﻿Einstein and Grossmanris Theory of Gravitation. 87 



and this must be the increase o£ the momentum present in 

 the element, if the law o£ conservation of momentum is to 

 be fulfilled. Thus we see that this law is expressed by the 

 equation : 



dX, 3X„ 3X 9T* 



3* d</ + B* B* ~ u * 



Similarly, if Sz, S y , S z , and E denote the currents of energy 

 in the field and the energy per unit volume, the law of 

 conservation of energy is expressed by the equation : 



B* + ~dy + ~dz + -dt ~ u * 



Xow, introducing the symmetrical coordinates 



x x -(s, ar 3 =y, # 3 = ~> aii=ict, 



and writing L^(o- = l, 2, 3, 4, p=l, 2, 3, 4) for our stresses, 

 momenta, and energy, so that 



L n 



Ll2 Lj3 



L u 



x, 



x y 



X 2 zVIx 



Ij21 



L 22 L 23 



J-J24 



Y, 



Y y 



Y z idy 



^31 



L32 L33 



L34 = 



Zx 



z y 



£ z icl e 



L 41 



L i2 L_i 3 



L M 



6 IN 



C 





-S. -E, 



z 



re see that these equations have all the same form, 



5|ju B^ia dL l3 SL I4 _ 



and that the laws of conservation of energy and momentum 

 can be concentrated in one formula : 



gBW =Q 



v Q3C V 



If we express the quantities L^ in terms of the components 

 of d and & according to the formula? oE Maxwell, Poynting, 

 and Abraham, we see that the set of the functions L ffv form 

 a symmetrical square. Here they are : 



i{d 2 - 2d x 2 + h 2 - 2 V}, - d,d y - h x h„ - d„d 2 - h x li,, /(d^ - d_-h,), 



-d^-h^ 4{d 2 -2d/ + h 2 -2h/}, -dA—hA- /(d z h,-d,h r ), 



-d z d z -h 2 h„ -d r d y -h^, ^{d 2 -2d/ + h--2h/}, /(dA-d.h,), 



« (dyh 2 -dzh y ), ?( d A-d,lu), i( d A- d A)* ~ K* 8 + &*)• 



