246 Mr, Woodhouse on the Integration 
<*/=^v/(^)- Let "= vTTT^r then 
( I +x/ i )» 
Let % 
V ( 1 + v *) (i + 6 a ^)' 
= » y[L±^- b —) , then v- = ^-■-tV0+?‘* , >0+<?‘* , > ; 
since (i-f^> 2 z*) (i-f-^ 2 ^ 2 )=x -[=2 . (2—6*) % 2 ~f b A %\ when 
/> = i-f v/( 1 — h 2 ) and q =1 — y/ ( 1 — 6* ) . 
Hence, since 
dx 
dz' 
V(i+^) (1 + ^ »*J 
- M- T^ii.+v^Kzr (P uttin s z = t’' 6= t= ^-i-) 
we have 
V(i+F« 2 ) (>+g a » z ) 
<7 1— V (*-r^) 
6 a t / 2 rfw 
V(i+w*) (i + ^ a t> 2 ) 
V 
h 2 <k/ 
b* 
Similarly, putting z "='p-^±fLy, "b= ■-/(»- ** . 1 . 
[ + V(i-' 4 *) 
V(i+2''-) (i+"6*z"*) = Z", 
'&* *'*. J*' 
b 1 / , w?\ 7 ,/ 'i a , . w i \ . "6* z" 4 rf«f 
T (i+ — ( 1 + 4 )— + 
Z' 
&C. &C. 
. i . dss' 1 +"Z> da" 
Consequently, since -p- — — -7— . -777 
i+"& 
Z" 
1+ *'' . &c. 
2 . 2 Z'" 
{7 ( 1 +'b) i« + 2? . . ^ . &r+ 2 1 ^ 1 Tm .&'"+&c. } 
r +C( 1 +'^). 
+< 
+ 
4 (»+'*) 
"b* 
(i+" 4 ) 
_+&c. 
■|S 2 
1+-6 
i+/n 
2 
2 i 
I 
1 +"'6 
,.i±e 
2 
+'"6) . . . . 
2 ’ 
i+g 
2 
V(x+n (i+/ 3 a n 
_ 
(!+'*) (1+'^) (I +/ 3 ) ’ V(x + ^) (i+i 3 a D ’ 
/ 3 , f , being the last terms of the series '6, "6, w 6, &c. z", z"\ &c. 
continued tow terms; put the product (1 -f'6) / 3 )='F, 
