THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
777 
at rest, would be violated were the eether put into a state of rotational motion. Now 
any modification of the laws of emission and absorption would be conditioned only by 
the motion of the aether close to the radiating surface ; and the motion at the surface 
bv DO means determines the motion throughout the enclosure, unless it is confined to 
be irrotational. Hence the theory of exchanges seems to require that any bodily 
motion that can be set up in the free aether must be of the irrotational kind. 
79. This modified characteristic equation of the rays also shows that in a 
heterogeneous isotropic medium containing moving bodies, the paths of the rays will 
be unaltered to a first approximation provided {u dx + v dy + id dz) is everywhere 
continuous and an exact differential; and this condition virtually implies (Lodge, loc. 
cih) Fresnel’s hypothesis. The interchange of radiation now depends partly on the 
reflexion and refraction at the different interfaces in the medium, as in the simple 
case calculated above; but we may take advantage of a device which has been 
employed in other connexions by Lord Rayleigh, and suppose the transitions to be 
gradual, that is to be each spread over a few wave-lengths; the reflexions will then 
be insensible, and the rays will thus be propagated with undiminished energy. We 
thus attain a general demonstration that the theory of exchanges of radiation demands 
Fresnel’s law of connexion between the velocity of the matter through the field of 
stationary aether and the alteration in the velocity of the light that is produced by it; 
while it also requires that any motion of the aether itself, such as occurs in a field of 
magnetic force, must be of irrotational type, 
80. This theory has been developed up to and including the first order of small 
quantities; it seems plain therefore that the experiments of Michelson on the effect 
produced by the motion of the earth on transmission through air are not in 
contradiction with it, for these experiments relate to terms of the second order of small 
quantities. To explain the remarkable, because precisely negative, result arrived at 
by Michelson would require the elaboration of a theory including the second order 
of small quantities. For example, when light is reflected, as in those experiments, at 
the surface of a body which is moving towards it through tlie stationary sether, the 
wave-length of the reflected light is diminished so as just to make up, to the first order 
of approximation, for the acceleration of phase caused by the reflector moving up to 
meet it. The mechanism involved in this alteration of wave-length is not known, nor 
what is going on at the surface of the advancing reflector ; and it seems to be a very 
uncertain step to assume that when terms of the second order are included, this effect 
on the wave-length is not subject to correction. As the circumstances of the reflexion 
are thus not known with sufficient exactness, it is necessary to fall back on general 
principles. Now Professor Lodge has emphasized the fact that, when a beam of light 
traverses a complete circuit in a medium containing moving bodies but devoid of 
magnetic intensity, the change of phase produced by their motion is null to the first 
order of small quantities. If it were exactly null, or null to the second order, the 
result of Michelson would follow ; and it would seem also that Michelson’s result 
MDCCCXCIV. — A. 
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