the beginner, however, to
spend all his time making simple drawings, without making them to scale,
in order to become so familiar with the use of the instruments as to
feel at home with them, avoiding the complication of early studies that
would accompany drawing to scale.

CHAPTER X.

_PROJECTIONS._

In projecting, the lines in one view are used to mark those in other
views, and to find their shapes or curvature as they will appear in
other views. Thus, in Figure 225_a_ we have a spiral, wound around a
cylinder whose end is cut off at an angle. The pitch of the spiral is
the distance A B, and we may delineate the curve of the spiral looking
at the cylinder from two positions (one at a right-angle to the other,
as is shown in the figure), by means of a circle having a circumference
equal to that of the cylinder.

The circumference of this circle we divide into any number of
equidistant divisions, as from 1 to 24. The pitch A B of the spiral or
thread is then divided off also into 24 equidistant divisions, as marked
on the left hand of the figure; vertical lines are then drawn from the
points of division on the circle to the points correspondingly numbered
on the lines dividing the pitch; and where line 1 on the circle
intersects line 1 on the pitch is one point in the curve. Similarly,
where point 2 on the circle intersects line 2 on the pitch is another
point in the curve, and so on for the whole 24 divisions on the circle
and on the pitch. In this view, however, the path of the spiral from
line 7 to line 19 lies on the other side of the cylinder, and is marked
in dotted lines, because it is hidden by the cylinder. In the
right-hand view, however, a different portion of the spiral or thread is
hidden, namely from lines 1 to 13 inclusive, being an equal proportion
to that hidden in the left-hand view.

[Illustration: Fig. 225 _a_.]

The top of the cylinder is shown in the left-hand view to be cut off at
an angle to the axis, and will therefore appear elliptical; in the
right-hand view, to delineate this oval, the same vertical lines from
the circle may be carried up as shown on the right hand, and horizontal
lines may be drawn from the inclined face in one view across the end of
the other view, as at P; the divisions on the circle may be carried up
on the right-hand view by means of straight lines, as Q, and arcs of
circle, as at R, and vertical lines drawn from these arcs, as line S,
and where these ve