Mathematics. — "On a non-si/)nineh-icnl afjine field theory." Bj 

 Prof. J. A. Schouten. (Coniiinuiicated by Prof. H. A. JjOHEntz.) 



(üommunicated at the meeting of October 27, 1923). 



1. Introduction. In liis last publications') Einstein has given a 

 tlieofj of gravitation wliicli only depends on a symmetrical linear 

 pseudo-parallel displacement ("affine Uebertragung") and a principle 

 of variation. From tlie equations, that result in this case, we see 

 that the electromagnetic field only depends on the curl of the electric 

 current vector, so thai the difficulty arises that the electromagnetic 

 field cannot exist in a place with vanishing current density. 



In the following pages will he shown that this difficulty disappears 

 when the more general supposition is made thai the original dis- 

 |)lac,ement is not necessarily symmetrical. 



The equations which define such a displacement are 



V« V = - — + r;„ t) 



Oaf 



in which the parameters P'xf, (with an accent to distinguish them 



from the F,'., of a symmetrical displacement) are not symmetrical 

 in X, II. 



Einstein') has defended the use of symmetrical parameters with 

 the remark that in the non symmetrical case not only 



but also 





r r „J M)„ 



O.Vf 



can be regarded as the covariant differential quotient (Erweiterung) 



1) Berliner Sitzungsberichte 1923 p. 32—38, 76—77, 137—140. 

 =) L.c. p. 33. 



