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Title: Encyclopaedia Britannica, 11th Edition, "Equation" to "Ethics"

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THE ENCYCLOPÆDIA BRITANNICA

A DICTIONARY OF ARTS, SCIENCES,
LITERATURE AND GENERAL INFORMATION
ELEVENTH EDITION

VOLUME IX SLICE VII

Equation to Ethics

Articles in This Slice

EQUATION ESCHEAT
EQUATION OF THE CENTRE ESCHENBURG, JOHANN JOACHIM
EQUATION OF TIME ESCHENMAYER, ADAM KARL AUGUST
VON
EQUATOR ESCHER VON DER LINTH, ARNOLD
EQUERRY ESCHSCHOLTZ, JOHANN FRIEDRICH
EQUIDAE ESCHWEGE
EQUILIBRIUM ESCHWEILER
EQUINOX ESCOBAR Y MENDOZA, ANTONIO
EQUITES ESCOIQUIZ, JUAN

EQUITY ESCOMBE, HARRY
EQUIVALENT ESCORIAL
ÉRARD, SÉBASTIEN ESCOVEDO, JUAN DE
ERASMUS, DESIDERIUS ESCUINTLA
ERASTUS, THOMAS ESCUTCHEON
ERATOSTHENES OF ESHER, WILLIAM BALIOL BRETT
ALEXANDRIA
ERBACH ESHER
ERBIUM ESKER
ERCILLA Y ZÚNIGA, ALONSO ESKILSTUNA
DE
ERCKMANN-CHATRIAN ESKIMO
ERDÉLYI, JÁNOS ESKI-SHEHR
ERDMANN, JOHANN EDUARD ESMARCH, JOHANNES FRIEDRICH
AUGUST VON
ERDMANN, OTTO LINNÉ ESNA
EREBUS ESOTERIC
ERECH ESPAGNOLS SUR MER, LES
ERECHTHEUM ESPALIER
ERECHTHEUS ESPARTERO, BALDOMERO
ERESHKIGAL ESPARTO
ERETRIA ESPERANCE
ERETRIAN SCHOOL OF ESPERANTO
PHILOSOPHY
ERFURT ESPINAY, TIMOLÉON D’
ERGOT ESPINEL, VICENTE MARTINEZ
ERIC XIV ESPIRITO SANTO
ERICACEAE ESPRONCEDA, JOSÉ IGNACIO JAVIER
ORIOL ENCARNACIÓN DE
ERICHSEN, SIR JOHN ERIC ESQUIRE
ERICHT, LOCH ESQUIROL, JEAN ÉTIENNE DOMINIQUE
ERICSSON, JOHN ESQUIROS, HENRI FRANÇOIS ALPHONSE
ERIDANUS ESS, JOHANN HEINRICH VAN
ERIDU ESSAY, ESSAYIST
ERIE (lake) ESSEG

ERIE (city) ESSEN
ERIGENA, JOHANNES ESSENES
SCOTUS
ERIGONE ESSENTUKI
ERIN ESSEQUIBO
ERINNA ESSEX, EARLS OF
ERINYES ESSEX, ARTHUR CAPEL
ERIPHYLE ESSEX, ROBERT DEVEREUX
ERIS ESSEX, ROBERT DEVEREUX
ERITH ESSEX, WALTER DEVEREUX
ERITREA ESSEX
ERIVAN (government of Russia) ESSEX, KINGDOM OF
ERIVAN (town of Russia) ESSLINGEN
ERLANGEN ESTABLISHMENT
ERLE, SIR WILLIAM ESTABLISHMENT OF A PORT
ERLKÖNIG ESTAING, CHARLES HECTOR
ERMAN, PAUL ESTATE
ERMANARIC ESTATE AND HOUSE AGENTS
ERMELAND ESTATE DUTY
ERMELO ESTCOURT, RICHARD
ERMINE ESTE (family)
ERMINE STREET ESTE (town)
ERMOLDUS NIGELLUS ESTÉBANEZ CALDERÓN, SERAFÍN
ERNE ESTELLA
ERNEST I ESTERHÁZY OF GALÁNTHA
ERNEST II ESTERS
ERNEST AUGUSTUS ESTHER
ERNESTI, JOHANN AUGUST ESTHONIA
ERNESTI, JOHANN ESTIENNE
CHRISTIAN GOTTLIEB
ERNST, HEINRICH WILHELM ESTON
ERODE ESTOPPEL
EROS (planet) ESTOUTEVILLE, GUILLAUME D’
EROS (god of love) ESTOVERS

ERPENIUS, THOMAS ESTRADA, LA
ERROLL, FRANCIS HAY ESTRADE
ERROR ESTRADES, GODEFROI
ERSCH, JOHANN SAMUEL ESTREAT
ERSKINE, EBENEZER ESTRÉES, GABRIELLE D’
ERSKINE, HENRY ESTREMADURA
ERSKINE, JOHN (Scottish ESTREMOZ
divine)
ERSKINE, JOHN (of Carnock) ESTUARY
ERSKINE, JOHN (of Dun) ESZTERGOM
ERSKINE, RALPH ÉTAGÈRE
ERSKINE, THOMAS (of ETAH
Linlathen)
ERSKINE, THOMAS ERSKINE ÉTAMPES, ANNE DE PISSELEU D’HEILLY
ERUBESCITE ÉTAMPES
ERYSIPELAS ÉTAPLES
ERYTHRAE ETAWAH
ERYTHRITE ETCHING
ERZERUM ETEOCLES
ERZGEBIRGE ETESIAN WIND
ERZINGAN ÉTEX, ANTOINE
ESAR-HADDON ETHER
ESAU ETHEREDGE, SIR GEORGE
ESBJERG ETHERIDGE, JOHN WESLEY
ESCANABA ETHERIDGE, ROBERT
ESCAPE ETHERS
ESCHATOLOGY ETHICS

EQUATION (from Lat. aequatio, aequare, to equalize), an expression or
statement of the equality of two quantities. Mathematical equivalence is
denoted by the sign =, a symbol invented by Robert Recorde (1510-1558), who
considered that nothing could be more equal than two equal and parallel
straight lines. An equation states an equality existing between two classes of
quantities, distinguished as known and unknown; these correspond to the data
of a problem and the thing sought. It is the purpose of the mathematician to
state the unknowns separately in terms of the knowns; this is called solving the
equation, and the values of the unknowns so obtained are called the roots or
solutions. The unknowns are usually denoted by the terminal letters, ... x, y, z,
of the alphabet, and the knowns are either actual numbers or are represented by
the literals a, b, c, &c..., i.e. the introductory letters of the alphabet. Any
number or literal which expresses what multiple of term occurs in an equation
is called the coefficient of that term; and the term which does not contain an
unknown is called the absolute term. The degree of an equation is equal to the
greatest index of an unknown in the equation, or to the greatest sum of the
indices of products of unknowns. If each term has the sum of its indices the
same, the equation is said to be homogeneous. These definitions are
exemplified in the equations:—

(1) ax² + 2bx + c = 0,
(2) xy² + 4a²x = 8a³,
(3) ax² + 2hxy + by² = 0.

In (1) the unknown is x, and the knowns a, b, c; the coefficients of x² and x are
a and 2b; the absolute term is c, and the degree is 2. In (2) the unknowns are x
and y, and the known a; the degree is 3, i.e. the sum of the indices in the term
xy². (3) is a homogeneous equation of the second degree in x and y. Equations
of the first degree are called simple or linear; of the second, quadratic; of the
third, cubic; of the fourth, biquadratic; of the fifth, quintic, and so on. Of
equations containing only one unknown the number of roots equals the degree

of the equation; thus a simple equation has one root, a quadratic two, a cubic
three, and so on. If one equation be given containing two unknowns, as for
example ax + by = c or ax² + by² = c, it is seen that there are an infinite number
of roots, for we can give x, say, any value and then determine the
corresponding value of y; such an equation is called indeterminate; of the
examples chosen the first is a linear and the second a quadratic indeterminate
equation. In general, an indeterminate equation results when the number of
unknowns exceeds by unity the number of equations. If, on the other hand, we
have two equations connecting two unknowns, it is possible to solve the
equations separately for one unknown, and then if we equate these values we
obtain an equation in one unknown, which is soluble if its degree does not
exceed the fourth. By substituting these values the corresponding values of the
other unknown are determined. Such equations are called simultaneous; and a
simultaneous system is a series of equations equal in number to the number of
unknowns. Such a system is not always soluble, for it may happen that one
equation is implied by the others; when this occurs the system is called
porismatic or poristic. An identity differs from an equation inasmuch as it
cannot be solved, the terms mutually cancelling; for example, the expression x²
− a² = (x − a)(x + a) is an identity, for on reduction it gives 0 = 0. It is usual to
employ the sign ≡ to express this relation.

An equation admits of description in two ways:—(1) It may be
regarded purely as an algebraic expression, or (2) as a geometrical locus.
In the first case there is obviously no limit to the number of unknowns and
to the degree of the equation; and, consequently, this aspect is the most
general. In the second case the number of unknowns is limited to three,
corresponding to the three dimensions of space; the degree is unlimited as
before. It must be noticed, however, that by the introduction of
appropriate hyperspaces, i.e. of degree equal to the number of unknowns,
any equation theoretically admits of geometrical visualization, in other
words, every equation may be represented by a geometrical figure and
every geometrical figure by an equation. Corresponding to these two

aspects, there are two typical methods by which equations can be solved,
viz. the algebraic and geometric. The former leads to exact results, or, by
methods of approximation, to results correct to any required degree of
accuracy. The latter can only yield approximate values: when theoretically
exact constructions are available there is a source of error in the
draughtsmanship, and when the constructions are only approximate, the
accuracy of the results is more problematical. The geometric aspect,
however, is of considerable value in discussing the theory of equations.

History.—There is little doubt that the earliest solutions of equations are
given, in the Rhind papyrus, a hieratic document written some 2000 years
before our era. The problems solved were of an arithmetical nature, assuming
such forms as “a mass and its 1⁄7th makes 19.” Calling the unknown mass x, we
have given x + 1⁄7 x = 19, which is a simple equation. Arithmetical problems
also gave origin to equations involving two unknowns; the early Greeks were
familiar with and solved simultaneous linear equations, but indeterminate
equations, such, for instance, as the system given in the “cattle problem” of
Archimedes, were not seriously studied until Diophantus solved many
particular problems. Quadratic equations arose in the Greek investigations in
the doctrine of proportion, and although they were presented and solved in a
geometrical form, the methods employed have no relation to the generalized
conception of algebraic geometry which represents a curve by an equation and
vice versa. The simplest quadratic arose in the construction of a mean
proportional (x) between two lines (a, b), or in the construction of a square
equal to a given rectangle; for we have the proportion a:x = x:b; i.e. x² = ab. A
more general equation, viz. x² − ax + a² = 0, is the algebraic equivalent of the
problem to divide a line in medial section; this is solved in Euclid, ii. 11. It is
possible that Diophantus was in possession of an algebraic solution of
quadratics; he recognized, however, only one root, the interpretation of both
being first effected by the Hindu Bhaskara. A simple cubic equation was
presented in the problem of finding two mean proportionals, x, y, between two
lines, one double the other. We have a:x = x:y = y:2a, which gives x² = ay and

xy = 2a²; eliminating y we obtain x³ = 2a³, a simple cubic. The Greeks could
not solve this equation, which also arose in the problems of duplicating a cube
and trisecting an angle, by the ruler and compasses, but only by mechanical
curves such as the cissoid, conchoid and quadratrix. Such solutions were much
improved by the Arabs, who also solved both cubics and biquadratics by
means of intersecting conics; at the same time, they developed methods,
originated by Diophantus and improved by the Hindus, for finding
approximate roots of numerical equations by algebraic processes. The
algebraic solution of the general cubic and biquadratic was effected in the 16th
century by S. Ferro, N. Tartaglia, H. Cardan and L. Ferrari (see Algebra:
History). Many fruitless attempts were made to solve algebraically the quintic
equation until P. Ruffini and N.H. Abel proved the problem to be impossible; a
solution involving elliptic functions has been given by C. Hermite and L.
Kronecker, while F. Klein has given another solution.

In the geometric treatment of equations the Greeks and Arabs based their
constructions upon certain empirically deduced properties of the curves and
figures employed. Knowing various metrical relations, generally expressed as
proportions, it was found possible to solve particular equations, but a general
method was wanting. This lacuna was not filled until the 17th century, when
Descartes discovered the general theory which explained the nature of such
solutions, in particular those wherein conics were employed, and, in addition,
established the most important facts that every equation represents a
geometrical locus, and conversely. To represent equations containing two
unknowns, x, y, he chose two axes of reference mutually perpendicular, and
measured x along the horizontal axis and y along the vertical. Then by the
methods described in the article Geometry: Analytical, he showed that—(1) a
linear equation represents a straight line, and (2) a quadratic represents a conic.
If the equation be homogeneous or break up into factors, it represents a number
of straight lines in the first case, and the loci corresponding to the factors in the
second. The solution of simultaneous equations is easily seen to be the values
of x, y corresponding to the intersections of the loci. It follows that there is

only one value of x, y which satisfies two linear equations, since two lines
intersect in one point only; two values which satisfy a linear and quadratic,
since a line intersects a conic in two points; and four values which satisfy two
quadratics, since two conics intersect in four points. It may happen that the
curves do not actually intersect in the theoretical maximum number of points;
the principle of continuity (see Geometrical Continuity) shows us that in such
cases some of the roots are imaginary. To represent equations involving three
unknowns x, y, z, a third axis is introduced, the z-axis, perpendicular to the
plane xy and passing through the intersection of the lines x, y. In this notation a
linear equation represents a plane, and two linear simultaneous equations
represent a line, i.e. the intersection of two planes; a quadratic equation
represents a surface of the second degree. In order to graphically consider
equations containing only one unknown, it is convenient to equate the terms to
y; i.e. if the equation be ƒ(x) = 0, we take y = ƒ(x) and construct this curve on
rectangular Cartesian co-ordinates by determining the values of y which
correspond to chosen values of x, and describing a curve through the points so
obtained. The intersections of the curve with the axis of x gives the real roots
of the equation; imaginary roots are obviously not represented.

In this article we shall treat of: (1) Simultaneous equations, (2)
indeterminate equations, (3) cubic equations, (4) biquadratic equations, (5)
theory of equations. Simple, linear simultaneous and quadratic equations are
treated in the article Algebra; for differential equations see Differential
Equations.

I. Simultaneous Equations.

Simultaneous equations which involve the second and higher powers of
the unknown may be impossible of solution. No general rules can be
given, and the solution of any particular problem will largely depend upon
the student’s ingenuity. Here we shall only give a few typical examples.

1. Equations which may be reduced to linear equations.—Ex. To solve
x(x − a) = yz, y (y − b) = zx, z (z − c) = xy. Multiply the equations by y, z
and x respectively, and divide the sum by xyz; then

a b c
+ + =0
z x y (1).

Multiply by z, x and y, and divide the sum by xyz; then

a b c
+ + =0
y z x (2).

From (1) and (2) by cross multiplication we obtain

1 1 1 1
= = = (suppose)
y (b² − ac) z (c² − ab) x (a² − bc) λ (3).

Substituting for x, y and z in x (x − a) = yz we obtain

1 3abc − (a³ + b³ + c³)
= ;
λ (a² − bc) (b² − ac) (c² − ab)

and therefore x, y and z are known from (3). The same artifice solves the
equations x² − yz = a, y² − xz = b, z² − xy = c.

2. Equations which are homogeneous and of the same degree.—These
equations can be solved by substituting y = mx. We proceed to explain the
method by an example.

Ex. To solve 3x² + xy + y² = 15, 31xy − 3x² − 5y² = 45. Substituting y =
mx in both these equations, and then dividing, we obtain 31m − 3 − 5m² =
3 (3 + m + m²) or 8m² − 28m + 12 = 0. The roots of this quadratic are m =
½ or 3, and therefore 2y = x, or y = 3x.

Taking 2y = x and substituting in 3x² + xy + y² = 0, we obtain y² (12 + 2
+ 1) = 15; ∴ y² = 1, which gives y = ±1, x = ±2. Taking the second value,

y = 3x, and substituting for y, we obtain x² (3 + 3 + 9) = 15; ∴ x² = 1,
which gives x = ±1, y = ±3. Therefore the solutions are x = ±2, y = ±1 and
x = ±1, y = ±3. Other artifices have to be adopted to solve other forms of
simultaneous equations, for which the reader is referred to J.J. Milne,
Companion to Weekly Problem Papers.

II. Indeterminate Equations.

1. When the number of unknown quantities exceeds the number of
equations, the equations will admit of innumerable solutions, and are
therefore said to be indeterminate. Thus if it be required to find two
numbers such that their sum be 10, we have two unknown quantities x and
y, and only one equation, viz. x + y = 10, which may evidently be satisfied
by innumerable different values of x and y, if fractional solutions be
admitted. It is, however, usual, in such questions as this, to restrict values
of the numbers sought to positive integers, and therefore, in this case, we
can have only these nine solutions,

x = 1, 2, 3, 4, 5, 6, 7, 8, 9;
y = 9, 8, 7, 6, 5, 4, 3, 2, 1;

which indeed may be reduced to five; for the first four become the same
as the last four, by simply changing x into y, and the contrary. This branch
of analysis was extensively studied by Diophantus, and is sometimes
termed the Diophantine Analysis.

2. Indeterminate problems are of different orders, according to the
dimensions of the equation which is obtained after all the unknown
quantities but two have been eliminated by means of the given equations.
Those of the first order lead always to equations of the form

ax ± by = ±c,

where a, b, c denote given whole numbers, and x, y two numbers to be
found, so that both may be integers. That this condition may be fulfilled, it
is necessary that the coefficients a, b have no common divisor which is
not also a divisor of c; for if a = md and b = me, then ax + by = mdx +
mey = c, and dx + ey = c/m; but d, e, x, y are supposed to be whole
numbers, therefore c/m is a whole number; hence m must be a divisor of
c.

Of the four forms expressed by the equation ax ± by = ±c, it is obvious
that ax + by = −c can have no positive integral solutions. Also ax − by =
−c is equivalent to by − ax = c, and so we have only to consider the forms
ax ± by = c. Before proceeding to the general solution of these equations
we will give a numerical example.

To solve 2x + 3y = 25 in positive integers. From the given equation we
have x = (25 − 3y) / 2 = 12 − y − (y − 1) / 2. Now, since x must be a whole
number, it follows that (y − 1)/2 must be a whole number. Let us assume
(y − 1) / 2 = z, then y = 1 + 2z; and x = 11 − 3z, where z might be any
whole number whatever, if there were no limitation as to the signs of x
and y. But since these quantities are required to be positive, it is evident,
from the value of y, that z must be either 0 or positive, and from the value
of x, that it must be less than 4; hence z may have these four values, 0, 1,
2, 3.

If z = 0, z = 1, z = 2, z = 3;

Then x = 11, x = 8, x = 5, x = 2,
y = 1, y = 3, y = 5, y = 7.

3. We shall now give the solution of the equation ax − by = c in positive
integers.

Convert a/b into a continued fraction, and let p/q be the convergent
immediately preceding a/b, then aq − bp = ±1 (see Continued Fraction).

(α) If aq − bp = 1, the given equation may be written

ax − by = c (aq − bp);
∴ a (x − cq) = b (y − cp).

Since a and b are prime to one another, then x − cq must be divisible by
b and y − cp by a; hence

(x − cq) / b = (y − cq) / a = t.

That is, x = bt + cq and y = at + cp.

Positive integral solutions, unlimited in number, are obtained by giving
t any positive integral value, and any negative integral value, so long as it
is numerically less than the smaller of the quantities cq/b, cp/a; t may also
be zero.

(β) If aq − bp = −1, we obtain x = bt − cq, y = at − cp, from which
positive integral solutions, again unlimited in number, are obtained by
giving t any positive integral value which exceeds the greater of the two
quantities cq/b, cp/a.

If a or b is unity, a/b cannot be converted into a continued fraction with
unit numerators, and the above method fails. In this case the solutions can
be derived directly, for if b is unity, the equation may be written y = ax −
c, and solutions are obtained by giving x positive integral values greater
than c/a.

4. To solve ax + by = c in positive integers. Converting a b into a
continued fraction and proceeding as before, we obtain, in the case of aq −
bp = 1,

x = cq − bt, y = at − cp.

Positive integral solutions are obtained by giving t positive integral
values not less than cp/a and not greater than cq/b.

In this case the number of solutions is limited. If aq − bp = −1 we
obtain the general solution x = bt − cq, y = cp − at, which is of the same
form as in the preceding case. For the determination of the number of
solutions the reader is referred to H.S. Hall and S.R. Knight’s Higher
Algebra, G. Chrystal’s Algebra, and other text-books.

5. If an equation were proposed involving three unknown quantities, as
ax + by + cz = d, by transposition we have ax + by = d − cz, and, putting d
− cz = c′, ax + by = c′. From this last equation we may find values of x
and y of this form,

x = mr + nc′, y = mr + n′c′,
or x = mr + n (d − cz), y = m′r + n′ (d − cz);

where z and r may be taken at pleasure, except in so far as the values of x,
y, z may be required to be all positive; for from such restriction the values
of z and r may be confined within certain limits to be determined from the
given equation. For more advanced treatment of linear indeterminate
equations see Combinatorial Analysis.

6. We proceed to indeterminate problems of the second degree: limiting
ourselves to the consideration of the formula y² = a + bx + cx², where x is
to be found, so that y may be a rational quantity. The possibility of
rendering the proposed formula a square depends altogether upon the
coefficients a, b, c; and there are four cases of the problem, the solution of
each of which is connected with some peculiarity in its nature.

Case 1. Let a be a square number; then, putting g² for a, we have y² = g²
+ bx + cx². Suppose √(g² + bx + cx²) = g + mx; then g² + bx + cx² = g² +
2gmx + m²x², or bx + cx² = 2gmx + m²x², that is, b + cx = 2gm + m²x;
hence

2gm − b cg − bm + gm²
x= , y = √(g² + bx + cx²)= .
c − m² c − m²

Case 2. Let c be a square number = g²; then, putting √(a + bx + g²x²) =
m + gx, we find a + bx + g²x² = m² + 2mgx + g²x², or a + bx = m² + 2mgx;
hence we find

m² − a bm − gm² − ag
x= , y = √(a + bx + g²x²) = .
b − 2mg b − 2mg

Case 3. When neither a nor c is a square number, yet if the expression a
+ bx + cx² can be resolved into two simple factors, as f + gx and h + kx,
the irrationality may be taken away as follows:—

Assume √(a + bx + cx²) = √{ (f + gx) (h + kx) } = m (f + gx), then (f +
gx) (h + kx) = m² (f + gx)², or h + kx = m² (f + gx); hence we find

fm² − h (fk − gh) m
x= , y = √{ (f + gx) (h + kx) } = ;
k − gm² k − gm²

and in all these formulae m may be taken at pleasure.

Case 4. The expression a + bx + cx² may be transformed into a square
as often as it can be resolved into two parts, one of which is a complete
square, and the other a product of two simple factors; for then it has this
form, p² + qr, where p, q and r are quantities which contain no power of x
higher than the first. Let us assume √(p² + qr) = p + mq; thus we have p² +
qr = p² + 2mpq + m²q² and r = 2mp + m²q, and as this equation involves
only the first power of x, we may by proper reduction obtain from it
rational values of x and y, as in the three foregoing cases.

The application of the preceding general methods of resolution to any
particular case is very easy; we shall therefore conclude with a single
example.

Ex. It is required to find two square numbers whose sum is a given
square number.

Let a² be the given square number, and x², y² the numbers required;
then, by the question, x² + y² = a², and y = √(a² − x²). This equation is
evidently of such a form as to be resolvable by the method employed in
case 1. Accordingly, by comparing √(a² − x²) with the general expression
√(g² + bx + cx²), we have g = a, b = 0, c = −1, and substituting these
values in the formulae, and also −n for +m, we find

2an a (n² − 1)
x= ,y= .
n² + 1 n² + 1

If a = n² + 1, there results x = 2n, y = n² − 1, a = n² + 1. Hence if r be an
even number, the three sides of a rational right-angled triangle are r, (½ r)²
− 1, (½ r)² + 1. If r be an odd number, they become (dividing by 2) r, ½ (r²
− 1), ½ (r² + 1).

For example, if r = 4, 4, 4 − 1, 4 + 1, or 4, 3, 5, are the sides of a right-
angled triangle; if r = 7, 7, 24, 25 are the sides of a right-angled triangle.

III. Cubic Equations.

1. Cubic equations, like all equations above the first degree, are divided
into two classes: they are said to be pure when they contain only one
power of the unknown quantity; and adfected when they contain two or
more powers of that quantity.

Pure cubic equations are therefore of the form x³ = r; and hence it
appears that a value of the simple power of the unknown quantity may
always be found without difficulty, by extracting the cube root of each
side of the equation. Let us consider the equation x³ − c³ = 0 more fully.
This is decomposable into the factors x − c = 0 and x² + cx + c² = 0. The

roots of this quadratic equation are ½ (−1 ± √−3) c, and we see that the
equation x³ = c³ has three roots, namely, one real root c, and two
imaginary roots ½ (−1 ± √−3) c. By making c equal to unity, we observe
that ½ (−1 ± √−3) are the imaginary cube roots of unity, which are
generally denoted by ω and ω², for it is easy to show that (½ (−1 − √−3))²
= ½ (−1 + √−3).

2. Let us now consider such cubic equations as have all their terms, and
which are therefore of this form,

x³ + Ax² + Bx + C = 0,

where A, B and C denote known quantities, either positive or negative.

This equation may be transformed into another in which the second
term is wanting by the substitution x = y − A/3. This transformation is a
particular case of a general theorem. Let xn + Axn−1 + Bxn−2 ... = 0.
Substitute x = y + h; then (y + h)n + A (y + h)n−1 ... = 0. Expand each term
by the binomial theorem, and let us fix our attention on the coefficient of
yn−1. By this process we obtain 0 = yn + yn−1(A + nh) + terms involving
lower powers of y.

Now h can have any value, and if we choose it so that A + nh = 0, then
the second term of our derived equation vanishes.

Resuming, therefore, the equation y³ + qy + r = 0, let us suppose y = v
+ z; we then have y³ = v³ + z³ + 3vz (v + z) = v³ + z³ + 3vzy, and the
original equation becomes v³ + z³ + (3vz + q) y + r = 0. Now v and z are
any two quantities subject to the relation y = v + z, and if we suppose 3vz
+ q = 0, they are completely determined. This leads to v³ + z³ + r = 0 and
3vz + q = 0. Therefore v³ and z³ are the roots of the quadratic t² + rt −
q²/27 = 0. Therefore

v³ = −½ r + √(1⁄27 q³ + ¼ r²); z³ = −½ r − √(1⁄27 q³ + ¼r²);

v= 3√{−½ r + √(1⁄27 q³ + ¼ r²) }; z = 3√{ (−½ r − √(1⁄27 q³ + ¼ r²) };
and y = v + z = 3√{−½ r + √(1⁄27q³ + ¼ r²) } + 3√{−½ r − √(1⁄27 q³ + ¼ r²) }.

Thus we have obtained a value of the unknown quantity y, in terms of the
known quantities q and r; therefore the equation is resolved.

3. But this is only one of three values which y may have. Let us, for the
sake of brevity, put

A = −½ r + √(1⁄27 q³ + ¼ r²), B = −½ r − √(1⁄27 q³ + ¼ r²),

and put α = ½ (−1 + √−3),
β = ½ (−1 − √−3).

Then, from what has been shown (§ 1), it is evident that v and z have each
these three values,

v = 3√A, v = α3√A, v = β3√A;
z = 3√B, z = α3√B, z = β3√B.

To determine the corresponding values of v and z, we must consider
that vz = −1⁄3 q = 3√(AB). Now if we observe that αβ = 1, it will
immediately appear that v + z has these three values,

v+z= 3√A + √B,
3

v + z = α3√A + β3√B,
v + z = β3√A + α3√B,

which are therefore the three values of y.

The first of these formulae is commonly known by the name of
Cardan’s rule (see Algebra: History).

The formulae given above for the roots of a cubic equation may be put
under a different form, better adapted to the purposes of arithmetical
calculation, as follows:—Because vz = −1⁄3 q, therefore z = −1⁄3q × 1/v =
−1⁄3 q / 3√A; hence v + z = 3√A − 1⁄3 q / 3√A: thus it appears that the three
values of y may also be expressed thus:

y= 3√A − 1⁄3 q / √A
3

y = α3√A − 1⁄3 qβ / 3√A
y = β3√A − 1⁄3 qα / 3√A.

See below, Theory of Equations, §§ 16 et seq.

IV. Biquadratic Equations.

1. When a biquadratic equation contains all its terms, it has this form,

x4 + Ax³ + Bx² + Cx + D = 0,

where A, B, C, D denote known quantities.

We shall first consider pure biquadratics, or such as contain only the
first and last terms, and therefore are of this form, x4 = b4. In this case it is
evident that x may be readily had by two extractions of the square root; by
the first we find x² = b², and by the second x = b. This, however, is only
one of the values which x may have; for since x4 = b4, therefore x4 − b4 =
0; but x4 − b4 may be resolved into two factors x² − b² and x² + b², each of
which admits of a similar resolution; for x² − b² = (x − b)(x + b) and x² +
b² = (x − b√−1)(x + b√−1). Hence it appears that the equation x4 − b4 = 0
may also be expressed thus,

(x − b) (x + b) (x − b√−1) (x + b√−1) = 0;

so that x may have these four values,

+b, −b, +b√−1, −b√−1,

two of which are real, and the others imaginary.

2. Next to pure biquadratic equations, in respect of easiness of
resolution, are such as want the second and fourth terms, and therefore
have this form,

x4 + qx² + s = 0.

These may be resolved in the manner of quadratic equations; for if we put
y = x², we have

y² + qy + s = 0,

from which we find y = ½ {−q ± √(q² − 4s) }, and therefore

x = ±√½ {−q ± √(q² − 4s) }.

3. When a biquadratic equation has all its terms, its resolution may be
always reduced to that of a cubic equation. There are various methods by
which such a reduction may be effected. The following was first given by
Leonhard Euler in the Petersburg Commentaries, and afterwards
explained more fully in his Elements of Algebra.

We have already explained how an equation which is complete in its
terms may be transformed into another of the same degree, but which
wants the second term; therefore any biquadratic equation may be reduced
to this form,

y4 + py² + qy + r = 0,

where the second term is wanting, and where p, q, r denote any known
quantities whatever.

That we may form an equation similar to the above, let us assume y =
√a + √b + √c, and also suppose that the letters a, b, c denote the roots of

the cubic equation

z³ + Pz² + Qz − R = 0;

then, from the theory of equations we have

a + b + c = −P, ab + ac + bc = Q, abc = R.

We square the assumed formula

y = √a + √b + √c,

and obtain y² = a + b + c + 2(√ab + √ac + √bc);

or, substituting −P for a + b + c, and transposing,

y² + P = 2(√ab + √ac + √bc).

Let this equation be also squared, and we have

y4 + 2Py² + P² = 4 (ab + ac + bc) + 8 (√a²bc + √ab²c + √abc²);

and since ab + ac + bc = Q,

and √a²bc + √ab²c + √abc² = √abc (√a + √b + √c) = √R·y,

the same equation may be expressed thus:

y4 + 2Py² + P² = 4Q + 8√R·y.

Thus we have the biquadratic equation

y4 + 2Py² − 8√R·y + P² − 4Q = 0,

one of the roots of which is y = √a + √b + √c, while a, b, c are the roots of
the cubic equation z³ + Pz² + Qz − R = 0.

4. In order to apply this resolution to the proposed equation y4 + py² +
qy + r = 0, we must express the assumed coefficients P, Q, R by means of

p, q, r, the coefficients of that equation. For this purpose let us compare
the equations

y4 + py² + qy + r = 0,
y4 + 2Py² − 8√Ry + P² − 4Q = 0,

and it immediately appears that

2P = p, −8√R = q, P² − 4Q = r;

and from these equations we find

P = ½ p, Q = 1⁄16 (p² − 4r), R = 1⁄64 q².

Hence it follows that the roots of the proposed equation are generally
expressed by the formula

y = √a + √b + √c;

where a, b, c denote the roots of this cubic equation,

p p² − 4r q²
z³ + z² + z− = 0.
2 16 64

But to find each particular root, we must consider, that as the square root
of a number may be either positive or negative, so each of the quantities
√a, √b, √c may have either the sign + or − prefixed to it; and hence our
formula will give eight different expressions for the root. It is, however, to
be observed, that as the product of the three quantities √a, √b, √c must be
equal to √R or to −1⁄8 q; when q is positive, their product must be a
negative quantity, and this can only be effected by making either one or
three of them negative; again, when q is negative, their product must be a
positive quantity; so that in this case they must either be all positive, or
two of them must be negative. These considerations enable us to
determine that four of the eight expressions for the root belong to the case
in which q is positive, and the other four to that in which it is negative.

5. We shall now give the result of the preceding investigation in the
form of a practical rule; and as the coefficients of the cubic equation
which has been found involve fractions, we shall transform it into another,
in which the coefficients are integers, by supposing z = ¼ v. Thus the
equation

p p² − 4r q²
z³ + z² + z− =0
2 16 64

becomes, after reduction,

v³ + 2pv² + (p² − 4r) v − q² = 0;

it also follows, that if the roots of the latter equation are a, b, c, the roots
of the former are ¼ a, ¼ b, ¼ c, so that our rule may now be expressed
thus:

Let y4 + py² + qy + r = 0 be any biquadratic equation wanting its second
term. Form this cubic equation

v³ + 2pv² + (p² − 4r) v − q² = 0,

and find its roots, which let us denote by a, b, c.

Then the roots of the proposed biquadratic equation are,

when q is negative, when q is positive,
y = ½ (√a + √b + √c), y = ½ (−√a − √b − √c),
y = ½ (√a − √b − √c), y = ½ (−√a + √b + √c),
y = ½ (−√a + √b − √c), y = ½ (√a − √b + √c),
y = ½ (−√a − √b + √c), y = ½ (√a + √b − √c).

See also below, Theory of Equations, § 17 et seq. (X.)

V. Theory of Equations.

1. In the subject “Theory of Equations” the term equation is used to denote
an equation of the form xn − p1xn−1 ... ± pn = 0, where p1, p2 ... pn are regarded
as known, and x as a quantity to be determined; for shortness the equation is
written ƒ(x) = 0.

The equation may be numerical; that is, the coefficients p1, p2n, ... pn are
then numbers—understanding by number a quantity of the form α + βi (α and
β having any positive or negative real values whatever, or say each of these is
regarded as susceptible of continuous variation from an indefinitely large
negative to an indefinitely large positive value), and i denoting √−1.

Or the equation may be algebraical; that is, the coefficients are not then
restricted to denote, or are not explicitly considered as denoting, numbers.

1. We consider first numerical equations. (Real theory, 2-6; Imaginary
theory, 7-10.)

Real Theory.

2. Postponing all consideration of imaginaries, we take in the first instance
the coefficients to be real, and attend only to the real roots (if any); that is, p1,
p2, ... pn are real positive or negative quantities, and a root a, if it exists, is a
positive or negative quantity such that an − p1an−1 ... ± pn = 0, or say, ƒ(a) = 0.

It is very useful to consider the curve y = ƒ(x),—or, what would come to the
same, the curve Ay = ƒ(x),—but it is better to retain the first-mentioned form
of equation, drawing, if need be, the ordinate y on a reduced scale. For
instance, if the given equation be x³ − 6x² + 11x − 6.06 = 0,1 then the curve y =
x³ − 6x² + 11x − 6.06 is as shown in fig. 1, without any reduction of scale for
the ordinate.

It is clear that, in general, y is a continuous one-valued function of x, finite
for every finite value of x, but becoming infinite when x is infinite; i.e.,
assuming throughout that the coefficient of xn is +1, then when x = ∞, y = +∞;
but when x = −∞, then y = +∞ or −∞, according as n is even or odd; the curve
cuts any line whatever, and in particular it cuts the axis (of x) in at most n
points; and the value of x, at any point of intersection with the axis, is a root of
the equation ƒ(x) = 0.

If β, α are any two values of x (α > β, that is, α nearer +∞), then if ƒ(β), ƒ(α)
have opposite signs, the curve cuts the axis an odd number of times, and
therefore at least once, between the points x = β, x = α; but if ƒ(β), ƒ(α) have
the same sign, then between these points the curve cuts the axis an even
number of times, or it may be not at all. That is, ƒ(β), ƒ(α) having opposite
signs, there are between the limits β, α an odd number of real roots, and
therefore at least one real root; but ƒ(β), ƒ(α) having the same sign, there are
between these limits an even number of real roots, or it may be there is no real
root. In particular, by giving to β, α the values -∞, +∞ (or, what is the same
thing, any two values sufficiently near to these values respectively) it appears
that an equation of an odd order has always an odd number of real roots, and
therefore at least one real root; but that an equation of an even order has an
even number of real roots, or it may be no real root.

If α be such that for x = or > a (that is, x nearer to +∞) ƒ(x) is always +, and
β be such that for x = or < β (that is, x nearer to −∞) ƒ(x) is always −, then the
real roots (if any) lie between these limits x = β, x = α; and it is easy to find by
trial such two limits including between them all the real roots (if any).

3. Suppose that the positive value δ is an inferior limit to the difference
between two real roots of the equation; or rather (since the foregoing
expression would imply the existence of real roots) suppose that there are not
two real roots such that their difference taken positively is = or < δ; then, γ
being any value whatever, there is clearly at most one real root between the
limits γ and γ + δ; and by what precedes there is such real root or there is not

such real root, according as ƒ(γ), ƒ(γ + δ) have opposite signs or have the same
sign. And by dividing in this manner the interval β to α into intervals each of
which is = or < δ, we should not only ascertain the number of the real roots (if
any), but we should also separate the real roots, that is, find for each of them
limits γ, γ + δ between which there lies this one, and only this one, real root.

In particular cases it is frequently possible to ascertain the number of
the real roots, and to effect their separation by trial or otherwise, without
much difficulty; but the foregoing was the general process as employed by
Joseph Louis Lagrange even in the second edition (1808) of the Traité de
la résolution des équations numériques;2 the determination of the limit δ
had to be effected by means of the “equation of differences” or equation
of the order ½ n(n − 1), the roots of which are the squares of the
differences of the roots of the given equation, and the process is a
cumbrous and unsatisfactory one.

4. The great step was effected by the theorem of J.C.F. Sturm (1835)—viz.
here starting from the function ƒ(x), and its first derived function ƒ′(x), we
have (by a process which is a slight modification of that for obtaining the
greatest common measure of these two functions) to form a series of functions

ƒ(x), ƒ′(x), ƒ2(x), ... ƒn(x)

of the degrees n, n − 1, n − 2 ... 0 respectively,—the last term ƒn(x) being thus
an absolute constant. These lead to the immediate determination of the number
of real roots (if any) between any two given limits β, α; viz. supposing α > β
(that is, α nearer to +∞), then substituting successively these two values in the
series of functions, and attending only to the signs of the resulting values, the
number of the changes of sign lost in passing from β to α is the required
number of real roots between the two limits. In particular, taking β, α = −∞, +∞
respectively, the signs of the several functions depend merely on the signs of
the terms which contain the highest powers of x, and are seen by inspection,
and the theorem thus gives at once the whole number of real roots.

And although theoretically, in order to complete by a finite number of
operations the separation of the real roots, we still need to know the value of
the before-mentioned limit δ; yet in any given case the separation may be
effected by a limited number of repetitions of the process. The practical
difficulty is when two or more roots are very near to each other. Suppose, for
instance, that the theorem shows that there are two roots between 0 and 10; by
giving to x the values 1, 2, 3, ... successively, it might appear that the two roots
were between 5 and 6; then again that they were between 5.3 and 5.4, then
between 5.34 and 5.35, and so on until we arrive at a separation; say it appears
that between 5.346 and 5.347 there is one root, and between 5.348 and 5.349
the other root. But in the case in question δ would have a very small value,
such as .002, and even supposing this value known, the direct application of
the first-mentioned process would be still more laborious.

5. Supposing the separation once effected, the determination of the single
real root which lies between the two given limits may be effected to any
required degree of approximation either by the processes of W.G. Horner and
Lagrange (which are in principle a carrying out of the method of Sturm’s
theorem), or by the process of Sir Isaac Newton, as perfected by Joseph
Fourier (which requires to be separately considered).

First as to Horner and Lagrange. We know that between the limits β, α
there lies one, and only one, real root of the equation; ƒ(β) and ƒ(α) have
therefore opposite signs. Suppose any intermediate value is θ; in order to
determine by Sturm’s theorem whether the root lies between β, θ, or
between θ, α, it would be quite unnecessary to calculate the signs of
ƒ(θ),ƒ′(θ), ƒ2(θ) ...; only the sign of ƒ(θ) is required; for, if this has the
same sign as ƒ(β), then the root is between β, θ; if the same sign as ƒ(α),
then the root is between θ, α. We want to make θ increase from the
inferior limit β, at which ƒ(θ) has the sign of ƒ(β), so long as ƒ(θ) retains
this sign, and then to a value for which it assumes the opposite sign; we

have thus two nearer limits of the required root, and the process may be
repeated indefinitely.

Horner’s method (1819) gives the root as a decimal, figure by figure;
thus if the equation be known to have one real root between 0 and 10, it is
in effect shown say that 5 is too small (that is, the root is between 5 and
6); next that 5.4 is too small (that is, the root is between 5.4 and 5.5); and
so on to any number of decimals. Each figure is obtained, not by the
successive trial of all the figures which precede it, but (as in the ordinary
process of the extraction of a square root, which is in fact Horner’s
process applied to this particular case) it is given presumptively as the
first figure of a quotient; such value may be too large, and then the next
inferior integer must be tried instead of it, or it may require to be further
diminished. And it is to be remarked that the process not only gives the
approximate value α of the root, but (as in the extraction of a square root)
it includes the calculation of the function ƒ(α), which should be, and
approximately is, = 0. The arrangement of the calculations is very elegant,
and forms an integral part of the actual method. It is to be observed that
after a certain number of decimal places have been obtained, a good many
more can be found by a mere division. It is in the progress tacitly assumed
that the roots have been first separated.

Lagrange’s method (1767) gives the root as a continued fraction a + 1/b
+ 1/c + ..., where a is a positive or negative integer (which may be = 0),
but b, c, ... are positive integers. Suppose the roots have been separated;
then (by trial if need be of consecutive integer values) the limits may be
made to be consecutive integer numbers: say they are a, a + 1; the value of
x is therefore = a + 1/y, where y is positive and greater than 1; from the
given equation for x, writing therein x = a + 1/y, we form an equation of
the same order for y, and this equation will have one, and only one,
positive root greater than 1; hence finding for it the limits b, b + 1 (where
b is = or > 1), we have y = b + 1/z, where z is positive and greater than 1;
and so on—that is, we thus obtain the successive denominators b, c, d ...

of the continued fraction. The method is theoretically very elegant, but the
disadvantage is that it gives the result in the form of a continued fraction,
which for the most part must ultimately be converted into a decimal.
There is one advantage in the method, that a commensurable root (that is,
a root equal to a rational fraction) is found accurately, since, when such
root exists, the continued fraction terminates.

6. Newton’s method (1711), as perfected by Fourier(1831), may be
roughly stated as follows. If x = γ be an approximate value of any root,
and γ + h the correct value, then ƒ(γ + h) = 0, that is,

h h²
ƒ(γ) + ƒ′(γ) + ƒ″(γ) + ... = 0;
1 1·2

and then, if h be so small that the terms after the second may be neglected,
ƒ(γ) + hƒ′(γ) = 0, that is, h = {−ƒ(γ)/ƒ′(γ) }, or the new approximate value
is x = γ − {ƒ(γ)/ƒ′(γ) }; and so on, as often as we please. It will be
observed that so far nothing has been assumed as to the separation of the
roots, or even as to the existence of a real root; γ has been taken as the
approximate value of a root, but no precise meaning has been attached to
this expression. The question arises, What are the conditions to be
satisfied by γ in order that the process may by successive repetitions
actually lead to a certain real root of the equation; or that, γ being an
approximate value of a certain real root, the new value γ − {ƒ(γ)/ƒ′(γ) }
may be a more approximate value.

Fig. 1.

Referring to fig. 1, it is easy to see that if OC represent the assumed
value γ, then, drawing the ordinate CP to meet the curve in P, and the
tangent PC′ to meet the axis in C′, we shall have OC′ as the new
approximate value of the root. But observe that there is here a real root
OX, and that the curve beyond X is convex to the axis; under these
conditions the point C′ is nearer to X than was C; and, starting with C′
instead of C, and proceeding in like manner to draw a new ordinate and
tangent, and so on as often as we please, we approximate continually, and
that with great rapidity, to the true value OX. But if C had been taken on
the other side of X, where the curve is concave to the axis, the new point
C′ might or might not be nearer to X than was the point C; and in this case
the method, if it succeeds at all, does so by accident only, i.e. it may
happen that C′ or some subsequent point comes to be a point C, such that
CO is a proper approximate value of the root, and then the subsequent
approximations proceed in the same manner as if this value had been
assumed in the first instance, all the preceding work being wasted. It thus
appears that for the proper application of the method we require more than
the mere separation of the roots. In order to be able to approximate to a

certain root α, = OX, we require to know that, between OX and some
value ON, the curve is always convex to the axis (analytically, between
the two values, ƒ(x) and ƒ″(x) must have always the same sign). When
this is so, the point C may be taken anywhere on the proper side of X, and
within the portion XN of the axis; and the process is then the one already
explained. The approximation is in general a very rapid one. If we know
for the required root OX the two limits OM, ON such that from M to X
the curve is always concave to the axis, while from X to N it is always
convex to the axis,—then, taking D anywhere in the portion MX and (as
before) C in the portion XN, drawing the ordinates DQ, CP, and joining
the points P, Q by a line which meets the axis in D′, also constructing the
point C′ by means of the tangent at P as before, we have for the required
root the new limits OD′, OC′; and proceeding in like manner with the
points D′, C′, and so on as often as we please, we obtain at each step two
limits approximating more and more nearly to the required root OX. The
process as to the point D′, translated into analysis, is the ordinate process
of interpolation. Suppose OD = β, OC = α, we have approximately ƒ(β +
h) = ƒ(β) + h{ƒ(α) − ƒ(β) } / (α − β), whence if the root is β + h then h = −
(α − β)ƒ(β) / {ƒ(α) − ƒ(β) }.

Returning for a moment to Horner’s method, it may be remarked that
the correction h, to an approximate value α, is therein found as a quotient
the same or such as the quotient ƒ(α) ÷ ƒ′(α) which presents itself in
Newton’s method. The difference is that with Horner the integer part of
this quotient is taken as the presumptive value of h, and the figure is
verified at each step. With Newton the quotient itself, developed to the
proper number of decimal places, is taken as the value of h; if too many
decimals are taken, there would be a waste of work; but the error would
correct itself at the next step. Of course the calculation should be
conducted without any such waste of work.

Imaginary Theory.

7. It will be recollected that the expression number and the correlative
epithet numerical were at the outset used in a wide sense, as extending to
imaginaries. This extension arises out of the theory of equations by a process
analogous to that by which number, in its original most restricted sense of
positive integer number, was extended to have the meaning of a real positive or
negative magnitude susceptible of continuous variation.

If for a moment number is understood in its most restricted sense as
meaning positive integer number, the solution of a simple equation leads to an
extension; ax − b = 0 gives x = b/a, a positive fraction, and we can in this
manner represent, not accurately, but as nearly as we please, any positive
magnitude whatever; so an equation ax + b = 0 gives x = −b/a, which
(approximately as before) represents any negative magnitude. We thus arrive at
the extended signification of number as a continuously varying positive or
negative magnitude. Such numbers may be added or subtracted, multiplied or
divided one by another, and the result is always a number. Now from a quadric
equation we derive, in like manner, the notion of a complex or imaginary
number such as is spoken of above. The equation x² + 1 = 0 is not (in the
foregoing sense, number = real number) satisfied by any numerical value
whatever of x; but we assume that there is a number which we call i, satisfying
the equation i² + 1 = 0, and then taking a and b any real numbers, we form an
expression such as a + bi, and use the expression number in this extended
sense: any two such numbers may be added or subtracted, multiplied or
divided one by the other, and the result is always a number. And if we consider
first a quadric equation x² + px + q = 0 where p and q are real numbers, and
next the like equation, where p and q are any numbers whatever, it can be
shown that there exists for x a numerical value which satisfies the equation; or,
in other words, it can be shown that the equation has a numerical root. The like
theorem, in fact, holds good for an equation of any order whatever; but

suppose for a moment that this was not the case; say that there was a cubic
equation x³ + px² + qx + r = 0, with numerical coefficients, not satisfied by any
numerical value of x, we should have to establish a new imaginary j satisfying
some such equation, and should then have to consider numbers of the form a +
bj, or perhaps a + bj + cj² (a, b, c numbers α + βi of the kind heretofore
considered),—first we should be thrown back on the quadric equation x² + px
+ q = 0, p and q being now numbers of the last-mentioned extended form—non
constat that every such equation has a numerical root—and if not, we might be
led to other imaginaries k, l, &c., and so on ad infinitum in inextricable
confusion.

But in fact a numerical equation of any order whatever has always a
numerical root, and thus numbers (in the foregoing sense, number = quantity of
the form α + βi) form (what real numbers do not) a universe complete in itself,
such that starting in it we are never led out of it. There may very well be, and
perhaps are, numbers in a more general sense of the term (quaternions are not a
case in point, as the ordinary laws of combination are not adhered to), but in
order to have to do with such numbers (if any) we must start with them.

8. The capital theorem as regards numerical equations thus is, every
numerical equation has a numerical root; or for shortness (the meaning being
as before), every equation has a root. Of course the theorem is the reverse of
self-evident, and it requires proof; but provisionally assuming it as true, we
derive from it the general theory of numerical equations. As the term root was
introduced in the course of an explanation, it will be convenient to give here
the formal definition.

A number a such that substituted for x it makes the function x1n −
p1xn−1 ... ± pn to be = 0, or say such that it satisfies the equation ƒ(x) = 0,
is said to be a root of the equation; that is, a being a root, we have

an − p1an−1 ... ± pn = 0, or say ƒ(a) = 0;

and it is then easily shown that x − a is a factor of the function ƒ(x), viz.
that we have ƒ(x) = (x − a)ƒ1(x), where ƒ1(x) is a function xn−1 − q1xn−2 ...
± qn−1 of the order n − 1, with numerical coefficients q1, q2 ... qn−1.

In general a is not a root of the equation ƒ1(x) = 0, but it may be so—
i.e. ƒ1(x) may contain the factor x − a; when this is so, ƒ(x) will contain
the factor (x − a)²; writing then ƒ(x) = (x − a)²ƒ2(x), and assuming that a is
not a root of the equation ƒ2(x) = 0, x = a is then said to be a double root
of the equation ƒ(x) = 0; and similarly ƒ(x) may contain the factor (x − a)³
and no higher power, and x = a is then a triple root; and so on.

Supposing in general that ƒ(x) = (x − a)αF(x) (α being a positive integer
which may be = 1, (x − a)α the highest power of x − a which divides ƒ(x),
and F(x) being of course of the order n − α), then the equation F(x) = 0
will have a root b which will be different from a; x − b will be a factor, in
general a simple one, but it may be a multiple one, of F(x), and ƒ(x) will
in this case be = (x − a)α (x − b)β Φ(x) (β a positive integer which may be
= 1, (x − b)β the highest power of x − b in F(x) or ƒ(x), and Φ(x) being of
course of the order n − α − β). The original equation ƒ(x) = 0 is in this
case said to have α roots each = a, β roots each = b; and so on for any
other factors (x − c)γ, &c.

We have thus the theorem—A numerical equation of the order n has in
every case n roots, viz. there exist n numbers, a, b, ... (in general all
distinct, but which may arrange themselves in any sets of equal values),
such that ƒ(x) = (x − a)(x − b)(x − c) ... identically.

If the equation has equal roots, these can in general be determined, and
the case is at any rate a special one which may be in the first instance
excluded from consideration. It is, therefore, in general assumed that the
equation ƒ(x) = 0 has all its roots unequal.

If the coefficients p1, p2, ... are all or any one or more of them
imaginary, then the equation ƒ(x) = 0, separating the real and imaginary
parts thereof, may be written F(x) + iΦ(x) = 0, where F(x), Φ(x) are each
of them a function with real coefficients; and it thus appears that the
equation ƒ(x) = 0, with imaginary coefficients, has not in general any real
root; supposing it to have a real root a, this must be at once a root of each
of the equations F(x) = 0 and Φ(x) = 0.

But an equation with real coefficients may have as well imaginary as
real roots, and we have further the theorem that for any such equation the
imaginary roots enter in pairs, viz. α + βi being a root, then α − βi will be
also a root. It follows that if the order be odd, there is always an odd
number of real roots, and therefore at least one real root.

9. In the case of an equation with real coefficients, the question of the
existence of real roots, and of their separation, has been already considered. In
the general case of an equation with imaginary (it may be real) coefficients, the
like question arises as to the situation of the (real or imaginary) roots; thus, if
for facility of conception we regard the constituents α, β of a root α + βi as the
co-ordinates of a point in plano, and accordingly represent the root by such
point, then drawing in the plane any closed curve or “contour,” the question is
how many roots lie within such contour.

This is solved theoretically by means of a theorem of A.L. Cauchy
(1837), viz. writing in the original equation x + iy in place of x, the
function ƒ(x + iy) becomes = P + iQ, where P and Q are each of them a
rational and integral function (with real coefficients) of (x, y). Imagining
the point (x, y) to travel along the contour, and considering the number of
changes of sign from − to + and from + to − of the fraction corresponding
to passages of the fraction through zero (that is, to values for which P
becomes = 0, disregarding those for which Q becomes = 0), the difference
of these numbers gives the number of roots within the contour.

It is important to remark that the demonstration does not presuppose the
existence of any root; the contour may be the infinity of the plane (such
infinity regarded as a contour, or closed curve), and in this case it can be
shown (and that very easily) that the difference of the numbers of changes
of sign is = n; that is, there are within the infinite contour, or (what is the
same thing) there are in all n roots; thus Cauchy’s theorem contains really
the proof of the fundamental theorem that a numerical equation of the nth
order (not only has a numerical root, but) has precisely n roots. It would
appear that this proof of the fundamental theorem in its most complete
form is in principle identical with the last proof of K.F. Gauss (1849) of
the theorem, in the form—A numerical equation of the nth order has
always a root.3

But in the case of a finite contour, the actual determination of the
difference which gives the number of real roots can be effected only in the
case of a rectangular contour, by applying to each of its sides separately a
method such as that of Sturm’s theorem; and thus the actual determination
ultimately depends on a method such as that of Sturm’s theorem.

Very little has been done in regard to the calculation of the imaginary
roots of an equation by approximation; and the question is not here
considered.

10. A class of numerical equations which needs to be considered is that of
the binomial equations xn − a = 0 (a = α + βi, a complex number).

The foregoing conclusions apply, viz. there are always n roots, which, it
may be shown, are all unequal. And these can be found numerically by the
extraction of the square root, and of an nth root, of real numbers, and by
the aid of a table of natural sines and cosines.4 For writing

α β
α + βi = √(α² + β²) { + i },
√(α² + β²) √(α² + β²)

there is always a real angle λ (positive and less than 2π), such that its
cosine and sine are = α / √(α² + β²) and β / √(α² + β²) respectively; that is,
writing for shortness √(α² + β²) = ρ, we have α + βi = ρ (cos λ + i sin λ), or
the equation is xn = ρ (cos λ + i sin λ); hence observing that (cos λ/n + i
sin λ/n )n = cos λ + i sin λ, a value of x is = n√ρ (cos λ/n + i sin λ/n). The
formula really gives all the roots, for instead of λ we may write λ + 2sπ, s
a positive or negative integer, and then we have

λ + 2sπ λ + 2sπ
x = n√ρ ( cos + i sin ),
n n

which has the n values obtained by giving to s the values 0, 1, 2 ... n − 1 in
succession; the roots are, it is clear, represented by points lying at equal
intervals on a circle. But it is more convenient to proceed somewhat
differently; taking one of the roots to be θ, so that θn = a, then assuming x
= θy, the equation becomes yn − 1 = 0, which equation, like the original
equation, has precisely n roots (one of them being of course = 1). And the
original equation xn − a = 0 is thus reduced to the more simple equation xn
− 1 = 0; and although the theory of this equation is included in the
preceding one, yet it is proper to state it separately.

The equation xn − 1 = 0 has its several roots expressed in the form 1, ω,
ω², ... ωn−1, where ω may be taken = cos 2π/n + i sin 2π/n; in fact, ω
having this value, any integer power ωk is = cos 2πk/n + i sin 2πk/n, and
we thence have (ωk)n = cos 2πk + i sin 2πk, = 1, that is, ωk is a root of the
equation. The theory will be resumed further on.

By what precedes, we are led to the notion (a numerical) of the radical
a1/n regarded as an n-valued function; any one of these being denoted by
n√a, then the series of values is n√a, ωn√a, ... ωn−1 n√a; or we may, if we

please, use n√a instead of a1/n as a symbol to denote the n-valued function.

As the coefficients of an algebraical equation may be numerical, all
which follows in regard to algebraical equations is (with, it may be, some
few modifications) applicable to numerical equations; and hence,
concluding for the present this subject, it will be convenient to pass on to
algebraical equations.

Algebraical Equations.

11. The equation is

xn − p1xn−1 + ... ± pn = 0,

and we here assume the existence of roots, viz. we assume that there are n
quantities a, b, c ... (in general all of them different, but which in particular
cases may become equal in sets in any manner), such that

xn − p1xn−1 + ... ± pn = 0;

or looking at the question in a different point of view, and starting with the
roots a, b, c ... as given, we express the product of the n factors x − a, x − b, ...
in the foregoing form, and thus arrive at an equation of the order n having the n
roots a, b, c.... In either case we have

p1 = Σa, p2 = Σab, ... pn = abc...;

i.e. regarding the coefficients p1, p2 ... pn as given, then we assume the
existence of roots a, b, c, ... such that p1 = Σa, &c.; or, regarding the roots as
given, then we write p1, p2, &c., to denote the functions Σa, Σab, &c.

As already explained, the epithet algebraical is not used in opposition to
numerical; an algebraical equation is merely an equation wherein the
coefficients are not restricted to denote, or are not explicitly considered as
denoting, numbers. That the abstraction is legitimate, appears by the
simplest example; in saying that the equation x² − px + q = 0 has a root x

= ½ {p + √(p² − 4q) }, we mean that writing this value for x the equation
becomes an identity, [½ {p + √(p² − 4q) }]² − p[½ {p + √(p² − 4q) }] + q =
0; and the verification of this identity in nowise depends upon p and q
meaning numbers. But if it be asked what there is beyond numerical
equations included in the term algebraical equation, or, again, what is the
full extent of the meaning attributed to the term—the latter question at any
rate it would be very difficult to answer; as to the former one, it may be
said that the coefficients may, for instance, be symbols of operation. As
regards such equations, there is certainly no proof that every equation has
a root, or that an equation of the nth order has n roots; nor is it in any wise
clear what the precise signification of the statement is. But it is found that
the assumption of the existence of the n roots can be made without
contradictory results; conclusions derived from it, if they involve the
roots, rest on the same ground as the original assumption; but the
conclusion may be independent of the roots altogether, and in this case it
is undoubtedly valid; the reasoning, although actually conducted by aid of
the assumption (and, it may be, most easily and elegantly in this manner),
is really independent of the assumption. In illustration, we observe that it
is allowable to express a function of p and q as follows,—that is, by
means of a rational symmetrical function of a and b, this can, as a fact, be
expressed as a rational function of a + b and ab; and if we prescribe that a
+ b and ab shall then be changed into p and q respectively, we have the
required function of p, q. That is, we have F(α, β) as a representation of
ƒ(p, q), obtained as if we had p = a + b, q = ab, but without in any wise
assuming the existence of the a, b of these equations.

12. Starting from the equation

xn − p1xn−1 + ... = x − a·x − b. &c.

or the equivalent equations p1 = Σa, &c., we find

an − p1an−1 + ... = 0,
bn − p1bn−1 + ... = 0;
· · ·
· · ·
· · ·

(it is as satisfying these equations that a, b ... are said to be the roots of xn −
p1xn−1 + ... = 0); and conversely from the last-mentioned equations, assuming
that a, b ... are all different, we deduce

p1 = Σa, p2 = Σab, &c.

and

xn − p1xn−1 + ... = x − a·x − b. &c.

Observe that if, for instance, a = b, then the equations an − p1an−1 + ... = 0, bn −
p1bn−1 + ... = 0 would reduce themselves to a single relation, which would not
of itself express that a was a double root,—that is, that (x − a)² was a factor of
xn − p1xn−1 +, &c; but by considering b as the limit of a + h, h indefinitely
small, we obtain a second equation

nan−1 − (n − 1) p1an−2 + ... = 0,

which, with the first, expresses that a is a double root; and then the whole
system of equations leads as before to the equations p1 = Σa, &c. But the
existence of a double root implies a certain relation between the coefficients;
the general case is when the roots are all unequal.

We have then the theorem that every rational symmetrical function of the
roots is a rational function of the coefficients. This is an easy consequence
from the less general theorem, every rational and integral symmetrical function
of the roots is a rational and integral function of the coefficients.

In particular, the sums of the powers Σa², Σa³, &c., are rational and integral
functions of the coefficients.

The process originally employed for the expression of other functions
Σaαbβ, &c., in terms of the coefficients is to make them depend upon the
sums of powers: for instance, Σaαbβ = ΣaαΣaβ − Σaα+β; but this is very
objectionable; the true theory consists in showing that we have systems of
equations

p1 = Σa,

p2 = Σab,
p1² = Σa² + 2Σab,

p3 = Σabc,
p1p2 = Σa²b + 3Σabc,
p1³ = Σa³ + 3Σa²b + 6Σabc,

where in each system there are precisely as many equations as there are
root-functions on the right-hand side—e.g. 3 equations and 3 functions
Σabc, Σa²b, Σa³. Hence in each system the root-functions can be
determined linearly in terms of the powers and products of the
coefficients:

Σab = p2,
Σa² = p1² − 2p2,

Σabc = p3,
Σa²b = p1p2 − 3p3,
Σa³ = p1³ − 3p1p2 + 3p3,

and so on. The other process, if applied consistently, would derive the
originally assumed value Σab = p2, from the two equations Σa = p, Σa² =
p1² − 2p2; i.e. we have 2Σab = Σa·Σa − Σa²,= p1² − (p1² − 2p2), = 2p2.

13. It is convenient to mention here the theorem that, x being determined as
above by an equation of the order n, any rational and integral function
whatever of x, or more generally any rational function which does not become
infinite in virtue of the equation itself, can be expressed as a rational and
integral function of x, of the order n − 1, the coefficients being rational
functions of the coefficients of the equation. Thus the equation gives xn a
function of the form in question; multiplying each side by x, and on the right-
hand side writing for xn its foregoing value, we have xn+1, a function of the
form in question; and the like for any higher power of x, and therefore also for
any rational and integral function of x. The proof in the case of a rational non-
integral function is somewhat more complicated. The final result is of the form
φ(x)/ψ(x) = I(x), or say φ(x) − ψ(x)I(x) = 0, where φ, ψ, I are rational and
integral functions; in other words, this equation, being true if only ƒ(x) = 0, can
only be so by reason that the left-hand side contains ƒ(x) as a factor, or we
must have identically φ(x) − ψ(x)I(x) = M(x)ƒ(x). And it is, moreover, clear
that the equation φ(x)/ψ(x) = I(x), being satisfied if only ƒ(x) = 0, must be
satisfied by each root of the equation.

From the theorem that a rational symmetrical function of the roots is
expressible in terms of the coefficients, it at once follows that it is possible
to determine an equation (of an assignable order) having for its roots the
several values of any given (unsymmetrical) function of the roots of the
given equation. For example, in the case of a quartic equation, roots (a, b,
c, d), it is possible to find an equation having the roots ab, ac, ad, bc, bd,
cd (being therefore a sextic equation): viz. in the product

(y − ab) (y − ac) (y − ad) (y − bc) (y − bd) (y − cd)

the coefficients of the several powers of y will be symmetrical functions
of a, b, c, d and therefore rational and integral functions of the coefficients
of the quartic equation; hence, supposing the product so expressed, and
equating it to zero, we have the required sextic equation. In the same
manner can be found the sextic equation having the roots (a − b)², (a − c)²,
(a − d)², (b − c)², (b − d)², (c − d)², which is the equation of differences
previously referred to; and similarly we obtain the equation of differences
for a given equation of any order. Again, the equation sought for may be
that having for its n roots the given rational functions φ(a), φ(b), ... of the
several roots of the given equation. Any such rational function can (as was
shown) be expressed as a rational and integral function of the order n − 1;
and, retaining x in place of any one of the roots, the problem is to find y
from the equations xn − p1xn−1 ... = 0, and y = M0xn−1 + M1xn−2 + ..., or,
what is the same thing, from these two equations to eliminate x. This is in
fact E.W. Tschirnhausen’s transformation (1683).

14. In connexion with what precedes, the question arises as to the number of
values (obtained by permutations of the roots) of given unsymmetrical
functions of the roots, or say of a given set of letters: for instance, with roots or
letters (a, b, c, d) as before, how many values are there of the function ab + cd,
or better, how many functions are there of this form? The answer is 3, viz. ab +
cd, ac + bd, ad + bc; or again we may ask whether, in the case of a given
number of letters, there exist functions with a given number of values, 3-
valued, 4-valued functions, &c.

It is at once seen that for any given number of letters there exist 2-
valued functions; the product of the differences of the letters is such a
function; however the letters are interchanged, it alters only its sign; or
say the two values are Δ and −Δ. And if P, Q are symmetrical functions of
the letters, then the general form of such a function is P + QΔ; this has
only the two values P + QΔ, P − QΔ.

In the case of 4 letters there exist (as appears above) 3-valued functions:
but in the case of 5 letters there does not exist any 3-valued or 4-valued
function; and the only 5-valued functions are those which are symmetrical
in regard to four of the letters, and can thus be expressed in terms of one
letter and of symmetrical functions of all the letters. These last theorems
present themselves in the demonstration of the non-existence of a solution
of a quintic equation by radicals.

The theory is an extensive and important one, depending on the notions of
substitutions and of groups (q.v.).

15. Returning to equations, we have the very important theorem that, given
the value of any unsymmetrical function of the roots, e.g. in the case of a
quartic equation, the function ab + cd, it is in general possible to determine
rationally the value of any similar function, such as (a + b)³ + (c + d)³.

The a priori ground of this theorem may be illustrated by means of a
numerical equation. Suppose that the roots of a quartic equation are 1, 2,
3, 4, then if it is given that ab + cd = 14, this in effect determines a, b to be
1, 2 and c, d to be 3, 4 (viz. a = 1, b = 2 or a = 2, b = 1, and c = 3, d = 4 or
c = 3, d = 4) or else a, b to be 3, 4 and c, d to be 1, 2; and it therefore in
effect determines (a + b)³ + (c + d)³ to be = 370, and not any other value;
that is, (a + b)³ + (c + d)³, as having a single value, must be determinable
rationally. And we can in the same way account for cases of failure as
regards particular equations; thus, the roots being 1, 2, 3, 4 as before, a²b
= 2 determines a to be = 1 and b to be = 2, but if the roots had been 1, 2, 4,
16 then a²b = 16 does not uniquely determine a, b but only makes them to
be 1, 16 or 2, 4 respectively.

As to the a posteriori proof, assume, for instance,

t1 = ab + cd, y1 = (a + b)³ + (c + d)³,
t2 = ac + bd, y2 = (a + c)³ + (b + d)³,
t3 = ad + bc, y3 = (a + d)³ + (b + c)³;

then y1 + y2 + y3, t1y1 + t2y2 + t3y3, t1²y1 + t2²y2 + t3²y3 will be
respectively symmetrical functions of the roots of the quartic, and
therefore rational and integral functions of the coefficients; that is, they
will be known.

Suppose for a moment that t1, t2, t3 are all known; then the equations
being linear in y1, y2, y3 these can be expressed rationally in terms of the
coefficients and of t1, t2, t3; that is, y1, y2, y3 will be known. But observe
further that y1 is obtained as a function of t1, t2, t3 symmetrical as regards
t2, t3; it can therefore be expressed as a rational function of t1 and of t2 +
t3, t2t3, and thence as a rational function of t1 and of t1 + t2 + t3, t1t2 + t1t3
+ t2t3, t1t2t3; but these last are symmetrical functions of the roots, and as
such they are expressible rationally in terms of the coefficients; that is, y1
will be expressed as a rational function of t1 and of the coefficients; or t1
(alone, not t2 or t3) being known, y1 will be rationally determined.

16. We now consider the question of the algebraical solution of equations,
or, more accurately, that of the solution of equations by radicals.

In the case of a quadric equation x² − px + q = 0, we can by the
assistance of the sign √( ) or ( )1/2 find an expression for x as a 2-valued
function of the coefficients p, q such that substituting this value in the
equation, the equation is thereby identically satisfied; it has been found
that this expression is

x = ½ {p ± √(p² − 4q) },

and the equation is on this account said to be algebraically solvable, or
more accurately solvable by radicals. Or we may by writing x = −½ p + z
reduce the equation to z² = ¼ (p² − 4q), viz. to an equation of the form x²
= a; and in virtue of its being thus reducible we say that the original
equation is solvable by radicals. And the question for an equation of any
higher order, say of the order n, is, can we by means of radicals (that is, by

aid of the sign m√( ) or ( )1/m, using as many as we please of such signs
and with any values of m) find an n-valued function (or any function) of
the coefficients which substituted for x in the equation shall satisfy it
identically?

It will be observed that the coefficients p, q ... are not explicitly
considered as numbers, but even if they do denote numbers, the question
whether a numerical equation admits of solution by radicals is wholly
unconnected with the before-mentioned theorem of the existence of the n
roots of such an equation. It does not even follow that in the case of a
numerical equation solvable by radicals the algebraical solution gives the
numerical solution, but this requires explanation. Consider first a
numerical quadric equation with imaginary coefficients. In the formula x
= ½ {p ± √(p² − 4q) }, substituting for p, q their given numerical values,
we obtain for x an expression of the form x = α + βi ± √(γ + δi), where α,
β, γ, δ are real numbers. This expression substituted for x in the quadric
equation would satisfy it identically, and it is thus an algebraical solution;
but there is no obvious a priori reason why √(γ + δi) should have a value
= c + di, where c and d are real numbers calculable by the extraction of a
root or roots of real numbers; however the case is (what there was no a
priori right to expect) that √(γ + δi) has such a value calculable by means
of the radical expressions √{√(γ² + δ²) ± γ}; and hence the algebraical
solution of a numerical quadric equation does in every case give the
numerical solution. The case of a numerical cubic equation will be
considered presently.

17. A cubic equation can be solved by radicals.

Taking for greater simplicity the cubic in the reduced form x³ + qx − r =
0, and assuming x = a + b, this will be a solution if only 3ab = q and a³ +
b³ = r, equations which give (a³ − b³)² = r² − 4⁄27 q³, a quadric equation
solvable by radicals, and giving a³ − b³ = √(r² − 4⁄27 q³), a 2-valued
function of the coefficients: combining this with a³ + b³ = r, we have a³ =

½ {r + √(r² − 4⁄27 q³) }, a 2-valued function: we then have a by means of a
cube root, viz.

a = 3√[½ {r + √(r² − 4⁄27 q³) }],

a 6-valued function of the coefficients; but then, writing q = b/3a, we
have, as may be shown, a + b a 3-valued function of the coefficients; and
x = a + b is the required solution by radicals. It would have been wrong to
complete the solution by writing

b = 3√[½ {r − √(r² − 4⁄27 q³) } ],

for then a + b would have been given as a 9-valued function having only 3
of its values roots, and the other 6 values being irrelevant. Observe that in
this last process we make no use of the equation 3ab = q, in its original
form, but use only the derived equation 27a³b³ = q³, implied in, but not
implying, the original form.

An interesting variation of the solution is to write x = ab(a + b), giving
a³b³ (a³ + b³) = r and 3a³b³ = q, or say a³ + b³ = 3r/q, a³b³ = 1⁄3 q; and
consequently

32 ⁄ ⁄
32
a³ = {r + √(r² − 4⁄27 q³) }, b³ = {r − √(r² − 4⁄27 q³) },
q q

i.e. here a³, b³ are each of them a 2-valued function, but as the only effect
of altering the sign of the quadric radical is to interchange a³, b³, they may
be regarded as each of them 1-valued; a and b are each of them 3-valued
(for observe that here only a³b³, not ab, is given); and ab(a + b) thus is in
appearance a 9-valued function; but it can easily be shown that it is (as it
ought to be) only 3-valued.

In the case of a numerical cubic, even when the coefficients are real,
substituting their values in the expression

x = 3√[½ {r + √(r² − 4⁄27 q³) }] + 1⁄3 q ÷ 3√[½ {r + √(r² − 4⁄27 q³) }],

this may depend on an expression of the form 3√(γ + δi) where γ and δ are
real numbers (it will do so if r² − 4⁄27 q³ is a negative number), and then we
cannot by the extraction of any root or roots of real positive numbers
reduce 3√(γ + δi) to the form c + di, c and d real numbers; hence here the
algebraical solution does not give the numerical solution, and we have
here the so-called “irreducible case” of a cubic equation. By what
precedes there is nothing in this that might not have been expected; the
algebraical solution makes the solution depend on the extraction of the
cube root of a number, and there was no reason for expecting this to be a
real number. It is well known that the case in question is that wherein the
three roots of the numerical cubic equation are all real; if the roots are two
imaginary, one real, then contrariwise the quantity under the cube root is
real; and the algebraical solution gives the numerical one.

The irreducible case is solvable by a trigonometrical formula, but this is
not a solution by radicals: it consists in effect in reducing the given
numerical cubic (not to a cubic of the form z³ = a, solvable by the
extraction of a cube root, but) to a cubic of the form 4x³ − 3x = a,
corresponding to the equation 4 cos³ θ − 3 cos θ = cos 3θ which serves to
determine cosθ when cos 3θ is known. The theory is applicable to an
algebraical cubic equation; say that such an equation, if it can be reduced
to the form 4x³ − 3x = a, is solvable by “trisection”—then the general
cubic equation is solvable by trisection.

18. A quartic equation is solvable by radicals, and it is to be remarked that
the existence of such a solution depends on the existence of 3-valued functions
such as ab + cd of the four roots (a, b, c, d): by what precedes ab + cd is the
root of a cubic equation, which equation is solvable by radicals: hence ab + cd
can be found by radicals; and since abcd is a given function, ab and cd can
then be found by radicals. But by what precedes, if ab be known then any

similar function, say a + b, is obtainable rationally; and then from the values of
a + b and ab we may by radicals obtain the value of a or b, that is, an
expression for the root of the given quartic equation: the expression ultimately
obtained is 4-valued, corresponding to the different values of the several
radicals which enter therein, and we have thus the expression by radicals of
each of the four roots of the quartic equation. But when the quartic is
numerical the same thing happens as in the cubic, and the algebraical solution
does not in every case give the numerical one.

It will be understood from the foregoing explanation as to the quartic
how in the next following case, that of the quintic, the question of the
solvability by radicals depends on the existence or non-existence of k-
valued functions of the five roots (a, b, c, d, e); the fundamental theorem
is the one already stated, a rational function of five letters, if it has less
than 5, cannot have more than 2 values, that is, there are no 3-valued or 4-
valued functions of 5 letters: and by reasoning depending in part upon this
theorem, N.H. Abel (1824) showed that a general quintic equation is not
solvable by radicals; and a fortiori the general equation of any order
higher than 5 is not solvable by radicals.

19. The general theory of the solvability of an equation by radicals
depends fundamentally on A.T. Vandermonde’s remark (1770) that,
supposing an equation is solvable by radicals, and that we have therefore
an algebraical expression of x in terms of the coefficients, then
substituting for the coefficients their values in terms of the roots, the
resulting expression must reduce itself to any one at pleasure of the roots
a, b, c ...; thus in the case of the quadric equation, in the expression x = ½
{p + √(p² − 4q) }, substituting for p and q their values, and observing that
(a + b)² − 4ab = (a − b)², this becomes x = ½ {a + b + √(a − b)²}, the value
being a or b according as the radical is taken to be +(a − b) or −(a − b).

So in the cubic equation x³ − px² + qx − r = 0, if the roots are a, b, c,
and if ω is used to denote an imaginary cube root of unity, ω² + ω + 1 = 0,

then writing for shortness p = a + b + c, L = a + ωb + ω²c, M = a + ω²b +
ωc, it is at once seen that LM, L³ + M³, and therefore also (L³ − M³)² are
symmetrical functions of the roots, and consequently rational functions of
the coefficients; hence

½ {L³ + M³ + √(L³ − M³)²}

is a rational function of the coefficients, which when these are replaced by
their values as functions of the roots becomes, according to the sign given
to the quadric radical, = L³ or M³; taking it = L³, the cube root of the
expression has the three values L, ωL, ω²L; and LM divided by the same
cube root has therefore the values M, ω²M, ωM; whence finally the
expression

⁄ [p + 3√{½ (L³ + M³ + √(L³ − M³)²) } + LM ÷ 3√{½ L³ + M³ + √(L³ −
13

M³)²) }]

has the three values

⁄ (p + L + M), 1⁄3 (p + ωL + ω²M), 1⁄3 (p + ω²L + ωM);
13

that is, these are = a, b, c respectively. If the value M³ had been taken
instead of L³, then the expression would have had the same three values a,
b, c. Comparing the solution given for the cubic x³ + qx − r = 0, it will
readily be seen that the two solutions are identical, and that the function r²
− 4⁄27 q³ under the radical sign must (by aid of the relation p = 0 which
subsists in this case) reduce itself to (L³ − M³)²; it is only by each radical
being equal to a rational function of the roots that the final expression can
become equal to the roots a, b, c respectively.

20. The formulae for the cubic were obtained by J.L. Lagrange (1770-1771)
from a different point of view. Upon examining and comparing the principal
known methods for the solution of algebraical equations, he found that they all
ultimately depended upon finding a “resolvent” equation of which the root is a

+ ωb + ω²c + ω³d + ..., ω being an imaginary root of unity, of the same order as
the equation; e.g. for the cubic the root is a + ωb + ω²c, ω an imaginary cube
root of unity. Evidently the method gives for L³ a quadric equation, which is
the “resolvent” equation in this particular case.

For a quartic the formulae present themselves in a somewhat different form,
by reason that 4 is not a prime number. Attempting to apply it to a quintic, we
seek for the equation of which the root is (a + ωb + ω²c + ω³d + ω4e), ω an
imaginary fifth root of unity, or rather the fifth power thereof (a + ωb + ω²c +
ω³d + ω4e)5; this is a 24-valued function, but if we consider the four values
corresponding to the roots of unity ω, ω², ω³, ω4, viz. the values

(a + ω b + ω²c + ω³d + ω4e)5,
(a + ω²b + ω4c + ω d + ω³e)5,
(a + ω³b + ω c + ω4d + ω²e)5,
(a + ω4b + ω³c + ω²d + ω e)5,

any symmetrical function of these, for instance their sum, is a 6-valued
function of the roots, and may therefore be determined by means of a sextic
equation, the coefficients whereof are rational functions of the coefficients of
the original quintic equation; the conclusion being that the solution of an
equation of the fifth order is made to depend upon that of an equation of the
sixth order. This is, of course, useless for the solution of the quintic equation,
which, as already mentioned, does not admit of solution by radicals; but the
equation of the sixth order, Lagrange’s resolvent sextic, is very important, and
is intimately connected with all the later investigations in the theory.

21. It is to be remarked, in regard to the question of solvability by radicals,
that not only the coefficients are taken to be arbitrary, but it is assumed that
they are represented each by a single letter, or say rather that they are not so
expressed in terms of other arbitrary quantities as to make a solution possible.
If the coefficients are not all arbitrary, for instance, if some of them are zero, a

sextic equation might be of the form x6 + bx4 + cx² + d = 0, and so be solvable
as a cubic; or if the coefficients of the sextic are given functions of the six
arbitrary quantities a, b, c, d, e, f, such that the sextic is really of the form (x² +
ax + b)(x4 + cx³ + dx² + ex + f) = 0, then it breaks up into the equations x² + ax
+ b = 0, x4 + cx³ + dx² + ex + f = 0, and is consequently solvable by radicals;
so also if the form is (x − a) (x − b) (x − c) (x − d) (x − e) (x − f) = 0, then the
equation is solvable by radicals,—in this extreme case rationally. Such cases of
solvability are self-evident; but they are enough to show that the general
theorem of the non-solvability by radicals of an equation of the fifth or any
higher order does not in any wise exclude for such orders the existence of
particular equations solvable by radicals, and there are, in fact, extensive
classes of equations which are thus solvable; the binomial equations xn − 1 = 0
present an instance.

22. It has already been shown how the several roots of the equation xn −
1 = 0 can be expressed in the form cos 2sπ/n + i sin 2sπ/n, but the question
is now that of the algebraical solution (or solution by radicals) of this
equation. There is always a root = 1; if ω be any other root, then obviously
ω, ω², ... ωn−1 are all of them roots; xn − 1 contains the factor x − 1, and it
thus appears that ω, ω², ... ωn−1 are the n-1 roots of the equation

xn−1 + xn−2 + ... x + 1 = 0;

we have, of course, ωn−1 + ωn−2 + ... + ω + 1 = 0.

It is proper to distinguish the cases n prime and n composite; and in the
latter case there is a distinction according as the prime factors of n are
simple or multiple. By way of illustration, suppose successively n = 15
and n = 9; in the former case, if α be an imaginary root of x³ − 1 = 0 (or
root of x² + x + 1 = 0), and β an imaginary root of x5 − 1 = 0 (or root of x4
+ x³ + x² + x + 1 = 0), then ω may be taken = αβ; the successive powers
thereof, αβ, α²β², β³, αβ4, α², β, αβ², α²β³, β4, α, α²β, β², αβ³, α²β4, are the
roots of x14 + x13 + ... + x + 1 = 0; the solution thus depends on the

solution of the equations x³ − 1 = 0 and x5 − 1 = 0. In the latter case, if α
be an imaginary root of x³ − 1 = 0 (or root of x² + x + 1 = 0), then the
equation x9 − 1 = 0 gives x³ = 1, α, or α²; x³ = 1 gives x = 1, α, or α²; and
the solution thus depends on the solution of the equations x³ − 1 = 0, x³ −
α = 0, x³ − α² = 0. The first equation has the roots 1, α, α²; if β be a root of
either of the others, say if β³ = α, then assuming ω = β, the successive
powers are β, β², α, αβ, αβ², α², α²β, α²β², which are the roots of the
equation x8 + x7 + ... + x + 1 = 0.

It thus appears that the only case which need be considered is that of n a
prime number, and writing (as is more usual) r in place of ω, we have r, r²,
r³,...rn−1 as the (n − 1) roots of the reduced equation

xn−1 + xn−2 + ... + x + 1 = 0;

then not only rn − 1 = 0, but also rn−1 + rn−2 + ... + r + 1 = 0.

23. The process of solution due to Karl Friedrich Gauss (1801) depends
essentially on the arrangement of the roots in a certain order, viz. not as above,
with the indices of r in arithmetical progression, but with their indices in
geometrical progression; the prime number n has a certain number of prime
roots g, which are such that gn−1 is the lowest power of g, which is ≡ 1 to the
modulus n; or, what is the same thing, that the series of powers 1, g, g², ... gn−2,
each divided by n, leave (in a different order) the remainders 1, 2, 3, ... n − 1;
hence giving to r in succession the indices 1, g, g²,...gn−2, we have, in a
different order, the whole series of roots r, r², r³,...rn−1.

In the most simple case, n = 5, the equation to be solved is x4 + x³ + x²
+ x + 1 = 0; here 2 is a prime root of 5, and the order of the roots is r, r²,
r4, r³. The Gaussian process consists in forming an equation for
determining the periods P1, P2, = r + r4 and r² + r³ respectively;—these
being such that the symmetrical functions P1 + P2, P1P2 are rationally
determinable: in fact P1 + P2 = −1, P1P2 = (r + r4) (r² + r³), = r³ + r4 + r6 +

r7, = r³ + r4 + r + r², = −1. P1, P2 are thus the roots of u² + u − 1 = 0; and
taking them to be known, they are themselves broken up into subperiods,
in the present case single terms, r and r4 for P1, r² and r³ for P2; the
symmetrical functions of these are then rationally determined in terms of
P1 and P2; thus r + r4 = P1, r·r4 = 1, or r, r4 are the roots of u² − P1u + 1 =
0. The mode of division is more clearly seen for a larger value of n; thus,
for n = 7 a prime root is = 3, and the arrangement of the roots is r, r³, r², r6,
r4, r5. We may form either 3 periods each of 2 terms, P1, P2, P3 = r + r6, r³
+ r4, r² + r5 respectively; or else 2 periods each of 3 terms, P1, P2 = r + r² +
r4, r³ + r6 + r5 respectively; in each ease the symmetrical functions of the
periods are rationally determinable: thus in the case of the two periods P1
+ P2 = −1, P1P2 = 3 + r + r² + r³ + r4 + r5 + r6, = 2; and the periods being
known the symmetrical functions of the several terms of each period are
rationally determined in terms of the periods, thus r + r² + r4 = P1, r·r² +
r·r4 + r²·r4 = P2, r·r²·r4 = 1.

The theory was further developed by Lagrange (1808), who, applying his
general process to the equation in question, xn−1 + xn−2 + ... + x + 1 = 0 (the
roots a, b, c... being the several powers of r, the indices in geometrical
progression as above), showed that the function (a + ωb + ω²c + ...)n−1 was in
this case a given function of ω with integer coefficients.

Reverting to the before-mentioned particular equation x4 + x³ + x² + x +
1 = 0, it is very interesting to compare the process of solution with that for
the solution of the general quartic the roots whereof are a, b, c, d.

Take ω, a root of the equation ω4 − 1 = 0 (whence ω is = 1, −1, i, or −i,
at pleasure), and consider the expression

(a + ωb + ω²c + ω³d)4,

the developed value of this is

= a4 + b4 + c4 + d4 + 6 (a²c² + b²d²) + 12 (a²bd + b²ca + c²db + d²ac)
+ω {4 (a³b + b³c + c³ + d³a) + 12 (a²cd + b²da + c²ab + d²bc) }
+ω² {6 (a²b² + b²c² + c²d² + d²a²) + 4 (a³c + b³d + c³a + d³b) + 24abcd}
+ω³ {4 (a³d + b³a + c³b + d³c) + 12 (a²bc + b²cd + c²da + d²ab) }

that is, this is a 6-valued function of a, b, c, d, the root of a sextic (which
is, in fact, solvable by radicals; but this is not here material).

If, however, a, b, c, d denote the roots r, r², r4, r³ of the special equation,
then the expression becomes

r4 + r³ + r + r² + 6 (1 + 1) + 12 (r² + r4 + r³ + r)
+ ω {4 (1 + 1 + 1 + 1) + 12 (r4 + r³ + r + r²) }
+ ω²{6 (r + r² + r4 + r³) + 4 (r² + r4 + r³ + r) }
+ ω³{4 (r + r² + r4 + r³) + 12 (r³ + r + r² + r4) }

viz. this is

= −1 + 4ω + 14ω² − 16ω³,

a completely determined value. That is, we have

(r + ωr² + ω²r4 + ω³r³) = −1 + 4ω + 14ω² − 16ω³,

which result contains the solution of the equation. If ω = 1, we have (r + r²
+ r4 + r³)4 = 1, which is right; if ω = −1, then (r + r4 − r² − r³)4 = 25; if ω =
i, then we have {r − r4 + i(r² − r³) }4 = −15 + 20i; and if ω = −i, then {r −
r4 − i (r² − r³) }4 = −15 − 20i; the solution may be completed without
difficulty.

The result is perfectly general, thus:—n being a prime number, r a root of
the equation xn−1 + xn−2 + ... + x + 1 = 0, ω a root of ωn−1 − 1 = 0, and g a

prime root of gn−1 ≡ 1 (mod. n), then

(r + ωr g + ... + ωn − 2r g n−2) n−1

is a given function M0 + M1ω ... + Mn−2ωn−2 with integer coefficients, and by
the extraction of (n − 1)th roots of this and similar expressions we ultimately
obtain r in terms of ω, which is taken to be known; the equation xn − 1 = 0, n a
prime number, is thus solvable by radicals. In particular, if n − 1 be a power of
2, the solution (by either process) requires the extraction of square roots only;
and it was thus that Gauss discovered that it was possible to construct
geometrically the regular polygons of 17 sides and 257 sides respectively.
Some interesting developments in regard to the theory were obtained by C.G.J.
Jacobi (1837); see the memoir “Ueber die Kreistheilung, u.s.w.,” Crelle, t. xxx.
(1846).

The equation xn−1 + ... + x + 1 = 0 has been considered for its own sake, but
it also serves as a specimen of a class of equations solvable by radicals,
considered by N.H. Abel (1828), and since called Abelian equations, viz. for
the Abelian equation of the order n, if x be any root, the roots are x, θx, θ²x, ...
θn−1x (θx being a rational function of x, and θnx = x); the theory is, in fact,
very analogous to that of the above particular case.

A more general theorem obtained by Abel is as follows:—If the roots
of an equation of any order are connected together in such wise that all
the roots can be expressed rationally in terms of any one of them, say
x; if, moreover, θx, θ1x being any two of the roots, we have θθ1x =
θ1θx, the equation will be solvable algebraically. It is proper to refer
also to Abel’s definition of an irreducible equation:—an equation φx =
0, the coefficients of which are rational functions of a certain number
of known quantities a, b, c ..., is called irreducible when it is impossible
to express its roots by an equation of an inferior degree, the coefficients
of which are also rational functions of a, b, c ... (or, what is the same
thing, when φx does not break up into factors which are rational
functions of a, b, c ...). Abel applied his theory to the equations which
present themselves in the division of the elliptic functions, but not to
the modular equations.

24. But the theory of the algebraical solution of equations in its most
complete form was established by Evariste Galois (born October 1811,
killed in a duel May 1832; see his collected works, Liouville, t. xl., 1846).
The definition of an irreducible equation resembles Abel’s,—an equation is
reducible when it admits of a rational divisor, irreducible in the contrary
case; only the word rational is used in this extended sense that, in
connexion with the coefficients of the given equation, or with the irrational
quantities (if any) whereof these are composed, he considers any number of
other irrational quantities called “adjoint radicals,” and he terms rational
any rational function of the coefficients (or the irrationals whereof they are
composed) and of these adjoint radicals; the epithet irreducible is thus taken
either absolutely or in a relative sense, according to the system of adjoint
radicals which are taken into account. For instance, the equation x4 + x³ +
x² + x + 1 = 0; the left hand side has here no rational divisor, and the
equation is irreducible; but this function is = (x² + ½ x + 1)² − 5⁄4 x², and it

has thus the irrational divisors x² + ½ (1 + √5)x + 1, x² + ½ (1 − √5)x + 1;
and these, if we adjoin the radical √5, are rational, and the equation is no
longer irreducible. In the case of a given equation, assumed to be
irreducible, the problem to solve the equation is, in fact, that of finding
radicals by the adjunction of which the equation becomes reducible; for
instance, the general quadric equation x² + px + q = 0 is irreducible, but it
becomes reducible, breaking up into rational linear factors, when we adjoin
the radical √(¼ p² − q).

The fundamental theorem is the Proposition I. of the “Mémoire sur
les conditions de résolubilité des équations par radicaux”; viz. given an
equation of which a, b, c ... are the m roots, there is always a group of
permutations of the letters a, b, c ... possessed of the following
properties:—

1. Every function of the roots invariable by the substitutions of the
group is rationally known.

2. Reciprocally every rationally determinable function of the roots is
invariable by the substitutions of the group.

Here by an invariable function is meant not only a function of which
the form is invariable by the substitutions of the group, but further, one
of which the value is invariable by these substitutions: for instance, if
the equation be φ(x) = 0, then φ(x) is a function of the roots invariable
by any substitution whatever. And in saying that a function is rationally
known, it is meant that its value is expressible rationally in terms of the
coefficients and of the adjoint quantities.

For instance in the case of a general equation, the group is simply
the system of the 1.2.3 ... n permutations of all the roots, since, in this
case, the only rationally determinable functions are the symmetric
functions of the roots.

In the case of the equation xn−1 ... + x + 1 = 0, n a prime number, a,
b, c ... k = r, r g, r g² ... r g n−2, where g is a prime root of n, then the
group is the cyclical group abc ... k, bc ... ka, ... kab ... j, that is, in this
particular case the number of the permutations of the group is equal to
the order of the equation.

This notion of the group of the original equation, or of the group of
the equation as varied by the adjunction of a series of radicals, seems to
be the fundamental one in Galois’s theory. But the problem of solution
by radicals, instead of being the sole object of the theory, appears as the
first link of a long chain of questions relating to the transformation and
classification of irrationals.

Returning to the question of solution by radicals, it will be readily
understood that by the adjunction of a radical the group may be
diminished; for instance, in the case of the general cubic, where the
group is that of the six permutations, by the adjunction of the square
root which enters into the solution, the group is reduced to abc, bca,
cab; that is, it becomes possible to express rationally, in terms of the
coefficients and of the adjoint square root, any function such as a²b +
b²c + c²a which is not altered by the cyclical substitution a into b, b into
c, c into a. And hence, to determine whether an equation of a given
form is solvable by radicals, the course of investigation is to inquire
whether, by the successive adjunction of radicals, it is possible to
reduce the original group of the equation so as to make it ultimately
consist of a single permutation.

The condition in order that an equation of a given prime order n may
be solvable by radicals was in this way obtained—in the first instance
in the form (scarcely intelligible without further explanation) that every
function of the roots x1, x2 ... xn, invariable by the substitutions xak + b

for xk, must be rationally known; and then in the equivalent form that
the resolvent equation of the order 1.2 ... (n − 2) must have a rational
root. In particular, the condition in order that a quintic equation may be
solvable is that Lagrange’s resolvent of the order 6 may have a rational
factor, a result obtained from a direct investigation in a valuable
memoir by E. Luther, Crelle, t. xxxiv. (1847).

Among other results demonstrated or announced by Galois may be
mentioned those relating to the modular equations in the theory of
elliptic functions; for the transformations of the orders 5, 7, 11, the
modular equations of the orders 6, 8, 12 are depressible to the orders 5,
7, 11 respectively; but for the transformation, n a prime number greater
than 11, the depression is impossible.

The general theory of Galois in regard to the solution of equations
was completed, and some of the demonstrations supplied by E. Betti
(1852). See also J.A. Serret’s Cours d’algèbre supérieure, 2nd ed.
(1854); 4th ed. (1877-1878).

25. Returning to quintic equations, George Birch Jerrard (1835)
established the theorem that the general quintic equation is by the extraction
of only square and cubic roots reducible to the form x5 + ax + b = 0, or what
is the same thing, to x5 + x + b = 0. The actual reduction by means of
Tschirnhausen’s theorem was effected by Charles Hermite in connexion
with his elliptic-function solution of the quintic equation (1858) in a very
elegant manner. It was shown by Sir James Cockle and Robert Harley
(1858-1859) in connexion with the Jerrardian form, and by Arthur Cayley
(1861), that Lagrange’s resolvent equation of the sixth order can be
replaced by a more simple sextic equation occupying a like place in the
theory.

The theory of the modular equations, more particularly for the case n = 5,
has been studied by C. Hermite, L. Kronecker and F. Brioschi. In the case n
= 5, the modular equation of the order 6 depends, as already mentioned, on
an equation of the order 5; and conversely the general quintic equation may
be made to depend upon this modular equation of the order 6; that is,
assuming the solution of this modular equation, we can solve (not by
radicals) the general quintic equation; this is Hermite’s solution of the
general quintic equation by elliptic functions (1858); it is analogous to the
before-mentioned trigonometrical solution of the cubic equation. The theory
is reproduced and developed in Brioschi’s memoir, “Über die Auflösung der
Gleichungen vom fünften Grade,” Math. Annalen, t. xiii. (1877-1878).

26. The modern work, reproducing the theories of Galois, and
exhibiting the theory of algebraic equations as a whole, is C. Jordan’s
Traité des substitutions et des équations algébriques (Paris, 1870). The
work is divided into four books—book i., preliminary, relating to the
theory of congruences; book ii. is in two chapters, the first relating to
substitutions in general, the second to substitutions defined
analytically, and chiefly to linear substitutions; book iii. has four
chapters, the first discussing the principles of the general theory, the
other three containing applications to algebra, geometry, and the theory
of transcendents; lastly, book iv., divided into seven chapters, contains
a determination of the general types of equations solvable by radicals,
and a complete system of classification of these types. A glance
through the index will show the vast extent which the theory has
assumed, and the form of general conclusions arrived at; thus, in book
iii., the algebraical applications comprise Abelian equations, equations
of Galois; the geometrical ones comprise Q. Hesse’s equation, R.F.A.
Clebsch’s equations, lines on a quartic surface having a nodal line,
singular points of E.E. Kummer’s surface, lines on a cubic surface,
problems of contact; the applications to the theory of transcendents

comprise circular functions, elliptic functions (including division and
the modular equation), hyperelliptic functions, solution of equations by
transcendents. And on this last subject, solution of equations by
transcendents, we may quote the result—“the solution of the general
equation of an order superior to five cannot be made to depend upon
that of the equations for the division of the circular or elliptic
functions”; and again (but with a reference to a possible case of
exception), “the general equation cannot be solved by aid of the
equations which give the division of the hyperelliptic functions into an
odd number of parts.” (See also Groups, Theory of.)
(A. Ca.)

Bibliography.—For the general theory see W.S. Burnside and A.W.
Panton, The Theory of Equations (4th ed., 1899-1901); the Galoisian
theory is treated in G.B. Matthews, Algebraic Equations (1907). See
also the Ency. d. math. Wiss. vol. ii.

1 The coefficients were selected so that the roots might be nearly 1, 2, 3.

2 The third edition (1826) is a reproduction of that of 1808; the first edition has the date
1798, but a large part of the contents is taken from memoirs of 1767-1768 and 1770-1771.

3 The earlier demonstrations by Euler, Lagrange, &c, relate to the case of a numerical
equation with real coefficients; and they consist in showing that such equation has always a
real quadratic divisor, furnishing two roots, which are either real or else conjugate
imaginaries α + βi (see Lagrange’s Équations numériques).

4 The square root of α + βi can be determined by the extraction of square roots of
positive real numbers, without the trigonometrical tables.

EQUATION OF THE CENTRE, in astronomy, the angular distance,
measured around the centre of motion, by which a planet moving in an
ellipse deviates from the mean position which it would occupy if it moved
uniformly. Its amount is the correction which must be applied positively or
negatively to the mean anomaly in order to obtain the true anomaly. It arises
from the ellipticity of the orbit, is zero at pericentre and apocentre, and
reaches its greatest amount nearly midway between these points. (See
Anomaly and Orbit.)

EQUATION OF TIME, the difference between apparent time,
determined by the meridian passage of the real sun, and mean time,
determined by the passage of the mean sun. It goes through a double period
in the course of a year. Its amount varies a fraction of a minute for the same
date, from year to year and from one longitude to another, on the same day.
The following table shows an average value for any date and for the
Greenwich meridian for a number of years, from which the actual value will
seldom deviate more than 20 seconds until after 1950. The + sign indicates
that the real sun reaches the meridian after mean noon; the − sign before
mean noon.

Table of the Equation of Time.

m. s. m. s. m. s.
Jan. 1 +3 26 Mar. 1 +12 39 May 1 −2 55

6 5 45 6 11 35 6 −3 27
11 7 51 11 10 20 11 −3 46
16 9 43 16 8 58 16 −3 51
21 11 19 21 7 30 21 −3 40
26 12 36 26 5 59 26 −3 16

Feb. 1 +13 42 Apr. 1 +4 9 June 1 −2 32
6 14 14 6 2 40 6 −1 44
11 14 25 11 +1 15 11 −0 48
16 14 17 16 −0 3 16 +0 14
21 13 52 21 −1 12 21 1 19
26 13 11 26 −2 10 26 2 24

July 1 +3 26 Sept. 1 +0 9 Nov. 1 −16 18
6 4 21 6 −1 28 6 −16 19
11 5 8 11 −3 10 11 −15 58
16 5 44 16 −4 55 16 −15 15
21 6 8 21 −6 41 21 −14 12
26 6 18 26 −8 25 26 −12 49

Aug. 1 +6 10 Oct. 1 −10 5 Dec. 1 −11 7
6 5 47 6 −11 38 6 −9 9
11 5 9 11 −13 2 11 −6 57
16 4 17 16 −14 14 16 −4 35
21 3 12 21 −15 11 21 −2 7
26 1 55 26 −15 52 26 +0 23

EQUATOR (Late Lat. aequator, from aequare, to make equal), in
geography, that great circle of the earth, equidistant from the two poles,

which divides the northern from the southern hemisphere and lies in a plane
perpendicular to the axis of the earth; this is termed the “geographical” or
“terrestrial equator.” In astronomy, the “celestial equator” is the name given
to the great circle in which the plane of the terrestrial equator intersects the
celestial sphere; it is consequently equidistant from the celestial poles. The
“magnetic equator” is an imaginary line encircling the earth, along which
the vertical component of the earth’s magnetic force is zero; it nearly
coincides with the terrestrial equator.

EQUERRY (from the Fr. écurie, a stable, through its older form escurie,
from the Med. Lat. scuria, a word of Teutonic origin for a stable or shed, cf.
Ger. Scheuer; the modern spelling has confused the word with the Lat.
equus, a horse), a contracted form of “gentleman of the equerry,” an officer
in charge of the stables of a royal household. At the British court, equerries
are officers attached to the department of the master of the horse, the first of
whom is called chief equerry (see Household, Royal).

EQUIDAE, the family of perissodactyle ungulate mammals typified by
the horse (Equus caballus); see Horse. According to the older classification
this family was taken to include only the forms with tall-crowned teeth,
more or less closely allied to the typical genus Equus. There is, however,

such an almost complete graduation from the former to earlier and more
primitive mammals with short-crowned cheek-teeth, at one time included in
the family Lophiodontidae (see Perissodactyla), that it has now become a
very general practice to include the whole “phylum” in the family Equidae.
The Equidae, in this extended sense, together with the extinct
Palaeotheriidae, are indeed now regarded as forming one of four main
groups into which the Perissodactyla are divided, the other groups being the
Tapiroidea, Rhinocerotoidea and Titanotheriide. For the horse-group the
name Hippoidea is employed. All four groups were closely connected in the
Lower Eocene, so that exact definition is almost impossible.

In the Hippoidea there is generally the full series of 44 teeth, but the first
premolar is often deciduous or wanting in the lower or in both jaws. The
incisors are chisel-shaped, and the canines tend to become isolated so as in
the now specialized forms to occupy nearly the middle of a longer or
shorter gap between the incisors and premolars. In the upper molars the two
outer columns of the primitive tubercular molar coalesce to form an outer
wall, from which proceed two crescentic transverse crests; the connexion
between the crests and the wall being imperfect or slight, and the crests
themselves sometimes tubercular. Each of the lower molars carries two
crescentic ridges. The number of toes ranges from four to one in the fore-
foot, and from three to one in the hind-foot. The paroccipital, postglenoid
and post-tympanic processes of the skull are large, and the latter always
distinct. Normally there are no traces of horn-cores. The calcaneum lacks
the facet for the fibula found in the Titanotheroidea.

In the earlier Equidae the teeth were short-crowned, with the premolars
simpler than the molars; but there is a gradual tendency to an increase in the
height of the crowns of the teeth, accompanied by increasing complexity of
structure and the filling up of the hollows with cement. Similarly the gap on
each side of the canine tooth in each jaw continues to increase in length;

while in all the later forms the orbit is surrounded by a ring of bone. A third
modification is the increasing length of limb (as well as in general bodily
size), accompanied by a gradual reduction in the number of toes from three
or four to one.

All the existing members of the
family, such as the domesticated
horse (Equus caballus) and its wild
or half-wild relatives, the asses and
the zebras, are included in the
typical genus. In all these the
crowns of the cheek-teeth are very
tall (fig. 1, b) and only develop roots
late in life; while their grinding-
surfaces (fig. 2, b and c) are very
complicated and have all the
hollows filled with cement. The
Fig. 1.—a, Side view of second upper
summits of the incisors are infolded, molar tooth of Anchitherium
(brachyodont form); b, corresponding
producing, when partially worn, the tooth of horse (hypsidont form).
“mark.” In the skull the orbit is
surrounded by bone, and there is no distinct depression in front of the same.
Each limb terminates in one large toe; the lateral digits being represented by
the splint-bones, corresponding to the lateral metacarpals and metatarsals of
Hipparion. Not unfrequently, however, the lower ends of the splint-bones
carry a small expansion, representing the phalanges.

Remains of horses indistinguishable from E. caballus occur in the
Pleistocene deposits of Europe and Asia; and it is from them that the dun-
coloured small horses of northern Europe and Asia are probably derived.
The ancestor of these Pleistocene horses is probably E. stenonis, of the
Upper Pliocene of Europe, which has a small depression in front of the

orbit, while the skull is relatively larger, the feet are rather shorter, and the
splint-bones somewhat more developed. In India a nearly allied species (E.
sivalensis), occurs in the Lower Pliocene, and may have been the ancestor
of the Arab stock, which shows traces of the depression in front of the orbit
characteristic of the earlier forms. In North America species of Equus occur
in the Pleistocene and from that continent others reached South America
during the same epoch. In the latter country occurs Hippidium, in which the
cheek-teeth are shorter and simpler, and the nasal bones very long and
slender, with elongated slits at the side. The limbs, especially the cannon-
bones, are relatively short, and the splint-bones large. The allied Argentine
Onohippidium, which is also Pleistocene, has still longer nasal bones and
slits, and a deep double cavity in front of the orbit, part of which probably
contained a gland. Onohippidium is certainly off the direct line of descent
of the modern horses, and, on account of the length of the nasals and their
slits, the same probably holds good for Hippidium.

Fig. 2.—a, Grinding surface of unworn right upper molar tooth of Anchitherium; b, corresponding
surface of unworn molar of young horse; c, the same tooth after it has been some time in use. The
uncoloured portions are the dentine or ivory, the shaded parts the cement filling the cavities and
surrounding the exterior. The black line separating these two structures is the enamel or hardest
constituent of the tooth.

Species from the Pliocene of Texas and the Upper Miocene (Loup Fork)
of Oregon were at one time assigned to Hippidium, but this is incorrect, that

genus being exclusively South American. The name Pliohippus has been
applied to species from the same two formations on the supposition that the
foot-structure was similar to that of Hippidium, but Mr J.W. Gidley is of
opinion that the lateral digits may have been fully developed.

Apparently there is here some gap in the line of descent of the horse, and
it may be suggested that the evolution took place, not as commonly
supposed, in North America, but in eastern central Asia, of which the
palaeontology is practically unknown; some support is given to this theory
by the fact that the earliest species with which we are acquainted occur in
northern India.

Fig. 3.—Successive stages of modification of the left fore-feet of extinct forms of horse-
like animals, showing gradual reduction of the outer and enlargement of the middle toe (III).

a, Hyracotherium (Eocene). d, Hipparion (Pliocene).
b, Mesohippus (Oligocene). e, Equus (Pleistocene).
c, Anchitherium (Miocene).

Be this as it may, the next North American representatives of the family
constitute the genera Protohippus and Merychippus of the Miocene, in both
of which the lateral digits are fully developed and terminate in small though

perfect hoofs. In both the cheek-teeth have moderately tall crowns, and in
the first named of the two those of the milk-series are nearly similar to their
permanent successors. In Merychippus, on the other hand, the milk-molars
have short crowns, without any cement in the hollows, thus resembling the
permanent molars of the under-mentioned genus Anchitherium. From the
well-known Hipparion, or Hippotherium, typically from the Lower
Pliocene of Europe, but also occurring in the corresponding formation in
North Africa, Persia, India and China, and represented in the Upper
Miocene Loup Fork beds of the United States by species which it has been
proposed to separate generically as Neohipparion, we reach small horses
which are now generally regarded as a lateral offshoot from the
Merychippus type. The cheek-teeth, which have crowns of moderate height,
differ from those of all the foregoing in that the postero-internal pillar (the
projection on the right-hand top corner of c in fig. 2) is isolated in place of
being attached by a narrow neck to the adjacent crescent. The skull, which
is relatively short, has a large depression in front of the orbit, commonly
supposed to have contained a gland, but this may be doubtful. In the typical,
and also in the North American forms these were complete, although small,
lateral toes in both feet (fig. 3, d), but it is possible that in H. antilopinum of
India the lateral toes had disappeared. If this be so, we have the
development of a monodactyle foot in this genus independently of Equus.

The foregoing genera constitute the subfamily Equinae, or the Equidae as
restricted by the older writers. In all the dentition is of the hypsodont type,
with the hollows of the cheek-teeth filled by cement, the premolars
molariform, and the first small and generally deciduous. The orbit is
surrounded by a bony ring; the ulna and radius in the fore, and the tibia and
fibula in the hind-limb are united, and the feet are of the types described
above. Between this subfamily and the second subfamily, Hyracotheriinae,
a partial connexion is formed by the North American Upper Miocene
genera Desmatippus and Anchippus or Parahippus. The characteristics of

the group will be gathered from the remarks on the leading genera; but it
may be mentioned that the orbit is open behind, the cheek-teeth are short-
crowned and without cement (fig. 1, a), the gap between the canine and the
outermost incisor is short, the bones of the middle part of the leg are
separate, and there are at least three toes to each foot.

The longest-known genus and the one containing the largest species is
Anchitherium, typically from the Middle Miocene of Europe, but also
represented by one species from the Upper Miocene of North America. The
European A. aurelianense was of the size of an ordinary donkey. The cheek-
teeth are of the type shown in a of figs. 1 and 2; the premolars, with the
exception of the small first one, being molar-like; and the lateral toes (fig. 3,
c) were to some extent functional. The summits of the incisors were
infolded to a small extent. Nearly allied is the American Mesohippus,
ranging from the Lower Miocene to the Lower Oligocene of the United
States, of which the earliest species stood only about 18 in. at the shoulder.
The incisors were scarcely, if at all, infolded, and there is a rudiment of the
fifth metacarpal (fig. 3, b). By some writers all the species of Mesohippus
are included in the genus Miohippus, but others consider that the two genera
are distinct.

Mesohippus and Miohippus are connected with the earliest and most
primitive mammal which it is possible to include in the family Equidae by
means of Epihippus of the Uinta or Upper Eocene of North America, and
Pachynolophus, or Orohippus, of the Middle and Lower Eocene of both
halves of the northern hemisphere. The final stage, or rather the initial
stage, in the series is presented by Hyracotherium (Protorohippus), a
mammal no larger than a fox, common to the Lower Eocene of Europe and
North America. The general characteristics of this progenitor of the horses
are those given above as distinctive of the group. The cheek-teeth are,
however, much simpler than those of Anchitherium; the transverse crests of

the upper molars not being fully connected with the outer wall, while the
premolars in the upper jaw are triangular, and thus unlike the molars. The
incisors are small and the canines scarcely enlarged; the latter having a gap
on each side in the lower, but only one on their hinder aspect in the upper
jaw. The fore-feet have four complete toes (fig. 3, a), but there are only
three hind-toes, with a rudiment of the fifth metatarsal. The vertebrae are
simpler in structure than in Equus. From Hyracotherium, which is closely
related to the Eocene representatives of the ancestral stocks of the other
three branches of the Perissodactyla, the transition is easy to Phenacodus,
the representative of the common ancestor of all the Ungulata.

See also H.F. Osborn, “New Oligocene Horses,” Bull. Amer. Mus.
vol. xx. p. 167 (1904); J.W. Gidley, Proper Generic Names of Miocene
Horses, p. 191; and the article Palaeontology.
(R. L.*)

EQUILIBRIUM (from the Lat. aequus, equal, and libra, a balance), a
condition of equal balance between opposite or counteracting forces. By the
“sense of equilibrium” is meant the sense, or sensations, by which we have
a feeling of security in standing, walking, and indeed in all the movements
by which the body is carried through space. Such a feeling of security is
necessary both for maintaining any posture, such as standing, or for
performing any movement. If this feeling is absent or uncertain, or if there
are contradictory sensations, then definite muscular movements are
inefficiently or irregularly performed, and the body may stagger or fall.
When we stand erect on a firm surface, like a floor, there is a feeling of

resistance, due to nervous impulses reaching the brain from the soles of the
feet and from the muscles of the limbs and trunk. In walking or running,
these feelings of resistance seem to precede and guide the muscular
movements necessary for the next step. If these are absent or perverted or
deficient, as is the case in the disease known as locomotor ataxia, then,
although there is no loss of the power of voluntary movement, the patient
staggers in walking, especially if he is not allowed to look at his feet, or if
he is blind-folded. He misses the guiding sensations that come from the
limbs; and with a feeling that he is walking on a soft substance, offering
little or no resistance, he staggers, and his muscular movements become
irregular. Such a condition maybe artificially brought about by washing the
soles of the feet with chloroform or ether. And it has been observed to exist
partially after extensive destruction of the skin of the soles of the feet by
burns or scalds. This shows that tactile impulses from the skin take a share
in generating the guiding sensation. In the disease above mentioned,
however, tactile impressions may be nearly normal, but the guiding
sensation is weak and inefficient, owing to the absence of impulses from the
muscles. The disease is known to depend on morbid changes in the
posterior columns of the spinal cord, by which impulses are not freely
transmitted upwards to the brain. These facts point to the existence of
impulses coming from the muscles and tendons. It is now known that there
exist peculiar spindles, in muscle, and rosettes or coils or loops of nerve
fibres in close proximity to tendons. These are the end organs of the sense.
The transmission of impulses gives rise to the muscular sense, and the
guiding sensation which precedes co-ordinated muscular movements
depends on these impulses. Thus from the limbs streams of nervous
impulses pass to the sensorium from the skin and from muscles and
tendons; these may or may not arouse consciousness, but they guide or
evoke muscular movements of a co-ordinated character, more especially of
the limbs.

In animals whose limbs are not adapted for delicate touch nor for the
performance of complicated movements, such as some mammals and birds
and fishes, the guiding sensations depend largely on the sense of vision.
This sense in man, instead of assisting, sometimes disturbs the guiding
sensation. It is true that in locomotor ataxia visual sensations may take the
place of the tactile and muscular sensations that are inefficient, and the man
can walk without staggering if he is allowed to look at the floor, and
especially if he is guided by transverse straight lines. On the other hand, the
acrobat on the wire-rope dare not trust his visual sensations in the
maintenance of his equilibrium. He keeps his eyes fixed on one point
instead of allowing them to wander to objects below him, and his muscular
movements are regulated by the impulses that come from the skin and
muscles of his limbs. The feeling of insecurity probably arises from a
conception of height, and also from the knowledge that by no muscular
movements can a man avoid a catastrophe if he should fall. A bird, on the
other hand, depends largely on visual impressions, and it knows by
experience that if launched into the air from a height it can fly. Here,
probably, is an explanation of the large size of the eyes of birds. Cover the
head, as in hooding a falcon, and the bird seems to be deprived of the power
of voluntary movement. Little effect will be produced if we attempt to
restrain the movements of a cat by covering its eyes. A fish also is deprived
of the power of motion if its eyes are covered. But both in the bird and in
the fish tactile and muscular impressions, especially the latter, come into
play in the mechanism of equilibrium. In flight the large-winged birds,
especially in soaring, can feel the most delicate wind-pressures, both as
regards direction and force, and they adapt the position of their body so as
to catch the pressure at the most efficient angle. The same is true of the fish,
especially of the flat-fishes. In mammals the sense of equilibrium depends,
then, on streams of tactile, muscular and visual impressions pouring in on
the sensorium, and calling forth appropriate muscular movements. It has

also been suggested that impulses coming from the abdominal viscera may
take part in the mechanism. The presence in the mesentery of felines (cats,
&c.) of large numbers of Pacinian corpuscles, which are believed to be
modified tactile bodies, favours this supposition. Such animals are
remarkable for the delicacy of such muscular movements, as balancing and
leaping.

There is another channel by which nervous impulses reach the sensorium
and play their part in the sense of equilibrium, namely, from the
semicircular canals, a portion of the internal ear. It is pointed out in the
article Hearing that the appreciation of sound is in reality an appreciation of
variations of pressure. The labyrinth consists of the vestibule, the cochlea
and the semicircular canals. The cochlea receives the sound-waves
(variations of pressure) that constitute musical tones. This it accomplishes
by the structures in the ductus cochlearis. In the vestibule we find two sacs,
the saccule next to and communicating with the ductus cochlearis, and the
utricle communicating with the semicircular canals. The base of the stapes
communicates pressures to the utricle. The membranous portion of the
semicircular canals consists of a tube, dilated at one end into a swelling or
pouch, termed the ampulla, and each end communicates freely with the
utricle. On the posterior wall of both the saccule and of the utricle there is a
ridge, termed in each case the macula acustica, bearing a highly specialized
epithelium. A similar structure exists in each ampulla. This would suggest
that all three structures have to do with hearing; but, on the other hand,
there is experimental evidence that the utricle and the canals may transmit
impressions that have to do with equilibrium. Pressure of the base of the
stapes is exerted on the utricle. This will compress the fluid in that cavity,
and tend to drive the fluid into the semicircular canals that communicate
with that cavity by five openings. Each canal is surrounded by a thin layer
of perilymph, so that it may yield a little to this pressure, and exert a pull or

pressure on the nerve-endings in each ampulla. Thus impulses may be
generated in the nerves of the ampullae.

The three semicircular canals lie in the three directions in space, and it
has been suggested that they have to do with our appreciation of the
direction of sound. But our appreciation of sound is very inaccurate: we
look with the eyes for the source of a sound, and instinctively direct the ears
or the head, or both, in the direction from which the sound appears to
proceed. But the relationship of the canals on the two sides must have a
physiological significance. Thus (1) the six canals are parallel, two and two;
or (2) the two horizontal canals are in the same plane, while the superior
canal on one side is nearly parallel with the posterior canal of the other.
These facts point to the two sets of canals and ampullae acting as one organ,
in a manner analogous to the action of two retinae for single vision.

We have next to consider how the canals may possibly act in connexion
with the sense of equilibrium. In 1820 J. Purkinje studied the vertigo that
follows rapid rotation of the body in the erect position on a vertical axis. On
stopping the rotation there is a sense of rotation in the opposite direction,
and this may occur even when the eyes are closed. Purkinje noticed that the
position of the imaginary axis of rotation depends on the axis around which
the head revolves. In 1828 M.J.P. Flourens discovered that injury to the
canals causes disturbance to the equilibrium and loss of co-ordination, and
that sections of the canals produce a rotatory movement of a kind
corresponding to the canal that had been divided. Thus division of a
membranous canal causes rotatory movements round an axis at right angles
to the plane of the divided canal. The body of the animal always moves in
the direction of the cut canal. Many other observers have corroborated these
experiments. F. Goltz was the first who formulated the conditions necessary
for equilibration. He put the matter thus:—(1) A central co-ordinating organ
—in the brain; (2) centripetal fibres, with their peripheral terminations—in

the ampullae; and (3) centrifugal fibres, with their terminal organs—in the
muscular mechanisms. A lesion of any one of these portions of the
mechanism causes loss or impairment of balancing. Cyon also investigated
the subject, and concluded:—(1) To maintain equilibrium, we must have an
accurate notion of the position of the head in space; (2) the function of the
semicircular canals is to communicate impressions that give a
representation of this position—each canal having a relation to one of the
dimensions of space; (3) disturbance of equilibrium follows section; (4)
involuntary movements following section are due to abnormal excitations;
(5) abnormal movements occurring a few days after the operation are
caused by irritation of the cerebellum.

On theoretical considerations of a physical character, E. Mach, Crum-
Brown and Breuer have advanced theories based on the idea of the canals
being organs for sensations of acceleration of movement, or for the sense of
rotation. Mach first pointed out that Purkinje’s phenomena, already alluded
to, were in all probability related to the semicircular canals. “He showed
that when the body is moved in space, in a straight line, we are not
conscious of the velocity of motion, but of variations in this velocity.
Similarly, if a body is rotated round a vertical axis, we perceive only
angular acceleration and not angular velocity. The sensations produced by
angular acceleration last longer than the acceleration itself, and the position
of the head during the movements enables us to determine direction.” Both
Mach and Goltz state that varying pressures of the fluid in the canals
produced by angular rotation produce sensations of movement (always in a
direction opposite to the rotation of the body), and that these, in turn, cause
the vertigo of Purkinje and the phenomena of Flourens. Mach, Crum-Brown
and Breuer advance hydrodynamical theories in which they assume that the
fluids move in the canals. Goltz, on the other hand, supports a hydrostatical
theory in which he assumes that the phenomena can be accounted for by
varying pressures. Crum-Brown differs from Mach and Breuer as follows:

—(1) In attributing movement or variation of pressure not merely to the
endolymph, but also to the walls of the membranous canals and to the
surrounding perilymph; and (2) in regarding the two labyrinths as one
organ, all the six canals being required to form a true conception of the
rotating motion of the head. He sums up the matter thus: “We have two
ways in which a relative motion can occur between the endolymph and the
walls of the cavity containing it—(1) When the head begins to move, here
the walls leave the fluid behind; (2) when the head stops, here the fluid
flows on. In both cases the sensation of rotation is felt. In the first this
sensation corresponds to a real rotation, in the second it does not, but in
both it corresponds to a real acceleration (positive or negative) of rotation,
using the word acceleration in its technical kinematical sense.”

Cyon states that the semicircular canals only indirectly assist in giving a
notion of spatial relations. “He holds that knowledge of the position of
bodies in space depends on nervous impulses coming from the contracting
ocular muscles; that the oculomotor centres are in intimate physiological
relationship with the centres receiving impulses from the nerves of the
semicircular canals; and that the oculomotor centres, thus excited, produce
the movements of the eyeballs, which then determine our notions of spatial
relations.” These views are supported by experiments of Lee on dog-fish.
When the fish is rotated round different axes there are compensating
movements of the eyes and fins. “It was observed that if the fish were
rotated in the plane of one of the canals, exactly the same movements of the
eyes and fins occurred as were produced by experimental operation and
stimulation of the ampulla of that canal.” Sewall, in 1883, carried out
experiments on young sharks and skates with negative results. Lee returned
to the subject in 1894, and, after numerous experiments on dog-fish, in
which the canals or the auditory nerves were divided, obtained evidence
that the ampullae contain sense-organs connected with the sense of
equilibrium.

It has been found by physicians and aurists that disease or injury of the
canals, occurring rapidly, produces giddiness, staggering, nystagmus (a
peculiar twitching movement of the muscles of the eyeballs), vomiting,
noises in the ear and more or less deafness. It is said, however, that if
pathological changes come on slowly, so that the canals and vestibule are
converted into a solid mass, none of these symptoms may occur. On the
whole, the evidence is in favour of the view that from the semicircular
canals nervous impulses are transmitted, which, co-ordinated with impulses
coming from the visual organs, from the muscles and from the skin, form
the bases of these guiding sensations on which the sense of equilibrium
depends. These impulses may not reach the level of consciousness, but they
call into action co-ordinated mechanisms by which complicated muscular
movements are effected.

Full bibliographical references are given in the article on “The Ear”
by J.G. McKendrick, in Schäfer’s Textbook of Physiology, vol. ii. p.
1194.
(J. G. M.)

EQUINOX (from the Lat. aequus, equal, and nox, night), a term used to
express either the moment at which, or the point at which, the sun
apparently crosses the celestial equator. Since the sun moves in the ecliptic,
it is in the last-named sense the point of intersection of the ecliptic and the
celestial equator. This is the usual meaning of the term in astronomy. There
are two such points, opposite each other, at one of which the sun crosses the
equator toward the north and at the other toward the south. They are called

vernal and autumnal respectively, from the relation of the corresponding
times to the seasons of the northern hemisphere. The line of the equinoxes
is the imaginary diameter of the celestial sphere which joins them.

The vernal equinox is the initial point from which the right ascensions
and the longitudes of the heavenly bodies are measured (see Astronomy:
Spherical). It is affected by the motions of Precession and Nutation, of
which the former has been known since the time of Hipparchus. The actual
equinox is defined by first taking the conception of a fictitious point called
the Mean Equinox, which moves at a nearly uniform rate, slow varying,
however, from century to century. The true equinox then moves around the
mean equinox in a period equal to that of the moon’s nodes. These two
motions are defined with greater detail in the articles Precession of the
Equinoxes and Nutation.

Equinoctial Gales.—At the time of the equinox it is commonly believed
that strong gales may be expected. This popular idea has no foundation in
fact, for continued observations have failed to show any unusual prevalence
of gales at this season. In one case observations taken for fifty years show
that during the five days from the 21st to the 25th of March and September,
there were fewer gales and storms than during the preceding and succeeding
five days.

EQUITES (“horsemen” or “knights,” from equus, “horse”), in Roman
history, originally a division of the army, but subsequently a distinct
political order, which under the empire resumed its military character.

According to the traditional account, Romulus instituted a cavalry corps,
consisting of three centuriae (“hundreds”), called after the three tribes from
which they were taken (Ramnes, Tities, Luceres), divided into ten turmae
(“squadrons”) of thirty men each. The collective name for the corps was
celeres (“the swift,” or possibly from κέλης, “a riding horse”); Livy,
however, restricts the term to a special body-guard of Romulus. The
statements in ancient authorities as to the changes in the number of the
equites during the regal period are very confusing; but it is regarded as
certain that Servius Tuillus found six centuries in existence, to which he
added twelve, making eighteen in all, a number which remained unchanged
throughout the republican period. A proposal by M. Porcius Cato the elder
to supplement the deficiency in the cavalry by the creation of four
additional centuries was not adopted. The earlier centuries were called sex
suffragia (“the six votes”), and at first consisted exclusively of patricians,
while those of Servius Tullius were entirely or for the most part plebeian.
Until the reform of the comitia centuriata (probably during the censorship
of Gaius Flaminius in 220 b.c.; see Comitia), the equites had voted first, but
after that time this privilege was transferred to one century selected by lot
from the centuries of the equites and the first class. The equites then voted
with the first class, the distinction between the sex suffragia and the other
centuries being abolished.

Although the equites were selected from the wealthiest citizens, service
in the cavalry was so expensive that the state gave financial assistance. A
sum of money (aes equestre) was given to each eques for the purchase of
two horses (one for himself and one for his groom), and a further sum for
their keep (aes hordearium); hence the name equites equo publico. In later
times, pay was substituted for the aes hordearium, three times as much as
that of the infantry. If competent, an eques could retain his horse and vote
after the expiration of his ten years’ service, and (till 129 b.c.) even after
entry into the senate.

As the demands upon the services of the cavalry increased, it was
decided to supplement the regulars by the enrolment of wealthy citizens
who kept horses of their own. The origin of these equites equo privato dates
back, according to Livy (v. 7), to the siege of Veii, when a number of young
men came forward and offered their services. According to Mommsen,
although the institution was not intended to be permanent, in later times
vacancies in the ranks were filled in this manner, with the result that service
in the cavalry, with either a public or a private horse, became obligatory
upon all Roman citizens possessed of a certain income. These equites equo
privato had no vote in the centuries, received pay in place of the aes
equestre, and did not form a distinct corps.

Thus, at a comparatively early period, three classes of equites may be
distinguished: (a) The patrician equites equo publico of the sex suffragia;
(b) the plebeian equites in the twelve remaining centuries; (c) the equites
equo privato, both patrician and plebeian.

The equites were originally chosen by the curiae, then in succession by
the kings, the consuls, and (after 443 b.c.) by the censors, by whom they
were reviewed every five years in the Forum. Each eques, as his name was
called out, passed before the censors, leading his horse. Those whose
physique and character were satisfactory, and who had taken care of their
horses and equipments, were bidden to lead their horse on (traducere
equum), those who failed to pass the scrutiny were ordered to sell it, in
token of their expulsion from the corps. This inspection (recognitio) must
not be confounded with the full-dress procession (transvectio) on the 15th
of July from the temple of Mars or Honos to the Capitol, instituted in 304
b.c. by the censor Q. Fabius Maximus Rullianus to commemorate the

miraculous intervention of Castor and Pollux at the battle of Lake Regillus.
Both inspection and procession were discontinued before the end of the
republic, but revived and in a manner combined by Augustus.

In theory, the twelve plebeian centuries were open to all freeborn youths
of the age of seventeen, although in practice preference was given to the
members of the older families. Other requirements were sound health, high
moral character and an honourable calling. At the beginning of the
republican period, senators were included in the equestrian centuries. The
only definite information as to the amount of fortune necessary refers to
later republican and early imperial times, when it is known to have been
400,000 sesterces (about £3500 to £4000). The insignia of the equites were,
at first, distinctly military—such as the purple-edged, short military cloak
(trabea) and decorations for service in the field.

With the extension of the Roman dominions, the equites lost their
military character. Prolonged service abroad possessed little attraction for
the pick of the Roman youth, and recruiting for the cavalry from the
equestrian centuries was discontinued. The equites remained at home, or
only went out as members of the general’s staff, their places being taken by
the equites equo privato, the cavalry of the allies and the most skilled
horsemen of the subject populations. The first gradually disappeared, and
Roman citizens were rarely found in the ranks of the effective cavalry. In
these circumstances there grew up in Rome a class of wealthy men, whose
sole occupation it was to amass large fortunes by speculation, and who
found a most lucrative field of enterprise in state contracts and the farming
of the public revenues. These tax-farmers (see Publicani) were already in
existence at the time of the Second Punic War; and their numbers and
influence increased as the various provinces were added to the Roman
dominions. The change of the equites into a body of financiers was further
materially promoted (a) by the lex Claudia (218 b.c.), which prohibited
senators from engaging in commercial pursuits, especially if (as seems
probable) it included public contracts (cf. Flaminius, Gaius); (b) by the
enactment in the time of Gaius Gracchus excluding members of the senate
from the equestrian centuries. These two measures definitely marked off the

aristocracy of birth from the aristocracy of wealth—the landed proprietor
from the capitalist. The term equites, originally confined to the purely
military equestrian centuries of Servius Tullius, now came to be applied to
all who possessed the property qualification of 400,000 sesterces.

As the equites practically monopolized the farming of the taxes, they
came to be regarded as identical with the publicani, not, as Pliny remarks,
because any particular rank was necessary to obtain the farming of the
taxes, but because such occupation was beyond the reach of all except those
who were possessed of considerable means. Thus, at the time of the
Gracchi, these equites-publicani formed a close financial corporation of
about 30,000 members, holding an intermediate position between the
nobility and the lower classes, keenly alive to their own interests, and ready
to stand by one another when attacked. Although to some extent looked
down upon by the senate as following a dishonourable occupation, they had
as a rule sided with the latter, as being at least less hostile to them than the
democratic party. To obtain the support of the capitalists, Gaius Gracchus
conceived the plan of creating friction between them and the senate, which
he carried out by handing over to them the control (a) of the jury-courts,
and (b) of the revenues of Asia.

(a) Hitherto, the list of jurymen for service in the majority of processes,
both civil and criminal, had been composed exclusively of senators. The
result was that charges of corruption and extortion failed, when brought
against members of that order, even in cases where there was little doubt of
their guilt. The popular indignation at such scandalous miscarriages of
justice rendered a change in the composition of the courts imperative.
Apparently Gracchus at first proposed to create new senators from the
equites and to select the jurymen from this mixed body, but this moderate
proposal was rejected in favour of one more radical (see W.W. Fowler in
Classical Review, July 1896). By the lex Sempronia (123 b.c.) the list was

to be drawn from persons of free birth over thirty years of age, who must
possess the equestrian census, and must not be senators. Although this
measure was bound to set senators and equites at variance, it in no way
improved the lot of those chiefly concerned. In fact, it increased the burden
of the luckless provincials, whose only appeal lay to a body of men whose
interests were identical with those of the publicani. Provided he left the tax-
gatherer alone, the governor might squeeze what he could out of the people,
while on the other hand, if he were humanely disposed, it was dangerous for
him to remonstrate.

(b) The taxes of Asia had formerly been paid by the inhabitants
themselves in the shape of a fixed sum. Gracchus ordered that the taxes,
direct and indirect, should be increased, and that the farming of them should
be put up to auction at Rome. By this arrangement the provincials were
ignored, and everything was left in the hands of the capitalists.

From this time dates the existence of the equestrian order as an officially
recognized political instrument. When the control of the courts passed into
the hands of the property equites, all who were summoned to undertake the
duties of judices were called equites; the ordo judicum (the official title)
and the ordo equester were regarded as identical. It is probable that certain
privileges of the equites were due to Gracchus; that of wearing the gold
ring, hitherto reserved for senators; that of special seats in the theatre,
subsequently withdrawn (probably by Sulla) and restored by the lex
Othonis (67 b.c.); the narrow band of purple on the tunic as distinguished
from the broad band worn by the senators.

Various attempts were made by the senate to regain control of the courts,
but without success. The lex Livia of M. Livius Drusus (q.v.), passed with
that object, but irregularly and by the aid of violence, was annulled by the
senate itself. In 82 Sulla restored the right of serving as judices to the
senate, to which he elevated 300 of the most influential equites, whose

support he thus hoped to secure; at the same time he indirectly dealt a blow
at the order generally, by abolishing the office of the censor (immediately
revived), in whom was vested the right of bestowing the public horse. To
this period Mommsen assigns the regulation, generally attributed to
Augustus, that the sons of senators should be knights by right of birth. By
the lex Aurelia (70 b.c.) the judices were to be chosen in equal numbers
from senators, equites and tribuni aerarii (see Aerarium), (the last-named
being closely connected with the equites), who thus practically commanded
a majority. About this time the influence of the equestrian order reached its
height, and Cicero’s great object was to reconcile it with the senate. In this
he was successful at the time of the Catilinarian conspiracy, in the
suppression of which he was materially aided by the equites. But the union
did not last long; shortly afterwards the majority ranged themselves on the
side of Julius Caesar, who did away with the tribuni aerarii as judices, and
replaced them by equites.

Augustus undertook the thorough reorganization of the equestrian order
on a military basis. The equites equo privato were abolished (according to
Herzog, not till the reign of Tiberius) and the term equites was officially
limited to the equites equo publico, although all who possessed the property
qualification were still considered to belong to the “equestrian order.” For
the equites equo publico high moral character, good health and the
equestrian fortune were necessary. Although free birth was considered
indispensable, the right of wearing the gold ring (jus anuli aurei) was
frequently bestowed by the emperor upon freedmen, who thereby became
ingenui and eligible as equites. Tiberius, however, insisted upon free birth
on the father’s side to the third generation. Extreme youth was no bar; the
emperor Marcus Aurelius had been an eques at the age of six. The sons of
senators were eligible by right of birth, and appear to have been known as
equites illustres. The right of bestowing the equus publicus was vested in

the emperor; once given, it was for life, and was only forfeitable through
degradation for some offence or the loss of the equestrian fortune.

Augustus divided the equites into six turmae (regarded by Hirschfeld as a
continuation of the sex suffragia). Each was under the command of a sevir
(ἴλαρχος), who was appointed by the emperor and changed every year.
During their term of command the seviri had to exhibit games (ludi
sevirales). Under these officers the equites formed a kind of corporation,
which, although not officially recognized, had the right of passing
resolutions, chiefly such as embodied acts of homage to the imperial house.
It is not known whether the turmae contained a fixed number of equites;
there is no doubt that, in assigning the public horse, Augustus went far
beyond the earlier figure of 1800. Thus, Dionysius of Halicarnassus
mentions 5000 equites as taking part in a review at which he himself was
present.

As before, the equites wore the narrow, purple-striped tunic, and the gold
ring, the latter now being considered the distinctive badge of knighthood.
The fourteen rows in the theatre were extended by Augustus to seats in the
circus.

The old recognitio was replaced by the probatio, conducted by the
emperor in his censorial capacity, assisted by an advisory board of specially
selected senators. The ceremony was combined with a procession, which,
like the earlier transvectio, took place on the 15th of July, and at such other
times as the emperor pleased. As in earlier times, offenders were punished
by expulsion.

In order to provide a supply of competent officers, each eques was
required to fill certain subordinate posts, called militiae equestres. These
were (1) the command of an auxiliary cohort; (2) the tribunate of a legion;
(3) the command of an auxiliary cavalry squadron, this order being as a rule

strictly adhered to. To these Septimius Severus added the centurionship.
Nomination to the militiae equestres was in the hands of the emperor. After
the completion of their preliminary military service, the equites were
eligible for a number of civil posts, chiefly those with which the emperor
himself was closely concerned. Such were various procuratorships; the
prefectures of the corn supply, of the fleet, of the watch, of the praetorian
guards; the governorships of recently acquired provinces (Egypt, Noricum),
the others being reserved for senators. At the same time, the abolition of the
indirect method of collecting the taxes in the provinces greatly reduced the
political influence of the equites. Certain religious functions of minor
importance were also reserved for them. In the jury courts, the equites,
thanks to Julius Caesar, already formed two-thirds of the judices; Augustus,
by excluding the senators altogether, virtually gave them the sole control of
the tribunals. One of the chief objects of the emperors being to weaken the
influence of the senate by the opposition of the equestrian order, the
practice was adopted of elevating those equites who had reached a certain
stage in their career to the rank of senator by adlectio. Certain official posts,
of which it would have been inadvisable to deprive senators, could thus be
bestowed upon the promoted equites.

The control of the imperial correspondence and purse was at first in the
hands of freedmen and slaves. The emperor Claudius tentatively entrusted
certain posts connected with these to the equites; in the time of Hadrian this
became the regular custom. Thus a civil career was open to the equites
without the obligation of preliminary military service, and the emperor was
freed from the pernicious influence of freedmen. After the reign of Marcus
Aurelius (according to Mommsen) the equites were divided into: (a) viri
eminentissimi, the prefects of the praetorian guard; (b) viri perfectissimi, the
other prefects and the heads of the financial and secretarial departments; (c)
viri egregii, first mentioned in the reign of Antoninus Pius, a title by right of
the procurators generally.

Under the empire the power of the equites was at its highest in the time
of Diocletian; in consequence of the transference of the capital to
Constantinople, they sank to the position of a mere city guard, under the
control of the prefect of the watch. Their history may be said to end with the
reign of Constantine the Great.

Mention may also be made of the equites singulares Augusti. The body-
guard of Augustus, consisting of foreign soldiers (chiefly Germans and
Batavians), abolished by Galba, was revived from the time of Trajan or
Hadrian under the above title. It was chiefly recruited from the pick of the
provincial cavalry, but contained some Roman citizens. It formed the
imperial “Swiss guard,” and never left the city except to accompany the
emperor. In the time of Severus, these equites were divided into two corps,
each of which had its separate quarters, and was commanded by a tribune
under the orders of the prefect of the praetorian guard. They were
subsequently replaced by the protectores Augusti.

See further article Rome: History; also T. Mommsen, Römisches
Staatsrecht, iii.; J.N. Madvig, Die Verfassung des römischen Staates, i.;
R. Cagnat in Daremberg and Saglio’s Dictionnaire des antiquités,
where full references to ancient authorities are given in the footnotes;
A.S. Wilkins in Smith’s Dictionary of Greek and Roman Antiquities
(3rd ed., 1891); E. Belot, Histoire des chevaliers romains (1866-1873);
H.O. Hirschfeld, Untersuchungen auf dem Gebiete der römischen
Verwaltungsgeschichte (Berlin, 1877); E. Herzog, Geschichte und
System der römischen Staatsverfassung (Leipzig, 1884-1891); A.H.
Friedländer, Sittengeschichte Roms, i. (1901); A.H.J. Greenidge,
History of Rome, i. (1904); J.B. Bury, The Student’s Roman Empire
(1893); T.M. Taylor, Political and Constitutional History of Rome
(1899). For a concise summary of different views of the sex suffragia
see A. Bouché-Leclercq’s Manuel des antiquités romaines, quoted in

Daremberg and Saglio; and on the equites singulares, T. Mommsen in
Hermes, xvi. (1881), p. 458. (J. H. F.)

EQUITY (Lat. aequitas), a term which in its most general sense means
equality or justice; in its most technical sense it means a system of law or a
body of connected legal principles, which have superseded or supplemented
the common law on the ground of their intrinsic superiority. Aristotle
(Ethics, bk. v. c. 10) defines equity as a better sort of justice, which corrects
legal justice where the latter errs through being expressed in a universal
form and not taking account of particular cases. When the law speaks
universally, and something happens which is not according to the common
course of events, it is right that the law should be modified in its application
to that particular case, as the lawgiver himself would have done, if the case
had been present to his mind. Accordingly the equitable man (ἐπιεικής) is
he who does not push the law to its extreme, but, having legal justice on his
side, is disposed to make allowances. Equity as thus described would
correspond rather to the judicial discretion which modifies the
administration of the law than to the antagonistic system which claims to
supersede the law.

The part played by equity in the development of law is admirably
illustrated in the well-known work of Sir Henry Maine on Ancient Law.
Positive law, at least in progressive societies, is constantly tending to fall
behind public opinion, and the expedients adopted for bringing it into
harmony therewith are three, viz. legal fictions, equity and statutory
legislation. Equity here is defined to mean “any body of rules existing by

the side of the original civil law, founded on distinct principles, and
claiming incidentally to supersede the civil law in virtue of a superior
sanctity inherent in those principles.” It is thus different from legal fiction,
by which a new rule is introduced surreptitiously, and under the pretence
that no change has been made in the law, and from statutory legislation, in
which the obligatory force of the rule is not supposed to depend upon its
intrinsic fitness. The source of Roman equity was the fertile theory of
natural law, or the law common to all nations. Even in the Institutes of
Justinian the distinction is carefully drawn in the laws of a country between
those which are peculiar to itself and those which natural reason appoints
for all mankind. The connexion in Roman law between the ideas of equity,
nature, natural law and the law common to all nations, and the influence of
the Stoical philosophy on their development, are fully discussed in the third
chapter of the work we have referred to. The agency by which these
principles were introduced was the edicts of the praetor, an annual
proclamation setting forth the manner in which the magistrate intended to
administer the law during his year of office. Each successive praetor
adopted the edict of his predecessor, and added new equitable rules of his
own, until the further growth of the irregular code was stopped by the
praetor Salvius Julianus in the reign of Hadrian.

The place of the praetor was occupied in English jurisprudence by the
lord high chancellor. The real beginning of English equity is to be found in
the custom of handing over to that officer, for adjudication, the complaints
which were addressed to the king, praying for remedies beyond the reach of
the common law. Over and above the authority delegated to the ordinary
councils or courts, a reserve of judicial power was believed to reside in the
king, which was invoked as of grace by the suitors who could not obtain
relief from any inferior tribunal. To the chancellor, as already the head of
the judicial system, these petitions were referred, although he was not at
first the only officer through whom the prerogative of grace was

administered. In the reign of Edward III. the equitable jurisdiction of the
court appears to have been established. Its constitutional origin was
analogous to that of the star chamber and the court of requests. The latter, in
fact, was a minor court of equity attached to the lord privy seal as the court
of chancery was to the chancellor. The successful assumption of
extraordinary or equitable jurisdiction by the chancellor caused similar
pretensions to be made by other officers and courts. “Not only the court of
exchequer, whose functions were in a peculiar manner connected with royal
authority, but the counties palatine of Chester, Lancaster and Durham, the
court of great session in Wales, the universities, the city of London, the
Cinque Ports and other places silently assumed extraordinary jurisdiction
similar to that exercised in the court of chancery.” Even private persons,
lords and ladies, affected to establish in their honours courts of equity.

English equity has one marked historical peculiarity, viz. that it
established itself in a set of independent tribunals which remained in
standing contrast to the ordinary courts for many hundred years. In Roman
law the judge gave the preference to the equitable rule; in English law the
equitable rule was enforced by a distinct set of judges. One cause of this
separation was the rigid adherence to precedent on the part of the common
law courts. Another was the jealousy prevailing in England against the
principles of the Roman law on which English equity to a large extent was
founded.

When a case of prerogative was referred to the chancellor in the reign of
Edward III., he was required to grant such remedy as should be consonant
to honesty (honestas). And honesty, conscience and equity were said to be
the fundamental principles of the court. The early chancellors were
ecclesiastics, and under their influence not only moral principles, where
these were not regarded by the common law, but also the equitable
principles of the Roman law were introduced into English jurisprudence.

Between this point and the time when equity became settled as a portion of
the legal system, having fixed principles of its own, various views of its
nature seem to have prevailed. For a long time it was thought that
precedents could have no place in equity, inasmuch as it professed in each
case to do that which was just; and we find this view maintained by
common lawyers after it had been abandoned by the professors of equity
themselves. G. Spence, in his book on the Equitable Jurisdiction of the
Court of Chancery, quotes a case in the reign of Charles II., in which chief
justice Vaughan said:

“I wonder to hear of citing of precedents in matter of equity, for if
there be equity in a case, that equity is an universal truth, and there can
be no precedent in it; so that in any precedent that can be produced, if it
be the same with this case, the reason and equity is the same in itself;
and if the precedent be not the same case with this it is not to be cited.”

But the lord keeper Bridgeman answered:

“Certainly precedents are very necessary and useful to us, for in
them we may find the reasons of the equity to guide us, and besides the
authority of those who made them is much to be regarded. We shall
suppose they did it upon great consideration and weighing of the
matter, and it would be very strange and very ill if we should disturb
and set aside what has been the course for a long series of times and
ages.”

Selden’s description is well known: “Equity is a roguish thing. ’Tis all
one as if they should make the standard for measure the chancellor’s foot.”
Lord Nottingham in 1676 reconciled the ancient theory and the established
practice by saying that the conscience which guided the court was not the
natural conscience of the man, but the civil and political conscience of the
judge. The same tendency of equity to settle into a system of law is seen in

the recognition of its limits—in the fact that it did not attempt in all cases to
give a remedy when the rule of the common law was contrary to justice.
Cases of hardship, which the early chancellors would certainly have
relieved, were passed over by later judges, simply because no precedent
could be found for their interference. The point at which the introduction of
new principles of equity finally stopped is fixed by Sir Henry Maine in the
chancellorship of Lord Eldon, who held that the doctrines of the court ought
to be as well settled and made as uniform almost as those of the common
law. From that time certainly equity, like common law, has professed to take
its principles wholly from recorded decisions and statute law. The view
(traceable no doubt to the Aristotelian definition) that equity mitigates the
hardships of the law where the law errs through being framed in universals,
is to be found in some of the earlier writings. Thus in the Doctor and
Student it is said:

“Law makers take heed to such things as may often come, and not to
every particular case, for they could not though they would; therefore,
in some cases it is necessary to leave the words of the law and follow
that reason and justice requireth, and to that intent equity is ordained,
that is to say, to temper and mitigate the rigour of the law.”

And Lord Ellesmere said:

“The cause why there is a chancery is for that men’s actions are so
divers and infinite that it is impossible to make any general law which
shall aptly meet with every particular act and not fail in some
circumstances.”

Modern equity, it need hardly be said, does not profess to soften the
rigour of the law, or to correct the errors into which it falls by reason of its
generality.

To give any account, even in outline, of the subject matter of equity
within the necessary limits of this article would be impossible. It will be
sufficient to say here that the classification generally adopted by text-
writers is based upon the relations of equity to the common law, of which
some explanation is given above. Thus equitable jurisdiction is said to be
exclusive, concurrent or auxiliary. Equity has exclusive jurisdiction where it
recognizes rights which are unknown to the common law. The most
important example is trusts. Equity has concurrent jurisdiction in cases
where the law recognized the right but did not give adequate relief, or did
not give relief without circuity of action or some similar inconvenience.
And equity has auxiliary jurisdiction when the machinery of the courts of
law was unable to procure the necessary evidence.

“The evils of this double system of judicature,” says the report of the
judicature commission (1863-1867), “and the confusion and conflict of
jurisdiction to which it has led, have been long known and acknowledged.”
A partial attempt to meet the difficulty was made by several acts of
parliament (passed after the reports of commissions appointed in 1850 and
1851), which enabled courts of law and equity both to exercise certain
powers formerly peculiar to one or other of them. A more complete remedy
was introduced by the Judicature Act 1873, which consolidated the courts
of law and equity, and ordered that law and equity should be administered
concurrently according to the rules contained in the 26th section of the act.
At the same time many matters of equitable jurisdiction are still left to the
chancery division of the High Court in the first instance. (See Chancery.)

Authorities.—The principles of equity as set out by the following
writers may be consulted: J. Story, J.W. Smith, H.A. Smith and W.
Ashburner; and for the history see G. Spence, The Equitable
Jurisdiction of the Court of Chancery (2 vols., 1846-1849); D.M.

Kerly, Historical Sketch of the Equitable Jurisdiction of the Court of
Chancery (1890).

EQUIVALENT, in chemistry, the proportion of an element which will
combine with or replace unit weight of hydrogen. When multiplied by the
valency it gives the atomic weight. The determination of equivalent weights
is treated in the article Stoichiometry. (See also Chemistry.) In a more
general sense the term “equivalent” is used to denote quantities of
substances which neutralize one another, as for example NaOH, HCl,
½H2SO4, ½Ba(OH)2.

ÉRARD, SÉBASTIEN (1752-1831), French manufacturer of musical
instruments, distinguished especially for the improvements he made upon
the harp and the pianoforte, was born at Strassburg on the 5th of April 1752.
While a boy he showed great aptitude for practical geometry and
architectural drawing, and in the workshop of his father, who was an
upholsterer, he found opportunity for the early exercise of his mechanical
ingenuity. When he was sixteen his father died, and he removed to Paris
where he obtained employment with a harpsichord maker. Here his
remarkable constructive skill, though it speedily excited the jealousy of his
master and procured his dismissal, almost equally soon attracted the notice

of musicians and musical instrument makers of eminence. Before he was
twenty-five he set up in business for himself, his first workshop being a
room in the hotel of the duchesse de Villeroi, who gave him warm
encouragement. Here he constructed in 1780 his first pianoforte, which was
also one of the first manufactured in France. It quickly secured for its maker
such a reputation that he was soon overwhelmed with commissions, and
finding assistance necessary, he sent for his brother, Jean Baptiste, in
conjunction with whom he established in the rue de Bourbon, in the
Faubourg St Germain, a piano manufactory, which in a few years became
one of the most celebrated in Europe. On the outbreak of the Revolution he
went to London where he established a factory. Returning to Paris in 1796,
he soon afterwards introduced grand pianofortes, made in the English
fashion, with improvements of his own. In 1808 he again visited London,
where, two years later, he produced his first double-movement harp. He had
previously made various improvements in the manufacture of harps, but the
new instrument was an immense advance upon anything he had before
produced, and obtained such a reputation that for some time he devoted
himself exclusively to its manufacture. It has been said that in the year
following his invention he made harps to the value of £25,000. In 1812 he
returned to Paris, and continued to devote himself to the further perfecting
of the two instruments with which his name is associated. In 1823 he
crowned his work by producing his model grand pianoforte with the double
escapement. Érard died at Passy, on the 5th of August 1831. (See also Harp
and Pianoforte.)

ERASMUS, DESIDERIUS (1466-1536), Dutch scholar and theologian,
was born on the night of the 27/28th of October, probably in 1466; but his
statements about his age are conflicting, and in view of his own uncertainty
(Ep. x. 29: 466) and the weakness of his memory for dates, the year of his
birth cannot be definitely fixed. His father’s name seems to have been
Rogerius Gerardus. He himself was christened Herasmus; but in 1503,
when becoming familiar with Greek, he assimilated the name to a fancied
Greek original, which he had a few years before Latinized into Desyderius.
A contemporary authority states that he was born at Gouda, his father’s
native town; but he adopted the style Rotterdammensis or Roterodamus, in
accordance with a story to which he himself gave credence. His first
schooling was at Gouda under Peter Winckel, who was afterwards vice-
pastor of the church. In the dull round of instruction in “grammar” he did
not distinguish himself, and was surpassed by his early friend and
companion, William Herman, who was Winckel’s favourite pupil. From
Gouda the two boys went to the school attached to St Lebuin’s church at
Deventer, which was one of the first in northern Europe to feel the influence
of the Renaissance. Erasmus was at Deventer from 1475 to 1484, and when
he left, had learnt from Johannes Sinthius (Syntheim) and Alexander
Hegius, who had come as headmaster in 1483, the love of letters which was
the ruling passion of his life. At some period, perhaps in an interval of his
time at Deventer, he was a chorister at Utrecht under the famous organist of
the cathedral, Jacob Obrecht.

About 1484 Erasmus’ father died, leaving him and an elder brother Peter,
both born out of wedlock, to the care of guardians, their mother having died
shortly before. Erasmus was eager to go to a university, but the guardians,
acting under a perhaps genuine enthusiasm for the religious life, sent the
boys to another school at Hertogenbosch; and when they returned after two
or three years, prevailed on them to enter monasteries. Peter went to Sion,
near Delft; Erasmus after prolonged reluctance became an Augustinian

canon in St Gregory’s at Steyn, a house of the same Chapter near Gouda.
There he found little religion and less refinement; but no serious difficulty
seems to have been made about his reading the classics and the Fathers with
his friends to his heart’s content. The monastery once entered, there was no
drawing back; and Erasmus passed through the various stages which
culminated in his ordination as priest on the 25th of April 1492.

But his ardent spirit could not long be content with monastic life. He
brought his attainments somehow to the notice of Henry of Bergen, bishop
of Cambrai, the leading prelate at the court of Brussels; and about 1494
permission was obtained for him to leave Steyn and become Latin secretary
to the bishop, who was then preparing for a visit to Rome. But the journey
was abandoned, and after some months Erasmus found that even with
occasional chances to read at Groenendael, the life of a court was hardly
more favourable to study than that of Steyn. At the suggestion of a friend,
James Batt, he applied to his patron for leave to go to Paris University. The
bishop consented and promised a small pension; and in August 1495
Erasmus entered the “domus pauperum” of the college of Montaigu, which
was then under the somewhat rigid rule of the reformer Jan Standonck. He
at once introduced himself to the distinguished French historian and
diplomatist Robert Gaguin (1425-1502) and published a small volume of
poems; and he became intimate with Johann Mauburnus (Mombaer), the
leader of a mission summoned from Windesheim in 1496 to reform the
abbey of Château-Landon. But the life at Montaigu was too hard for him.
Every Lent he fell ill and had to return to Holland to recover. He continued
to read nevertheless for a degree in theology, and at some time completed
the requirements for the B.D. After a year or two he left Montaigu and eked
out his money from the bishop by taking pupils. One of these, a young
Englishman, William Blount, 4th Baron Mountjoy (d. 1534), persuaded him
to visit England in the spring of 1499.

Being without a benefice, he had no settled income to look to, and apart
from the precarious profits of teaching and writing books, could only wait
on the generosity of patrons to supply him with the leisure he craved. The
faithful Batt had sought a pension for him from his own patroness, Anne of
Borsselen, the Lady of Veere, who resided at the castle of Tournehem near
Calais, and whose son Batt was now teaching. But as nothing promised at
once, Erasmus accepted Mountjoy’s offer, and thus a tie was formed which
led Mountjoy then or a few years later to grant him a pension of £20 for
life. Otherwise the visit to England gave no hope of preferment; and in the
summer Erasmus prepared to leave. He was delayed, and used the interval
to spend two or three months at Oxford, where he found John Colet
lecturing on the Epistle to the Romans. Discussions between them on
theological questions soon convinced Colet of Erasmus’ worth, and he
sought to persuade him to stay and teach at Oxford. But Erasmus could not
be content with the Bible in Latin. Oxford could teach him no Greek, so
away he must go.

In January 1500 he returned to Paris, which though it could offer no
Greek teacher better than George Hermonymus, was at least a better centre
for buying and for printing books. The next few years were spent still in
preparation, supported by pupils’ fees and the dedications of books; the
Collectanea adagiorum in June 1500 to Mountjoy, and some devotional and
moral compositions to Batt’s patroness and her son. When the plague drove
him from Paris, he went to Orleans or Tournehem or St Omer, as the way
opened. From 1502 to 1504 he was at Louvain, still declining to teach
publicly; among his friends being the future Pope Adrian VI. In January
1504 the archduke Philip gave him fifty livres for the Panegyric which “ung
religieux de l’ordre de St Augustin” had composed on his Spanish journey;
and in October, ten more, for the maintenance of his studies.

He had been working hard at Greek, of which he now felt himself master,
at the Fathers (above all at Jerome), and at the Epistles of St Paul, fulfilling
the promise made to Colet in Oxford, to give himself to sacred learning. But
the bent of his reading is shown by the manuscript with which he returned
to Paris at the close of 1504—Valla’s Annotations on the New Testament,
which Badius printed for him in 1505.

Shortly afterwards Lord Mountjoy invited him again to England, and this
visit was more successful. He found in London a circle of learned friends
through whom he was introduced to William Warham, archbishop of
Canterbury, Richard Foxe, bishop of Winchester and other dignitaries. John
Fisher (bishop of Rochester), who was then superintending the foundation
of Christ’s College for the Lady Margaret, took him down to Cambridge for
the king’s visit; and at length the opportunity came to fulfil his dream of
seeing Italy. Baptista Boerio, the king’s physician, engaged him to
accompany his two sons thither as supervisor of their studies. In September
1506 he set foot on that sacred soil, and took his D.D. at Turin. For a year
he remained with his pupils at Bologna, and then, his engagement
completed, negotiated with Aldus Manutius for a new edition of his Adagia
upon a very different scale. The volume of 1500 had been jejune, written
when he knew nothing of Greek; 800 adages put together with scanty
elucidations. In 1508 he had conceived a work on lines more to the taste of
the learned world, full of apt and recondite learning, and now and again
relieved by telling comments or lively anecdotes. Three thousand and more
collected justified a new title—Chiliades adagiorum; and the author’s
reputation was now established. So secure in public favour did the book in
time become, that the council of Trent, unable to suppress it and not daring
to overlook it, ordered the preparation of a castrated edition.

To print the Adagia he had gone to Venice, where he lived with Andrea
Torresano of Asola (Asulanus) and did the work of two men, writing and

correcting proof at the same time. When it was finished, with an ample re-
dedication to Mountjoy, a new pupil presented himself, Alexander Stewart,
natural son of James IV. of Scotland—perhaps through a connexion formed
in early days at Paris. They went together to Siena and Rome and then on to
Campania, thirsty under the summer sun. When they returned to Rome, his
pupil departed to Scotland, to fall a few years later by his father’s side at
Flodden; Erasmus also found a summons to call him northwards.

On the death of Henry VII. Lord Mountjoy, who had been companion to
Prince Henry in his studies, had become a person of influence. He wrote to
Erasmus of a land flowing with milk and honey under the “divine” young
king, and with Warham sent him £10 for journey money. At first Erasmus
hesitated. He had been disappointed in Italy, to find that he had not much to
learn from its famed scholarship; but he had made many friends in Aldus’s
circle—Marcus Musurus, John Lascaris, Baptista Egnatius, Paul
Bombasius, Scipio Carteromachus; and his reception had been flattering,
especially in Rome, where cardinals had delighted to honour him. But to
remain in Rome was to sell himself. He might have the leisure which was
so indispensable, but at price of the freedom to read, think, write what he
liked. He decided, therefore, to go, though with regrets; which returned
upon him sometimes in after years, when the English hopes had not borne
fruit.

In the autumn he reached London, and in Thomas More’s house in
Bucklersbury wrote the witty satire which Milton found “in every one’s
hands” at Cambridge in 1628, and which is read to this day. The Moriae
encomium was a sign of his decision. In it kings and princes, bishops and
popes alike are shown to be in bondage to Folly; and no class of men is
spared. Its author was willing to be beholden to any one for leisure; but he
would be no man’s slave. For the next eighteen months he is entirely lost to
view; when he reappears in April 1511, he is leaving More’s house and

taking the Moria to be printed privily in Paris. Wherever they were spent,
these must have been months of hard work, as were the years that followed.
His time was now come. The long preparation and training, bought by
privation and uncongenial toil, was over, and he was ready to apply himself
to the scientific study of sacred letters. His English patrons were liberal.
Fisher sent him in August 1511 to teach in Cambridge; Warham gave him a
benefice, Aldington in Kent, worth £33, 6s. 8d. a year, and in violation of
his own rule commuted it for a pension of £20 charged on the living; and
the dedications of his books were fruitful. In Cambridge he completed his
work on the New Testament, the Letters of Jerome, and Seneca; and then in
1514, when there seemed no prospect of ampler preferment, he determined
to transfer himself to Basel and give the results of his labours to the world.

The origin of Erasmus’s connexion with Johann Froben is not clear. In
1511 he was preparing to reprint his Adagia with Jodocus Badius, who in
the following year was to have also Seneca and Jerome. But in 1513
Froben, who had just reprinted the Aldine Adagia, acquired through a
bookseller-agent Erasmus’ amended copy which had been destined for
Badius. That the agent was acting entirely on his own responsibility may be
doubted; for within a few months Erasmus had decided to betake himself to
Basel, bearing with him Seneca and Jerome, the latter to be incorporated in
the great edition which Johannes Amerbach and Froben had had in hand
since 1510. In Germany he was widely welcomed. The Strassburg Literary
Society fêted him, and Johannes Sapidus, headmaster of the Latin school at
Schlettstadt, rode with him into Basel. Froben received him with open arms,
and the presses were soon busy with his books. Through the winter of 1514-
1515 Erasmus worked with the strength of ten; and after a brief visit to
England in the spring, the New Testament was set up. Around him was a
circle of students, some young, some already distinguished—the three sons
of Froben’s partner, Johannes Amerbach, who was now dead, Beatus
Rhenanus, Wilhelm Nesen, Ludwig Ber, Heinrich Glareanus, Nikolaus

Gerbell, Johannes Oecolampadius—who looked to him as their head and
were proud to do him service.

Though from this time forward Basel became the centre of occupation
and interest for Erasmus, yet for the next few years he was mainly in the
Netherlands. On the completion of the New Testament in 1516 he returned
to his friends in England; but his appointment, then recent, as councillor to
the young king Charles, brought him back to Brussels in the autumn. In the
spring of 1517 he went for the last time to England, about a dispensation
from wearing his canonical dress, obtained originally from Julius II. and
recently confirmed by Leo X., and in May 1518 he journeyed to Basel for
three months to set the second edition of the New Testament in progress.
But with these exceptions he remained in proximity to the court, living
much at Louvain, where he took great interest in the foundation of
Hieronymus Busleiden’s Collegium Trilingue. His circumstances had
improved so much, by pensions, the presents which were showered upon
him, and the sale of his books, that he was now in a position to refuse all
proposals which would have interfered with his cherished independence.
The general ardour for the restoration of the arts and of learning created an
aristocratic public, of which Erasmus was supreme pontiff. Luther spoke to
the people and the ignorant; Erasmus had the ear of the educated class. His
friends and admirers were distributed over all the countries of Europe, and
presents were continually arriving from small as well as great, from a
donation of 200 florins, made by Pope Clement VII., down to sweetmeats
and comfits contributed by the nuns of Cologne (Ep. 666). From England,
in particular, he continued to receive supplies of money. In the last year of
his life Thomas Cromwell sent him 20 angels, and Archbishop Cranmer 18.
Though Erasmus led a very hard-working and far from luxurious life, and
had no extravagant habits, yet he could not live upon little. The excessive
delicacy of his constitution, not pampered appetite, exacted some unusual
indulgences. He could not bear the stoves of Germany, and required an

open fireplace in the room in which he worked. He was afflicted with the
stone, and obliged to be particular as to what he drank. Beer he could not
touch. The white wines of Baden or the Rhine did not suit him; he could
only drink those of Burgundy or Franche-Comté. He could neither eat, nor
bear the smell of, fish. “His heart,” he said, “was Catholic, but his stomach
was Lutheran.” For his constant journeys he required two horses, one for
himself and one for his attendant. And though he was almost always found
in horse-flesh by his friends, the keep had to be paid for. For his literary
labours and his extensive correspondence he required one or more
amanuenses. He often had occasion, on his own business, or on that of
Froben’s press, to send special couriers to a distance, employing them by
the way in collecting the free gifts of his tributaries.

Precarious as these means of subsistence seem, he preferred the
independence thus obtained to an assured position which would have
involved obligations to a patron or professional duties which his weak
health would have made onerous. The duke of Bavaria offered to dispense
with teaching, if he would only reside, and would have named him on these
terms to a chair in his new university of Ingolstadt, with a salary of 200
ducats, and the reversion of one or more prebendal stalls. The archduke
Ferdinand offered a pension of 400 florins, if he would only come to reside
at Vienna. Adrian VI. offered him a deanery, but the offer seems to have
been of a possible and not an actual deanery. Offers, flattering but equally
vague, were made from France, on the part of the bishop of Bayeux, and
even of Francis I. “Invitor amplissimis conditionibus; offeruntur dignitates
et episcopatus; plane rex essem, si juvenis essem” (Ep. xix. 106; 735).
Erasmus declined all, and in November 1521 settled permanently at Basel,
in the capacity of general editor and literary adviser of Froben’s press. As a
subject of the emperor, and attached to his court by a pension, it would have
been convenient to him to have fixed his residence in Louvain. But the
bigotry of the Flemish clergy, and the monkish atmosphere of the university

of Louvain, overrun with Dominicans and Franciscans, united for once in
their enmity to the new classical learning, inclined Erasmus to seek a more
congenial home in Basel. To Froben his arrival was the advent of the very
man whom he had long wanted. Froben’s enterprise, united with Erasmus’s
editorial skill, raised the press of Basel, for a time, to be the most important
in Europe. The death of Froben in 1527, the final separation of Basel from
the Empire, the wreck of learning in the religious disputes, and the cheap
paper and scamped work of the Frankfort presses, gradually withdrew the
trade from Basel. But during the years of Erasmus’s co-operation the
Froben press took the lead of all the presses in Europe, both in the standard
value of the works published and in style of typographical execution. Like
some other publishers who preferred reputation to returns in money, Froben
died poor, and his impressions never reached the splendour afterwards
attained by those of the Estiennes, or of Plantin. The series of the Fathers
alone contains Jerome (1516), Cyprian (1520), Pseudo-Arnobius (1522),
Hilarius (1523), Irenaeus (Latin, 1526), Ambrose (1527), Augustine (1528),
Chrysostom (Latin, 1530), Basil (Greek, 1532, the first Greek author
printed in Germany), and Origen (Latin, 1536). In these editions, partly
texts, partly translations, it is impossible to determine the respective shares
of Erasmus and his many helpers. The prefaces and dedications are all
written by him, and some of them, as that to the Hilarius, are of importance
for the history as well of the times as of Erasmus himself. Of his most
important edition, that of the Greek text of the New Testament, something
will be said farther on.

In this “mill,” as he calls it, Erasmus continued to grind incessantly for
eight years. Besides his work as editor, he was always writing himself some
book or pamphlet called for by the event of the day, some general fray in
which he was compelled to mingle, or some personal assault which it was
necessary to repel. But though painfully conscious how much his reputation
as a writer was damaged by this extempore production, he was unable to

resist the fatal facility of print. He was the object of those solicitations
which always beset the author whose name upon the title page assures the
sale of a book. He was besieged for dedications, and as every dedication
meant a present proportioned to the circumstances of the dedicatee, there
was a natural temptation to be lavish of them. Add to this a correspondence
so extensive as to require him at times to write forty letters in one day. “I
receive daily,” he writes, “letters from remote parts, from kings, princes,
prelates and men of learning, and even from persons of whose existence I
was ignorant.” His day was thus one of incessant mental activity; but hard
work was so far from breeding a distaste for his occupation, that reading
and writing grew ever more delightful to him (literarum assiduitas non
modo mihi fastidium non parit, sed voluptatem; crescit scribendo scribendi
studium).

Shortly after Froben’s death the disturbances at Basel, occasioned by the
zealots for the religious revolution which was in progress throughout
Switzerland, began to make Erasmus desirous of changing his residence. He
selected Freiburg in the Breisgau, as a city which was still in the dominion
of the emperor, and was free from religious dissension. Thither he removed
in April 1529. He was received with public marks of respect by the
authorities, who granted him the use of an unfinished residence which had
been begun to be built for the late emperor Maximilian. Erasmus proposed
only to remain at Freiburg for a few months, but found the place so suited to
his habits that he bought a house of his own, and remained there six years.
A desire for change of air—he fancied Freiburg was damp—rumours of a
new war with France, and the necessity of seeing his Ecclesiastes through
the press, took him back to Basel in 1535. He lived now a very retired life,
and saw only a small circle of intimate friends. A last attempt was made by
the papal court to enlist him in some public way against the Reformation.
On the election of Paul III. in 1534, he had, as usual, sent the new pope a
congratulatory letter. After his arrival in Basel, he received a complimentary

answer, together with the nomination to the deanery of Deventer, the
income of which was reckoned at 600 ducats. This nomination was
accompanied with an intimation that more was in store for him, and that
steps would be taken to provide for him the income, viz., 3000 ducats,
which was necessary to qualify for the cardinal’s hat. But Erasmus was
even less disposed now than he had been before to barter his reputation for
honours. His health had been for some years gradually declining, and
disease in the shape of gout gaining upon him. In the winter of 1535-1536
he was confined entirely to his chamber, many days to his bed. Though thus
afflicted he never ceased his literary activity, dictating his tract On the
Purity of the Church, and revising the sheets of a translation of Origen
which was passing through the Froben press. His last letter is dated the 28th
of June 1536, and subscribed “Eras. Rot. aegra manu.” “I have never been
so ill in my life before as I am now,—for many days unable even to read.”
Dysentery setting in carried him off on the 12th of July 1536, in his 70th
year.

By his will, made on the 12th of February 1536, he left what he had to
leave, with the exception of some legacies, to Bonifazius Amerbach, partly
for himself, partly in trust for the benefit of the aged and the infirm, or to be
spent in portioning young girls, and in educating young men of promise. He
left none of the usual legacies for masses or other clerical purposes, and
was not attended by any priest or confessor in his last moments.

Erasmus’s features are familiar to all, from Holbein’s many portraits or
their copies. Beatus Rhenanus, “summus Erasmi observator,” as he is called
by de Thou, describes his person thus: “In stature not tall, but not noticeably
short; in figure well built and graceful; of an extremely delicate
constitution, sensitive to the slightest changes of climate, food or drink.
After middle life he suffered from the stone, not to mention the common
plague of studious men, an irritable mucous membrane. His complexion

was fair; light blue eyes, and yellowish hair. Though his voice was weak,
his enunciation was distinct; the expression of his face cheerful; his manner
and conversation polished, affable, even charming.” His highly nervous
organization made his feelings acute, and his brain incessantly active.
Through his ready sympathy with all forms of life and character, his
attention was always alive. The active movement of his spirit spent itself,
not in following out its own trains of thought, but in outward observation.
No man was ever less introspective, and though he talks much of himself,
his egotism is the genial egotism which takes the world into its confidence,
not the selfish egotism which feels no interest but in its own woes. He says
of himself, and justly, “that he was incapable of dissimulation” (Ep. xxvi.
19; 1152). There is nothing behind, no pose, no scenic effect. It may be said
of his letters that in them “tota patet vita senis.” His nature was flexible
without being faultily weak. He has many moods and each mood imprints
itself in turn on his words. Hence, on a superficial view, Erasmus is set
down as the most inconsistent of men. Further acquaintance makes us feel a
unity of character underlying this susceptibility to the impressions of the
moment. His seeming inconsistencies are reconciled to apprehension, not
by a formula of the intellect, but by the many-sidedness of a highly
impressible nature. In the words of J. Nisard, Erasmus was one of those
“dont la gloire a été de beaucoup comprendre et d’affirmer peu.”

This equal openness to every vibration of his environment is the key to
all Erasmus’s acts and words, and among them to the middle attitude which
he took up towards the great religious conflict of his time. The reproaches
of party assailed him in his lifetime, and have continued to be heaped upon
his memory. He was loudly accused by the Catholics of collusion with the
enemies of the faith. His powerful friends, the pope, Wolsey, Henry VIII.,
the emperor, called upon him to declare against Luther. Theological
historians from that time forward have perpetuated the indictment that
Erasmus sided with neither party in the struggle for religious truth. The

most moderate form of the censure presents him in the odious light of a
trimmer; the vulgar and venomous assailant is sure that Erasmus was a
Protestant at heart, but withheld the avowal that he might not forfeit the
worldly advantages he enjoyed as a Catholic. When by study of his writings
we come to know Erasmus intimately, there is revealed to us one of those
natures to which partisanship is an impossibility. It was not timidity or
weakness which kept Erasmus neutral, but the reasonableness of his nature.
It was not only that his intellect revolted against the narrowness of party, his
whole being repudiated its clamorous and vulgar excesses. As he loathed
fish, so he loathed clerical fanaticism. Himself a Catholic priest—“the glory
of the priesthood and the shame”—the tone of the orthodox clergy was
distasteful to him; the ignorant hostility to classical learning which reigned
in their colleges and convents disgusted him. In common with all the
learned men of his age, he wished to see the power of the clergy broken, as
that of an obscurantist army arrayed against light. He had employed all his
resources of wit and satire against the priests and monks, and the
superstitions in which they traded, long before Luther’s name was heard of.
The motto which was already current in his lifetime, “that Erasmus laid the
egg and Luther hatched it,” is so far true, and no more. Erasmus would have
suppressed the monasteries, put an end to the domination of the clergy, and
swept away scandalous and profitable abuses, but to attack the church or re-
mould received theology was far from his thoughts. And when out of
Luther’s revolt there arose a new fanaticism—that of evangelism, Erasmus
recoiled from the violence of the new preachers. “Is it for this,” he writes to
Melanchthon (Ep. xix. 113; 703), “that we have shaken off bishops and
popes, that we may come under the yoke of such madmen as Otto and
Farel?” Passages have been collected, and it is an easy task, from the
writings of Erasmus to prove that he shared the doctrines of the Reformers.
Passages equally strong might be culled to show that he repudiated them.
The truth is that theological questions in themselves had no attraction for

him. And when a theological position was emphasized by party passion it
became odious to him. In the words of Drummond: “Erasmus was in his
own age the apostle of common sense and of rational religion. He did not
care for dogma, and accordingly the dogmas of Rome, which had the
consent of the Christian world, were in his eyes preferable to the dogmas of
Protestantism.... From the beginning to the end of his career he remained
true to the purpose of his life, which was to fight the battle of sound
learning and plain common sense against the powers of ignorance and
superstition, and amid all the convulsions of that period he never once lost
his mental balance.”

Erasmus is accused of indifference. But he was far from indifferent to the
progress of the revolution. He was keenly alive to its pernicious influence
on the cherished interest of his life, the cause of learning. “I abhor the
evangelics, because it is through them that literature is everywhere
declining, and upon the point of perishing.” He had been born with the
hopes of the Renaissance, with its anticipation of a new Augustan age, and
had seen this fair promise blighted by the irruption of a new horde of
theological polemics, worse than the old scholastics, inasmuch as they were
revolutionary instead of conservative. Erasmus never flouted at religion nor
even at theology as such, but only at blind and intemperate theologians.

In the mind of Erasmus there was no metaphysical inclination; he was a
man of letters, with a general tendency to rational views on every subject
which came under his pen. His was not the mind to originate, like Calvin, a
new scheme of Christian thought. He is at his weakest in defending free
will against Luther, and indeed he can hardly be said to enter on the
metaphysical question. He treats the dispute entirely from the outside. It is
impossible in reading Erasmus not to be reminded of the rationalist of the
18th century. Erasmus has been called the “Voltaire of the Renaissance.”
But there is a vast difference in the relations in which they respectively

stood to the church and to Christianity. Voltaire, though he did not originate,
yet adopted a moral and religious scheme which he sought to substitute for
the church tradition. He waged war, not only against the clergy, but against
the church and its sovereigns. Erasmus drew the line at the first of these. He
was not an anticipation of the 18th century; he was the man of his age, as
Voltaire of his; though Erasmus did not intend it, he undoubtedly shook the
ecclesiastical edifice in all its parts; and, as Melchior Adam says of him,
“pontifici Romano plus nocuit jocando quam Lutherus stomachando.”

But if Erasmus was unlike the 18th century rationalist in that he did not
declare war against the church, but remained a Catholic and mourned the
disruption, he was yet a true rationalist in principle. The principle that
reason is the one only guide of life, the supreme arbiter of all questions,
politics and religion included, has its earliest and most complete exemplar
in Erasmus. He does not dogmatically denounce the rights of reason, but he
practically exercises them. Along with the charm of style, the great
attraction of the writings of Erasmus is this unconscious freedom by which
they are pervaded.

It must excite our surprise that one who used his pen so freely should
have escaped the pains and penalties which invariably overtook minor
offenders in the same kind. For it was not only against the clergy and the
monks that he kept up a ceaseless stream of satiric raillery; he treated
nobles, princes and kings with equal freedom. No 18th century republican
has used stronger language than has this pensioner of Charles V. “The
people build cities, princes pull them down; the industry of the citizens
creates wealth for rapacious lords to plunder; plebeian magistrates pass
good laws for kings to violate; the people love peace, and their rulers stir up
war.” Such outbursts are frequent in the Adagia. These freedoms are part
cause of Erasmus’s popularity. He was here in sympathy with the secret
sore of his age, and gave utterance to what all felt but none dared to whisper

but he. It marks the difference between 1513 and 1669 that, in a reprint of
the Julius Exclusus published in 1669 at Oxford, it was thought necessary to
leave out a sentence in which the writer of that dialogue, supposed by the
editor to be Erasmus, asserts the right of states to deprive and punish bad
kings. It is difficult to say to what we are to ascribe his immunity from
painful consequences. We have to remember that he was removed from the
scene early in the reaction, before force was fully organized for the
suppression of the revolution. And his popular works, the Adagia, and the
Colloquia (1524), had established themselves as standard books in the more
easy going age, when power, secure in its unchallenged strength, could
afford to laugh with the laughers at itself. At the date of his death the
Catholic revival, with its fell antipathy to art and letters, was only in its
infancy; and when times became dangerous, Erasmus cautiously declined to
venture out of the protection of the Empire, refusing repeated invitations to
Italy and to France. “I had thought of going to Besançon,” he said, “ne non
essem in ditione Caesaris” (Ep. xxx. 74; 1299). In Italy a Bembo and a
Sadoleto wrote a purer Latin than Erasmus, but contented themselves with
pretty phrases, and were careful to touch no living chord of feeling. In
France it was necessary for a Rabelais to hide his free-thinking under a
disguise of revolting and unintelligible jargon. It was only in the Empire
that such liberty of speech as Erasmus used was practicable, and in the
Empire Erasmus passed for a moderate man. Upon the strength of an
established character for moderation he enjoyed an exceptional licence for
the utterance of unwelcome truths; and in spite of his flings at the rich and
powerful, he remained through life a privileged person with them.

But though the men of the keys and the sword let him go his way
unmolested, it was otherwise with his brethren of the pen. A man who is
always launching opinions must expect to be retorted on. And when these
judgments were winged by epigram, and weighted by the name of Erasmus,
who stood at the head of letters, a widespread exasperation was the

consequence. Disraeli has not noticed Erasmus in his Quarrels of Authors,
perhaps because Erasmus’s quarrels would require a volume to themselves.
“So thin-skinned that a fly would draw blood,” as the prince of Carpi
expressed it, he could not himself restrain his pen from sarcasm. He forgot
that though it is safe to lash the dunces, he could not with equal impunity
sneer at those who, though they might not have the ear of the public as he
had, could yet contradict and call names. And when literary jealousy was
complicated with theological differences, as in the case of the free-thinkers,
or with French vanity, as in that of Budaeus, the cause of the enemy was
espoused by a party and a nation. The quarrel with Budaeus was strictly a
national one. Cosmopolitan as Erasmus was, to the French literati he was
still the Teuton. Étienne Dolet calls him “enemy of Cicero, and jealous
detractor of the French name.” The only contemporary name which could
approach to a rivalry with his was that of Budaeus (Budé), who was exactly
contemporary, having been born in the same year as Erasmus. Rivals in
fame, they were unlike in accomplishment, each having the quality which
the other wanted. Budaeus, though a Frenchman, knew Greek well;
Erasmus, though a Dutchman, very imperfectly. But the Frenchman
Budaeus wrote an execrable Latin style, unreadable then as now, while the
Teuton Erasmus charmed the reading world with a style which, though far
from good Latin, is the most delightful which the Renaissance has left us.

The style of Erasmus is, considered as Latin, incorrect, sometimes even
barbarous, and far removed from any classical model. But it has qualities
far above purity. The best Italian Latin is but an echo and an imitation; like
the painted glass which we put in our churches, it is an anachronism.
Bembo, Sadoleto and the rest write purely in a dead language. Erasmus’s
Latin was a living and spoken tongue. Though Erasmus had passed nearly
all his life in England, France and Germany, his conversation was Latin;
and the language in which he talked about common things he wrote. Hence
the spontaneity and naturalness of his page, its flavour of life and not of

books. He writes from himself, and not out of Cicero. Hence, too, he
spoiled nothing by anxious revision in terror lest some phrase not of the
golden age should escape from his pen. He confesses apologetically to
Christopher Longolius (Ep. iii. 63; 402) that it was his habit to extemporize
all he wrote, and that this habit was incorrigible; “effundo verius quam
scribo omnia.” He complains that much reading of the works of St Jerome
had spoiled his Latin; but, as Scaliger says (Scaliga 2a), “Erasmus’s
language is better than St Jerome’s.” The same critic, however, thought
Erasmus would have done better “if he had kept more closely to the
classical models.”

In the annals of classical learning Erasmus may be regarded as
constituting an intermediate stage between the humanists of the Latin
Renaissance and the learned men of the age of Greek scholarship, between
Angelo Poliziano and Joseph Scaliger. Erasmus, though justly styled by
Muretus (Varr. Lectt. 7, 15) “eruditus sane vir, ac multae lectionis,” was not
a “learned” man in the special sense of the word—not an “érudit.” He was
more than this; he was the “man of letters”—the first who had appeared in
Europe since the fall of the Roman empire. His acquirements were vast, and
they were all brought to bear upon the life of his day. He did not make a
study apart of antiquity for its own sake, but used it as an instrument of
culture. He did not worship, imitate and reproduce the classics, like the
Latin humanists who preceded him; he did not master them and reduce
them to a special science, as did the French Hellenists who succeeded him.
He edited many authors, it is true, but he had neither the means of forming a
text, nor did he attempt to do so. In editing a father, or a classic, he had in
view the practical utility of the general reader, not the accuracy required by
the gild of scholars. “His Jerome,” says J. Scaliger, “is full of sad blunders”
(Scaliga 2a). Even Julien Garnier could discover that Erasmus “falls in his
haste into grievous error in his Latin version of St Basil, though his Latinity
is superior to that of the other translators” (Pref. in Opp. St. Bas., 1721). It

must be remembered that the commercial interests of Froben’s press led to
the introduction of Erasmus’s name on many a title page when he had little
to do with the book, e.g. the Latin Josephus of 1524 to which Erasmus only
contributed one translation of 14 pages; or the Aristotle of 1531, of which
Simon Grynaeus was the real editor. Where Erasmus excelled was in
prefaces—not philological introductions to each author, but spirited appeals
to the interest of the general reader, showing how an ancient book might be
made to minister to modern spiritual demands.

Of Erasmus’s works the Greek Testament is the most memorable. It has
no title to be considered as a work of learning or scholarship, yet its
influence upon opinion was profound and durable. It contributed more to
the liberation of the human mind from the thraldom of the clergy than all
the uproar and rage of Luther’s many pamphlets. As an edition of the Greek
Testament it has no critical value. But it was the first, and it revealed the
fact that the Vulgate, the Bible of the church, was not only a second-hand
document, but in places an erroneous document. A shock was thus given to
the credit of the clergy in the province of literature, equal to that which was
given in the province of science by the astronomical discoveries of the 17th
century. Even if Erasmus had had at his disposal the MSS. subsidia for
forming a text, he had not the critical skill required to use them. He had at
hand a few late Basel MSS., one of which he sent straight to press,
correcting them in places by collations of others which had been sent to him
by Colet in England. In four reprints, 1519, 1522, 1527, 1535, Erasmus
gradually weeded out many of the typographical errors of his first edition,
but the text remained essentially such as he had first printed it. The Greek
text indeed was only a part of his scheme. An important feature of the
volume was the new Latin version, the original being placed alongside as a
guarantee of the translator’s good faith. This translation, with the
justificatory notes which accompanied it, though not itself a work of critical
scholarship, became the starting-point of modern exegetical science.

Erasmus did nothing to solve the problem, but to him belongs the honour of
having first propounded it.

Besides translating and editing the New Testament, Erasmus paraphrased
the whole, except the Apocalypse, between 1517 and 1524. The paraphrases
were received with great applause, even by those who had little
appreciation for Erasmus. In England a translation of them made in 1548
was ordered to be placed in all parish churches beside the Bible. His
correspondence is perhaps the part of his works which has the most
permanent value; it comprises about 3000 letters, which form an important
source for the history of that period. For the same purpose his Colloquia
may be consulted. They are a series of dialogues, written first for pupils in
the early Paris days as formulae of polite address, but afterwards expanded
into lively conversations, in which many of the topics of the day are
discussed. Later in the century they were read in schools, and some of
Shakespeare’s lines are direct reminiscences of Erasmus.

His complete works have been printed twice; by the Froben firm
under the direction of his literary executors (9 vols., Basel, 1540); and
by Leclerc at Leiden (11 vols., 1703-1706). For his life the chief
contemporary sources are a Compendium vitae written by himself in
1524, and a sketch prefixed by Beatus Rhenanus to the Basel edition of
1540. Of his writings he gives an account in his Catalogus
lucubrationum, composed first in January 1523 and enlarged in
September 1524; and also in a letter to Hector Boece of Aberdeen,
written in 1530. An elaborate bibliography, entitled Bibliotheca
Erasmiana, was undertaken by the officials of the Ghent University
Library; it is divided into three sections, for Erasmus’s writings, the
books he edited, and the literature about him. Listes sommaires were
issued in 1893; and since 1897 the completed volumes have been
appearing at intervals. There is an excellent sketch of Erasmus’s life

down to 1519 in F. Seebohm’s Oxford Reformers (3rd ed., 1887); and
of the many biographies those by S. Knight (1726), J. Jortin (2 vols.,
1758-1760) and R.B. Drummond (2 vols., 1873) may be mentioned.
There are also two volumes (1901-1904) of translations by F.M.
Nichols from Erasmus’s letters down to 1517, with an ample
commentary which amounts almost to a biography; and an edition of
the letters, in Latin, was begun by the Oxford University Press in 1906
(vol. ii., 1910). (M. P.; P. S. A.)

ERASTUS, THOMAS (1524-1583), German-Swiss theologian, whose
surname was Lüber, Lieber, or Liebler, was born of poor parents on the 7th
of September 1524, probably at Baden, canton of Aargau, Switzerland. In
1540 he was studying theology at Basel. The plague of 1544 drove him to
Bologna and thence to Padua as student of philosophy and medicine. In
1553 he became physician to the count of Henneberg, Saxe-Meiningen, and
in 1558 held the same post with the elector-palatine, Otto Heinrich, being at
the same time professor of medicine at Heidelberg. His patron’s successor,
Frederick III., made him (1559) a privy councillor and member of the
church consistory. In theology he followed Zwingli, and at the
sacramentarian conferences of Heidelberg (1560) and Maulbronn (1564) he
advocated by voice and pen the Zwinglian doctrine of the Lord’s Supper,
replying (1565) to the counter arguments of the Lutheran Johann Marbach,
of Strassburg. He ineffectually resisted the efforts of the Calvinists, led by
Caspar Olevianus, to introduce the Presbyterian polity and discipline, which
were established at Heidelberg in 1570, on the Genevan model. One of the

first acts of the new church system was to excommunicate Erastus on a
charge of Socinianism, founded on his correspondence with Transylvania.
The ban was not removed till 1575, Erastus declaring his firm adhesion to
the doctrine of the Trinity. His position, however, was uncomfortable, and
in 1580 he returned to Basel, where in 1583 he was made professor of
ethics. He died on the 31st of December 1583. He published several pieces
bearing on medicine, astrology and alchemy, and attacking the system of
Paracelsus. His name is permanently associated with a posthumous
publication, written in 1568. Its immediate occasion was the disputation at
Heidelberg (1568) for the doctorate of theology by George Wither or
Withers, an English Puritan (subsequently archdeacon of Colchester),
silenced (1565) at Bury St Edmunds by Archbishop Parker. Withers had
proposed a disputation against vestments, which the university would not
allow; his thesis affirming the excommunicating power of the presbytery
was sustained. Hence the treatise of Erastus. It was published (1589) by
Giacomo Castelvetri, who had married his widow, with the title Explicatio
gravissimae quaestionis utrum excommunicatio, quatenus religionem
intelligentes et amplexantes, a sacramentorum usu, propter admissum
facinus arcet, mandato nitatur divino, an excogitata sit ab hominibus. The
work bears the imprint Pesclavii (i.e. Poschiavo in the Grisons) but was
printed by John Wolfe in London, where Castelvetri was staying; the name
of the alleged printer is an anagram of Jacobum Castelvetrum. In the
Stationers’ Register (June 20, 1589) the printing is said to have been
“alowed” by Archbishop Whitgift. It consists of seventy-five Theses,
followed by a Confirmatio in six books, and an appendix of letters to
Erastus by Bullinger and Gualther, showing that his Theses, written in 1568,
had been circulated in manuscript. An English translation of the Theses,
with brief life of Erastus (based on Melchior Adam’s account), was issued
in 1659, entitled The Nullity of Church Censures; it was reprinted as A
Treatise of Excommunication (1682), and, as revised by Robert Lee, D.D.,

in 1844. The aim of the work is to show, on Scriptural grounds, that sins of
professing Christians are to be punished by civil authority, and not by
withholding of sacraments on the part of the clergy. In the Westminster
Assembly a party holding this view included Selden, Lightfoot, Coleman
and Whitelocke, whose speech (1645) is appended to Lee’s version of the
Theses; but the opposite view, after much controversy, was carried,
Lightfoot alone dissenting. The consequent chapter of the Westminster
Confession (“Of Church Censures”) was, however, not ratified by the
English parliament. “Erastianism,” as a by-word, is used to denote the
doctrine of the supremacy of the state in ecclesiastical causes; but the
problem of the relations between church and state is one on which Erastus
nowhere enters. What is known as “Erastianism” would be better connected
with the name of Grotius. The only direct reply made to the Explicatio was
the Tractatus de vera excommunicatione (1590) by Theodore Beza, who
found himself rather savagely attacked in the Confirmatio thesium; e.g.
“Apostolum et Mosen adeoque Deum ipsum audes corrigere.”

See A. Bonnard, Thomas Éraste et la discipline ecclésiastique
(1894); Gass, in Allgemeine deutsche Biog. (1877); G.V. Lechler and
R. Stähelin, in A. Hauck’s Realencyklop. für prot. Theol. u. Kirche
(1898).
(A. Go.*)

ERATOSTHENES OF ALEXANDRIA (c. 276-c. 194 b.c.), Greek
scientific writer, was born at Cyrene. He studied grammar under
Callimachus at Alexandria, and philosophy under the Stoic Ariston and the

Academic Arcesilaus at Athens. He returned to Alexandria at the summons
of Ptolemy III. Euergetes, by whom he was appointed chief librarian in
place of Callimachus. He is said to have died of voluntary starvation, being
threatened with total blindness. Eratosthenes was one of the most learned
men of antiquity, and wrote on a great number of subjects. He was the first
to call himself Philologos (in the sense of the “friend of learning”), and the
name Pentathlos was bestowed upon him in honour of his varied
accomplishments. He was also called Beta as being second in all branches
of learning, though not actually first in any. In mathematics he wrote two
books On means (Περὶ μεσοτήτων) which are lost, but appear, from a
remark of Pappus, to have dealt with “loci with reference to means.” He
devised a mechanical construction for two mean proportionals, reproduced
by Pappus and Eutocius (Comm. on Archimedes). His κόσκινον or sieve
(cribrum Eratosthenis) was a device for discovering all prime numbers. He
laid the foundation of mathematical geography in his Geographica, in three
books. His greatest achievement was his measurement of the earth. Being
informed that at Syene (Assuan), on the day of the summer solstice at noon,
a well was lit up through all its depth, so that Syene lay on the tropic, he
measured, at the same hour, the zenith distance of the sun at Alexandria. He
thus found the distance between Syene and Alexandria (known to be 5000
stadia) to correspond to 1⁄50th of a great circle, and so arrived at 250,000
stadia (which he seems subsequently to have corrected to 252,000) as the
circumference of the earth. He is credited by Ptolemy and his commentator
Theon with having found the distance between the tropics to be 11⁄83 rds. of
the meridian circle, which gives 23° 51’ 20″ for the obliquity of the ecliptic.
His astronomical poem Hermes began apparently with the birth and exploits
of Hermes, then passed to the legend of his having ordered the heavens, the
zones and the stars, and gave a history of the latter. His Erigone, of which a
few fragments are also preserved, is sometimes spoken of as a separate
poem, but it may have belonged to the Hermes, which appears also to have

been known by other names such as Catalogi. The still extant Catasterismi,
containing the story of certain stars in prose, is probably not by
Eratosthenes.

Eratosthenes was the founder of scientific chronology in his
χρονογραφία in which he endeavoured to fix the dates of the chief literary
and political events from the conquest of Troy. An important work was his
treatise on the old comedy, dealing with theatres and theatrical apparatus
generally, and discussing the works of the principal comic poets
themselves. Works on moral philosophy, history, and a number of letters
were also attributed to him.

There is a complete edition of the fragments of Eratosthenes by
Bernhardy (1822); poetical fragments, Hillier (1872); geographical,
Seidel (1799) and Berger (1880); καταστερισμοι, Schaubach (1795)
and Robert (1878). See Sandys, Hist. Class. Schol. i. (1906).
(T. L. H.)

ERBACH, a town of Germany, in the grand-duchy of Hesse-Darmstadt,
on the Mümling, 22 m. S.E. of Darmstadt. It has cloth mills and ivory-
turning, for which last branch it possesses a technical school. Wool and
cattle fairs are held twice a year. Pop. 2800. The castle contains an
interesting collection of weapons and pictures, and in the chapel are the
coffins of Einhard, the friend and biographer of Charlemagne, and his wife,
Emma.

Erbach has long been the residence of the counts of Erbach, who trace
their descent back to the 12th century, and who held the office of cupbearer
to the electors palatine of the Rhine until 1806. In 1532 the emperor Charles
V. made the county a direct fief of the Empire, on account of the services
rendered by Count Eberhard during the Peasants’ War. Since 1717 the
family has been divided into the three lines of Erbach-Fürstenau, Erbach-
Erbach and Erbach-Schönberg, who rank for precedence, not according to
the age of their descent, but according to the age of the chief of their line. In
1818 the counts of Erbach-Erbach inherited the county of Wartenberg-Roth,
and in 1903 the count of Erbach-Schönberg was granted the title of prince.
The county was mediatized in 1806, and is now incorporated with the
duchy of Hesse-Darmstadt.

See Simon, Die Geschichte der Dynasten und Grafen zu Erbach
(Frankfort, 1858).

ERBIUM (symbol, Er; atomic weight, 165-166), one of the metals of the
rare earths. The first of the rare earth minerals was discovered in 1794 by J.
Gadolin and was named gadolinite from its discoverer. In 1797 Ekeberg
showed that gadolinite contained another rare earth, which was given the
name yttria. Yttria is an exceedingly complex mixture, which has been
decomposed, yielding as an intermediate product terbia. This latter
substance in its turn has been split by J.L. Soret, P.T. Cleve, Lecoq de
Boisbaudran and others into erbia, holmia, thulia and dysprosia, but it is
still doubtful whether any one of these four splitting products is a single
substance. The rare earth metals are found in the minerals gadolinite,

samarskite, fergusonite, euxenite and cerite. They are separated from the
minerals by converting them into oxalates, which by ignition give the
corresponding oxides. The oxides are then converted into double sulphates
which are separated from each other by repeated fractional crystallization or
by fractional precipitation with ammonia or some other base. Erbium forms
rose-coloured salts and a rose-coloured oxide. The oxide dissolves slowly in
acids; it is not reduced by hydrogen and is infusible. The salts show a
characteristic absorption spectrum.

See J.F. Bahr and R. Bunsen (Ann., 1866, 137, p. 1); A. v. Welsbach
(Monats., 1883, 4, p. 641; 1884, 5, p. 508; 1885, 6, p. 477); P.T. Cleve
(Comptes rendus, 1879, 89, p. 478; 1880, 91, pp. 328, 381; 1882, 95, p.
1225; Bull. de la soc. chim., 1874, 21, p. 196; 1883, 39, p. 287); C.
Marignac (Ann. Chim. phys., 1849 [3] 27, p. 226); B. Brauner
(Monats., 1882, 3, p. 13); W. Crookes (Proc. Roy. Soc., 1886, 40, p.
502); Lecoq de Boisbaudran (Comptes rendus, 1886, 102, p. 1005); A.
Bettendorf (Ann., 1892, 270, p. 376); M. Muthmann (Ber., 1898, 31, p.
1718; 1900, 33, p. 42); G. Krüss (Zeit. f. anorg. Chem., 1893, 3, p.
108).

ERCILLA Y ZÚNIGA, ALONSO DE (1533-1595), Spanish soldier
and poet, was born in Madrid on the 7th of August 1533. In 1548 he was
appointed page to the heir-apparent, afterwards Philip II. In this capacity
Ercilla visited Italy, Germany and the Netherlands, and was present in 1554
at the marriage of his master to Mary of England. Hearing that an
expedition was preparing to subdue the Araucanians of Chile, he joined the

adventurers. He distinguished himself in the ensuing campaign; but, having
quarrelled with a comrade, he was condemned to death in 1558 by his
general, Garcia Hurtado de Mendoza. The sentence was commuted to
imprisonment, but Ercilla was speedily released and fought at the battle of
Quipeo (14th of December 1558). He returned to Spain in 1562, visited
Italy, France, Germany, Bohemia, and in 1570 married Maria de Bazán, a
lady distantly connected with the Santa Cruz family; in 1571 he was made
knight of the order of Santiago, and in 1578 he was employed by Philip II.
on a mission to Saragossa. He complained of living in poverty but left a
modest fortune, and was obviously disappointed at not being offered the
post of secretary of state. His principal work is La Araucana, a poem based
on the events of the wars in which he had been engaged. It consists of three
parts, of which the first, composed in Chile and published in 1569, is a
versified narrative adhering strictly to historic fact; the second, published in
1578, is encumbered with visions and other romantic machinery; and the
third, which appeared in 1589-1590, contains, in addition to the subject
proper, a variety of episodes mostly irrelevant. This so-called epic lacks
symmetry, and has been over-praised by Cervantes and Voltaire; but it is
written in excellent Spanish, and is full of vivid rhetorical passages. An
analysis of the poem was given by Hayley in his Essay on Epic Poetry
(1782).

A good biography precedes the Morceaux choisis (Paris, 1900) by
Jean Ducamin.

ERCKMANN-CHATRIAN, the joint names of two French writers
whose collaboration made their work that of, so to speak, one personality.
Émile Erckmann (1822-1899) was born on the 20th of May 1822 at
Phalsbourg, and Louis Gratien Charles Alexandre Chatrian (1826-1890)
on the 18th of December 1826 at Soldatenthal, Lorraine. In 1847 they
began to write together, and continued doing so till 1889. Chatrian died in
1890 at Villemomble near Paris, and Erckmann at Lunéville in 1899. The
list of their publications is a long one, ranging from the Histoires et contes
fantastiques (1849; reprinted from the Démocrate du Rhin), L’Illustre
Docteur Mathéus (1859), Madame Thérèse (1863), L’Ami Fritz (1864),
Histoire d’un conscrit de 1813 (1864), Waterloo (1865), Le Blocus (1867),
Histoire d’un paysan (4 vols., 1868-1870), L’Histoire du plébiscite (1872),
to Le Grand-père Lebigue (1880); besides dramas like Le Juif polonais
(1869) and Les Rantzau (1882). Without any special literary claim, their
stories are distinguished by simplicity and genuine descriptive power,
particularly in the battle scenes and in connexion with Alsatian peasant life.
They are marked by a genuine democratic spirit, and by real patriotism,
which developed after 1870 into hatred of the Germans. The authors
attacked militarism by depicting the horrors of war in the plainest terms.

See also J. Claretie, Erckmann-Chatrian (1883), in the series of
“Célébrités contemporaines.”

ERDÉLYI, JÁNOS (1814-1868), Hungarian poet and author, was born
in 1814 at Kapos, in the county of Ungvár, and educated at the Protestant
college of Sárospatak. In 1833 he removed to Pest, where he was, in 1839,
elected member of the Hungarian Academy of Sciences. His literary fame
was made by his collection of Hungarian national poems and folk-tales,
Magyar Népköltési Gyüjtemény, Népdalok és Mondák (Pest, 1846-1847).
This work, published by the Kisfaludy Society, was supplemented by a
dissertation upon Hungarian national poetry, afterwards partially translated
into German by Stier (Berlin, 1851). Erdélyi also compiled for the
Kisfaludy Society an extensive collection of Hungarian proverbs—Magyar
Közmondások könyve (Pest, 1851),—and was for some time editor of the
Szépirodalmi Szemle (Review of Polite Literature). In 1848 he was
appointed director of the national theatre at Pest; but after 1849 he resided
at his native town. He died on the 23rd of January 1868. A collection of
folklore was published the year after his death, entitled A Nép Koltészete
népdalok, népmesék és közmondások (Pest, 1869). This work contains 300
national songs, 19 folk-tales and 7362 Hungarian proverbs.

ERDMANN, JOHANN EDUARD (1805-1892), German philosophical
writer, was born at Wolmar in Livonia on the 13th of June 1805. He studied
theology at Dorpat and afterwards at Berlin, where he fell under the

influence of Hegel. From 1829 to 1832 he was a minister of religion in his
native town. Afterwards he devoted himself to philosophy, and qualified in
that subject at Berlin in 1834. In 1836 he was professor-extraordinary at
Halle, became full professor in 1839, and died there on the 12th of June
1892. He published many philosophical text-books and treatises, and a
number of sermons; but his chief claim to remembrance rests on his
elaborate Grundriss der Geschichte der Philosophie (2 vols., 1866), the 3rd
edition of which has been translated into English. Erdmann’s special merit
is that he does not rest content with being a mere summarizer of opinions,
but tries to exhibit the history of human thought as a continuous and ever-
developing effort to solve the great speculative problems with which man
has been confronted in all ages. His chief other works were: Leib und Seele
(1837), Grundriss der Psychologie (1840), Grundriss der Logik und
Metaphysik (1841), and Psychologische Briefe (1851).

ERDMANN, OTTO LINNÉ (1804-1869), German chemist, son of Karl
Gottfried Erdmann (1774-1835), the physician who introduced vaccination
into Saxony, was born at Dresden on the 11th of April 1804. In 1820 he
began to attend the medico-chirurgical academy of his native place, and in
1822 he entered the university of Leipzig where in 1827 he became
extraordinary professor, and in 1830 ordinary professor of chemistry. This
office he held until his death, which happened at Leipzig on the 9th of
October 1869. He was particularly successful as a teacher, and the
laboratory established at Leipzig under his direction in 1843 was long
regarded as a model institution. As an investigator he is best known for his

work on nickel and indigo and other dye-stuffs. With R.F. Marchand (1813-
1850) he also carried out a number of determinations of atomic weights. In
1828, in conjunction with A.F.G. Werther (1815-1869), he founded the
Journal für technische und ökonomische Chemie, which became in 1834 the
Journal für praktische Chemie. He was also the author of Über das Nickel
(1827), Lehrbuch der Chemie (1828), Grundriss der Waarenkunde (1833),
and Über das Studium der Chemie (1861).

EREBUS, in Greek mythology, son (according to Hesiod, Theog. 123) of
Chaos, and father of Aether (upper air) and Hemera (day) by his sister Nyx
(night). The word, which signifies darkness, is in Homer the gloomy
subterranean region through which the departed shades pass into Hades.
The entrance to it was in the extreme west, on the borders of Ocean, in the
mythical land of the Cimmerians. It is to be distinguished from Tartarus, the
place of punishment for the wicked.

ERECH (Uruk in the Babylonian inscriptions; Gr. Orchoë), the Biblical
name of an ancient city of Babylonia, situated E. of the present bed of the
Euphrates, on the line of the ancient Nil canal, in a region of marshes, about
140 m. S.S.E. from Bagdad. It was one of the oldest and most important
cities of Babylonia, and the site of a famous temple, called E-Anna,

dedicated to the worship of Nana, or Ishtar. Erech played a very important
part in the political history of the country from an early time, exercising
hegemony in Babylonia at a period before the time of Sargon. Later it was
prominent in the national struggles of the Babylonians against Elam (2000
b.c. and earlier), in which it suffered severely; recollections of these

conflicts are embodied in the Gilgamesh epic, as it has come down to us
through the library of Assur-bani-pal. Erech enjoyed much distinction in the
later times, as a seat of learning and of the worship of Ishtar, and Assur-
bani-pal drew largely on its literary stores for his library at Nineveh, from
which we derive our principal information concerning ancient Babylonian
literature. The inscriptions found here show that it continued in existence
through the Persian and Seleucid periods. The ruins of the ancient site,
known as Warka, which are among the largest in all Babylonia, forming an
irregular circle nearly 6 m. in circumference, bounded by a wall, still
standing in some places to the height of 40 ft., were explored and partially
excavated by W.K. Loftus in 1850 and 1854. The most conspicuous ruin,
now called Abu-Berdi, “Father of Marsh Grass,” or Buwariye, “reed
matting,” because of the layers of reeds between each twelve courses of
unbaked brick, is the ziggurat (tower) of the ancient temple of E-Anna. It is
about 100 ft. in height, and strikingly resembles in general appearance the
ruins of the ziggurat of the temple of Enlil at Nippur. Second to this in size
was the ruin called Wuswas, a walled quadrangle, including an area of more
than seven and a half acres, within which was an edifice 246 ft. long and
174 ft. wide, elevated on an artificial platform 50 ft. in height. The south-
west façade, still standing in some places to the height of 23 ft., exhibited
an interesting use of half columns, and stepped recesses for purposes of
decoration. In another ruin Loftus found a wall, 30 ft. long, composed
entirely of small yellow terra-cotta nail-headed cones, such as have been
discovered in great numbers, inscribed and uninscribed, used for votive
purposes in connexion with walls at Tello and elsewhere in Babylonia. His

excavations being superficial, the Babylonian inscriptions found by him,
about one hundred in all, exclusive of the ancient Ur-Gur bricks from the
temple, belong in general to the neo-Babylonian, Persian and Seleucid
periods. The older remains are buried deep beneath the huge mass of later
debris. Loftus also discovered at Erech, almost everywhere within and
without the walls, great numbers of clay coffins, piled one above another, to
the height of over 30 ft., forming a vast and, on the whole, well-ordered
cemetery belonging to the Persian, Parthian and later occupations of
Babylonia, during which period Erech, like other cities of the south,
evidently became a necropolis for a large extent of country. After Loftus’s
time the mounds were visited by various travellers, but no further
excavations have been conducted. Work on this important part of the site is
attended with very great difficulties, owing to the inaccessible position of
the ruins, the unsettled character of the country, the frequent sand-storms,
and above all, the immense mass of material of later periods which must be
removed before a systematic excavation of the more ancient and interesting
ruins could be undertaken. A curious feature of the Warka neighbourhood is
the existence of conical sand-hills, rising to a considerable height, so
compact as to be almost like stone. These hills extend from Warka
northward as far as Tel Ede.

See W.K. Loftus, Chaldaea and Susiana (1857); J.P. Peters, Nippur
(1897); E. Sachau, Am Euphrat und Tigris (1900). Cf. also Nippur and
authorities there quoted.
(J. P. Pe.)

ERECHTHEUM, a temple (commonly called after Erechtheus, to
whom a portion of it was dedicated) on the acropolis at Athens, unique in
plan, and in its execution the most refined example of the Ionic order. There
is no clear evidence as to when the building was begun, some placing it
among the temples projected by Pericles, others assigning it to the time
after the peace of Nicias in 421 b.c. The work was interrupted by the stress
of the Peloponnesian War, but in 409 b.c. a commission was appointed to
make a report on the state of the building and to undertake its completion,
which was carried out in the following year.

The peculiar plan of the Erechtheum has given rise to much speculation.
It may be due partly to the natural conformation of the rock and the
differences of level, partly to the necessity of enclosing within a single
building several objects of ancient sanctity, such as the mark of Poseidon’s
trident and the spring that arose from it, the sacred olive tree of Athena, and
the tomb of Cecrops. But there are some features which cannot be so
explained, and which have led Professor W. Dörpfeld and others to believe
that the plan, as we now have it, is a modification or abridgment of the
original design, due to the same conservative influences as led to the
curtailment of the plan of the Propylaea (q.v.).

The building as completed consisted of a temple of the ordinary type,
opening by a door and two windows to the east front, before which stood a
portico of six Ionic columns. This part was the temple of Athena Polias.
Adjoining it on the west was the central chamber, on a lower level; this
chamber was separated by a partition, originally of wood and later of
marble, from the western compartment of the temple, which was of peculiar
construction. The west end was formed by a wall, on which stood four
columns between antae; but the main entrance to this western compartment
was through a large and very ornate doorway on the north; and a large Ionic
portico, consisting of four columns in the front, and one in the return on
each side, was placed in front of this door. At the south end of the western
compartment was a smaller door, with steps leading up to the higher level,

within a projecting space enclosed by a low wall and covered with a
projecting porch carried by six “maidens” or caryatides. The construction of
the building at this south-western corner shows that there was some sacred
object that had to be bridged over by a huge block of marble; this we know
from inscriptions to have been the Cecropeum or tomb of Cecrops. In the
north portico a square hole in the floor, with a corresponding hole in the
roof above it, must have given access to another sacred object, the mark of
Poseidon’s trident in the rock. The sacred olive tree probably stood just
outside the temple to the west in the Pandroseion. The Ionic order, as used
in this temple, is of the most ornate Attic type. The bases of the columns are
either reeded or decorated with a plait-pattern; the capital has the broad
channel between the volutes subdivided by a carefully-profiled incision;
and the top of the shafts is ornamented by a broad band of palmette or
honeysuckle pattern. A similar band of ornament runs round the top of the
walls outside, and at their base is a reeded torus. The frieze consisted of
white marble figures in relief, affixed to a background of black Eleusinian
stone.

The contents of the Erechtheum are described by Pausanias. It contained
the ancient image of Athena Polias, and three altars, one to Poseidon and
Erechtheus, one to Butes and one to Hephaestus; there were portraits of the
family of the Butadae on the walls. Within it was also the gold lamp of
Callimachus, which burnt for a year without refilling, and had a chimney in
the form of a palm-tree.

The Erechtheum was damaged by a fire, soon after its completion, in 406
b.c., but was repaired early in the following century. The west end appears
to have been damaged in Roman times and to have been replaced by the
attached columns with windows between them which appear in old
drawings and are still partially extant. It was used as a church in Christian
times, and under Turkish rule as the harem of the governor of Athens. Lord

Elgin carried off to London, about 1801-1803, one of the columns of the
east portico and one of the caryatides; these were replaced later by terra-
cotta casts. During the siege of the Acropolis in 1827, the roof of the north
portico was thrown down and the building was otherwise much damaged. It
was partially rebuilt between 1838 and 1846; the west front was blown
down in a storm in 1852. Since 1900 the project of rebuilding the
Erechtheum as far as possible with the original blocks has again been
undertaken.

See Stuart, Antiquities of Athens; Inwood, The Erechtheum; H.
Forster in Papers of American School at Athens, i. (1882-1883); J.H.
Middleton, Plans and Drawings of Athenian Buildings (1900), pls.
xiv.-xxii.; E.A. Gardner, Ancient Athens, chap. viii.; W. Dörpfeld, “Der
ursprungliche Plan des Erechtheion” in Mitteil. Athen., 1904, p. 101,
taf. 6; G.P. Stevens, “The East Wall of the Erechtheum,” in American
Journ. Arch., 1906, pls. vi.-ix.
(E. Gr.)

ERECHTHEUS, in Greek legend, a mythical king of Athens, originally
identified with Erichthonius, but in later times distinguished from him.
According to Homer, who knows nothing of Erichthonius, he was the son of
Aroura (Earth), brought up by Athena, with whom his story is closely
connected. In the later story, Erichthonius (son of Hephaestus and Atthis or
Athena herself) was handed over by Athena to the three daughters of
Cecrops—Aglauros (or Agraulos), Herse and Pandrosos—in a chest, which
they were forbidden to open. Aglauros and Herse disobeyed the injunction,

and when they saw the child (which had the form of a snake, or round
which a snake was coiled) they went mad with fright, and threw themselves
from the rock of the Acropolis (or were killed by the snake). Athena herself
then undertook the care of Erichthonius, who, when he grew up, drove out
Amphictyon and took possession of the kingdom of Athens. Here he
established the worship of Athena, instituted the Panathenaea, and built an
Erechtheum. The Erechtheus of later times was supposed to be the grandson
of Erechtheus-Erichthonius, and was also king of Athens. When Athens was
attacked by the Thracian Eumolpus (or by the Eleusinians assisted by
Eumolpus) victory was promised Erechtheus if he sacrificed one of his
daughters. Eumolpus was slain and Erechtheus was victorious, but was
himself killed by Poseidon, the father of Eumolpus, or by a thunderbolt
from Zeus. The contest between Erechtheus and Eumolpus formed the
subject of a lost tragedy by Euripides; Swinburne has utilized the legend in
his Erechtheus. The scene of the opening of the chest is represented on a
Greek vase in the British Museum. The name Erichthonius is connected
with χθών (“earth”) and the representation of him as half-snake, like
Cecrops, indicates that he was regarded as one of the autochthones, the
ancestors of the Athenians who sprung from the soil.

See Apollodorus iii. 14. 15; Euripides, Ion; Ovid, Metam. ii. 553;
Hyginus, Poët. astron. ii. 13; Pausanias i. 2. 5. 8; E. Ermatinger, Die
attische Autochthonensage (1897); article by J.A. Hild in Daremberg
and Saglio’s Dictionnaire des antiquités; B. Powell in Cornell Studies,
xvii. (1906), who identifies Erechtheus, Erichthonius, Poseidon and
Cecrops, all denoting the sacred serpent of Athena, whose cult she first
contested, but then amalgamated with her own. The birth of
Erichthonius (as a corn-spirit) is interpreted by Mannhardt as a
mythical way of describing the growth of the corn, and by J.E.
Harrison (Myths and Monuments of Ancient Athens, xxvii.-xxxvi.) as a
fiction to explain the ceremony performed by the two maidens called

Arrephori. See also Farnell, Cults of the Greek States, i. 270; and
Frazer’s Pausanias, ii. 169.

ERESHKIGAL, also known as Allatu, the name of the chief
Babylonian goddess of the nether-world where the dead are gathered. Her
name signifies “lady of the nether-world.” She is known to us chiefly
through two myths, both symbolizing the change of seasons, but intended
also to illustrate certain doctrines developed in the temple-schools of
Babylonia. One of these myths is the famous story of Ishtar’s descent to
Irkalla or Arālu, as the lower world was called, and her reception by her
sister who presides over it; the other is the story of Nergal’s offence against
Ereshkigal, his banishment to the kingdom controlled by the goddess and
the reconciliation between Nergal and Ereshkigal through the latter’s offer
to have Nergal share the honours of the rule over Irkalla. The story of
Ishtar’s descent is told to illustrate the possibility of an escape from Irkalla,
while the other myth is intended to reconcile the existence of two rulers of
Irkalla—a goddess and a god.

It is evident that it was originally a goddess who was supposed to be in
control of Irkalla, corresponding to Ishtar in control of fertility and
vegetation on earth. Ereshkigal is therefore the sister of Ishtar and from one
point of view her counterpart, the symbol of nature during the non-
productive season of the year. As the doctrine of two kingdoms, one of this
world and one of the world of the dead, becomes crystallized, the
dominions of the two sisters are sharply differentiated from one another.
The addition of Nergal represents the harmonizing tendency to unite with

Ereshkigal as the queen of the nether-world the god who, in his character as
god of war and of pestilence, conveys the living to Irkalla and thus becomes
the one who presides over the dead.
(M. Ja.)

ERETRIA (mod. Aletria), an ancient coast town of Euboea about 15 m.
S.E. of Chalcis, opposite to Oropus. Eretria, like its neighbour Chalcis
(q.v.), early entered upon a commercial and colonizing career. Besides
founding townships in the west and north of Greece, it acquired
dependencies among the Cyclades and joined the great mercantile alliance
of Miletus and Aegina. Since the so-called Lelantine War (7th century b.c.)
against the coming league of Chalcis, it began to be overshadowed by its
rivals. The interference of Eretria in the Ionian revolt (498) brought upon it
the vengeance of the Persians, who captured and destroyed it shortly before
the battle of Marathon (490). The city was soon rebuilt, and as a member of
both the Delian Leagues attached itself by numerous treaties to the
Athenians. The latter, through their general Phocion, rescued it from the
tyrants suborned by Philip of Macedon (354 and 341). Under Macedonian
and Roman rule Eretria fell into insignificance; for a short period under
Mark Antony, the triumvir, it became a possession of Athens. Eretria was
the birthplace of the tragedian Achaeus and of the “Megarian” philosopher
Menedemus.

The modern village, which is sometimes called Nea Psará because the
inhabitants of Psará were transferred there in 1821, is on unhealthy low-
lying ground near the sea. The excavation of the site was carried out by the

American School of Athens (1890-1895). At the foot of the Acropolis Hill,
where the ground begins to rise, the theatre lies; and though the material of
which this was built is rough, and only seven imperfect rows of seats
remain, a good part of the scena and of the chambers behind it is preserved,
and beneath these there runs a tunnel, which, together with other peculiar
features, has raised interesting questions in connexion with the arrangement
of the Greek theatre, the orchestra being at present on a level about 12 ft.
below that of the rooms in the scena. Near by are the substructions of a
temple of Dionysus and a large altar, and also a gymnasium with
arrangements for bathing. Besides these, in 1900 the substructions of a
temple of Apollo Daphnephoros were unearthed. Both the northern and the
southern side of the hill are flanked by walls, which seem to have reached
the sea, where there was a mole and a harbour; and the wall of the acropolis
itself remains in one part to the height of eight courses.

Authorities.—Strabo x. 447 f.; Herodotus v. 99, vi. 101; Corpus
Inscr. Atticarum, i. 339, iv. (2), pp. 5, 10, 22; H. Heinze, De rebus
Eretriensium (Göttingen, 1869); W.M. Leake, Travels in Northern
Greece (London, 1835), ii. 266, 443; B.V. Head, Historia numorum
(Oxford, 1887), pp. 305-308; Papers of the American School at Athens,
vol. vi.
(E. Gr.)

ERETRIAN SCHOOL OF PHILOSOPHY. This Greek school was the
continuation of the Elian school, which was transferred to Eretria by
Menedemus. It was of small importance, and in the absence of certain

knowledge must be supposed to have adhered to the doctrines of Socrates.
(See Menedemus.)

ERFURT, a city of Germany, in Prussian Saxony, on the Gera, and the
railway Halle-Bebra, about midway between Gotha and Weimar, which are
14 m. distant. Pop. (1875) 48,025; (1905) 100,065. The city, which is
dominated on the west by the two citadels of Petersberg and Cyriaxburg, is
irregularly built, the only feature in its plan, or want of plan, being the
Friedrich Wilhelmsplatz, a broad open space of irregular shape abutting on
the Petersberg. On the south-western side of this square, which contains a
monument to the elector Frederick Charles Joseph of Mainz (1719-1802), is
the Domberg, an eminence on which stand, side by side, the cathedral and
the great church of St Severus with its three spires (14th century). The
churches are approached by a flight of forty-eight stone steps, the grouping
of the whole mass of buildings being exceedingly impressive. The cathedral
(Beatae Mariae Virginis) is one of the finest churches in Germany. It was
begun in the 12th century, but the nave was rebuilt in the 13th in the Gothic
style. The magnificent chancel (1349-1372), with the 14th-century crypt
below, rests on massive substructures, known as the Cavate. The twin
towers are set between the chancel and nave. The cathedral contains,
besides fine 15th-century glass, some very rich portal sculptures and bronze
castings, among others the coronation of the Virgin by Peter Vischer. In one
of its towers is the famous bell, called Maria Gloriosa, which bears the date
1497, and weighs 270 cwt. Besides the cathedral and St Severus, which are
Roman Catholic, Erfurt possesses several very interesting medieval

churches, now Evangelical. Among these may be mentioned the
Predigerkirche, dating from the latter half of the 12th century; the
Reglerkirche, a Romanesque building (restored in 1859) with a 12th-
century tower; and the Barfüsserkirche, a Gothic building containing fine
14th-century monuments. All these were originally monastic churches. Of
the former religious houses there survive a Franciscan convent, with a girls’
school attached, and an Ursuline convent. The Augustinian monastery, in
which Luther lived as a friar, is now used as an orphanage, under the name
of the Martinsstift. The cell of Luther was destroyed by fire in 1872. A
bronze statue of the reformer was erected in the Anger, the chief street of
the town, in 1890. At one time Erfurt had a university, of which the charter
dated from 1392; but it was suppressed in 1816, and its funds devoted to
other purposes, among these being the endowment of an institution founded
in 1758 and now called the royal academy of sciences, and the support of
the royal library, which now contains 60,000 volumes and over 1000
manuscripts. On the W. and S.W. extensive new quarters have grown up
within recent years, e.g. Hirschbrühl. The interior of the town hall (1869-
1875) is adorned with legendary and historical frescoes by Kämpfer and
Peter Janssen. Erfurt possesses also a picture gallery and an antiquarian
collection.

The educational establishments of the town include a gymnasium, a
realgymnasium, a realschule, technical schools for building and handicrafts,
a high-class commercial school, a school of agriculture, and an academy of
music. The most notable industry of Erfurt is the culture of flowers and of
vegetables, which is very extensively carried on. This industry had its origin
in the large gardens attached to the monasteries. It has also important and
growing manufactures of ladies’ mantles, boots and shoes, machines,
furniture, woollen goods, musical instruments, agricultural machinery and
implements, leather, tobacco, chemicals, &c. Brewing, bleaching and

dyeing are also carried on on a large scale, and there are extensive railway
works and a government rifle factory.

Erfurt (Med. Erpesfurt, Erphorde, Lat. Erfordia) is a town of great
antiquity. Its origin is obscure, but in 741 it was sufficiently important for St
Boniface to found a bishopric here, which was, however, after the
martyrdom of the first bishop, Adolar, in 755, reabsorbed in that of Mainz.
In 805 the place received certain market rights from the emperor
Charlemagne. Later the overlordship was claimed by the archbishops of
Mainz, on the strength of charters granted by the emperor Otto I., and their
authority in Erfurt was maintained by a burgrave and an advocatus, the
office of the latter becoming in the 12th century hereditary in the family of
the counts of Gleichen. In spite of many vicissitudes (from 1109 to 1137,
for instance, the town was subject to the landgraves of Thuringia), and of a
charter granted in 1242 by the emperor Frederick II., the archbishops
succeeded in upholding their claims. In 1255, however, Archbishop Gerhard
I. had to grant the city municipal rights, the burgraviate disappeared, and
Erfurt became practically a free town. Its power was at its height early in
the 15th century, when it joined the Hanseatic League. It had acquired by
force or purchase various countships and other fiefs in the neighbourhood,
and ruled a considerable territory; and its wealth was so great that in 1378 it
established a university, the first in Europe that embraced the four faculties.
By the end of the century, however, its prosperity had sunk owing to the
perpetual feud with Mainz, the internecine war in Saxony, and the
consequent dwindling of trade. By the convention of Amorbach in 1483 the
overlordship of Erfurt was ultimately transferred by the electors of Mainz to
Saxony. The political and religious quarrels of the 16th century still further
depressed the city, in which the reformed religion was established in 1521.
Then came the Thirty Years’ War, during which Erfurt was for a while
occupied by the Swedes. After the peace of Westphalia (1648) the city was
assigned by the emperor to the elector of Mainz, and, on its refusal to

submit, it was placed under the ban of the Empire (1660). In 1664 it was
captured by the troops of the archbishop of Mainz, and remained in the
possession of the electorate till 1802, when it came into the possession of
Prussia. In 1808 it was the scene of the memorable interview between
Napoleon and the emperor Alexander I. of Russia, at which the kings of
Bavaria, Saxony, Westphalia and Württemberg also assisted, which is
known as the congress of Erfurt. Here in 1850 the parliament of the short-
lived Prussian Northern Union (known as the Erfurt parliament) held its
sittings. In 1902 the 100th anniversary of the city’s incorporation with
Prussia was celebrated.

See W.J.A. von Tettau, Erfurt in seiner Vergangenheit und
Gegenwart (Erfurt, 1880); C. Beyer, Geschichte der Stadt Erfurt
(Erfurt, 1900); and F.W. Kampschulte, Die Universität Erfurt in ihrem
Verhältnisse zu dem Humanismus und der Reformation (1856-1858).
For a detailed bibliography see U. Chevalier, Répertoire des sources.
Topo-bibliographie (Montebéliard, 1894-1899), s.v.

ERGOT, or Spurred Rye, the drug ergota or Secale cornutum (Ger.
Mutterkorn; Fr. seigle ergoté), consisting of the sclerotium (or hard resting
condition) of a fungus, Claviceps purpurea, parasitic on the pistils of many
members of the Grass family, but obtained almost exclusively from rye,
Secale cereale. In the ear of rye that is infected with ergot a species of
fermentation takes place, and there exudes from it a sweet yellowish mucus,
which after a time disappears. The ear loses its starch, and ceases to grow,
and its ovaries become penetrated with the white spongy tissue of the

mycelium of the fungus which towards the end of the season forms the
sclerotium, in which state the fungus lies dormant through the winter.

The drug consists of grains, usually curved (hence the name, from the O.
Fr. argot, a cock’s spur), which are violet-black or dark-purple externally,
and whitish with a tinge of pink within, are between 1⁄3 and 1½ in. long, and
from 1 to 4 lines broad, and have two lateral furrows, a close fracture, a
disagreeable rancid taste, and a faint, fishy odour, which last becomes more
perceptible when the powder of the drug is mixed with potash solution.
Ergot should be kept in stoppered bottles in order to preserve it from the
attacks of a species of mite, and to prevent the oxidation of its fatty oil.

The extremely complex composition of this drug has been studied in
great detail, and with such important results that instead of giving ergot
itself by the mouth in doses of 20 to 60 grains, it is now possible to obtain
much more rapid and certain results by giving one three-hundredth of a
grain of one of its constituents hypodermically. This constituent is the
alkaloid cornutine, which is the valuable ingredient of the drug. Other
ingredients are a fixed oil, present to the extent of 30%, ergotinic acid, a
glucoside, trimethylamine, which gives the drug its unpleasant odour, and
sphacelinic acid, a non-nitrogenous resinoid body. Of the numerous
preparations only two need be mentioned—the liquid extract (dose 10
minims to 2 drachms or more), and the hypodermic injection. The latter
does not keep well, and the best way of using ergot is to dissolve tablets
obtained from a reputable maker, and containing some of the active
principles, in pure water, the solution being injected subcutaneously.

Ergot has no external action. Given internally it stimulates the intestinal
muscles and may cause diarrhoea. After absorption it slows the pulse by
stimulation of the vagus nerves. It has indeed been asserted that the slow
pulse characteristic of the puerperal period is really due to the common
administration of ergot at that time. This is probably an exaggeration. The

important actions of ergot are on the blood-vessels and the uterus. The drug
greatly raises the blood-pressure by causing extreme contraction of the
arteries. This is mainly due to a direct action on the muscular coats of the
vessels, but is also partly of central origin, since the drug also stimulates the
vaso-motor centre in the medulla oblongata. This action on the vessels is so
marked as to constitute the drug a haemostatic, not only locally but also
remotely. It may arrest bleeding from the nose, for instance, when injected
hypodermically. Nearly all the constituents share in causing this action, but
the sphacelinic acid is probably the most potent. Ergot is the most powerful
known stimulant of the pregnant uterus. The action is a double one. At least
four of its constituents act directly on the muscular fibre of the uterus,
whilst the cornutine acts through the nerves. Of great practical importance
is the fact that the cornutine causes rhythmic contractions such as naturally
occur, whilst the sphacelinic acid produces a tonic contraction of the uterus,
which is unnatural and highly inimical to the life of the foetus. Ergot is used
in therapeutics as a haemostatic, and is very valuable in haemoptysis and
sometimes in haematemesis. But its great use is in obstetrics. The drug
should regularly be given hypodermically, and it is important to note that if
the injection be made immediately under the skin, an abscess, or
considerable discomfort, may ensue. The injection should be intra-
muscular, the needle being boldly plunged into a muscular mass, such as
that of the deltoid or the gluteal region. The indications for the use of ergot
in obstetrics are highly complex and demand detailed treatment. It can only
be said here that the drug should only in the rarest possible cases be given
whilst the child is still in utero. This rule is necessitated by the sphacelinic
acid, which causes an unnatural state of the organ. When it is possible to
obtain pure cornutine, which is unfortunately very expensive, the
precautions necessary in other cases may be abrogated.

Chronic poisoning, or ergotism, used frequently to occur amongst the
poor fed on rye infected with the Claviceps. As it is practically impossible

to reproduce the symptoms of ergotism nowadays, whether experimentally
in the lower animals, or when the drug is being administered to a human
being for some therapeutic purpose, it is believed that the symptoms of
ergotism were rendered possible only by the semi-starvation which must
have ensued from the use of such rye-bread; for the grain disappears as the
fungus develops. There were two types of ergotism. In the gangrenous form
various parts of the body underwent gangrene as a consequence of the arrest
of blood-supply produced by the action of sphacelinic acid on the arteries.
In the spasmodic form the symptoms were of a nervous character. The
initial indications of the disease were cutaneous itching, tingling and
formication, which gave place to actual loss of cutaneous sensation, first
observed in the extremities. Amblyopia and some loss of hearing also
occurred, as well as mental failure. With weakness of the voluntary muscles
went intermittent spasms which weakened the patient and ultimately led to
death by implication of the respiratory muscles. The last-known “epidemic”
of ergotism occurred in Lorraine and Burgundy in the year 1816.

ERIC XIV. (1533-1577), king of Sweden, was the only son of Gustavus
Vasa and Catherine of Saxe-Lauenburg. The news of his father’s death
reached Eric as he was on the point of embarking for England to press in
person his suit for the hand of Queen Elizabeth. He hastened back to
Stockholm, after burying his father, summoned a Riksdag, which met at
Arboga on the 15th of April 1561, and adopted the royal propositions
known as the Arboga articles, considerably curtailing the authority of the
royal dukes, John and Charles, in their respective provinces. Two months

later Eric was crowned at Upsala, on which occasion he first introduced the
titles of baron and count into Sweden, by way of attaching to the crown the
higher nobility, these new counts and barons receiving lucrative fiefs
adequate to the maintenance of their new dignities.

From the very beginning of his reign Eric’s morbid fear of the upper
classes drove him to give his absolute confidence to a man of base origin
and bad character, though, it must be admitted, of superior ability. This was
Göran Persson, born about 1530, who had been educated abroad in
Lutheran principles, and after narrowly escaping hanging at the hands of
Gustavus Vasa for some vile action entered the service of his son. This
powerful upstart was the natural enemy of the nobility, who suffered much
at his hands, though it is very difficult to determine whether the initiative in
these prosecutions proceeded from him or his master. Göran was also a
determined opponent of Duke John, with whom Eric in 1563 openly
quarrelled, because John, contrary to the royal orders, had married (Oct. 4,
1562) Catherine, daughter of Sigismund I. of Poland, engaging at the same
time to assist the Polish king to conquer Livonia. This act was a flagrant
breach of that paragraph of the Arboga articles which forbade the royal
dukes to contract any political treaty without the royal assent. An army of
10,000 men was immediately sent by Eric to John’s duchy of Finland, and
John and his consort were seized, brought over to Sweden and detained as
prisoners of state in Gripsholm Castle. But Eric did not stop here. His
suspicion suggested to him that, if his own brother failed him, the loyalty of
the great nobles, especially the members of the ancient Sture family, who
had been notable in Sweden when the Vasas were unknown, could not be
depended upon. The head of the Sture family at this time was Count Svante,
who had married a sister of Gustavus Vasa’s second wife, and had by her a
numerous family, of whom two sons, Nils and Eric, still survived. The dark
tragedy, known as the Sture murders, began with Eric XIV.’s strange
treatment of young Count Nils. In 1566 he was summoned before a newly

erected tribunal and condemned to death for gross neglect of duty, though
not one of the frivolous charges brought against him could be substantiated.
The death penalty was commuted into a punishment worse because more
shameful than death. On the 15th of June 1566 the unfortunate youth,
bruised and bleeding from shocking ill-treatment, was placed upon a
wretched hack, with a crown of straw on his head, and led in derision
through the streets of Stockholm. The following night he was sent a
prisoner to the fortress of Örbyhus. A few days later he was appointed
ambassador extraordinary, and despatched to Lorraine to resume the
negotiations for Eric’s marriage with the princess Renata. Before he
returned, however, Eric had resolved to marry Karin, or Kitty Månsdatter,
the daughter of a common soldier, who had been his mistress since 1565. In
January 1567 Eric extorted a declaration from two of his senators that they
would assist him to punish all who should try to prevent his projected
marriage; and, in the middle of May, a Riksdag was summoned to Upsala to
judge between the king and those of the aristocracy whom he regarded as
his personal enemies. Eric himself arrived at Upsala on the 16th in a
condition of incipient insanity. On the 19th he opened parliament in a
speech which, as he explained, he had to deliver extempore owing to “the
treachery” of his secretary. Two days later Nils Sture arrived at Upsala fresh
from his embassy to Lorraine, and was at once thrown into prison, where
other members of the nobility were already detained. On the following day
Eric murdered Nils in his cell with his own hand, and by his order the other
prisoners were despatched by the royal provost marshal forthwith. These
murders were committed so promptly and secretly that it is doubtful
whether the estates, actually in session at the same place, knew what had
been done when, on the 26th of May, under violent pressure from Göran
Persson, they signed a document declaring that all the accused gentlemen
under detention had acted like traitors, and confirming all sentences already
passed or that might be passed upon them.

During the greater part of 1567 Eric was so deranged that a committee of
senators was appointed to govern the kingdom. One of his illusions was that
not he was king but his brother John, whom he now set at liberty. When, at
the beginning of 1568, Eric recovered his reason, a reconciliation was
effected between the king and the duke, on condition that John recognized
the legality of his brother’s marriage with Karin Månsdatter, and her
children as the successors to the throne. A month later, on the 4th of July, he
was solemnly married to Karin at Stockholm by the primate. The next day
Karin was crowned queen of Sweden and her infant son Gustavus
proclaimed prince-royal. Shortly after his marriage Eric issued a circular
ordering a general thanksgiving for his delivery from the assaults of the
devil. This document, in every line of which madness is legible, convinced
most thinking people that Eric was unfit to reign. The royal dukes, John and
Charles, had already taken measures to depose him; and in July the
rebellion broke out in Östergötland. Eric at first offered a stout resistance
and won two victories; but on the 17th of September the dukes stood before
Stockholm, and Eric, after surrendering Göran Persson to the horrible
vengeance of his enemies, himself submitted, and resigned the crown. On
the 30th of September 1568 John III. was proclaimed king by the army and
the nobility; and a Riksdag, summoned to Stockholm, confirmed the choice
and formally deposed Eric on the 25th of January 1569. For the next seven
years the ex-king was a source of the utmost anxiety to the new
government. No fewer than three rebellions, with the object of releasing and
reinstating him, had to be suppressed, and his prison was changed half a
dozen times. On the 10th of March 1575, an assembly of notables, lay and
clerical, at John’s request, pronounced a formal sentence of death upon him.
Two years later, on the 24th of February 1577, he died suddenly in his new
prison at Örbyhus, poisoned, it is said, by his governor, Johan Henriksen.

See Sveriges Historia, vol. iii. (Stockholm, 1880); Robert Nisbet
Bain, Scandinavia, cap. 4-6 (Cambridge, 1905); Eric Tegel, Konung

Eriks den XIV. historia (Stockholm, 1751). (R. N. B.)

ERICACEAE, in
botany, a natural order of
plants belonging to the
higher or gamopetalous
division of Dicotyledons.
They are woody plants,
sometimes with a slender
creeping stem as in
bilberry, Vaccinium (fig.
1), or Andromeda (fig. 2),
or forming low bushes as
in the heaths, or larger,
sometimes becoming tree-
like, as in species of
Rhododendron. The
leaves are alternate,
opposite or whorled in
Fig. 1.—Vaccinium vitis-idaea, with leaf and flower,
arrangement, and in their nat. size. 1, Flower of V. myrtillus, cut lengthwise. 2,
Fruit of same.
form and structure show
well-marked adaptation
for life in dry or exposed situations. Thus in the true heaths they are needle-
like, with the margins often rolled back to form a groove or an almost
closed chamber on the under side. In others such as Rhododendron or

Arbutus they are often leathery and evergreen, the strongly cuticularized
upper surface protecting a water-storing tissue situated above the green
layers of the leaf. The flowers are sometimes solitary and axillary or
terminal as in Andromeda, but are generally arranged in racemose
inflorescences at the end of the branches as in Arbutus and Rhododendron,
or on small lateral shoots as in Erica. They are hermaphrodite and generally
regular with parts in 4 or 5, thus: sepals 4 or 5, petals 4 or 5, stamens 8 or
10 in two series, the outer of which is opposite the petals, and carpels 4 or
5. The corolla is usually more or less bell-shaped, and in the heaths persists
in a dry state in the fruit. The petals with the stamens are situated on the
outer edge of a honey-secreting disk. The anthers show a very great variety
in shape, the halves are often more or less free and often appendaged; they
open to allow the escape of the pollen by a terminal pore or slit. The carpels
are united to form a 4- to 5-chambered ovary, which bears a simple
elongated style ending in a capitate stigma; each ovary-chamber contains
one to many ovules attached to a central placenta. The brightly coloured
corolla, the presence of nectar and the scent render the flowers attractive to
insects, and the projection of the stigma beyond the anthers favours
crossing. The fruit is generally a capsule containing many seeds, as in Erica
(fig. 3) or Rhododendron; sometimes a berry as in Arbutus.

Fig. 2.—Andromeda Hypnoides, nat. size. 1, Flower; 2, Unripe fruit cut across; 3, Stamen—all
enlarged.

Fig. 3.

1, Flowering shoot of Erica cinerea, about 4, Capsule showing the loculicidal
1½ nat. size. dehiscence; a few seeds remain
2, Flower cut lengthwise. attached to the central axis.
3, Stamen showing appendages and 5, Diagram of the flower having four
porous dehiscence of anther. sepals, four divisions of the corolla,
eight stamens in two rows, and four
divisions of the pistil.

The order falls into four distinct tribes, which are characterized by the
relative position of the ovary and by the fruit and seed. They are as follows:
—

1. Rhododendron tribe, characterized by capsular fruit, seed with a loose
coat, deciduous petals and anthers without appendages. It consists mainly of
the great genus Rhododendron (in which Azalea is included by recent
botanists), which is chiefly developed in the mountains of eastern Asia,
many species occurring on the Himalayas. Dabeocia, St Dabeoc’s heath,
occurs in Ireland.

2. Arbutus Tribe.—Fruit a berry or capsule, petals deciduous and anthers
with bristle-like appendages, chiefly north temperate to arctic in
distribution. Arbutus Unedo, the strawberry-tree, so called from its large
scarlet berry, is a southern European species which extends into south
Ireland. Arctostaphylos (bearberry) and Andromeda are arctic and alpine
genera occurring in Britain. Epigaea repens is the trailing arbutus or
mayflower of Atlantic America.

3. Vaccinium Tribe.—Ovary inferior, fruit a berry. Extends from the north
temperate zone to the mountains of the tropics. Vaccinium, the largest
genus, has four British species: V. Myrtillus is the bilberry(q.v.), blaeberry
or whortleberry, V. Vitis-Idaea the cowberry, and V. Oxycoccos the cranberry

(q.v.). This tribe is sometimes regarded as a separate order Vacciniaceae,
distinguished by its inferior ovary.

4. Erica Tribe.—Fruit usually a capsule, seeds round, not winged; corolla
persisting round the ripe fruit; anthers often appendaged. The largest genus
is Erica, the true heath (q.v.), with over 400 species, the great majority of
which are confined to the Cape; others occur on the mountains of tropical
Africa and in Europe and North Africa, especially the Mediterranean
region. E. cinerea (purple heather) and E. Tetralix (cross-leaved heath) are
common British heaths. Calluna is the ling or Scotch heather.

ERICHSEN, SIR JOHN ERIC, Bart. (1818-1896), British surgeon,
born on the 19th of July 1818 at Copenhagen, was the son of Eric Erichsen,
a member of a well-known Danish family. He studied medicine at
University College, London, and at Paris, devoting himself in the early
years of his career to physiology, and lecturing on general anatomy and
physiology at University College hospital. In 1844 he was secretary to the
physiological section of the British Association, and in 1845 he was
awarded the Fothergillian gold medal of the Royal Humane Society for his
essay on asphyxia. In 1848 he was appointed assistant surgeon at University
College hospital, and in 1850 became full surgeon and professor of surgery,
his lectures and clinical teaching being much admired; and in 1875 he
joined the consulting staff. His Science and Art of Surgery (1853) went
through many editions. He rose to be president of the College of Surgeons
in 1880. From 1879 to 1881 he was president of the Royal Medical and
Chirurgical Society. He was created a baronet in 1895, having been for

some years surgeon-extraordinary to Queen Victoria. As a surgeon his
reputation was world-wide, and he counts (says Sir W. MacCormac in his
volume on the Centenary of the Royal College of Surgeons) “among the
makers of modern surgery.” He was a recognized authority on concussion
of the spine, and was often called to give evidence in court on obscure cases
caused by railway accidents, &c. He died at Folkestone on the 23rd of
September 1896.

ERICHT, LOCH, a lake partly in Inverness-shire and partly in
Perthshire, Scotland, lying between the districts of Badenoch on the N. and
Rannoch on the S. The boundary line is drawn from a point opposite to the
mouth of the Alder, and follows the centre of the longitudinal axis north-
eastwards to 56° 50′ N., where it strikes eastwards to the shore. All of the
lake to the S. and E. of this line belongs to Perthshire, the rest, forming the
major portion, to Inverness-shire. It is a lonely lake, situated in extremely
wild surroundings at a height of 1153 ft. above the sea, being thus the
loftiest lake of large size in the United Kingdom. It is over 14½ m. long,
with a mean breadth of half a mile and over 1 m. at its maximum. Its area
amounts to some 7¼ sq. m., and it receives the drainage of an area of nearly
50½ sq. m. The mean depth is 189 ft., and the maximum 512 ft. It has a
general trend from N.E. to S.W., the head lying 1 m. from Dalwhinnie
station on the Highland railway. It receives many streams, and discharges at
the south-western extremity by the Ericht. Salmon and trout afford good
fishing. The surrounding mountains are lofty and rugged. Ben Alder (3757
ft.) on the west shore is the chief feature of the great Corrour deer forest.

The only point of interest on the banks is the cavern, near the mouth of the
Alder, in which Prince Charles Edward concealed himself for a time after
the battle of Culloden.

ERICSSON, JOHN (1803-1889), Swedish-American naval engineer,
was born at Langbanshyttan, Wermland, Sweden, on the 31st of July 1803.
He was the second son of Olaf Ericsson, an inspector of mines, who died in
1818. Showing from his earliest years a strong mechanical bent, young
Ericsson, at the age of twelve, was employed as a draughtsman by the
Swedish Canal Company. From 1820 to 1827 he served in the army, where
his drawing and military maps attracted the attention of the king, and he
soon attained the rank of captain. In 1826 he went to London, at first on
leave of absence from his regiment, and in partnership with John
Braithwaite constructed the “Novelty,” a locomotive engine for the
Liverpool & Manchester railway competition at Rainhill in 1829, when the
prize, however, was won by Stephenson’s “Rocket.” The number of
Ericsson’s inventions at this period was very great. Among other things he
worked out a plan for marine engines placed entirely below the water-line.
Such engines were made for the “Victory,” for Captain (afterwards Sir)
John Ross’s voyage to the Arctic regions in 1829, but they did not prove
satisfactory. In 1833 his caloric engine was made public. In 1836 he took
out a patent for a screw-propeller, and though the priority of his invention
could not be maintained, he was afterwards awarded a one-fifth share of the
£20,000 given by the Admiralty for it. At this time Captain Stockton, of the
United States navy, gave an order for a small iron vessel to be built by Laird

of Birkenhead, and to be fitted by Ericsson with engines and screw. This
vessel reached New York in May 1839. A few months later Ericsson
followed his steamer to New York, and there he resided for the rest of his
life, establishing himself as an engineer and a builder of iron ships. In 1848
he was naturalized as a citizen of the United States. He had many
difficulties to contend with, and it was only by slow degrees that he
established his fame and won his way to competence. At his death he seems
to have been worth about £50,000. The provision of defensive armour for
ships of war had long occupied his attention, and he had constructed plans
and a model of a vessel lying low in the water, carrying one heavy gun in a
circular turret mounted on a turntable. In 1854 he sent his plans to the
emperor of the French. Louis Napoleon, however, acting probably on the
advice of Dupuy de Lôme, declined to use them. The American Civil War,
and the report that the Confederates were converting the “Merrimac” into
an ironclad, caused the navy department to invite proposals for the
construction of armoured ships. Among others, Ericsson replied, and as it
was thought that his design might be serviceable in inland waters, the first
armoured turret ship, the “Monitor,” was ordered; she was launched on the
30th of January 1862, and on the 9th of March she fought the celebrated
action with the Confederate ram “Merrimac.” The peculiar circumstances in
which she was built, the great importance of the battle, and the decisive
nature of the result gave the “Monitor” an exaggerated reputation, which
further experience did not confirm. In later years Ericsson devoted himself
to the study of torpedoes and sun motors. He published Solar Investigations
(New York, 1875) and Contributions to the Centennial Exhibition (New
York, 1877). He died in New York on the 8th of March 1889, and in the
following year, on the request of the Swedish government, his body was
sent to Stockholm and thence into Wermland, where, at Filipstad, it was
buried on the 15th of September.

A Life of Ericsson by William Conant Church was published in New
York in 1890 and in London in 1893.

ERIDANUS, or Fluvius (“the river”), in astronomy, a constellation of
the southern hemisphere, mentioned by Eudoxus (4th century b.c.) and
Aratus (3rd century b.c.); Ptolemy catalogued 34 stars in it. θ Eridani, a fine
double star of magnitudes 3.5 and 5.5, is now of the third magnitude. It is
supposed to be identical with the Achernar of Al-Sufi, who described it as
of the first magnitude; this star has therefore decreased in brilliancy in
historic times. The star ο2 Eridani (numbered 40 by Flamsteed) was
discovered to be a ternary star group by Herschel in 1783; it consists of a
close pair, of magnitudes 9.2 and 10.9, revolving in a period of 180 years,
associated with a star of magnitude 4.5, which is distant from the pair by
82″; these stars have an exceptionally swift proper motion, about 4″ per
annum. Eridanus was the ancient name of the river Po.

ERIDU, one of the oldest religious centres of the Sumerians, described
in the ancient Babylonian records as the “city of the deep.” The special god
of this city was Ea (q.v.), god of the sea and of wisdom, and the prominence
given to this god in the incantation literature of Babylonia and Assyria
suggests not only that many of our magical texts are to be traced ultimately

to the temple of Ea at Eridu, but that this side of the Babylonian religion
had its origin in that place. Certain of the most ancient Babylonian myths,
especially that of Adapa, may also be traced back to the shrine of Ea at
Eridu. But while of the first importance in matters of religion, there is no
evidence in Babylonian literature of any special political importance
attaching to Eridu, and certainly at no time within our knowledge did it
exercise hegemony in Babylonia. The site of Eridu was discovered by J.E.
Taylor in 1854, in a ruin then called by the natives Abu-Shahrein, a few
miles south-south-west of Moghair, ancient Ur, nearly in the centre of the
dry bed of an inland sea, a deep valley, 15 m. at its broadest, covered for the
most part with a nitrous incrustation, separated from the alluvial plain about
Moghair by a low, pebbly, sandstone range, called the Hazem, but open
toward the north to the Euphrates and stretching southward to the Khanega
wadi below Suk-esh-Sheiukh. In the rainy season this valley becomes a sea,
flooded by the discharge of the Khanega; in summer the Arabs dig holes
here which supply them with brackish water. The ruins, in which Taylor
conducted brief excavations, consist of a platform of fine sand enclosed by
a sandstone wall, 20 ft. high, the corners toward the cardinal points, on the
N.W. part of which was a pyramidal tower of two stages, constructed of
sun-dried brick, cased with a wall of kiln-burned brick, the whole still
standing to a height of about 70 ft. above the platform. The summit of the
first stage was reached by a staircase on the S.E. side, 15 ft. wide and 70 ft.
long, constructed of polished marble slabs, fastened with copper bolts,
flanked at the foot by two curious columns. An inclined road led up to the
second stage on the N.W. side. Pieces of polished alabaster and marble,
with small pieces of pure gold and gold-headed copper nails, found on and
about the top of the second stage, indicated that a small but richly adorned
sacred chamber, apparently plated within or without in gold, formerly
crowned the top of this structure. Around the whole tower was a pavement
of inscribed baked bricks, resting on a layer of clay 2 ft. thick. On the S.E.

part of the terrace were the remains of several edifices, containing suites of
rooms. Inscriptions on the bricks identified the site as that of Eridu. Since
Taylor’s time the place has not been visited by any explorer, owing to the
unsafe condition of the neighbourhood; but T.K. Loftus (1854) and J.P.
Peters (1890) both report having seen it from the summit of Moghair. The
latter states that the Arabs at that time called the ruin Nowawis, and
apparently no longer knew the name Abu-Shahrein. Through an error, in
many recent maps and Assyriological publications Eridu is described as
located in the alluvial plain, between the Tigris and the Euphrates. It was, in
fact, an island city in an estuary of the Persian Gulf, stretching up into the
Arabian plateau. Originally “on the shore of the sea,” as the old records
aver, it is now about 120 m. from the head of the Persian Gulf. Calculating
from the present rate of deposit of alluvium at the head of that gulf, Eridu
should have been founded as early as the seventh millennium b.c. It is
mentioned in historical inscriptions from the earliest times onward, as late
as the 6th century b.c. From the evidence of Taylor’s excavations, it would
seem that the site was abandoned about the close of the Babylonian period.

See J.E. Taylor, Journal of the Royal Asiatic Society, vol. xv. (1855);
F. Delitzsch, Wo lag das Paradies? (1881); J.P. Peters, Nippur (1897);
M. Jastrow, The Religion of Babylonia and Assyria (1898); H.V.
Hilprecht, Excavations in Assyria and Babylonia (1904); L.W. King, A
History of Sumer and Akkad (1910).
(J. P. Pe.)

ERIE, the most southerly of the Great Lakes of North America, between
41° 23′ and 42° 53′ N., and 78° 51′ and 83° 28′ W., bounded W. by the state
of Michigan, S. and S.E. by Ohio, Pennsylvania and New York, and N. by
the province of Ontario. It is nearly elliptical, the major axis, 250 m. long,
lying east and west; its greatest breadth is 60 m.; its area about 10,000 sq.
m.; and the total area of its basin 34,412 sq. m. Its elevation above mean
sea-level is 573 ft.; and its surface is nearly 9 ft. below that of Lake Huron,
which discharges into it through St Clair river, Lake St Clair and Detroit
river, and is 327 ft. above that of Lake Ontario, this great difference being
absorbed by the rapids and falls in the Niagara river, which joins the two
lakes. Lake Erie is very shallow, and may be divided into three basins, the
western extending to Point Pelee and including all the islands, containing
about 1200 sq. m., with a comparatively flat bottom at 5 to 6 fathoms; the
main basin, between Point Pelee and the narrows at Long Point, containing
about 6700 sq. m., and having a marked shelving bottom deepening
gradually to 14 fathoms; and the portion east of the narrows, containing
about 2100 sq. m., having a depression 30 fathoms deep just east from Long
Point, with an extensive flat of 11 fathoms depth between it and the main
basin. The Canadian shore is low and flat throughout, the United States
shore is low but bordered by an elevated plateau through which the rivers
have cut deep channels. The lake basin is relatively so small that the rivers
are without importance; Grand river, on the north shore, is the largest
tributary. The flat alluvial soil bordering on the lake is very fertile, and the
climate is well adapted for fruit cultivation. Large quantities of peaches,
grapes and small fruits are grown; the islands in the west end have a climate
much warmer and more equable than the adjoining mainland, and are
practically covered with vineyards. The low clayey or sandy shores are
subject to erosion by waves. In severe storms the water near shore is filled
with sand, which is deposited where the currents are checked around the
ends of jetties in such a way as to form bars out into the lake across

improved channels. This shoaling has rendered continuous dredging
necessary at every harbour on the lake west of Erie, Pa. In consequence of
the shallowness of the lake its waters are easily disturbed, making
navigation very rough and dangerous, and causing large fluctuations of
surface. Strong winds are frequent, as nearly every cyclonic depression
traversing North America, either from the westward or the Gulf of Mexico,
passes near enough to Lake Erie to be felt. Westerly gales are more
frequent, and have more effect on the water surface than easterly ones,
lowering the water as much as 7 to 8 ft. at the west end and raising it 5 to 8
ft. at the east end. The worst storms occur in autumn, when the immense
quantity of shipping on the lake makes them specially destructive. There are
no tides, and usually only a slight current towards the outlet, though
powerful currents are temporarily produced by the rapid return of waters
after a storm, and during the height of a westerly gale there is invariably a
reflex current into the west end of the lake. There is an annual fluctuation in
the level of the lake, varying from a minimum of 9 in. to a maximum of 2
ft., the normal low level occurring in February and the high level in
midsummer. Standard high water (of 1838) is 575.11 ft. above mean sea-
level, and the lowest record was 570.8 in November 1895. The harbours
and exits of the lake freeze over, but the body of the lake never freezes
completely.

Ice-breaking car ferries run across the lake all winter. General navigation
opens as a rule in the middle of April and closes in the middle of December.
The volume of traffic is immense, because practically all freight from the
more westerly lakes finds terminal harbours in Lake Erie. Official statistics
of commerce passing through the Detroit river into the lake during the
season of 1906 show that 35,128 vessels, having a net register of
50,673,897 tons, carried 63,805,571 (short) tons of freight, valued at
$662,971,053. The 1175 vessels engaged in this business were valued at
$106,223,000. Over 90% of the whole traffic is in United States ships to

United States ports. Fine passenger steamers run nightly between Buffalo
and Cleveland and Detroit, and there are many shorter passenger routes.

The large traffic on Lake Erie has brought into existence a number of
important harbours on the south shore, nearly all artificially made and
deepened, with entrances between two breakwaters running into the lake at
right angles to the coast line. The principal of these are Toledo, Sandusky,
Huron, Vermilion, Lorain, Cleveland, Fairport, Ashtabula, Conneaut, Erie (a
natural harbour), Dunkirk and Buffalo, Rondeau, Port Stanley, Port
Burwell, Port Dover, Port Maitland and Port Colborne. The Miami and Erie
canal, leading from Maumee river to Cincinnati, 244½ m., with a branch to
Port Jefferson, 14 m., with locks 90 by 15 by 4 ft., connects with Lake Erie
through Toledo. The Erie canal leading from Buffalo to the Hudson river at
Troy, and connecting with Lake Ontario at Oswego, had a capacity for boats
98 ft. long, 17 ft. 10 in. beam, with 6 ft. draught, until in 1907 the State of
New York undertook its deepening to accommodate boats of 1000 tons
capacity. Buffalo from its position at the eastern limit of deep draught lake
navigation is a city of first rate commercial importance. Its harbour is
formed by an artificial breakwater, built parallel with the shore about half a
mile distant from it. It receives practically all the Lake Erie grain shipments
besides large quantities of iron ore, lumber and copper, and is a large
shipping port for coal, principally anthracite. It has over 600 m. of railway
tracks to accommodate lake freights. The Welland canal, 26¾ m. long,
connecting Lake Ontario and Lake Erie, with locks 270 by 45 by 14 ft.,
leaves Lake Erie at Port Colborne, where the Canadian government have
constructed an artificial harbour and elevators for transhipment of grain
from upper lake freighters to lighters of canal capacity.

Fishing operations are carried on extensively in Lake Erie, the fish being
taken with gill nets, seines and pound nets. Each state touching the lake has
its own fishery regulations, which differ amongst themselves as well as

from those of the Dominion. Both nations maintain a Fishery Protection
Service, and the fisheries are replenished from artificial hatcheries. The
most numerous and valuable fish are the lesser white fish (Coregonus
artedi, Le Sueur), pickerel (Stizostedion vitreum, Walb.), pike (Lucius
lucius, L.), and white fish (Coregonus clupeiformis, Mitchill), in the order
named. The fish caught are estimated to be worth annually $1,000,000.
They are collected in fishing tugs and distributed by rail throughout the
United States and Canada.

Bibliography.—Bulletin No. 17, Survey of Northern and North-
western Lakes, U.S. Lake Survey Office, War Dept. (Detroit, 1907);
U.S. Hydrographic Office, Publication No. 108D, Sailing Directions
for Lake Erie, &c. (Washington, 1902); Sailing Directions for the
Canadian Shore of Lake Erie, Department of Marine and Fisheries
(Ottawa, 1897); J.O. Curwood, The Great Lakes (New York, 1909); E.
Channing and M.F. Lansing, The Great Lakes (New York, 1909).
(W. P. A.)

ERIE, a city, a port of entry, and the county-seat of Erie county,
Pennsylvania, U.S.A., on Lake Erie, 148 m. by rail N. of Pittsburg and near
the N.W. corner of the state. Pop. (1890) 40,634; (1900) 52,733, of whom
11,957 were foreign-born, including 5226 from Germany and 1468 from
Ireland, and 26,797 were of foreign parentage (both parents foreign-born),
including 13,316 of German parentage and 4203 of Irish parentage; (1910
census) 66,525. Erie is served by the New York, Chicago & St Louis, the
Lake Shore & Michigan Southern, the Erie & Pittsburg (Pennsylvania

Company), the Philadelphia & Erie (Pennsylvania railway), and the
Bessemer & Lake Erie railways, and by steamboat lines to many important
lake ports. The city extends over an area of about 7 sq. m., which for the
most part is quite level and is from 50 to 175 ft. above the lake. Erie has a
fine harbour about 4 m. in length, more than 1 m. in width, and with an
average depth of about 20 ft.; it is nearly enclosed by Presque Isle, a long
narrow strip of land of about 3000 acres from 300 ft. to 1 m. in width, and
the national government has protected its entrance and deepened its channel
by constructing two long breakwaters. Most of the streets of the city are 60
ft. wide—a few are 100 ft.—and nearly all intersect at right angles; they are
paved with brick and asphalt, and many in the residential quarters are
shaded with fine elms and maples. The city has four parks, in one of which
is a soldiers’ and sailors’ monument of granite and bronze, and not far away,
along the shore of lake and bay, are several attractive summer resorts.
Among Erie’s more prominent buildings are the United States government
building, the city hall, the public library, and the county court house. The
city’s charitable institutions consist of two general hospitals, each of which
has a training school for nurses; a municipal hospital, an orphan asylum, a
home for the friendless, two old folks’ homes, and a bureau of charities;
here, also, on a bluff, within a large enclosure and overlooking both lake
and city, is the state soldiers’ and sailors’ home, and near by is a monument
erected to the memory of General Anthony Wayne, who died here on the
15th of December 1796.

Erie is the commercial centre of a large and rich grape-growing and
agricultural district, has an extensive trade with the lake ports and by rail
(chiefly in coal, iron ore, lumber and grain), and is an important
manufacturing centre, among its products being iron, engines, boilers, brass
castings, stoves, car heaters, flour, malt liquors, lumber, planing mill
products, cooperage products, paper and wood pulp, cigars and other
tobacco goods, gas meters, rubber goods, pipe organs, pianos and

chemicals. In 1905 the city’s factory products were valued at $19,911,567,
the value of foundry and machine-shop products being $6,723,819, of flour
and grist-mill products $1,444,450, and of malt liquors $882,493. The
municipality owns and operates its water-works.

On the site of Erie the French erected Fort Presque Isle in 1753, and
about it founded a village of a few hundred inhabitants. George
Washington, on behalf of the governor of Virginia, came in the same year to
Fort Le Bœuf (on the site of the present Waterford), 20 m. distant, to protest
against the French fortifying this section of country. The protest, however,
was unheeded. The village was abandoned in or before 1758, owing
probably to an epidemic of smallpox, and the fort was abandoned in 1759.
It was occupied by the British in 1760, but on the 22nd of June 1763 this
was one of the several forts captured by the Indians during the Conspiracy
of Pontiac. In 1764 the British regained nominal control and retained it until
1785, when it passed into the possession of the United States. The place
was laid out as a town in 1795; in 1800 it became the county-seat of the
newly-erected county of Erie; it was incorporated as a borough in 1805, the
charter of that year being revised in 1833; and in 1851 it was incorporated
as a city. At Erie were built within less than six months most of the vessels
with which Commodore Oliver H. Perry won his naval victory over the
British off Put-in-Bay on the 10th of September 1813.

ERIGENA, JOHANNES SCOTUS (c. 800-c. 877), medieval
philosopher and theologian. His real name was Johannes Scotus (Scottus) or
John the Scot. The combination Johannes Scotus Erigena has not been

traced earlier than Ussher and Gale; even Gale uses it only in the heading of
the version of St Maximus. The date of Erigena’s birth is very uncertain,
and there is no evidence to show definitely where he was born. The name
Scotus, which has often been taken to imply Scottish origin, really favours
the theory that he was an Irishman according to the then usage of Scotus or
Scotigena. Prudentius, bishop of Troyes, definitely states that he was of
Irish extraction. The pseudonym commonly read Erigena, used by himself
in the titles of his versions of Dionysius the Areopagite, is Ierugena (in later
MSS. Erugena and Eriugena), formed apparently on the analogy of
Graiugena (“Greek-born”), which he applies to St Maximus. There seems
no reason to doubt that Eriugena is connected with Erin, the name for
Ireland, and Ierugena suggests the Greek ἱερός, ἱερὸς, νῆσος being a
common name for Ireland. On the other hand, William of Malmesbury
prefers to read Heruligena, which would make Scotus a Pannonian, while
Bale says he was born at St David’s, Dempster connects him with Ayr, and
Gale with Eriuven in Hereford. Some early writers thought there were two
persons, John Scotus and John Erigena.

Of Erigena’s early life nothing is known. Bale quotes the story that he
travelled in Greece, Italy and Gaul, and studied not only Greek, but also
Arabic and Chaldaean. Since, however, Bale describes him as “ex patricio
genitore natus,” it is a reasonable inference (so R.L. Poole) that Bale
confused him with one John, the son of Patricius, a Spaniard, who tells
much the same story of his own travels. The knowledge of Greek displayed
in Erigena’s works is not such as to compel us to conclude that he had
actually visited Greece. That he had a competent acquaintance with Greek
is manifest from his translations of Dionysius the Areopagite and of
Maximus, from the manner in which he refers to Aristotle, and from his
evident familiarity with Neoplatonist writers and the fathers of the early
church. Roger Bacon, in his severe criticism on the ignorance of Greek

displayed by the most eminent scholastic writers, expressly exempts
Erigena, and ascribes to him a knowledge of Aristotle in the original.

Among other legends which have at various times been attached to
Erigena are that he was invited to France by Charlemagne, and that he was
one of the founders of the university of Paris. The only portion of Erigena’s
life as to which we possess accurate information was that spent at the court
of Charles the Bald. Charles invited him to France soon after his accession
to the throne, probably in the year 843, and placed him at the head of the
court school (schola palatina). The reputation of this school seems to have
increased greatly under Erigena’s leadership, and the philosopher himself
was treated with indulgence by the king. William of Malmesbury’s amusing
story illustrates both the character of Scotus and the position he occupied at
the French court. The king having asked, “Quid distat inter sottum et
Scottum?” Erigena replied, “Mensa tantum.”

The first of the works known to have been written by Erigena during this
period was a treatise on the eucharist, which has not come down to us (by
some it has been identified with a treatise by Ratramnus, De corpore et
sanguine Domini). In it he seems to have advanced the doctrine that the
eucharist was merely symbolical or commemorative, an opinion for which
Berengarius was at a later date censured and condemned. As a part of his
penance Berengarius is said to have been compelled to burn publicly
Erigena’s treatise. So far as we can learn, however, Erigena’s orthodoxy
was not at the time suspected, and a few years later he was selected by
Hincmar, archbishop of Reims, to defend the doctrine of liberty of will
against the extreme predestinarianism of the monk Gottschalk
(Gotteschalchus). The treatise De divina praedestinatione, composed on
this occasion, has been preserved, and from its general tenor one cannot be
surprised that the author’s orthodoxy was at once and vehemently
suspected. Erigena argues the question entirely on speculative grounds, and

starts with the bold affirmation that philosophy and religion are
fundamentally one and the same—“Conficitur inde veram esse
philosophiam veram religionem, conversimque veram religionem esse
veram philosophiam.” Even more significant is his handling of authority
and reason, to which we shall presently refer. The work was warmly
assailed by Drepanius Florus, canon of Lyons, and Prudentius, and was
condemned by two councils—that of Valence in 855, and that of Langres in
859. By the former council his arguments were described as Pultes
Scotorum (“Scots porridge”) and commentum diaboli (“an invention of the
devil”).

Erigena’s next work was a Latin translation of Dionysius the Areopagite
(see Dionysius Areopagiticus) undertaken at the request of Charles the
Bald. This also has been preserved, and fragments of a commentary by
Erigena on Dionysius have been discovered in MS. A translation of the
Areopagite’s pantheistical writings was not likely to alter the opinion
already formed as to Erigena’s orthodoxy. Pope Nicholas I. was offended
that the work had not been submitted for approval before being given to the
world, and ordered Charles to send Erigena to Rome, or at least to dismiss
him from his court. There is no evidence, however, that this order was
attended to.

The latter part of his life is involved in total obscurity. The story that in
882 he was invited to Oxford by Alfred the Great, that he laboured there for
many years, became abbot at Malmesbury, and was stabbed to death by his
pupils with their “styles,” is apparently without any satisfactory foundation,
and doubtless refers to some other Johannes. Erigena in all probability
never left France, and Hauréau has advanced some reasons for fixing the
date of his death about 877.

Erigena is the most interesting figure among the middle-age writers. The
freedom of his speculation, and the boldness with which he works out his

logical or dialectical system of the universe, altogether prevent us from
classing him along with the scholastics properly so called. He marks,
indeed, a stage of transition from the older Platonizing philosophy to the
later and more rigid scholasticism. In no sense whatever can it be affirmed
that with Erigena philosophy is in the service of theology. The above-
quoted assertion as to the substantial identity between philosophy and
religion is indeed repeated almost totidem verbis by many of the later
scholastic writers, but its significance altogether depends upon the selection
of one or other term of the identity as fundamental or primary. Now there is
no possibility of mistaking Erigena’s position: to him philosophy or reason
is first, is primitive; authority or religion is secondary, derived. “Auctoritas
siquidem ex vera ratione processit, ratio vero nequaquam ex auctoritate.
Omnis enim auctoritas, quae vera ratione non approbatur, infirma videtur
esse. Vera autem ratio, quum virtutibus suis rata atque immutabilis munitur,
nullius auctoritatis adstipulatione roborari indiget” (De divisione naturae, i.
71). F.D. Maurice, the only historian of note who declines to ascribe a
rationalizing tendency to Erigena, obscures the question by the manner in
which he states it. He asks his readers, after weighing the evidence
advanced, to determine “whether he (Erigena) used his philosophy to
explain away his theology, or to bring out what he conceived to be the
fullest meaning of it.” These alternatives seem to be wrongly put.
“Explaining away theology” is something wholly foreign to the philosophy
of that age; and even if we accept the alternative that Erigena endeavours
speculatively to bring out the full meaning of theology, we are by no means
driven to the conclusion that he was primarily or principally a theologian.
He does not start with the datum of theology as the completed body of truth,
requiring only elucidation and interpretation; his fundamental thought is
that of the universe, nature, τὸ πᾶν, or God, as the ultimate unity which
works itself out into the rational system of the world. Man and all that
concerns man are but parts of this system, and are to be explained by

reference to it; for explanation or understanding of a thing is determination
of its place in the universal or all. Religion or revelation is one element or
factor in the divine process, a stage or phase of the ultimate rational life.
The highest faculty of man, reason, intellectus, intellectualis visio, is that
which is not content with the individual or partial, but grasps the whole and
thereby comprehends the parts. In this highest effort of reason, which is
indeed God thinking in man, thought and being are at one, the opposition of
being and thought is overcome. When Erigena starts with such propositions,
it is clearly impossible to understand his position and work if we insist on
regarding him as a scholastic, accepting the dogmas of the church as
ultimate data, and endeavouring only to present them in due order and
defend them by argument.

Erigena’s great work, De divisione naturae, which was condemned
by a council at Sens, by Honorius III. (1225), who described it as
“swarming with worms of heretical perversity,” and by Gregory XIII.
in 1585, is arranged in five books. The form of exposition is that of
dialogue; the method of reasoning is the syllogistic. The leading
thoughts are the following. Natura is the name for the universal, the
totality of all things, containing in itself being and non-being. It is the
unity of which all special phenomena are manifestations. But of this
nature there are four distinct classes:—(1) that which creates and is not
created; (2) that which is created and creates; (3) that which is created
and does not create; (4) that which neither is created nor creates. The
first is God as the ground or origin of all things, the last is God as the
final end or goal of all things, that into which the world of created
things ultimately returns. The second and third together compose the
created universe, which is the manifestation of God, God in processu,
Theophania. Thus we distinguish in the divine system beginning,
middle and end; but these three are in essence one—the difference is
only the consequence of our finite comprehension. We are compelled to

envisage this eternal process under the form of time, to apply temporal
distinctions to that which is extra- or supra-temporal. The universe of
created things, as we have seen, is twofold:—first, that which is created
and creates—the primordial ideas, archetypes, immutable relations,
divine acts of will, according to which individual things are formed;
second, that which is created and does not create, the world of
individuals, the effects of the primordial causes, without which the
causes have no true being. Created things have no individual or self-
independent existence; they are only in God; and each thing is a
manifestation of the divine, theophania, divina apparitio.

God alone, the uncreated creator of all, has true being. He is the true
universal, all-containing and incomprehensible. The lower cannot
comprehend the higher, and therefore we must say that the existence of
God is above being, above essence; God is above goodness, above
wisdom, above truth. No finite predicates can be applied to him; his
mode of being cannot be determined by any category. True theology is
negative. Nevertheless the world, as the theophania, the revelation of
God, enables us so far to understand the divine essence. We recognize
his being in the being of all things, his wisdom in their orderly
arrangement, his life in their constant motion. Thus God is for us a
Trinity—the Father as substance or being (οὐσία), the Son as wisdom
(δύναμις), the Spirit as life (ἐνέργια). These three are realized in the
universe—the Father as the system of things, the Son as the word, i.e.
the realm of ideas, the Spirit as the life or moving force which
introduces individuality and which ultimately draws back all things
into the divine unity. In man, as the noblest of created things, the
Trinity is seen most perfectly reflected; intellectus (νοῦς), ratio
(λογος) and sensus (διάνοια) make up the threefold thread of his
being. Not in man alone, however, but in all things, God is to be
regarded as realizing himself, as becoming incarnate.

The infinite essence of God, which may indeed be described as
nihilum (nothing) is that from which all is created, from which all
proceeds or emanates. The first procession or emanation, as above
indicated, is the realm of ideas in the Platonic sense, the word or
wisdom of God. These ideas compose a whole or inseparable unity, but
we are able in a dim way to think of them as a system logically
arranged. Thus the highest idea is that of goodness; things are, only if
they are good; being without well-being is naught. Essence participates
in goodness—that which is good has being, and is therefore to be
regarded as a species of good. Life, again, is a species of essence,
wisdom a species of life, and so on, always descending from genus to
species in a rigorous logical fashion.

The ideas are the eternal causes, which, under the moving influence
of the spirit, manifest themselves in their effects, the individual created
things. Manifestation, however, is part of the being or essence of the
causes, that is to say, if we interpret the expression, God of necessity
manifests himself in the world and is not without the world. Further, as
the causes are eternal, timeless, so creation is eternal, timeless. The
Mosaic account, then, is to be looked upon merely as a mode in which
is faintly shadowed forth what is above finite comprehension. It is
altogether allegorical, and requires to be interpreted. Paradise and the
Fall have no local or temporal being. Man was originally sinless and
without distinction of sex. Only after the introduction of sin did man
lose his spiritual body, and acquire the animal nature with its
distinction of sex. Woman is the impersonation of man’s sensuous and
fallen nature; on the final return to the divine unity, distinction of sex
will vanish, and the spiritual body will be regained.

The most remarkable and at the same time the most obscure portion
of the work is that in which the final return to God is handled.

Naturally sin is a necessary preliminary to this redemption, and Erigena
has the greatest difficulty in accounting for the fact of sin. If God is
true being, then sin can have no substantive existence; it cannot be said
that God knows of sin, for to God knowing and being are one. In the
universe of things, as a universe, there can be no sin; there must be
perfect harmony. Sin, in fact, results from the will of the individual
who falsely represents something as good which is not so. This
misdirected will is punished by finding that the objects after which it
thirsts are in truth vanity and emptiness. Hell is not to be regarded as
having local existence; it is the inner state of the sinful will. As the
object of punishment is not the will or the individual himself, but the
misdirection of the will, so the result of punishment is the final
purification and redemption of all. Even the devils shall be saved. All,
however, are not saved at once; the stages of the return to the final
unity, corresponding to the stages in the creative process, are
numerous, and are passed through slowly. The ultimate goal is
deificatio, theosis or resumption into the divine being, when the
individual soul is raised to a full knowledge of God, and where
knowing and being are one. After all have been restored to the divine
unity, there is no further creation. The ultimate unity is that which
neither is created nor creates.

Editions.—There is a complete edition of Erigena’s works in J.P.
Migne’s Patrologiae cursus completus (vol. cxxii.), edited by H.J.
Floss (Paris, 1853). The De divina praedestinatione was published in
Gilbert Mauguin’s Veterum auctorum qui nono saeculo de
praedestinatione et gratia scripserunt opera et fragmenta (Paris,
1650). The commentary (“Expositiones”) on Dionysius’ Hierarchiae
caelestes appeared in the Appendix ad opera edita ab A. Maio (ed. J.
Cozza, Rome, 1871). Of the De divisione naturae, editions have been
published by Thomas Gale (Oxford, 1681); C.B. Schlüter (Münster,

1838); and in Floss’s Opera omnia; there is a German translation by
Ludwig Noack, Johannes Scotus Erigena über die Eintheilung der
Natur (3 vols., 1874-1876). Erigena was also the author of some poems
edited by L. Traube in Monumenta Germaniae historica. Poëtae Latini
aevi Carolini, iii. (1896). A commentary on the Opuscula sacra of
Boëtius is attributed to him and edited by E.K. Rand (1906).
Monographs on Erigena’s life and works are numerous; see St René
Taillandier, Scot Érigène et la philosophie scholastique (1843); T.
Christlieb, Leben u. Lehre des Johannes Scotus Erigena (Gotha, 1860);
J.N. Huber, Johannes Scotus Erigena (Munich, 1861); W. Kaulich, Das
speculative System des Johannes Scotus Erigena (Prague, 1860); A.
Stöckl, De Joh. Scoto Erigena (1867); L. Noack, Über Leben und
Schriften des Joh. Scotus Erigena: die Wissenschaft und Bildung seiner
Zeit (Leipzig, 1876); R.L. Poole, Medieval Thought (1884), and article
in Dictionary of National Biography; T. Wotschke, Fichte und Erigena
(Halle, 1896); M. Baumgartner in Wetzer and Welte’s Kirchenlexikon,
x. (1897); Alice Gardner’s Studies in John the Scot (1900); J. Dräseke,
Joh. Scotus Erigena und seine Gewährsmänner (Leipzig, 1902); S.M.
Deutsch in Herzog-Hauck’s Realencyklopädie für protestantische
Theologie, xviii. (1906); J.E. Sandys, Hist. of Classical Scholarship
(1906), pp. 491-495. See also the general works on scholastic
philosophy, especially Hauréau, Stöckl and Kaulich. An admirable
résumé is given by F.D. Maurice, Medieval Phil. pp. 45-79.
(R. Ad.; J. M. M.)

ERIGONE, in Greek mythology, daughter of Icarius, the hero of the
Attic deme Icaria. Her father, who had been taught by Dionysus to make
wine, gave some to some shepherds, who became intoxicated. Their
companions, thinking they had been poisoned, killed Icarius and buried him
under a tree on Mount Hymettus (or threw his body into a well). Erigone,
guided by her faithful dog Maera, found his grave, and hanged herself on
the tree. Dionysus sent a plague on the land, and all the maidens of Athens,
in a fit of madness, hanged themselves like Erigone. Icarius, Erigone and
Maera were set among the stars as Boötes (or Arcturus), Virgo and Procyon.
The festival called Aeora (the “swing”) was subsequently instituted to
propitiate Icarius and Erigone. Various small images (in Lat. oscilla) were
suspended on trees and swung backwards and forwards, and offerings of
fruit were made (Hyginus, Fab. 130, Poët. astron. ii. 4; Apollodorus iii. 14).
The story was probably intended to explain the origin of these oscilla, by
which Dionysus, as god of trees (Dendrites), was propitiated, and the
baneful influence of the dog-star averted (see also Oscilla).

ERIN, an ancient name for Ireland. The oldest form of the word is Ériu,
of which Érinn is the dative case. Ériu was itself almost certainly a
contraction from a still more primitive form Iberiu or Iveriu; for when the
name of the island was written in ancient Greek it appeared as Ἰουερνιά
(Ivernia), and in Latin as Iberio, Hiberio or Hibernia, the first syllable of
the word Ériu being thus represented in the classical languages by two
distinct vowel sounds separated by b or v. Of the Latin variants, Iberio is
the form found in the most ancient Irish MSS., such as the Confession of St

Patrick, and the same saint’s Epistle to Coroticus. Further evidence to the
same effect is found in the fact that the ancient Breton and Welsh names for
Ireland were Ywerddon or Iverdon. In later Gaelic literature the primitive
form Ériu became the dissyllable Éire; hence the Norsemen called the
island the land of Éire, i.e. Ireland, the latter word being originally
pronounced in three syllables. (See Ireland: Notices of Ireland in Greek
and Roman writers.) Nothing is known as to the meaning of the word in any
of its forms, and Whitley Stokes’s suggestion that it may have been
connected with the Sanskrit avara, meaning “western,” is admittedly no
more than conjecture. There was, indeed, a native Irish legend, worthless
from the standpoint of etymology, to account for the origin of the name.
According to this myth there were three kings of the Dedannans reigning in
Ireland at the coming of the Milesians, named MacColl, MacKecht and
MacGrena. The wife of the first was Eire, and from her the name of the
country was derived. Curiously, Ireland in ancient Erse poetry was often
called “Fodla” or “Bauba,” and these were the wives of the other two kings
in the legend.

ERINNA, Greek poet, contemporary and friend of Sappho, a native of
Rhodes or the adjacent island of Telos, flourished about 600 (according to
Eusebius, 350 b.c.). Although she died at the early age of nineteen, her
poems were among the most famous of her time and considered to rank
with those of Homer. Of her best-known poem, Ἠλακάτη (the Distaff),
written in a mixture of Aeolic and Doric, which contained 300 hexameter

lines, only 4 lines are now extant. Three epigrams in the Palatine anthology,
also ascribed to her, probably belong to a later date.

The fragments have been edited (with those of Alcaeus) by J.
Pellegrino (1894).

ERINYES (Lat. Furiae), in Greek mythology, the avenging deities,
properly the angry goddesses or goddesses of the curse pronounced upon
evil-doers. According to Hesiod (Theog. 185) they were the daughters of
Earth, and sprang from the blood of the mutilated Uranus; in Aeschylus
(Eum. 321) they are the daughters of Night, in Sophocles (O.C. 40) of
Darkness and Earth. Sometimes one Erinys is mentioned, sometimes
several; Euripides first spoke of them as three in number, to whom later
Alexandrian writers gave the names Alecto (unceasing in anger), Tisiphone
(avenger of murder), Megaera (jealous). Their home is the world below,
whence they ascend to earth to pursue the wicked. They punish all offences
against the laws of human society, such as perjury, violation of the rites of
hospitality, and, above all, the murder of relations. But they are not without
benevolent and beneficent attributes. When the sinner has expiated his
crime they are ready to forgive. Thus, their persecution of Orestes ceases
after his acquittal by the Areopagus. It is said that on this occasion they
were first called Eumenides (“the kindly”), a euphemistic variant of their
real name. At Athens, however, where they had a sanctuary at the foot of the
Areopagus hill and a sacred grove at Colonus, their regular name was
Semnae (venerable). Black sheep were sacrificed to them during the night
by the light of torches. A festival was held in their honour every year,

superintended by a special priesthood, at which the offerings consisted of
milk and honey mixed with water, but no wine. In Aeschylus, the Erinyes
are represented as awful, Gorgon-like women, wearing long black robes,
with snaky locks, bloodshot eyes and claw-like nails. Later, they are winged
maidens of serious aspect, in the garb of huntresses, with snakes or torches
in their hair, carrying scourges, torches or sickles. The identification of
Erinyes with Sanskrit Saranyu, the swift-speeding storm cloud, is rejected
by modern etymologists; according to M. Bréal, the Erinyes are the
personification of the formula of imprecation (ἀρά), while E. Rohde sees in
them the spirits of the dead, the angry souls of murdered men.

See C.O. Müller, Dissertations on the Eumenides of Aeschylus, (Eng.
tr., 1835); A. Rosenberg, Die Erinyen (1874); J.E. Harrison,
Prolegomena to the Study of Greek Religion (1903); and Journal of
Hellenic Studies, xix. p. 205, according to whom the Erinyes were
primarily local ancestral ghosts, potent for good or evil after death,
earth genii, originally conceived as embodied in the form of snakes,
whose primitive haunt and sanctuary was the omphalos at Delphi; E.
Rohde, Psyche (1903); A. Rapp in Roscher’s Lexikon der Mythologie,
and J.A. Hild in Daremberg and Saglio’s Dictionnaire des antiquités,
s.v. Furiae.

ERIPHYLE, in Greek mythology, sister of Adrastus and wife of
Amphiaraus. Having been bribed by Polyneices with the necklace of
Harmonia, she persuaded her husband to take part in the expedition of the
Seven against Thebes, although he knew it would prove fatal to him. Before

setting out, the seer charged his sons to slay their mother as soon as they
heard of his death. The attack on Thebes was repulsed, and during the flight
the earth opened and swallowed up Amphiaraus together with his chariot.
His son Alcmaeon, as he had been bidden, slew his mother, and was driven
from place to place by the Erinyes, seeking purification and a new home
(Apollodorus iii. 6. 7).

ERIS, in Greek mythology, a sister of the war-god Ares (Homer, Iliad, iv.
440), and in the Hesiodic theogony (225) a daughter of Night. In the later
legends of the Trojan War, Eris, not having been invited to the marriage
festival of Peleus and Thetis, flings a golden apple (the “apple of discord”)
among the guests, to be given to the most beautiful. The claims of the three
deities Hera, Aphrodite and Athena are decided by Paris in favour of
Aphrodite, who as a reward assists him to gain possession of Helen
(Hyginus, Fab. 92; Lucian, Charidemus, 17). Hesiod also mentions (W. and
D. 24) a beneficent Eris, the personification of honourable rivalry. In Virgil
(Aeneid, viii. 702) and other Roman poets Eris is represented by Discordia.

ERITH, an urban district in the north-western parliamentary division of
Kent, England, 14 m. E. by S. of London, on the South Eastern & Chatham
railway. Pop. (1891) 13,414; (1901) 25,296. It lies on the south bank of the

Thames and extends up the hills above the shore, many villas having been
erected on the higher ground. The park of a former seat, Belvedere, was
thus built over (c. 1860), and the mansion became a home for disabled
seamen. The church of St John the Baptist, though largely altered by
modern restoration, retains Early English to Perpendicular portions, and
some early monuments and brasses. Erith has large engineering and gun
factories, and in the neighbourhood are gunpowder, oil, glue and manure
works. The southern outfall works of the London main drainage system are
at Crossness in the neighbouring lowland called Plumstead Marshes. Erith
is the headquarters of several yacht clubs. Erith, the name of which is
commonly derived from A.S. Ærra-hythe (old haven), was anciently a
borough, and was granted a market and fairs in 1313. Down to the close of
the 17th century it was of some importance as a naval station.

ERITREA, an Italian colony on the African coast of the Red Sea. It
extends from Ras Kasar, a cape 110 m. S. of Suakin, in 18° 2′ N., as far as
Ras Dumeira (12° 42′ N.), in the Strait of Bab-el-Mandeb, a coast-line of
about 650 m. The colony is bounded inland by the Anglo-Egyptian Sudan,
Abyssinia and French Somaliland. It consists of the coast lands lying
between the capes named and of part of the northern portion of the
Abyssinian plateau. The total area is about 60,000 sq. m. The population is
approximately 450,000, of which, exclusive of soldiers, not more than 3000
are whites.

The land frontier starting from Ras Kasar runs in a south-westerly
direction until in about 14° 15′ N., 36° 35′ E. it reaches the river Setit, some

distance above the junction of that stream with the Atbara. This, the farthest
point inland, is 198 m. S.W. of Massawa. The frontier now turns east,
following for a short distance the course of the river Setit; thence it strikes
north-easterly to the Mareb, and from 38° E. follows that river and its
tributaries the Belesa and Muna, until within 42 m. of the sea directly south
of Annesley Bay. At this point the frontier turns south and east, crossing the
Afar or Danakil country at a distance of 60 kilometres (37.28 m.) from the
coast-line. About 12° 20′ N. the French possessions in Somaliland are
reached. Here the frontier turns N.E. and so continues until the coast of the
Red Sea is again reached at a point south of the town of Raheita. In the
southern part of the colony are small sultanates, such as those of Aussa and
Raheita, which are under Italian protection. The Dahlak archipelago and
other groups of islands along the coast belong to Eritrea.

Physical Features.—The coast-line is of coral formation and is, in
the neighbourhood of Massawa, thickly studded with small islands.
The chief indentations are Annesley Bay, immediately south of
Massawa, and Assab Bay in the south. The colony consists of two
widely differing regions. The northern division is part of the
Abyssinian highlands. The southern division, part of the Afar or
Danakil country, includes all the territory of the colony south of
Annesley Bay. These two regions are connected by a narrow strip of
land behind Annesley Bay, where the Abyssinian hills approach close
to the sea. From this bay the coast-line trends S.E. so that at Tajura Bay
the distance between the Abyssinian hills and the sea is over 200 m.
The Afar country is part of the East African rift-valley, and in the
southern parts of the valley its surface is diversified by ranges of hills,
frequently volcanic, and by lakes. The plains, however, extend over
large areas, they are generally arid and are often covered with mimosa
trees which form a kind of jungle called by the natives khala. The
torrents which descend from the Abyssinian plateau usually fail to

reach the sea. They are mostly bordered by dense vegetation; in the dry
season water is found in pools in the river beds or can be obtained by
digging. The principal rivers enter and are lost in one or other of two
salt plains or basins, that of Asali in the north and that of Aussa in the
south. The Hawash flows through the Aussa country in a N.E.
direction, but is lost in lakes Abbebad and Aussa (see Abyssinia). The
Raguali and other rivers drain into the Asali basin. This basin, like that
of Aussa, is in places 200 ft. below sea-level. On the west the Asali
basin reaches to the Abyssinian foot-hills; in its southern part is the
small lake Alelbad. The eastern edge of the basin is formed by a ridge
of gypsum and on its margin grow palms. In parts the salt lies thick on
the plain, which then has the appearance of a lake frozen over. South of
Lake Alelbad is a volcano called Artali or Erta-alé (“the smoky”), and
farther to the S.E., in about 13° 15′ N., is the peak of Afdera, which
was in eruption in June 1907. The hills, 1000 to 4000 ft. in height,
which run more or less parallel to and a few miles from the coast,
include the volcano of Dubbi (reported active in 1861), some 30 m. S.
of the port of Edd (Eddi). In 14° 52′ N., 39° 53′ E. and near the
northern end of the zone of depression the volcano of Alid (2985 ft.)
rises from the trough. Its chief crest forms an elongated ring and
encloses a crater over half a mile in diameter and with walls 350 ft.
high. North and south of Alid extends a vast lava field. Dubbi and Alid
are in Italian territory; the greater part of Afar belongs to Abyssinia.

At Annesley Bay the narrow coast plain is succeeded by foothills
separated by small valleys through which flow innumerable streams.
From these hills the ascent to the plateau which constitutes northern
Eritrea is very steep. This tableland, which has a general elevation of
about 6500 ft., is fairly fertile despite a desert region—Sheb—to the
S.E. of Keren. It is characterized by rich, well-watered valleys, verdant
plains and flat-topped hills with steep sides, running in ranges or

isolated. The highest hills in Eritrean territory rise to about 10,000 ft.
The plateau is known by various names, the region directly west of
Massawa being called Hamasen. To the west and north the plateau
sinks in terraces to the plains of the Sudan, and eastward falls more
abruptly to the Red Sea, the coast plain, known as the Samhar,
consisting of sandy country covered with mimosa and, along the khors,
with a somewhat richer vegetation.

The colony contains no navigable streams. For a short distance the
Setit (known in its upper course as the Takazze), a tributary of the
Atbara, forms the frontier, as does also in its upper course the Gash or
Mareb (see Abyssinia). The Mareb, often dry in summer, in the floods
is a large and impassable river. Both the Setit and Mareb have a general
westerly course across the Abyssinian plateau. The Baraka (otherwise
Barka) and Anseba rise in the Hamasen plateau near Asmara within a
short distance of each other. The Baraka flows west and then north; the
Anseba, which has a more easterly course, also flows northward and
joins the Baraka a little N. of 17° N. A few miles below the confluence
the Baraka leaves Italian territory. It is (as is the Anseba) an
intermittent stream. After heavy rain it discharges some of its water
into the Red Sea north of Tokar. The whole of the hill country north of
Asmara belongs to the drainage area of the Baraka or Anseba. Of the
numerous streams which, north of the Danakil country, run direct from
the hills to the Red Sea, the Hadas may be mentioned, as along the
valley of that stream is one of the most frequented routes to the
tableland. The Hadas, in time of flood, reaches the ocean near Adulis in
Annesley Bay.

Climate.—The climate in different parts of the colony varies greatly.
Three distinct climatic zones are found:—(1) that of the coastlands,
including altitudes up to 1650 ft., (2) that of the escarpments and

valleys, and (3) that of the high plateau and alpine summits. In the
coast zone the heat and humidity are excessive during most of the year,
June, September and October being the hottest months. Rains occur
between November and April, during which time the temperature is
lower. In this zone malarial fevers prevail in winter. The heat is greatest
at Massawa, where the mean temperature averages 88° F., but where, in
summer, the thermometer often rises to 120° F. in the shade. In the
second zone the climate is more temperate and there is considerable
variation in temperature owing to nocturnal radiation. This zone falls
within the régime of the summer monsoon rains, while those districts
adjoining the coast zone enjoy also winter rains. August is the most
rainy and May the hottest month. On the high plateau, i.e. the third
zone, the climate is generally moderately cool. Slight rain falls in the
spring and abundant monsoon rains from June to September. The heat
is greatest in the dry season, November to April. Above 8500 ft. the
climate becomes sub-alpine in character.

Flora and Fauna.—In the low country the flora differs little from
that of tropical Africa generally, whilst on the plateau the vegetation is
characteristic of the temperate zone. The olive tree grows on the high
plateau and covers the flanks of the hills to within 3000 ft. of sea-level.
The sycamore-fig tree grows to enormous proportions in parts of the
plateau. Lower down durra, maize and bultuc grow in profusion. In the
northern part of the colony, especially along the Khor Baraka, the dom
palm flourishes. The fauna includes, in the low country, the lion,
panther, elephant, camel, and antelope of numerous species. On the
plateau the fauna is that of Abyssinia (q.v.).

Inhabitants.—The inhabitants of the plains and foothills are for the
most part semi-nomad shepherds, living on durra and milk. In the north
these people are largely of Arab or Hamitic stock, such as the Beni-

Amer, but include various negro tribes. Afar and Somali form the
population of the southern regions. The inhabitants of the plateau are
Abyssinians. The nomads are Mussulmans and are, as a rule, docile and
pacific, though the Danakils are given to occasional raiding. The
Abyssinians are more warlike, but they have settled down under Italian
rule. Among the native industries are mat-weaving, cotton-weaving,
silver-working and rudimentary iron and leather working. (See Afars;
Somaliland and Abyssinia.)

Towns.—The principal places on the coast are Massawa (q.v.), pop.
about 10,000, the chief seaport of the colony, Assab, chief town of the
Danakil region, to which converges the trade from Abyssinia across the
Aussa country, and Zula (q.v.), identified with the ancient Adulis. The
chief town in the interior is Asmara (q.v.), the capital of the colony and
under the Abyssinians capital of the province of Hamasen, and
favourite headquarters of Ras Alula (see below and also Abyssinia). It
is situated 7800 ft. above the sea, and has something of the aspect of a
European town. Keren, 50 m. N.W. of Asmara, is the centre for a
district (Bogos) fertilized by the upper course of the Anseba; Agordat,
on the river Baraka, on the road from Keren to Kassala, is the centre of
the Beni-Amer, Algheden and Sabderat tribes; Mogolo, on the lower
Mareb, is the rendezvous of the Baria and Baza tribes. Towards
Abyssinia the chief towns are Saganeiti (capital of the Okulé-Kusai
province), Godofelassi and Adi-Ugri, the two latter situated in the
fertile plain of the Seraé; Adiquala, on the edge of the Mareb gorge;
and Arrasa, the centre of the districts constituting the province of Deki-
Tesfa.

Agriculture and Trade.—The nomads of the plains possess large
herds of cattle and camels. The low country is almost entirely pastoral
and unsuited for the cultivation of crops. On the other hand almost all

European cereals flourish in the intermediate zone and on the high
plateau, and the Abyssinian is a good agriculturist and understands
irrigation. Numbers of emigrants from Italy possess farms on the
plateau. Experiments in the cultivation of coffee, tobacco and cotton
have given good results in the intermediate zone. Besides camels and
oxen, sheep and goats are numerous, and meat, hides and butter are
articles of local trade. Hides are the principal export (about £50,000 a
year). Wax, gum, coffee and ivory are also exported. Pearl fishing is
carried on at Massawa and the Dahlak islands. The annual value of the
fisheries is about £40,000 (pearls £10,000, mother of pearl £30,000).
Gold mines are worked near Asmara. Salt, obtained from the salt lakes
in the Aussa and Danakil countries, is a valuable article of commerce.
Cotton goods are the chief imports. There is a little trade with northern
Abyssinia, but it is undeveloped. For the five years 1901-1905 the
average value of the external trade was £456,000 per annum. The
imports more than doubled the exports.

Communications.—A railway, 65 m. long, connects Massawa with
Asmara. An extension of the line is planned from Asmara to Sabderat
and Kassala. The whole territory is crossed by camel and mule paths
between the sea and the high plateau, and between the various centres
of population. Every valley that brings water to the Red Sea has a route
leading to the high plateau. The great arteries, however, number three,
which, starting from Massawa by way of Asmara, run, two to
Abyssinia, and one to Kassala and Khartum. They are all more or less
practicable for carts, and are flanked by a good telegraph line as long
as they lie in Italian territory. There are also two caravan routes from
Assab Bay, across the Danakil country to southern Abyssinia. The
northern leads by a comparatively easy ascent to Yejju, the more
southern follows the valley of the Hawash. A telegraph line 500 m.
long connects Massawa with Adis Ababa via Asmara. Massawa is also

telegraphically connected with the outside world by a cable to Perim
via Assab. There is regular steamship communication with Italy.

Administration.—Eritrea is administered by a civil governor
responsible to the ministry of foreign affairs at Rome. It is divided into
six provinces, each governed by a regional commissioner. Some tracts
of frontier territory are detached from the various regions and entrusted
to political residents, as, for instance, on the Sudan frontier and also on
the Abyssinian boundary, where strict surveillance is necessary to
repress raiding incursions from Tigré, and where the chief intelligence
department is established. The six regions or principal provinces are:—
Asmara, which includes Hamasen and other small districts; Keren,
which comprises the high territories to the north of Asmara, i.e. the
Bogos country; Massawa, extending over all the tribes between the
high plateau and the sea from the Hababs to the Danakil; Assab, which
extends from Edd to Raheita; Okulé-Kusai, the plateau country S.E. of
Asmara; Seraé, including Deki-Tesfa, the country S.W. of Asmara. The
regional commissioners and the political residents act either by means
of the village headmen (Shum or Chicca), by the chiefs of districts in
the few localities where villages are still organized in districts, or by
the headmen of tribes, and by the councils of the elders wherever these
remain.

Revenue is derived from customs duties, direct taxation and tribute
paid by the nomad tribes. The local revenue, which for the period
1897-1907 was about £100,000 a year, is supplemented by grants from
Italy, the total cost of the administration being about £400,000 yearly.
Nearly half the expenditure is on the military force maintained.

Justice.—Civil justice for natives is administered, in the first
instance, by the headmen of villages, provinces, tribes, or by councils
of notables (Shumagalle); in appeal, by the residents and regional

tribunals, and, in the last instance, by the colonial court of appeal.
Europeans are entirely under Italian jurisdiction. Penal justice is
administered by Italian judges only. An administrative tribunal settles,
without appeal, questions of tribute, disputes concerning family, village
or tribal landmarks, as well as suits involving the colonial government.
The civil laws for the natives are those established by local usage.
Europeans are answerable to the Italian civil code. Penal laws are the
same as in Italy, except where modified by local usages. Appeal to the
Rome court of cassation is admitted against all penal and civil
sentences.

Defence.—Defence is entrusted to a corps of colonial troops, partly
Italian and partly native; to a militia (milizia mobile) formed by natives
who have already served in the colonial corps; and to the chitet or
general levy which, in time of war, places all male able-bodied
inhabitants under arms. The regional commissioners and political
residents have at their disposal some hundreds of irregular paid soldiers
under native chiefs. In war time these irregulars form part of the
colonial corps, but in time of peace serve as frontier police. The
colonial corps, about 5000 strong, garrisons the chief places of
strategic importance, such as Asmara, Keren and Saganeiti. The
irregular troops, on foot, or mounted on camels, number about 1000
men. The militia consists of 3500 men of all arms, and is intended in
time of war to reinforce the various divisions of the colonial corps. The
chitet yields between 3000 and 4000 men, to be employed on the lines
of communication or in caravan service. All these troops are intended
to ward off a first attack, so as to allow time for the arrival of
reinforcements from Italy. The customs and political surveillance along
the coast is entrusted, afloat, to the Massawa naval station, and, ashore,
to a coastguard company 400 strong stationed at Meder, with
detachments at Assab, Massawa, Raheita, Edd and Taclai.

History.—Traces of the ancient Eritrean civilization are scarce. During
the prosperous periods of ancient Egypt, Egyptian squadrons asserted their
rule over the west Red Sea coast, and under the Ptolemies the port of
Golden Berenice (Adulis?) was an Egyptian fortress, afterwards abandoned.
During the early years of the Roman empire, Eritrea formed part of an
important independent state—that of the Axumites (Assamites). At the end
of the reign of Nero, and perhaps even earlier, the king of the Axumites
ruled over the Red Sea coast from Suakin to the strait of Bab-el-Mandeb,
and traded constantly with Egypt. This potentate called himself “king of
kings,” commanded an army and a fleet, coined money, adopted Greek as
the official language, and lived on good terms with the Roman empire. The
Axumites belonged originally to the Hamitic race, but the immigration of
the Himyaritic tribes of southern Arabia speedily imposed a new language
and civilization. Therefore the ancient Abyssinian language, Geez, and its
living dialects, Amharic and Tigrina, are Semitic, although modified by the
influence of the old Hamitic Agau or Agao. Adulis (Adovlis), slightly to the
north of Zula (q.v.), was the chief Axumite port. From Adulis started the
main road, which led across the high plateau to the capital Axomis (Axum).
Along the road are still to be seen vestiges of cities and inscribed
monuments, such as the Himyaritic inscriptions on the high plateau of
Kohait, the six obelisks with a Saban inscription at Toconda, and an obelisk
with an inscription at Amba Sait. Other monuments exist elsewhere, as well
as coins of the Axumite period with Greek and Ethiopian inscriptions. After
the rise of the Ethiopian empire the history of Eritrea is bound up with that
of Ethiopia, but not so entirely as to be completely fused. The documents of
the Portuguese expedition of the 16th century and other Ethiopian records
show that all the country north of the Mareb enjoyed relative autonomy
under a vassal of the Ethiopian emperor.

Michael, counsellor of Solomon, who was king of the country north of
the Mareb, usurped the throne of Solomon during the reign of the Emperor

Atzié Jasu II. (1729-1753), and, after proclaiming himself ras of Tigré and
“protector of the empire,” ceded the North Mareb country to an enemy of
the rightful dynasty. Hence a long struggle between the dispossessed family
and the occupants of the North Mareb throne. The coast regions had
meantime passed from the control of the Abyssinians. In the 16th century
the Turks made themselves masters of Zula, Massawa, &c., and these places
were never recovered by the Abyssinians. In 1865 Massawa and the
neighbouring coast was acquired by Egypt, the khedive Ismail entertaining
projects for connecting the port by railway with the Nile. The Egyptians
took advantage of civil war in Abyssinia to seize Keren and the Bogos
country in 18721, an action against which the negus Johannes (King John),
newly come to the throne, did not at the time protest. In 1875 and 1876 the
Egyptians, who sought to increase their conquests, were defeated by the
Abyssinians at Gundet and Gura. Walad Michael, the hereditary ruler of
Bogos, fought as ally of King John at Gundet and of the Egyptians at Gura.
For two years Walad Michael continued to harass the border, but in
December 1878 he submitted to King John, by whose orders he was (Sept.
1879) imprisoned upon an amba, or flat-topped mountain, whence he only
succeeded in escaping in 1890. In 1879 his territory was given by King
John to Ras Alula, who retained it until, in August 1889, the Italians
occupied Asmara (see Abyssinia: History).

An Egyptian garrison remained at Keren in the Bogos country until 1884,
when in consequence of the revolt of the Mahdi it was withdrawn, Bogos
being occupied by Abyssinia on the 12th of September of that year. On the
5th of February 1885 an Italian force, with the approval of Great Britain,
occupied Massawa, the Egyptian garrison returning to Egypt. This
occupation led to wars with Abyssinia and finally to the establishment of
the colony in its present limits. The history of the Italian-Abyssinian
relations is fully told in the articles Italy and Abyssinia (history sections).

It was not, however, at Massawa that Italy first obtained a foothold in
eastern Africa. The completion of the Suez Canal led Italy as well as Great
Britain and France to seek territorial rights on the Red Sea coasts. The
purchase of Assab and the neighbouring region for £1880, from the sultan
Berehan of Raheita for use as a coaling station by the Italian Rubattino
Steamship Company, in March 1870, formed the nucleus of Italy’s colonial
possessions. This purchase was protested against by Egypt, Turkey and
Great Britain; the last named power being willing to recognize an Italian
commercial settlement, but nothing more. (The Indian government viewed
the establishment of the Italians on the new highway to the East with a good
deal of ill-humour.) Eventually, the British opposition being overcome and
that of Egypt and Turkey disregarded, Assab, by a decree of the 5th of July
1882, was declared an Italian colony. Between 1883 and 1888 various
treaties were concluded with the sultan of Aussa ceding the Danakil coast to
Italy and recognizing an Italian protectorate over the whole of his country—
through which passes the trade route from Assab Bay to Shoa.

On the 1st of January 1890 the various Italian possessions on the coast of
the Red Sea were united by royal decree into one province under the title of
the Colony of Eritrea—so named after the Erythraeum Mare of the Romans.
At first the government of the colony was purely military, but after the
defeat of the Italians by the Abyssinians at Adowa, the administration was
placed upon a civil basis (1898-1900). The frontiers were further defined by
a French-Italian convention (24th of January 1900) fixing the frontier
between French Somaliland and the Italian possessions at Raheita, and also
by various agreements with Great Britain and Abyssinia. A tripartite
agreement between Italy, Abyssinia and Great Britain, dated the 15th of
May 1902, placed the territory of the Kanama tribe, on the north bank of the
Setit, within Eritrea. A convention of the 16th of May 1908 settled the
Abyssinian-Eritrean frontier in the Afar country, the boundary being fixed
at 60 kilometres from the coast. The task of reconstructing the

administration on a civil basis and of developing the commerce of the
colony was entrusted to Signor F. Martini, who was governor for nine years
(1898-1906). Under civil rule the colony made steady though somewhat
slow progress.

Authorities.—See B. Melli, La Colonia Eritrea dalle sue origini al
anno 1901 (Parma, 1901); G.B. Penne, Per l’Italia Africana. Studio
critico (Rome, 1906); R. Perini, Di qua dal Marèb (Florence, 1905), a
monograph on the Asmara zone; F. Martini, Nell’ Africa Italiana (3rd
ed., Milan, 1891); A.B. Wylde, Modern Abyssinia, chaps. v.-ix.
(London, 1901); E.D. Schoenfeld, Erythräa und der ägyptische Sudân,
chaps. i.-xii. (Berlin, 1904); Luigi Chiala, La Spedizione di Massana
(Turin, 1888); Abyssinian Green Books published at intervals in 1895
and 1896, covering the period from 1870 to the end of the Italo-
Abyssinian War; Vico Mantegazza, La Guerra in Africa (Florence,
1896); General Baratieri, Memorie d’Africa (Rome, 1898); C. de la
Jonquière, Les Italiens en Érythrée (Paris, 1897); G.F.H. Berkeley, The
Campaign of Adowa (London, 1902). For orography and geology see
an article by P. Verri in Boll. Soc. geog. italiana, 1909, and for climate
an article in Rivista coloniale (1906), by A. Tancredi. A. Allori
compiled a Piccolo Dizionario eritreo, italiano-arabo-amarico (Milan,
1895).

For Afar consult W. Munzinger, “A Journey through the Afar
Country” in Journ. Royal Geog. Soc. for 1869; V. Bottego, “Nella Terra
dei Danakil,” in Boll. Soc. Geog. Italiana, 1892; Count C. Rossini, “Al
Rágali” in L’Espl. Comm. of Milan, 1903-1904; and articles by G.
Dainelli and O. Marinelli in the Riv. Geog. Italiana of Florence for
1906-1908, dealing with the volcanic regions.

Bibliographies will be found in G. Fumagalli’s Bibliografia Etiopica
(Milan, 1893) and in the Riv. Geog. Italiana for 1907.

1 During the Second Empire unsuccessful efforts were made by France to obtain a Red
Sea port and a foothold in northern Abyssinia. (See Somaliland: French.)

ERIVAN, a government of Russia, Transcaucasia, having the province of
Kars on the W., the government of Tiflis on the N., that of Elisavetpol on
the N. and E., and Persia and Turkish Armenia on the S. It occupies the top
of an immense plateau (6000-8000 ft.). Continuous chains of mountains are
met with only on its borders, and in the E., but the whole surface is thickly
set with short ridges and isolated mountains of volcanic origin, of which
Alagöz (14,440 ft.) and Ararat (16,925 ft.) are the most conspicuous and the
most important. Both must have been active in Tertiary times. Lake Gok-
cha (540 sq. m.) is encircled by such volcanoes, and the neighbourhood of
Alexandropol is a “volcanic amphitheatre,” being entirely buried under
volcanic deposits. The same is true of the slopes leading down to the river
Aras; and the valley of the upper Aras is a stony desert, watered only by
irrigation, which is carried on with great difficulty owing to the character of
the soil. The government is drained by the Aras, which forms the boundary
with Persia and flows with great velocity down its stony bed, the fall being
17-22 ft. per mile in its upper course, and 9 ft. at Ordubad, where it quits
the government, while lower down it again increases to 23 ft. Many of the
small lakes, filling volcanic craters, are of great depth. Timber is very
scarce. A variety of useful minerals exists, but only rock-salt is obtained, at
Nakhichevan and Kulp. The climate is extremely varied, the following
being the average temperatures and mean annual rainfall at Alexandropol
(alt. 5078 ft.) and Aralykh (2755 ft.) respectively: year 42°, January 12°,
July 65°, mean rainfall 16.2 in.; and year 53°, January 20.5°, July 79°,

rainfall 6.3 in. The population numbered 829,578 in 1897 (only 375,086
women), of whom 82,278 lived in the towns. An estimate in 1906 gave a
total of 909,100. They consist chiefly of Armenians (441,000), Tatars
(40%), Kurds (49,389), with Russians, Greeks and Tates. Most of the
Armenians belong to the Gregorian (Christian) Church, and only 4020 to
the Armenian Catholic Church. The Tatars are mostly Shiite Mussulmans,
only 27,596 being Sunnites; 7772 belong to the peculiar faith of the Yezids.
While barley only can be grown on the high parts of the plateau, cotton,
mulberry, vines and all sorts of fruit are cultivated in the valley of the Aras.
Cattle-breeding is extensively carried on; camels also are bred, and leeches
are collected out of the swamps and exported to Persia. Industry is in its
infancy, but cottons, carpets, and felt goods are made in the villages. A
considerable trade is carried on with Persia, but trade with Asia Minor is
declining. The government is divided into seven districts—Erivan,
Alexandropol, Echmiadzin (chief town, Vagarshapat), Nakhichevan,
Novobayazet, Surmali (chief town, Igdyr), and Sharur-daralagöz (chief
town, Norashen). The principal towns are Erivan (see below), Alexandropol
(32,018 inhabitants in 1897), Novobayazet (8507), Nakhichevan (8845),
and Vagarshapat (3400).

ERIVAN, or Irwan, in Persian, Rewan, a town of Russia, capital of the
government of the same name, situated in 40° 14′ N., 44° 38′ E., 234 m. by
rail S.S.W. of Tiflis, on the Zanga river, from which a great number of
irrigation canals are drawn. Altitude, 3170 ft. Pop. (1873) 11,938; (1897)
29,033. The old Persian portion of the town consists mainly of narrow

crooked lanes enclosed by mud walls, which effectually conceal the houses,
and the modern Russian portion is laid out in long ill-paved streets. On a
steep rock, rising about 600 ft. above the river, stand the ruins of the 16th-
century Turkish fortress, containing part of the palace of the former Persian
governors, a handsome but greatly dilapidated mosque, a modern Greek
church and a cannon foundry. One chamber, called the Hall of the Sardar,
bears witness to former splendour in its decorations. The finest building in
the city is the mosque of Hussein Ali Khan, familiarly known as the Blue
Mosque from the colour of the enamelled tiles with which it is richly
encased. At the mosque of Zal Khan a passion play is performed yearly
illustrative of the assassination of Hussein, the son of Ali. Erivan is an
Armenian episcopal see, and has a theological seminary. The only
manufactures are a little cotton cloth, leather, earthenware and blacksmiths’
work. The fruits of the district are noted for their excellence—especially the
grapes, apples, apricots and melons. Armenians, Persians and Tatars are the
principal elements in the population, besides some Russians and Greeks.
The town fell into the power of the Turks in 1582, was taken by the
Persians under Shah Abbas in 1604, besieged by the Turks for four months
in 1615, and reconquered by the Persians under Nadir Shah in the 18th
century. In 1780 it was successfully defended against Heraclius, prince of
Georgia; and in 1804 it resisted the Russians. At length in 1827 Paskevich
took the fortress by storm, and in the following year the town and
government were ceded to Russia by the peace of Turkman-chai. A Tatar
poem in celebration of the event has been preserved by the Austrian poet,
Bodenstedt, in his Tausend und ein Tage im Orient (1850).

ERLANGEN, a town of Germany, in the kingdom of Bavaria, on a
fertile plain, at the confluence of the Schwabach and the Regnitz, 11 m.
N.W. of Nuremberg, on the railway from Munich to Bamberg. Pop. (1905)
23,720. It is divided into an old and a new town, the latter consisting of
wide, straight and well-built streets. The market place is a fine square. Upon
it stand the town-hall and the former palace of the margraves of Bayreuth,
now the main building of the university. The latter was founded by the
margrave Frederick (d. 1763), who, in 1742, established a university at
Bayreuth, but in 1743 removed it to Erlangen. A statue of the founder,
erected in 1843 by King Louis I. of Bavaria, stands in the centre of the
square and faces the university buildings. The university has faculties of
philosophy, law, medicine and Protestant theology. Connected with it are a
library of over 200,000 volumes, geological, anatomical and mineralogical
institutions, a hospital, several clinical establishments, laboratories and a
botanical garden. Among the churches of the town (six Protestant and one
Roman Catholic), only the new town church, with a spire 220 ft. high, is
remarkable. The chief industries of Erlangen are spinning and weaving, and
the manufacture of glass, paper, brushes and gloves. The brewing industry
is also important, the beer of Erlangen being famous throughout Germany
and large quantities being exported.

Erlangen owes the foundation of its prosperity chiefly to the French
Protestant refugees who settled here on the revocation of the edict of Nantes
and introduced various manufactures. In 1017 the place was transferred
from the bishopric of Würzburg to that of Bamberg; in 1361 it was sold to
the king of Bohemia. It became a town in 1398 and passed into the hands of
the Hohenzollerns, burgraves of Nuremberg, in 1416. There for nearly three
centuries it was the property of the margraves of Bayreuth, being ceded
with the rest of Bayreuth to Prussia in 1791. In 1810 it came into the
possession of Bavaria. Erlangen was for many years the residence of the

poet Friedrich Rückert, and of the philosophers Johann Gottlieb Fichte and
Friedrich Wilhelm von Schnelling.

See Stein and Müller, Die Geschichte von Erlangen (1898).

ERLE, SIR WILLIAM (1793-1880), English lawyer and judge, was
born at Fifehead-Magdalen, Dorset, on the 1st of October 1793, and was
educated at Winchester and at New College, Oxford. Having been called to
the bar at the Middle Temple in 1819 he went the western circuit, became
counsel to the Bank of England, sat in parliament from 1837 to 1841 for the
city of Oxford, and, although of opposite politics to Lord Lyndhurst, was
made by him a judge of the common pleas in 1845. He was transferred to
the queen’s bench in the following year, and in 1859 came back to the
common pleas as chief justice upon the promotion of Sir Alexander
Cockburn. He retired in 1866, receiving the highest eulogiums for the
ability and impartiality with which he had discharged the judicial office. He
died at his estate at Bramshott, Hampshire, on the 28th of January 1880,
and a monument without his name but in his memory (sometimes
erroneously supposed to mark the place where an old gibbet was) stands on
the top of Hindhead.

See E. Manson, Builders of our Law (1904).

ERLKÖNIG, or Erl-King, a mythical character in modern German
literature, represented as a gigantic bearded man with a golden crown and
trailing garments, who carries children away to that undiscovered country
where he himself abides. There is no such personage in ancient German
mythology, and the name is linguistically nothing more than the
perpetuation of a blunder. It first appeared in Herder’s Stimmen der Völker
(1778), where it is used in the translation of the Danish song of the Elf-
King’s Daughter as equivalent to the Danish ellerkonge, or ellekonge, that
is, elverkonge, the king of the elves; and the true German word would have
been Elbkönig or Elbenkönig, afterwards used under the modified form of
Elfenkönig by Wieland in his Oberon (1780). Herder was probably misled
by the fact that the Danish word elle signifies not only elf, but also alder
tree (Ger. Erle). His mistake at any rate has been perpetuated by both
English and French translators, who speak of a “king of the alders,” “un roi
des aunes,” and find an explanation of the myth in the tree-worship of early
times, or in the vapoury emanations that hang like weird phantoms round
the alder trees at night. The legend was adopted by Goethe as the subject of
one of his finest ballads, rendered familiar to English readers by the
translations of Lewis and Sir Walter Scott; and since then it has been treated
as a musical theme by Reichardt and Schubert.

ERMAN, PAUL (1764-1851), German physicist, was born in Berlin on
the 29th of February 1764. He was the son of the historian Jean Pierre
Erman (1735-1814), author of Histoire des réfugiés. He became teacher of
science successively at the French gymnasium in Berlin, and at the military

academy, and on the foundation of the university of Berlin in 1810 he was
chosen professor of physics. He died at Berlin on the 11th of October 1851.
His work was mainly concerned with electricity and magnetism, though he
also made some contributions to optics and physiology. His son, Georg
Adolf Erman (1806-1877), was born in Berlin on the 12th of May 1806,
and after studying natural science at Berlin and Königsberg, spent from
1828 to 1830 in a journey round the world, an account of which he
published in Reise um die Erde durch Nordasien und die beiden Ozeane
(1833-1848). The magnetic observations he made during his travels were
utilized by C.F. Gauss in his theory of terrestrial magnetism. He was
appointed professor of physics at Berlin in 1839, and died there on the 12th
of July 1877. From 1841 to 1865 he edited the Archiv für wissenschaftliche
Kunde von Russland, and in 1874 he published, with H.J.R. Petersen, Die
Grundlagen der Gauss’schen Theorie und die Erscheinungen des
Erdmagnetismus im Jahre 1829.

His son Johann Peter Adolf Erman (1854- ), a famous Egyptologist,
was born in Berlin on the 31st of October 1854. Educated at Leipzig and
Berlin, he became extraordinary professor in 1883 and ordinary professor in
1892 of Egyptology in the university of Berlin, and in 1885 he was
appointed director of the Egyptian department of the royal museum. For an
account of the Egyptological work of Erman and his school, see Egypt:
Language.

ERMANARIC (fl. 350-376), king of the East Goths, belonged to the
Amali family, and was the son of Achiulf. His name occurs as Ermanaricus

(Jordanes), Aírmanareiks (Gothic), Eormenríc (A. Sax.), Jörmunrek
(Norse), Ermenrîch (M.H. German). Ermanaric built up for himself a vast
kingdom, which eventually extended from the Danube to the Baltic and
from the Don to the Theiss. He drove the Vandals out of Dacia, compelled
the allegiance of the neighbouring tribes of West Goths, procured the
submission of the Herules, of many Slav and Finnish tribes, and even of the
Esthonians on the shores of the Gulf of Bothnia. In his later days the west
Goths threw off his yoke, and, on the invasion of the Huns, rather than
witness the downfall of his kingdom he is said by Ammianus Marcellinus to
have committed suicide. His fate early became the centre of popular
tradition, which found its way into the narrative of Jordanes or Jornandes
(De rebus geticis, chap. 24), who compared him to Alexander the Great and
certainly exaggerated the extent of his kingdom. He is there said to have
caused a certain Sunilda or Sanielh to be torn asunder by wild horses on
account of her husband’s traitorous conduct. Her brothers Sarus and
Ammius sought to avenge her. They succeeded in wounding, not in killing
the Gothic king, whose death supervened in his one hundred and tenth year
from the joint effects of his wound and fear of the Hunnish invasion. This is
evidently a paraphrase of popular story which sought to supply plausible
reasons for Ermanaric’s end. In German legend Ermanaric became the
typical cruel tyrant, and references to his crimes abound in German epic and
in Anglo-Saxon poetry. He is made to replace Odoacer as the enemy of
Dietrich of Bern, his nephew, and his history is related in the Norse Vilkina
or Thidrekssagà, which chiefly embodies German tradition. His evil genius,
Sifka, Sibicho or Bicci, brings about the death of his three sons. The
Harlungs, Imbrecke and Fritile,1 are his nephews, whom he has strangled
for the sake of their treasure, the Brîsingo meni. Sonhild or Svanhild
becomes the wife of Ermanaric, and the motive for her murder is replaced
by an accusation of adultery between Svanhild and her stepson. The story
was already connected with the Nibelungen when it found its way to the

Scandinavian north by way of Germany. In the Völsunga Saga Svanhild is
the daughter of Sigurd and Gudrun. She is given in marriage to the Gothic
king Jörmunrek (Ermanaric), who sends his son Randver as proxy wooer in
company of Bicci, the evil counsellor. Randver is persuaded by Bicci to
take his father’s bride for himself. Randver is hanged and Svanhild
trampled to death by horses in the gate of the castle. Gudrun eggs on Sörli
and Hamdir or Hamtheow, her two sons by her third husband, Jonakr the
Hun, to avenge their sister. On the way they slay their half-brother Erp,
whom they suspect of lukewarmness in the cause; arrived in the hall of
Ermanaric they make a great slaughter of the Goths, and hew off the hands
and feet of Ermanaric, but they themselves are slain with stones. The tale is
told with variations by Saxo Grammaticus (Historia Danica, ed. Müller, p.
408, &c.), and in the Icelandic poems, the Lay of Hamtheow, Gudrun’s
Chain of Woe, and in the prose Edda.

Bibliography.—W. Grimm, in Die deutsche Heldensage (2nd ed.,
Berlin, 1867), quotes the account given by Jordanes, references in
Beowulf, in the Wanderer’s Song, Exeter Book, in Parcival, in
Dietrichs Flucht, the account given in the Quedlinburg Chronicle, by
Ekkehard in the Chronicon Urspergense, by Saxo Grammaticus, &c.
See also Vigfússon and Powell, Corpus poëticum boreale, vol. i.
(Oxford, 1883), and H. Symons, “Die deutsche Heldensage” in Paul’s
Grundriss d. german. Phil. vol. iii. (Strassburg, 1900).

1 Emerka and Fridla (Beowulf, Quedlingburg Chron.), Aki and Etgard (Vilkina Saga).
In the original myth the Harlungs, who are not to be confused with the Hartung brothers,
were sent to bring home Sūryā, the bride of the sky-god, Irmintiu.

ERMELAND, or Ermland (Varmia), a district of Germany, in East
Prussia, extending from the Frisches Haff, a bay in the Baltic, inland
towards the Polish frontier. It is a well-wooded sandy tract of country, has
an area of about 1650 sq. m., a population of 240,000, and is divided into
the districts of Braunsberg, Heilsberg, Rössel and Allenstein.

Ermeland was originally one of the eleven districts of old Prussia and
was occupied by the Teutonic Knights (Deutscher Orden), being made in
1250 one of the four bishoprics of the country under their sway. The bishop
of Ermeland shortly afterwards declared himself independent of the order,
and became a prince of the Empire. In 1466 Ermeland, together with West
Prussia, was by the peace of Thorn attached to the crown of Poland, and the
bishop had a seat in the Polish senate. In 1772 it was again incorporated

with Prussia. Among the bishops of the see, which still exists, with its seat
in Frauenberg, may be mentioned Aeneas Sylvius Piccolomini, afterwards
Pope Pius II., and Cardinal Stanislaus Hosius (1504-1579), the founder of
the Jesuit college in Braunsberg.

See Hipler, Literaturgeschichte des Bisthums Ermeland (Braunsberg,
1873); the Monumenta historiae Warmiensis (Mainz, 1860-1864, and
Braunsberg, 1866-1872, 4 vols.); and Buchholz, Abriss einer
Geschichte des Ermlands (Braunsberg, 1903.)

ERMELO, a district and town of the Transvaal. The district lies in the
south-east of the province and is traversed by the Drakensberg. In it are
Lake Chrissie, the only true lake in the country, and the sources of the Vaal,
Olifants, Komati, and Usuto rivers, which rise within 30 m. of one another.
The region has a general elevation of about 5500 ft. and is fine agricultural
and pastoral country, besides containing valuable minerals, including coal
and gold. Ermelo town, pop. (1904) 1451, is by rail 175 m. S.E. of
Johannesburg, and 74 m. S.S.W. of Machadodorp on the Pretoria-Delagoa
Bay railway. A government experimental farm, with some 1000 acres of
plantations, is maintained here.

ERMINE, an alternative
name for the stoat (Putorius
ermineus), apparently
applicable in its proper sense
only when the animal is in its
white winter coat. This
animal measures 10 in. in
length exclusive of the tail,
which is about 4 in. long, and
becomes bushy towards the
Ermine or Stoat (Putorius ermineus).
point. The fur in summer is
reddish brown above and white beneath, changing in the winter of northern
latitudes to snowy whiteness, except at the tip of the tail, which at all
seasons is black. In Scottish specimens this change in winter is complete,
but in those found in the southern districts of England it is usually only
partial, the ermine presenting during winter a piebald appearance. The white
colour is evidently protective, enabling the animals to elude the
observations of their enemies, and to steal unobserved on their prey. It also
retains heat better than a dark covering, and may thus serve to maintain an
equable temperature at all seasons within the body. The colour change
seems to be due to phagocytes devouring the pigment-bodies of the hair,
and not to a moult.

The species is a native of the temperate and subarctic zones of the Old
World, and is represented in America by a form which can scarcely be
regarded as specifically distinct. It inhabits thickets and stony places, and
frequently makes use of the deserted burrows of moles and other
underground mammals. Exceedingly sanguinary in disposition, and agile in
its movements, it feeds principally on rats, water-rats and rabbits, which it
pursues with pertinacity and boldness, hence the name stoat, signifying
bold, by which it is commonly known. It takes readily to water, and will

even climb trees in pursuit of prey. It is particularly destructive to poultry
and game, and has often been known to attack hares, fixing itself to the
throat of its victim, and defying all the efforts of the latter to disengage it.
The female brings forth five young ones about the beginning of summer.
The winter coat of the ermine forms one of the most valuable of
commercial furs, and is imported in enormous quantities from Norway,
Sweden, Russia and Siberia. It is largely used for muffs and tippets, and as
a trimming for state robes, the jet black points of the tails being inserted at
regular intervals as an ornament. In the reign of Edward III. the wearing of
ermine was restricted to members of the royal family; but it now enters into
almost all state robes, the rank and position of the wearer being in many
cases indicated by the presence or absence, and the disposition, of the black
spots. (See also Fur.)

ERMINE STREET. Documents and writers of the 11th and succeeding
centuries occasionally mention four “royal roads” in Britain—Icknield
Street, Erning or Ermine Street, Watling Street and Foss Way—as standing
apart from all other existing roads and enjoying the special protection of the
king. Unfortunately these authorities are not at all agreed as to their precise
course; the roads themselves do not occur as specially privileged in actual
legal or other practice, and it is likely that the category of Four Roads is the
invention of a lawyer or an antiquary. The names are, however, attested to
some extent by early charters which name them among other roads, as
boundaries. From these charters we know that Icknield Street ran along the
Berkshire downs and the Chilterns, that Ermine Street ran more or less due

north through Huntingdonshire, that Watling Street ran north-west across
the midlands from London to Shrewsbury, and Foss diagonally to it from
Lincoln or Leicester to Bath and mid-Somerset. This evidence only proves
the existence of these roads in Saxon and Norman days. But they all seem
to be much older. Icknield Street is probably a prehistoric ridgeway along
the downs, utilized perhaps by the Romans near its eastern end, but in
general not Roman. Ermine Street coincides with part of a line of Roman
roads leading north from London through Huntingdon to Lincoln. This line
is followed by the Old North Road through Cheshunt, Buntingford,
Royston, and Huntingdon to Castor near Peterborough; and thence it can be
traced through lanes and byways past Ancaster to Lincoln. Watling Street is
the Roman highway from London by St Alban’s (Verulamium) to Wroxeter
near Shrewsbury (Viroconium). Foss is the Roman highway from Lincoln
to Bath and Exeter. Hence it has been supposed, and is still frequently
alleged, that the Four Roads were the principal highways of Roman Britain.
This, however, is not the case. Icknield Street is not Roman and the three
roads which follow Roman lines, Ermine Street, Watling Street, and Foss,
held no peculiar position in the Romano-British road system (see Britain:
Roman). In later times, the names Ermine Street, Icknield Street and
Watling Street have been applied to other roads of Roman or supposed
Roman origin. This, however, is wholly the work of Elizabethan or
subsequent antiquaries and deserves no credence.

The derivations of the four names are unknown. Icknield, Ermine and
Watling may be from English personal names; Foss, originally Fos, seems
to be the Lat. fossa in its occasional medieval sense of a bank of upcast
earth or stones, such as the agger of a road.
(F. J. H.)

ERMOLDUS NIGELLUS, or Ermold the Black, was a monk of
Aquitaine, who accompanied King Pippin, son of the emperor Louis I., on a
campaign into Brittany in 824. Subsequently he was banished from Pippin’s
court on a charge of inciting the king against his father, and retired to
Strassburg, where he sought to regain the emperor’s favour by writing a
poem on his life and deeds. About 830 he obtained his recall, and has been
identified with Hermoldus, who appears as Pippin’s chancellor in 838.
Ermoldus was a cultured man with a knowledge of the Latin poets, and this
poem, In honorem Hludovici imperatoris, has some historical value. It
consists of four books and deals with the life and exploits of Louis from
781 to 826. He also wrote two poems in imitation of Ovid, which were
addressed to Pippin.

His writings are published in the Monumenta Germaniae historica,
Scriptores, Band 2 (Hanover, 1826 fol.); by J.P. Migne in the
Patrologia Latina, tome 105 (Paris, 1844); and by E. Dümmler in the
Poëtae Latini aevi Carolini, Band 2 (Berlin, 1881-1884). See W.O.
Henkel, Über den historischen Werth der Gedichte des Ermoldus
Nigellus (Eilenburg, 1876); W. Wattenbach, Deutschlands
Geschichtsquellen, Band 1 (Berlin, 1904); and A. Potthast, Bibliotheca
historica, pp. 430-431 (Berlin, 1896).

ERNE, the name of a river and two lakes in the north-west of Ireland.
The river rises in Lough Gowna, county Longford, 214 ft. above sea-level,
flows north through Lough Oughter with a serpentine course and a direction
generally northward, and then broadens into the Upper Lough Erne, a

shallow irregular sheet of water 13 m. long, so beset with islands as to
present the appearance of a number of water-channels ramifying through
the land. The river then winds past the town of Enniskillen on its island, and
enters Lough Erne, a beautiful lake nearly 18 m. long and 5 m. in extreme
width, containing many islands, but less closely covered with them than the
upper lough. One of them, Devenish, is celebrated for its antiquarian
remains (see Enniskillen). The river then runs westward to Donegal Bay,
forming a fine fall at Ballyshannon (q.v.). Lough Erne contains trout and
pike. These waters admit of navigation by small steamers, but little trade is
carried on. The area of the Erne basin, which includes a vast number of
small loughs, is about 1600 sq. m., and it covers part of the counties Cavan,
Longford, Leitrim, Fermanagh and Donegal. The length of the Erne valley
is about 70 m.

ERNEST I. [Ernst Anton Karl Ludwig], duke of Saxe-Coburg-Gotha
(1784-1844), was the son of Francis, duke of Saxe-Coburg-Saalfeld, and
was born on the 2nd of January 1784. At the time of his father’s death (9th
of December 1806) the duchy of Coburg was occupied by Napoleon as
conquered territory, and Ernest did not come into his inheritance till after
the peace of Tilsit (July 1807). Owing to the part he had played in assisting
the Prussians at the battle of Auerstädt he continued out of favour with
Napoleon, and he threw himself with vigour into the war of liberation
against the French. After the battle of Leipzig he was given the command of
the V. army corps and reduced Mainz by blockade; he also commanded the
Saxon troops during the campaign of 1815. By the congress of Vienna he

was rewarded with the principality of Lichtenberg on the left bank of the
Rhine, which received a slight augmentation after the second peace of Paris.
These territories he sold to Prussia in 1834. In 1826, in the division of the
territories of the duchy of Saxe-Gotha which followed the death of its last
duke (February 1825), he received the duchy of Gotha, ceding that of
Saalfeld to the duke of Meiningen; and he now exchanged his style of
Ernest III. of Saxe-Coburg-Saalfeld for that of Ernest I. of Saxe-Coburg-
Gotha. In 1821 he had given a constitution to Coburg, but he did not
interfere with the traditional system of estates at Gotha. He died on the 29th
of January 1844.

Duke Ernest, who was not only a good soldier and keen sportsman, but
an enlightened patron of the arts and sciences, did much for the economic,
educational and constitutional development of his territories; and his advice
always carried great weight in the councils of the other German sovereigns.
It was, however, for the splendid international position attained by the
house of Coburg under him that his reign is chiefly distinguished. His
younger brother Leopold (q.v.) became king of the Belgians; his brother
Ferdinand (b. 1785) married the wealthy princess Antoinette von Kohary
(1816) and was the father of the duchess of Nemours and of the future King
Ferdinand of Portugal. Of his sisters, Antoinette (1779-1824) married Duke
Alexander of Württemberg; Juliane [Alexandra Feodorovna] (1781-1860)
married the Russian cesarevich Constantine, from whom she was, however,
divorced in 1820; and Victoria (1786-1861), wife of Edward Augustus,
duke of Kent, became the mother of Queen Victoria. Duke Ernest was twice
married: (1) in 1817 to Louise, daughter of Duke Augustus of Saxe-Gotha,
whom he finally divorced in 1826; (2) in 1831 to Maria, daughter of Duke
Alexander of Württemberg. Of his sons, by his first wife, Ernest succeeded
him in the duchy, and Albert married Queen Victoria.

ERNEST II., duke of Saxe-Coburg-Gotha (1818-1893), was born at
Coburg on the 21st of June 1818, being the eldest son of Duke Ernest I. He
enjoyed a varied education; he studied at the university of Bonn with his
brother Albert; his military training he received in the Saxon army. The
widespread connexions of his family opened to him many courts of Europe,
and after he became of age he travelled much. The position of his uncle
Leopold, who was king of the Belgians, and especially the marriage of his
brother Albert to the queen of England, his cousin, gave him peculiar
opportunities for becoming acquainted with the political problems of
Europe. In 1840-1841 he undertook a journey to Spain and Portugal; in the
latter country another cousin, Ferdinand, was king-consort. In 1844 he
succeeded his father. His own character and the influence of the king of the
Belgians made him one of the most Liberal princes in Germany. He was
able to bring to a satisfactory conclusion disputes with the Coburg estates.
He passed through the ordeal of the revolution of 1848 with little trouble,
for he anticipated the demands of the people of Gotha for a reform, and in
1852 introduced a new constitution by which the administration of his two
duchies was assimilated in many points. The government of his small
dominions did not afford sufficient scope for his restless and versatile
ambition; his desire to play a great part in German affairs was probably
increased by the feeling that, though he was the head of his house, he was to
some extent overshadowed by the younger branches of the family which
ruled in Belgium, England and Portugal. He was one of the foremost
supporters of every attempt made to reform the German constitution and
bring about the unity of Germany. He took a warm interest in the
proceedings of the Frankfort parliament, and it was often said, probably
without reason, that he hoped to be chosen emperor himself. However that
may be, he strongly urged the king of Prussia to accept that position when it
was offered him in 1849; he took a very prominent part in the complicated
negotiations of the following year, and it was at his suggestion that a

congress of princes met at Berlin in 1850. He highly valued the
opportunities which this and similar meetings gave him for exercising
political influence, and he would have felt most at home as a member of a
permanent council of the German princes.

Ambitious also of military distinction, and sympathizing with the rising
of the people of Schleswig-Holstein against the Danes in 1849, Ernest
accepted a command in the federal army. In the engagement of Eckernförde
in April 1849 the troops under his orders succeeded in capturing two Danish
frigates, a remarkable feat of which he was justly proud. His greatest
services to Germany were performed during the years of reaction which
followed; almost alone among the German princes he remained faithful to
the Liberal and National ideals, and he allowed his dominions to be used as
an asylum by the writers and politicians who had to leave Prussia and
Saxony. The reactionary parties looked on him with great suspicion, and it
was at this time that he formed a friendship with Gustav Freytag, the
celebrated novelist, whom he protected when the Prussian government
demanded his arrest. His connexion with the English court gave him a
position of much influence, but no one was more purely German in his
feelings and opinions. The marriage of his niece Victoria with Frederick, the
heir to the Prussian throne, strengthened his connexion with Prussia, but
caused the Conservative party to look with increased suspicion on the
Coburg influence. He was the first German prince to visit Napoleon III.,
and was present when Orsini made his celebrated attempt on the emperor’s
life. After 1860 he became the chief patron and protector of the National
Verein; he encouraged the newly-formed rifle clubs, and notwithstanding
the strong disapproval of his fellow-monarchs, allowed his court to become
the centre of the rising national agitation. Still a warm adherent of Prussia,
in 1862 he set an example to the other princes by voluntarily making an
agreement by which his troops were placed in war under the command of
the king of Prussia. Like all the other Nationalists, he was much

embarrassed by the policy of Bismarck, and the democratic opinions of the
Coburg court, which were shared by the crown prince Frederick, were a
serious embarrassment to that minister. The opposition became more
accentuated when the duke allowed his dominions to be used as the
headquarters of the agitation in favour of Frederick, duke of Augustenburg,
who claimed the duchies of Schleswig and Holstein, and it was at this time
that Bismarck is reported to have said that if Frederick the Great had been
alive the duke would have been in the fortress of Spandau. In 1863 he was
present at the Fürstentag in Frankfort, and from this time was in more
frequent communication with the Austrian court, where his cousin
Alexander, Count Mensdorff, was minister. However, when war broke out
in 1866, he at once placed his troops at the disposition of Prussia; Bismarck
had in an important letter explained to him his policy and tactics. He was
personally concerned in one of the most interesting events of the war; for
the Hanoverian army, in its attempt to march south and join the Bavarians,
had to pass through Thuringia, and the battle of Langensalza was fought in
the immediate neighbourhood of Gotha. His troops took part in the battle,
which ended in the rout of the Prussians, the duke, who was not present
during the fight, in vain attempting to stop it. He bore an important share in
the negotiations before and after the battle, and his action at this time has
been the subject of much controversy, for it was suggested that while he
offered to mediate he really acted as a partisan of Prussia. For his services
to Prussia he received as a present the forest of Schmalkalden. He was with
the Prussian headquarters in Bohemia during the latter part of the war.

With the year 1866 the political rôle which Ernest had played ended. The
result was perhaps not quite equal to his expectations, but it must be
remembered how difficult was the position of the minor German princes;
and he quoted with great satisfaction the words used in 1871 by the emperor
William at Versailles, that “to him in no small degree was due the
establishment of the empire.” He was a man of varied tastes, a good

musician—he composed several operas and songs—and a keen sportsman,
a quality in which he differed from his brother. Notwithstanding his
Liberalism, he had a great regard for the dignity of his rank and family, and
in his support of constitutional government would never have sacrificed the
essential prerogatives of sovereignty. He died at Reinhardsbrunn on the
22nd of August 1893. In 1842 the duke married Alexandrine, daughter of
the grandduke of Baden; there were no children by this marriage and the
succession to Saxe-Coburg-Gotha passed therefore to the children of his
younger brother Albert. By Albert’s marriage contract the duchy could not
be held together with the English crown; thus his eldest son, afterwards
Edward VII., was passed over and it came to his second son, Alfred, duke of
Edinburgh (1844-1900). When Alfred died without sons in July 1900 the
succession to the duchy passed to a younger brother Arthur, duke of
Connaught; but the duke and his son, Arthur, passed on their claim to
Charles Edward, duke of Albany (b. 1884), who became duke of Saxe-
Coburg-Gotha in succession to his uncle Alfred. In 1905 Charles Edward
married Victoria Adelaide (b. 1885), princess of Schleswig-Holstein, by
whom he has a son John Leopold (b. 1906).

Duke Ernest was something of a writer. He brought out an account of the
travels in Egypt and Abyssinia which he undertook in 1862 as Reise des
Herzogs Ernst von Sachsen-Koburg-Gotha nach Ägypten (Leipzig, 1864);
and he published his memoirs, Aus meinem Leben und aus meiner Zeit
(Berlin, 1887-1889). This work is in three volumes and contains much
valuable information on a most critical period of German history; there is
an English translation by P. Andreae (1888-1890).

See also Sir T. Martin, Life of H.R.H. the Prince Consort (1875-
1880); Hon. C. Grey, Early Years of the Prince Consort (1867); A.
Ohorn, Herzog Ernst II., ein Lebensbild (Leipzig, 1894); and E.

Tempeltey, Herzog Ernst von Koburg und das Jahr 1866 (Berlin,
1898). (J. W. He.)

ERNEST AUGUSTUS (1771-1851), king of Hanover and duke of
Cumberland, fifth son of the English king George III., was born at Kew on
the 5th of June 1771. Having studied at the university of Göttingen, he
entered the Hanoverian army, serving as a leader of cavalry when war broke
out between Great Britain and France in 1793, and winning a reputation for
bravery. He lost the sight of one eye at the battle of Tournai in May 1794,
and when Hanover withdrew from the war in 1795 he returned to England,
being made lieutenant-general in the British army in 1799. In the same year
he was created duke of Cumberland and Teviotdale and granted an
allowance of £12,000 a year, after which he held several lucrative military
positions in England, and began to attend the sittings of the House of Lords
and to take part in political life. A stanch Tory, the duke objected to all
proposals of reform, especially to the granting of any relief to the Roman
Catholics, and had great influence with his brother the prince regent,
afterwards King George IV., in addition to being often consulted by the
Tory leaders. In 1810 he was severely injured by an assassin, probably his
valet Sellis, who was found dead; and subsequently two men were
imprisoned for asserting that the duke had murdered his valet. Recovering
from his wounds, Cumberland again proceeded to the seat of war; and
having been made a British field-marshal, was in command of the
Hanoverian army during the campaigns of 1813 and 1814, being present,
although not in action, at the battle of Leipzig. In May 1815 Ernest married

his cousin, Frederica (1778-1841), daughter of Charles II. duke of
Mecklenburg-Strelitz and widow of Frederick, prince of Solms-Braunfels, a
union which was very repugnant to his mother Queen Charlotte, and was
disliked in England, where the duke’s strong Toryism had made him
unpopular. Parliament refused to increase his allowance from £18,000, to
which it had been raised in 1804, to £24,000 a year, and indignant at the
treatment he received the duke spent some years in Berlin. Returning to
England after the accession of George IV. in 1820, his political power was
again considerable, while deaths in the royal family made it likely that he
would succeed to the throne. Although his personal influence with the
sovereign ceased upon the death of George IV. in 1830, the duke continued
to oppose all measures for the extension of civil and religious liberty,
including the Reform Bill of 1832; and his unpopularity was augmented by
suspicions that he had favoured the formation of Orange lodges in the army.
When William IV. died in June 1837, the crowns of Great Britain and
Hanover were separated; and Ernest, as the nearest male heir of the late
king, became king of Hanover. At once cancelling the constitution which
William had given to his kingdom in 1833, he acted as an absolute
monarch, and the constitution which he sanctioned in 1840 was permeated
with his own illiberal ideas. In German politics he was vigilant and active,
and mindful of the material interests of his country. His reign, however, was
a stormy one, and serious trouble between king and people had arisen when
he died at Herrenhausen on the 18th of November 1851 (see Hanover:
History). In spite of his arbitrary rule and his reactionary ideas the king was
popular among his subjects, and his statue in Hanover bears the words
“Dem Landes Vater sein treues Volk.” Ernest, who is generally regarded as
the ablest of the sons of George III., left an only child, George, who
succeeded him as king of Hanover.

See C.A. Wilkinson, Reminiscences of the Court and Times of King
Ernest of Hanover (London, 1886); von Malortie, König Ernst August

(Hanover, 1861); and the various histories of Great Britain and
Hanover for the period.

ERNESTI, JOHANN AUGUST (1707-1781), German theologian and
philologist, was born on the 4th of August 1707, at Tennstädt in Thuringia,
of which place his father was pastor, besides being superintendent of the
electoral dioceses of Thuringia, Salz and Sangerhausen. At the age of
sixteen he was sent to the celebrated Saxon cloister school of Pforta
(Schulpforta). At twenty he entered the university of Wittenberg, and
studied afterwards at the university of Leipzig. In 1730 he was made master
in the faculty of philosophy. In the following year he accepted the office of
conrector in the Thomas school of Leipzig, of which J.M. Gesner was then
rector, an office to which Ernesti succeeded in 1734. He was, in 1742,
named professor extraordinarius of ancient literature in the university of
Leipzig, and in 1756 professor ordinarius of rhetoric. In the same year he
received the degree of doctor of theology, and in 1759 was appointed
professor ordinarius in the faculty of theology. Through his learning and his
manner of discussion, he co-operated with S.J. Baumgarten of Halle (1706-
1757) in disengaging the current dogmatic theology from its many
scholastic and mystical excrescences, and thus paved a way for a revolution
in theology. He died, after a short illness, in his seventy-sixth year, on the
11th of September 1781.

It is perhaps as much from the impulse which Ernesti gave to sacred and
profane criticism in Germany, as from the intrinsic excellence of his own
works in either department, that he must derive his reputation as a

philologist or theologian. With J.S. Semler he co-operated in the revolution
of Lutheran theology, and in conjunction with Gesner he instituted a new
school in ancient literature. He detected grammatical niceties in Latin, in
regard to the consecution of tenses which had escaped preceding critics. His
canons are, however, not without exceptions. As an editor of the Greek
classics, Ernesti hardly deserves to be named beside his Dutch
contemporaries, Tiberius Hemsterhuis (1685-1766), L.C. Valckenaer (1715-
1785), David Ruhnken (1723-1798), or his colleague J.J. Reiske (1716-
1774). The higher criticism was not even attempted by Ernesti. But to him
and to Gesner is due the credit of having formed, by discipline and by
example, philologists greater than themselves, and of having kindled the
national enthusiasm for ancient learning. It is chiefly in hermeneutics that
Ernesti has any claim to eminence as a theologian. But here his merits are
distinguished, and, at the period when his Institutio Interpretis N. T. was
published (1761), almost peculiar to himself. In it we find the principles of
a general interpretation, formed without the assistance of any particular
philosophy, but consisting of observations and rules which, though already
enunciated, and applied in the criticism of the profane writers, had never
rigorously been employed in biblical exegesis. He was, in fact, the founder
of the grammatico-historical school. He admits in the sacred writings as in
the classics only one acceptation, and that the grammatical, convertible into
and the same with the logical and historical. Consequently he censures the
opinion of those who in the illustration of the Scriptures refer everything to
the illumination of the Holy Spirit, as well as that of others who,
disregarding all knowledge of the languages, would explain words by
things. The “analogy of faith,” as a rule of interpretation, he greatly limits,
and teaches that it can never afford of itself the explanation of words, but
only determine the choice among their possible meanings. At the same time
he seems unconscious of any inconsistency between the doctrine of the

inspiration of the Bible as usually received and his principles of
hermeneutics.

Among his works the more important are:—I. In classical literature:
Initia doctrinae Solidioris (1736), many subsequent editions; Initia
rhetorica (1730); editions, mostly annotated, of Xenophon’s
Memorabilia (1737), Cicero (1737-1739), Suetonius (1748), Tacitus
(1752), the Clouds of Aristophanes (1754), Homer (1759-1764),
Callimachus (1761), Polybius (1764), as well as of the Quaestura of
Corradus, the Greek lexicon of Hedericus, and the Bibliotheca Latina
of Fabricius (unfinished); Archaeologia litteraria (1768), new and
improved edition by Martini (1790); Horatius Tursellinus De particulis
(1769). II. In sacred literature: Antimuratorius sive confutatio
disputationis Muratorianae de rebus liturgicis (1755-1758); Neue
theologische Bibliothek, vols. i. to x. (1760-1769); Institutio interpretis
Nov. Test. (3rd ed., 1775); Neueste theologische Bibliothek, vols. i. to x.
(1771-1775). Besides these, he published more than a hundred smaller
works, many of which have been collected in the three following
publications:—Opuscula oratoria (1762, 2nd ed., 1767); Opuscula
philologica et critica (1764, 2nd ed., 1776); Opuscula theologica
(1773). See Herzog-Hauck, Realencyklopädie; J.E. Sandys, Hist. of
Class. Schol. iii. (1908).

ERNESTI, JOHANN CHRISTIAN GOTTLIEB (1756-1802), German
classical scholar, was born at Arnstadt, Thuringia, and studied under his
uncle, J.A. Ernesti, at the university of Leipzig. On the 5th of June, 1782, he

was made supplementary professor of philosophy at his own university; and
on the death of his cousin August Wilhelm in 1801 he was for five months
professor of rhetoric. He died on the 5th of June of the following year.

His principal works are:—Editions of Aesop’s Fabulae (1781); of
the Glossae sacrae of Hesychius (1785) and Suidas and Phavorinus
(1786); and of Silius Italicus Punica (1791-1792); Lexicon
Technologiae Graecorum rhetoricae (1795); Lexicon technologiae
Latinorum rhetoricae (1797), and Cicero’s Geist und Kunst (1799-
1802).

ERNST, HEINRICH WILHELM (1814-1865), German violinist and
composer, was born at Brünn, in Moravia, in 1814. He was educated at the
Conservatorium of Vienna, studying the violin under Joseph Böhm and
Joseph Mayseder, and composition under Ignaz von Seyfried. At the age of
sixteen he made a concert tour in south Germany, which established his
reputation as a violinist of the highest promise. In 1832 he went to Paris,
where he lived for several years. During this period he formed an intimacy
with Stephen Heller, which resulted in their charming joint compositions—
the Pensées fugitives for piano and violin. In 1843 he paid his first visit to
London. The impression which he then made as a violinist was more than
confirmed in the following year, when his rare powers were recognized by
the musical public. Thenceforward he visited England nearly every year,
until his health broke down owing to long-continued neuralgia of a most
severe kind. The last seven years of his life were spent in retirement, chiefly
at Nice, where he died on the 8th of October 1865. As a violinist Ernst was

distinguished by his almost unrivalled executive power, loftiness of
conception, and intensely passionate expression. As a composer he wrote
chiefly for his own instrument, and his Elegie and Otello Fantasia rank
among the most treasured works for the violin.

ERODE, a town of British India, in the Coimbatore district of Madras,
situated on the right bank of the river Cauvery, which is here crossed by an
iron railway girder bridge of 22 spans. Pop. (1901) 15,529. Here the South
Indian railway joins the South-Western line of the Madras railway, 243 m.
from Madras. There are exports of cotton and saltpetre; and the town has a
steam cotton press.

EROS, a minor planet discovered by Witt at Berlin on the 14th of August
1898, and, so far as yet known, unique in that its perihelion lies far within
the orbit of Mars.

EROS, in Greek mythology, the god of love. He is not mentioned in
Homer; in Hesiod (Theog. 120) he is one of the oldest and the most
beautiful of the gods, whose power neither gods nor men can resist. He also
evolves order and harmony out of Chaos by uniting the separated elements.
This cosmic Eros, who in Orphic cosmogony sprang from the world-egg
which Chronos, or Time, laid in the bosom of Chaos, and which is the
origin of all created beings, degenerated in later mythology into the
capricious god of sexual passion, the son of Aphrodite and Zeus, Ares or
Hermes. He is commonly represented as a mischievous boy, the tormentor
of gods and men, even his own mother not being proof against his attacks.
His brother is Anteros, the god of mutual love, who punishes those who do
not return the love of others, without which Eros could not thrive; he is
sometimes described as the opponent of Eros. The chief associates of Eros
are Pothos and Himeros (Longing and Desire), Peitho (Persuasion), the
Muses and the Graces; he himself is in constant attendance on Aphrodite.
Later writers (Euripides being the first) assumed the existence of a number
of Erotes (like the Roman Amores and Cupidines) with similar attributes.
According to the philosophers, Eros was not only the god of sexual love,
but also of the loyal and devoted friendship of men; hence the Theban
“Sacred Band” was devoted to him, and the Cretans and Spartans offered
sacrifice to him before going into battle (Athenaeus xiii. p. 561). In
Alexandrian poetry Eros is at one time the powerful god who conquers all,
at another the elfish god of love. For the Roman adaptation of Eros see
Cupid, and for the later legend of Cupid and Psyche see Psyche.

In art Eros is represented as a beautiful youth or a winged child. His
attributes are the bow and arrows and a burning torch. The rose, the hare,
the cock and the goat are frequently associated with him. The most
celebrated statue of him was at Thespiae, the work of Praxiteles. Other
famous representations are the Vatican torso and Eros trying his bow (in the
Capitoline museum).

See J.E. Harrison, Prolegomena to the Study of Greek Religion
(1903); G.F. Schömann, De Cupidine Cosmogonico (1852); E.
Gerhard, Über den Gott Eros (1850); articles in Roscher’s Lexikon der
Mythologie, Daremberg and Saglio’s Dictionnaire des antiquités, and
Pauly-Wissowa’s Realencyclopädie.

ERPENIUS (original name van Erpe), THOMAS (1584-1624), Dutch
Orientalist, was born at Gorcum, in Holland, on the 11th of September
1584. After completing his early education at Leiden, he entered the
university of that city, and in 1608 took the degree of master of arts. By the
advice of Scaliger he studied Oriental languages whilst taking his course of
theology. He afterwards travelled in England, France, Italy and Germany,
forming connexions with learned men, and availing himself of the
information which they communicated. During his stay at Paris he
contracted a friendship with Casaubon, which lasted during his life, and
also took lessons in Arabic from an Egyptian, Joseph Barbatus, otherwise
called Abu-dakni. At Venice he perfected himself in the Turkish, Persic and
Ethiopic languages. After a long absence, Erpenius returned to his own
country in 1612, and on the 10th of February 1613 he was appointed
professor of Arabic and other Oriental languages, Hebrew excepted, in the
university of Leiden. Soon after his settlement at Leiden, animated by the
example of Savary de Brèves, who had established an Arabic press at Paris
at his own charge, he caused new Arabic characters to be cut at a great
expense, and erected a press in his own house. In 1619 the curators of the
university of Leiden instituted a second chair of Hebrew in his favour. In

1620 he was sent by the States of Holland to induce Pierre Dumoulin or
André Rivet to settle in that country; and after a second journey he was
successful in inducing Rivet to comply with their request. Some time after
the return of Erpenius, the states appointed him their interpreter; and in this
capacity he had the duty imposed upon him of translating and replying to
the different letters of the Moslem princes of Asia and Africa. His
reputation had now spread throughout all Europe, and several princes, the
kings of England and Spain, and the archbishop of Seville made him the
most flattering offers; but he constantly refused to leave his native country.
He was preparing an edition of the Koran with a Latin translation and notes,
and was projecting an Oriental library, when he died prematurely on the
13th of November 1624.

Among his works may be mentioned his Grammatica Arabica,
published originally in 1613 and often reprinted; Rudimenta linguae
Arabicae (1620); Grammatica Ebraea generalis (1621); Grammatica
Chaldaica et Syria (1628); and an edition of Elmacin’s History of the
Saracens.

ERROLL (or Errol), FRANCIS HAY, 9th Earl of (d. 1631), Scottish
nobleman, was the son of Andrew, 8th earl, and of Lady Jean Hay, daughter
of William, 6th earl. The date of his birth is unrecorded, but he succeeded to
the earldom (cr. 1453) in 1585, was early converted to Roman Catholicism,
and as the associate of Huntly joined in the Spanish conspiracies against the
throne of Elizabeth. A letter written by him, declaring his allegiance to the
king of Spain, having been intercepted and sent by Elizabeth to James in

February 1589, he was declared a rebel by the council. He engaged with
Huntly and Crawford in a rebellion in the north of Scotland, but their forces
surrendered at Aberdeen on the arrival of the king in April; and in July
Erroll gave himself up to James, who leniently refrained from exacting any
penalty. In September of the same year he entered into a personal bond with
Huntly for mutual assistance; and in 1590 displeased the king by marrying,
in spite of his prohibition, Lady Elizabeth Douglas, daughter of the earl of
Morton. He was imprisoned on suspicion of complicity in the attempt made
by Gray and Bothwell to surprise the king at Falkland in June 1592; and
though he obtained his release, he was again proclaimed a rebel on account
of the discovery of his signature to two of the “Spanish Blanks,” unwritten
sheets subscribed with the names of the chief conspirators in a plot for a
Spanish invasion of Scotland, to be filled up later with the terms of the
projected treaty. After a failure to apprehend him in March 1593, Erroll and
his companions were sentenced to abjure Romanism or leave the kingdom;
and on their non-compliance were in 1594 declared traitors. On the 3rd of
October they defeated at Glenlivet a force sent against them under Argyll;
though Erroll himself was severely wounded, and Slains Castle, his seat,
razed to the ground. The rebel lords left Scotland in 1595, and Erroll, on
report of his further conspiracies abroad, was arrested by the states of
Zealand, but was afterwards allowed to escape. He returned to Scotland
secretly in 1596, and on the 20th of June 1597 abjured Romanism and made
his peace with the Kirk. He enjoyed the favour of the king, and in 1602 was
appointed a commissioner to negotiate the union with England. His
relations with the Kirk, however, were not so amicable. The reality of his
conversion was disputed, and on the 21st of May 1608 he was confined to
the city of Perth “for the better resolution of his doubts,” being
subsequently declared an obstinate “papist,” excommunicated, deprived of
his estate, and imprisoned at Dumbarton; and after some further vacillation
was finally released in May 1611. Lord Erroll died on the 16th of July 1631,

and was buried in the church of Slains. He married (1) Anne, daughter of
John, 4th earl of Atholl; (2) Margaret, daughter of the regent Murray; and
(3) Elizabeth, daughter of William, 6th earl of Morton. By his third wife he
had several children, of whom his eldest son, William, succeeded him. The
dispute which began in his lifetime concerning the hereditary office of lord
high constable between the families of Erroll and of the Earl Marischal was
settled finally in favour of the former; thus establishing the precedence
enjoyed by the earls of Erroll next after the royal family over all other
subjects in Scotland.

See The Erroll Papers (Spalding Club Miscellany, vol. ii. 211);
Andrew Lang, Hist. of Scotland, vol. ii.; Hist. MSS. Comm. MSS. of
Earl of Mar and Kellie; D. Calderwood’s Hist. of the Church of
Scotland; John Spalding’s Memorials (Spalding Club, 1850); Collected
Essays of T.G. Law, ed. by P.H. Brown (1904); Treason and Plot, by
M.A.S. Hume (1901).

ERROR (Lat. error, from errare, to wander, to err), a mistake, a
departure or deviation from what is true, exact or right. For the legal
process by which a judgment could be reversed on the ground of error,
known as a “writ of error,” see Writ and Appeal. The words “error
excepted” or “errors and omissions excepted” (contracted to “E.E.” “E. &
O.E.”), are frequently placed at the end of a statement of account or an
invoice, so that the accounting party may reserve the right to correct any
errors or omissions which may be subsequently discovered, or make further
claims in respect of them. In mathematics, “error” is the deviation of an

observed or calculated quantity from its true value. The calculus of errors
leads to the formulation of the “law of error,” which is an analytical
expression of the most probably true value of a series of discordant values
(see Probability).

ERSCH, JOHANN SAMUEL (1766-1828), the founder of German
bibliography, was born at Grossglogau, in Silesia, on the 23rd of June 1766.
In 1785 he entered the university of Halle with the view of studying
theology; but soon his whole attention became engrossed by history,
bibliography and geography. At Halle he made the acquaintance of J.E.
Fabri, professor of geography; and when the latter was made professor of
history and statistics at Jena, Ersch accompanied him thither, and aided him
in the preparation of several works. In 1788 he published the Verzeichnis
aller anonymischen Schriften, as a supplement to the 4th edition of
Meusel’s Gelehrtes Deutschland. The researches required for this work
suggested to him the preparation of a Repertorium über die allgemeinen
deutschen Journale und andere periodische Sammlungen für
Erdbeschreibung, Geschichte, und die damit verwandten Wissenschaften
(Lemgo, 1790-1792). The fame which this publication acquired him led to
his being engaged by Schütz and Hufeland to prepare an Allgemeines
Repertorium der Literatur, published in 8 vols. (Jena and Weimar, 1793-
1809), which condensed the literary productions of 15 years (1785-1800),
and included an account not merely of the books published during that
period, but also of articles in periodicals and magazines, and even of the
criticisms to which each book had been subjected. While engaged in this

great work he also projected La France littéraire, which was published at
Hamburg in 5 vols., from 1797 to 1806. In 1795 he went to Hamburg to edit
the Neue Hamburger Zeitung, founded by Victor Klopstock, brother of the
poet, but returned in 1800 to Jena to take active part in the Allgemeine
Literaturzeitung. He also obtained in the same year the office of librarian in
the university, and in 1802 was made professor of philosophy. In 1803 he
accepted the chair of geography and statistics at Halle, and in 1808 was
made principal librarian. He here projected a Handbuch der deutschen
Literatur seit der Mitte des 18. Jahrh. bis auf die neueste Zeit (Leipzig,
1812-1814) and, along with Johann Gottfried Gruber (q.v.), the Allgemeine
Encyklopädie der Wissenschaften und Künste (Leipzig, 1818 ffg.) which he
continued as far as the 21st volume. The accuracy and thoroughness of this
monumental encyclopaedia make it still an indispensable book of reference.
Ersch died at Halle on the 16th of January 1828.

ERSKINE, EBENEZER (1680-1754), Scottish divine, the chief founder
of the Secession Church (formed of dissenters from the Church of
Scotland), was born on the 22nd of June 1680, most probably at Dryburgh,
Berwickshire. His father, Henry Erskine, who was at one time minister at
Cornhill, Durham, was ejected in 1662 by the Act of Uniformity, and, after
suffering some years’ imprisonment, was after the Revolution appointed to
the parish of Chirnside, Berwickshire. After studying at the university of
Edinburgh, Ebenezer became minister of Portmoak, Kinross-shire. There he
remained for twenty-eight years, after which, in the autumn of 1731, he was
translated to the West Church, Stirling. Some time before this, he, along

with some other ministers, was “rebuked and admonished,” by the general
assembly, for defending the doctrines contained in the Marrow of Modern
Divinity (see Boston, Thomas). A sermon which he preached on lay
patronage before the synod of Perth in 1733 furnished new grounds of
accusation, and he was compelled to shield himself from rebuke by
appealing to the general assembly. Here, however, the sentence of the synod
was confirmed, and after many fruitless attempts to obtain a hearing, he,
along with William Wilson of Perth, Alexander Moncrieff of Abernethy and
James Fisher of Kinclaven, was suspended from the ministry by the
commission in November of that year. Against this sentence they protested,
and constituted themselves into a separate church court, under the name of
the associate presbytery. In 1739 they were again summoned before the
assembly, and in their corporate capacity declined to acknowledge the
authority of the church, and were deposed in the following year. They
received numerous accessions to their communion, and remained in
harmony with each other till 1747, when a division took place in regard to
the nature of the oath administered to burgesses. Erskine joined with the
“burgher” section, and became their professor of theology. He continued
also to preach to a numerous congregation in Stirling till his death, which
took place on the 2nd of June 1754. Erskine was a very popular preacher,
and a man of considerable force of character; he acted throughout on
principle with honesty and courage. The burgher and anti-burgher sections
of the Secession Church were reunited in 1820, and in 1847 they united
with the relief synod in forming the United Presbyterian Church.

Erskine’s published works consist chiefly of sermons. His Life and
Diary, edited by the Rev. Donald Fraser, was published in 1840. His
Works were published in 1785.

ERSKINE, HENRY (1746-1817), lord advocate of Scotland, the second
son of Henry David, 10th earl of Buchan and brother of the lord chancellor
Erskine, was born in Edinburgh on the 1st of November 1746. He was
educated at the universities of St Andrews, Glasgow and Edinburgh, and
was admitted a member of the faculty of advocates in 1768. His reputation
as a clever and fluent speaker was first made in the debates of the general
assembly, of which he had been early elected an elder. In 1783 he was
appointed to the office of lord advocate, which he held during the brief
coalition ministry of Fox and North. In 1785 he was elected dean of the
faculty of advocates, and was re-elected annually till 1796, when his
conduct in moving a series of resolutions at a public meeting, condemning
the government’s sedition and treason bills, brought on him the opposition
of the ministerial party, and he was deposed in favour of Robert Dundas. On
the formation of the Grenville ministry in 1806 he again became lord
advocate and was returned to parliament for the Haddington burghs, which
he exchanged at the general election of the same year for the Dumfries
burghs. His tenure of the lord advocateship ended in March 1807 on the
downfall of the ministry. In 1811 he gave up his practice at the bar and
retired to his country residence of Almondel, in Linlithgowshire, where he
died on the 8th of October 1817.

His eldest son, Henry David (1783-1857), succeeded as 12th earl of
Buchan on his uncle’s death in 1829.

Erskine’s reputation will survive as the finest and most eloquent orator of
his day at the Scottish bar; added to a charming forensic style was a most
captivating wit, which, as Lord Jeffrey said, was “all argument, and each of
his delightful illustrations a material step in his reasoning.” Erskine was
also the author of some poems, of which the best known is “The Emigrant”
(1783).

See Lieut.-Col. A. Fergusson’s Henry Erskine (1882).

ERSKINE, JOHN (1721-1803), Scottish divine, son of John Erskine of
Carnock, was born on the 2nd of June 1721. He studied law for a time after
completing his course in arts at the university of Edinburgh, but was
eventually licensed to preach in 1743; and was successively parish minister
of Kirkintilloch, near Glasgow, Culross, in Fifeshire (1753), New Greyfriars
church in Edinburgh (1758), and Old Greyfriars church in 1768, where he
became the colleague of Principal Robertson, the historian. Here he
remained until his death, which took place on the 19th of January 1803. Dr
Erskine’s writings consist chiefly of controversial pamphlets on theological
subjects. His sermons are clear, vigorous expositions of a moderate
Calvinism, in which metaphysical argument and practical morality are
happily blended. In church politics he was the leader of the evangelical
party; and was much beloved for his high character and amiability.

For his life and works see Sir H. Moncreiff Wellwood, Life and
Writings of J. Erskine, D.D. (Edinburgh, 1818).

ERSKINE, JOHN, of Carnock (1695-1768), Scottish jurist, son of
Lieut.-Colonel John Erskine, was born in 1695. He was admitted a member
of the faculty of advocates in 1719. Although he never enjoyed much
practice at the bar, he acquired a high reputation as a sound and learned

lawyer, and in 1737 was appointed professor of Scots law in the university
of Edinburgh. In 1754 he published his Principles of the Law of Scotland.
He retired from his chair in 1765; and during the remainder of his
uneventful life he occupied himself with the preparation of his great work,
the Institutes of the Law of Scotland, which he did not live to publish. He
died at Cardross, Perthshire, on the 1st of March 1768.

Erskine’s Institutes, although not exhibiting the grasp of principle which
distinguished his great predecessor Lord Stair, is so conspicuous for
learning, accuracy and sound good sense, that it has always been esteemed
of the highest authority on the law of Scotland. The first edition appeared in
1773 and it has been many times reprinted. The Principles, although
published first, is substantially an abridgment of the larger work, and is in
some respects superior to it, being more concise and direct. It retains its
place as the text-book on Scots law, and is frequently being re-edited.

ERSKINE, JOHN, of Dun (1509-1591), Scottish reformer, the son of
Sir John Erskine, laird of Dun, was born in 1509, and was educated at
King’s College, Aberdeen. At the age of twenty-one Erskine was the cause
—probably by accident—of a priest’s death, and was forced to go abroad,
where he came under the influence of the new learning. It was through his
agency that Greek was first taught in Scotland by Petrus de Marsiliers at
Montrose. This fact counted for much in the progress of the Reformation.
Erskine was also drawn towards the new faith, being a close friend of
George Wishart, the reformer, from whose fate he was saved by his wealth
and influence, and of John Knox, whose advice openly to discountenance

the mass was given in the lodgings of the laird of Dun. In the stormy
controversies of the time of Mary Stuart and James VI. Erskine was a
conspicuous figure and a moderating influence. He was able to soothe the
queen when her feelings had been outraged by Knox’s denunciations—
being a man “most gentill of nature”—and frequently acted as mediator
both between the catholic and reforming parties, and among the reformers
themselves. In 1560 he was appointed—though a layman—superintendent
of the reformed church of Scotland for Angus and Mearns, and in 1572 he
gave his assent to the modified episcopacy proposed by Morton at the Leith
convention. Though never himself ordained, he was held in such high
esteem by the leaders of the church as to be more than once elected
moderator of the general assembly (first in 1564), and he was amongst
those who in 1578 drew up the Second Book of Discipline. From 1579 he
was a member of the king’s council. He died in 1591. Erskine owed his
peculiar influence among the Scottish reformers to the union—rare in those
days—of steadfast convictions with a conciliatory manner; Queen Mary
described him as “a mild and sweet-natured man, with true honesty and
uprightness.”

See the “Dun Papers” in the Spalding Club Miscellany, vol. iv.
(1849), and the article by T.F. Henderson in the Dict. Nat. Biog.

ERSKINE, RALPH (1685-1752), Scottish divine, brother of Ebenezer
Erskine (q.v.), was born on the 18th of March 1685. After studying at the
university of Edinburgh, he was in 1711 ordained assistant minister at
Dunfermline. He homologated the protests which his brother laid on the

table of the assembly after being rebuked for his synod sermon, but he did
not formally withdraw from the establishment till 1737. He was also
present, though not as a member, at the first meeting of the associate
presbytery. When the severance took place on account of the oath
administered to burgesses, he adhered, along with his brother, to the burgher
section. He died after a short illness on the 6th of November 1752.

His works consist of sermons, poetical paraphrases and gospel
sonnets. The Gospel Sonnets have frequently appeared separately. His
Life and Diary, edited by the Rev. D. Fraser, was published in 1842.

ERSKINE, THOMAS, of Linlathen (1788-1870), Scottish theologian,
youngest son of David Erskine, writer to the signet in Edinburgh, and of
Anne Graham, of the Grahams of Airth, was born on the 13th of October
1788. He was a descendant of John, 1st or 6th earl of Mar, regent of
Scotland in the reign of James VI., a grandson of Colonel John Erskine of
Carnock. After being educated at the high school of Edinburgh and at
Durham, he attended the literary and law classes at the university of
Edinburgh, and becoming in 1810 a member of the Edinburgh faculty of
advocates, he for some time enjoyed the intimate acquaintance of
Cockburn, Jeffrey, Scott and other distinguished men whose talent then lent
lustre to the Scottish bar. In 1816 he succeeded to the family estate of
Linlathen, near Dundee, and devoted himself to theology. The writings of
Erskine, especially his published letters, are distinguished by a graceful
style, and possess originality and interest. His theological views have a
considerable similarity to those of Frederick Denison Maurice, who

acknowledges having been indebted to him for his first true conception of
the meaning of Christ’s sacrifice. Erskine had little interest in the “historical
criticism” of Christianity, and regarded as the only proper criterion of its
truth its conformity or nonconformity with man’s spiritual nature, and its
adaptability or non-adaptability to man’s spiritual needs. He considered the
incarnation of Christ as the necessary manifestation to man of an eternal
sonship in the divine nature, apart from which those filial qualities which
God demands from man could have no sanction; by faith as used in
Scripture he understood to be meant a certain moral or spiritual activity or
energy which virtually implied salvation, because it implied the existence of
a principle of spiritual life possessed of an immortal power. This faith, he
believed, could be properly awakened only by the manifestation, through
Christ, of love as the law of life, and as identical with an eternal
righteousness which it was God’s purpose to bestow on every individual
soul. As an interpreter of the mystical side of Calvinism and of the
psychological conditions which correspond with the doctrines of grace
Erskine is unrivalled. During the last thirty-three years of his life Erskine
ceased from literary work. Among his friends were Madame Vernet, the
duchess de Broglie, the younger Mdme de Stael, M. Vinet of Lausanne,
Edward Irving, Frederick D. Maurice, Dean Stanley, Bishop Ewing, Dr
John Brown and Thomas Carlyle. His wide influence was due to his high
character and unassuming earnestness. He died at Edinburgh on the 20th of
March 1870.

His principal works are Remarks on the Internal Evidence for the
Truth of Revealed Religion (1820), an Essay on Faith (1822), and the
Unconditional Freeness of the Gospel (1828). These have all passed
through several editions, and have also been translated into French. He
is also the author of the Brazen Serpent (1831), the Doctrine of
Election (1839), several “Introductory Essays” to editions of Christian
Authors, and a posthumous work entitled Spiritual Order and Other

Papers (1871). Two vols. of his letters, edited by William Hanna, D.D.,
with reminiscences by Dean Stanley and Principal Shairp, appeared in
1877.

ERSKINE, THOMAS ERSKINE, 1st Baron (1750-1823), lord
chancellor of England, was the third and youngest son of Henry David, 10th
earl of Buchan, and was born in Edinburgh on the 10th of January 1750.
From an early age he showed a strong desire to enter one of the learned
professions; but his father, owing to his straitened circumstances, was
unable to do more than give him a good school education at the high school
of Edinburgh and the grammar school of St Andrews. In 1764 he was sent
as a midshipman on board the “Tartar,” but on finding, when he returned to
this country after four years’ absence in North America and the West Indies,
that there was little immediate chance of his rank of acting lieutenant being
confirmed, he quitted the service and entered the army, purchasing a
commission in the 1st Royals with the meagre patrimony which had been
left to him. But promotion here was as slow as in the navy; while in 1770 he
had added greatly to his difficulties by marrying the daughter of Daniel
Moore, M.P. for Marlow, an excellent wife, but as poor as himself.
However, an accidental visit to an assize court in the town in which he was
quartered, and an interview with Lord Mansfield, the presiding judge,
confirmed his resolve to quit the army for the law. Accordingly on the 26th
of April 1775 he was admitted a student of Lincoln’s Inn. He also on the
13th of January following entered himself as a gentleman commoner on the

books of Trinity College, Cambridge, but merely that by graduating he
might be called two years earlier.

He read in the chambers of Francis Buller (afterwards Mr Justice Buller)
and George (afterwards Baron) Wood, and was called to the bar on the 3rd
of July 1778. His success was immediate and brilliant. An accident was the
means of giving him his first case, Rex v. Baillie, in which he appeared for
Captain Thomas Baillie, the lieutenant-governor of Greenwich hospital,
who had published a pamphlet animadverting in severe terms upon the
abuses which Lord Sandwich, the first lord of the admiralty, had introduced
into the management of the hospital, and against whom a rule had been
obtained from the court of king’s bench to show cause why a criminal
information for libel should not be filed. Erskine was the junior of five
counsel; and it was his good fortune that the prolixity of his leaders
consumed the whole of the first day, thereby giving the advantage of
starting afresh next morning. He made use of this opportunity to deliver a
speech of wonderful eloquence, skill and courage, which captivated both
the audience and the court. The rule was discharged, and Erskine’s fortune
was made. He received, it is said, thirty retainers before he left the court. In
1781 he delivered another remarkable speech, in defence of Lord George
Gordon—a speech which gave the death-blow to the doctrine of
constructive treason. In 1783, when the Coalition ministry came into power,
he was returned to parliament as member for Portsmouth. His first speech in
the House of Commons was a failure; and he never in parliamentary debate
possessed anything like the influence he had at the bar. He lost his seat at
the dissolution in the following year, and remained out of parliament until
1790, when he was again returned for Portsmouth. But his success at the bar
continued unimpaired. In 1783 he received a patent of precedence. His first
special retainer was in defence of Dr W.D. Shipley, dean of St Asaph, who
was tried in 1784 at Shrewsbury for seditious libel—a defence to which was
due the passing of the Libel Act 1792, laying down the principle that it is

for the jury, and not for the judge to decide the question whether or no a
publication is a libel. In 1789 he was counsel for John Stockdale, a
bookseller, who was charged with seditious libel in publishing a pamphlet
in favour of Warren Hastings, whose trial was then proceeding; and his
speech on this occasion, probably his greatest effort, is a consummate
specimen of the art of addressing a jury. Three years afterwards he brought
down the opposition alike of friends and foes by defending Thomas Paine,
author of The Rights of Man—holding that an advocate has no right, by
refusing a brief, to convert himself into a judge. As a consequence he lost
the office of attorney-general to the prince of Wales, to which he had been
appointed in 1786; the prince, however, subsequently made amends by
making him his chancellor. Among Erskine’s later speeches may be
mentioned those for Horne Tooke and the other advocates of parliamentary
reform, and that for James Hadfield, who was accused of shooting at the
king. On the accession of the Grenville ministry in 1806 he was made lord
chancellor, an office for which his training had in no way prepared him, but
which he fortunately held only during the short period his party was in
power. Of the remainder of his life it would be well if nothing could be said.
Occasionally speaking in parliament, and hoping that he might return to
office should the prince become regent, he gradually degenerated into a
state of useless idleness. Never conspicuous for prudence, he aggravated his
increasing poverty by an unfortunate second marriage.

His first wife had died in 1805, and he married at Gretna Green a Miss
Mary Buck. The date of this marriage is not definitely known. Once only—
in his conduct in the case of Queen Caroline—does he recall his former
self. He died at Almondell, Linlithgowshire, on the 17th of November 1823,
of pneumonia, caught on the voyage to Scotland.

Erskine’s great forensic reputation was, to a certain extent, a concomitant
of the numerous political trials of the day, but it was also due to his

impassioned eloquence and undaunted courage, which so often carried
audience and jury and even the court along with him. As a judge he did not
succeed; and it has been questioned whether under any circumstances he
could have succeeded. For the office of chancellor he was plainly unfit. As
a lawyer he was well read, but by no means profound. His strength lay in
the keenness of his reasoning faculty, in his dexterity and the ability with
which he disentangled complicated masses of evidence, and above all in his
unrivalled power of fixing and commanding the attention of juries. To no
department of knowledge but law had he applied himself systematically,
with the single exception of English literature, of which he acquired a
thorough mastery in early life, at intervals of leisure in college, on board
ship, or in the army. Vanity is said to have been his ruling personal
characteristic; but those who knew him, while they admit the fault, say that
in him it never took an offensive form, even in old age, while the singular
grace and attractiveness of his manner endeared him to all with whom he
came in contact.

By his first wife he had four sons and four daughters. His eldest son,
David Montagu (1776-1855), was a well-known diplomatist; his second
son, Henry David (1786-1859), was dean of Ripon; and his third son,
Thomas (1788-1864), became a judge of the court of common pleas. By his
second wife he had one son, born in 1821.

In 1772 Erskine published Observations on the Prevailing Abuses in
the British Army, a pamphlet which had a large circulation, and in later
life, Armata, an imitation of Gulliver’s Travels. His most noted
speeches have repeatedly appeared in a collected form. See Campbell’s
Lives of the Chancellors; Moore’s Diaries; Fergusson’s Henry Erskine
(1882); Dumerit’s Henry Erskine, a Study (Paris, 1883); Lord
Brougham’s Memoir, prefixed to Erskine’s Speeches (1847); Romilly’s
Memoirs; the Croker Papers; Lord Holland’s Memoirs.

ERUBESCITE, a native copper-iron sulphide, Cu5FeS4, of importance
as an ore of copper. It crystallizes in the cubic system, the usual form being
that of interpenetrating cubes twinned on an octahedral plane. The faces are
usually curved and rough, and the crystals confusedly aggregated together.
Compact and granular masses are of more frequent occurrence. The colour
on a freshly fractured surface is bronzy or coppery, but in moist air this
rapidly tarnishes with iridescent blue and red colours; hence the names
purple copper ore, variegated copper ore (Ger. Buntkupfererz), horse-flesh
ore, and erubescite (from the Lat. erubescere, “to grow red”). The lustre is
metallic, and the streak greyish-black; hardness 3; sp. gr. 5.0. Bornite (after
Baron Ignaz von Born, b. 1742, d. 1791) is a name in common use for this
mineral, and it predates erubescite, the name given by J.D. Dana in 1850,
but afterwards rejected by him; French authors use the name phillipsite,
after the English mineralogist, R. Phillips, who analysed the mineral; both
these earlier names had, however, been previously used for other minerals.

Owing to the frequent presence of mechanically admixed chalcopyrite
and chalcocite, the published analyses of erubescite show wide variations,
the copper, for example, varying from 50 to 70%. Even the best Cornish
crystals enclose a nucleus of chalcopyrite (CuFeS2), and an analysis of
these made in 1839 led to the long-accepted formula Cu3FeS3. Recently,
B.J. Harrington has analysed carefully selected material and obtained the
formula Cu5FeS4.

Erubescite occurs in copper-bearing veins, and has been mined as an ore
of copper at Redruth in Cornwall, Montecatini in the province of Pisa,
Tuscany, Bristol in Connecticut, Acton in Canada, and other localities in

North America. The best crystallized specimens are from the Carn Brea
mine and other copper mines in the neighbourhood of Redruth, and from
Bristol in Connecticut. Recently a few large isolated crystals with the form
of icositetrahedra have been found with calcite and albite in a gold-vein on
Frossnitz-Alpe in the Gross-Venediger, Tirol.
(L. J. S.)

ERYSIPELAS (a Greek word, probably derived from ἐρυθρός, red, and
πέλλα, skin)—synonyms, the Rose, St Anthony’s Fire—an acute contagious
disease, characterized by a special inflammation of the skin, caused by a
streptococcus. Erysipelas is endemic in most countries, and epidemic at
certain seasons, particularly the spring of the year. The poison is not very
virulent, but it certainly can be conveyed by bedding and the clothes of a
third person. Two varieties are occasionally described, a traumatic and an
idiopathic, but the disease seems to depend in all cases upon the existence
of a wound or abrasion. In the so-called idiopathic variety, of which facial
erysipelas is the best known, the point of entry is probably an abrasion by
the lachrymal duct.

When the erysipelas is of moderate character there is simply a redness of
the integument, which feels somewhat hard and thickened, and upon which
there often appear small vesications. This redness, though at first
circumscribed, tends to spread and affect the neighbouring sound skin, until
an entire limb or a large area of the body may become involved in the
inflammatory process. There is usually considerable pain, with heat and
tingling in the affected part. As the disease advances the portions of skin

first attacked become less inflamed, and exhibit a yellowish appearance,
which is followed by slight desquamation of the cuticle. The inflammation
in general gradually disappears. Sometimes, however, it breaks out again,
and passes over the area originally affected the second time. But besides the
skin, the subjacent tissues may become involved in the inflammation, and
give rise to the formation of pus. This is termed phlegmonous erysipelas,
and is much more apt to occur in connexion with the traumatic variety of
the disease. Occasionally the affected parts become gangrenous. Certain
complications are apt to arise in erysipelas affecting the surface of the body,
particularly inflammation of serous membranes, such as the pericardium or
pleura.

Erysipelas of the face usually begins with symptoms of general illness,
the patient feeling languid, drowsy and sick, while frequently there is a
distinct rigor followed with fever. Sore throat is sometimes felt, but in
general the first indication of the local affection is a red and painful spot at
the side of the nose or on one of the cheeks or ears. Occasionally it would
appear that the inflammation begins in the throat, and reaches the face
through the nasal fossae. The redness gradually spreads over the whole
surface of the face, and is accompanied with swelling, which in the lax
tissues of the cheeks and eyelids is so great that the features soon become
obliterated and the countenance wears a hideous expression. Advancing
over the scalp, the disease may invade the neck and pass on to the trunk, but
in general the inflammation remains confined to the face and head. While
the disease progresses, besides the pain, tenderness and heat of the affected
parts, the constitutional symptoms are very severe. The temperature rises
often to 105° or higher, remains high for four or five days, and then falls by
crisis. Delirium is a frequent accompaniment. The attack in general lasts for
a week or ten days, during which the inflammation subsides in the parts of
the skin first attacked, while it spreads onwards in other directions, and

after it has passed away there is, as already observed, some slight
desquamation of the cuticle.

Although in general the termination is favourable, serious and
occasionally fatal results follow from inflammation of the membranes of
the brain, and in some rare instances sudden death has occurred from
suffocation arising from oedema glottidis, the inflammatory action having
spread into and extensively involved the throat. One attack of this disease,
so far from protecting from, appears rather to predispose to others. It is
sometimes a complication in certain forms of exhausting disease, such as
phthisis or typhoid fever, and is then to be regarded as of serious import. A
very fatal form occasionally attacks new-born infants, particularly in the
first four weeks of their lives. In epidemics of puerperal fever this form of
erysipelas has been specially found to prevail.

The treatment of erysipelas is best conducted on the expectant system.
The disease in most instances tends to a favourable termination; and beyond
attention to the condition of the stomach and bowels, which may require the
use of some gentle laxative, little is necessary in the way of medicine. The
employment of preparations of iron in large doses is strongly recommended
by many physicians. But the chief point is the administration of abundant
nourishment in a light and digestible form. Of the many local applications
which may be employed, hot fomentations will be found among the most
soothing. Dusting the affected part with powdered starch, and wrapping it in
cotton wadding, is also of use.

In the case of phlegmonous erysipelas complicating wounds, free
incisions into the part are necessary.

ERYTHRAE [mod. Litri], one of the Ionian cities of Asia Minor,
situated on a small peninsula stretching into the Bay of Erythrae, at an equal
distance from the mountains Mimas and Corycus, and directly opposite the
island of Chios. In the peninsula excellent wine was produced. The town
was said to have been founded by Ionians under Knopos, son of Codrus.
Never a large city, it sent only eight ships to the battle of Lade. The
Erythraeans owned for a considerable time the supremacy of Athens, but
towards the close of the Peloponnesian war they threw off their allegiance
to that city. After the battle of Cnidus, however, they received Conon, and
paid him honours in an inscription, still extant. Erythrae was the birthplace
of two prophetesses—one of whom, Sibylla, is mentioned by Strabo as
living in the early period of the city; the other, Athenais, lived in the time of
Alexander the Great. The ruins include well-preserved Hellenistic walls
with towers, of which five are still visible. The acropolis (280 ft.) has the
theatre on its N. slope, and eastwards lie many remains of Byzantine
buildings. Modern Litri is a considerable place and port, extending from the
ancient harbour to the acropolis. The smaller coasting steamers call, and
there is an active trade with Chios and Smyrna.

ERYTHRITE, the name given to (1) a mineral composed of a hydrated
cobalt arsenate, and (2) in chemistry, a tetrahydric alcohol. (1) The mineral
erythrite has the formula Co3(AsO4)2·8H2O, and crystallizes in the
monoclinic system and is isomorphous with vivianite. It sometimes occurs
as beautiful radially-arranged groups of blade-shaped crystals with a bright
crimson colour and brilliant lustre. On exposure to light the colour and

lustre deteriorate. There is a perfect cleavage parallel to the plane of
symmetry, on which the lustre is pearly. Cleavage flakes are soft (H = 2),
sectile and flexible; specific gravity 2.95. The mineral is, however, more
often found as an earthy encrustation with a peach-blossom colour, and in
this form was early (1727) known as cobalt-bloom (Ger. Kobaltblüthe). The
name erythrite, from ἐρυθρός, “red,” was given by F.S. Beudant in 1382.
Erythrite occurs as a product of alteration of smaltite (CoAs2) and other
cobaltiferous arsenides. The finest crystallized specimens are from
Schneeberg in Saxony. The earthy variety has been found in Thuringia and
Cornwall and some other places. (2) The alcohol erythrite has the
constitutional formula HO·H2C·CH(OH)·CH(OH)·CH2OH; it is also
known as erythrol, erythroglucin and phycite. It corresponds to tartaric acid,
and, like this substance, it occurs in four stereo-isomeric forms. The
internally compensated modification, i-erythrite, corresponding to
mesotartaric acid, occurs free in the algae Protococcus vulgaris, and as the
orsellinate, erythrin, C4H6(OH)2(O·C8H7O3)2, in many lichens and algae,
especially Roccella montagnei. It has a sweet taste, melts at 126°, and boils
at 330°. Careful oxidation with dilute nitric acid gives erythrose or tetrose,
which is probably a mixture of a trioxyaldehyde and trioxyketone.
Energetic oxidation gives erythritic acid and mesotartaric acid. i-Erythrite
and the racemic mixture of the dextro and laevo varieties were synthesized
by Griner in 1893 from divinyl.

ERZERUM, or Arzrum (Arm. Garin), the chief town of an important
vilayet of the same name in Asiatic Turkey. It is a military station and a

fortress of considerable strategical value, closing the roads from Kars, Olti
and other parts of the frontier. Several important routes from Trebizond and
various parts of Anatolia converge towards it from the west. It is situated at
the eastern end of an open bare plain, 30 m. long and about 12 wide,
bordered by steep, rounded mountains and traversed by the Kara Su, or
western Euphrates, which has its source in the Dumlu Dagh a few miles
north of that town, which lies at an elevation of 6250 ft. above sea-level,
while the near hills rise to 10,000 ft. The scenery in the neighbourhood is
striking, lofty bare mountains being varied by open plains and long valleys
dotted with villages. Just east of the town is the broad ridge of the
Deveboyun (“Camel’s Neck”), across which the road passes to Kars. To the
south is the Palanduken range, from which emerge numerous streams,
supplying the town with excellent water. In the plain to the north the Kara
Su traverses extensive marshes which afford good wildfowl-shooting in the
spring.

The town is surrounded by an earthen enceinte or rampart with some
forts on the hills just above it, and others on the Deveboyun ridge facing
east, the whole forming a position of considerable strength. The old walls
and the citadel have disappeared. Inside the ramparts the town lies rather
cramped, with narrow, crooked streets, badly drained and dirty; the houses
are generally built of dark grey volcanic stone with flat roofs, the general
aspect, owing to the absence of trees, being somewhat gloomy. The water-
supply from Palanduken is distributed by wooden pipes to numerous public
fountains. The town has a population of about 43,000, including about
10,000 Armenians, 2000 Persians and a few Jews. It has a garrison in peace
of about 5000 men. It is the seat of the British consulate for Kurdistan, and
there are other European consulates besides an American mission with
schools. The great altitude accounts for very severe winter cold,
occasionally 10° to 25° below zero F., accompanied by blizzards (tipi)

sometimes fatal to travellers overtaken by them. The summer heat is
moderate (59° to 77°).

There are several well-built mosques (none older than the 16th century),
public baths, and several good khans. There are Armenian and Catholic
churches, but the most beautiful building is a medresse erected in the 12th
century by the Seljuks, with ornamental doorway and two graceful minarets
known as the Chifte Minare.

Situated on the main road from Trebizond into north-west Persia, the
town has always a large caravan traffic, principally of camels, but since the
improvement of communications in Russia this has declined. A good
carriage-road leads to the coast at Trebizond, the journey being made in five
or six days. There are also roads to Kars, Bayazid, Erzingan and Kharput.
Blacksmiths’ and coppersmiths’ work is better here than in most Turkish
towns; horse-shoes and brasswork are also famous. There are several
tanneries, and Turkish boots and saddles are largely made. Jerked beef
(pasdirma) is also prepared in large quantities for winter use. The plain
produces wheat, barley, millet and vegetables. Wood fuel is scarce, the
present supply being from the Tortum district, whence surface coal and
lignite are also brought; but the usual fuel is tezek or dried cow-dung. The
bazaars are of no great interest. Good Persian carpets and similar goods can
be obtained.

Erzerum is a town of great antiquity, and has been identified with the
Armenian Garin Kalakh, the Arabic Kalikale, and the Byzantine
Theodosiopolis of the 5th century, when it was a frontier fortress of the
empire—hence its name Erzen-er-Rum. It was captured by the Seljuks in
1201, when it was an important city, and it fell into Turkish possession in
1517. In July 1829 it was captured by the Russian general Paskevich, and
the occupation continued until the peace of Adrianople (September 1829).
The town was unsuccessfully attacked by the Russians on the 9th of

November 1877 after a victory gained by them a short time previously on
the Deveboyun heights; it was occupied by them during the armistice (7th
of February 1878) and restored to Turkey after the treaty of Berlin. In 1859
a severe earthquake destroyed much of the town, and another in November
1901 caused much damage.

The Erzerum vilayet extends from the Persian frontier at Bayazid, all
along the Russian frontier and westward into Anatolia at Baiburt and
Erzingan. It is divided into the three sanjaks of Bayazid, Erzerum, and
Erzingan. It includes the highest portion of the Armenian plateau, and
consists of bare undulating uplands varied by lofty ranges. The deep gorges
of the Chorokh and Tortum streams north of the town alone have a different
appearance, being well wooded in places. Both arms of the Euphrates have
their rise in this country as well as the Aras (Araxes) and the Chorokh
(Acampsis). It is an agricultural country with few industries. Besides
forests, iron, salt, sulphur and other mineral springs are found. Some of the
coal and lignite mines in Tortum have been recently worked to supply fuel
for Erzerum. The population is largely Armenian and Kurd with some Turks
(Moslems 500,000, Christians 140,000).
(C. W. W.; F. R. M.)

ERZGEBIRGE, a mountain chain of Germany, extending in a W.S.W.
direction from the Elbe to the Elstergebirge along the frontier between
Saxony and Bohemia. Its length from E.N.E. to W.S.W. is about 80 m., and
its average breadth about 25 m. The southern declivity is generally steep
and rugged, forming in some places an almost perpendicular wall of the

height of from 2000 to 2500 ft.; while the northern, divided at intervals into
valleys, sometimes of great fertility and sometimes wildly romantic, slopes
gradually towards the great plain of northern Germany. The central part of
the chain forms a plateau of an average height of more than 3000 ft. At the
extremities of this plateau are situated the highest summits of the range:—in
the south-east the Keilberg (4080 ft.); in the north-east the Fichtelberg
(3980 ft.); and in the south-west the Spitzberg (3650 ft.). Between the
Keilberg and the Fichtelberg, at the height of about 3300 ft., is situated
Gottesgab, the highest town in Bohemia. Geologically, the Erzgebirge range
consists mainly of gneiss, mica and phyllite. As its name (Ore Mountains)
indicates, it is famous for its mineral ores. These are chiefly silver and lead,
the layers of both of which are very extensive, tin, nickel, copper and iron.
Gold is found in several places, and some arsenic, antimony, bismuth,
manganese, mercury and sulphur. The Erzgebirge is celebrated for its lace
manufactures, introduced by Barbara Uttmann in 1541, embroideries, silk-
weaving and toys. The climate is in winter inclement in the higher
elevations, and, as the snow lies deep until the spring, the range is largely
frequented by devotees of winter sport, ski, toboganning, &c. In summer
the air is bracing, and many climatic health resorts have sprung into
existence, among which may be mentioned Kipsdorf, Bärenfels and
Oberwiesenthal. Communication with the Erzgebirge is provided by
numerous lines of railway, some, such as that from Freiberg to Brüx, that
from Chemnitz to Komotau, and that from Zwickau to Carlsbad, crossing
the range, while various local lines serve the higher valleys.

The Elstergebirge, a range some 16 m. in length, in which the Weisse
Elster has its source, runs S.W. from the Erzgebirge to the Fichtelgebirge
and attains a height of 2630 ft.

See Grohmann, Das Obererzgebirge und seine Städte (1903), and
Schurtz, Die Pässe des Erzgebirges (1891); also Daniel, Deutschland,

vol. ii., and Gebauer, Länder und Völkerkunde, vol. i.

ERZINGAN, or Erzinjan (Arsinga of the middle ages), the chief town of
a sanjak in the Erzerum vilayet of Asiatic Turkey. It is the headquarters of
the IV. army corps, being a place of some military importance, with large
barracks and military factories. It is situated at an altitude of 3900 ft., near
the western end of a rich well-watered plain through which runs the Kara
Su or western Euphrates. It is surrounded by orchards and gardens, and is
about a mile from the right bank of the river, which here runs in two wide
channels crossed by bridges. One wide street traverses the town from east to
west, but the others are narrow, unpaved and dirty, except near the new
government buildings and the large modern mosque of Hajji Izzet Pasha to
the north, which are the only buildings of note. The principal barracks,
military hospital and clothing factory are at Karateluk on the plain and
along the foot-hills to the north 3 m. off, one recent addition to the business
buildings having electric power and modern British machinery; some older
barracks and a military tannery and boot factory being in the town. The
population numbers about 15,000, of whom about half are Armenians living
in a separate quarter. The principal industries are the manufacture of silk
and cotton and of copper dishes and utensils. The climate is hot in summer
but moderate in winter. A carriage-road leads to Trebizond, and other roads
to Sivas, Karahissar, Erzerum and Kharput. The plain, almost surrounded
by lofty mountains, is highly productive with many villages on it and the
border hills. Wheat, fruit, vines and cotton are largely grown, and cattle and
sheep are bred. Water is everywhere abundant, and there are iron and hot

sulphur springs. The battle in which the sultan of Rum (1243) was defeated
by the Mongols took place on the plain, and the celebrated Armenian
monastery of St Gregory, “the Illuminator,” lies on the hills 11 m. S.W. of
the town.

Erzingan occupies the site of an early town in which was a temple of
Anaitis. It was an important place in the 4th century when St Gregory lived
in it. The district passed from the Byzantines to the Seljuks after the defeat
of Romanus, 1071, and from the latter to the Mongols in 1243. After having
been held by Mongols, Tatars and Turkomans, it was added to the Osmanli
empire by Mahommed II. in 1473. In 1784 the town was almost destroyed
by an earthquake.
(C. W. W.; F. R. M.)

ESAR-HADDON [Assur-akhi-iddina, “Assur has given a brother”],
Assyrian king, son of Sennacherib; before his accession to the throne he had
also borne another name, Assur-etil-ilani-yukin-abla. At the time of his
father’s murder (the 20th of Tebet, 681 b.c.) he was commanding the
Assyrian army in a war against Ararat. The conspirators, after holding
Nineveh for 42 days, had been compelled to fly northward and invoke the
aid of the king of Ararat. On the 12th of Iyyar (680 b.c.) a decisive battle
was fought near Malatia, in which the veterans of Assyria won the day, and
at the close of it saluted Esar-haddon as king. He returned to Nineveh, and
on the 8th of Sivan was crowned king. A good general, Esar-haddon was
also an able and conciliatory administrator. His first act was to crush a
rebellion among the Chaldaeans in the south of Babylonia and then to

restore Babylon, the sacred city of the West, which had been destroyed by
his father. The walls and temple of Bel were rebuilt, its gods brought back,
and after his right to rule had been solemnly acknowledged by the
Babylonian priesthood Esar-haddon made Babylon his second capital. A
year or two later Media was invaded and Median chiefs came to Nineveh to
offer homage to their conqueror. He now turned to Palestine, where the
rebellion of Abdi-milkutti of Zidon was suppressed, its leader beheaded,
and a new Zidon built out of the ruins of the older city (676-675 b.c.). All
Palestine now submitted to Assyria, and 12 Syrian and 10 Cyprian princes
(including Manasseh of Judah) came to pay him homage and supply him
with materials for his palace at Nineveh. But a more formidable enemy had
appeared on the Assyrian frontier (676 b.c.). The Cimmerii (see Scythia)
under Teuspa poured into Asia Minor; they were, however, overthrown in
Cilicia, and the Cilician mountaineers who had joined them were severely
punished. It was next necessary to secure the southern frontier of the
empire. Esar-haddon accordingly marched into the heart of Arabia, to a
distance of about 900 m., across a burning and waterless desert, and struck
terror into the Arabian tribes. At last he was free to complete the policy of
his predecessors by conquering Egypt, which alone remained to threaten
Assyrian dominion in the West. Baal of Tyre had transferred his allegiance
from Esar-haddon to the Egyptian king Tirhaka and opened to the latter the
coast road of Palestine; leaving a force, therefore, to invest Tyre, Esar-
haddon led the main body of the Assyrian troops into Egypt on the 5th of
Adar, 673 b.c. The desert was crossed with the help of the Arabian sheikh.
Egypt seems to have submitted to the invader and was divided into twenty
satrapies. Another campaign, however, was needed before it could be finally
subdued. In 670 b.c. Esar-haddon drove the Egyptian forces before him in
15 days (from the 3rd to the 18th of Tammuz) all the way from the frontier
to Memphis, thrice defeating them with heavy loss and wounding Tirhaka
himself. Three days after Memphis fell, and this was soon afterwards

followed by the surrender of Tyre and its king. In 668 b.c. Egypt again
revolted, and while on the march to reduce it Esar-haddon fell ill and died
on the 10th of Marchesvan. His empire was divided between his two sons
Assur-bani-pal and Samas-sum-yukin, Assur-bani-pal receiving Assyria and
his brother Babylonia, an arrangement, however, which did not prove to be
a success. Esar-haddon was the builder of a palace at Nineveh as well as of
one which he erected at Calah for Assur-bani-pal.

Authorities.—E.A.W. Budge, History of Esarhaddon (1880); E.
Schrader, Keilinschriftliche Bibliothek, ii. (1889) (Abel and Winckler in
ii. pp. 120-153); G. Maspero, Passing of the Empires, pp. 345 sqq.; F.
von Luschan, “Ausgrabungen in Sendschirli,” i. (Mitteilungen aus den
orientalischen Sammlungen, 1893).
(A. H. S.)

ESAU, the son of Isaac and Rebecca, in the Bible, and the elder twin
brother of Jacob. He was so called because he was red (admōnī) and hairy
when he was born, and the name Edom (red) was given to him when he
sold his birthright to Jacob for a meal of red lentil pottage (Gen. xxv. 21-
34). Another story of the manner in which Jacob obtained the superiority is
related in Gen. xxvii. Here the younger brother impersonated the elder, and
succeeded in deceiving his blind father by imitating the hairiness of his
brother. He thus gained the blessing intended for the first-born, and Esau,
on hearing how he had been forestalled, vowed to kill him. Jacob
accordingly fled to his mother’s relatives, and on his return, many years
later, peace was restored between them (xxxii. sq.). These primitive stories

of the relations between the eponymous heads of the Edomites and
Israelites are due to the older (Judaean) sources; the late notices of the
Priestly school (see Genesis) preserve a different account of the parting of
the two (Gen. xxxvi. 6-8), and lay great stress upon Esau’s marriages with
the Canaanites of the land, unions which were viewed (from the writer’s
standpoint) with great aversion (Gen. xxvi. 34 sq., xxvii. 46). For “Esau” as
a designation of the Edomites, cf. Jer. xlix. 8, Obad. vv. 6, 8, and on their
history, see Edom.

Esau’s characteristic hairiness (Gen. xxv. 25, xxvii. 11) has given
rise to the suggestion that his name is properly ‘ēshav, from a root
corresponding to the Arab. ‘athiya, to have thick or matted hair. Mt
Seir, too, where he resided, etymologically suggests a “shaggy”
mountain-land. According to Hommel (Sud-arab. Chrestom. p. 39 sq.)
the name Esau has S. Arabian analogies. On the possible identity of the
name with Usoos, the Phoenician demi-god (Philo of Byblus, ap.
Eusebius, Praep. Evang. i. 10), see Cheyne, Encyc. Bib. col. 1333;
Lagrange, Études sur les religions sémitiques, p. 416 (Paris, 1905); Ed.
Meyer, Israeliten, 278 sq. (and, on general questions, ib. 128 sq., 329
sqq.).
(S. A. C.)

ESBJERG, a seaport of Denmark in the amt (county) of Ribe, 18 m.
from the German frontier on the west coast of Jutland. It has railway
communication with the east and north of Jutland, and with Germany. It
was granted municipal rights in 1900, having grown with astonishing

rapidity from 13 inhabitants in 1868 to 13,355 in 1901. This growth it owes
to the construction of a large harbour in 1868-1888. It is the principal outlet
westward for S. Jutland; exports pork and meat, butter, eggs, fish, cattle and
sheep, skins, lard and agricultural seeds, and has regular communication
with Harwich and Grimsby in England. Three miles S.E. is Nordby on the
island of Fanö, the northernmost of the North Frisian chain. It is an arid
bank of heathland and dunes, but both Nordby and Sönderho in the south
are frequented as seaside resorts. The former has a school of navigation.
The fisheries are valuable.

ESCANABA, a city and the county-seat of Delta county, Michigan,
U.S.A., on Little Bay de Noquette, an inlet of Green Bay, about 60 m. S. of
Marquette. Pop. (1890) 6808; (1900) 9549, of whom 3214 were foreign-
born; (1910 census) 13,194. It is served by the Chicago & North-Western
and the Escanaba & Lake Superior railways. It is built on a picturesque
promontory which separates the waters of Green Bay from Little Bay de
Noquette, and its delightful summer climate, wild landscape scenery and
facilities for boating and trout fishing make it a popular summer resort.
Escanaba has a water front of 8 m., and is an important centre for the
shipment of iron-ore, for which eight large and well-equipped docks are
provided—there is an ore-crushing plant here; considerable quantities of
lumber and fish are also shipped, and furniture, flooring (especially of
maple) and wooden ware (butter-dishes and clothes-pins) are manufactured.
There is a large tie-preserving plant here. Good water power is supplied by

the Escanaba river. Escanaba was settled in 1863, was incorporated as a
village in 1883, and was first chartered as a city in the same year.

ESCAPE (in mid. Eng. eschape or escape, from the O. Fr. eschapper,
modern échapper, and escaper, low Lat. escapium, from ex, out of, and
cappa, cape, cloak; cf. for the sense development the Gr. ἐκδύεσθαι,
literally to put off one’s clothes, hence to slip out of, get away), a verb
meaning to get away from, especially from impending danger or harm, to
avoid capture, to regain one’s liberty after capture. As a substantive,
“escape,” in law, is the regaining of liberty by one in custody contrary to
due process of law. Such escape may be by force, if out of prison it is
generally known as “prison-breach” or “prison-breaking,” or by the
voluntary or negligent act of the custodian. Where the escape is caused by
the force or fraud of others it is termed “rescue” (q.v.). “Escape” is used in
botany of a cultivated plant found growing wild. The word is also used of a
means of escape, e.g. “fire-escape,” and of a loss or leakage of gas, current
of electricity or water.

ESCHATOLOGY (Gr. ἔσχατος, last, and λόγος, science; the “doctrine
of last things”), a theological term derived from the New Testament phrases
“the last day” (ἐν τῇ ἐσχάτῃ ἡμέρᾳ, John vi. 39), “the last times” (ἐπ᾽

ἐσχάτων τῶν χρόνων, 1 Peter i. 20), “the last-state” (τὰ ἔσχατα, Matt.
xii. 45), a conception taken over from ancient prophecy (Is. ii. 2; Mal. iv. 1).
It was the common belief in the apostolic age that the second advent of
Christ was near, and would give the divine completion to the world’s
history. The use of the term, however, has been extended so as to include all
that is taught in the Scriptures about the future life of the individual as well
as the final destiny of the world. The reasons for the belief in a life after
death are discussed in the article Immortality. The present article, after a
brief glance at the conceptions of the future of the individual or the world
found in other religions, will deal with the teaching of the Old and New
Testaments, the Jewish and the Christian Church regarding the hereafter.

There is a bewildering variety in the views of the future life and world
held by different peoples. The future life may be conceived as simply a
continuation of the present life in its essential features, although under
conditions more or less favourable. It may also be thought of as retributive,
as a reversal of present conditions so that the miserable are comforted, and
the prosperous laid low, or as a reward or punishment for good or evil
desert here. Personal identity may be absorbed, as in the transmigration of
souls, or it may even be denied, while the good or bad result of one life is
held to determine the weal or woe of another. The scene of the future life
may be thought of on earth, in some distant part of it, or above the earth, in
the sky, sun, moon or stars, or beneath the earth. The abodes of bliss and the
places of torment may be distinguished, or one last dwelling-place may be
affirmed for all the dead. Sometimes the good find their abiding home with
the gods; sometimes a number of heavens of varying degrees of blessedness
is recognized (see F.B. Jevons, An Introduction to the History of Religion,
chs. xxi. and xxii., 1902; and J.A. MacCulloch’s Comparative Theology,
xiv., 1902).

(1) Confucius, though unwilling to discuss any questions concerning the
dead, by approving ancestor-worship recognized a future life. (2) Taoism
promises immortality as the reward of merit. (3) The Book of the Dead—a
guide-book for the departed on his long journey in the
Eastern Religions. unseen world to the abode of the blessed—shows the
attention the Egyptian religion gave to the state of the
dead. (4) Although the Babylonian religion presents a very gloomy view of
the world of the dead, it is not without a few faint glimpses of a hope that a
few mortals at least may gain deliverance from the dread doom. (5) A
characteristic feature of Indian thought is the transmigration of the soul
from one mode of life to another, the physical condition of each being
determined by the moral and religious character of the preceding. But
deliverance from this cycle of existences, which is conceived as misery, is
promised by means of speculation and asceticism. Denying the continuance
of the soul, Buddhism affirmed a continuity of moral consequences
(Karma), each successive life being determined by the total moral result of
the preceding life. Its doctrine of salvation was a guide to, if not absolute
non-existence, yet cessation of all consciousness of existence (Nirvana).
Later Buddhism has, however, a doctrine of many heavens and hells. (6) In
Zoroastrianism not only was continuance of life recognized, but a strict
retribution was taught. Heaven and hell were very clearly distinguished, and
each soul according to its works passed to the one or to the other. But this
faith did not concern itself only with the future lot of the individual soul. It
was also interested in the close of the world’s history, and taught a decisive,
final victory of Ormuzd over Ahriman, of the forces of good over the forces
of evil. It is not at all improbable that Jewish eschatology in its later
developments was powerfully influenced by the Persian faith. (7)
Mahommedanism reproduces and exaggerates the lower features of popular
Jewish and Christian eschatology (see the separate articles on these
religions).