1086 



For the volume integral 1 x¥^/ Trover a spherical space with radkis?' 

 we obtain 



4 jr X I r" W dr =z ^ jir' . 



J " 







If we integrate over the same sphere and apply the lawofGACSs, 

 equation (20) gives again 







where <5, is the component of the quasi-vector (^ directed radially 

 outward. In consequence of the spherical symmetry there does not 

 exist a component of ^ perpendicular to the radius. Thus we have 



^r = -^— (43) 



u 



In our orthogonal system of coordinates we have as component 

 in the direction of the AV-axis 



tVr 2 Ü* w' 



(ir = -—— T=:l,2,3 . . . . (44) 



r u 



Combined with our former formula (18) or with (21) our last 

 formulae give also an expression for the total energy at rest and for 

 the mass of tlie system. Taking r greater than the radius R of the 

 material body we obtain 



"* Wdrz=4: n c r^ (è,-=4 Jicr^ , 



u 

 



4:7tcr^ 2»' w' 



E= ^ {r>R) (45) 



X u 



This formula expresses the mass of the body by means of the 

 gravitation field outside the body. This shows at the same time the 

 meaning of the constant on the right-hand side of equation (42). 



In our considerations of this ^ we assumed the field to be 

 thus, that there exists at least one system of coordinates in which 

 the field is stationary and to have spherical symmetry; and our 

 formulae hold for such a system of coordinates that has its origin in the 

 centre of symmetry of the material system and that has such a 

 time-coordinate that y^^ = g^^ = g^^ = 0. If however there exists 



