and corresponding Gravitational Fields. 711 



Substituting these values in the equations (8), we obtain 

 for the geodesies the equations following : — 



£ /*. Vl*J.o. (26) 



a^ \l — 2mjrdsds v ' 



AVe may interpret these as the equations of motion of 

 a particle in the gravitational field of an infinitely extended 

 uniform rectilinear distribution of mass along the z axis. 

 From (25) we see that if the particle is moving initially 

 in the plane s= constant, it must remain in this plane ; 

 i. e., we have always 



J = (25') 



From (24) we have 



'• j f = *, (m 



where It is a constant of integration. Tliis equation simply 

 states that a radius vector sweeps out equal areas in equal 

 times. From (26) we get 



? , / -4m \ 



~ = cr Kl -* J (26') 



ds 



where c is a constant of integration. 



.Substituting these values of -," and — from (25') and 

 ° ds ds v y 



(260 i» (23), we write (23) and (24) in the form : 

 ds 2 \ds J ~ i r \-%m 



^_ (<t\ 2 \ (27) 



r^ = I, 

 as 



(28) 



