532 Mr. R. T. Glazebrook on the Application of the 



direction. The formulas obtained by taking only the term 

 — n(ii — U) have been discussed at length by Von Helniholtz* 

 and Sir W. Thomson f. 



Sir W. Thomson has shown that while the theory will 

 account for dispersion it fails when we come to double refrac- 

 tion, for it makes that depend on the period J. 



d 2 

 The first term —r-ja i u ~ *U) leads to equations for an iso- 

 tropic medium which are practically identical with those 

 employed by Ketteler. In fact he first suggested its use§ . 



He dismisses it shortly afterwards for reasons which do 

 not seem to me to have great weight. The point is discussed 

 in the Eeport on Optical Theories, p. 229. The theory leads 

 to an account of dispersion which certainly agrees closely 

 with experiment, and it will, as we shall see, explain double 

 refraction satisfactorily, if we may assume Sir W. Thomson's 

 theory of a contractile aether. For if we write p r for r in 

 Ketteler's expression and p for the density in free space, the 

 equations of motion become 



, ^ = (A-B)g + BvW^(»-U).. • (41) 



Now in a transparent medium in which there is no absorp- 

 tion, the value of U will be indefinitely small compared with 

 that of u, and omitting it from the equation we get 



0>o+/>')$=(A-B)|;+BV 2 « (42) 



This is the equation which we have been dealing with all along. 

 In a crystal the resistance offered to the motion of the 

 aether will depend on the direction, and p f will have different 

 values for the three axes. We then get 



, # § = (A-B)2 + BV%. • . . (43) 



and these are the equations for a crystal. 



The assumption, therefore, that the mutual reaction depends 

 on the relative accelerations of matter and sether gives us 

 formulas which explain double refraction. To explain dis- 



* Helmholtz, Pogg. Ami. t. cliv. p. 582. 



t Thomson, Baltimore Lectures. 



X According to an account given recently in ' Nature ' of the work of 

 Prof. Lindemann on this subject, 'Nature/ August 23, 1888, he has 

 surmounted this difficulty. 



§ " Optische Controversen/' Wied. Arm. t. sviii. p. £97, "Eine Pritte 

 Annahme," 



