678 Profs. Morley and Miller : Experiments to 



and then decompose these residual aberrations into terms 

 depending on the squares and on the cubes of the ratio of 

 velocities. To a thousandth part of the residual aberrations, 

 their difference is represented by the equation 



8' — 8 = ™ cos ^+ T7a( V 0*5 sin 2« + -g- sin 4a + cos a). 



For the velocity-ratio 10,000 the agreement would be much 



closer. Fig. 9 (PI. IX.) A shows the laws of the variation in 



the residual aberrations of the two rays I and II, coming 



from the mirrors I and II. The unit for A and C is 



v 2 v 3 



sm -1 v™, and for B and D, sin -1 ^. The curves A are 



nearly represented by ^ (sin 2a + -J cos 2a). Subtracting 



the ordinates given by this expression from the actual ordi- 

 nates, we get the residuals shown (after multiplication by the 

 reciprocal of the velocity-ratio) at B. C shows the difference 

 of the curves I. and II. of A, and thus gives directly the 

 angle of divergence of the emergent wave-fronts which is 

 the object of our study. D gives the difference between this 



curve and the sine curve 8' — 8= ~™ cos 2a. The latter curve 



shows that the difference of the aberrations of I and II is 

 at an undisturbed maximum at 90° and at 270° ; at 0°, 

 it is less than the undisturbed maximum by the quantity 



™ cos a, or ™ ; at 180° it is greater by the same quantity. 



It may be thought that the adjustment of the angles 

 between the mirrors which has been assumed will limit too 

 narrowly the use of the apparatus. We may simply say that 

 experience with mirrors as nearly plane as those used by us 

 has shown us that the method of observation supposed would 

 suffice for angles of aberration at least twenty-five times that 

 expected if the velocity-ratio is 10,000. 



Since the experiment gives a null result, it is not worth the 

 space to prove that what is true of this adjustment is true 

 with sufficient approximation for an adjustment which differs 

 from the assumed adjustment only by the rotation of mirror I 

 by an angle often seconds around a perpendicular axis passing- 

 through its surface. Instead, we may compare the results 

 here obtained with those of Dr. Hicks. 



In the first place, he declares that the position of the 

 fringes is displaced by aberration. This point is eliminated 

 from our discussion by the fact that the fringes are infinitely 



