1885.] equations of vibrations of ether in a light wave. 287 

 For P xy - P yx 



d% d v \ [d% | d v | <%] x d&Z) d ( v , g) _ 



d?/ <W [da; dy dz) d (x, y) d (z, x) 



Hence d (g) ^^ ^ (10). 



rf (#, ?/) cZ (z, x) 



And these minors must be each 0, for otherwise the Jacobian 

 above could be proved symmetrical, and therefore the disturbance 

 would be without rotation, contrary to our hypothesis. 



As a consequence of these conditions we have 

 d% d% d£ _dr) dr) dr\ _d% d"C, t it, _ , , , 



dx ' dy ' dz dx ' dy ' dz dx ' dy ' dz 1- 2 " 



We use these relations in simplifying P XX} P xy , P xz , etc. 



Thus 



P =7i^ + b d ^ + c^ + l(4fg-c^+mco 2 



-{® ,+ ® v ffll- , S-S) ,+1 ^ ™> 



= n & dv + dZ dv + d% dv\ _ l {<% _ dvl (<% _ <%} , 13 n 



\dx ' dx dy' dy dz' dz) [dy dz) \dx dz)" 



with similar quantities which can now be written down. 

 Before proceeding we will evaluate co 2 , w 3 , and co 3 '. 

 First, 



2ft) 2 = n {a 2 + b 2 + c 2 + 2e 2 + 2/ 2 + 2g 2 } 



■®^®;+«v®' ^ 



V * dx 2 efov \ 2 dx dx) \dx 1 dx) j 



I \ sJ nr> H T ^ ft T J 



= n 



d l) + ( d l)\( d H ] \(. 

 dx) ' Vc?#/ \dz) \dx) \dy) ' \dz 



/d> 



+ {d: 



S' + ®' + ®' + *- d*> 



\<£c/ \d#/ vW 



20—2 



