500 ON THE SUMMATION OF SERIES, ETC. 
Here we have o(v) =2 .. o'(@) = 1, and e@) 
(2) 
bi as ee ey woo 
= (2) — ity . &, (7) = 2? o,(v)= pia Xe., &e. 
Similarly o(y) =— , ay) = = ae ®; Qe = 
x 
=e, &e. ie @o(2) d= y — &. 
y y 
Substitute these values in equation (31), and 
we shall have, when a = e, 
lft 1 
Lv y L+4 Dix Ya =e ag 
[x]=1.23...0=[y]xo mbt. 
x 
yts 
y 
1 1 l 1 1 
re ao a 5 & 3s) —e....(33) 
This series, which is very convergent, is also 
very convenient to calculate. The greater we 
take y, the more rapid will the series converge. 
I would, however, here suggest, that y be uni- 
formly taken equal to 10, as a convenient num- 
ber for calculation. 
