54 < 
Mr. Ivory on the Attractions of an 
please : for abridging expressions let 
(T — i — n .i — n — l . i — n — 2 i — n — m -f- 1 ; 
t = i + » + 1 •*" + « + 2 . i + n + 3 i -\-n + 
then after m successive operations we shall get, 
fi —p)* ■ p?.p . 1 x f{i -i *>«+«. ^ Cil 
J r J d^ n « r.r J K dl/ 'Ti+ 
m 
d m P , 
da. 
dn m ' r 
d m P 
If w, less than t — denote the dimensions of P, then 
will be a constant quantity, and the fluent on the right-hand 
side will be =0 (No. 2) : hence this theorem, viz. 
“ If P be a rational and integral function of jx, and of less 
“ dimensions than i — n, then 
/( 1 —1^)” 77 ° ■ P-^ = o 
UjW, 
“ when the whole fluent is taken between the limits ^ = — 1 
“ and [j. = 1.” 
If the dimensions of P be not less than i — n y put m = i — «, 
and for write its value, 1.3 ....2/ — • 1 (3); and the pre- 
dy} 
ceding formula will become 
r, - n d n 
J i 1 p ) • — 
7W)' " i -" p 
and hence, /3 
. P . d = i - ” + 1 • ■' + 1- i d -j; 
• 2.4.6 
dy}~ n 
l — «+ I . I — M + 2 J+« 
, we have 
e® ./(.-xr- JT-P-+ 
2.4.6 
21 
