of computing Logarithms. 
3-9 
With respect to the logs, of — , 
IO 100 
IOOO 
, &c. their compu- 
tation is very easy,* they being the respective sums of the 
series 
i 
IO 
■f 2 X 
IOl 
1 
1000 
+ 2 X 
lOOOp 
&C. 
+ 7 x =p + ♦ x 
+ § * 
iol 
i 
loop 
iooo J 
-f &C. 
— p- &C. 
-f> &c. 
of which series each is more easily summed than the pre- 
ceding. 
With respect to the logarithms of 2 and to there are, it is 
well known, various ways of computing them, and the time 
requisite depends greatly on the practical habits of the calcu- 
lator. Among other ways, they may be computed by the 
method given in this Paper, and with what degree of expe- 
dition, may be seen by the examples to the rules, where they 
are both of them worked. •f 
• Ex. 
, iooo i _ i 
H. 1. — 1 + t x - — 
999 iooo iooop 
i st term — ,001 
2d term — ,0000005 
3d term — ,000000000333 
-j- &c. 
Sum rz ,001000500333, which is true to the last place of decimals. 
f It may be seen there that the logarithm of 10 by this method requires very little 
work. The log. of 2 may also be computed from the log. of 10 as follows. 
2 10 = 1024 =z iooo x (1 + therefore log. 2 ,0 — 3X log. 10 + log. (1 + 
2 4 \ 
iooo I 
=3 x log. 10 + 
2 4 t 2 4f + A x -Hi 3 
iooo 2 iooop 3 iooo[ 3 
U u 2 
