[ 89 ] 
But this general expreffion, as feveral of the fadors 
deftroy each other, may be transformed to another, 
which is more commodious. Thus 
in the firft line, will, by breaking the numerator and 
denominator into two parts, become 
n. n+ 7 . n+2. »+3-. qy. ^+3. y+«— I _ 
~ • . ■ ' ‘ ^ • 
I. 2 . 3. n. «+ 3 . q 
which, by equal 'divihon, is reduced to 
q. q-\-l. ffl _ q+n—l. q-\-n—'l q 
1 . 2 . 3. - - - - n — I I. 2 - - - - n — I 
1)5 fuppofing/»(=y + «)=^‘y + 
In the very fame manner, making q~q — and 
p (=?rh«) = p—^y It appears, that 
and confequently, that our whole given expreffion 
(fuppofing p' = p — iWy p"' — p — 3W, ^c.) will be 
transformed to ( 
4 - tUl.t 3 (^J2 1 ) f-m 
'123' ' 
p ' — I P ' — 2 p ' — 3 / \ _ 
‘i - — — - (n — I ) X wr” 
3 ^ y 
k'/ 
2 
hii 
3 
k'// 
P'" 1 p'" 2 p'" 3 , « 
J- •i. (n — i)x-« 
I 2 3 ' 1 
&C. ' ’ &C. 
n — I 
2 
n — I 
n—l 
2 
3 
Which expreffiion is to be continued till the fadlors 
become nothing, or negative ; and which, ’ when 
V0L.49. N r = i. 
