339 
of computing Logarithms. 
or more places to the right ; add ; and proceed with the sum 
in the same manner, till you have obtained a number, N ± a, 
the difference between which and N shall be inconsiderable. 
Let b, c, d, &c. denote as in the rule. 
Then P x x x ^11“ x &c. =N± a. 
Therefore log. Nt« = log. P -f- b x log. ii 4 * Cx log. 
-f- d x log. -f which call B. 
And log. N = log. -OL- 4 . log. N±a= log. -5^; + B. 
Now we may either carry the operation so far that 
log- *nTT ma y neglected, or we may actually divide N by 
N — a, or N-{-<z by N ( according as the sign is — or -f- ) and 
add or subtract the quotient from B. 
Various artifices may be occasionally used to shorten the 
computation both in the method of subtraction, and in this of 
addition ; and the two may sometimes be advantageously 
combined together. 
It should be observed that, in setting down the numbers, 
the last figure set down ought to be increased by unity when 
the figure immediately following in the neglected part ex- 
ceeds 4» 
