4 Messrs. 0. Wiener and W. Wedding. Magnetic [Dec. 5, 

 So far our. calculation agrees with Mr. Ward's. 



To continue : let /3 vary under the influence of double refraction 

 alone by 8/3$ = h dz, when the vibration advances through dz ; then 

 the alteration of to is 8w = — \Tc sin 4w tan /3 dz. 



Under the influence of rotation alone, let oo vary by 8w r = mdz; then 

 the total alteration of ta with z is given by the equation — 



^ = — t sin 4w tan B + rn. (3.) 



dz 4 v ' 



In this equation /3 is still unknown ; it is also variable with the 

 double refraction and with the rotation. We must therefore form a 

 second differential equation for /3. We already know the alteration of 

 /3 due to double refraction alone; it is 8/3$ = kdz. In order to learn 

 the variation of /3 with rotation alone, we are in need of a relation 

 between /3 and w, in which only /3 and to are variable in consequence 

 of rotation. This relation is — 



tan /3 sin 2w = K, (4.) 



_ 2k 

 where K — 



if h is the ratio of the minor and major axes of the ellipse. This 

 ratio, as a matter of fact, does not alter with rotation. 

 From this follows — 



8/3 _ sin 2/3 



2,,, ~~ tan 2w' ^ 



But since 8ov — m dz, the variation of /3 by rotation alone is 



tan 2u 

 by the equation — 



8/3 r = — m S * n ^ 8^. The total variation of /3 with z is hence given 

 tan 2w 



d/3 7 sin 2/3 



_i- — A:— m . (6.) 



dz tan 2w 



Thus the complete solution of the problem is contained in the 

 two simultaneous differential equations — 



div h . . ^ 

 — — t sin 4to tan B-\-m 



dz 4 



(7.) 



(Z/3 7 sin 2/3 



y- = h—m- — . 



tan Ztu J 



Mr. Ward's solution, however, consists in the single differential 

 equation — 



