Plane trigonometry, by S.L. Loney.

TABLES OF LOGARITHMIC SINES, ETC.

165

trigonometrical functions of angles. As before it is only
necessary to construct the tables for angles between 0~
and 45~.
Since the sine of an angle is always less than unity,
the logarithm of its sine is always negative (Art. 142).
Again, since the tangent of an angle between 0~ and
45~ is less than unity its logarithm is negative, whilst the
logarithm of the tangent of an angle between 45~ and
90~ is the logarithm of a number greater than unity and is
therefore positive.
157. To avoid the trouble and inconvenience of printing the proper sign to the logarithms of the trigonometric
functions, the logarithms as tabulated are not the true
logarithms, but the true logarithms increased by 10.
For example, sine 30 =-.
Hence log sin 30~ = log - = - log 2
- 30103 = 1-69897.
The logarithm tabulated is therefore
10 + log sin 30~, i.e. 9'69897.
Again, tan 60~ = V/3.
Hence log tan 60~ = I log 3 = ' ((4771213)
= -2385606.
The logarithm tabulated is therefore
10 +2385606, i.e. 10'2385606.
The symbol L is used to denote these "tabular
logarithms," i.e. the logarithms as found in the English
books of tables.
Thus L sin 15~ 25' = 10 + log sin 15~ 25',
and L sec 48~ 23' = 10 + log sec 48~ 23'.