l g 6 Mr. Hellins's Improvement in the Computation 
to others, the terms of which decrease by the powers of 80 ; 
so that their convergency is swift, and the divisions by 80 are 
easily made. 
2. Mr. Jones considered the number 10 as composed of 
2 x 2 x 2 x f ; and consequently obtained the logarithm of 10 
by adding three times the logarithm of 2 to the logarithm of 
The algebraic series which he used on this occasion was 
— + —7- 4 - 4 - —— 7", &c. and the numerical value of — 
s' 3 s 3 1 5 s 5 1 7 s 7 * s 
was for the logarithm of 2, and j- for the logarithm of £ ; 
so that he has 
Sum of «< 
3L. 2 = 
! L. i.: 
6 
3 3 3 
2 
To 3 
+ 
5-3 
+ w> &c-l 
W’ &c - J 
L. 10. 
q. Now the series — -\ — — 3 
° 3 1 3-3 
+ 77 + 
+ 7 F + 7 F’ &c ' (= 3 L ' 2 ) 
is evidently = yx: 1 + pr -f -pr + &c. = 2 x : 1 
— - — j l — -1 — I —r, &c. And if the first, third, fifth, &c. 
term of this series be written in one line, and the second, 
fourth, sixth, &c. in another, we shall have 
Lsj f 2 * : 1 + 77 + 77 + 777 ’ &c ' 
3 ] + 3 x : 77 + 77 + 777 + 777 ’ &e ‘ 
L 1 3-9 1 .7-9 
which two series are evidently 
2 x : 1 + *^7 + -p~ 
-, &c. 
13 . 81 3 
+ T x : f + TsT + 771T + TpF’ &c * 
And Mr. Jones’s other series, -f pr + pr -f- &c * 
=L. is evidently = f x : 1 + + 77>&c- = 
9 ' 3-9 
1 
3 - 9 * 
