or 



o= -/,'(*) {fJM -/ 2 'K)[ + // ( t ) {/,'(«i)+/.'W){-. 



. -/,'« {//w +//K)} - £/,« {//w -//w } ; 



X 



0= Jtffc) {/,'(»,) -/ 2 'K) } + J //(*) {//(a,,) +/.'W J 



o= {£//(«) +//(0_}/ s 'M - {£/?(») -/,'(0}/ 2 'K) 

 - {*//(*) +/.'« }/»'(*») + {£/.' to -/ a '(0}//K), 



The addition and subtraction of the last two equations give us 



he first of which, when arranged according to the partial differ- 

 ential coefficients of / 2 , will stand 



o= (| /,»(.) +a'Aa»j - J/x'w .//« -/,'(»,)/,' w j (H) 



the auxiliary equations for the integration of which by Lagrange's 

 method are 



= ^ tif. 



Of these equations, the first By means of the second may be put 

 under the form 



0=f l l (x)dx+f<(t)dt+f l >(cD l )dco l3 



or, since dco 2 = 0j 



