34:2 Michelson and Morley — Relative Motion of the 



preparation of this paper. This is founded on the fact that re- 

 flection from surfaces in motion varies from the ordinary laws 

 of reflection. 



Let ab (fig. 1) be a plane wave falling on the mirror ran at an 

 incidence of 45°. If the mirror is at rest, the wave front after 

 reflection will be ac. 



Now suppose the mirror to move in a direction which makes 



an angle a with its normal, with a velocity to. Let V be the 



velocity of light in the ether supposed stationary, and let cd be 



the increase in the distance the light has to travel to reach d. 



cd 



In this time the mirror will have moved a distance — - . 



\/2 cos a 



-rrr . cd (0 i/2 COS a. , . , , ttC 



We have— r = =ff which put = r, and — r = 1 — r. 



ad V ad 



In order to find the new wave front, draw the arc ^7 with b as 

 a center 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 the angle d which it is required to find. From the equal- 

 ity of the triangles adb and edb it follows that d=2y>, ab=ac, 



6 



tan t 



tan adb= tan(45° ~) = rr =— 1 =1 — /*, 



,= lan ( 46 ° - 4-) = — — § 



1+ tan — 



f-tan^ 



ad 



or neglecting terms of the order r s , 



a , r 9 4/ 2w cos a . of 

 d=r+ Y = ? f-^cosa. 



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



iiii 1 a — \/2a) cos a a) 2 „ 

 should then have v = — - — = h -^ cos"a, and the total de- 

 viation would be d-\-d / — 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 J=2 j o 2 =0-004 // . " With fifty 

 such couples the displacement would be 0-2". But astronomi- 

 cal observations in circumstances far less favorable 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 cc are two glass mirrors opti- 

 callj' 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 



