12 



where P is given by (J 5) 1915. As the Lagrangian function defined 

 by (11) 19J5 equally falls under this form and also the sum of this 

 function and the new term, the expression (71) may be regarded as the 

 total function L. The function (p may be left indeterminate. If now 

 with this function the calculations of §§ 5 and 6, 1915 are repeated, 

 we find the components of the stress-energy-tensor of the matter. 



The equations for the gravitation field again take the form (65). 

 Tah is defined by an equation of the form (63), where on the left 

 hand side we must differentiate while the z/;«'s are kept constant. 

 Relation {QQ) can again be verified without difficulty. 



We shall not, however, dwell upon this, as the following consider- 

 ations are more general and apply e.g. also to systems of material 

 points that are anisotropic as regards the configuration and the 

 molecular actions. 



§ 44. At any point P of the field-figure the Lagrangian function 

 L will evidently be determined by the course and the mutual 

 situation of the world-lines of the material points in the neighbour- 

 hood of P. This leads to the assumption that for constant ^„^'s the 

 variation öL is a homogeneous linear function of the virtual dis- 

 placements öjCa of the material points and of the differential coefficients 



these last quautities evidently determining the deformation of an 

 infinitesimal part of the figure formed by the world-lines '). 

 The calculation becomes most simple if we put 



^ = \/^öH (72) 



and for constant gah^ 



f)H=:S{a)Uaflva^2{ab)V^'~'^ .... (73) 



OXf, 



Considerations corresponding exactly to those mentioned in §§ 4 

 — 6, 1915, now lead to the equations of motion and to the follow- 

 ing expressions for the components of the stress-energy-tensor 



K = -^-\^^^c (74) 



and for h =\= c 



te=-^-lK ........ (75) 



The differential equations again take the form (65) if the quantities 

 Tai are defined by 



1) In the cases considered in § 43, ^L can indeed be represented in this way. 



