Scale - Spatial Mathematics: Theory and Practice through Mapping - page 109

5.1 Introduction
The scale of a map represents the ratio of the distance between two points on
a map to the corresponding distance on the surface of the Earth. Map Scale
is Map Distance divided by Ground Distance. Suppose one inch on the map
represents one mile on the surface of the Earth. There are a several common
ways to express this idea. Verbal Scale simply states the relationship as: “One
inch represents one mile.” A Bar Scale shows graphically the relationship
between the map distance and the surface distance, and is typically used
to visualize distances on a map. Finally, map scale may be represented as
a numerical ratio, called a Representative Fraction (RF), which is free from
units. If, for example, RF = 1/24,000, then one meter on the map represents
24,000 meters on the surface of the Earth. Or, one foot on the map represents
24,000 feet on the surface of the Earth. It is convenient to capture the idea
using notation such as 1:24,000, 1:63,360 (which is a scale of one inch to one
mile), or 1:1,000,000.
Consider the difference in the following maps: Figure 5.1a (RF 1:24,000)
shows a view of part of Chesapeake Bay; Figure 5.1b (RF 1:100,000) shows
more of the bay, and Figure 5.1c (RF 1:250,000) shows more yet. Topographic
maps of the United States are most often produced, by the United States
Figure 5.1 (a) 1:24,000. (b) 1:100,000. (c) 1:250,000. Scale change displayed. Each
cell depicts the area shown by maps at each scale indicated. The larger represen-
tative fractions display “large scale” maps. Source: National Atlas of the United
States, March 5, 2003, http://nationalatlas.gov.