Measurements.

39

place-By similar triangles.-To show how the breadth of a river may be measured without instruments, without any table, and without crossing it, I have taken the following useful problem from the French ` 1Tanuel 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 B, produce it for any distance, as to D ; from D, in any convenient G direction, take any equal distances, D

C,

a 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, &c., 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 measuring 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". 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 0 A B by reference to a proper table. In the same way the

A

a