The contours of a concave (hollowed out) cone (Fig. 9) are close together at the center (top) and far apart at the outside (bottom).

[Ill.u.s.tration: Fig. 9]

The following additional points about contours should be remembered:

(a) A Water Shed or Spur, along with rain water divides, flowing away from it on both sides, is indicated by the higher contours bulging out toward the lower ones (F-H, Fig. 6).

(b) A Water Course or Valley, along which rain falling on both sides of it joins in one stream, is indicated by the lower contours curving in toward the higher ones (M-N, Fig. 6).

(c) The contours of different heights which unite and become a single line, represent a vertical cliff (K, Fig. 6).

(d) Two contours which cross each other represent an overhanging cliff.

(e) A closed contour without another contour in it, represents either in elevation or a depression, depending on whether its reference number is greater or smaller than that of the outer contour. A hilltop is shown when the closed contour is higher than the contour next to it; a depression is shown when the closed contour is lower than the one next to it.

If the student will first examine the drainage system, as shown by the courses of the streams on the map, he can readily locate all the valleys, as the streams must flow through valleys. Knowing the valleys, the ridges or hills can easily be placed, even without reference to the numbers on the contours.

=For example:= On the Elementary Map, Woods Creek flows north and York Creek flows south. They rise very close to each other, and the ground between the points at which they rise must be higher ground, sloping north on one side and south on the other, as the streams flow north and south, respectively (see the ridge running west from Twin Hills).

The course of Sandy Creek indicates a long valley, extending almost the entire length of the map. Meadow Creek follows another valley, and Deep Run another. When these streams happen to join other streams, the valleys must open into each other.

=1867. Map Distances (or horizontal equivalents).= The horizontal distance between contours on a map (called map distance, or M. D.; or horizontal equivalents or H. E.) is inversely proportional to the slope of the ground represented--that it to say, the greater the slope of the ground, the less is the horizontal distance between the contours; the less the slope of the ground represented, the greater is the horizontal distance between the contours.

[Ill.u.s.tration: Fig. 10]

+-----------+--------+--------------+ | Slope | Rise | Horizontal | | (degrees) | (feet) | Distance | | | | (inches) | +-----------+--------+--------------+ | 1 deg. | 1 | 688 | | 2 deg. | 1 | 688/2 = 344 | | 3 deg. | 1 | 688/3 = 229 | | 4 deg. | 1 | 688/4 = 172 | | 5 deg. | 1 | 688/5 = 138 | +-----------+--------+--------------+

It is a fact that 688 inches horizontally on a 1 degree slope gives a vertical rise of one foot; 1376 inches, two feet, 2064 inches, three feet, etc., from which we see that on a slope of 1 degree, 688 inches multiplied by vertical rises of 1 foot, 2 feet, 3 feet, etc., gives us the corresponding horizontal distance in inches. For example, if the contour interval (Vertical Interval, V. I.) of a map is 10 feet, then 688 inches 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 a.s.sume 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 = 6880/(15840 2) = .22 inch;

M. D. for 3 = 6880/(15840 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 V. I. (feet) 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:

[Ill.u.s.tration: Fig. 11]

The left-hand division is marked 1/2; the next division (one-half as long) 1; the next division (one-half the length of the 1 division) 2, and so on. The 1/2 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 s.p.a.ce between adjacent contours equal to the 1 s.p.a.ce shown on the scale means a 1 slope, and so on.

What is a slope of 1? By a slope of 1 we mean that the surface of the ground makes an angle of 1 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 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 or steeper. Ground having a slope of less than 1/2 is practically level.

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

1st. A one degree slope means that the angle between the horizontal and the given line is 1 degree (1). 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.

[Ill.u.s.tration: 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.

[Ill.u.s.tration: 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 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.

[Ill.u.s.tration: 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 magnetic qualities, attracts one end of all compa.s.s needles and causes them to point towards it, and as it is near the True North Pole, this serves to indicate the direction of north to a person using a compa.s.s.

Of course, the angle which the Magnetic needle makes with the True Meridian (called the Magnetic Declination) varies at different points on the earth. In some places it points east of the True Meridian and in others it points west of it.

It is important to know this relation because maps usually show the True Meridian and an observer is generally supplied with a magnetic compa.s.s. Fig. 15 shows the usual type of Box Compa.s.s. It has 4 cardinal points, N, E, S and W marked, as well as a circle graduated in degrees from zero to 360, clockwise around the circle. To read the magnetic angle (called magnetic azimuth) of any point from the observer's position the north point of the compa.s.s circle is pointed toward the object and the angle indicated by the north end of the needle is read.

[Ill.u.s.tration: Fig. 15]

You now know from the meridians, for example, in going from York to Oxford (see Elementary Map) that you travel north; from Boling to Salem you must travel south; going from Salem to York requires you to travel west; and from York to Salem you travel east. Suppose you are in command of a patrol at York and are told to go to Salem by the most direct line across country. You look at your map and see that Salem is exactly east of York. Next you take out your field compa.s.s (Figure 15, Par. 1870), raise the lid, hold the box level, allow the needle to settle and see in what direction the north end of the needle points (it would point toward Oxford). You then know the direction of north from York, and you can turn your right and go due east towards Salem.

Having once discovered the direction of north on the ground, you can go to any point shown on your map without other a.s.sistance. If you stand at York, facing north and refer to your map, you need no guide to tell you that Salem lies directly to your right; Oxford straight in front of you; Boling in a direction about halfway between the directions of Salem and Oxford, and so on.

=1871. Determination of positions of points on map.= If the distance, height and direction of a point on a map are known with respect to any other point, then the position of the first point is fully determined.