16 



/ S'^i , sat; _S:'" \ _ !tf- 



3/317 V "^ ^'^^h ^ ^/i'h "^ "" 3/33y' J - ^ ' 



I^T V ^^^ ^ ^ 3«3/33y ^ My"- ) -^ ' 

 MN — M" + iVP — iV'» + PJ»/ — P'« =: »"', 



we find, by the equations (M), 



V"W"=^v"^, V"S'=v"S: (N) 



and therefore 



^^ ~ W W fV" ' Tyh ~ W 3/33^ ~W~' ^ (^^ 



3'F _ S' 3'» _ v"P 3'F y_ _3_'£_ _ t;"/^ 



IP ~ W T^ IV" ' hh ~ W" 3y3« "F'^ 



3' V 

 The coefficients of the forin -j-^— . may also be deduced from those 



of the form -j^"r > in the following manner. Differentiating the equa- 

 tions {K) we obtain 



1 , JIf 3« + M'3^ + P'3y = 3' 5^ , 



M%» + iV3/3 + A-'3y = 3' 1^ , V (P) 



3y 

 3y 



3^' 

 P'3« + A''3/3 + p3y= 3'r^; 



