On Material Molecules and the Etherial Medium. 259 



where d* Xi d<p x , &c, are given by (3.), (5.), and similar ex- 

 pressions. 



Let m be the mass of one of the particles of ether. Then, 

 if r-^r be the law of action of the etherial particles upon 

 each other 



= m,'2{'^r 1 (x l —x)} 

 or putting x 1 — x = h x 



9* = m 2 H> i M 



ax 1 ax 



For shortness put p\ = — 



.-. ^ = v + ^4 • • • • (7) 



Similarly 



- »i 2 | p> t /*! fcj J . . (8) 



a\ r _ d<p x 



Now 



And 



1 %i 1 <&i f 



"! = « + *! S + ~dy + l *Tz 



d 2 u 7 o d 2 w , „ d 2 w 

 ~S 2 



1 ( 7 9 a 2 ?^ , 9 crw . 



- + 2 ^ £ + »a & ! + te (10) 



In finding the value of s| ^ u x j let us suppose the 



sphere of action of the molecular forces to be so small that 

 ^>i\ becomes insensible when multiplied by factors higher 

 than the third in h x k x J } . Then since h x h x \ are of the 



VOL. III. 2 L 



