1312 



and consequently we must use K -\- yp — A instead of li -\- icp. 

 The equatioji (13) is not affected, but we now have K* = K — 

 ^(3K-\-üi> — )■), and again K*=zK; therefore instead of (14) we 

 find 3 K -\- up — P. = 0, but the general solution of (^13) remains the 

 same. This solution, expressed in my notation, is 



[// =^ a^ cos X -r ax sin yi sin ^, ...... (5) 



/? being the "latitude" referred to a plane of symmetry, whose 

 inclination e and node rf, on the plane if? = are given by 



6, -.= «J R sin e sin d-^, 

 b^=i — a,, b^ z=z — a^ R sin t cos i>,, 

 b^ =: a^ R cos s. 

 bg . . . b, being the constants of integration introduced by Levi-Civita. 

 The condition of isotropy now is a, = 0. If this is introduced 

 (5) is reduced to (4 B), and it tiius appears that my solution B is 

 the general solution for the case of a static and isotropic gravitational 

 field in the absence of matter. 



