336 Miclielson and Morley — Relative Motion of the 



tions and distances traversed by the rays will be altered thus : — 

 The ray sa is reflected along ab, fig. 2 ; the angle bab / being 

 equal to the aberration = a, is returned along ba„ (aba t = 2a), and 

 goes to the focus of the telescope, whose direction is unaltered. 

 The transmitted ray goes along ac, is returned along ca n and is 

 reflected at a ., making ca t e equal 90— a, and therefore still coin- 

 ciding with the first ray. It may be remarked that the rays ba, 

 and ca n do not now meet exactly in the same point a n though 

 the difference is of the second order ; this does not affect the 

 validity of the reasoning. Let it now be required to find the 

 difference in the two paths aba n and aca r 

 Let V= velocity of light. 



v= velocity of the earth in its orbit. 



D=distance ab or ac, fig. 1. 



T=time light occupies to pass from a to c. 



T^time light occupies to return from c to a n (fig. 2.) 



Then T=^ — , T.== . The whole time of going and com- 



V 

 ing is T + T =2D ™ — 5 , and the distance traveled in this time 

 ' V -v ' 



2D(1 + _V neglecting terms of the fourth order. 

 The length of the other path is evidently 2J)a/ i - i — , or to the 

 same degree of accuracy, 2D(l+-™j. The difference is there- 



fore D^5- If now the whole apparatus be turned through 90°, 

 the difference will be in the opposite direction, hence the dis- 



v 



placement of the interference fringes should be 2D_. Con- 

 sidering onty the velocity of the earth in its orbit, this would 

 be 2DxlO -8 . If, as was the case in the first experiment, 

 D = 2xl0 6 waves of yellow light, the displacement to be 

 expected t would be 0'04 of the distance between the interference 

 fringes. 



In the first experiment one of the principal difficulties en- 

 countered was that of revolving the apparatus without produ- 

 cing distortion ; and another was its extreme sensitiveness to 

 vibration. This was so great that it was impossible to see the 

 interference fringes except at brief intervals when working in 

 the city, even at two o'clock in the morning. Finally, as be- 

 fore remarked, the quantity to be observed, namely, a displace- 

 ment of something less than a twentieth of the distance be- 

 tween the interference fringes may have been too small to be 

 detected when masked by experimental errors. 



