[Illustration: _Fig. 2._]
II. 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, ⅛ or ⅒ 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 GE : AE :: FI : CD.
[Illustration: _Fig. 3._]
LANDMAN’S
_Practical Geometry on the Ground_.
III. 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 ¼, 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 CD : DE :: CA: AB.
NOTE. 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 CE : DE:: CB
: BA.
IV. The distance of a battery, or other object, may be ascertained by
the tangent scale on the breach 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 length of 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.