lly 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,
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. The units in which the base is measured may be feet, yards,
minutes, or hours' journey, or whatever else is convenient. Any multiple
or divisor of 100 may be used for the base, if the tabular number be
similarly multiplied. Therefore a traveller may ascertain the breadth of
a river, or that of a valley, or the distance of any object on either
side of his line of march, by taking not more than some sixty additional
paces, and by making a single reference to my table. Particular care must
be taken to walk in a straight line from A to B, by sighting some more
distant object in a line with B. It will otherwise surprise most people,
on looking back at their track, to see how curved it has been and how far
their b' B is from being in the right direction.

[Contains Table for Rough Triangulation without the usual instruments,
and without Calculation"].

Measurement of Tim