radients (grades).

1st. A one degree slope means that the angle between the horizontal
and the given line is 1 degree (1 deg.). See Fig. 10, Par. 1867.

2d. A slope is said to be 1, 2, 3, etc., per cent, when 100 units
horizontally correspond to a rise of 1, 2, 3, etc., units vertically.

[Illustration: Fig. 12]

3d. A slope is said to be one on one (1/1), two on three, (2/3), etc.,
when one unit horizontal corresponds to 1 vertical; three horizontal
correspond to two vertical, etc. The numerator usually refers to the
vertical distance, and the denominator to the horizontal distance.

[Illustration: Fig. 13]

Degrees of slope are usually used in military matters; percentages are
often used for roads, almost always of railroads; gradients are used
of steep slopes, and usually of dimensions of trenches.

=1869. Effect of Slope on Movements=

60 degrees or 7/4 inaccessible for infantry;
45 degrees or 1/1 difficult for infantry;
30 degrees or 4/7 inaccessible for cavalry;
15 degrees or 1/4 inaccessible for artillery;
5 degrees or 1/12 accessible for wagons.

The normal system of scales prescribed for U. S. Army field sketches
is as follows: For road sketches, 3 inches = 1 mile, vertical
interval between contours (V. I.) = 20 ft.; for position sketches, 6
inches = 1 mile, V. I. = 10 ft.; for fortification sketches, 12 inches
= 1 mile, V. I. = 5 ft. On this system any given length of M. D.
corresponds to the same slope on each of the scales. For instance, .15
inch between contours represents a 5 deg. slope on the 3-inch, 6-inch and
12-inch maps of the normal system. Figure 11, Par. 1867a, gives the
normal scale of M. D.'s for slopes up to 8 degrees. A scale of M. D.'s
is usually printed on the margin of maps, near the geographical scale.

=1870. Meridians.= If you look along the upper left hand border of the
Elementary Map (back of Manual), you will see two arrows, as shown in
Fig. 14, pointing towards the top of the map.

[Illustration: Fig. 14]

They are pointing in the direction that is north on the map. The arrow
with a full barb points toward the north pole (the True North Pole) of
the earth, and is called the True Meridian.

The arrow with but half a barb points toward what is known as the
Magnetic Pole of the earth, and is called the Magnetic Meridian.

The Magnetic Pole is a point up in the arctic regions, near the
geographical or True North Pole, which, on account of its magneti