On Material Molecules and the Etherial Medium. 267 



WjWj', u 2 u 2 , i^V' v 2 2v 2> & c *> De tne corresponding values 

 of uu\ vv', &c. 

 Then, from (28) 



X 2 



-~ Ml 2 4- B'm 2 + C'ji 2 

 w/ v t ' w( v 2 — A 



~ A'Z 2 + B'm 2 + C'n 2 



U n V n V)c 



(29) 

 (30) 



u x u 2 _ u x u 2 + v 1 v 2 + w x w 2 



u Y u 2 u^u 2 + v x v 2 + w^w 2 



Now, in order that the two rays may be polarised in planes 

 at right angles to each other, we must have for all values 

 of Z, m, n, 



u x u 2 + v ± v 2 + w 1 w 2 = 0 



u-^Lv 2 + v x 'v 2 + w^iu 2 = 0. 



Multiplying the expressions (29) and (30), and substituting 

 for the values of v x 2 and v 2 from (27), w T e easily find 



Ul u 2 + . . . . _ P>> A'Z 2 + B'm 2 + C'n 2 

 u{u 2 ' +...." X' 4 FZ 2 + Gw 2 + Hn 2 



In order that this may become of the form g for all 



values of Z, m, n, we must have 



A' = B' = C = 0 

 F = G- = H = 0 



and then from (27) 



V = A . 

 jfc»t/ s * = F7 2 + G'm 2 + Wn? 



that is, one of the rays in every biaxal crystal follows the 

 ordinary law of refraction, which is known not to be the case. 



Hence the particular manner in which we have above 

 attempted to take into account the action of the material 

 molecules, although being remarkable as leading 'to a quad- 

 ratic equation for the determination of the velocity of pro- 

 pagation of plane waves through crystallised media, fails 

 when developed further. 



VOL. III. 2 M 



