248 
Mr. Woodhouse on the Integration 
L ( 1 _L b • T+V& 1 b • V& • O+'ft) I 1 
2 \ ‘ 2 . 2 ~ 2 . 2 . 2 . 2* * J 
+ f-'P-'Q-M i± ^— )•* 
but it has been shown that, /( 1 ) denoting the integral of 
dx - y / [ 1= ^) when * = i>/( 0 = 2 /(^ = 7(Tw) _1 + 
consequently, 
/(!) = ! 
_ ft (* • _i_ 6 •' t - ('.ffl j. & c , 1 
\ 2, . 2 *2.2. 2. 2 1 J 
( 8 ) 
+ ^P.'Q.Z. (i±$±*}. 
Since s b = 
'6* 
&c. 
(i + VCi-ft 1 )) 4 ’ (I + V(1-^)) 2 
the terms v 6,"6,'"6, &c. decrease very rapidly; and 6 being a small 
fraction, '6 is nearly = "6 more nearly = "'6 more nearly = 
, &c. Suppose, then, in the series ' b , "#,'"6, &c. /3, that /3 v , /3^, j 6 vVV , 
gl g * 2 . 
&c. are the terms preceding (3, (3= -j-, (3== , &c. consequently, 
/ [ i+v/O +f) \ — 7 JL_ __ x J ± — jl 7 — o I J_ __ s } m : 
1 V/3 J“ L ' VP “ 2 *** 0 “ 2 ' L 0 *. “ 2 * L ' VIS, “ 5 s mi 
larly, 2 *. = 2 3 . /. &c. Hence, supposing i m )b the term in 
the series ' b , "6, &c.* after which, without sensible error, each 
term = \ of the square of the preceding term, we have 
/(!)=! 
— b 
b . I +'6 
H- 
+ 4 .'p:qj. 
2 • 2 < 
/ 2 
+ &c.} 
(S) 
,V <”)* 
Or, h ,,,-I±^L = ,^ 
+a/i+£ 
Z-lX + krlij + i, 
2-44 ,/ (? 4 
very nearly instead of l. 
2 
y/K * 4 4 
i 
vX 
. J 2 B .2 B * 
* wc may put /. or + — 
2 B 4 2 B 8 2 
or 2* /. -7^— + or 23 . J. -JJ- H or 2 n — “ l. ~^r > very nearly. 
