AND THE NEBULAR HYPOTHESIS. ,,, ., 



then, as in equations (31) and (32), a and b must satisfy 



m. . . . ....... (43) 



AAOta) = -' 



whence 



b-A. 



The potential of the mass, V m , can be regarded as arising from a distribution of 

 density P inside the cylinder r = a, together with a surface density b<r cos n0 spread 

 over the surface of the cylinder. 



The first part of the potential, evaluated at R, 6, is 



G ~ jj[ log { 7J + R2 - 2r ft cos (0-6)}] [j + Vo (<r) + A.J. (*r) cos n01r drde 



rir ^ ~i r * 



= 0-2 logR-2 - r coss(0-0) + A J (*r)+A 

 JJ|_ i slv JL2 



f" 2?r 7*" 



= A. n ) - r-j J B (AT?-) r dr cos n6 + terms independent of 



- A B J n+1 (*) cos n0+ terms independent of 0. 

 The potential of the surface distribution is 



so that, at r = a, 



v. = { 



I Kn 

 while, by equation (5), 



If, as before, we express the tide-generating potential V-V. in the form 

 Vt>+v n cos 0, we obtain for the value of v n , at R = a, 



A B J B+1 (o)+ 2* cos n6+ terms independent of 6, 



H ) 



11 



(45) 



- J,M 



2xr/ 

 It will be seen that this equation is exactly analogous to the former equation (37), 



