in every instance. It is inattention to such details which produces the errors of makers complained of by Saunier in section 696 of his "Modern Horology," and which he attempts to correct by drawing the locking face at fifteen degrees draw.

We shall show that neither _C_ nor _C'_, Fig. 85, is the theoretically correct position for the pallet center for a tangential locking.

We will now take up the consideration of a club-tooth lever escapement with circular pallets and tangential lockings; but previous to making the drawings we must decide several points, among which are the thickness of the pallet arms, which establishes the angular motion of the escape wheel utilized by such pallet arms, and also the angular motion imparted to the pallets by the impulse faces of the teeth. We will, for the present, accept the thickness of the arms as being equivalent to five degrees of angular extent of the pitch circle of the escape wheel.

[Ill.u.s.tration: Fig. 87]

[Ill.u.s.tration: Fig. 88]

In making our drawings we commence, as on former occasions, by establishing the center of our escape wheel at _A_, Fig. 87, and sweeping the arc _a a_ to represent the pitch circle of such wheel.

Through the center _A_ we draw the vertical line _A B_, which is supposed to also pa.s.s through the center of the pallet staff. The intersection of the line _A B_ with the arc _a_ we term the point _d_, and from this point we lay off on said arc _a_ thirty degrees each side of said intersection, and thus establish the points _c b_. From _A_, through the point _c_, we draw the line _A c c'_. On the arc _a a_ and two and a half degrees to the left of the point _c_ we establish the point _f_, which s.p.a.ce represents half of the thickness of the entrance pallet. From _A_ we draw through the point _f_ the line _A f f'_. From _f_, and at right angles to said line _A f_, we draw the line _f e_ until it crosses the line _A B_.

Now this line _f e_ is tangent to the arc _a_ from the point _f_, and consequently a locking placed at the point _f_ is a true tangential locking; and if the resting or locking face of a pallet was made to coincide with the line _A f'_, such locking face would be strictly "dead" or neutral. The intersection of the line _f e_ with the line _A B_ we call the point _C_, and locate at this point the center of our pallet staff. According to the method of delineating the lever escapement by Moritz Grossmann the tangent line for locating the center of the pallet staff is drawn from the point _c_, which would locate the center of the pallet staff at the point _h_ on the line _A B_.

Grossmann, in delineating his locking face for the draw, shows such face at an angle of twelve degrees to the radial line _A f'_, when he should have drawn it twelve degrees to an imaginary line shown at _f i_, which is at right angles to the line _f h_. To the writer's mind this is not just as it should be, and may lead to misunderstanding and bad construction. We should always bear in mind the fact that the basis of a locking face is a neutral plane placed at right angles to the line of thrust, and the "draw" comes from a locking face placed at an angle to such neutral plane. A careful study of the diagram at Fig. 88 will give the reader correct ideas. If a tooth locks at the point _c_, the tangential thrust would be on the line _c h'_, and a neutral locking face would be on the line _A c_.

NEUTRAL LOCKINGS.

To aid in explanation, let us remove the pallet center to _D_; then the line of thrust would be _c D_ and a neutral locking face would coincide with the line _m m_, which is at right angles to the line _c D_. If we should now make a locking face with a "draw" and at an angle to the line _c D_, say, for ill.u.s.tration, to correspond to the line _c c'_ (leaving the pallet center at _D_), we would have a strong draw and also a cruel engaging friction.

If, however, we removed the engaging tooth, which we have just conceived to be at _c_, to the point _k_ on the arc _a' a'_, Fig. 88, the pallet center _D_ would then represent a tangential locking, and a neutral pallet face would coincide with the radial line _A k'_; and a locking face with twelve degrees draw would coincide nearly with the line _l_.

Let us next a.n.a.lyze what the effect would be if we changed the pallet center to _h'_, Fig. 88, leaving the engaging tooth still at _k_. In this instance the line _l l_ would then coincide with a neutral locking face, and to obtain the proper draw we should delineate the locking face to correspond to the line _k n_, which we a.s.sume to be twelve degrees from _k l_.

It is not to be understood that we insist on precisely twelve degrees draw from a neutral plane for locking faces for lever pallets. What we do insist upon, however, is a "safe and sure draw" for a lever pallet which will hold a fork to the banks and will also return it to such banks if by accident the fork is moved away. We are well aware that it takes lots of patient, hard study to master the complications of the club-tooth lever escapement, but it is every watchmaker's duty to conquer the problem. The definition of "lock," in the detached lever escapement, is the stoppage or arrest of the escape wheel of a watch while the balance is left free or detached to perform the greater portion of its arc of vibration. "Draw" is a function of the locking parts to preserve the fork in the proper position to receive and act on the jewel pin of the balance.

It should be borne in mind in connection with "lock" and "draw," that the line of thrust as projected from the locked tooth of the escape wheel should be as near tangential as practicable. This maxim applies particularly to the entrance pallet. We would beg to add that practically it will make but little odds whether we plant the center of our pallet staff at _C_ or _h_, Fig. 87, provided we modify the locking and impulse angles of our pallets to conform to such pallet center. But it will not do to arrange the parts for one center and then change to another.

PRACTICAL HINTS FOR LEVER ESCAPEMENTS.

Apparently there seems to be a belief with very many watchmakers that there is a set of shorthand rules for setting an escapement, especially in American watches, which, if once acquired, conquers all imperfections. Now we wish to disabuse the minds of our readers of any such notions. Although the lever escapement, as adopted by our American factories, is constructed on certain "lines," still these lines are subject to modifications, such as may be demanded for certain defects of construction. If we could duplicate every part of a watch movement perfectly, then we could have certain rules to go by, and fixed templets could be used for setting pallet stones and correcting other escapement faults.

Let us now make an a.n.a.lysis of the action of a lever escapement. We show at Fig. 89 an ordinary eighteen-size full-plate lever with fork and pallets. The dotted lines _a b_ are supposed to represent an angular movement of ten degrees. Now, it is the function of the fork to carry the power of the train to the balance. How well the fork performs its office we will consider subsequently; for the present we are dealing with the power as conveyed to the fork by the pallets as shown at Fig.

89.

[Ill.u.s.tration: Fig. 89]

The angular motion between the lines _a c_ (which represents the lock) is not only absolutely lost--wasted--but during this movement the train has to retrograde; that is, the dynamic force stored in the momentum of the balance has to actually turn the train backward and against the force of the mainspring. True, it is only through a very short arc, but the necessary force to effect this has to be discounted from the power stored in the balance from a former impulse. For this reason we should make the angular motion of unlocking as brief as possible. Grossmann, in his essay, endorses one and a half degrees as the proper lock.

In the description which we employed in describing the large model for ill.u.s.trating the action of the detached lever escapement, we cut the lock to one degree, and in the description of the up-to-date lever escapement, which we shall hereafter give, we shall cut the lock down to three-quarters of a degree, a perfection easily to be attained by modern tools and appliances. We shall also cut the drop down to three-quarters of a degree. By these two economies we more than make up for the power lost in unlocking. With highly polished ruby or sapphire pallets ten degrees of draw is ample. But such draw must positively be ten degrees from a neutral locking face, not an escapement drawn on paper and called ten degrees, but when actually measured would only show eight and a half or nine degrees.

THE PERFECTED LEVER ESCAPEMENT.

With ten degrees angular motion of the lever and one and a half degrees lock, we should have eight and a half degrees impulse. The pith of the problem, as regards pallet action, for the practical workman can be embodied in the following question: What proportion of the power derived from the twelve degrees of angular motion of the escape wheel is really conveyed to the fork? The great leak of power as transmitted by the lever escapement to the balance is to be found in the pallet action, and we shall devote special attention to finding and stopping such leaks.

WHEN POWER IS LOST IN THE LEVER ESCAPEMENT.

If we use a ratchet-tooth escape wheel we must allow at least one and a half degrees drop to free the back of the tooth; but with a club-tooth escape wheel made as can be constructed by proper skill and care, the drop can be cut down to three-quarters of a degree, or one-half of the loss with the ratchet tooth. We do not wish our readers to imagine that such a condition exists in most of the so-called fine watches, because if we take the trouble to measure the actual drop with one of the little instruments we have described, it will be found that the drop is seldom less than two, or even three degrees.

If we measure the angular movement of the fork while locked, it will seldom be found less than two or three degrees. Now, we can all understand that the friction of the locking surface has to be counted as well as the recoil of the draw. Locking friction is seldom looked after as carefully as the situation demands. Our factories make the impulse face of the pallets rounded, but leave the locking face flat. We are aware this condition is, in a degree, necessary from the use of exposed pallets. In many of the English lever watches with ratchet teeth, the locking faces are made cylindrical, but with such watches the pallet stones, as far as the writer has seen, are set "close"; that is, with steel pallet arms extending above and below the stone.

There is another feature of the club-tooth lever escapement that next demands our attention which we have never seen discussed. We refer to arranging and disposing of the impulse of the escape wheel to meet the resistance of the hairspring. Let us imagine the dotted line _A d_, Fig.

89, to represent the center of action of the fork. We can readily see that the fork in a state of rest would stand half way between the two banks from the action of the hairspring, and in the pallet action the force of the escape wheel, one tooth of which rests on the impulse face of a pallet, would be exerted against the elastic force of the hairspring. If the force of the mainspring, as represented by the escape-wheel tooth, is superior to the power of the hairspring, the watch starts itself. The phases of this important part of the detached lever escapement will be fully discussed.

ABOUT THE CLUB-TOOTH ESCAPEMENT.

We will now take up a study of the detached lever escapement as relates to pallet action, with the point specially in view of constructing an escapement which cannot "set" in the pocket, or, in other words, an escapement which will start after winding (if run down) without shaking or any force other than that supplied by the train as impelled by the mainspring. In the drawing at Fig. 90 we propose to utilize eleven degrees of escape-wheel action, against ten and a half, as laid down by Grossmann. Of this eleven degrees we propose to divide the impulse arc of the escape wheel in six and five degrees, six to be derived from the impulse face of the club tooth and five from the impulse plane of the pallet.

The pallet action we divide into five and four, with one degree of lock.

Five degrees of pallet action is derived from the impulse face of the tooth and four from the impulse face of the pallet. The reader will please bear in mind that we do not give these proportions as imperative, because we propose to give the fullest evidence into the reader's hands and enable him to judge for himself, as we do not believe in laying down imperious laws that the reader must accept on our a.s.sertion as being correct. Our idea is rather to furnish the proper facts and put him in a situation to know for himself.

The reader is urged to make the drawings for himself on a large scale, say, an escape wheel 10" pitch diameter. Such drawings will enable him to realize small errors which have been tolerated too much in drawings of this kind. The drawings, as they appear in the cut, are one-fourth the size recommended, and many of the lines fail to show points we desire to call attention to. As for instance, the pallet center at _B_ is tangential to the pitch circle _a_ from the point of tooth contact at _f_. To establish this point we draw the radial lines _A c_ and _A d_ from the escape-wheel center _A_, as shown, by laying off thirty degrees on each side of the intersection of the vertical line _i_ (pa.s.sing through the centers _A B_) with the arc _a_, and then laying off two and a half degrees on _a_ and establishing the point _f_, and through _f_ from the center _A_ draw the radial line _A f'_. Through the point _f_ we draw the tangent line _b' b b''_, and at the intersection of the line _b_ with _i_ we establish the center of our pallet staff at _B_. At two and a half degrees from the point _c_ we lay off two and a half degrees to the right of said point and establish the point _n_, and draw the radial line _A n n'_, which establishes the extent of the arc of angular motion of the escape wheel utilized by the pallet arm.

[Ill.u.s.tration: Fig. 90]

We have now come to the point where we must exercise our reasoning powers a little. We know the locking angle of the escape-wheel tooth pa.s.ses on the arc _a_, and if we utilize the impulse face of the tooth for five degrees of pallet or lever motion we must shape it to this end.

We draw the short arc _k_ through the point _n_, knowing that the inner angle of the pallet stone must rest on this arc wherever it is situated.

As, for instance, when the locking face of the pallet is engaged, the inner angle of the pallet stone must rest somewhere on this arc (_k_) inside of _a_, and the extreme outer angle of the impulse face of the tooth must part with the pallet on this arc _k_.

HOW TO LOCATE THE PALLET ACTION.

With the parts related to each other as shown in the cut, to establish where the inner angle of the pallet stone is located in the drawing, we measure down on the arc _k_ five degrees from its intersection with _a_, and establish the point _s_. The line _B b_, Fig. 90, as the reader will see, does not coincide with the intersection of the arcs _a_ and _k_, and to conveniently get at the proper location for the inner angle of our pallet stone, we draw the line _B b'_, which pa.s.ses through the point _n_ located at the intersection of the arc _a_ with the arc _k_.

From _B_ as a center we sweep the short arc _j_ with any convenient radius of which we have a sixty-degree scale, and from the intersection of _B b'_ with _j_ we lay off five degrees and draw the line _B s'_, which establishes the point _s_ on the arc _k_. As stated above, we allow one degree for lock, which we establish on the arc _o_ by laying off one degree on the arc _j_ below its intersection with the line _B b_. We do not show this line in the drawing, from the fact that it comes so near to _B b'_ that it would confuse the reader. Above the arc _a_ on the arc _k_ at five degrees from the point _n_ we establish the point _l_, by laying off five degrees on the arc _j_ above the intersection of the line _B b_ with _j_.

The point _l_, Fig. 90, establishes where the outer angle of the tooth will pa.s.s the arc _k_ to give five degrees of angular motion to the lever. From _A_ as a center we sweep the arc _m_, pa.s.sing through the point _l_. The intersection of the arc _m_ with the line _A h_ we call the point _r_, and by drawing the right line _r f_ we delineate the impulse face of the tooth. On the arc _o_ and one degree below its intersection with the line _B b_ we establish the point _t_, and by drawing a right line from _t_ to _s_ we delineate the impulse face of our entrance pallet.

"ACTION" DRAWINGS.

One great fault with most of our text books on horology lies in the fact that when dealing with the detached lever escapement the drawings show only the position of the pallets when locked, and many of the conditions a.s.sumed are arrived at by mental processes, without making the proper drawings to show the actual relation of the parts at the time such conditions exist. For ill.u.s.tration, it is often urged that there is a time in the action of the club-tooth lever escapement action when the incline on the tooth and the incline on the pallet present parallel surfaces, and consequently endure excessive friction, especially if the oil is a little thickened.

We propose to make drawings to show the exact position and relation of the entrance pallet and tooth at three intervals viz: (1) Locked; (2) the position of the parts when the lever has performed one-half of its angular motion; (3) when half of the impulse face of the tooth has pa.s.sed the pallet. The position of the entrance pallet when locked is sufficiently well shown in Fig. 90 to give a correct idea of the relations with the entrance pallet; and to conform to statement (2), as above. We will now delineate the entrance pallet, not in actual contact, however, with the pallet, because if we did so the lines we employed would become confused. The methods we use are such that _we can delineate with absolute correctness either a pallet or tooth at any point in its angular motion_.

We have previously given instructions for drawing the pallet locked; and to delineate the pallet after five degrees of angular motion, we have only to conceive that we subst.i.tute the line _s'_ for the line _b'_. All angular motions and measurements for pallet actions are from the center of the pallet staff at _B_. As we desire to now delineate the entrance pallet, it has pa.s.sed through five degrees of angular motion and the inner angle _s_ now lies on the pitch circle of the escape wheel, the angular s.p.a.ce between the lines _b' s'_ being five degrees, the line _b''_ reducing the impulse face to four degrees.

DRAWING AN ESCAPEMENT TO SHOW ANGULAR MOTION.

To delineate our locking face we draw a line at right angles to the line _B b''_ from the point _t_, said point being located at the intersection of the arc _o_ with the line _B b''_. To draw a line perpendicular to _B b''_ from the point _t_, we take a convenient s.p.a.ce in our dividers and establish on the line _B b''_ the points _x x'_ at equal distances from the point _t_. We open the dividers a little (no special distance) and sweep the short arcs _x'' x'''_, as shown at Fig. 91. Through the intersection of the short arcs _x'' x'''_ and to the point _t_ we draw the line _t y_. The reader will see from our former explanations that the line _t y_ represents the neutral plane of the locking face, and that to have the proper draw we must delineate the locking face of our pallet at twelve degrees. To do this we draw the line _t x'_ at twelve degrees to the line _t y_, and proceed to outline our pallet faces as shown. We can now understand, after a moment's thought, that we can delineate the impulse face of a tooth at any point or place we choose by laying off six degrees on the arc _m_, and drawing radial lines from _A_ to embrace such arc. To ill.u.s.trate, suppose we draw the radial lines _w' w''_ to embrace six degrees on the arc _a_. We make these lines contiguous to the entrance pallet _C_ for convenience only. To delineate the impulse face of the tooth, we draw a line extending from the intersection of the radial line _A' w'_ with the arc _m_ to the intersection of the arc _a_ with the radial line _A w''_.

[Ill.u.s.tration: Fig. 91]

We next desire to know where contact will take place between the wheel-tooth _D_ and pallet _C_. To determine this we sweep, with our dividers set so one leg rests at the escape-wheel center _A_ and the other at the outer angle _t_ of the entrance pallet, the short arc _t' w_.

Where this arc intersects the line _w_ (which represents the impulse face of the tooth) is where the outer angle _t_ of the entrance pallet _C_ will touch the impulse face of the tooth. To prove this we draw the radial line _A v_ through the point where the short arc _t t'_ pa.s.ses through the impulse face _w_ of the tooth _D_. Then we continue the line _w_ to _n_, to represent the impulse face of the tooth, and then measure the angle _A w n_ between the lines _w n_ and _v A_, and find it to be approximately sixty-four degrees. We then, by a similar process, measure the angle _A t s'_ and find it to be approximately sixty-six degrees.