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.
HOW TO DESIGN A DOUBLE-ROLLER ESCAPEMENT.
We have already given very desirable forms for the parts of a double-roller escapement, consequently we shall now deal chiefly with acting principles as regards the rollers, but will give, at Fig. 82, a very well proportioned and practical form of fork. The pitch circle of the jewel pin is indicated by the dotted circle a, and the jewel pin of the usual cylindrical form, with two-fifths cut away. The safety roller is three-fifths of the diameter of the pitch diameter of the jewel-pin action, as indicated by the dotted circle a.
The safety roller is shown in full outline at B', and the passing hollow at E. It will be seen that the arc of intersection embraced between the radial lines B c and B d is about sixty-one and a half degrees for the roller, but the angular extent of the passing hollow is only a little over thirty-two degrees. The passing hollow E is located and defined by drawing the radial line B c from the center B through the intersection of radial line A i with the dotted arc b, which represents the pitch circle of the safety roller. We will name this intersection the point l. Now the end of the guard point C terminates at the point l, and the passing hollow E extends on b sixteen degrees on each side of the radial line B c.
The roller action is supposed to continue through thirty degrees of angular motion of the balance staff, and is embraced on the circle a between the radial line B k and B o. To delineate the inner face of the horn p of the fork F we draw the short arc g, from A as a center, and on said arc locate at two degrees from the center at B the point f. We will designate the upper angle of the outer face of the jewel pin D as the point s and, from A as a center, sweep through this point s the short arc n n. Parallel with the line A i and at the distance of half the diameter of the jewel pin D, we draw the short lines t t', which define the inner faces of the fork.
The intersection of the short line t with the arc n we will designate the point r. With our dividers set to embrace the space between the point r and the point f, we sweep the arc which defines the inner face of the prong of the fork. The space we just made use of is practically the same as the radius of the circle a, and consequently of the same curvature. Practically, the length of the guard point C' is made as long as will, with certainty, clear the safety roller B in all positions. While we set the point f at two degrees from the center B, still, in a well-constructed escapement, one and a half degrees should be sufficient, but the extra half degree will do no harm. If the roller B' is accurately made and the guard point C' properly fitted, the fork will not have half a degree of play.
The reader will remember that in the escapement model we described we cut down the drop to one degree, being less by half a degree than advised by Grossmann and Saunier. We also advised only one degree of lock. In the perfected lever escapement, which we shall describe and give working drawings for the construction of, we shall describe a detached lever escapement with only eight degrees fork and pallet action, with only three-fourths of a degree drop and three-fourths of a degree lock, which we can assure our readers is easily within the limits of practical construction by modern machinery.