216 ON THE DETERMINATION OF THE ATTRACTIONS 



But the last quantity may easily be put under the form of 

 a definite integral, by writing - in the place of a under the 



sign of integration, and again inverting the limits. Thus there 

 will result 



A = 



which agrees with the ordinary formula, since the mass of the 



. ., . ^irab'c , , 2 7 o 

 ellipsoid is and a = a + h . 



Examination of a particular Case of the General Theory exposed 

 in the former Part of this Paper. 



14. There is a particular case of the general theory first 

 considered, which merits notice, in consequence of the simplicity 

 of the results to which it leads. The case in question is that 

 where we have generally whatever r may be 



/ / 

 a r = a . 



Then the equation (19) which serves to determine (/>, becomes 

 by supposing k = k. a 2 



If now we employ a transformation similar to that used in 

 obtaining the formula (14), No. 6, by making 



f j = p cos 0J, f 2 = p sin O l cos 2 , f 3 = p sin 0, sin 2 cos 3 , &c. 



and then conceive the equation (39) deduced from the condition 

 that 



must be a minimum (vide No. 8), we shall have 



