^89 



Christoffei/s symbol " has here the meaning: 



= ^(7^ 



X (I 



where .^'"'^ is the algebraical minor of ^.t in the ^^-determinant divided 

 by this determinant, and 



X ft 

 1' 



1 /ógr;, dg^, dgxy. 



2 ydxfx dtP^ d.Vv 



As independent variable we chose one of the coordinates, e.g. x„. 

 In this case 



dwv ds (hvv (l^Xv f ds V dxv d*s d^x^ 



ds dx. dx, ds^ \d,v.^J ds dx* dxj 



especially for a-'v = .t'. 



d*x„ / c?s \' 



dx„ d^s 



(4) 



(4') 



ds* ydx^J ds dx^ 



If therefore we multiply the former of the equations 



d^Xv \X a\ dxx dxu 



<^«' x,/j. { V ] ds ds 



d*x^ iX^ldxx dx/j. 



ds^ A,//. I ) t/s ds 



by I T~ » *^*^ latter by ( -r- -j^ , we find after subtraction By 



\dxj \dxj dx, •'.. 



the aid of (4) and (4') 



d*Xv 



+ ^ 



^ ft ) I ^ f^ ) dx^ 



V \ I \ dx^ 



dxi dxju 

 dx^ dx. 



= 



(5) 



These are the equations of the geodesic which we had in 

 view. Taken as the equations of the geodesic of a two-dimen- 

 sional space (a surface in the usual meaning), they give 



d^v 1 2 2 j /dv 

 du* I 1 1 \du 



2 2 

 2 



+ 2 



1 2 



1 2 

 1 



1 1) 



1 i\\dv 

 1 )du^ I 2 



dv\* 

 duj 



0, 



a well known form, which is often taken as the starting point for 

 the discussion of the properties of this line. 



