from the convection of the material through the aether
must be independent of the sign of v and therefore be of
the second order. Now the electric force (P,Q,R) is the
force acting on the electrons of the medium moving with
velocity v; consequently by Faraday's electrodynamic law
(P,Q,R) = (P',Q' - vc, R'- vb)
where (P', Q', R') is the force that would act on electrons
at rest, and (a,b,c) is the magnetic induction. The
latter force is, by Maxwell's hypothesis or by the dynamical
theory of an aether pervaded by electrons, the same as
that which strains the aether, and may be called the
aethereal force; it thereby produces an aethereal electric
displacement, say (y,g,h), according to the relation
(f,g,h) = (4pc2) - (P', Q', R'),
in which c is a constant belonging to the aether, which turns
out to be the velocity of light. The current of aethereal
displacement d/dt(f,g,h) is what adds on to the true electric
current to produce the total circuital current of Maxwell.
We have now to substitute these data in the universally
valid circuital relations---namely, (i) line integral of
magnetic force round a circuit is equal to 4p times the
current through its aperture, which may be regarded as a
definition of the constitution of the aether and its relation
to the electrons involved in it; and (ii) line integral
of the electric force belonging to any material circuit
(i.e. acting on the electrons situated on it which move
with the velocity of the matter) is equal to minus the
time-rate of change of the magnetic induction through that
circuit as it moves with the matter, this being a dynamical
consequence of the aethereal constitution assigned in (i).
We may now, as is somewhat the more natural course in the
terrestrial application, take axes (x,y,z) which move with the
matter; but the current must be invariably defined by the flux
across surfaces fixed in space, so that we may say that relation
(i) refers to a circuit fixed in space, while (ii) refers to
one moving with the matter. These circuital relations, when
expressed analytically, are then for a dielectric medium of types
dg/dy - db/dz = 4pu,...,..., where
(u,v,w) = (d/dt + v(d/dx))(f',g',h') + (d/dt)(f,g,h)
and
dR/dy - dQ/dz = -da/dt',...,...,.
where, when magnetic quality is inoperative, the magnetic
induction (a,b,c) is identical with the magnetic force (a,b,g.)
These equations determine all the phenomena. They take this simple
form, however, only when the movement of the matter is one of
translation. If v varies with respect to locality, or if there
is a velocity of convection (p,q,r) variable with respect to
direction and position, and analytical expression of the relation
(ii) assumes a more complex form; we thus derive the most general
equations of electrodynamic propagation for matter treated
as continuous, anyhow distributed and moving in any manner.
For the simplest case of polarized waves travelling parallel
to the axis of x, with the magnetic oscillation g along z
and the electric oscillation Q along y, all the quantities
are functions of x and t alone; the total current is
along y and given with respect to our moving axes by
v = (d/dt - v(d/dx))(Q+vg)/4pc2 + (d/dt)((K-1)/4pc2)Th;
also the circuital relations here reduce to
-dg/dx = 4pv, dQ/dx = -dg/dt;
thus
d2Q/dx2 = 4pdv/dt
giving, on substitution for v,
(c2-v2)d2Q/dx2 = Kd2Q/dt2 - 2vd2Q/dxdt.
For a simple wave-train, Q varies as sin m(x-Vt), leading
on substitution to the velocity of propagation V relative
to the moving material, by means of the equation KV2 + 2
vV = c2-v2; this gives, to the first order of v/c,
V = c/sqrt. K - v/K, which is in accordance with Fresnel's
law. Trains of waves nearly but not quite homogeneous as
regards wave-length will as usual be propagated as wave-groups
travelling with the slightly different velocity d(Vl-1)/
dl-1, the value of K occurring in V being a function of
l determined by the law of optical dispersion of the medium.
For purposes of theoretical discussions relating to moving radiators
and reflectors, it is important to remember that the dynamics
of all this theory of electrons involves the neglect of terms of
the order (v/c)2, not merely in the value of K but throughout.
Recent Experimental Developments.---The modification of
the spectrum of a radiating gas by a magnetic field, such
as would result from the hypothesis that the radiators are
the system of revolving or oscillating electrons in the
molecule, was detected by P. Zeeman in 1896, and worked
up, in conjunction with H. A. Lorentz, on the general lines
suggested by the electron-theory of molecular constitution.
While it cannot be said that the full significance of this
very definite phenomenon, consisting of the splitting of
the spectral line into a number of polarized components, has
yet been made out, a wide field of correlation with optical
theory, especially in the neighbourhood of absorption bands,
has been developed by Zeeman himself, by A. H. Becquerel,
by D. Macaluso and O. M. Corbino, and by other workers.
The most fundamental experimental confirmation that the theory
of the aether has received on the optical side in recent
years has been the verification of Maxwell's proposition that
radiation exerts mechanical force on a material system, on
which it falls, which may be represented in all cases as the
resultant of pressures operating along the rays, and of intensity
equal at each point of free space to the density of radiant
energy. A high vacuum is needed for the detection of the
minute forces here concerned; but just in that case the indirect
radiometer-effect of the heating of the residual gas masks the
effect. P. N. Lebedew in 1900 succeeded, by operating on
metallic vanes so thin that the exposed and averted faces
were practically at the same temperature, in satisfactorily
verifying the relation for metals; and very soon after, E.
F. Nichols and G. F. Hull published accounts of an exact
and extensive research, in which the principle had been
fully and precisely confirmed as regards both transparent
and opaque bodies. The experiment of J. H. Poynting may
also be mentioned, in which the tangential component of
the thrust of obliquely incident radiation is separately
put in evidence, by the torsion produced in an arrangement
which is not sensitive to the normal component or to the
radiometer-pressure of the residual gas. (See RADIOMETER.)
Next to these researches on the pressure of radiation, which,
by forming the mechanical link between radiation and matter,
are fundamental for the thermodynamics of radiant energy,
the most striking recent result has been the discovery of H.
Rubens and E. Hagen that for dark heat rays of only about ten
times the wave-length of luminous radiation, the properties
of metals are determined by their electric resistance alone,
which then masks all resonance due to periods of free vibration
of the molecules; and, moreover, that the resistance for such
alternations is practically the same as the ohmic resistance
for ordinary steady currents. They found that the absorbing
powers of the metals, and therefore, by the principle of
exchanges, their radiating powers also, are proportional to
the square roots of their electric conductivities. Maxwell had
himself, at an early stage of his theory, tested the absorbing
power of gold-leaf for light, and found that the effective
conductivity for luminous vibrations must be very much greater
than its steady ohmic value; it is, in fact, there a case of
incipient conductivity, which is continually being undone on
account of the rapid alternation of force before it is fully
established. That, however, complete conduction should
arrive with alternations only ten times slower than light
was an unexpected and remarkable fact, which verifies the
presumption that the process of conduction is one in which
the dynamic activities of the molecules do not come into
play. The corollary, that the electric resistance of a
metal can be determined in absolute units by experiments on
the reflexion of heat-rays from its surface, is a striking
illustration of the unification of the various branches
of physical science, which has come in the train of the
development of the theory of the aether. (See RADIATION.)
Finally, reference should be made to the phenomena of
radioactivity, whether excited by the electric discharge
in vacuum tubes, foreshadowed in part by Sir Wm. Crookes
and G. G. Stokes, and later by A. Schuster and others, but
first fully developed with astonishing results including
the experimental discovery of the free electron by J. J.
Thomson, or the correlated phenomena occurring spontaneously
in radio-active bodies as discovered by H. Becquerel and
by M. and Mme Curie, and investigated by them and by E.
Rutherford and others. These results constitute a far-reaching
development of the modern or electrodynamic theory of the
aether, of which the issue can hardly yet be foreseen.
REFERENCES.--Maxwell, Collected Papers H. A. Lorentz,
Archives Neerlandaises, xxi. 1887, and xxv. 1892, and a
tract, Versuch einer Theorie der electrischen und optischen
Erscheinungen in bewegten Korpern (Leyden, 1895); also
recent articles ``Elektrodynamik'' and ``Elektronentheorie''
in the Encyk. der Math. Wissenschaften, Band v. 13, 14;
O. Lodge, ``On Aberration Problems,'' Phil. Trans. 1893
and 1897; J. Larmor, Phil. Trans. 1894--95--97, and a
treatise, Aether and Motter (1900), where full references are
given. Of recent years most treatises on physical optics,
e.g. those of P. K. L. Drude, A. Schuster, R. W. Wood, have
been written largely on the basis of the general physics of
the aether; while the Collected Papers of Lord Rayleigh
should be accessible to all who desire a first-hand knowledge
of the development of the optical side of the subject. See
also MOLECULE, ELECTRICITY, LIGHT and RADIATION. (J. L.*)
1 See H. A. Lorentz, loc. cit. infra.; J.
Larmor, Aether and Matter, p. 262 and passim.
AETHICUS (=ETHICUS) ISTER, ``the philosopher of
Istria,'' the supposed but unknown author of a description
of the world written in Greek. An abridgment, under the
title of Cosmographia Ethici, written in barbarous Latin,
and wrongly described as the work of St Jerome, probably
belongs to the 7th century. After a discussion of the
creation of the world and a description of the earth, an
account of the wonderful journeys of Aethicus is given, with
digressions on various subjects, such as Alexander the Great
and the kings of Rome, full of obscure and fabulous details.
The name Aethicus is also attached to another geographical
treatise probably dating from the 6th century, a reproduction,
with some unimportant additions, of the cosmography--little
else than a dry list of names--of Julius Honorius.
Editions.--D'Avezac (1852); Pertz (1853); Wuttke
(1854); Riese's Lexicographi Latini Minores (1878);
see also Bunbury, History of Ancient Geography.
AETIOLOGY, or ETIOLOGY (from Gr. aitia. cause, and
logia, discourse), strictly, the science or philosophy of
causation, but generally used to denote the part of any special
science (and especially of that of medicine and disease)
which investigates the causes and origin of its phenomena.
An aetiological myth is one which is regarded as having
been invented ex post facto to explain some fact, name or
coincidence, the true account or origin of which has been
forgotten. Such myths were often based on grotesque philological
