S.--A useful tool is called the proportional
dividers, the legs of which are hinged together intermediate the ends,
so that the pivotal joint is adjustable. By means of this tool the scale
of work may be changed, although its widest field of usefulness is work
laid off on a scale which you intend to reduce or enlarge
proportionally.

DETERMINING ANGLES.--Now, in order to lay out work the boy should know
quickly and accurately how to determine various angles used or required
in his work. The quickest way in which to learn this is to become
familiar with the degree in its various relations.

[Illustration: _Fig. 51._]

DEFINITION OF DEGREE.--A degree is not a measure, as we would designate
a foot or a pound to determine distance or quantity. It is used to
denote a division, space, interval or position. To illustrate, look at
the circle, Fig. 51. The four cardinal points are formed by the cross
lines (A, B), and in each one of the quadrants thus formed the circle is
divided into 90 degrees. Look at the radial lines (C, D), and you will
find that the distance between these lines is different along the
curved line (E) than along the curved line (F). The degree is,
therefore, to indicate only the space, division or interval in the
circle.

THE MOST IMPORTANT ANGLE.--Most important for one to know at a glance is
that of 45 degrees, because the one can the more readily calculate the
other degrees, approximately, by having 45 degrees once fixed in the
mind, and impressed on the visual image. With a square and a compass it
is a comparatively easy matter accurately to step off 45 degrees, as it
is the line C, midway between A and B, and the other degrees may be
calculated from the line C and the cardinal lines A or B.

DEGREES WITHOUT A COMPASS.--But in the absence of a compass and when you
do not wish to step off a circle, you will in such case lay down the
square, and mark off at the outer margin of the limbs two equal
dimensions. Suppose we take 2 inches on each limb of the square. The
angle thus formed by the angle square blade is 45 degrees. To find 30
degrees allow the blade of the angle square to run from 2 inches on one
limb to 3-1/2 inches on the other limb, and it will be found that for 15
degrees the blade runs from 2 inches on one limb to 7-1/2 inches on the
other limb. It would be well to fix firmly these three points, at least,
in your mind, as they will be of the utmost value to you. It is a
comparatively easy