Roy. Geograph. Soc. 1860,
p. 122) the advantage to travellers, unprovided with angular instruments,
of measure the chords of the angles they wish to determine. He showed
that a person who desired to make a rude measurement of the angle C A B,
in the figure (p. 40), has simply to pace for any convenient length from
A towards C, reaching, we will say, the point a' and then to pace an
equal distance from A towards B, reaching the point a ae. Then it remains
for him to pace the distance a' a" which is the chord of the angle A to
the radius A a'. Knowing this, he can ascertain the value of the angle C
A B by reference to a proper table. In the same way the angle C B A can
be ascertained. Lastly, by pacing the distance A B, to serve as a base,
all the necessary data will have been obtained for determining the lines
A C and B C. The problem can be worked out, either by calculation or by
protraction. I have made numerous measurements in this way, and find the
practical error to be within five per cent.
Table for rude triangulation by Chords.--It occurred to me that the plan
described in the foregoing paragraph might be exceedingly simplified by a
table, such as that which I annex in which different values of a' a" are
given for a radius of 10, and in which the calculations are made for a
base = 100. The units in which A a', A a", and B b', Bb", are to be
measured are intended to be paces, though, of course, any other units
would do.
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