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 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.