18 



These relations give 



v.< « A.-* • 





and therefore, by (C), 



^^ . ^5 ^^ j_ s ^^ - n- 



a condition which resolves itself into the three following, 



11- 



r-v 



+ /5 



Jx3y 



+ y 





= 0; 



-1:5^+ ""^T"'' ^~¥^- ' 





Sz* 



(H) 



3a;32 ' '' "iyiz 



and combining these three equations (fl) with those which are ob- 

 tained by differentiating (C), we find, 



/^F , PV . ^FX-Sy /^F jSd , S'F 3t> J'F Ji; \ 



> (I) 



in which 



V" - 



PV S>F 



Jo;' V V^^Jj// 



/S'Fx^ , S'F S'F /^FV ^^tL_ /JIHV 



and 



so that 



^xf = J'x — « («Ja: + % + yJz), 

 ?«' = fe — y («3a; + /3Sy + yiz) ; 



