w 



f S'F / J«V , yv /.2v\ 





VV a3i; 



e&)oi) 



+ 2 



S'F 



01) ('&)+^-i:^ ('&)('£)}• 



(L) 



in which, without violating the conditions (iO, the variations 5a, 3^, 

 3y, may be considered as independent, and which is consequently 

 equivalent to six expressions for the six partial diiferential coefficients 

 of W, of the second order. 



These six expressions may be put under the following form : 



(M) 



S«^ 3/3'' 



and 





( 



5'i) 3^F 

 '3/3" V 



32/* 

 3*1; 3»F 



3«» 3^;=' +3/3" Sv* + 3y' 3z* + ^ 3c«3/3 3% "^ * 3/31^ l^^SF "^ * 3^§« 3^3^ 



f 3'F , - 3*1) 3'F , - 3"t) 3*F 





These expressions enable us to deduce the partial differential 

 coefficients of W, of the second order, from the corresponding diffe- 

 rentials of F; they may also be employed to deduce the latter from 

 the former. For if we put 



