turn his attention to optics, and, as was usual with him,
his whole mind became absorbed in this subject as if nothing else had ever
occupied him. His cash-book for this time has been discovered, and the
entries show that he is buying prisms and lenses and polishing powder at
the beginning of 1667. He was anxious to improve telescopes by making
more perfect lenses than had ever been used before. Accordingly he
calculated out their proper curves, just as Descartes had also done, and then
proceeded to grind them as near as he could to those figures. But the images
did not please him; they were always blurred and rather indistinct.

At length, it struck him that perhaps it was not the lenses but the light
which was at fault. Perhaps light was so composed that it could not be
focused accurately to a sharp and definite point. Perhaps the law of
refraction was not quite accurate, but only an approximation. So he bought
a prism to try the law. He let in sunlight through a small round hole in a
window shutter, inserted the prism in the light, and received the deflected
beam on a white screen; turning the prism about till it was deviated as little
as possible. The patch on the screen was not a round disk, as it would have
been without the prism, but was an elongated oval and was coloured at its
extremities. Evidently refraction was not a simple geometrical deflection of
a ray, there was a spreading out as well.

Fig. 63.—A prism not only deviates a beam of sunlight, but also spreads it out or
disperses it.

Why did the image thus spread out? If it were due to irregularities in the
glass a second prism should rather increase them, but a second prism when
held in appropriate position was able to neutralise the dispersion and to
reproduce the simple round white spot without deviation. Evidently the
spreading out of the beam was connected in some definite way with its
refraction. Could it be that the light particles after passing through the prism
travelled in variously curved lines, as spinning racquet balls do? To
examine this he measured the length of the oval patch when the screen was
at different distances from the prism, and found that the two things were
directly proportional to each other. Doubling the distance of the screen
doubled the length of the patch. Hence the rays travelled in straight lines
from the prism, and the spreading out was due to something that occurred
within its substance. Could it be that white light was compound, was a
mixture of several constituents, and that its different constituents were
differently bent? No sooner thought than tried. Pierce the screen to let one
of the constituents through and interpose a second prism in its path. If the
spreading out depended on the prism only it should spread out just as much
as before, but if it depended on the complex character of white light, this
isolated simple constituent should be able to spread out no more. It did not
spread out any more: a prism had no more dispersive power over it; it was
deflected by the appropriate amount, but it was not analysed into
constituents. It differed from sunlight in being simple. With many ingenious

and beautifully simple experiments, which are quoted in full in several
books on optics, he clinched the argument and established his discovery.
White light was not simple but compound. It could be sorted out by a prism
into an infinite number of constituent parts which were differently refracted,
and the most striking of which Newton named violet, indigo, blue, green,
yellow, orange, and red.

Fig. 64.—A single constituent of white light, obtained by the use of perforated
screens is capable of no more dispersion.

At once the true nature of colour became manifest. Colour resided not in
the coloured object as had till now been thought, but in the light which
illuminated it. Red glass for instance adds nothing to sunlight. The light
does not get dyed red by passing through the glass; all that the red glass
does is to stop and absorb a large part of the sunlight; it is opaque to the
larger portion, but it is transparent to that particular portion which affects
our eyes with the sensation of red. The prism acts like a sieve sorting out
the different kinds of light. Coloured media act like filters, stopping certain
kinds but allowing the rest to go through. Leonardo's and all the ancient
doctrines of colour had been singularly wrong; colour is not in the object
but in the light.

Goethe, in his Farbenlehre, endeavoured to controvert Newton, and to
reinstate something more like the old views; but his failure was complete.

Refraction analysed out the various constituents of white light and
displayed them in the form of a series of overlapping images of the
aperture, each of a different colour; this series of images we call a spectrum,
and the operation we now call spectrum analysis. The reason of the defect
of lenses was now plain: it was not so much a defect of the lens as a defect

of light. A lens acts by refraction and brings rays to a focus. If light be
simple it acts well, but if ordinary white light fall upon a lens, its different
constituents have different foci; every bright object is fringed with colour,
and nothing like a clear image can be obtained.

Fig. 65.—Showing the boundary rays of a parallel beam passing through a lens.

A parallel beam passing through a lens becomes conical; but instead of a
single cone it is a sheaf or nest of cones, all having the edge of the lens as
base, but each having a different vertex. The violet cone is innermost, near
the lens, the red cone outermost, while the others lie between. Beyond the
crossing point or focus the order of cones is reversed, as the above figure
shows. Only the two marginal rays of the beam are depicted.

If a screen be held anywhere nearer the lens than the place marked 1
there will be a whitish centre to the patch of light and a red and orange
fringe or border. Held anywhere beyond the region 2, the border of the
patch will be blue and violet. Held about 3 the colour will be less marked
than elsewhere, but nowhere can it be got rid of. Each point of an object
will be represented in the image not by a point but by a coloured patch: a
fact which amply explains the observed blurring and indistinctness.

Newton measured and calculated the distance between the violet and red
foci—VR in the diagram—and showed that it was 1⁄50th the diameter of the
lens. To overcome this difficulty (called chromatic aberration) telescope
glasses were made small and of very long focus: some of them so long that
they had no tube, all of them egregiously cumbrous. Yet it was with such
instruments that all the early discoveries were made. With such an

instrument, for instance, Huyghens discovered the real shape of Saturn's
ring.

The defects of refractors seemed irremediable, being founded in the
nature of light itself. So he gave up his "glass works"; and proceeded to
think of reflexion from metal specula. A concave mirror forms an image just
as a lens does, but since it does so without refraction or transmission
through any substance, there is no accompanying dispersion or chromatic
aberration.

The first reflecting telescope he made was 1 in. diameter and 6 in. long,
and magnified forty times. It acted as well as a three or four feet refractor of
that day, and showed Jupiter's moons. So he made a larger one, now in the
library of the Royal Society, London, with an inscription:

"The first reflecting telescope, invented by Sir Isaac Newton, and made
with his own hands."

This has been the parent of most of the gigantic telescopes of the present
day. Fifty years elapsed before it was much improved on, and then, first by
Hadley and afterwards by Herschel and others, large and good reflectors
were constructed.

The largest telescope ever made, that of Lord Rosse, is a Newtonian
reflector, fifty feet long, six feet diameter, with a mirror weighing four tons.
The sextant, as used by navigators, was also invented by Newton.

The year after the plague, in 1667, Newton returned to Trinity College,
and there continued his experiments on optics. It is specially to be noted
that at this time, at the age of twenty-four, Newton had laid the foundations
of all his greatest discoveries:—

Fig. 66.—Newton's telescope.

The Theory of Fluxions; or, the Differential Calculus.

The Law of Gravitation; or, the complete theory of astronomy.

The compound nature of white light; or, the beginning of Spectrum
Analysis.

Fig. 67.—The sextant, as now made.

His later life was to be occupied in working these incipient discoveries
out. But the most remarkable thing is that no one knew about any one of
them. However, he was known as an accomplished young mathematician,
and was made a fellow of his college. You remember that he had a friend
there in the person of Dr. Isaac Barrow, first Lucasian Professor of
Mathematics in the University. It happened, about 1669, that a
mathematical discovery of some interest was being much discussed, and Dr.
Barrow happened to mention it to Newton, who said yes, he had worked out
that and a few other similar things some time ago. He accordingly went and
fetched some papers to Dr. Barrow, who forwarded them to other
distinguished mathematicians, and it thus appeared that Newton had
discovered theorems much more general than this special case that was
exciting so much interest. Dr. Barrow, being anxious to devote his time
more particularly to theology, resigned his chair the same year in favour of
Newton, who was accordingly elected to the Lucasian Professorship, which
he held for thirty years. This chair is now the most famous in the University,
and it is commonly referred to as the chair of Newton.

Still, however, his method of fluxions was unknown, and still he did not
publish it. He lectured first on optics, giving an account of his experiments.
His lectures were afterwards published both in Latin and English, and are
highly valued to this day.

The fame of his mathematical genius came to the ears of the Royal
Society, and a motion was made to get him elected a fellow of that body.
The Royal Society, the oldest and most famous of all scientific societies
with a continuous existence, took its origin in some private meetings, got up
in London by the Hon. Robert Boyle and a few scientific friends, during all
the trouble of the Commonwealth.

After the restoration, Charles II. in 1662 incorporated it under Royal
Charter; among the original members being Boyle, Hooke, Christopher
Wren, and other less famous names. Boyle was a great experimenter, a
worthy follower of Dr. Gilbert. Hooke began as his assistant, but being of a
most extraordinary ingenuity he rapidly rose so as to exceed his master in
importance. Fate has been a little unkind to Hooke in placing him so near to
Newton; had he lived in an ordinary age he would undoubtedly have shone
as a star of the first magnitude. With great ingenuity, remarkable scientific
insight, and consummate experimental skill, he stands in many respects
almost on a level with Galileo. But it is difficult to see stars even of the first
magnitude when the sun is up, and thus it happens that the name and fame
of this brilliant man are almost lost in the blaze of Newton. Of Christopher
Wren I need not say much. He is well known as an architect, but he was a
most accomplished all-round man, and had a considerable taste and faculty
for science.

These then were the luminaries of the Royal Society at the time we are
speaking of, and to them Newton's first scientific publication was
submitted. He communicated to them an account of his reflecting telescope,
and presented them with the instrument.

Their reception of it surprised him; they were greatly delighted with it,
and wrote specially thanking him for the communication, and assuring him
that all right should be done him in the matter of the invention. The Bishop
of Salisbury (Bishop Burnet) proposed him for election as a fellow, and
elected he was.

In reply, he expressed his surprise at the value they set on the telescope,
and offered, if they cared for it, to send them an account of a discovery
which he doubts not will prove much more grateful than the communication
of that instrument, "being in my judgment the oddest, if not the most
considerable detection that has recently been made into the operations of
Nature."

So he tells them about his optical researches and his discovery of the
nature of white light, writing them a series of papers which were long
afterwards incorporated and published as his Optics. A magnificent work,
which of itself suffices to place its author in the first rank of the world's
men of science.

The nature of white light, the true doctrine of colour, and the differential
calculus! besides a good number of minor results—binomial theorem,
reflecting telescope, sextant, and the like; one would think it enough for one
man's life-work, but the masterpiece remains still to be mentioned. It is as
when one is considering Shakspeare: King Lear, Macbeth, Othello,—surely
a sufficient achievement,—but the masterpiece remains.

Comparisons in different departments are but little help perhaps,
nevertheless it seems to me that in his own department, and considered
simply as a man of science, Newton towers head and shoulders over, not
only his contemporaries—that is a small matter—but over every other
scientific man who has ever lived, in a way that we can find no parallel for
in other departments. Other nations admit his scientific pre-eminence with
as much alacrity as we do.

Well, we have arrived at the year 1672 and his election to the Royal
Society. During the first year of his membership there was read at one of the
meetings a paper giving an account of a very careful determination of the
length of a degree (i.e. of the size of the earth), which had been made by
Picard near Paris. The length of the degree turned out to be not sixty miles,
but nearly seventy miles. How soon Newton heard of this we do not learn—
probably not for some years,—Cambridge was not so near London then as
it is now, but ultimately it was brought to his notice. Armed with this new
datum, his old speculation concerning gravity occurred to him. He had
worked out the mechanics of the solar system on a certain hypothesis, but it
had remained a hypothesis somewhat out of harmony with apparent fact.
What if it should turn out to be true after all!

He took out his old papers and began again the calculation. If gravity
were the force keeping the moon in its orbit, it would fall toward the earth
sixteen feet every minute. How far did it fall? The newly known size of the
earth would modify the figures: with intense excitement he runs through the
working, his mind leaps before his hand, and as he perceives the answer to
be coming out right, all the infinite meaning and scope of his mighty
discovery flashes upon him, and he can no longer see the paper. He throws
down the pen; and the secret of the universe is, to one man, known.

But of course it had to be worked out. The meaning might flash upon
him, but its full detail required years of elaboration; and deeper and deeper
consequences revealed themselves to him as he proceeded.

For two years he devoted himself solely to this one object. During those
years he lived but to calculate and think, and the most ludicrous stories are
told concerning his entire absorption and inattention to ordinary affairs of
life. Thus, for instance, when getting up in a morning he would sit on the
side of the bed half-dressed, and remain like that till dinner time. Often he
would stay at home for days together, eating what was taken to him, but
without apparently noticing what he was doing.

One day an intimate friend, Dr. Stukely, called on him and found on the
table a cover laid for his solitary dinner. After waiting a long time, Dr.
Stukely removed the cover and ate the chicken underneath it, replacing and
covering up the bones again. At length Newton appeared, and after greeting
his friend, sat down to dinner, but on lifting the cover he said in surprise,
"Dear me, I thought I had not dined, but I see I have."

It was by this continuous application that the Principia was
accomplished. Probably nothing of the first magnitude can be accomplished
without something of the same absorbed unconsciousness and freedom
from interruption. But though desirable and essential for the work, it was a
severe tax upon the powers of the man. There is, in fact, no doubt that
Newton's brain suffered temporary aberration after this effort for a short
time. The attack was slight, and it has been denied; but there are letters
extant which are inexplicable otherwise, and moreover after a year or two
he writes to his friends apologizing for strange and disjointed epistles,
which he believed he had written without understanding clearly what he
wrote. The derangement was, however, both slight and temporary: and it is
only instructive to us as showing at what cost such a work as the Principia
must be produced, even by so mighty a mind as that of Newton.

The first part of the work having been done, any ordinary mortal would
have proceeded to publish it; but the fact is that after he had sent to the
Royal Society his papers on optics, there had arisen controversies and
objections; most of them rather paltry, to which he felt compelled to find
answers. Many men would have enjoyed this part of the work, and taken it
as evidence of interest and success. But to Newton's shy and retiring
disposition these discussions were merely painful. He writes, indeed, his
answers with great patience and ability, and ultimately converts the more
reasonable of his opponents, but he relieves his mind in the following letter
to the secretary of the Royal Society: "I see I have made myself a slave to
philosophy, but if I get free of this present business I will resolutely bid
adieu to it eternally, except what I do for my private satisfaction or leave to
come out after me; for I see a man must either resolve to put out nothing

new, or to become a slave to defend it." And again in a letter to Leibnitz: "I
have been so persecuted with discussions arising out of my theory of light
that I blamed my own imprudence for parting with so substantial a blessing
as my quiet to run after a shadow." This shows how much he cared for
contemporary fame.

So he locked up the first part of the Principia in his desk, doubtless
intending it to be published after his death. But fortunately this was not so
to be.

In 1683, among the leading lights of the Royal Society, the same sort of
notions about gravity and the solar system began independently to be
bruited. The theory of gravitation seemed to be in the air, and Wren, Hooke,
and Halley had many a talk about it.

Hooke showed an experiment with a pendulum, which he likened to a
planet going round the sun. The analogy is more superficial than real. It
does not obey Kepler's laws; still it was a striking experiment. They had
guessed at a law of inverse squares, and their difficulty was to prove what
curve a body subject to it would describe. They knew it ought to be an
ellipse if it was to serve to explain the planetary motion, and Hooke said he
could prove that an ellipse it was; but he was nothing of a mathematician,
and the others scarcely believed him. Undoubtedly he had shrewd inklings
of the truth, though his guesses were based on little else than a most
sagacious intuition. He surmised also that gravity was the force concerned,
and asserted that the path of an ordinary projectile was an ellipse, like the
path of a planet—which is quite right. In fact the beginnings of the
discovery were beginning to dawn upon him in the well-known way in
which things do dawn upon ordinary men of genius: and had Newton not
lived we should doubtless, by the labours of a long chain of distinguished
men, beginning with Hooke, Wren, and Halley, have been now in
possession of all the truths revealed by the Principia. We should never have
had them stated in the same form, nor proved with the same marvellous
lucidity and simplicity, but the facts themselves we should by this time have

arrived at. Their developments and completions, due to such men as
Clairaut, Euler, D'Alembert, Lagrange, Laplace, Airy, Leverrier, Adams, we
should of course not have had to the same extent; because the lives and
energies of these great men would have been partially consumed in
obtaining the main facts themselves.

The youngest of the three questioners at the time we are speaking of was
Edmund Halley, an able and remarkable man. He had been at Cambridge,
doubtless had heard Newton lecture, and had acquired a great veneration for
him.

In January, 1684, we find Wren offering Hooke and Halley a prize, in the
shape of a book worth forty shillings, if they would either of them bring
him within two months a demonstration that the path of a planet subject to
an inverse square law would be an ellipse. Not in two months, nor yet in
seven, was there any proof forthcoming. So at last, in August, Halley went
over to Cambridge to speak to Newton about the difficult problem and
secure his aid. Arriving at his rooms he went straight to the point. He said,
"What path will a body describe if it be attracted by a centre with a force
varying as the inverse square of the distance." To which Newton at once
replied, "An ellipse." "How on earth do you know?" said Halley in
amazement. "Why, I have calculated it," and began hunting about for the
paper. He actually couldn't find it just then, but sent it him shortly by post,
and with it much more—in fact, what appeared to be a complete treatise on
motion in general.

With his valuable burden Halley hastened to the Royal Society and told
them what he had discovered. The Society at his representation wrote to Mr.
Newton asking leave that it might be printed. To this he consented; but the
Royal Society wisely appointed Mr. Halley to see after him and jog his
memory, in case he forgot about it. However, he set to work to polish it up
and finish it, and added to it a great number of later developments and
embellishments, especially the part concerning the lunar theory, which gave
him a deal of trouble—and no wonder; for in the way he has put it there

never was a man yet living who could have done the same thing.
Mathematicians regard the achievement now as men might stare at the work
of some demigod of a bygone age, wondering what manner of man this
was, able to wield such ponderous implements with such apparent ease.

To Halley the world owes a great debt of gratitude—first, for
discovering the Principia; second, for seeing it through the press; and third,
for defraying the cost of its publication out of his own scanty purse. For
though he ultimately suffered no pecuniary loss, rather the contrary, yet
there was considerable risk in bringing out a book which not a dozen men
living could at the time comprehend. It is no small part of the merit of
Halley that he recognized the transcendent value of the yet unfinished work,
that he brought it to light, and assisted in its becoming understood to the
best of his ability.

Though Halley afterwards became Astronomer-Royal, lived to the ripe
old age of eighty-six, and made many striking observations, yet he would
be the first to admit that nothing he ever did was at all comparable in
importance with his discovery of the Principia; and he always used to
regard his part in it with peculiar pride and pleasure.

And how was the Principia received? Considering the abstruse nature of
its subject, it was received with great interest and enthusiasm. In less than
twenty years the edition was sold out, and copies fetched large sums. We
hear of poor students copying out the whole in manuscript in order to
possess a copy—not by any means a bad thing to do, however many copies
one may possess. The only useful way really to read a book like that is to
pore over every sentence: it is no book to be skimmed.

While the Principia was preparing for the press a curious incident of
contact between English history and the University occurred. It seems that
James II., in his policy of Catholicising the country, ordered both
Universities to elect certain priests to degrees without the ordinary oaths.
Oxford had given way, and the Dean of Christ Church was a creature of

James's choosing. Cambridge rebelled, and sent eight of its members,
among them Mr. Newton, to plead their cause before the Court of High
Commission. Judge Jeffreys presided over the Court, and threatened and
bullied with his usual insolence. The Vice-Chancellor of Cambridge was
deprived of office, the other deputies were silenced and ordered away. From
the precincts of this court of justice Newton returned to Trinity College to
complete the Principia.

By this time Newton was only forty-five years old, but his main work
was done. His method of fluxions was still unpublished; his optics was
published only imperfectly; a second edition of the Principia, with
additions and improvements, had yet to appear; but fame had now come
upon him, and with fame worries of all kinds.

By some fatality, principally no doubt because of the interest they
excited, every discovery he published was the signal for an outburst of
criticism and sometimes of attack. I shall not go into these matters: they are
now trivial enough, but it is necessary to mention them, because to Newton
they evidently loomed large and terrible, and occasioned him acute torment.

Fig. 68.—Newton when young.
(From an engraving by B. Reading after Sir Peter Lely.)

No sooner was the Principia put than Hooke put in his claims for
priority. And indeed his claims were not altogether negligible; for vague
ideas of the same sort had been floating in his comprehensive mind, and he
doubtless felt indistinctly conscious of a great deal more than he could
really state or prove.

By indiscreet friends these two great men were set somewhat at
loggerheads, and worse might have happened had they not managed to
come to close quarters, and correspond privately in a quite friendly manner,
instead of acting through the mischievous medium of third parties. In the
next edition Newton liberally recognizes the claims of both Hooke and
Wren. However, he takes warning betimes of what he has to expect, and

writes to Halley that he will only publish the first two books, those
containing general theorems on motion. The third book—concerning the
system of the world, i.e. the application to the solar system—he says "I now
design to suppress. Philosophy is such an impertinently litigious lady that a
man had as good be engaged in law-suits as have to do with her. I found it
so formerly, and now I am no sooner come near her again but she gives me
warning. The two books without the third will not so well bear the title
'Mathematical Principles of Natural Philosophy,' and therefore I had altered
it to this, 'On the Free Motion of Two Bodies'; but on second thoughts I
retain the former title: 'twill help the sale of the book—which I ought not to
diminish now 'tis yours."

However, fortunately, Halley was able to prevail upon him to publish the
third book also. It is, indeed, the most interesting and popular of the three,
as it contains all the direct applications to astronomy of the truths
established in the other two.

Some years later, when his method of fluxions was published, another
and a worse controversy arose—this time with Leibnitz, who had also
independently invented the differential calculus. It was not so well
recognized then how frequently it happens that two men independently and
unknowingly work at the very same thing at the same time. The history of
science is now full of such instances; but then the friends of each accused
the other of plagiarism.

I will not go into the controversy: it is painful and useless. It only served
to embitter the later years of two great men, and it continued long after
Newton's death—long after both their deaths. It can hardly be called ancient
history even now.

But fame brought other and less unpleasant distractions than
controversies. We are a curious, practical, and rather stupid people, and our
one idea of honouring a man is to vote for him in some way or other; so
they sent Newton to Parliament. He went, I believe, as a Whig, but it is not

recorded that he spoke. It is, in fact, recorded that he was once expected to
speak when on a Royal Commission about some question of chronometers,
but that he would not. However, I dare say he made a good average
member.

Then a little later it was realized that Newton was poor, that he still had
to teach for his livelihood, and that though the Crown had continued his
fellowship to him as Lucasian Professor without the necessity of taking
orders, yet it was rather disgraceful that he should not be better off. So an
appeal was made to the Government on his behalf, and Lord Halifax, who
exerted himself strongly in the matter, succeeding to office on the accession
of William III., was able to make him ultimately Master of the Mint, with a
salary of some £1,200 a year. I believe he made rather a good Master, and
turned out excellent coins: certainly he devoted his attention to his work
there in a most exemplary manner.

But what a pitiful business it all is! Here is a man sent by Heaven to do
certain things which no man else could do, and so long as he is
comparatively unknown he does them; but so soon as he is found out, he is
clapped into a routine office with a big salary: and there is, comparatively
speaking, an end of him. It is not to be supposed that he had lost his power,
for he frequently solved problems very quickly which had been given out
by great Continental mathematicians as a challenge to the world.

We may ask why Newton allowed himself to be thus bandied about
instead of settling himself down to the work in which he was so pre-
eminently great. Well, I expect your truly great man never realizes how
great he is, and seldom knows where his real strength lies. Certainly
Newton did not know it. He several times talks of giving up philosophy
altogether; and though he never really does it, and perhaps the feeling is one
only born of some temporary overwork, yet he does not sacrifice everything
else to it as he surely must had he been conscious of his own greatness. No;
self-consciousness was the last thing that affected him. It is for a great
man's contemporaries to discover him, to make much of him, and to put him

in surroundings where he may flourish luxuriantly in his own heaven-
intended way.

However, it is difficult for us to judge of these things. Perhaps if he had
been maintained at the national expense to do that for which he was
preternaturally fitted, he might have worn himself out prematurely; whereas
by giving him routine work the scientific world got the benefit of his
matured wisdom and experience. It was no small matter to the young Royal
Society to be able to have him as their President for twenty-four years. His
portrait has hung over the President's chair ever since, and there I suppose it
will continue to hang until the Royal Society becomes extinct.

The events of his later life I shall pass over lightly. He lived a calm,
benevolent life, universally respected and beloved. His silver-white hair
when he removed his peruke was a venerable spectacle. A lock of it is still
preserved, with many other relics, in the library of Trinity College. He died
quietly, after a painful illness, at the ripe age of eighty-five. His body lay in
state in the Jerusalem Chamber, and he was buried in Westminster Abbey,
six peers bearing the pall. These things are to be mentioned to the credit of
the time and the country; for after we have seen the calamitous spectacle of
the way Tycho and Kepler and Galileo were treated by their ungrateful and
unworthy countries, it is pleasant to reflect that England, with all its
mistakes, yet recognized her great man when she received him, and
honoured him with the best she knew how to give.

Fig. 69.—Sir Isaac Newton.

Concerning his character, one need only say that it was what one would
expect and wish. It was characterized by a modest, calm, dignified
simplicity. He lived frugally with his niece and her husband, Mr. Conduit,
who succeeded him as Master of the Mint. He never married, nor
apparently did he ever think of so doing. The idea, perhaps, did not
naturally occur to him, any more than the idea of publishing his work did.

He was always a deeply religious man and a sincere Christian, though
somewhat of the Arian or Unitarian persuasion—so, at least, it is asserted
by orthodox divines who understand these matters. He studied theology
more or less all his life, and towards the end was greatly interested in
questions of Biblical criticism and chronology. By some ancient eclipse or
other he altered the recognized system of dates a few hundred years; and his
book on the prophecies of Daniel and the Revelation of St. John, wherein he

identifies the beast with the Church of Rome in quite the orthodox way, is
still by some admired.

But in all these matters it is probable that he was a merely ordinary man,
with natural acumen and ability doubtless, but nothing in the least
superhuman. In science, the impression he makes upon me is only
expressible by the words inspired, superhuman.

And yet if one realizes his method of work, and the calm, uninterrupted
flow of all his earlier life, perhaps his achievements become more
intelligible. When asked how he made his discoveries, he replied: "By
always thinking unto them. I keep the subject constantly before me, and
wait till the first dawnings open slowly by little and little into a full and
clear light." That is the way—quiet, steady, continuous thinking,
uninterrupted and unharassed brooding. Much may be done under those
conditions. Much ought to be sacrificed to obtain those conditions. All the
best thinking work of the world has been thus done.[18] Buffon said:
"Genius is patience." So says Newton: "If I have done the public any
service this way, it is due to nothing but industry and patient thought."
Genius patience? No, it is not quite that, or, rather, it is much more than
that; but genius without patience is like fire without fuel—it will soon burn
itself out.

NOT E S F OR L E CT URE I X

The Principia published 1687.
Newton died 1727.

The Law of Gravitation.—Every particle of matter attracts every other
particle of matter with a force proportional to the mass of each and to the
inverse square of the distance between them.

Some of Newton's Deductions.

1. Kepler's second law (equable description of areas) proves that each
planet is acted on by a force directed towards the sun as a centre of force.

2. Kepler's first law proves that this central force diminishes in the same
proportion as the square of the distance increases.

3. Kepler's third law proves that all the planets are acted on by the same
kind of force; of an intensity depending on the mass of the sun.[19]

4. So by knowing the length of year and distance of any planet from the
sun, the sun's mass can be calculated, in terms of that of the earth.

5. For the satellites, the force acting depends on the mass of their central
body, a planet. Hence the mass of any planet possessing a satellite becomes
known.

6. The force constraining the moon in her orbit is the same gravity as
gives terrestrial bodies their weight and regulates the motion of projectiles.
[Because, while a stone drops 16 feet in a second, the moon, which is 60
times as far from the centre of the earth, drops 16 feet in a minute.]

7. The moon is attracted not only by the earth, but by the sun also; hence
its orbit is perturbed, and Newton calculated out the chief of these
perturbations, viz.:—
(The equation of the centre, discovered by Hipparchus.)

(a) The evection, discovered by Hipparchus and Ptolemy.

(b) The variation, discovered by Tycho Brahé.

(c) The annual equation, discovered by Tycho Brahé.

(d) The retrogression of the nodes, then being observed at Greenwich by Flamsteed.

(e) The variation of inclination, then being observed at Greenwich by Flamsteed.

(f) The progression of the apses (with an error of one-half).

(g) The inequality of apogee, previously unknown.
(h) The inequality of nodes, previously unknown.

8. Each planet is attracted not only by the sun but by the other planets,
hence their orbits are slightly affected by each other. Newton began the
theory of planetary perturbations.

9. He recognized the comets as members of the solar system, obedient to
the same law of gravity and moving in very elongated ellipses; so their
return could be predicted (e.g. Halley's comet).

10. Applying the idea of centrifugal force to the earth considered as a
rotating body, he perceived that it could not be a true sphere, and calculated
its oblateness, obtaining 28 miles greater equatorial than polar diameter.

11. Conversely, from the observed shape of Jupiter, or any planet, the
length of its day could be estimated.

12. The so-calculated shape of the earth, in combination with centrifugal
force, causes the weight of bodies to vary with latitude; and Newton
calculated the amount of this variation. 194 lbs. at pole balance 195 lbs. at
equator.

13. A homogeneous sphere attracts as if its mass were concentrated at its
centre. For any other figure, such as an oblate spheroid, this is not exactly
true. A hollow concentric spherical shell exerts no force on small bodies
inside it.

14. The earth's equatorial protuberance, being acted on by the attraction
of the sun and moon, must disturb its axis of rotation in a calculated
manner; and thus is produced the precession of the equinoxes. [The
attraction of the planets on the same protuberance causes a smaller and
rather different kind of precession.]

15. The waters of the ocean are attracted towards the sun and moon on
one side, and whirled a little further away than the solid earth on the other
side: hence Newton explained all the main phenomena of the tides.

16. The sun's mass being known, he calculated the height of the solar
tide.

17. From the observed heights of spring and neap tides he determined
the lunar tide, and thence made an estimate of the mass of the moon.

Reference Table of Numerical Data.

Masses in Solar Height dropped by a Length of Day or
System. stone in first second. time of rotation.

Mercury ·065 7·0 feet 24 hours
Venus ·885 15·8 " 23½ "
Earth 1·000 16·1 " 24 "
Mars ·108 6·2 " 24½ "
Jupiter 300·8 45·0 " 10 "
Saturn 89·7 18·4 " 10½ "
The Sun 316000· 436·0 " 608 "
The Moon about ·012 3·7 " 702 "

The mass of the earth, taken above as unity, is 6,000 trillion tons.

Observatories.—Uraniburg flourished from 1576 to 1597; the Observatory
of Paris was founded in 1667; Greenwich Observatory in 1675.

Astronomers-Royal.—Flamsteed, Halley, Bradley, Bliss, Maskelyne,
Pond, Airy, Christie.

LECTURE IX

Newton's "Principia"

The law of gravitation, above enunciated, in conjunction with the laws
of motion rehearsed at the end of the preliminary notes of Lecture VII., now
supersedes the laws of Kepler and includes them as special cases. The more
comprehensive law enables us to criticize Kepler's laws from a higher
standpoint, to see how far they are exact and how far they are only
approximations. They are, in fact, not precisely accurate, but the reason for
every discrepancy now becomes abundantly clear, and can be worked out
by the theory of gravitation.

We may treat Kepler's laws either as immediate consequences of the law
of gravitation, or as the known facts upon which that law was founded.
Historically, the latter is the more natural plan, and it is thus that they are
treated in the first three statements of the above notes; but each proposition
may be worked inversely, and we might state them thus:—

1. The fact that the force acting on each planet is directed to the sun,
necessitates the equable description of areas.

2. The fact that the force varies as the inverse square of the distance,
necessitates motion in an ellipse, or some other conic section, with the sun
in one focus.

3. The fact that one attracting body acts on all the planets with an inverse
square law, causes the cubes of their mean distances to be proportional to
the squares of their periodic times.

Not only these but a multitude of other deductions follow rigorously
from the simple datum that every particle of matter attracts every other
particle with a force directly proportional to the mass of each and to the
inverse square of their mutual distance. Those dealt with in the Principia

are summarized above, and it will be convenient to run over them in order,
with the object of giving some idea of the general meaning of each, without
attempting anything too intricate to be readily intelligible.

Fig. 70.

No. 1. Kepler's second law (equable description of areas) proves that
each planet is acted on by a force directed towards the sun as a centre of
force.

The equable description of areas about a centre of force has already been
fully, though briefly, established. (p. 175.) It is undoubtedly of fundamental
importance, and is the earliest instance of the serious discussion of central
forces, i.e. of forces directed always to a fixed centre.

We may put it afresh thus:—OA has been the motion of a particle in a
unit of time; at A it receives a knock towards C, whereby in the next unit it
travels along AD instead of AB. Now the area of the triangle CAD, swept
out by the radius vector in unit time, is ½bh; h being the perpendicular
height of the triangle from the base AC. (Fig. 70.) Now the blow at A, being
along the base, has no effect upon h; and consequently the area remains just
what it would have been without the blow. A blow directed to any point
other than C would at once alter the area of the triangle.

One interesting deduction may at once be drawn. If gravity were a
radiant force emitted from the sun with a velocity like that of light, the
moving planet would encounter it at a certain apparent angle (aberration),
and the force experienced would come from a point a little in advance of
the sun. The rate of description of areas would thus tend to increase;
whereas in reality it is constant. Hence the force of gravity, if it travel at all,
does so with a speed far greater than that of light. It appears to be
practically instantaneous. (Cf. "Modern Views of Electricity," § 126, end of
chap. xii.) Again, anything like a retarding effect of the medium through
which the planets move would constitute a tangential force, entirely un-
directed towards the sun. Hence no such frictional or retarding force can
appreciably exist. It is, however, conceivable that both these effects might
occur and just neutralize each other. The neutralization is unlikely to be
exact for all the planets; and the fact is, that no trace of either effect has as
yet been discovered. (See also p. 176.)

The planets are, however, subject to forces not directed towards the sun,
viz. their attractions for each other; and these perturbing forces do produce
a slight discrepancy from Kepler's second law, but a discrepancy which is
completely subject to calculation.

No. 2. Kepler's first law proves that this central force diminishes in the
same proportion as the square of the distance increases.

To prove the connection between the inverse-square law of distance, and
the travelling in a conic section with the centre of force in one focus (the
other focus being empty), is not so simple. It obviously involves some
geometry, and must therefore be left to properly armed students. But it may
be useful to state that the inverse-square law of distance, although the
simplest possible law for force emanating from a point or sphere, is not to
be regarded as self-evident or as needing no demonstration. The force of a
magnetic pole on a magnetized steel scrap, for instance, varies as the
inverse cube of the distance; and the curve described by such a particle
would be quite different from a conic section—it would be a definite class
of spiral (called Cotes's spiral). Again, on an iron filing the force of a single
pole might vary more nearly as the inverse fifth power; and so on. Even
when the thing concerned is radiant in straight lines, like light, the law of
inverse squares is not universally true. Its truth assumes, first, that the
source is a point or sphere; next, that there is no reflection or refraction of
any kind; and lastly, that the medium is perfectly transparent. The law of
inverse squares by no means holds from a prairie fire for instance, or from a
lighthouse, or from a street lamp in a fog.

Mutual perturbations, especially the pull of Jupiter, prevent the path of a
planet from being really and truly an ellipse, or indeed from being any
simple re-entrant curve. Moreover, when a planet possesses a satellite, it is
not the centre of the planet which ever attempts to describe the Keplerian
ellipse, but it is the common centre of gravity of the two bodies. Thus, in
the case of the earth and moon, the point which really does describe a close
attempt at an ellipse is a point displaced about 3000 miles from the centre
of the earth towards the moon, and is therefore only 1000 miles beneath the
surface.

No. 3. Kepler's third law proves that all the planets are acted on by the
same kind of force; of an intensity depending on the mass of the sun.

The third law of Kepler, although it requires geometry to state and
establish it for elliptic motion (for which it holds just as well as it does for

circular motion), is very easy to establish for circular motion, by any one
who knows about centrifugal force. If m is the mass of a planet, v its
velocity, r the radius of its orbit, and T the time of describing it; 2πr = vT,
and the centripetal force needed to hold it in its orbit is

mv2 4π2mr
or
r T2

Now the force of gravitative attraction between the planet and the sun is

VmS
,
r2

where v is a fixed quantity called the gravitation-constant, to be determined
if possible by experiment once for all. Now, expressing the fact that the
force of gravitation is the force holding the planet in, we write,

4π2mr VmS
= ,
T2 r2

whence, by the simplest algebra,

r3mr VS
= .
T2 4π2

The mass of the planet has been cancelled out; the mass of the sun
remains, multiplied by the gravitation-constant, and is seen to be
proportional to the cube of the distance divided by the square of the
periodic time: a ratio, which is therefore the same for all planets controlled
by the sun. Hence, knowing r and T for any single planet, the value of VS is
known.

No. 4. So by knowing the length of year and distance of any planet from
the sun, the sun's mass can be calculated, in terms of that of the earth.

No. 5. For the satellites, the force acting depends on the mass of their
central body, a planet. Hence the mass of any planet possessing a satellite
becomes known.

The same argument holds for any other system controlled by a central
body—for instance, for the satellites of Jupiter; only instead of S it will be
natural to write J, as meaning the mass of Jupiter. Hence, knowing r and T
for any one satellite of Jupiter, the value of VJ is known.

Apply the argument also to the case of moon and earth. Knowing the
distance and time of revolution of our moon, the value of VE is at once
determined; E being the mass of the earth. Hence, S and J, and in fact the
mass of any central body possessing a visible satellite, are now known in
terms of E, the mass of the earth (or, what is practically the same thing, in
terms of V, the gravitation-constant). Observe that so far none of these
quantities are known absolutely. Their relative values are known, and are
tabulated at the end of the Notes above, but the finding of their absolute
values is another matter, which we must defer.

But, it may be asked, if Kepler's third law only gives us the mass of a
central body, how is the mass of a satellite to be known? Well, it is not
easy; the mass of no satellite is known with much accuracy. Their mutual
perturbations give us some data in the case of the satellites of Jupiter; but to
our own moon this method is of course inapplicable. Our moon perturbs at
first sight nothing, and accordingly its mass is not even yet known with
exactness. The mass of comets, again, is quite unknown. All that we can be
sure of is that they are smaller than a certain limit, else they would perturb
the planets they pass near. Nothing of this sort has ever been detected. They
are themselves perturbed plentifully, but they perturb nothing; hence we
learn that their mass is small. The mass of a comet may, indeed, be a few
million or even billion tons; but that is quite small in astronomy.

But now it may be asked, surely the moon perturbs the earth, swinging it
round their common centre of gravity, and really describing its own orbit

about this point instead of about the earth's centre? Yes, that is so; and a
more precise consideration of Kepler's third law enables us to make a fair
approximation to the position of this common centre of gravity, and thus
practically to "weigh the moon," i.e. to compare its mass with that of the
earth; for their masses will be inversely as their respective distances from
the common centre of gravity or balancing point—on the simple steel-yard
principle.

Hitherto we have not troubled ourselves about the precise point about
which the revolution occurs, but Kepler's third law is not precisely accurate
unless it is attended to. The bigger the revolving body the greater is the
discrepancy: and we see in the table preceding Lecture III., on page 57, that
Jupiter exhibits an error which, though very slight, is greater than that of
any of the other planets, when the sun is considered the fixed centre.
Let the common centre of gravity of earth and moon be displaced a distance x from
the centre of the earth, then the moon's distance from the real centre of revolution is
not r, but r-x; and the equation of centrifugal force to gravitative-attraction is strictly

4π2 VE
(r – x) = ,
T2 r2

instead of what is in the text above; and this gives a slightly modified "third law."
From this equation, if we have any distinct method of determining VE (and the next
section gives such a method), we can calculate x and thus roughly weigh the moon,
since

r–x E
= ,
r E+M

but to get anything like a reasonable result the data must be very precise.

No. 6. The force constraining the moon in her orbit is the same gravity
as gives terrestrial bodies their weight and regulates the motion of
projectiles.

Here we come to the Newtonian verification already several times
mentioned; but because of its importance I will repeat it in other words. The
hypothesis to be verified is that the force acting on the moon is the same

kind of force as acts on bodies we can handle and weigh, and which gives
them their weight. Now the weight of a mass m is commonly written mg,
where g is the intensity of terrestrial gravity, a thing easily measured; being,
indeed, numerically equal to twice the distance a stone drops in the first
second of free fall. [See table p. 205.] Hence, expressing that the weight of
a body is due to gravity, and remembering that the centre of the earth's
attraction is distant from us by one earth's radius (R), we can write

VmE
mg = ,
R2

or

VE = gR2 = 95,522 cubic miles-per-second per second.

But we already know vE, in terms of the moon's motion, as 4π2r3/T2
approximately, [more accurately, see preceding note, this quantity is V(E +
M)]; hence we can easily see if the two determinations of this quantity
agree.[20]

All these deductions are fundamental, and may be considered as the
foundation of the Principia. It was these that flashed upon Newton during
that moment of excitement when he learned the real size of the earth, and
discovered his speculations to be true.

The next are elaborations and amplifications of the theory, such as in
ordinary times are left for subsequent generations of theorists to discover
and work out.

Newton did not work out these remoter consequences of his theory
completely by any means: the astronomical and mathematical world has
been working them out ever since; but he carried the theory a great way,
and here it is that his marvellous power is most conspicuous.

It is his treatment of No. 7, the perturbations of the moon, that perhaps
most especially has struck all future mathematicians with amazement. No.

7, No. 14, No. 15, these are the most inspired of the whole.

No. 7. The moon is attracted not only by the earth, but by the sun also;
hence its orbit is perturbed, and Newton calculated out the chief of these
perturbations.

Now running through the perturbations (p. 203) in order:—The first is in
parenthesis, because it is mere excentricity. It is not a true perturbation at
all, and more properly belongs to Kepler.

(a) The first true perturbation is what Ptolemy called "the evection," the
principal part of which is a periodic change in the ellipticity or excentricity
of the moon's orbit, owing to the pull of the sun. It is a complicated matter,
and Newton only partially solved it. I shall not attempt to give an account of
it.

(b) The next, "the variation," is a much simpler affair. It is caused by the
fact that as the moon revolves round the earth it is half the time nearer to
the sun than the earth is, and so gets pulled more than the average, while for
the other fortnight it is further from the sun than the earth is, and so gets
pulled less. For the week during which it is changing from a decreasing half
to a new moon it is moving in the direction of the extra pull, and hence
becomes new sooner than would have been expected. All next week it is
moving against the same extra pull, and so arrives at quadrature (half moon)
somewhat late. For the next fortnight it is in the region of too little pull, the
earth gets pulled more than it does; the effect of this is to hurry it up for the
third week, so that the full moon occurs a little early, and to retard it for the
fourth week, so that the decreasing half moon like the increasing half occurs
behind time again. Thus each syzygy (as new and full are technically
called) is too early; each quadrature is too late; the maximum hurrying and
slackening force being felt at the octants, or intermediate 45° points.

(c) The "annual equation" is a fluctuation introduced into the other
perturbations by reason of the varying distance of the disturbing body, the

sun, at different seasons of the year. Its magnitude plainly depends simply
on the excentricity of the earth's orbit.

Both these perturbations, (b) and (c), Newton worked out completely.

(d) and (e) Next come the retrogression of the nodes and the variation of
the inclination, which at the time were being observed at Greenwich by
Flamsteed, from whom Newton frequently, but vainly, begged for data that
he might complete their theory while he had his mind upon it. Fortunately,
Halley succeeded Flamsteed as Astronomer-Royal [see list at end of notes
above], and then Newton would have no difficulty in gaining such
information as the national Observatory could give.

The "inclination" meant is the angle between the plane of the moon's
orbit and that of the earth. The plane of the earth's orbit round the sun is
called the ecliptic; the plane of the moon's orbit round the earth is inclined
to it at a certain angle, which is slowly changing, though in a periodic
manner. Imagine a curtain ring bisected by a sheet of paper, and tilted to a
certain angle; it may be likened to the moon's orbit, cutting the plane of the
ecliptic. The two points at which the plane is cut by the ring are called
"nodes"; and these nodes are not stationary, but are slowly regressing, i.e.
travelling in a direction opposite to that of the moon itself. Also the angle of
tilt is varying slowly, oscillating up and down in the course of centuries.

(f) The two points in the moon's elliptic orbit where it comes nearest to
or farthest from the earth, i.e. the points at the extremity of the long axis of
the ellipse, are called separately perigee and apogee, or together "the apses."
Now the pull of the sun causes the whole orbit to slowly revolve in its own
plane, and consequently these apses "progress," so that the true path is not
quite a closed curve, but a sort of spiral with elliptic loops.

But here comes in a striking circumstance. Newton states with reference
to this perturbation that theory only accounts for 1½° per annum, whereas
observation gives 3°, or just twice as much.

This is published in the Principia as a fact, without comment. It was for
long regarded as a very curious thing, and many great mathematicians
afterwards tried to find an error in the working. D'Alembert, Clairaut, and
others attacked the problem, but were led to just the same result. It
constituted the great outstanding difficulty in the way of accepting the
theory of gravitation. It was suggested that perhaps the inverse square law
was only a first approximation; that perhaps a more complete expression,
such as

A B
+ ,
r2 r4

must be given for it; and so on.

Ultimately, Clairaut took into account a whole series of neglected terms,
and it came out correct; thus verifying the theory.

But the strangest part of this tale is to come. For only a few years ago,
Prof. Adams, of Cambridge (Neptune Adams, as he is called), was editing
various old papers of Newton's, now in the possession of the Duke of
Portland, and he found manuscripts bearing on this very point, and
discovered that Newton had reworked out the calculations himself, had
found the cause of the error, had taken into account the terms hitherto
neglected, and so, fifty years before Clairaut, had completely, though not
publicly, solved this long outstanding problem of the progression of the
apses.

(g) and (h) Two other inequalities he calculated out and predicted, viz.
variation in the motions of the apses and the nodes. Neither of these had
then been observed, but they were afterwards detected and verified.

A good many other minor irregularities are now known—some thirty, I
believe; and altogether the lunar theory, or problem of the moon's exact
motion, is one of the most complicated and difficult in astronomy; the

perturbations being so numerous and large, because of the enormous mass
of the perturbing body.

The disturbances experienced by the planets are much smaller, because
they are controlled by the sun and perturbed by each other. The moon is
controlled only by the earth, and perturbed by the sun. Planetary
perturbations can be treated as a series of disturbances with some
satisfaction: not so those of the moon. And yet it is the only way at present
known of dealing with the lunar theory.

To deal with it satisfactorily would demand the solution of such a
problem as this:—Given three rigid spherical masses thrown into empty
space with any initial motions whatever, and abandoned to gravity: to
determine their subsequent motions. With two masses the problem is simple
enough, being pretty well summed up in Kepler's laws; but with three
masses, strange to say, it is so complicated as to be beyond the reach of
even modern mathematics. It is a famous problem, known as that of "the
three bodies," but it has not yet been solved. Even when it is solved it will
be only a close approximation to the case of earth, moon, and sun, for these
bodies are not spherical, and are not rigid. One may imagine how absurdly
and hopelessly complicated a complete treatment of the motions of the
entire solar system would be.

No. 8. Each planet is attracted not only by the sun but by the other
planets, hence their orbits are slightly affected by each other.

The subject of planetary perturbation was only just begun by Newton.
Gradually (by Laplace and others) the theory became highly developed;
and, as everybody knows, in 1846 Neptune was discovered by means of it.

No. 9. He recognized the comets as members of the solar system,
obedient to the same law of gravity and moving in very elongated ellipses;
so their return could be predicted.

It was a long time before Newton recognized the comets as real
members of the solar system, and subject to gravity like the rest. He at first
thought they moved in straight lines. It was only in the second edition of the
Principia that the theory of comets was introduced.

Halley observed a fine comet in 1682, and calculated its orbit on
Newtonian principles. He also calculated when it ought to have been seen in
past times; and he found the year 1607, when one was seen by Kepler; also
the year 1531, when one was seen by Appian; again, he reckoned 1456,
1380, 1305. All these appearances were the same comet, in all probability,
returning every seventy-five or seventy-six years. The period was easily
allowed to be not exact, because of perturbing planets. He then predicted its
return for 1758, or perhaps 1759, a date he could not himself hope to see.
He lived to a great age, but he died sixteen years before this date.

As the time drew nigh, three-quarters of a century afterwards,
astronomers were greatly interested in this first cometary prediction, and
kept an eager look-out for "Halley's comet." Clairaut, a most eminent
mathematician and student of Newton, proceeded to calculate out more
exactly the perturbing influence of Jupiter, near which it had passed. After
immense labour (for the difficulty of the calculation was extreme, and the
mass of mere figures something portentous), he predicted its return on the
13th of April, 1759, but he considered that he might have made a possible
error of a month. It returned on the 13th of March, 1759, and established
beyond all doubt the rule of the Newtonian theory over comets.

Fig. 71.—Well-known model exhibiting the oblate spheroidal form as a
consequence of spinning about a central axis. The brass strip a looks like a
transparent globe when whirled, and bulges out equatorially.

No. 10. Applying the idea of centrifugal force to the earth considered as
a rotating body, he perceived that it could not be a true sphere, and
calculated its oblateness, obtaining 28 miles greater equatorial than polar
diameter.

Here we return to one of the more simple deductions. A spinning body of
any kind tends to swell at its circumference (or equator), and shrink along
its axis (or poles). If the body is of yielding material, its shape must alter
under the influence of centrifugal force; and if a globe of yielding substance
subject to known forces rotates at a definite pace, its shape can be
calculated. Thus a plastic sphere the size of the earth, held together by its
own gravity, and rotating once a day, can be shown to have its equatorial
diameter twenty-eight miles greater than its polar diameter: the two
diameters being 8,000 and 8,028 respectively. Now we have no guarantee
that the earth is of yielding material: for all Newton could tell it might be
extremely rigid. As a matter of fact it is now very nearly rigid. But he
argued thus. The water on it is certainly yielding, and although the solid
earth might decline to bulge at the equator in deference to the diurnal
rotation, that would not prevent the ocean from flowing from the poles to
the equator and piling itself up as an equatorial ocean fourteen miles deep,
leaving dry land everywhere near either pole. Nothing of this sort is
observed: the distribution of land and water is not thus regulated. Hence,

whatever the earth may be now, it must once have been plastic enough to
accommodate itself perfectly to the centrifugal forces, and to take the shape
appropriate to a perfectly plastic body. In all probability it was once molten,
and for long afterwards pasty.

Thus, then, the shape of the earth can be calculated from the length of its
day and the intensity of its gravity. The calculation is not difficult: it
consists in imagining a couple of holes bored to the centre of the earth, one
from a pole and one from the equator; filling these both with water, and
calculating how much higher the water will stand in one leg of the gigantic
V tube so formed than in the other. The answer comes out about fourteen
miles.

The shape of the earth can now be observed geodetically, and it accords
with calculation, but the observations are extremely delicate; in Newton's
time the size was only barely known, the shape was not observed till long
after; but on the principles of mechanics, combined with a little common-
sense reasoning, it could be calculated with certainty and accuracy.

No. 11. From the observed shape of Jupiter or any planet the length of its
day could be estimated.

Jupiter is much more oblate than the earth. Its two diameters are to one
another as 17 is to 16; the ellipticity of its disk is manifest to simple
inspection. Hence we perceive that its whirling action must be more violent
—it must rotate quicker. As a matter of fact its day is ten

Fig. 72.—Jupiter.

hours long—five hours daylight and five hours night. The times of
rotation of other bodies in the solar system are recorded in a table above.

No. 12. The so-calculated shape of the earth, in combination with
centrifugal force, causes the weight of bodies to vary with latitude; and
Newton calculated the amount of this variation. 194 lbs. at pole balance 195
lbs. at equator.

But following from the calculated shape of the earth follow several
interesting consequences. First of all, the intensity of gravity will not be the
same everywhere; for at the equator a stone is further from the average bulk
of the earth (say the centre) than it is at the poles, and owing to this fact a
mass of 590 pounds at the pole; would suffice to balance 591 pounds at the
equator, if the two could be placed in the pans of a gigantic balance whose
beam straddled along an earth's quadrant. This is a true variation of gravity
due to the shape of the earth. But besides this there is a still larger apparent
variation due to centrifugal force, which affects all bodies at the equator but
not those at the poles. From this cause, even if the earth were a true sphere,
yet if it were spinning at its actual pace, 288 pounds at the pole could
balance 289 pounds at the equator; because at the equator the true weight of

the mass would not be fully appreciated, centrifugal force would virtually
diminish it by 1⁄289th of its amount.

In actual fact both causes co-exist, and accordingly the total variation of
gravity observed is compounded of the real and the apparent effects; the
result is that 194 pounds at a pole weighs as much as 195 pounds at the
equator.

No. 13. A homogeneous sphere attracts as if its mass were concentrated
at its centre. For any other figure, such as an oblate spheroid, this is not
exactly true. A hollow concentric spherical shell exerts no force on small
bodies inside it.

A sphere composed of uniform material, or of materials arranged in
concentric strata, can be shown to attract external bodies as if its mass were
concentrated at its centre. A hollow sphere, similarly composed, does the
same, but on internal bodies it exerts no force at all.

Hence, at all distances above the surface of the earth, gravity decreases
in inverse proportion as the square of the distance from the centre of the
earth increases; but, if you descend a mine, gravity decreases in this case
also as you leave the surface, though not at the same rate as when you went
up. For as you penetrate the crust you get inside a concentric shell, which is
thus powerless to act upon you, and the earth you are now outside is a
smaller one. At what rate the force decreases depends on the distribution of
density; if the density were uniform all through, the law of variation would
be the direct distance, otherwise it would be more complicated. Anyhow,
the intensity of gravity is a maximum at the surface of the earth, and
decreases as you travel from the surface either up or down.

No. 14. The earth's equatorial protuberance, being acted on by the
attraction of the sun and moon, must disturb its axis of rotation in a
calculated manner; and thus is produced the precession of the equinoxes.

Here we come to a truly awful piece of reasoning. A sphere attracts as if
its mass were concentrated at its centre (No. 12), but a spheroid does not.
The earth is a spheroid, and hence it pulls and is pulled by the moon with a
slightly uncentric attraction. In other words, the line of pull does not pass
through its precise centre. Now when we have a spinning body, say a top,
overloaded on one side so that gravity acts on it unsymmetrically, what
happens? The axis of rotation begins to rotate cone-wise, at a pace which
depends on the rate of spin, and on the shape and mass of the top, as well as
on the amount and leverage of the overloading.

Newton calculated out the rapidity of this conical motion of the axis of
the earth, produced by the slightly unsymmetrical pull of the moon, and
found that it would complete a revolution in 26,000 years—precisely what
was wanted to explain the precession of the equinoxes. In fact he had
discovered the physical cause of that precession.

Observe that there were three stages in this discovery of precession:—

First, the observation by Hipparchus, that the nodes, or intersections of
the earth's orbit (the sun's apparent orbit) with the plane of the equator, were
not stationary, but slowly moved.

Second, the description of this motion by Copernicus, by the statement
that it was due to a conical motion of the earth's axis of rotation about its
centre as a fixed point.

Third, the explanation of this motion by Newton as due to the pull of the
moon on the equatorial protuberance of the earth.

The explanation could not have been previously suspected, for the shape
of the earth, on which the whole theory depends, was entirely unknown till
Newton calculated it.

Another and smaller motion of a somewhat similar kind has been
worked out since: it is due to the unsymmetrical attraction of the other
planets for this same equatorial protuberance. It shows itself as a periodic

change in the obliquity of the ecliptic, or so-called recession of the apses,
rather than as a motion of the nodes.[21]

No. 15. The waters of the ocean are attracted towards the sun and moon
on one side, and whirled a little farther away than the solid earth on the
other side: hence Newton explained all the main phenomena of the tides.

And now comes another tremendous generalization. The tides had long
been an utter mystery. Kepler likens the earth to an animal, and the tides to
his breathings and inbreathings, and says they follow the moon.

Galileo chaffs him for this, and says that it is mere superstition to
connect the moon with the tides.

Descartes said the moon pressed down upon the waters by the
centrifugal force of its vortex, and so produced a low tide under it.

Everything was fog and darkness on the subject. The legend goes that an
astronomer threw himself into the sea in despair of ever being able to
explain the flux and reflux of its waters.

Newton now with consummate skill applied his theory to the effect of
the moon upon the ocean, and all the main details of tidal action gradually
revealed themselves to him.

He treated the water, rotating with the earth once a day, somewhat as if it
were a satellite acted on by perturbing forces. The moon as it revolves
round the earth is perturbed by the sun. The ocean as it revolves round the
earth (being held on by gravitation just as the moon is) is perturbed by both
sun and moon.

The perturbing effect of a body varies directly as its mass, and inversely
as the cube of its distance. (The simple law of inverse square does not
apply, because a perturbation is a differential effect: the satellite or ocean
when nearer to the perturbing body than the rest of the earth, is attracted
more, and when further off it is attracted less than is the main body of the

earth; and it is these differences alone which constitute the perturbation.)
The moon is the more powerful of the two perturbing bodies, hence the
main tides are due to the moon; and its chief action is to cause a pair of low
waves or oceanic humps, of gigantic area, to travel round the earth once in a
lunar day, i.e. in about 24 hours and 50 minutes. The sun makes a similar
but still lower pair of low elevations to travel round once in a solar day of
24 hours. And the combination of the two pairs of humps, thus periodically
overtaking each other, accounts for the well-known spring and neap tides,—
spring tides when their maxima agree, neap tides when the maximum of one
coincides with the minimum of the other: each of which events happens
regularly once a fortnight.

These are the main effects, but besides these there are the effects of
varying distances and obliquity to be taken into account; and so we have a
whole series of minor disturbances, very like those discussed in No. 7,
under the lunar theory, but more complex still, because there are two
perturbing bodies instead of only one.

The subject of the tides is, therefore, very recondite; and though one may
give some elementary account of its main features, it will be best to defer
this to a separate lecture (Lecture XVII).

I had better, however, here say that Newton did not limit himself to the
consideration of the primary oceanic humps: he pursued the subject into
geographical detail. He pointed out that, although the rise and fall of the
tide at mid-ocean islands would be but small, yet on stretches of coast the
wave would fling itself, and by its momentum would propel the waters, to a
much greater height—for instance, 20 or 30 feet; especially in some funnel-
shaped openings like the Bristol Channel and the Bay of Fundy, where the
concentrated impetus of the water is enormous.

He also showed how the tidal waves reached different stations in
successive regular order each day; and how some places might be fed with
tide by two distinct channels; and that if the time of these channels

happened to differ by six hours, a high tide might be arriving by one
channel and a low tide by the other, so that the place would only feel the
difference, and so have a very small observed rise and fall; instancing a port
in China (in the Gulf of Tonquin) where that approximately occurs.

In fact, although his theory was not, as we now know, complete or final,
yet it satisfactorily explained a mass of intricate detail as well as the main
features of the tides.

No. 16. The sun's mass being known, he calculated the height of the
solar tide.

No. 17. From the observed heights of spring and neap tides he
determined the lunar tide, and thence made an estimate of the mass of the
moon.

Knowing the sun's mass and distance, it was not difficult for Newton to
calculate the height of the protuberance caused by it in a pasty ocean
covering the whole earth. I say pasty, because, if there was any tendency for
impulses to accumulate, as timely pushes given to a pendulum accumulate,
the amount of disturbance might become excessive, and its calculation
would involve a multitude of data. The Newtonian tide ignored this, thus
practically treating the motion as either dead-beat, or else the impulses as
very inadequately timed. With this reservation the mid-ocean tide due to the
action of the sun alone comes out about one foot, or let us say one foot for
simplicity. Now the actual tide observed in mid-Atlantic is at the springs
about four feet, at the neaps about two. The spring tide is lunar plus solar;
the neap tide is lunar minus solar. Hence it appears that the tide caused by
the moon alone must be about three feet, when unaffected by momentum.
From this datum Newton made the first attempt to approximately estimate
the mass of the moon. I said that the masses of satellites must be estimated,
if at all, by the perturbation they are able to cause. The lunar tide is a
perturbation in the diurnal motion of the sea, and its amount is therefore a
legitimate mode of calculating the moon's mass. The available data were

not at all good, however; nor are they even now very perfect; and so the
estimate was a good way out. It is now considered that the mass of the
moon is about one-eightieth that of the earth.

Such are some of the gems extracted from their setting in the Principia,
and presented as clearly as I am able before you.

Do you realize the tremendous stride in knowledge—not a stride, as
Whewell says, nor yet a leap, but a flight—which has occurred between the
dim gropings of Kepler, the elementary truths of Galileo, the fascinating but
wild speculations of Descartes, and this magnificent and comprehensive
system of ordered knowledge. To some his genius seemed almost divine.
"Does Mr. Newton eat, drink, sleep, like other men?" said the Marquis de
l'Hôpital, a French mathematician of no mean eminence; "I picture him to
myself as a celestial genius, entirely removed from the restrictions of
ordinary matter." To many it seemed as if there was nothing more to be
discovered, as if the universe were now explored, and only a few fragments
of truth remained for the gleaner. This is the attitude of mind expressed in
Pope's famous epigram:—
"Nature and Nature's laws lay hid in Night,
God said, Let Newton be, and all was light."

This feeling of hopelessness and impotence was very natural after the
advent of so overpowering a genius, and it prevailed in England for fully a
century. It was very natural, but it was very mischievous; for, as a
consequence, nothing of great moment was done by England in science, and
no Englishman of the first magnitude appeared, till some who are either
living now or who have lived within the present century.

It appeared to his contemporaries as if he had almost exhausted the
possibility of discovery; but did it so appear to Newton? Did it seem to him
as if he had seen far and deep into the truths of this great and infinite

universe? It did not. When quite an old man, full of honour and renown,
venerated, almost worshipped, by his contemporaries, these were his words:
—

"I know not what the world will think of my labours, but to myself it
seems that I have been but as a child playing on the sea-shore; now finding
some pebble rather more polished, and now some shell rather more
agreeably variegated than another, while the immense ocean of truth
extended itself unexplored before me."

And so it must ever seem to the wisest and greatest of men when brought
into contact with the great things of God—that which they know is as
nothing, and less than nothing, to the infinitude of which they are ignorant.

Newton's words sound like a simple and pleasing echo of the words of
that great unknown poet, the writer of the book of Job:—
"Lo, these are parts of His ways,
But how little a portion is heard of Him;
The thunder of His power, who can understand?"

END OF PART I.

PART II
A COUPLE OF CENTURIES' PROGRESS.

NOT E S TO L E CT URE X

Science during the century after Newton

The Principia published, 1687

Roemer 1644–1710
James Bradley 1692–1762
Clairaut 1713–1765
Euler 1707–1783
D'Alembert 1717–1783
Lagrange 1736–1813
Laplace 1749–1827
William Herschel 1738–1822

Olaus Roemer was born in Jutland, and studied at Copenhagen. Assisted
Picard in 1671 to determine the exact position of Tycho's observatory on
Huen. Accompanied Picard to Paris, and in 1675 read before the Academy
his paper "On Successive Propagation of Light as revealed by a certain
inequality in the motion of Jupiter's First Satellite." In 1681 he returned to
Copenhagen as Professor of Mathematics and Astronomy, and died in 1710.
He invented the transit instrument, mural circle, equatorial mounting for
telescopes, and most of the other principal instruments now in use in
observatories. He made as many observations as Tycho Brahé, but the
records of all but the work of three days were destroyed by a great fire in
1728.

Bradley, Professor of Astronomy at Oxford, discovered the aberration of
light in 1729, while examining stars for parallax, and the nutation of the
earth's axis in 1748. Was appointed Astronomer-Royal in 1742.

LECTURE X

ROEMER AND BRADLEY AND THE VELOCITY OF LIGHT

At Newton's death England stood pre-eminent among the nations of
Europe in the sphere of science. But the pre-eminence did not last long.

Two great discoveries were made very soon after his decease, both by
Professor Bradley, of Oxford, and then there came a gap. A moderately
great man often leaves behind him a school of disciples able to work
according to their master's methods, and with a healthy spirit of rivalry
which stimulates and encourages them. Newton left, indeed, a school of
disciples, but his methods of work were largely unknown to them, and such
as were known were too ponderous to be used by ordinary men. Only one
fresh result, and that a small one, has ever been attained by other men
working according to the methods of the Principia. The methods were
studied and commented on in England to the exclusion of all others for nigh
a century, and as a consequence no really important work was done.

On the Continent, however, no such system of slavish imitation
prevailed. Those methods of Newton's which had been simultaneously
discovered by Leibnitz were more thoroughly grasped, modified, extended,
and improved. There arose a great school of French and German
mathematicians, and the laurels of scientific discovery passed to France and
Germany—more especially, perhaps, at this time to France. England has
never wholly recovered them. During the present century this country has
been favoured with some giants who, as they become distant enough for
their true magnitude to be perceived, may possibly stand out as great as any
who have ever lived; but for the mass and bulk of scientific work at the
present day we have to look to Germany, with its enlightened Government
and extensive intellectual development. England, however, is waking up,
and what its Government does not do, private enterprise is beginning to
accomplish. The establishment of centres of scientific and literary activity
in the great towns of England, though at present they are partially
encumbered with the supply of education of an exceedingly rudimentary
type, is a movement that in the course of another century or so will be seen
to be one of the most important and fruitful steps ever taken by this country.
On the Continent such centres have long existed; almost every large town is
the seat of a University, and they are now liberally endowed. The University

of Bologna (where, you may remember, Copernicus learnt mathematics) has
recently celebrated its 800th anniversary.

The scientific history of the century after Newton, summarized in the
above table of dates, embraces the labours of the great mathematicians
Clairaut, Euler, D'Alembert, and especially of Lagrange and Laplace.

But the main work of all these men was hardly pioneering work. It was
rather the surveying, and mapping out, and bringing into cultivation, of
lands already discovered. Probably Herschel may be justly regarded as the
next true pioneer. We shall not, however, properly appreciate the stages
through which astronomy has passed, nor shall we be prepared adequately
to welcome the discoveries of modern times unless we pay some attention
to the intervening age. Moreover, during this era several facts of great
moment gradually came into recognition; and the importance of the
discovery we have now to speak of can hardly be over-estimated.

Our whole direct knowledge of the planetary and stellar universe, from
the early observations of the ancients down to the magnificent discoveries
of a Herschel, depends entirely upon our happening to possess a sense of
sight. To no other of our senses do any other worlds than our own in the
slightest degree appeal. We touch them or hear them never. Consequently, if
the human race had happened to be blind, no other world but the one it
groped its way upon could ever have been known or imagined by it. The
outside universe would have existed, but man would have been entirely and
hopelessly ignorant of it. The bare idea of an outside universe beyond the
world would have been inconceivable, and might have been scouted as
absurd. We do possess the sense of sight; but is it to be supposed that we
possess every sense that can be possessed by finite beings? There is not the
least ground for such an assumption. It is easy to imagine a deaf race or a
blind race: it is not so easy to imagine a race more highly endowed with
senses than our own; and yet the sense of smell in animals may give us
some aid in thinking of powers of perception which transcend our own in
particular directions. If there were a race with higher or other senses than

our own, or if the human race should ever in the process of development
acquire such extra sense-organs, a whole universe of existent fact might
become for the first time perceived by us, and we should look back upon
our past state as upon a blind chrysalid form of existence in which we had
been unconscious of all this new wealth of perception.

It cannot be too clearly and strongly insisted on and brought home to
every mind, that the mode in which the universe strikes us, our view of the
universe, our whole idea of matter, and force, and other worlds, and even of
consciousness, depends upon the particular set of sense-organs with which
we, as men, happen to be endowed. The senses of force, of motion, of
sound, of light, of touch, of heat, of taste, and of smell—these we have, and
these are the things we primarily know. All else is inference founded upon
these sensations. So the world appears to us. But given other sense-organs,
and it might appear quite otherwise. What it is actually and truly like,
therefore, is quite and for ever beyond us—so long as we are finite beings.

Without eyes, astronomy would be non-existent. Light it is which
conveys all the information we possess, or, as it would seem, ever can
possess, concerning the outer and greater universe in which this small world
forms a speck. Light is the channel, the messenger of information; our eyes,
aided by telescopes, spectroscopes, and many other "scopes" that may yet
be invented, are the means by which we read the information that light
brings.

Light travels from the stars to our eyes: does it come instantaneously? or
does it loiter by the way? for if it lingers it is not bringing us information
properly up to date—it is only telling us what the state of affairs was when
it started on its long journey.

Now, it is evidently a matter of interest to us whether we see the sun as
he is now, or only as he was some three hundred years ago. If the
information came by express train it would be three hundred years behind
date, and the sun might have gone out in the reign of Queen Anne without

our being as yet any the wiser. The question, therefore, "At what rate does
our messenger travel?" is evidently one of great interest for astronomers,
and many have been the attempts made to solve it. Very likely the ancient
Greeks pondered over this question, but the earliest writer known to me
who seriously discussed the question is Galileo. He suggests a rough
experimental means of attacking it. First of all, it plainly comes quicker
than sound. This can be perceived by merely watching distant hammering,
or by noticing that the flash of a pistol is seen before its report is heard, or
by listening to the noise of a flash of lightning. Sound takes five seconds to
travel a mile—it has about the same speed as a rifle bullet; but light is much
quicker than that.

The rude experiment suggested by Galileo was to send two men with
lanterns and screens to two distant watch-towers or neighbouring mountain
tops, and to arrange that each was to watch alternate displays and
obscurations of the light made by the other, and to imitate them as promptly
as possible. Either man, therefore, on obscuring or showing his own light
would see the distant glimmer do the same, and would be able to judge if
there was any appreciable interval between his own action and the response
of the distant light. The experiment was actually tried by the Florentine
Academicians,[22] with the result that, as practice improved, the interval
became shorter and shorter, so that there was no reason to suppose that
there was any real interval at all. Light, in fact, seemed to travel
instantaneously.

Well might they have arrived at this result. Even if they had made far
more perfect arrangements—for instance, by arranging a looking-glass at
one of the stations in which a distant observer might see the reflection of his
own lantern, and watch the obscurations and flashings made by himself,
without having to depend on the response of human mechanism—even then
no interval whatever could have been detected.

If, by some impossibly perfect optical arrangement, a lighthouse here
were made visible to us after reflection in a mirror erected at New York, so

that the light would have to travel across the Atlantic and back before it
could be seen, even then the appearance of the light on removing a shutter,
or the eclipse on interposing it, would seem to happen quite instantaneously.
There would certainly be an interval: the interval would be the fiftieth part
of a second (the time a stone takes to drop 1⁄13th of an inch), but that is too
short to be securely detected without mechanism. With mechanism the thing
might be managed, for a series of shutters might be arranged like the teeth
of a large wheel; so that, when the wheel rotates, eclipses follow one
another very rapidly; if then an eye looked through the same opening as that
by which the light goes on its way to the distant mirror, a tooth might have
moved sufficiently to cover up this space by the time the light returned; in
which case the whole would appear dark, for the light would be stopped by
a tooth, either at starting or at returning, continually. At higher speeds of
rotation some light would reappear, and at lower speeds it would also
reappear; by noticing, therefore, the precise speed at which there was
constant eclipse the velocity of light could be determined.

Fig. 73.—Diagram of eye looking at a light reflected in a distant mirror
through the teeth of a revolving wheel.

This experiment has now been made in a highly refined form by Fizeau,
and repeated by M. Cornu with prodigious care and accuracy. But with
these recent matters we have no concern at present. It may be instructive to
say, however, that if the light had to travel two miles altogether, the wheel
would have to possess 450 teeth and to spin 100 times a second (at the risk
of flying to pieces) in order that the ray starting through any one of the gaps
might be stopped on returning by the adjacent tooth.

Well might the velocity of light be called instantaneous by the early
observers. An ordinary experiment seemed (and was) hopeless, and light
was supposed to travel at an infinite speed. But a phenomenon was noticed
in the heavens by a quick-witted and ingenious Danish astronomer, which
was not susceptible of any ordinary explanation, and which he perceived
could at once be explained if light had a certain rate of travel—great,
indeed, but something short of infinite. This phenomenon was connected
with the satellites of Jupiter, and the astronomer's name was Roemer. I will
speak first of the observation and then of the man.

Fig. 74.—Fizeau's wheel, shewing the appearance of distant image seen through
its teeth. 1st, when stationary, next when revolving at a moderate speed, last
when revolving at the high speed just sufficient to cause eclipse.

Jupiter's satellites are visible, precisely as our own moon is, by reason of
the shimmer of sunlight which they reflect. But as they revolve round their
great planet they plunge into his shadow at one part of their course, and so
become eclipsed from sunshine and invisible to us. The moment of
disappearance can be sharply observed.

Take the first satellite as an example. The interval between successive
eclipses ought to be its period of revolution round Jupiter. Observe this
period. It was not uniform. On the average it was 42 hours 47 minutes, but
it seemed to depend on the time of year. When Roemer observed in spring it
was less, and in autumn it was more than usual. This was evidently a
puzzling fact: what on earth can our year have to do with the motion of a
moon of Jupiter's? It was probably, therefore, only an apparent change,
caused either by our greater or less distance from Jupiter, or else by our
greater or less speed of travelling to or from him. Considering it thus, he
was led to see that, when the time of revolution seemed longest, we were
receding fastest from Jupiter, and when shortest, approaching fastest.

If, then, light took time on its journey, if it travelled progressively, the
whole anomaly would be explained.

In a second the earth goes nineteen miles; therefore in 42¾ hours (the
time of revolution of Jupiter's first satellite) it goes 2·9 million (say three
million) miles. The eclipse happens punctually, but we do not see it till the
light conveying the information has travelled the extra three million miles
and caught up the earth. Evidently, therefore, by observing how much the
apparent time of revolution is lengthened in one part of the earth's orbit and
shortened in another, getting all the data accurately, and assuming the truth
of our hypothetical explanation, we can calculate the velocity of light. This
is what Roemer did.

Now the maximum amount of retardation is just about fifteen seconds.
Hence light takes this time to travel three million miles; therefore its
velocity is three million divided by fifteen, say 200,000, or, as we now
know more exactly, 186,000 miles every second. Note that the delay does
not depend on our distance, but on our speed. One can tell this by common-
sense as soon as we grasp the general idea of the explanation. A velocity
cannot possibly depend on a distance only.

Fig. 75.—Eclipses of one of Jupiter's satellites. A diagram intended to illustrate
the dependence of its apparent time of revolution (from eclipse to eclipse) on
the motion of the earth; but not illustrating the matter at all well. TT' T'' are
successive positions of the earth, while JJ' J'' are corresponding positions of
Jupiter.

Roemer's explanation of the anomaly was not accepted by astronomers.
It excited some attention, and was discussed, but it was found not obviously
applicable to any of the satellites except the first, and not very simply and
satisfactorily even to that. I have, of course, given you the theory in its most
elementary and simple form. In actual fact a host of disturbing and

complicated considerations come in—not so violently disturbing for the
first satellite as for the others, because it moves so quickly, but still
complicated enough.

The fact is, the real motion of Jupiter's satellites is a most difficult
problem. The motion even of our own moon (the lunar theory) is difficult
enough: perturbed as its motion is by the sun. You know that Newton said it
cost him more labour than all the rest of the Principia. But the motion of
Jupiter's satellites is far worse. No one, in fact, has yet worked their theory
completely out. They are perturbed by the sun, of course, but they also
perturb each other, and Jupiter is far from spherical. The shape of Jupiter,
and their mutual attractions, combine to make their motions most peculiar
and distracting.

Hence an error in the time of revolution of a satellite was not certainly
due to the cause Roemer suggested, unless one could be sure that the
inequality was not a real one, unless it could be shown that the theory of
gravitation was insufficient to account for it. This had not then been done;
so the half-made discovery was shelved, and properly shelved, as a brilliant
but unverified speculation. It remained on the shelf for half a century, and
was no doubt almost forgotten.

Fig. 76.—A Transit-instrument for the British astronomical expedition, 1874.
Shewing in its essential features the simplest form of such an instrument.

Now a word or two about the man. He was a Dane, educated at
Copenhagen, and learned in the mathematics. We first hear of him as
appointed to assist Picard, the eminent French geodetic surveyor (whose
admirable work in determining the length of a degree you remember in
connection with Newton), who had come over to Denmark with the object
of fixing the exact site of the old and extinct Tychonic observatory in the
island of Huen. For of course the knowledge of the exact latitude and
longitude of every place whence numerous observations have been taken
must be an essential to the full interpretation of those observations. The
measurements being finished, young Roemer accompanied Picard to Paris,
and here it was, a few years after, that he read his famous paper concerning
"An Inequality in the Motion of Jupiter's First Satellite," and its explanation
by means of an hypothesis of "the successive propagation of light."

The later years of his life he spent in Copenhagen as a professor in the
University and an enthusiastic observer of the heavens,—not a descriptive
observer like Herschel, but a measuring observer like Sir George Airy or
Tycho Brahé. He was, in fact, a worthy follower of Tycho, and the main
work of his life is the development and devising of new and more accurate
astronomical instruments. Many of the large and accurate instruments with
which a modern observatory is furnished are the invention of this Dane.
One of the finest observatories in the world is the Russian one at Pulkowa,
and a list of the instruments there reads like an extended catalogue of
Roemer's inventions.

He not only invented the instruments, he had them made, being allowed
money for the purpose; and he used them vigorously, so that at his death he
left great piles of manuscript stored in the national observatory.

Unfortunately this observatory was in the heart of the city, and was thus
exposed to a danger from which such places ought to be as far as possible
exempt.

Some eighteen years after Roemer's death a great conflagration broke
out in Copenhagen, and ruined large portions of the city. The successor to
Roemer, Horrebow by name, fled from his house, with such valuables as he
possessed, to the observatory, and there went on with his work. But before
long the wind shifted, and to his horror he saw the flames coming his way.
He packed up his own and his predecessor's manuscript observations in two
cases, and prepared to escape with them, but the neighbours had resorted to
the observatory as a place of safety, and so choked up the staircase with
their property that he was barely able to escape himself, let alone the
luggage, and everything was lost.

Fig. 77.—Diagram of equatorially mounted telescope; CE is the polar axis
parallel to the axis of the earth; AB the declination axis. The diurnal motion is
compensated by motion about the polar axis only, the other being clamped.

Of all the observations, only three days' work remains, and these were
carefully discussed by Dr. Galle, of Berlin, in 1845, and their nutriment
extracted. These ancient observations are of great use for purposes of
comparison with the present state of the heavens, and throw light upon
possible changes that are going on. Of course nowadays such a series of
observations would be printed and distributed in many libraries, and so
made practically indestructible.

Sad as the disaster was to the posthumous fame of the great observer, a
considerable compensation was preparing. The very year that the fire
occurred in Denmark a quiet philosopher in England was speculating and
brooding on a remarkable observation that he had made concerning the
apparent motion of certain stars, and he was led thereby to a discovery of
the first magnitude concerning the speed of light—a discovery which
resuscitated the old theory of Roemer about Jupiter's satellites, and made
both it and him immortal.

James Bradley lived a quiet, uneventful, studious life, mainly at Oxford
but afterwards at the National Observatory at Greenwich, of which he was
third Astronomer-Royal, Flamsteed and Halley having preceded him in that
office. He had taken orders, and lectured at Oxford as Savilian Professor. It
is said that he pondered his great discovery while pacing the Long Walk at
Magdalen College—and a beautiful place it is to meditate in.

Bradley was engaged in making observations to determine if possible the
parallax of some of the fixed stars. Parallax means the apparent relative
shift of bodies due to a change in the observer's position. It is parallax
which we observe when travelling by rail and looking out of window at the
distant landscape. Things at different distances are left behind at different
apparent rates, and accordingly they seem to move relatively to each other.
The most distant objects are least affected; and anything enormously
distant, like the moon, is not subject to this effect, but would retain its
position however far we travelled, unless we had some extraordinarily
precise means of observation.

So with the fixed stars: they were being observed from a moving
carriage—viz. the earth—and one moving at the rate of nineteen miles a
second. Unless they were infinitely distant, or unless they were all at the
same distance, they must show relative apparent motions among
themselves. Seen from one point of the earth's orbit, and then in six months
from an opposite point, nearly 184 million miles away, surely they must
show some difference of aspect.

Remember that the old Copernican difficulty had never been removed. If
the earth revolved round the sun, how came it that the fixed stars showed no
parallax? The fact still remained a surprise, and the question a challenge.
Picard, like other astronomers, supposed that it was only because the
methods of observation had not been delicate enough; but now that, since
the invention of the telescope and the founding of National Observatories,
accuracy hitherto undreamt of was possible, why not attack the problem
anew? This, then, he did, watching the stars with great care to see if in six
months they showed any change in absolute position with reference to the
pole of the heavens; any known secular motion of the pole, such as
precession, being allowed for. Already he thought he detected a slight
parallax for several stars near the pole, and the subject was exciting much
interest.

Bradley determined to attempt the same investigation. He was not
destined to succeed in it. Not till the present century was success in that
most difficult observation achieved; and even now it cannot be done by the
absolute methods then attempted; but, as so often happens, Bradley, in
attempting one thing, hit upon another, and, as it happened, one of still
greater brilliance and importance. Let us trace the stages of his discovery.

Atmospheric refraction made horizon observations useless for the
delicacy of his purpose, so he chose stars near the zenith, particularly one—
γ Draconis. This he observed very carefully at different seasons of the year
by means of an instrument specially adapted for zenith observations, viz. a
zenith sector. The observations were made in conjunction with a friend of

his, an amateur astronomer named Molyneux, and they were made at Kew.
Molyneux was shortly made First Lord of the Admiralty, or something
important of that sort, and gave up frivolous pursuits. So Bradley observed
alone. They observed the star accurately early in the month of December,
and then intended to wait six months. But from curiosity Bradley observed
it again only about a week later. To his surprise, he found that it had already
changed its position. He recorded his observation on the back of an old
envelope: it was his wont thus to use up odd scraps of paper—he was not, I
regret to say, a tidy or methodical person—and this odd piece of paper
turned up long afterwards among his manuscripts. It has been photographed
and preserved as an historical relic.

Again and again he repeated the observation of the star, and continually
found it moving still a little further and further south, an excessively small
motion, but still an appreciable one—not to be set down to errors of
observation. So it went on till March. It then waited, and after a bit longer
began to return, until June. By September it was displaced as much to the
north as it had been to the south, and by December it had got back to its
original position. It had described, in fact, a small oscillation in the course
of the year. The motion affected neighbouring stars in a similar way, and
was called an "aberration," or wandering from their true place.

For a long time Bradley pondered over this observation, and over others
like them which he also made. He found one group of stars describing small
circles, while others at a distance from them were oscillating in straight
lines, and all the others were describing ellipses. Unless this state of things
were cleared up, accurate astronomy was impossible. The fixed stars!—they
were not fixed a bit. To refined and accurate observation, such as was now
possible, they were all careering about in little orbits having a reference to
the earth's year, besides any proper motion which they might really have of
their own, though no such motion was at present known. Not till Herschel
was that discovered; not till this extraordinary aberration was allowed for
could it be discovered. The effect observed by Bradley and Molyneux must
manifestly be only an apparent motion: it was absurd to suppose a real

stellar motion regulating itself according to the position of the earth.
Parallax could not do it, for that would displace stars relatively among each
other—it would not move similarly a set of neighbouring stars.

At length, four years after the observation, the explanation struck him,
while in a boat upon the Thames. He noticed the apparent direction of the
wind changed whenever the boat started. The wind veered when the boat's
motion changed. Of course the cause of this was obvious enough—the
speed of the wind and the speed of the boat were compounded, and gave an
apparent direction of the wind other than the true direction. But this
immediately suggested a cause for what he had observed in the heavens. He
had been observing an apparent direction of the stars other than the true
direction, because he was observing from a moving vehicle. The real
direction was doubtless fixed: the apparent direction veered about with the
motion of the earth. It must be that light did not travel instantaneously, but
gradually, as Roemer had surmised fifty years ago; and that the motion of
the light was compounded with the motion of the earth.

Think of a stream of light or anything else falling on a moving carriage.
The carriage will run athwart the stream, the occupants of the carriage will
mistake its true direction. A rifle fired through the windows of a railway
carriage by a man at rest outside would make its perforations not in the true
line of fire unless the train is stationary. If the train is moving, the line
joining the holes will point to a place in advance of where the rifle is really
located.

So it is with the two glasses of a telescope, the object-glass and eye-
piece, which are pierced by the light; an astronomer, applying his eye to the
tube and looking for the origin of the disturbance, sees it apparently, but not
in its real position—its apparent direction is displaced in the direction of the
telescope's motion; by an amount depending on the ratio of the velocity of
the earth to the velocity of light, and on the angle between those two
directions.

Fig. 78.—Aberration diagram. The light-ray L penetrates the object-glass of the
moving telescope at O, but does not reach the eye-piece until the telescope
has travelled to the second position. Consequently a moving telescope does
not point out the true direction of the light, but aims at a point a little in
advance.

But how minute is the displacement! The greatest effect is obtained
when the two motions are at right angles to each other, i.e. when the star
seen is at right angles to the direction of the earth's motion, but even then it
is only 20", or 1⁄180th part of a degree; one-ninetieth of the moon's apparent
diameter. It could not be detected without a cross-wire in the telescope, and
would only appear as a slight displacement from the centre of the field,
supposing the telescope accurately pointed to the true direction.

But if this explanation be true, it at once gives a method of determining
the velocity of light. The maximum angle of deviation, represented as a
ratio of arc ÷ radius, amounts to

1 1
– ·0001 =
180 × 57⅓ 10,000

(a gradient of 1 foot in two miles). In other words, the velocity of light must
be 10,000 times as great as the velocity of the earth in its orbit. This
amounts to a speed of 190,000 miles a second—not so very different from
what Roemer had reckoned it in order to explain the anomalies of Jupiter's
first satellite.

Stars in the direction in which the earth was moving would not be thus
affected; there would be nothing in mere approach or recession to alter
direction or to make itself in any way visible. Stars at right angles to the
earth's line of motion would be most affected, and these would be all
displaced by the full amount of 20 seconds of arc. Stars in intermediate
directions would be displaced by intermediate amounts.

But the line of the earth's motion is approximately a circle round the sun,
hence the direction of its advance is constantly though slowly changing, and
in one year it goes through all the points of the compass. The stars, being
displaced always in the line of advance, must similarly appear to describe
little closed curves, always a quadrant in advance of the earth, completing
their orbits once a year. Those near the pole of the ecliptic will describe
circles, being always at right angles to the motion. Those in the plane of the
ecliptic (near the zodiac) will be sometimes at right angles to the motion,
but at other times will be approached or receded from; hence these will
oscillate like pendulums once a year; and intermediate stars will have
intermediate motions—that is to say, will describe ellipses of varying
excentricity, but all completed in a year, and all with the major axis 20".
This agreed very closely with what was observed.

The main details were thus clearly and simply explained by the
hypothesis of a finite velocity for light, "the successive propagation of light
in time." This time there was no room for hesitation, and astronomers hailed
the discovery with enthusiasm.

Not yet, however, did Bradley rest. The finite velocity of light explained
the major part of the irregularities he had observed, but not the whole. The
more carefully he measured the amount of the deviation, the less
completely accurate became its explanation.

There clearly was a small outstanding error or discrepancy; the stars
were still subject to an unexplained displacement—not, indeed, a
displacement that repeated itself every year, but one that went through a
cycle of changes in a longer period.

The displacement was only about half that of aberration, and having a
longer period was rather more difficult to detect securely. But the major
difficulty was the fact that the two sorts of disturbances were co-existent,
and the skill of disentangling them, and exhibiting the true and complete
cause of each inequality, was very brilliant.

For nineteen years did Bradley observe this minor displacement, and in
that time he saw it go through a complete cycle. Its cause was now clear to
him; the nineteen-year period suggested the explanation. It is the period in
which the moon goes through all her changes—a period known to the
ancients as the lunar cycle, or Metonic cycle, and used by them to predict
eclipses. It is still used for the first rough approximation to the prediction of
eclipses, and to calculate Easter. The "Golden Number" of the Prayer-book
is the number of the year in this cycle.

The cause of the second inequality, or apparent periodic motion of the
stars, Bradley made out to be a nodding motion of the earth's axis.

The axis of the earth describes its precessional orbit or conical motion
every 26,000 years, as had long been known; but superposed upon this great
movement have now been detected minute nods, each with a period of
nineteen years.

The cause of the nodding is completely accounted for by the theory of
gravitation, just as the precession of the equinoxes was. Both disturbances

result from the attraction of the moon on the non-spherical earth—on its
protuberant equator.

"Nutation" is, in fact, a small perturbation of precession. The motion
may be observed in a non-sleeping top. The slow conical motion of the top's
slanting axis represents the course of precession. Sometimes this path is
loopy, and its little nods correspond to nutation.

The probable existence of some such perturbation had not escaped the
sagacity of Newton, and he mentions something about it in the Principia,
but thinks it too small to be detected by observation. He was thinking,
however, of a solar disturbance rather than a lunar one, and this is certainly
very small, though it, too, has now been observed.

Newton was dead before Bradley made these great discoveries, else he
would have been greatly pleased to hear of them.

These discoveries of aberration and nutation, says Delambre, the great
French historian of science, secure to their author a distinguished place after
Hipparchus and Kepler among the astronomers of all ages and all countries.

NOT E S TO L E CT URE XI

Lagrange and Laplace, both tremendous mathematicians, worked very
much in alliance, and completed Newton's work. The Mécanique Céleste
contains the higher intricacies of astronomy mathematically worked out
according to the theory of gravitation. They proved the solar system to be
stable; all its inequalities being periodic, not cumulative. And Laplace
suggested the "nebular hypothesis" concerning the origin of sun and
planets: a hypothesis previously suggested, and to some extent, elaborated,
by Kant.

A list of some of the principal astronomical researches of Lagrange and
Laplace:—Libration of the moon. Long inequality of Jupiter and Saturn.
Perturbations of Jupiter's satellites. Perturbations of comets. Acceleration of
the moon's mean motion. Improved lunar theory. Improvements in the
theory of the tides. Periodic changes in the form and obliquity of the earth's
orbit. Stability of the solar system considered as an assemblage of rigid
bodies subject to gravity.

The two equations which establish the stability of the solar system are:
—

Sum (me2√d) = constant,

and

Sum (m tan2θ√d) = constant;

where m is the mass of each planet, d its mean distance from the sun, e the
excentricity of its orbit, and θ the inclination of its plane. However the
expressions above formulated may change for individual planets, the sum of
them for all the planets remains invariable.

The period of the variations in excentricity of the earth's orbit is 86,000
years; the period of conical revolution of the earth's axis is 25,800 years.
About 18,000 years ago the excentricity was at a maximum.

LECTURE XI

LAGRANGE AND LAPLACE—THE STABILITY OF THE SOLAR
SYSTEM, AND THE NEBULAR HYPOTHESIS

Laplace was the son of a small farmer or peasant of Normandy. His
extraordinary ability was noticed by some wealthy neighbours, and by them
he was sent to a good school. From that time his career was one brilliant
success, until in the later years of his life his prominence brought him
tangibly into contact with the deteriorating influence of politics. Perhaps
one ought rather to say trying than deteriorating; for they seem trying to a
strong character, deteriorating to a weak one—and unfortunately, Laplace
must be classed in this latter category.

It has always been the custom in France for its high scientific men to be
conspicuous also in politics. It seems to be now becoming the fashion in
this country also, I regret to say.

The life of Laplace is not specially interesting, and I shall not go into it.
His brilliant mathematical genius is unquestionable, and almost unrivalled.
He is, in fact, generally considered to come in this respect next after
Newton. His talents were of a more popular order than those of Lagrange,
and accordingly he acquired fame and rank, and rose to the highest
dignities. Nevertheless, as a man and a politician he hardly commands our
respect, and in time-serving adjustability he is comparable to the
redoubtable Vicar of Bray. His scientific insight and genius were however
unquestionably of the very highest order, and his work has been invaluable
to astronomy.

I will give a short sketch of some of his investigations, so far as they can
be made intelligible without overmuch labour. He worked very much in
conjunction with Lagrange, a more solid though a less brilliant man, and it
is both impossible and unnecessary for us to attempt to apportion respective
shares of credit between these two scientific giants, the greatest scientific
men that France ever produced.

First comes a research into the libration of the moon. This was
discovered by Galileo in his old age at Arcetri, just before his blindness.
The moon, as every one knows, keeps the same face to the earth as it

revolves round it. In other words, it does not rotate with reference to the
earth, though it does rotate with respect to outside bodies. Its libration
consists in a sort of oscillation, whereby it shows us now a little more on
one side, now a little more on the other, so that altogether we are cognizant
of more than one-half of its surface—in fact, altogether of about three-
fifths. It is a simple and unimportant matter, easily explained.
The motion of the moon may be analyzed into a rotation about its own axis
combined with a revolution about the earth. The speed of the rotation is quite uniform,
the speed of the revolution is not quite uniform, because the orbit is not circular but
elliptical, and the moon has to travel faster in perigee than in apogee (in accordance
with Kepler's second law). The consequence of this is that we see a little too far round
the body of the moon, first on one side, then on the other. Hence it appears to oscillate
slightly, like a lop-sided fly-wheel whose revolutions have been allowed to die away
so that they end in oscillations of small amplitude.[23] Its axis of rotation, too, is not
precisely perpendicular to its plane of revolution, and therefore we sometimes see a
few hundred miles beyond its north pole, sometimes a similar amount beyond its
south. Lastly, there is a sort of parallax effect, owing to the fact that we see the rising
moon from one point of view, and the setting moon from a point 8,000 miles distant;
and this base-line of the earth's diameter gives us again some extra glimpses. This
diurnal or parallactic libration is really more effective than the other two in extending
our vision into the space-facing hemisphere of the moon.

These simple matters may as well be understood, but there is nothing in them to
dwell upon. The far side of the moon is probably but little worth seeing. Its features
are likely to be more blurred with accumulations of meteoric dust than are those of
our side, but otherwise they are likely to be of the same general character.

The thing of real interest is the fact that the moon does turn the same
face towards us; i.e. has ceased to rotate with respect to the earth (if ever it
did so). The stability of this state of things was shown by Lagrange to
depend on the shape of the moon. It must be slightly egg-shape, or prolate
—extended in the direction of the earth; its earth-pointing diameter being a
few hundred feet longer than its visible diameter; a cause slight enough, but
nevertheless sufficient to maintain stability, except under the action of a
distinct disturbing cause. The prolate or lemon-like shape is caused by the
gravitative pull of the earth, balanced by the centrifugal whirl. The two
forces balance each other as regards motion, but between them they have

strained the moon a trifle out of shape. The moon has yielded as if it were
perfectly plastic; in all probability it once was so.

It may be interesting to note for a moment the correlative effect of this
aspect of the moon, if we transfer ourselves to its surface in imagination,
and look at the earth (cf. Fig. 41). The earth would be like a gigantic moon
of four times our moon's diameter, and would go through its phases in
regular order. But it would not rise or set: it would be fixed in the sky, and
subject only to a minute oscillation to and fro once a month, by reason of
the "libration" we have been speaking of. Its aspect, as seen by markings on
its surface, would rapidly change, going through a cycle in twenty-four
hours; but its permanent features would be usually masked by lawless
accumulations of cloud, mainly aggregated in rude belts parallel to the
equator. And these cloudy patches would be the most luminous, the whitest
portions; for of course it would be their silver lining that we would then be
looking on.[24]

Next among the investigations of Lagrange and Laplace we will mention
the long inequality of Jupiter and Saturn. Halley had found that Jupiter was
continually lagging behind its true place as given by the theory of
gravitation; and, on the other hand, that Saturn was being accelerated. The
lag on the part of Jupiter amounted to about 34½ minutes in a century.
Overhauling ancient observations, however, Halley found signs of the
opposite state of things, for when he got far enough back Jupiter was
accelerated and Saturn was being retarded.

Here was evidently a case of planetary perturbation, and Laplace and
Lagrange undertook the working of it out. They attacked it as a case of the
problem of three bodies, viz. the sun, Jupiter, and Saturn; which are so
enormously the biggest of the known bodies in the system that insignificant
masses like the Earth, Mars, and the rest, may be wholly neglected. They
succeeded brilliantly, after a long and complex investigation: succeeded, not
in solving the problem of the three bodies, but, by considering their mutual
action as perturbations superposed on each other, in explaining the most

conspicuous of the observed anomalies of their motion, and in laying the
foundation of a general planetary theory.

Fig. 79.—Shewing the three conjunction places in the orbits of Jupiter and
Saturn. The two planets are represented as leaving one of the conjunctions
where Jupiter was being pulled back and Saturn being pulled forward by their
mutual attraction.
One of the facts that plays a large part in the result was known to the old
astrologers, viz. that Jupiter and Saturn come into conjunction with a certain
triangular symmetry; the whole scheme being called a trigon, and being mentioned
several times by Kepler. It happens that five of Jupiter's years very nearly equal two
of Saturn's,[25] so that they get very nearly into conjunction three times in every five
Jupiter years, but not exactly. The result of this close approach is that periodically one
pulls the other on and is itself pulled back; but since the three points progress, it is not
always the same planet which gets pulled back. The complete theory shows that in the
year 1560 there was no marked perturbation: before that it was in one direction, while
afterwards it was in the other direction, and the period of the whole cycle of
disturbances is 929 of our years. The solution of this long outstanding puzzle by the
theory of gravitation was hailed with the greatest enthusiasm by astronomers, and it
established the fame of the two French mathematicians.

Next they attacked the complicated problem of the motions of Jupiter's
satellites. They succeeded in obtaining a theory of their motions which

represented fact very nearly indeed, and they detected the following curious
relationship between the satellites:—The speed of the first satellite + twice
the speed of the second is equal to the speed of the third.

They found this, not empirically, after the manner of Kepler, but as a
deduction from the law of gravitation; for they go on to show that even if
the satellites had not started with this relation they would sooner or later, by
mutual perturbation, get themselves into it. One singular consequence of
this, and of another quite similar connection between their positions, is that
all three satellites can never be eclipsed at once.

The motion of the fourth satellite is less tractable; it does not so readily
form an easy system with the others.

After these great successes the two astronomers naturally proceeded to
study the mutual perturbations of all other bodies in the solar system. And
one very remarkable discovery they made concerning the earth and moon,
an account of which will be interesting, though the details and processes of
calculation are quite beyond us in a course like this.

Astronomical theory had become so nearly perfect by this time, and
observations so accurate, that it was possible to calculate many
astronomical events forwards or backwards, over even a thousand years or
more, with admirable precision.

Now, Halley had studied some records of ancient eclipses, and had
calculated back by means of the lunar theory to see whether the calculation
of the time they ought to occur would agree with the record of the time they
did occur. To his surprise he found a discrepancy, not a large one, but still
one quite noticeable. To state it as we know it now:—An eclipse a century
ago happened twelve seconds later than it ought to have happened by
theory; two centuries back the error amounted to forty-eight seconds, in
three centuries it would be 108 seconds, and so on; the lag depending on the
square of the time. By research, and help from scholars, he succeeded in
obtaining the records of some very ancient eclipses indeed. One in Egypt

towards the end of the tenth century a.d.; another in 201 a.d.; another a little
before Christ; and one, the oldest of all of which any authentic record has
been preserved, observed by the Chaldæan astronomers in Babylon in the
reign of Hezekiah.

Calculating back to this splendid old record of a solar eclipse, over the
intervening 2,400 years, the calculated and the observed times were found
to disagree by nearly two hours. Pondering over an explanation of the
discrepancy, Halley guessed that it must be because the moon's motion was
not uniform, it must be going quicker and quicker, gaining twelve seconds
each century on its previous gain—a discovery announced by him as "the
acceleration of the moon's mean motion." The month was constantly getting
shorter.

What was the physical cause of this acceleration according to the theory
of gravitation? Many attacked the question, but all failed. This was the
problem Laplace set himself to work out. A singular and beautiful result
rewarded his efforts.

You know that the earth describes an elliptic orbit round the sun: and
that an ellipse is a circle with a certain amount of flattening or
"excentricity."[26] Well, Laplace found that the excentricity of the earth's
orbit must be changing, getting slightly less; and that this change of
excentricity would have an effect upon the length of the month. It would
make the moon go quicker.

One can almost see how it comes about. A decrease in excentricity
means an increase in mean distance of the earth from the sun. This means to
the moon a less solar perturbation. Now one effect of the solar perturbation
is to keep the moon's orbit extra large: if the size of its orbit diminishes, its
velocity must increase, according to Kepler's third law.

Laplace calculated the amount of acceleration so resulting, and found it
ten seconds a century; very nearly what observation required; for, though I

have quoted observation as demanding twelve seconds per century, the facts
were not then so distinctly and definitely ascertained.

This calculation for a long time seemed thoroughly satisfactory, but it is
not the last word on the subject. Quite lately an error has been found in the
working, which diminishes the theoretical gravitation-acceleration to six
seconds a century instead of ten, thus making it insufficient to agree exactly
with fact. The theory of gravitation leaves an outstanding error. (The point
is now almost thoroughly understood, and we shall return to it in Lecture
XVIII).

But another question arises out of this discussion. I have spoken of the
excentricity of the earth's orbit as decreasing. Was it always decreasing? and
if so, how far back was it so excentric that at perihelion the earth passed
quite near the sun? If it ever did thus pass near the sun, the inference is
manifest—the earth must at one time have been thrown off, or been
separated off, from the sun.

If a projectile could be fired so fast that it described an orbit round the
earth—and the speed of fire to attain this lies between five and seven miles
a second (not less than the one, nor more than the other)—it would ever
afterwards pass through its point of projection as one point of its elliptic
orbit; and its periodic return through that point would be the sign of its
origin. Similarly, if a satellite does not come near its central orb, and can be
shown never to have been near it, the natural inference is that it has not
been born from it, but has originated in some other way.

The question which presented itself in connexion with the variable
ellipticity of the earth's orbit was the following:—Had it always been
decreasing, so that once it was excentric enough just to graze the sun at
perihelion as a projected body would do?

Into the problem thus presented Lagrange threw himself, and he
succeeded in showing that no such explanation of the origin of the earth is
possible. The excentricity of the orbit, though now decreasing, was not

always decreasing; ages ago it was increasing: it passes through periodic
changes. Eighteen thousand years ago its excentricity was a maximum;
since then it has been diminishing, and will continue to diminish for 25,000
years more, when it will be an almost perfect circle; it will then begin to
increase again, and so on. The obliquity of the ecliptic is also changing
periodically, but not greatly: the change is less than three degrees.

This research has, or ought to have, the most transcendent interest for
geologists and geographers. You know that geologists find traces of
extraordinary variations of temperature on the surface of the earth. England
was at one time tropical, at another time glacial. Far away north, in
Spitzbergen, evidence of the luxuriant vegetation of past ages has been
found; and the explanation of these great climatic changes has long been a
puzzle. Does not the secular variation in excentricity of the earth's orbit,
combined with the precession of the equinoxes, afford a key? And if a key
at all, it will be an accurate key, and enable us to calculate back with some
precision to the date of the glacial epoch; and again to the time when a
tropical flora flourished in what is now northern Europe, i.e. to the date of
the Carboniferous era.

This aspect of the subject has recently been taught with vigour and
success by Dr. Croll in his book "Climate and Time."

A brief and partial explanation of the matter may be given, because it is a point of
some interest and is also one of fair simplicity.

Every one knows that the climatic conditions of winter and summer are inverted in
the two hemispheres, and that at present the sun is nearest to us in our (northern)
winter. In other words, the earth's axis is inclined so as to tilt its north pole away from
the sun at perihelion, or when the earth is at the part of its elliptic orbit nearest the
sun's focus; and to tilt it towards the sun at aphelion. The result of this present state of
things is to diminish the intensity of the average northern winter and of the average
northern summer, and on the other hand to aggravate the extremes of temperature in
the southern hemisphere; all other things being equal. Of course other things are not
equal, and the distribution of land and sea is a still more powerful climatic agent than
is the three million miles or so extra nearness of the sun. But it is supposed that the
Antarctic ice-cap is larger than the northern, and increased summer radiation with
increased winter cold would account for this.

But the present state of things did not always obtain. The conical movement of the
earth's axis (now known by a curious perversion of phrase as "precession") will in the
course of 13,000 years or so cause the tilt to be precisely opposite, and then we shall
have the more extreme winters and summers instead of the southern hemisphere.

If the change were to occur now, it might not be overpowering, because now the
excentricity is moderate. But if it happened some time back, when the excentricity
was much greater, a decidedly different arrangement of climate may have resulted.
There is no need to say if it happened some time back: it did happen, and accordingly
an agent for affecting the distribution of mean temperature on the earth is to hand;
though whether it is sufficient to achieve all that has been observed by geologists is a
matter of opinion.

Once more, the whole diversity of the seasons depends on the tilt of the earth's
axis, the 23° by which it is inclined to a perpendicular to the orbital plane; and this
obliquity or tilt is subject to slow fluctuations. Hence there will come eras when all
causes combine to produce a maximum extremity of seasons in the northern
hemisphere, and other eras when it is the southern hemisphere which is subject to
extremes.

But a grander problem still awaited solution—nothing less than the fate
of the whole solar system. Here are a number of bodies of various sizes
circulating at various rates round one central body, all attracted by it, and all
attracting each other, the whole abandoned to the free play of the force of
gravitation: what will be the end of it all? Will they ultimately approach and
fall into the sun, or will they recede further and further from him, into the
cold of space? There is a third possible alternative: may they not alternately

approach and recede from him, so as on the whole to maintain a fair
approximation to their present distances, without great and violent extremes
of temperature either way?

If any one planet of the system were to fall into the sun, more especially
if it were a big one like Jupiter or Saturn, the heat produced would be so
terrific that life on this earth would be destroyed, even at its present
distance; so that we are personally interested in the behaviour of the other
planets as well as in the behaviour of our own.

The result of the portentously difficult and profoundly interesting
investigation, here sketched in barest outline, is that the solar system is
stable: that is to say, that if disturbed a little it will oscillate and return to its
old state; whereas if it were unstable the slightest disturbance would tend to
accumulate, and would sooner or later bring about a catastrophe. A hanging
pendulum is stable, and oscillates about a mean position; its motion is
periodic. A top-heavy load balanced on a point is unstable. All the changes
of the solar system are periodic, i.e. they repeat themselves at regular
intervals, and they never exceed a certain moderate amount.

The period is something enormous. They will not have gone through all
their changes until a period of 2,000,000 years has elapsed. This is the
period of the planetary oscillation: "a great pendulum of eternity which
beats ages as our pendulums beat seconds." Enormous it seems; and yet we
have reason to believe that the earth has existed through many such periods.
The two laws of stability discovered and stated by Lagrange and Laplace I can
state, though they may be difficult to understand:—

Represent the masses of the several planets by m1, m2, &c.; their mean distances
from the sun (or radii vectores) by r1, r2, &c.; the excentricities of their orbits by e1,
e2, &c.; and the obliquity of the planes of these orbits, reckoned from a single plane
of reference or "invariable plane," by θ1, θ2, &c.; then all these quantities (except m)
are liable to fluctuate; but, however much they change, an increase for one planet will
be accompanied by a decrease for some others; so that, taking all the planets into
account, the sum of a set of terms like these, m1e22√r1 + m2e22√r2 + &c., will
remain always the same. This is summed up briefly in the following statement:

Σ(me2√r) = constant.

That is one law, and the other is like it, but with inclination of orbit instead of
excentricity, viz.:

Σ(mθ2√r) = constant.

The value of each of these two constants can at any time be calculated. At present
their values are small. Hence they always were and always will be small; being, in
fact, invariable. Hence neither e nor r nor θ can ever become infinite, nor can their
average value for the system ever become zero.

The planets may share the given amount of total excentricity and
obliquity in various proportions between themselves; but even if it were all
piled on to one planet it would not be very excessive, unless the planet were
so small a one as Mercury; and it would be most improbable that one planet
should ever have all the excentricity of the solar system heaped upon itself.
The earth, therefore, never has been, nor ever will be, enormously nearer
the sun than it is at present: nor can it ever get very much further off. Its
changes are small and are periodic—an increase is followed by a decrease,
like the swing of a pendulum.

The above two laws have been called the Magna Charta of the solar
system, and were long supposed to guarantee its absolute permanence. So
far as the theory of gravitation carries us, they do guarantee its permanence;
but something more remains to be said on the subject in a future lecture
(XVIII).

And now, finally, we come to a sublime speculation, thrown out by
Laplace, not as the result of profound calculation, like the results hitherto
mentioned, not following certainly from the theory of gravitation, or from
any other known theory, and therefore not to be accepted as more than a
brilliant hypothesis, to be confirmed or rejected as our knowledge extends.
This speculation is the "Nebular hypothesis." Since the time of Laplace the
nebular hypothesis has had ups and downs of credence, sometimes being
largely believed in, sometimes being almost ignored. At the present time it
holds the field with perhaps greater probability of ultimate triumph than has

ever before seemed to belong to it—far greater than belonged to it when
first propounded.

It had been previously stated clearly and well by the philosopher Kant,
who was intensely interested in "the starry heavens" as well as in the "mind
of man," and who shewed in connexion with astronomy also a most
surprising genius. The hypothesis ought by rights perhaps to be known
rather by his name than by that of Laplace.

The data on which it was founded are these:—Every motion in the solar
system known at that time took place in one direction, and in one direction
only. Thus the planets revolve round the sun, all going the same way round;
moons revolve round the planets, still maintaining the same direction of
rotation, and all the bodies that were known to rotate on their own axis did
so with still the same kind of spin. Moreover, all these motions take place in
or near a single plane. The ancients knew that sun moon and planets all
keep near to the ecliptic, within a belt known as the zodiac: none strays
away into other parts of the sky. Satellites also, and rings, are arranged in or
near the same plane; and the plane of diurnal spin, or equator of the
different bodies, is but slightly tilted.

Now all this could not be the result of chance. What could have caused
it? Is there any connection or common ancestry possible, to account for this
strange family likeness? There is no connection now, but there may have
been once. Must have been, we may almost say. It is as though they had
once been parts of one great mass rotating as a whole; for if such a rotating
mass broke up, its parts would retain its direction of rotation. But such a
mass, filling all space as far as or beyond Saturn, although containing the
materials of the whole solar system in itself, must have been of very rare
consistency. Occupying so much bulk it could not have been solid, nor yet
liquid, but it might have been gaseous.

Are there any such gigantic rotating masses of gas in the heaven now?
Certainly there are; there are the nebulæ. Some of the nebulæ are now

known to be gaseous, and some of them at least are in a state of rotation.
Laplace could not have known this for certain, but he suspected it. The first
distinctly spiral nebula was discovered by the telescope of Lord Rosse; and
quite recently a splendid photograph of the great Andromeda nebula, by our
townsman, Mr. Isaac Roberts, reveals what was quite unsuspected—and
makes it clear that this prodigious mass also is in a state of extensive and
majestic whirl.

Very well, then, put this problem:—A vast mass of rotating gas is left to
itself to cool for ages and to condense as it cools: how will it behave? A
difficult mathematical problem, worthy of being attacked to-day; not yet at
all adequately treated. There are those who believe that by the complete
treatment of such a problem all the history of the solar system could be
evolved.

Fig. 80.—Lord Rosse's drawing of the spiral nebula in Canes Venatici, with the
stub marks of the draughtsman unduly emphasised into features by the
engraver.

Laplace pictured to himself this mass shrinking and thereby whirling
more and more rapidly. A spinning body shrinking in size and retaining its

original amount of rotation, as it will unless a brake is applied, must spin
more and more rapidly as it shrinks. It has what mathematicians call a
constant moment of momentum; and what it loses in leverage, as it shrinks,
it gains in speed. The mass is held together by gravitation, every particle
attracting every other particle; but since all the particles are describing
curved paths, they will tend to fly off tangentially, and only a small excess
of the gravitation force over the centrifugal is left to pull the particles in,
and slowly to concentrate the nebula. The mutual gravitation of the parts is
opposed by the centrifugal force of the whirl. At length a point is reached
where the two forces balance. A portion outside a certain line will be in
equilibrium; it will be left behind, and the rest must contract without it. A
ring is formed, and away goes the inner nucleus contracting further and
further towards a centre. After a time another ring will be left behind in the
same way, and so on. What happens to these rings? They rotate with the
motion they possess when thrown or shrunk off; but will they remain rings?
If perfectly regular they may; if there be any irregularity they are liable to
break up. They will break into one or two or more large masses, which are
ultimately very likely to collide and become one. The revolving body so
formed is still a rotating gaseous mass; and it will go on shrinking and
cooling and throwing off rings, like the larger nucleus by which it has been
abandoned. As any nucleus gets smaller, its rate of rotation increases, and so
the rings last thrown off will be spinning faster than those thrown off
earliest. The final nucleus or residual central body will be rotating fastest of
all.

The nucleus of the whole original mass we now see shrunk up into what
we call the sun, which is spinning on its axis once every twenty-five days.
The rings successively thrown off by it are now the planets—some large,
some small—those last thrown off rotating round him comparatively
quickly, those outside much more slowly. The rings thrown off by the
planetary gaseous masses as they contracted have now become satellites;
except one ring which has remained without breaking up, and is to be seen
rotating round Saturn still.

One other similar ring, an abortive attempt at a planet, is also left round
the sun (the zone of asteroids).

Such, crudely and baldly, is the famous nebular hypothesis of Laplace. It
was first stated, as has been said above, by the philosopher Kant, but it was
elaborated into much fuller detail by the greatest of French mathematicians
and astronomers.

The contracting masses will condense and generate great quantities of
heat by their own shrinkage; they will at a certain stage condense to liquid,
and after a time will begin to cool and congeal with a superficial crust,
which will get thicker and thicker; but for ages they will remain hot, even
after they have become thoroughly solid. The small ones will cool fastest;
the big ones will retain their heat for an immense time. Bullets cool quickly,
cannon-balls take hours or days to cool, planets take millions of years. Our
moon may be nearly cold, but the earth is still warm—indeed, very hot
inside. Jupiter is believed by some observers still to glow with a dull red
heat; and the high temperature of the much larger and still liquid mass of
the sun is apparent to everybody. Not till it begins to scum over will it be
perceptibly cooler.

Fig. 81.—Saturn.

Many things are now known concerning heat which were not known to
Laplace (in the above paragraph they are only hinted at), and these confirm
and strengthen the general features of his hypothesis in a striking way; so
do the most recent telescopic discoveries. But fresh possibilities have now
occurred to us, tidal phenomena are seen to have an influence then wholly
unsuspected, and it will be in a modified and amplified form that the
philosopher of next century will still hold to the main features of this
famous old Nebular Hypothesis respecting the origin of the sun and planets
—the Evolution of the solar system.

NOT E S TO L E CT URE XI I

The subject of stellar astronomy was first opened up by Sir William
Herschel, the greatest observing astronomer.

Frederick William Herschel was born in Hanover in 1738, and brought
up as a musician. Came to England in 1756. First saw a telescope in 1773.
Made a great many himself, and began a survey of the heavens. His sister
Caroline, born in 1750, came to England in 1772, and became his devoted
assistant to the end of his life. Uranus discovered in 1781. Music finally
abandoned next year, and the 40-foot telescope begun. Discovered two
moons of Saturn and two of Uranus. Reviewed, described, and gauged all
the visible heavens. Discovered and catalogued 2,500 nebulæ and 806
double stars. Speculated concerning the Milky Way, the nebulosity of stars,
the origin and growth of solar systems. Discovered that the stars were in
motion, not fixed, and that the sun as one of them was journeying towards a
point in the constellation Hercules. Died in 1822, eighty-four years old.
Caroline Herschel discovered eight comets, and lived on to the age of
ninety-eight.

LECTURE XII

HERSCHEL AND THE MOTION OF THE FIXED STARS

We may admit, I think, that, with a few notable exceptions, the work of
the great men we have been recently considering was rather to complete
and round off the work of Newton, than to strike out new and original lines.

This was the whole tendency of eighteenth century astronomy. It
appeared to be getting into an adult and uninteresting stage, wherein
everything could be calculated and predicted. Labour and ingenuity, and a
severe mathematical training, were necessary to work out the remote
consequences of known laws, but nothing fresh seemed likely to turn up.
Consequently men's minds began turning in other directions, and we find
chemistry and optics largely studied by some of the greatest minds, instead
of astronomy.

But before the century closed there was destined to arise one remarkable
exception—a man who was comparatively ignorant of that which had been
done before—a man unversed in mathematics and the intricacies of science,
but who possessed such a real and genuine enthusiasm and love of Nature
that he overcame the force of adverse circumstances, and entering the
territory of astronomy by a by-path, struck out a new line for himself, and
infused into the science a healthy spirit of fresh life and activity.

This man was William Herschel.

"The rise of Herschel," says Miss Clerke, "is the one conspicuous
anomaly in the otherwise somewhat quiet and prosy eighteenth century. It
proved decisive of the course of events in the nineteenth. It was
unexplained by anything that had gone before, yet all that came after hinged
upon it. It gave a new direction to effort; it lent a fresh impulse to thought.

It opened a channel for the widespread public interest which was gathering
towards astronomical subjects to flow in."

Herschel was born at Hanover in 1738, the son of an oboe player in a
military regiment. The father was a good musician, and a cultivated man.
The mother was a German Frau of the period, a strong, active, business-like
woman, of strong character and profound ignorance. Herself unable to
write, she set her face against learning and all new-fangled notions. The
education of the sons she could not altogether control, though she lamented
over it, but the education of her two daughters she strictly limited to
cooking, sewing, and household management. These, however, she taught
them well.

It was a large family, and William was the fourth child. We need only
remember the names of his younger brother Alexander, and of his much
younger sister Caroline.

They were all very musical—the youngest boy was once raised upon a
table to play the violin at a public performance. The girls were forbidden to
learn music by their mother, but their father sometimes taught them a little
on the sly. Alexander was besides an ingenious mechanician.

At the age of seventeen, William became oboist to the Hanoverian
Guards, shortly before the regiment was ordered to England. Two years
later he removed himself from the regiment, with the approval of his
parents, though probably without the approbation or consent of the
commanding officer, by whom such removal would be regarded as simple
desertion, which indeed it was; and George III. long afterwards handed him
an official pardon for it.

At the age of nineteen, he was thus launched in England with an outfit of
some French, Latin, and English, picked up by himself; some skill in
playing the hautboy, the violin, and the organ, as taught by his father; and
some good linen and clothing, and an immense stock of energy, provided by
his mother.

He lived as musical instructor to one or two militia bands in Yorkshire,
and for three years we hear no more than this of him. But, at the end of that
time, a noted organist, Dr. Miller, of Durham, who had heard his playing,
proposed that he should come and live with him and play at concerts, which
he was very glad to do. He next obtained the post of organist at Halifax; and
some four or five years later he was invited to become organist at the
Octagon Chapel in Bath, and soon led the musical life of that then very
fashionable place.

About this time he went on a short visit to his family at Hanover, by all
of whom he was very much beloved, especially by his young sister
Caroline, who always regarded him as specially her own brother. It is rather
pitiful, however, to find that her domestic occupations still unfairly
repressed and blighted her life. She says:—
"Of the joys and pleasures which all felt at this long-wished-for meeting with my
—let me say my dearest—brother, but a small portion could fall to my share; for with
my constant attendance at church and school, besides the time I was employed in
doing the drudgery of the scullery, it was but seldom I could make one in the group
when the family were assembled together."

While at Bath he wrote many musical pieces—glees, anthems, chants,
pieces for the harp, and an orchestral symphony. He taught a large number
of pupils, and lived a hard and successful life. After fourteen hours or so
spent in teaching and playing, he would retire at night to instruct his mind
with a study of mathematics, optics, Italian, or Greek, in all of which he
managed to make some progress. He also about this time fell in with some
book on astronomy.

In 1763 his father was struck with paralysis, and two years later he died.

William then proposed that Alexander should come over from Hanover
and join him at Bath, which was done. Next they wanted to rescue their
sister Caroline from her humdrum existence, but this was a more difficult
matter. Caroline's journal gives an account of her life at this time that is
instructive. Here are a few extracts from it:—

"My father wished to give me something like a polished education, but my mother
was particularly determined that it should be a rough, but at the same time a useful
one; and nothing further she thought was necessary but to send me two or three
months to a sempstress to be taught to make household linen....

"My mother would not consent to my being taught French, ... so all my father
could do for me was to indulge me (and please himself) sometimes with a short lesson
on the violin, when my mother was either in good humour or out of the way.... She
had cause for wishing me not to know more than was necessary for being useful in the
family; for it was her certain belief that my brother William would have returned to
his country, and my eldest brother not have looked so high, if they had had a little less
learning."

However, seven years after the death of their father, William went over
to Germany and returned to England in triumph, bringing Caroline with
him: she being then twenty-two.

So now began a busy life in Bath. For Caroline the work must have been
tremendous. For, besides having to learn singing, she had to learn English.
She had, moreover, to keep accounts and do the marketing.

When the season at Bath was over, she hoped to get rather more of her
brother William's society; but he was deep in optics and astronomy, used to
sleep with the books under his pillow, read them during meals, and scarcely
ever thought of anything else.

He was determined to see for himself all the astronomical wonders; and
there being a small Gregorian reflector in one of the shops, he hired it. But
he was not satisfied with this, and contemplated making a telescope 20 feet
long. He wrote to opticians inquiring the price of a mirror suitable, but
found there were none so large, and that even the smaller ones were beyond
his means. Nothing daunted, he determined to make some for himself.
Alexander entered into his plans: tools, hones, polishers, and all sorts of
rubbish were imported into the house, to the sister's dismay, who says:—

Fig. 82.—Principle of Newtonian reflector.
"And then, to my sorrow, I saw almost every room turned into a workshop. A
cabinet-maker making a tube and stands of all descriptions in a handsomely furnished
drawing-room; Alex. putting up a huge turning-machine (which he had brought in the
autumn from Bristol, where he used to spend the summer) in a bed-room, for turning
patterns, grinding glasses, and turning eye-pieces, &c. At the same time music durst
not lie entirely dormant during the summer, and my brother had frequent rehearsals at
home."

Finally, in 1774, at the age of thirty-six, he had made himself a 5½-foot
telescope, and began to view the heavens. So attached was he to the
instrument that he would run from the concert-room between the parts, and
take a look at the stars.

He soon began another telescope, and then another. He must have made
some dozen different telescopes, always trying to get them bigger and
bigger; at last he got a 7-foot and then a 10-foot instrument, and began a
systematic survey of the heavens; he also began to communicate his results
to the Royal Society.

He now took a larger house, with more room for workshops, and a grass
plot for a 20-foot telescope, and still he went on grinding mirrors—literally
hundreds of them.

I read another extract from the diary of his sister, who waited on him and
obeyed him like a spaniel:—
"My time was taken up with copying music and practising, besides attendance on
my brother when polishing, since by way of keeping him alive I was constantly
obliged to feed him by putting the victuals by bits into his mouth. This was once the
case when, in order to finish a 7-foot mirror, he had not taken his hands from it for

sixteen hours together. In general he was never unemployed at meals, but was always
at those times contriving or making drawings of whatever came in his mind.
Generally I was obliged to read to him whilst he was at the turning-lathe, or polishing
mirrors—Don Quixote, Arabian Nights' Entertainments, the novels of Sterne,
Fielding, &c.; serving tea and supper without interrupting the work with which he was
engaged, ... and sometimes lending a hand. I became, in time, as useful a member of
the workshop as a boy might be to his master in the first year of his apprenticeship....
But as I was to take a part the next year in the oratorios, I had, for a whole
twelvemonth, two lessons per week from Miss Fleming, the celebrated dancing-
mistress, to drill me for a gentlewoman (God knows how she succeeded). So we lived
on without interruption. My brother Alex. was absent from Bath for some months
every summer, but when at home he took much pleasure in executing some turning or
clockmaker's work for his brother."

The music, and the astronomy, and the making of telescopes, all went on
together, each at high pressure, and enough done in each to satisfy any
ordinary activity. But the Herschels knew no rest. Grinding mirrors by day,
concerts and oratorios in the evening, star-gazing at night. It is strange his
health could stand it.

The star-gazing, moreover, was no dilettante work; it was based on a
serious system—a well thought out plan of observation. It was nothing less
than this—to pass the whole heavens steadily and in order through the
telescope, noting and describing and recording every object that should be
visible, whether previously known or unknown. The operation is called
sweeping; but it is not a rapid passage from one object to another, as the
term might suggest; it is a most tedious business, and consists in following
with the telescope a certain field of view for some minutes, so as to be sure
that nothing is missed, then shifting it to the next overlapping field, and
watching again. And whatever object appears must be scrutinized anxiously
to see what there is peculiar about it. If a star, it may be double, or it may be
coloured, or it may be nebulous; or again it may be variable, and so its
brightness must be estimated in order to compare with a subsequent
observation.

Four distinct times in his life did Herschel thus pass the whole visible
heavens under review; and each survey occupied him several years. He