extensive Class of Spheroids. 
57 
B (h) denotes a quantity that does not contain ^ ; therefore the 
general term of the series for is . (1 — p*)* . < L£} ^ . 
df*. n 
cos. mp : but as p and f enter alike into the expression of Q^\ 
it is clear that they will be both equally concerned in every 
term of its expansion : therefore the general term of the series 
will be. 
. (i-k) 1 '- (WE- 
d n c (i) d n c (i ) 
. n 
dts* 
m 
COS. Jlip, 
where C'^ is put to denote the same function of f that 
does of and j 3 ^ is a quantity that contains neither p nor 
jw,', and which can only be a numeral coefficient, and is all that 
now remains unknown. 
In order to determine f£ n \ we must follow the process of 
Laplace.* It is to be observed that is the coefficient of 
in the expansion of the radical jr* — 2 ra . y -j» a* j = 
| r — zra . ( + %/ 1 — ^ . y / 1 — - . cos. <p ) -f- a* J * 
which, when the squares and other higher powers are neg- 
lected, will be equal to 
jr 4 — 2 ra . cos. <p -f- u 9 |” r -f ra • 2ra . cos. <p 
+ 
from the first term of this expression are derived all the parts 
of the expansion of the radical |/ a — 2 ra . y ^ which 
are independent on p and f ; and from the second term of it 
are derived all those parts which contain only juf, without the 
squares and higher powers : now if we determine the parts, 
* Mec. Cel. Liv. 3c, No. 15, 
Mncccxn. 
