19 



the corresponding quantities for the matter or the electro-magnetic 

 system with the opposite sign. It is obvious that by this the condi- 

 tion of the conservation of momentum and energy for the iuhole 

 system would be immediately fulfilled. It was in fact this circum- 

 stance that made me think of the tensor t^ = — ^. The way in 

 which éo was introduced in ^ 38 and 39 has only been chosen in 

 order to lay stress on (58) being an identity, so that equation (85) 

 is but another form of (79). 



At first sight the relations (87) and the conception to which they 

 have led, may look somewhat startling. According toit we should have 

 to imagine that behind the directly observable world with its stresses, 

 energy etc. there is hidden the gravitation field with stresses, energy 

 etc. that are everywhere equal and opposite to the former; evidently 

 this is in agreement with the interchange of momentum and energy 

 which accompanies the action of gravitation. On the way of a light- 

 beam e.g. there would be everywhere in the gravitation field an 

 energy current equal and opposite to the one existing in the beam. If 

 we remember that this hidden energy-current can be fully described 

 mathematically by the quantities gab and that only the interchange 

 just mentioned makes it perceptible to us, this mode of viewing 

 the phenomena does not seem unacceptable. At all events we are 

 forcibly led to it if we want to preserve the advantage of a stress- 

 en ergy-/é^?i6'07" also for the gravitation field. It can namely be shown 

 that a tensor which is transformed in the same way as the tensor 

 t„ defined by (57) and (86) and which in every system of coor- 

 dinates has the same divergency as the latter, must coincide with f^. 



Finally we may remark that (78), (86), (58), (87) give 

 div t = div tfl = — div J, 

 so that we have, both from (79) and from (85), Kh = 0. 



The question is this, that, so long as the gravitation field is con- 

 sidered as given, we may introduce "external" forces, but that in 

 the equations for the gravitation field itself we must also take into 

 consideration the stress-energy-tensor of the system by which those 

 forces are exerted. 



