262 Proceedings of the Eoyal Physical Society. 



one belonging to the prismatic system. Biaxal crystals 

 belonging to the oblique and anorthic systems may, for the 

 purposes of this investigation, be considered as formed by 

 the combination of hemihedral and tetrahedral forms of the 

 prismatic system. 



In the prismatic system the molecules are symmetrically 

 arranged with respect to three planes at right angles to each 

 other. Also, if a very small crystal be taken out of a larger 

 crystal by cleavage or otherwise, it is also biaxal, and possesses 

 optical properties similar to those of the larger crystal, the 

 optic axes being in the same direction, &c The larger 

 crystal may therefore be considered to be built up of an 

 indefinite number of very small crystals of the prismatic 

 system, and each of these small crystals may be supposed to 

 contain all the material molecules which are capable of 

 influencing the motion of the ether within them. Hence at 

 every point of a crystal we may suppose that the molecules 

 which can affect the motion of the ether at that point are 

 symmetrically arranged with respect to three planes at right 

 angles to each other, and parallel to the principal planes of 

 the crystal. 



Hence 



2 { 7 f r> h ' k ' } = °> &c - 



= „ 5=0, by (18) and (18*). 



And ^ = - " 4 ' 2 { !■' f r ~ K 2 + /v } = - p> say 



dit x dit x dffjc t-v /irkx 



•■• *r" + dy v + -di w = -^> ■ - ■ < 19 ' 



Also d<ir x = 2 \ — , u + -7-7 v + 7 r w f 

 \ dx ^ dy' dz I 



Hence by analogy, from the value of dtp x , we may put 



» / . a / dp" n t^., d? 1 u n .. d^ u /r»i\l 



*** 7 VU + d? 2 + ~dy" 2 + (hf* ■ < 20) 



where A' B' C are constants depending on the arrange- 

 ment of the material molecules, that is, on the crystalline 



