and two arcs as 5 and
6 drawn, giving two more points in the curve of the ellipse. The
compasses are then set to the length of line _h_ (that is, from centre
line D to point of division _b_), and this distance is transferred,
setting the compasses on centre line G where it is intersected by line
_u_, and arcs 7, 8 are marked, giving two more points in the ellipse. In
like manner points 9 and 10 are obtained from the length of line _i_, 11
and 12 from that of _j_; points 13 and 14 from the length of _k_, and 15
and 16 from _l_, and the ellipse may be drawn in from these points.

It may be pointed out, however, that since points 5 and 6 are the same
distance from G that points 15 and 16 are, and since points 7 and 8 are
the same distance from G that points 13 and 14 are, while points 9 and
10 are the same distance from G that 11 and 12 are, the lines, _j_, _k_,
_l_ are unnecessary, since _l_ and _g_ are of equal length, as are also
_h_ and _k_ and _i_ and _j_. In Figure 232 the cylinders are line shaded
to make them show plainer to the eye, and but three lines (_a_, _b_,
_c_) are used to get the radius wherefrom to mark the arcs where the
points in the ellipse shall fall; thus, radius _a_ gives points 1, 2, 3
and 4; radius _b_ gives points 5, 6, 7 and 8, and radius _c_ gives 9,
10, 11 and 12, the extreme diameter being obtained from lines S, Z, and
H, H.

CHAPTER XI.

_DRAWING GEAR WHEELS._

The names given to the various lines of a tooth on a gear-wheel are as
follows:

In Figure 233, A is the face and B the flank of a tooth, while C is the
point, and D the root of the tooth; E is the height or depth, and F the
breadth. P P is the pitch circle, and the space between the two teeth,
as H, is termed a space.

[Illustration: Fig. 233.]

[Illustration: Fig. 234.]

It is obvious that the points of the teeth and the bottoms of the
spaces, as well as the pitch circle, are concentric to the axis of the
wheel bore. And to pencil in the teeth these circles must be fully
drawn, as in Figure 234, in which P P is the pitch circle. This circle
is divided into as many equal divisions as the wheel is to have teeth,
these divisions being denoted by the radial lines, A, B, C, etc. Where
these divisions intersect the pitch circle are the centres from which
all the teeth curves may be drawn. The compasses are set to a radius
equal to the pitch, less one-half the thickness of the tooth, and from a
centre, as R, two face cu