the teeth. As relates to the escape-wheel action of the ten and one-half degrees, which gives impulse to the escapement, five and one-half degrees are utilized by the driving planes on the teeth and five by the impulse face of the pallet. Of the ten degrees of fork action, four and a half degrees relate to the impulse face of the teeth, one and a half degrees to lock, and four degrees to the driving plane of the pallets.
In delineating such a club-tooth escapement, we commence, as in former examples, by first assuming the center of the escape wheel at A, and with the dividers set at five inches sweeping the arc a a. Through A we draw the vertical line A B'. On the arc a a, and each side of its intersection with the line A B', we lay off thirty degrees, as in former drawings, and through the points so established on the arc a a we draw the radial lines A b and A c. From the intersection of the radial line A b with the arc a we draw the line h h at right angles to A b. Where the line h intersects the radial lines A B' is located the center of the pallet staff, as shown at B. Inasmuch as we decided to let the pallet utilize five degrees of escape-wheel action, we take a space of two and a half degrees in the dividers, and on the arc a a lay off the said two and a half degrees to the left of this intersection, and through the point so established draw the radial line A g. From B as a center we sweep the arc d d so it passes through the point of intersection of the arc a with the line A g.
We again lay off two and a half degrees from the intersection of the line A b with the arc a, but this time to the right of said intersection, and through the point so established, and from B as a center, we sweep the arc e. From the intersection of the radial line A g with the arc a we lay off to the left five and a half degrees on said arc, and through the point so established draw the radial line A f. With the dividers set at five inches we sweep the short arc m from B as a center. From the intersection of the line h B h' with the arc m we lay off on said arc and above the line h' four and a half degrees, and through the point so established draw the line B j.
We next set the dividers so they embrace the space on the radial line A b between its intersection with the line B j and the center A, and from A as a center sweep the arc i, said arc defining the addendum of the escape-wheel teeth. We draw a line from the intersection of the radial line A f with the arc i to the intersection of the radial line A g with the arc a, and thus define the impulse face of the escape-wheel tooth D. For defining the locking face of the tooth we draw a line at an angle of twenty-four degrees to the line A g, as previously described. The back of the tooth is defined with a curve swept from some point on the addendum circle i, such as our judgment will dictate.
In the drawing shown at Fig. 20 the radius of this curve was obtained by taking eleven and a half degrees from the degree arc of 5" radius in the dividers, and setting one leg at the intersection of the radial line A f with the arc i, and placing the other on the line i, and allowing the point so established to serve as a center, the arc was swept for the back of the tooth, the small circle at n denoting one of the centers just described. The length for the face of the tooth was obtained by taking eleven degrees from the degree arc just referred to and laying that space off on the line p, which defined the face of the tooth. The line B k is laid off one and a half degrees below B h on the arc m. The extent of this arc on the arc d defines the locking face of the entrance pallet. We set off four degrees on the arc m below the line B k, and through the point so established draw the line B l. We draw a line from the intersection of the line A g with the line c h to the intersection of the arc e with the line c l, and define the impulse face of the entrance pallet.
RELATIONS OF THE SEVERAL PARTS.
Before we proceed to delineate the exit pallet of our escapement, let us reason on the relations of the several parts.
The club-tooth lever escapement is really the most complicated escapement made. We mean by this that there are more factors involved in the problem of designing it correctly than in any other known escapement. Most—we had better say all, for there are no exceptions which occur to us—writers on the lever escapement lay down certain empirical rules for delineating the several parts, without giving reasons for this or that course. For illustration, it is an established practice among escapement makers to employ tangential lockings, as we explained and illustrated in Fig. 16.
Now, when we adopt circular pallets and carry the locking face of the entrance pallet around to the left two and a half degrees, the true center for the pallet staff, if we employ tangent lockings, would be located on a line drawn tangent to the circle a a from its intersection with the radial line A k, Fig. 21. Such a tangent is depicted at the line s l'. If we reason on the situation, we will see that the line A k is not at right angles to the line s l; and, consequently, the locking face of the entrance pallet E has not really the twelve-degree lock we are taught to believe it has.
We will not discuss these minor points further at present, but leave them for subsequent consideration. We will say, however, that we could locate the center of the pallet action at the small circle B' above the center B, which we have selected as our fork-and-pallet action, and secure a perfectly sound escapement, with several claimed advantages.
Let us now take up the delineation of the exit pallet. It is very easy to locate the outer angle of this pallet, as this must be situated at the intersection of the addendum circle i and the arc g, and located at o. It is also self-evident that the inner or locking angle must be situated at some point on the arc h. To determine this location we draw the line B c from B (the pallet center) through the intersection of the arc h with the pitch circle a.
Again, it follows as a self-evident fact, if the pallet we are dealing with was locked, that is, engaged with the tooth D'', the inner angle n of the exit pallet would be one and a half degrees inside the pitch circle a. With the dividers set at 5", we sweep the short arc b b, and from the intersection of this arc with the line B c we lay off ten degrees, and through the point so established, from B, we draw the line B d. Below the point of intersection of the line B d with the short arc b b we lay off one and a half degrees, and through the point thus established we draw the line B e.
LOCATING THE INNER ANGLE OF THE EXIT PALLET.
The intersection of the line B e with the arc h, which we will term the point n, represents the location of the inner angle of the exit pallet. We have already explained how we located the position of the outer angle at o. We draw the line n o and define the impulse face of the exit pallet. If we mentally analyze the problem in hand, we will see that as the exit pallet vibrates through its ten degrees of arc the line B d and B c change places, and the tooth D'' locks one and a half degrees. To delineate the locking face of the exit pallet, we erect a perpendicular to the line B e from the point n, as shown by the line n p.
From n as a center we sweep the short arc t t, and from its intersection with the line n p we lay off twelve degrees, and through the point so established we draw the line n u, which defines the locking face of the exit pallet. We draw the line o o' parallel with n u and define the outer face of said pallet. In Fig. 21 we have not made any attempt to show the full outline of the pallets, as they are delineated in precisely the same manner as those previously shown.
We shall next describe the delineation of a club-tooth escapement with pallets having equidistant locking faces; and in Fig. 22 we shall show pallets with much wider arms, because, in this instance, we shall derive more of the impulse from the pallets than from the teeth. We do this to show