nt.

On account of the necessary inaccuracy of all maps it is impossible to
determine exactly how much ground is visible from any given
point--that is, if a correct reading of the map shows a certain point
to be just barely visible, then it would be unsafe to say positively
that on the ground this point could be seen or could not be seen. It
is, however, of great importance for one to be able to determine at a
glance, within about one contour interval, whether or not such and
such a point is visible; or whether a given road is generally visible
to a certain scout, etc. For this reason no effort is made to give an
exact mathematical solution of problems in visibility further than
would be useful in practical work with a map in the solution of map
problems in patrolling.

In the solution of visibility problems, it is necessary that one
should thoroughly understand the meaning of profiles and their
construction. A profile is the line supposed to be cut from the
surface of the earth by an imaginary vertical (up and down) plane.
(See Fig. 21.) The representation of this line to scale on a sheet of
paper is also called a profile. Figure 21 shows a profile on the line
D--y (Figure 20) in which the horizontal scale is the same as that of
the map (Figure 20) and the vertical scale is 1 inch = 40 feet. It is
customary to draw a profile with a greater vertical than horizontal
scale in order to make the slopes on the profile appear to the eye as
they exist on the ground. Consequently, always note especially the
vertical scale in examining any profile; the horizontal scale is
usually that of the map from which the profile is taken.

[Illustration: Fig. 20]

[Illustration: Fig. 21]

A profile is constructed as follows: (Fig. 21): Draw a line D'--y'
equal in length to D--y on the map. Lay off on this line from D'
distances equal to the distances of the successive contours from D on
the map. At each of these contour points erect a perpendicular equal
to the elevation of this particular contour, as shown by the vertical
scale (960, 940, 920, etc.) on the left. Join successively these
verticals by a smooth curve, which is the required profile. Cross
section paper with lines printed 1/10 inch apart horizontally and
vertically simplifies the work of construction, by avoiding the
necessity of laying off each individual distance.

=1876. Visibility Problem.= To determine whether an observer with his
eye at D can see the bridge at XX