With this s.p.a.ce in the dividers one leg is set at the point _c_, measuring down on the arc _c'_ and establishing the point _t_. The points _p_ and _t_ are then connected, and thus the impulse face of the entrance pallet _B_ is defined. From the point _t_ is drawn the line _t t'_, parallel to the line _b s_, thus defining the inner face of the entrance pallet.

DELINEATING THE EXIT PALLET.

To delineate the exit pallet, sweep the short arc _u u_ (from _g_ as a center) with the dividers set at five inches, and from the intersection of this arc with the line _g j'_ set off eight and one-half degrees and draw the line _g l_. At one degree below this line is drawn the line _g m_.

The s.p.a.ce on the arc _f_ between these lines defines the locking face of the exit pallet. The point where the line _g m_ intersects the arc _f_ is named the point _x_. From the point _x_ is erected the line _x w_, perpendicular to the line _g m_. From _x_ as a center, and with the dividers set at five inches, the short arc _y y_ is swept, and on this arc are laid off twelve degrees, and the line _x z_ is drawn, which line defines the locking face of the exit pallet.

Next is taken ten and one-half degrees from the bra.s.s degree-scale, and from the point _d_ on the arc _n_ the s.p.a.ce named is laid off, and thus is established the point _v_; and from _g_ as a center is swept the arc _v' v'_ through the point _v_. It will be evident on a little thought, that if the tooth _A'_ impelled the exit pallet to the position shown, the outer angle of the pallet must extend down to the point _v_, on the arc _v' v'_; consequently, we define the impulse face of this pallet by drawing a line from point _x_ to _v_. To define the outer face of the exit pallet, we draw the line _v e_ parallel to the line _x z_.

There are no set rules for drawing the general form of the pallet arms, only to be governed by and conforming to about what we would deem appropriate, and to accord with a sense of proportion and mechanical elegance. Ratchet-tooth pallets are usually made in what is termed "close pallets"; that is, the pallet jewel is set in a slot sawed in the steel pallet arm, which is undoubtedly the strongest and most serviceable form of pallet made. We shall next consider the ratchet-tooth lever escapement with circular pallets and ten degrees of pallet action.

DELINEATING CIRCULAR PALLETS.

To delineate "circular pallets" for a ratchet-tooth lever escapement, we proceed very much as in the former drawing, by locating the point _A_, which represents the center of the escape wheel, at some convenient point, and with the dividers set at five inches, sweep the arc _m_, to represent the periphery of the escape wheel, and then draw the vertical line _A B'_, Fig. 19. We (as before) lay off thirty degrees on the arc _m_ each side of the intersection of said arc with the line _A B'_, and thus establish on the arc _m_ the points _a b_, and from _A_ as a center draw through the points so established the radial lines _A a'_ and _A b'_.

We erect from the point _a_ a perpendicular to the line _A a_, and, as previously explained, establish the pallet center at _B_. Inasmuch as we are to employ circular pallets, we lay off to the left on the arc _m_, from the point _a_, five degrees, said five degrees being half of the angular motion of the escape wheel utilized in the present drawing, and thus establish the point _c_, and from _A_ as a center draw through this point the radial line _A c'_. To the right of the point _a_ we lay off five degrees and establish the point _d_. To ill.u.s.trate the underlying principle of our circular pallets: with one leg of the dividers set at _B_ we sweep through the points _c a d_ the arcs _c'' a'' d''_.

From _B_ as a center, we continue the line _B a_ to _f_, and with the dividers set at five inches, sweep the short arc _e e_. From the intersection of this arc with the line _B f_ we lay off one and a half degrees and draw the line _B g_, which establishes the extent of the lock on the entrance pallet. It will be noticed the linear extent of the locking face of the entrance pallet is greater than that of the exit, although both represent an angle of one and a half degrees.

Really, in practice, this discrepancy is of little importance, as the same side-shake in banking would secure safety in either case.

[Ill.u.s.tration: Fig. 19]

The fault we previously pointed out, of the generally accepted method of delineating a detached lever escapement, is not as conspicuous here as it is where the pallets are drawn with equidistant locking faces; that is, the inner angle of the entrance pallet (shown at _s_) does not have to be carried down on the arc _d'_ as far to insure a continuous pallet action of ten degrees, as with the pallets with equidistant locking faces. Still, even here we have carried the angle _s_ down about half a degree on the arc _d'_, to secure a safe lock on the exit pallet.

THE AMOUNT OF LOCK.

If we study the large drawing, where we delineate the escape wheel ten inches in diameter, it will readily be seen that although we claim one and a half degrees lock, we really have only about one degree, inasmuch as the curve of the peripheral line _m_ diverges from the line _B f_, and, as a consequence, the absolute lock of the tooth _C_ on the locking face of the entrance pallet _E_ is but about one degree. Under these conditions, if we did not extend the outer angle of the exit pallet at _t_ down to the peripheral line _m_, we would scarcely secure one-half a degree of lock. This is true of both pallets. We must carry the pallet angles at _r s n t_ down on the circles _c'' d'_ if we would secure the lock and impulse we claim; that is, one and a half degrees lock and eight and a half degrees impulse.

Now, while the writer is willing to admit that a one-degree lock in a sound, well-made escapement is ample, still he is not willing to allow of a looseness of drawing to incorporate to the extent of one degree in any mechanical matter demanding such extreme accuracy as the parts of a watch. It has been claimed that such defects can, to a great extent, be remedied by setting the escapement closer; that is, by bringing the centers of the pallet staff and escape wheel nearer together. We hold that such a course is not mechanical and, further, that there is not the slightest necessity for such a policy.

ADVANTAGE OF MAKING LARGE DRAWINGS.

By making the drawings large, as we have already suggested and insisted upon, we can secure an accuracy closely approximating perfection. As, for instance, if we wish to get a lock of one and a half degrees on the locking face of the entrance pallet _E_, we measure down on the arc _c''_ from its intersection with the peripheral line _m_ one and a half degrees, and establish the point _r_ and thus locate the outer angle of the entrance pallet _E_, so there will really be one and a half degrees of lock; and by measuring down on the arc _d'_ ten degrees from its intersection with the peripheral line _m_, we locate the point _s_, which determines the position of the inner angle of the entrance pallet, and we know for a certainty that when this inner angle is freed from the tooth it will be after the pallet (and, of course, the lever) has pa.s.sed through exactly ten degrees of angular motion.

For locating the inner angle of the exit pallet, we measure on the arc _d'_, from its intersection with the peripheral line _m_, eight and a half degrees, and establish the point _n_, which locates the position of this inner angle; and, of course, one and a half degrees added on the arc _d'_ indicates the extent of the lock on this pallet. Such drawings not only enable us to theorize to extreme exactness, but also give us proportionate measurements, which can be carried into actual construction.

THE CLUB-TOOTH LEVER ESCAPEMENT.

We will now take up the club-tooth form of the lever escapement. This form of tooth has in the United States and in Switzerland almost entirely superceded the ratchet tooth. The princ.i.p.al reason for its finding so much favor is, we think, chiefly owing to the fact that this form of tooth is better able to stand the manipulations of the able-bodied watchmaker, who possesses more strength than skill. We will not pause now, however, to consider the comparative merits of the ratchet and club-tooth forms of the lever escapement, but leave this part of the theme for discussion after we have given full instructions for delineating both forms.

With the ratchet-tooth lever escapement all of the impulse must be derived from the pallets, but in the club-tooth escapement we can divide the impulse planes between the pallets and the teeth to suit our fancy; or perhaps it would be better to say carry out theories, because we have it in our power, in this form of the lever escapement, to indulge ourselves in many changes of the relations of the several parts. With the ratchet tooth the princ.i.p.al changes we could make would be from pallets with equidistant lockings to circular pallets. The club-tooth escape wheel not only allows of circular pallets and equidistant lockings, but we can divide the impulse between the pallets and the teeth in such a way as will carry out many theoretical advantages which, after a full knowledge of the escapement action is acquired, will naturally suggest themselves. In the escapement shown at Fig. 20 we have selected, as a very excellent example of this form of tooth, circular pallets of ten degrees fork action and ten and a half degrees of escape-wheel action.

It will be noticed that the pallets here are comparatively thin to those in general use; this condition is accomplished by deriving the princ.i.p.al part of the impulse from driving planes placed on 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 a.s.suming 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 s.p.a.ce 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 pa.s.ses through the point of intersection of the arc _a_ with the line _A g_.

[Ill.u.s.tration: Fig. 20]

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 s.p.a.ce 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 s.p.a.ce 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 ill.u.s.tration, it is an established practice among escapement makers to employ tangential lockings, as we explained and ill.u.s.trated 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.

[Ill.u.s.tration: Fig. 21]

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 a.n.a.lyze 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 the horological student the facility with which the club-tooth lever escapement can be manipulated. We wish also to impress on his mind the facts that the employment of thick pallet arms and thin pallet arms depends on the teeth of the escape wheel for its efficiency, and that he must have knowledge enough of the principles of action to tell at a glance on what lines the escapement was constructed.

Suppose, for ill.u.s.tration, we get hold of a watch which has thin pallet arms, or stones, if they are exposed pallets, and the escape was designed for pallets with thick arms. There is no sort of tinkering we can do to give such a watch a good motion, except to change either the escape wheel or the pallets. If we know enough of the lever escapement to set about it with skill and judgment, the matter is soon put to rights; but otherwise we can look and squint, open and close the bankings, and tinker about till doomsday, and the watch be none the better.

CLUB-TOOTH LEVER WITH EQUIDISTANT LOCKING FACES.

In drawing a club-tooth lever escapement with equidistant locking, we commence, as on former occasions, by producing the vertical line _A k_, Fig. 22, and establishing the center of the escape wheel at _A_, and with the dividers set at 5" sweep the pitch circle _a_. On each side of the intersection of the vertical line _A k_ with the arc _a_ we set off thirty degrees on said arc, and through the points so established draw the radial lines _A b_ and _A c_.

From the intersection of the radial line _A b_ with the arc _a_ lay off three and a half degrees to the left of said intersection on the arc _a_, and through the point so established draw the radial line _A e_.

From the intersection of the radial line _A b_ with the arc _a_ erect the perpendicular line _f_, and at the crossing or intersection of said line with the vertical line _A k_ establish the center of the pallet staff, as indicated by the small circle _B_. From _B_ as a center sweep the short arc _l_ with a 5" radius; and from the intersection of the radial line _A b_ with the arc _a_ continue the line _f_ until it crosses the short arc _l_, as shown at _f'_. Lay off one and a half degrees on the arc _l_ below its intersection with the line _f'_, and from _B_ as a center draw the line _B_ _i_ through said intersection.

From _B_ as a center, through the intersection of the radial line _A b_ and the arc _a_, sweep the arc _g_.

The s.p.a.ce between the lines _B f'_ and _B i_ on the arc _g_ defines the extent of the locking face of the entrance pallet _C_. The intersection of the line _B f'_ with the arc _g_ we denominate the point _o_, and from this point as a center sweep the short arc _p_ with a 5" radius; and on this arc, from its intersection with the radial line _A b_, lay off twelve degrees, and through the point so established, from _o_ as a center, draw the radial line _o m_, said line defining the locking face of the entrance pallet _C_.