without instruments, without any table, and without crossing it, I have
taken the following useful problem from the French 'Manuel du Genie.'
Those usually given by English writers for the same purpose are,
strangely enough, unsatisfactory, for they require the measurement of an
angle. This plan requires pacing only. To measure A G, produce it for any
distance, as to D; from D, in any convenient direction, take any equal
distances, D C, c d; produce B C to b, making c B--C B; join d b, and
produce it to a, that is to say, to the point where A C produced
intersects it; then the triangles to the left of C, are similar to those
on the right of C, and therefore a b is equal to A B. The points D C,
etc., may be marked by bushes planted in the ground, or by men standing.


The disadvantages of this plan are its complexity, and the usual
difficulty of finding a sufficient space of level ground, for its
execution. The method given in the following paragraph is incomparably
more facile and generally applicable.

Triangulation by measurement of Chords.--Colonel Everest, the late
Surveyor-General of India, pointed out (Journ. 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,