contour interval (Vertical Interval, V. I.) of a map is 10 feet, then
688 inches x 10 equals 6880 inches, gives the horizontal ground
distance corresponding to a rise of 10 feet on a 1 degree slope. To
reduce this horizontal ground distance to horizontal map distance, we
would, for example, proceed as follows:

Let us assume the R. F. to be 1/15840--that is to say, 15,840 inches
on the ground equals 1 inch on the map, consequently, 6880 inches on
the ground equals 6880/15840, equals .44 inch on the map. And in the
case of 2 degrees, 3 degrees, etc., we would have:

M. D. for 2 deg. = 6880/(15840 x 2) = .22 inch;

M. D. for 3 deg. = 6880/(15840 x 3) = .15 inch, etc.

From the above, we have this rule:

To construct a scale of M. D. for a map, multiply 688 by the contour
interval (in feet) and the R. F. of the map, and divide the results by
1, 2, 3, 4, etc., and then lay off these distances as shown in Fig.
11, Par. 1867a.

FORMULA

M. D. (inches) = (688 x V. I. (feet) x R. F.) /
(Degrees (1, 2, 3, 4, etc.))

=1867a. Scale of Map Distances (or, Scale of Slopes).= On the
Elementary Map, below the scale of miles and scale of yards, is a
scale similar to the following one:

[Illustration: Fig. 11]

The left-hand division is marked 1/2 deg.; the next division (one-half as
long) 1 deg.; the next division (one-half the length of the 1 deg. division)
2 deg., and so on. The 1/2 deg. division means that where adjacent contours on
the map are just that distance apart, the ground has a slope of 1/2 a
degree between these two contours, and slopes up toward the contour
with the higher reference number; a space between adjacent contours
equal to the 1 deg. space shown on the scale means a 1 deg. slope, and so on.

What is a slope of 1 deg.? By a slope of 1 deg. we mean that the surface of
the ground makes an angle of 1 deg. with the horizontal (a level surface.
See Fig. 10, Par. 1867). The student should find out the slope of some
hill or street and thus get a concrete idea of what the different
degrees of slope mean. A road having a 5 deg. slope is very steep.

By means of this scale of M. D.'s on the map, the map reader can
determine the slope of any portion of the ground represented, that is,
as steep as 1/2 deg. or steeper. Ground having a slope of less than 1/2 deg.
is practically level.

=1868. Slopes.= Slopes are usually given in one of three ways: 1st, in
degrees; 2d, in percentages; 3d, in g