﻿86 Dr. A. D. Fokker : A Summary of 



considered this set degenerated in a set of four : 



#11= #28 =#33= — 1> 9U = C' 2 , (#12=#13=#14=#23 = #24=#34=0), 



of which only g u = c' 2 was a variable function of the co- 

 ordinates. In the absence of a gravitation field even this 

 potential becomes a constant. 



If we write the fundamental equation 



8{Jrf*}=0, (2) 



in the form of Hamilton's principle, 



by putting 



then we know that this equation is equivalent to 



dt\ x) ox 



It is through the ten potentials g^ v that H' depends on the 

 coordinates. 



Laics of Conservation. 



9. In order to show how phenomena are affected by gravi- 

 tation, and the gravitational field is created by matter, and 

 how the laws of conservation of energy and momentum are 

 preserved in the theory, we shall have to use tensors. To 

 introduce them it will be best to show how the laws of con- 

 servation can be expressed for a special case in electro- 

 dynamics, and in absence of a gravitational field. 



Let d and h denote the electric and magnetic vectors in 

 free space. We may conceive stresses X z , X y , X z , &c, 

 existing in the electromagnetic field, and also an electro- 

 magnetic momentum Ix, I y , I 2 per unit volume. If X x 

 denotes the pressure per unit area exerted on the field at 

 the positive Y side of a surface perpendicular to the axis of 

 X by the field at the negative side of this surface, and if 

 X v denotes the force per unit area in the direction of X 

 exerted through a surface perpendicular to the field at the 

 negative side of it on the field at the positive side, and 

 if X~ denotes the same with regard to a surface perpen- 

 dicular to the Z-axis, then the X-component of the total 

 force upon an element dx dy dz is 



/BX J: \ dXA 

 — ( -^— + -=—• + -~ — ) dx dy dz, 

 \ OX OV OZ J 



