for computing Logarithms. 
3 T 3 
orem i .) i log. ff + log. 
= log. |4« Here the frac- 
tion, whofe odd powers are to be uled in the feries, is 
jfpj, and the very firft term of it, will give the logarithm 
true to twelve places of figures. 
Again, if the logarithm of || were to be computed 
from that of fy found above, we fhould have 2 log. || 
+ log- 
Here the fraction to be ufed in 
the feries is jf T , the firft term of which will give the 
logarithm true to ten places of figures. 
In like manner, from the logarithm of ff we may find 
that of f; from logarithm of f that of f ; and from the 
logarithm of f that of f, as is done above. The respec- 
tive fractions for the feries will be ~, and T j. 
Thus far the fractions I have taken have even num- 
bers for their numerators ; let us now take one whofe 
numerator is an odd number Here n being = 3I,. 
log. f ( f| ) = 2 log. | + log. If; and the fraction whofe odd 
powers are to be ufed is Hence we have the log. 
of j (for f-f-f = j) and may proceed to find the loga- 
rithm of 2 as above. But the logarithm of f may be 
diredtly derived from the equation thus : the equation in 
other terms is, log. 9 - log. 7 = 2 log. 9-2 log. 8 + log. ff ; 
then, by tranfpofition, log. 8 - log. 7 = log. 9 - log. 8 
+ l °g- fj> or log. f = log. f + log. ff. 
3 
But 
