of the Hyperbola . 
251 
= 7*4349912, and their difference, d , = 67989144 ; we need 
only to verify that work, which may easily be done by the 
Formula given in Art. 25 and 27, thus : denoting the value of 
the ascending series corresponding to the ordinate ™ by and 
the value of the descending series corresponding to the same 
ordinate by S, we have. 
Art. 25, d = 1 -f* e 
8*0710678 ] 
1*2721536 j 
by Art. 27, d = 2S — 1 
= 6*7389142; 
f = 14-8693824 1 
1— 8-0710678] 
= 67989146; 
the difference in the last figures of the results arising from 
the inaccuracy of decimal fractions, and being wholly incon- 
siderable. 
The rest of the work may stand as follows : when y is = 
10, then, [a being = 7, and = V aa -f - 1 = 
A 
B 
C 
h l . yj& ± '± 
y 
-Vtay+O 
A 
2 
0*0338341, 
■ 0-0003323, 
0*0000020; 
2yy 
—V(yv- f -0 ___ 3B 
4 T 4 
of which terms two only are wanted to obtain a result true to 
seven places of figures. Hence we have 
U 2 
