ur times as large as the engraving, which brings us
to the subject of enlarging or reducing scales.

REDUCING SCALES.

[Illustration: Fig. 223.]

[Illustration: Fig. 224.]

[Illustration: Fig. 225.]

It is sometimes necessary to reduce a drawing to a smaller scale, or to
find a minute fraction of a given dimension, such fraction not being
marked on the lineal measuring rules at hand. Figure 224 represents a
scale for finding minute fractions. Draw seven lines parallel to each
other, and equidistant draw vertical lines dividing the scale into
half-inches, as at _a_, _b_, _c_, etc. Divide the first space _e d_ into
equal halves, draw diagonal lines, and number them as in the figure. The
distance of point 1, which is at the intersection of diagonal with the
second horizontal line, will be 1/24 inch from vertical line _e_. Point
2 will be 2/24 inch from line _e_, and so on. For tenths of inches there
would require to be but six horizontal lines, the diagonals being drawn
as before. A similar scale is shown in Figure 225. Draw the lines A B, B
D, D C, C A, enclosing a square inch. Divide each of these lines into
ten equal divisions, and number and letter them as shown. Draw also the
diagonal lines A 1, _a_ 2, B 3, and so on; then the distances from the
line A C to the points of intersection of the diagonals with the
horizontal lines represent hundredths of an inch.

Suppose, for example, we trace one diagonal line in its path across the
figure, taking that which starts from A and ends at 1 on the top
horizontal line; then where the diagonal intersects _horizontal_ line 1,
is 99/100 from the line B D, and 1/100 from the line A C, while where it
intersects _horizontal_ line 2, is 98/100 from line B D, and 2/100 from
line A C, and so on. If we require to set the compasses to 67/100 inch,
we set them to the radius of _n_, and the figure 3 on line B D, because
from that 3 to the vertical line _d_ 4 is 6/10 or 60/100 inch, and from
that vertical line to the diagonal at _n_ is seven divisions from the
line C D of the figure.

In making a drawing to scale, however, it is an excellent plan to draw a
line and divide it off to suit the required scale. Suppose, for example,
that the given scale is one-quarter size, or three inches per foot; then
a line three inches long may be divided into twelve equal divisions,
representing twelve inches, and these may be subdivided into half or
quarter inches and so on. It is recommended to