460 Messrs. Michelson and Morley on the Relative Motion 



In order to find the new wave-front, draw the arc fg with b 

 as a centre and ad as radius ; the tangent to this arc from d 

 will be the new wave-front, and the normal to the tangent 

 from b will be the new direction. This will differ from the 

 direction ba by 6, which it is required to find. From the 

 equality of the triangles adb and edb it follows that 6 = 2<p, 

 ab = ac, 



, ft \ 1— tan ^ 



tan adb = tan ( 45° - j)=— ~=z°£ = 1-n 



-f-tan^ ad 



or, neglecting terms of the order r 3 



2 



a , r 2 >v/2a)COSa , &) 2 2 



Now let the light fall on a parallel mirror facing the first, 

 we should then have 



/, — J 2co cos OL . (tP a 



e < = —^-Y + y* 008 *> 



and the total deviation would be 



+ y ^=2p 2 COS 2 a, 



where p is the angle of aberration, if only the orbital motion 

 of the earth is considered. The maximum displacement 

 obtained by revolving the whole apparatus through 90° 

 would be 



A = 2/j 2 = 0-004". 



With fifty such couples the displacement would be 0-2". 

 But astronomical observations in circumstances far less favour- 

 able than those in which these may be taken have been made 

 to hundredths of a second ; so that this new method bids 

 fair to be at least as sensitive as the former. 



The arrangement of apparatus might be as in fig. 2 ; s, in 

 the focus of the lens a, is a slit. bb t cc t are two glass mirrors 

 optically plane, and so silvered as to allow say one twentieth 

 of the light to pass through, and reflecting say ninety per 

 cent. The intensity of the light falling on the observing 

 telescope df would be about one millionth of the original 

 intensity, so that if sunlight or the electric arc were used 

 it could still be readily seen. The mirrors bb / and cc / would 

 differ from parallelism sufficiently to separate the successive 

 images. Finally, the apparatus need not be mounted so as to 

 revolve, as the earth's rotation would be sufficient. 



If it were possible to measure with sufficient accuracy the 



