02 
MPu J. II. JEAXS OX THE EQUILIBRIUM 
+ f — 
o_ J 1 8 0. ,3 _ 2^-2_5 
8 
y-t - 
4375 
27'if 
_i_ A § J 4A.J, I I 
H- 8 ^21 2 5^ 32^3 • 
I ? I 4 I ^ I I 
+ Sj ■! s’) + 3, + 27 f + 
Wr-AHX-||I + ... + 8A2>) + 7; + 7U + -- 
S 1480 
oT] SU;'^ 
and hence, by multiplication Ayith (105), 
ISO^I + I § 2 ^ + (S0I2 + I § 2 ^) (34= - ¥) 
— A0 2_5„u _ 1 2 7.1 2 .-s„3 I .8 1 2 .1 ,, _ '3,12-1 
— 5 6 V ■ 86 6 ^ li :}o2',] 
C)20 
+ ^2 i + Cr? + ■(? - + • 
Ot; 
We have from equations (80) and ( 100 ) 
, 5 , .to , 1000 , 
+24iy + --- 
f.= = ‘Jr,* - 20 ,'= + + ... 
and hence, by multijilication, ve lind 
= h" + 
Aini I I 
Therefore (So^i)' (3^u) = fit’?' + - W’? + 
From equations ( 01 ) and (80) we have 
J-A<iy 3 _ 28_2_Ae _ 4 5 3 _ 10 2 5 
7 So 2 8 So — 147 5 6 7 
and from equation (03), 
§ 0^1 = ¥t 
Iiv multiplication of these last two series, 
% t /ISO e 3 _ 1^2 5y \ _ 6 7 5 .5 _ 
° 0 Sl I 7 so 2 8 so/ — ll-lV 
21,875 
144>? 
2125 , 154,375 
847? 
q_ 
■847?3 
+ -• 
, 
1 2 I o- .1 u • ■ • 
2(7?’ 
2 6 2 5. .3 _ 312 5 | ^^oO 
ij-i V S36 V ^ W ■ 
< V 
50 
We have also 
So^i aI{ s’? + 3 ’^ + 2^1 + 
= §21 iV + ^ + ^ ■ + •■■}• 
■W 
10 
+ 0 . 1 ? '+...} 
I 
•J 
The last series we require is By multijilication of the series (91) and ( 02 ), 
we find 
^0' — 3 T’?' + ft’?' + Alt’? 043,^' + • • • • 
If we now collect the various series ivhicli have been obtained and substitute them 
in equation ( 102 ), we find, as the equivalent of this equation, 
