124 Cataclysmic Motion [OH. vi 



second degree terms. The potential V b at the boundary may be put in the 

 form 



where ( V b \ is the potential when ^r = 0, arid ( F & )^ represents the terms 

 in ^ which are of degrees 1, 3, 4, .... 



Equating terms of degree 2 in equation (372), we obtain 



++ ...... (373). 



On equating separate coefficients of a?, y 2 - and z* we obtain precisely our 

 previous equations (350) (352) except that 0" replaces &. On adding 

 corresponding sides we obtain equation (349), with 0" replacing 6'. Hence 

 6" must be the same as our former ff, and it appears that the changes in the 

 fundamental spheroid will be just the same as in the former problem in 

 which -\Jr was absent. 



On subtracting corresponding sides of equations (373) and (372), we find 



Using the values of M* and ty already assumed in equations (368) and 

 (369), we have 



In ( Fj)^ the coefficient of P l may be supposed to be 



Thus on equating coefficients in equation (374) we obtain a system 

 of equations of which a typical one is 



l ...(375). 



This and equations such as (370) are the equations of motion giving 

 changes in the p's and <?'s. From them the stability of the motion may be 

 determined. 



Eliminating p l from equations (370) and (375) we find 



125. In general these equations are so complicated that no progress 

 can be made. We have, however, seen that the changes in a, b, c are the 



