Plane trigonometry, by S.L. Loney.

160

TRIGONOMETRY.

From (1) and (2) we see that for an increase 1 in the
number the increase in the logarithm is '0000059.
The Theory of Proportional Parts then states that for
an increase of -3 in the number the increase in the
logarithm is
*3 x 0000059, i.e., -00000177.
Hence log 74583-3 = 4-8726398 + -00000177
= 487264157.
149. As another example we shall find the value of
log 0382757 and shall exhibit the working in a more
concise form.
From the tables we obtain
log 038275 = 2-5829152
log -038276 = 2-5829265.
Hence difference for
*000001 = -0000113.
Therefore the difference for
0000007 = 7 x '0000113
= 00000791,. log -0382757 = 2-5829152
+ -00000791
= 258292311.
Since we only require logarithms to seven places of
decimals we omit the last digit and the answer is
25829231.
150. The converse question is often met with, viz.,
to find the number whose logarithm is given. If the
logarithm be one of those tabulated the required number
is easily found. The method to be followed when this is
not the case is shewn in the following examples.