blish the points
_g h_. From _A_ as a center, through the points just established we draw
the radial lines _A g'_ and _A h'_. The angular extent between these
lines defines the limit of our roller action.

Now if we lay off on the arc _f_ six degrees each side of its
intersection with the line _A B_, we define the extent of the jewel pin;
that is, on the arc _f_ we establish the points _l m_ at six degrees
from the line _A B_, and through the points _l m_ draw, from _A_ as a
center, the radial lines _A l'_ and _A m'_. The extent of the space
between the lines _A l'_ and _A m'_ on the circle _a_ defines the size
of our jewel pin.

TO DETERMINE THE SIZE OF A JEWEL PIN.

[Illustration: Fig. 56]

To make the situation better understood, we make an enlarged drawing of
the lines defining the jewel pin at Fig. 56. At the intersection of the
line _A B_ with the arc _a_ we locate the point _k_, and from it as a
center we sweep the circle _i_ so it passes through the intersection of
the lines _A l'_ and _A m'_ with the arc _a_. We divide the radius of
the circle _i_ on the line _A B_ into five equal parts, as shown by the
vertical lines _j_. Of these five spaces we assume three as the extent
of the jewel pin, cutting away that portion to the right of the heavy
vertical line at _k_.

[Illustration: Fig. 57]

We will now proceed to delineate a fork and roller as the parts are
related on first contact of jewel pin with fork and initial with the
commencing of the act of unlocking a pallet. The position and relations
are also the same as at the close of the act of impulse. We commence the
drawing at Fig. 57, as before, by drawing the line _A B_ and the arcs
_a_ and _b_ to represent the pitch circles. We also sweep the arc _f_ to
enable us to delineate the line _A g'_. Next in order we draw our jewel
pin as shown at _D_. In drawing the jewel pin we proceed as at Fig. 56,
except we let the line _A g'_, Fig. 57, assume the same relations to the
jewel pin as _A B_ in Fig. 56; that is, we delineate the jewel pin as if
extending on the arc _a_ six degrees on each side of the line _A g'_,
Fig. 57.

THE THEORY OF THE FORK ACTION.

To aid us in reasoning, we establish the point _m_, as in Fig. 55, at
_m_, Fig. 57, and proceed to delineate another and imaginary jewel pin
at _D'_ (as we show in dotted outline). A brief reasoning will show that
in allowing thirty degrees of contact of the fork with the jewel pin,
the center of the