42 ME. J. H. JEANS ON THE POTENTIAL OF ELLIPSOIDAL BODIES, AND 



The value of v t already obtained (equation (39)) is 



........... (47) 



and the value of u 2 (equation (40)) is 



(48) 







Hence from equations (45) 



<* 



w = -f V 2 , f ?{ a cZX, 



Jo 



DV ............ (49) 



= -if V 



Jo 



15. This completes the solution as far as the second order of small quantities. We 

 shall not attempt to evaluate ?/ 3 and v 3 , as the problems discussed in the present paper 

 require a solution as far as e 2 only. 



As far as e a , the value of <p has been seen to be given by 



= u+fv = e(M 1 +/v,) + e 2 (w !1 +/tt>+/V) ...... (50) 



and the potentials can now be found directly from the formula ( ll) 



As in 7, examine a function V^ defined by 



then 



}(ZX ........ (51) 



Now the value of J + (\) V 2 fdX is by 10, equal to -4w/>, while from equation (31) 



