1. Wishing to know the distance of the object A from B ([fig. 1.]) place a picket at B and another at C, at a few fathoms distance, making A B C a right angle, and divide B C into 4, 5, or any number of equal parts: make another similar angle at C, in a direction from the object, and walk along the line C D till you bring yourself in a line with the object A, and any of the divisions, (say o) of the line B C. Then, as Co : C D ∷ Bo : B A. Vauban.
Fig. 2.
2. To gain the distance between two objects C and D ([fig. 2.]) from any point A, taken in the line C D, erect the perpendicular A E: on which set off from A to E, 1 or 200 feet, more or less, according to the distance between the points C and D; set off from E to G in the prolongation A E, one eighth or one tenth of A E; at G raise the perpendicular G F, and produce it towards I; plant pickets at E and G, then move with another picket on G F till it becomes in a line with E and D: and on the prolongation of the perpendicular F G place another picket at I in the line with E and C; measure F I, and it will be as G E : A E ∷ F I : C D.
Fig. 3.
3. To gain the inaccessible length A B, ([fig. 3.]) of the front of a fortification; plant a picket at C, from whence both points may be seen: find the lengths C A and C B by the method just given ([No. 1.]) make C E ¹⁄₄, or any part of C B, and make C D bear the same proportion to C A: measure D E, then it will be as C D : D E ∷ C A : A B.
See Am. Mil. Lib. Article Field Fortification.
Nearly after the same manner may be ascertained the distance from B to A when the point B is accessible; for having measured the line C B, and made the angle C E D equal to C B A, it will be, as C E : D E ∷ C B : B A.
4. The distance of a battery, or other object, may be ascertained by the tangent scale on the breech of a gun. It is however necessary in this case to know the height of the object, the distance of which is required. Lay the gun by the upper line of metal for the top of the object, then raise the tangent scale till the top of the scale and the notch at the muzzle are in a line with the bottom of the object, and note what height of the tangent scale is required: then say, as the length of the scale above the base ring of the gun is to the length from the base ring to the swell of the muzzle, so is the height of the object to its distance from the muzzle of the gun.