﻿88 Dr. A. D. Fokker : A Summary of 



When there are external forces acting upon the field 

 through the electrons, the laws of conservation are no 

 longer fulfilled for the field alone, the equations are to be 

 replaced by four other ones, contracted into 



where F ff denotes the force from the charge upon the field, 



and the work done upon the field - 



F^-ZCv^ + vA + vA), 



these being equal and opposite to the force of the field upon 

 the charge. 



But F<r being the force exerted by material agents upon 

 the field, there must be an equal loss of momentum and 

 energy of these agents per unit time. Denoting by M^ the 

 stresses, momenta, currents, and energy in the matter, the 

 laws of conservation demand that 



Thus, finally, the laws of conservation are now expressed 



Thus, finally, the la 





Tensors. 



10. A set of sixteen quantities such as L av is called a 

 tensor of the second order. It is a fundamental property 

 of a tensor that when a transformation of coordinates is 

 executed the components L<t„ of the tensor transform them- 

 selves like dx a dx v . For instance, when we transform our 

 coordinates in the following manner 



' r 2=2-h2<l'l + P22*2 +P23<'V + P24^4 r i 

 *S= J Pl3*l / +^W +P33V3 +Pu*i, 

 *\=Pu<t'l + /*>W +PU&Z T2?44*/i 



then a tensor as a "geometrical quantity" is mathematically 



