jewel pin will pass through an arc of thirty degrees,
as shown on the arcs _a_ and _f_. Now here is an excellent opportunity
to impress on our minds the true value of angular motion, inasmuch as
thirty degrees on the arc _f_ is of more than twice the linear extent as
on the arc _a_.

Before we commence to draw the horn of the fork engaging the jewel pin
_D_, shown at full line in Fig. 57, we will come to perfectly understand
what mechanical relations are required. As previously stated, we assume
the jewel pin, as shown at _D_, Fig. 57, is in the act of encountering
the inner face of the horn of the fork for the end or purpose of
unlocking the engaged pallet. Now if the inner face of the horn of the
fork was on a radial line, such radial line would be _p B_, Fig. 57. We
repeat this line at _p_, Fig. 56, where the parts are drawn on a larger
scale.

To delineate a fork at the instant the last effort of impulse has been
imparted to the jewel pin, and said jewel pin is in the act of
separating from the inner face of the prong of the fork--we would also
call attention to the fact that relations of parts are precisely the
same as if the jewel pin had just returned from an excursion of
vibration and was in the act of encountering the inner face of the prong
of the fork in the act of unlocking the escapement.

We mentioned this matter previously, but venture on the repetition to
make everything clear and easily understood. We commence by drawing the
line _A B_ and dividing it in four equal parts, as on previous
occasions, and from _A_ and _B_ as centers draw the pitch circles _c d_.
By methods previously described, we draw the lines _A a_ and _A a'_,
also _B b_ and _B b'_ to represent the angular motion of the two
mobiles, viz., fork and roller action. As already shown, the roller
occupies twelve degrees of angular extent. To get at this conveniently,
we lay off on the arc by which we located the lines _A a_ and _A a'_ six
degrees above the line _A a_ and draw the line _A h_.

Now the angular extent on the arc _c_ between the lines _A a_ and _A h_
represents the radius of the circle defining the jewel pin. From the
intersection of the line _A a_ with the arc _c_ as a center, and with
the radius just named, we sweep the small circle _D_, Fig. 58, which
represents our jewel pin; we afterward cut away two-fifths and draw the
full line _D_, as shown. We show at Fig. 59 a portion of Fig. 58,
enlarged four times, to show certain