posite to I. Join H and I and draw the intermediate lines through B,
C, etc., parallel to H-I. These lines divide A-I into 7 equal parts,
each 500 yards long. The left part, called the Extension, is similarly
divided into 5 equal parts, each representing 100 yards.

=3. To construct a scale for a map with no scale.= In this case,
measure the distance between any two definite points on the ground
represented, by pacing or otherwise, and scale off the corresponding
map distance. Then see how the distance thus measured corresponds with
the distance on the map between the two points. For example, let us
suppose that the distance on the ground between two given points is
one mile and that the distance between the corresponding points on the
map is 3/4 inch. We would, therefore, see that 3/4 inch on the map =
one mile on the ground. Hence 1/4 inch would represent 1/3 of a mile,
and 4-4, or one inch, would represent 4 x 1/3 = 4/3 = 1-1/3 miles.

The R. F. is found as follows:

R. F. 1 inch/(1-1/3 mile) = 1 inch/(63,360 x 1-1/3 inches) = 1/84480.

From this a scale of yards is constructed as above (2).

4. To construct a graphical scale from a scale expressed in unfamiliar
units. There remains one more problem, which occurs when there is a
scale on the map in words and figures, but it is expressed in
unfamiliar units, such as the meter (= 39.37 inches), strides of a man
or horse, rate of travel of column, etc. If a noncommissioned officer
should come into possession of such a map, it would be impossible for
him to have a correct idea of the distances on the map. If the scale
were in inches to miles or yards, he would estimate the distance
between any two points on the map to be so many inches and at once
know the corresponding distance on the ground in miles or yards. But
suppose the scale found on the map to be one inch = 100 strides
(ground), then estimates could not be intelligently made by one
unfamiliar with the length of the stride used. However, suppose the
stride was 60 inches long; we would then have this: Since 1 stride =
60 inches, 100 strides = 6,000 inches. But according to our
supposition, 1 inch on the map = 100 strides on the ground; hence 1
inch on the map = 6,000 inches on the ground, and we have as our R.
F., 1 inch (map)/6,000 inches (ground) = 1/6000. A graphical scale can
now be constructed as in (2).

Problems in Scales

=1864.= The following problems should be solved to become familiar
with the