290 



dXr 



^ 2. We multiply (5) by g.p-j^ and sum with respect to v and 9 ; 

 the equation thus found 



9^p 





^ ^ gyp 



I P. fi I \ ^- f* ( ^^'' 



\ dx 



0_ 



c?.c;, £?ir^A dxp 



(6) 



may be reduced to a different form. 

 Let us consider the first term : 



^^ tt' X -J (XtV Q 



As g.,p = gp, we may also write this 



1 /d^Xvdxp d^Xpdxv\ I d /dx^ dxp\ 



'2 v,p ^'^ \dx,' dx, dx, dxj 2 v,p '^ c?^, \dx, dxj 



In the second term 



{^Xfi 





^X [x] dx) dXfx dxp 

 V \ dx. dx. dx. 



we replace ] ' [ by its expression between the square brackets and 

 apply a reduction 



^ 9^pf 



[':_ 



dxi dx/j, dxp 



dx, dx, dx, x,/jL,- 



T 



— 2 



'^ uT] dx'j, dxu ^^ dxp 



~ ^ 9"^ 9-^P — 



X J dx, dx, v,p dx 



dxi dxfj. dXf 

 dx, dx,dx. 



as 



^r.9vp ^ 



1 (for Q ^=zr) 

 (for QT^r)' 



According to the meaning of the symbols [ ], we may replace 

 the expression thus found by 



1 ^ Ö^^A' dx^ dx^ dxr 1 y, dx/ dxj^ dgj/j, 



2 x.ix,T ö^T dx, dx, dx, 2 ;,^. dx, dx, dx. 



The two former terms of (6) may therefore be combined to: 



1 d dxx dxjuL 1 d ^ ds 



2 dx, x,/^^ dx, dx,~~ 2 dx,\dx. 



We write the third term 

 2 9,p 



\f>.,v,p 



X n\ dxv dxi dXfx dxp 

 V \ dx^ dx. dx. dx. 



