[1861]. Scales. In order that you may be able to tell the distance between any two points on a map, the map must be drawn to scale,—that is, it must be so drawn that a certain distance on the map, say, one inch, represents a certain distance on the ground, say, one mile. On such a map, then, two inches would represent two miles on the ground; three inches, three miles, and so on. Therefore, we may say—
The scale of a map is the ratio between actual distances on the ground and those between the same points as represented on the map.
[1862]. Methods of representing scales. There are three ways in which the scale of a map may be represented:
1st. By words and figures, as 3 inches = 1 mile; 1 inch = 200 feet.
2d. By Representative Fraction (abbreviated R. F.), which is a fraction whose numerator represents units of distance on the map and whose denominator, units of distance on the ground.
For example, R. F. = 1 inch (on map)/1 mile (on ground) which is equivalent to R. F. = 1/63360, since 1 mile = 63,360 inches. So the expression, "R. F. 1/63360" on a map merely means that 1 inch on the map represents 63,360 inches (or 1 mile) on the ground. This fraction is usually written with a numerator 1, as above, no definite unit of inches or miles being specified in either the numerator or denominator. In this case the expression means that one unit of distance on the map equals as many of the same units on the ground as are in the denominator. Thus, 1/63360 means that 1 inch on the map = 63,360 inches on the ground, 1 foot on the map = 63,360 feet on the ground; 1 yard on the map = 63,360 yards on the ground, etc.
3d. By Graphical Scale, that is, a drawn scale. A graphical scale is a line drawn on the map, divided into equal parts, each part being marked not with its actual length, but with the distance which it represents on the ground. Thus:
Fig. 1
For example, the distance from 0 to 50 represents fifty yards on the ground; the distance from 0 to 100, one hundred yards on the ground, etc.