304 



LIPKA. 



by means of (34'), the above 48 terms reduce to 33, viz. : 



(45) 



+ 



+ 



+ 



+ 



+ 



+ 



(u 



w 



). 



The coefficients in parentheses in (45) may now be taken as inde- 

 pendent quantities, and for (45) to vanish identically, we must have 

 the vanishing of all the expressions in brackets. Hence, the first 8 

 terms give 



dFi dF2 „ 



P2- 2^17— = 0; 



a^^a dps 



Pi 



Pi 



dFi 



dp2 

 dFs 

 dpo 



dFi ^ 

 p4 7— = 0; 

 dp2 



dFi 

 ps—- = 0; 

 dp2 



dF, dFs ^ dFs dFi ^ 



/>3 — - - i>2 ^ = 0; ^^4 7 2^3 r— = 0; 



dpi dpi dpi dpi 



dFi dFs ^ dF2 dFi „ 



Ps- Pi 7— = 0; Pi- P2 — - = 0; 



opi dpi dpi dpi 



P2 



dFi 



dp» 



dF2 „ 



Pi--^0. 

 dps 



