752 
DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
space, It is necessary'^ that the ditFerence of potential between two points A. and B 
should be the same whether the space between is filled with dense matter or not (or, 
say, whether tlie ray-patli is taken through or outside a portion of dense medium); in 
other words (calling (f) the outside and (f)' the inside potential-function), in order to 
secure that T' shall not differ from jxT by anything depending on the first povrer of 
motion, it is necessary that — (f)\ shall equal — <^, 4 , t.e., that the potential 
inside and outside matter shall be the same up to a constant, or that 
cos 9' = V cos 9 ; wliich for the case of drift along a ray is precisely Fresnel’s 
liypotliesis. 
Another way of putting the matter is to say that to the first power of drift 
velocity 
r = pT - f(pVcos0- vcosd) cls/y\ 
and that the second or disturbino- term must vanish. 
29. Hence Fresnel’s hypothesis as to the behaviour of ether inside matter is 
equivalent to the assumption that a potential-function, Jp^v cos 9 ch, exists throughout 
all transparent space, so far as motion of ether alone is concerned. 
Given that condition, no first-order interference effect due to drift can be obtained 
from stationary matter by sending rays round any kind of closed contour, nor can 
the path of a ray be altered by ethereal drift through any stationary matter. 
As soon as matter is locally moved, however, its motion may readily produce an 
effect, for it has no potential conditions to satisfy; it may easily be moved in a closed 
contour. Suppose it moves with velocity u, always with the light, the relative drift 
of ether thereby caused in it must, as above, be i/ypkand so it may be said to virtually 
carry the ether inside it forward with velocity u — ujij? ; for that is the amount by 
whicli it affects the time of journey of a ray. This does not mean that it carries 
with it any ether of spa,ce ; in fact, it definitely means that it does not appreciably 
disturb the ether of space {cf. § 3, h). 
The equation to a ray in moving matter, subject to an independent ether drift, is 
(Is 
Vjfji cos e -L r/p^ cos 6 -|- u [1 — (1/p")] cos 0 
— const. 
30. It is noteworthy that almost all the observations which have been made with 
negative results as to the effect of the Earth’s orbital motion on the ether are equally 
consistent with complete connexion and complete independence between ether and 
* [The argument has here been slightly expanded since the MS. was sent in to meet a suggestion of 
inadequacy made hy Dr. Schuster, to whom I am also indebted for an objection to the term “ velocity- 
potential ” at first applied to this function 0'. As Professor Fitzgerald has observed, it is more general 
than a velocity-potential, though it reduces to that when the medium is homogeneous, or when « = 1. 
The text has been altered accordingly.—July, 1893.] 
