of certain differential Expressions , 
231 
z V[ i+b z z *) 
— V CI+**J 
— (Dl“^6 2 + Dl-^D 2 l“4 4 -f-D E l“iD 3 l“i j[ l.zj-yf (l + %*) 
““ V(*+* a )" } 
-{ 4 -} 
V' 1 -J-; 
^ i ft 4 . z f z* z 1 1 
V(I+^) l 4 4 - *•» 
T»» — 1 f a ; 6 a 4 
£ 1 ' V(l+* a ) l 6 6.4 
■— &C. 
6.4.2 
} 
Now, from this series, as it stands, the whole integral of 
dx J ^r*j cannot be computed, because x being = 
when x=i, z is infinite : therefore, we must use an artifice similar 
to that by which has been computed ; which artifice con- 
sists in finding v a function of x, such that J~==~ (between x 
= o and x — a , a z_ 1) +^~ = shall = whole integral of 
^ r0m x ~ O to JC = 1 . }> 
Let therefore 1 z= v / / ( ~^r) > which case, HfihziH 1 
consequently, dx J 
V(i 
V[i- 
and 
* jf vV(i- v*) \ 
~ e X ^W{ !-«*»*) 
Hence, 
(1-2^+ g* V*) 
-\/[i — v 1 ) (x— e z v % )i 
Jdxj (^) (/)+/*/ [^) =^^ + Corr (€) 
when x = 1, t; = o. Let the whole integral of dx J 
from x = o to x = 1, be denoted by/ ( 1) . • . C =/( 1), 
mdccciv, H h 
