and corresponding Gravitational Fields. 709 

 latter become : 



i/*"-i\y+ 4 V 2 = "V' + ^fixv-{A . (13) 



i/*''-i*V+V»= -j^-'-^y, (u) 



X' = /+*', (15) 



4/aV= -i^+JW-iv' 1 . . . . (16) 



1-+. 



/• 



Substituting the value of V given by (15) in (13), (14), 

 and (16), we obtain the equations : 





M +f"-a*> =" + -1 • • • • (17) 



r i 



M" + 7 = 0, (18) 



""+7=0 (19) 



From (18) and (19) we find 



, — im 



and therefore from (15) 



. , _ — 4m + a 



x > 



where ±m and a are constants of integration. 



Substituting these values of fi' and v in (17) we see 

 that 



4:111 



whence 



1 -—dm 



and therefore 



, 4m 



v = ,si "' 3 ] 



1 — 2ui ' r" 



