50 
Mr. Ivory on the Attractions of an 
- « • (i - »-r • m + 
2. Let j be reduced into a series of the descending powers 
of r; then 
f=c |0) . - + c (1) . 4+ c (2) .4---- + c (i) . -4-, &c. 
and C(0 will be a rational and integral function of jx of i dimen- 
sions: substitute this series for S in the equation last found 
{n being = o), and we shall obtain 
dc(*‘) 
i (i + 1) c(‘> + 
df*. 
(>)• 
Again, take the fluxions n times successively in —r and like- 
wise in the series equivalent to it, making [xthe only variable ; 
and we shall get 
a I f i d"C(tt)_|_ a d n C( n-{- 1) 
a+i 1.3.5. ..2 «— 1‘ X l r 2 n + r' ~df r 2n + 2‘ dy. n 
f 
j — n 
r'+« + 1 du. n ) 
substitute this series for S in the equation of No. 1, and we 
shall get 
d«d f ) , l ( d^ + 1 J 
(/-„) (! + « + l). (l-f*’)*. 
+ 
( 2 )- 
From this last equation it follows that 
n d n 
. [X = 0 
when the fluent is taken between the limits fx = — 1 and 
