The fork action we shall consider at present is ten degrees, but subsequently we shall consider a double-roller action in which the fork and pallet action is reduced to eight degrees.  We shall conceive the play between the guard point and the safety roller as one degree, which will leave half a degree of lock remaining in action on the engaged pallet.

THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED.

In the drawing at Fig. 81 we show a diagram of the action of the double-roller escapement.  The small circle at A represents the center of the pallet staff, and the one at B the center of the balance staff.  The radial lines A d and A d’ represent the arc of angular motion of fork action.  The circle b b represents the pitch circle of the jewel pin, and the circle at c c the periphery of the guard or safety roller.  The points established on the circle c c by intersection of the radial lines A d and A d’ we will denominate the points h and h’.  It is at these points the end of the guard point of the fork will terminate.  In construction, or in delineating for construction, we show the guard enough short of the points h h’ to allow the fork an angular motion of one degree, from A as a center, before said point would come in contact with the safety roller.

[Illustration:  Fig. 81]

We draw through the points h h’, from B as a center, the radial lines B g and B g’.  We measure this angle by sweeping the short arc i with any of the radii we have used for arc measurement in former delineations, and find it to be a trifle over sixty degrees.  To give ourselves a practical object lesson, let us imagine that a real guard point rests on the circle c at h.  Suppose we make a notch in the guard roller represented by the circle c, to admit such imaginary guard point, and then commence to revolve the circle c in the direction of the arrow j, letting the guard point rest constantly in such notch.  When the notch n in c has been carried through thirty degrees of arc, counting from B as a center, the guard point, as relates to A as a center, would only have passed through an arc of five degrees.  We show such a guard point and notch at o n.  In fact, if a jewel pin was set to engage the fork on the pitch circle b a, the escapement would lock.  To obviate such lock we widen the notch n to the extent indicated by the dotted lines n’, allowing the guard point to fall back, so to speak, into the notch n, which really represents the passing hollow.  It is not to be understood that the extended notch at n is correctly drawn as regards position, because when the guard point was on the line A f the point o would be in the center of the extended notch, or passing hollow.  We shall next give the details of drawing the double roller, but before doing so we deemed it important to explain the action of such guard points more fully than has been done heretofore.