S 3 s 
Mr. Hellins’s improved Solution of 
:(a-\-b) 2 x 
-1 
:( a-\-b ) 2 x 
2 V V 
^(vv—cc) 
2 , 
2W 
\/(vv—cc) 
( 1 4- ■£» 4- .^1 4- Mr _L -3AZT 
^ * 2 T- 2. 4 -r 2.4.6 1 2.4.6.8» 
3 V 
3-5 v 
3 - 5*7 v * 
+ 
3 vv 
3.5 v ♦ 
.Z f 1 -Lg..|. 3:ir I 3-5 '7 v Mr) 
S(vv-cc)& lm r 4 T- 4 .6 T 4.6.8 
And the fluents of these several terms, without their coeffi- 
cients, are as follows : 
/ <V V 
*/(yv—cc) 
f — ± 
J */(vv—cc) 
r vy* 
J ^(vv—cc) 
f 
IS 
t/{vv—cc) t 
C C V ’ 
H L v +*/( vv - cc ) 
c 
*y[v V — C C ) V-\-C C a 
n> v 4 
\/(yV—CC) T/ 3 -f 3 ccQ 
— - 
_ a /{ w — <cc) V s + 5C C y 
— 6 ” 
&c: 
:a; 
J; 
a/ (»•» — cc) 
a/ (v v — c c) 
These fluents, being multiplied by their proper coefficients, 
and collected together, and the whole multiplied by the com- 
-3. 
mon factor (a-f b) 2 , the fluent sought will be 
f 2 ^/ (VV— CC) 
(tf+6) 2 x • 
l 
ccv 
6. We must now inquire what value this series has when 
z — o ; in which case, x being = 1, vv is = -—-y = cc. And 
it will appear that, with this value of vv, every term of the se- 
ries vanishes, so that the fluent needs no correction. If, there- 
fore, we compute the value of this series when z === tt, i. e. when 
x =s — 1, and vv 
a 4- b 
d -j- b 
1, we shall have the value of Av, 
