of the Hyperbolic Logarithm of to. 
141 
to another series which converges by the powers of ~^ QQO , 
by which the numerical calculation is greatly facilitated. 
8. For the two series in the preceding article (the sum of 
which is = H. L, of 10), are evidently = 
“ X ; 1 + At + T5T*- + &c ‘ 
and x : 1 + 
253 ' 
3.81 
9 
+ 
5 .Si 
9 Z 
+ 
7.81 3 » 
9 3 
&C. 
3.64009 ' 5.64 0 09 2, * 7.64009** 
And these two series, when transformed by the theorem 
abovementioned, and the terms abbreviated, become 
9 a 
and 
9-253 
3.40 
9 a 
+ 
+ 
2B 
3 C 
+ 
4 P 
5.4O 
7.4O 
9.40 : 
2.9B 
3 - 9 c 
+ 
4.9D 
&c. 
&c. 
32000 3.32000 
Which series admit of some other abbreviations similar to those 
pointed out in article 6 ; and by them may the hyperbolic 
logarithm of 10 be very easily and expeditiously computed. 
June 24, 1795. 
