s£o Mr. Woodhouse on the Integration 
Consequently, 
(‘ r = 1 ) = ?/v( I -*•[ ( I -«* V Vli+6) ) ’ 
( 1 +g') ( i + g") i -j- g r dv 
but 
rda: 
JvF- 
•v/(i— * 2 ) (I— e 1 X*) 2 . 2 2 J Vl 1- ' 1 ) 
=(i-f-e') (i-fe") l + e . when x=i. 
A g ain >/^— — =/fenT 7 Fvr> P uttin s * = 
•) (i + 6 2 p 2 ) 
^■ - l+ l- : ' : - 1+ ! *• (f+yi+n. 
V'l+fl 1 
and, when v = that is, when a? : 
V(h-M* 
/ rfp 
V(I 
i+'& . i+"6 .... 1+jS 
V(I+V 2 ) (i + & 2 p 2 ) 
•M 
i + V(i+< 3 ) 
V /3 
Hence. 
. /T(fw / i \ fdx 
:,smceJ V[i+vZ][i+b i v * ] {? — ) —J V[l _ x * ] (I _ 6 »**)' 
(*= 
we 
Vli+fr) 
) ~ (!_£*»*; ( x — J )* 
have 2 . 
+'*) (i+^)-.... i +<3 
}/• 
HyiHf ) 1 
V /3 
= ( 1+0 .... ( 1+0 -f- 
Let now •*• b=Vi *'='&, e"—"b &c. and e =/3 
2 . 1 . ( I V ( I + j3) ___ w # 
* * ” X W ‘ ~ ’ 
or, from what has preceded. 
Mb 
In particular cases, 
-^==2- 3 . == (more nearly) 2“\ /. (more nearly) 
• Or thus, when e—*j\. e iv will be a very small fraction, for io zeros will precede the 
first significant figure. 
(i + e v ) (i + e vi ] (i-f-e vil ) (J-h 6 ) “ — 22 5 * t. 
V v b 
or (i + e v ) (i + e v1 )- (i + e vil ) .... (i + E ) . — - 2~* . h 
or very nearly — == 2— * . /. 
