extensive Class of Spheroids . 
67 
%/i — ft' 2 . sin. •Sr'. It is to be understood that a . ( 1 + « .y ) 
denotes that radius of the spheroid which, produced if neces- 
sary, passes through the attracted point; andy is whaty' be- 
comes when pi = jw. and = w. 
Supposing the attracted point to be without the surface, we 
have No. 7, 
„ B(°) , Bl 1 ) , B( 2 ) 
— r • r » "T r 3 
b(*) 
4 - — ..&c. 
T r‘+‘ 
B ( '’ = ^ .ff R' +3 . 4 <.'.^'.Q 
0 
1 
I 
and by substituting a . (1 -j- a, . y') for R and retaining only 
quantities of the first order with regard to a, we shall get, 
B( ° = 7TJ ■ d + ^ ffy ■ W ■ <&' Q (0 : 
but, as has already been proved (No. nff q <0 . d\d . dzo'zzz 0 1 
therefore 
B (0 = « . a i+ 3 .ffy' . dp! . . Q (0 : 
thus the value of depends upon the integral jf y ' . d[d * 
did . Q^\ which may be found by means of the analytical for- 
mulas in the first part of this discourse, as we now proceed 
to show. 
In the first place, when y' is a rational and integral function 
of p/ only without ®-', which will be the case in spheroids of 
revolution : substitute for its developement in No. 5, writ- 
ing h'— -us for ip ; integrate from ® = 0 to 2 tt, observing 
that the fluents of all the terms which contain the cosines of 
73'— us are of the same magnitude at both the limits, and there- 
fore they will add nothing to the value of the integral taken 
between these limits: then we shall have simply 
Kg 
