DR. OLIVER LODGE ON ARERRATTON PROBLEMS. 
793 
and the lag 
2r cos e 
Y (I — 
becomes 
2/aj' cos e ■ 
V (1 - ’ 
approximately p, times as great as before. But althougli this is the case, the extra 
lag caused hy motion is not so great inside tlie medium as it was in vacuo, for 
'lyuT cos e' 
V 
'Ir COS 6 'Ir cos e 
VTf^ «~) ” (1 - «-) 
[ p cos e' (1 
2 \ 
« ) 
COS e 
or, approximately, 
2 (p — 1) r COS e 2p?’ 
V (1 - o?-) ~ 
[The conclusion here is that whatever may be the effect of a dense medium it is 
independent of d, and therefore can have nothing to say to Michelson’s experiment, 
which entirely depends on a difference between what can be observed with Q — t) and 
d = 90°.—July, 1893.] 
The Laws of Reflexion and Refraction as modified hy Motion. 
63. It is necessary now to enter on the somewhat thorny question as to the effect of 
motion upon the laws of reflexion and refraction. Fresnel by considering some 
special cases satisfled himself that no discrepancy need be expected on his version 
of the undulatory theory ; and Sir George Stokes, examining the cjuestion in a more 
general manner in 1846, proved that, at least as far as the first order of minutim, the 
laws were obeyed in spite of any relative motion between mirror and medium 
(motion of source has obviously nothing to do with it, unless it affects the shape of 
the incident w^ave). And the long continued use of artificial horizons by astronomers 
shows that there has been no practical doubt on tlie subject, at least as far as reflexion 
j is concerned. 
But these statements do not by any means exhaust the subject ; the law of 
reflexion is not precisely obeyed in a moving medium, and recently Michelson has 
proposed to utilize the theoretical error (which has never yet been practically 
realized) as a fresh method of attacking the problem of the relative motion of the 
, ether and the earth. 
I propose, therefore, to enter upon it, and I must confess that though the results 
are easily stated, they have given me much troid^le to be sure of, and I have found a 
good many mare’s nests by the way. 
The reasoning for reflexion and refraction is much the same, and I attend more 
pronouncedly to reflexion because without assuming Fresnel’s theory as to the motion 
I of ether inside dense matter we have no guide to what shall happen in refraction ; 
MDCCCXCTir.—A. 5 T 
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