854 



tlie equation (15) passes into: 



(11,) V* /•"-'/, /" a,, V. /' = - '/, a': i^ - A': S''+ V. 5. g". 

 Traiisvection of this equation with (/^^ gives: 



(20) - <?,iv V. g^' = - V, 2. + 5 S., 



so (hat we get the resulting equation : 



(21) v:<7 



and 



'/, A^ i + '/, i« (/ ' — /!,' \S ~ Su g 



[1/1) 



V ^ = /i ^^ ' + /. 'x {J — 2 Sc g , 



in wliich V 's 'he ditterential operator belonging to F;^. 

 From (21) we deduce: 



(22) J- „ = r^^ j - V. 9'f^ i'^ + V. ^I i,- + '/. 4 i' - 7, ^> Sv - '/. A S, . 

 so tliat, witli regard lo (1): 



(23) rv = 



'-1 S'/.u I -f Ve -^' '," + '/. ^y *' — ^> ^Z'- 



Siibslituling (22) into (3), we obtain: 



(24) R'u, = Ka, + 7, (Vttj - V* i.) f 7, V »■' - ', .( V,« -S, - V* 5,u) - 



-•/, V^ «, + •/. ^&, 



in wliicli K,y is tiie contracted curvature quantity IQu',' belonging 

 to the fundamental tensor </;„. By substifuliiig (24) into (4) we obtain 

 the field equations: 



UV) 



From (/F) follows for the bi\ector F^i of the electromagnetic 

 field ; 



