To measure the altitude of a tower, &c., on a height.
[[Fig. 4], Plate, Surveying, and Reconnoitring.]
From the first station, near the base, take the altitude of the hill, and also that of the tower above it, and note down these angles; proceed to another station in a straight line with the former one, measuring its length, and again observe the angular height of the hill, and also that of the top of the tower.
Similarly to the previously described mode, ascertain, first, the height of the hill; second, the height of the hill, and tower; deduct the first calculation from the second, which will leave the height of the tower.
In all the foregoing cases the heights may be correctly ascertained by trigonometrical calculations (vide [Trigonometry], without logarithms, [page 303]).
4.—BY THE SHADOW OF THE OBJECT,
to ascertain the height.
Set up vertically a staff of known length, and measure the length of its shadow upon a horizontal, or other plane; measure also the length of the shadow of the object of which the altitude is required. Then, by the property of similar triangles,
As the length of the shadow of the staff
is to the altitude of the staff,
so is the length of the shadow of the object
to the altitude of the object.
5.—WHEN THERE IS NO SHADOW,