Plane Trigonometry and Numerical Computation
Chapter VI
Logarithmic Computation
45. Logarithmic Computation. In the last
chapter a few examples of the use of logarithms in computation were given
in connection with a four-place table. Such a table suffices for
data and results accurate to four significant figures. When greater accuracy is
desired we use a five-, six-, or seven-place table.
No subject is better adapted to illustrate the use of
logarithmic computation than the solution of triangles, which we shall consider in
some detail. Five-place tables and logarithmic solutions ordinarily are used at
the same time, since both tend toward greater speed and accuracy.
46. Five-place Tables of Logarithms and
Trigonometric Functions. The use of a five-place table of logarithms differs
from that of a four-place table in the general use of so-called "interpolation
tables" or "tables of proportional parts," to facilitate interpolation. Since
the use of such tables of proportional parts is fully explained in every good set
of tables, it is unnecessary to give such an explanation here. It will be assumed
that the student has made himself familiar with their use.[1]
In the logarithmic solution of a triangle we nearly
always need to find the logarithms of certain trigonometric functions. For example,
if the angles A and B and the side a are given, we find
the side b from the law of sines given in § 30,
a sin B
b = —————————.
sin A
[1] For this chapter, such a five-place table should be
purchased. See, for example, THE MACMILLAN TABLES, which contain all the
tables mentioned here with an explanation of their use.
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