18 



It is also remarkable that in real eases the first term in (83) 

 can be much larger than the following ones. If we consider e. g. 

 a point P outside the attracting sphere, we can prove that the 

 ratio of the first term to the third is of the same order as the 

 ratio of the square of the velocity of light to the square of the 

 velocity with which a material point can describe a circular orbit 

 passing through P. 



The following must also be noticed. In the system of polar coor- 

 dinates used above there will exist in the field without gravitation 



the stress f/ = — . If a stress of this magnitude were produced by 



means of actions which give rise to a stress-energy-^(^?i50y, the passage 

 to rectangular coordinates would give us a stress which becomes 

 infinite at the point 0. In those coordinates we should namely have 



sin^d- 1 



§ 52. Evidently it would be more satisfactory if we could ascribe 

 a stress-energy-/(?7i5(?r to the gravitation field. Now this can really 

 be done. Indeed, the quantities é«y^ determined by (57) form a tensor 

 and according to (58j, (79) may be replaced by 



Kk = — divk J — divk to , (85) 



if t, is defined by a relation similar to (78), viz. 



■ tQh=—^lh (86) 



Equation (85) shows that, just as well as t«"/,, we may consider the 

 quantities t^Qh as the stresses etc. in the gravitation field. This way 

 of interpretation is very simple. With a view to (41) we can namely 

 derive from the equations for the gravitation field (65) 



and 



'J\b = [Gab— è 9abG). 



Further we find from (66) 



1 1 



'Ih = — G^{a)^<^^gak ^(a)jn«ö„A 



2>t X 



and from (57) and (86) 



tlk^-ll . (87) 



At every point of the field-figure the components of the stress- 

 energy-tensor of the gravitation field would therefore be equal to 



