*Project Gutenberg*. Public domain.

*A v*through the point where the short arc

*t t’*passes through the impulse face

*w*of the tooth

*D*. Then we continue the line

*w*to

*n*, to represent the impulse face of the tooth, and then measure the angle

*A w n*between the lines

*w n*and

*v A*, and find it to be approximately sixty-four degrees. We then, by a similar process, measure the angle

*A t s’*and find it to be approximately sixty-six degrees. When contact ensues between the tooth

*D*and pallet

*C*the tooth

*D*will attack the pallet at the point where the radial line

*A v*crosses the tooth face. We have now explained how we can delineate a tooth or pallet at any point of its angular motion, and will next explain how to apply this knowledge in actual practice.

PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT.

To delineate our entrance pallet after one-half of
the engaged tooth has passed the inner angle of the
entrance pallet, we proceed, as in former illustrations,
to establish the escape-wheel center at *A*, and
from it sweep the arc *b*, to represent the pitch
circle. We next sweep the short arcs *p s*,
to represent the arcs through which the inner and
outer angles of the entrance pallet move. Now,
to comply with our statement as above, we must draw
the tooth as if half of it has passed the arc *s*.

To do this we draw from *A* as a center the radial
line *A j*, passing through the point *s*,
said point *s* being located at the intersection
of the arcs *s* and *b*. The tooth *D*
is to be shown as if one half of it has passed the
point *s*; and, consequently, if we lay off three
degrees on each side of the point *s* and establish
the points *d m*, we have located on the arc
*b* the angular extent of the tooth to be drawn.
To aid in our delineations we draw from the center
*A* the radial lines *A d’* and *A
m’*, passing through the points *d m*.
The arc *a* is next drawn as in former instructions
and establishes the length of the addendum of the
escape-wheel teeth, the outer angle of our escape-wheel
tooth being located at the intersection of the arc
*a* with the radial line *A d’*.

As shown in Fig. 92, the impulse planes of the tooth
*D* and pallet *C* are in contact and, consequently,
in parallel planes, as mentioned on page 91.
It is not an easy matter to determine at exactly what
degree of angular motion of the escape wheel such
condition takes place; because to determine such relation
mathematically requires a knowledge of higher mathematics,
which would require more study than most practical
men would care to bestow, especially as they would
have but very little use for such knowledge except
for this problem and a few others in dealing with
epicycloidal curves for the teeth of wheels.