HOW TO FIND THE ROLLER DIAMETER FROM THE LENGTH OF THE FORK.

To illustrate, let us imagine the small circles A B, Fig. 54, to represent the center of a pallet staff and balance staff in the order named. We divide this space into four equal parts, as shown, and the third space will represent the point at which the pitch circles of the fork and roller will intersect, as shown by the arc a and circle b. Now if the length of the radii of these circles stand to each other as three to one, and the fork vibrates through an arc of ten degrees, the jewel pin engaging such fork must remain in contact with said fork for thirty degrees of angular motion of the balance.



Or, in other words, the ratio of angular motion of two mobiles acting on each must be in the same ratio as the length of their radii at the point of contact. If we desire to give the jewel pin, or, in ordinary horological phraseology, have a greater arc of roller action, we would extend the length of fork (say) to the point c, which would be one-fifth of the space between A and B, and the ratio of fork to roller action would be four to one, and ten degrees of fork action would give forty degrees of angular motion to the roller—and such escapements have been constructed.

WHY THIRTY DEGREES OF ROLLER ACTION IS ABOUT RIGHT.

Now we have two sound reasons why we should not extend the arc of vibration of the balance: (a) If there is an advantage to be derived from a detached escapement, it would surely be policy to have the arc of contact, that is, for the jewel pin to engage the fork, as short an arc as is compatible with a sound action. (b) It will be evident to any thinking mechanic that the acting force of a fork which would carry the jewel pin against the force exerted by the balance spring through an arc of fifteen degrees, or half of an arc of thirty degrees, would fail to do so through an arc of twenty degrees, which is the condition imposed when we adopt forty degrees of roller action.

For the present we will accept thirty degrees of roller action as the standard. Before we proceed to delineate our fork and roller we will devote a brief consideration to the size and shape of a jewel pin to perform well. In this matter there has been a broad field gone over, both theoretically and in practical construction. Wide jewel pins, round jewel pins, oval jewel pins have been employed, but practical construction has now pretty well settled on a round jewel pin with about two-fifths cut away. And as regards size, if we adopt the linear extent of four degrees of fork or twelve degrees of roller action, we will find it about right.

HOW TO SET A FORK AND ROLLER ACTION RIGHT.

As previously stated, frequently the true place to begin to set a lever escapement right is with the roller and fork. But to do this properly we should know when such fork and roller action is right and safe in all respects. We will see on analysis of the actions involved that there are three important actions in the fork and roller functions: (a) The fork imparting perfect impulse through the jewel pin to the balance. (b) Proper unlocking action. (c) Safety action. The last function is in most instances sadly neglected and, we regret to add, by a large majority of even practical workmen it is very imperfectly understood. In most American watches we have ample opportunity afforded to inspect the pallet action, but the fork and roller action is placed so that rigid inspection is next to impossible.

The Vacheron concern of Swiss manufacturers were acute enough to see the importance of such inspection, and proceeded to cut a circular opening in the lower plate, which permitted, on the removal of the dial, a careful scrutiny of the action of the roller and fork. While writing on this topic we would suggest the importance not only of knowing how to draw a correct fork and roller action, but letting the workman who desires to be au fait in escapements delineate and study the action of a faulty fork and roller action—say one in which the fork, although of the proper form, is too short, or what at first glance would appear to amount to the same thing, a roller too small.

Drawings help wonderfully in reasoning out not only correct actions, but also faulty ones, and our readers are earnestly advised to make such faulty drawings in several stages of action. By this course they will educate the eye to discriminate not only as to correct actions, but also to detect those which are imperfect, and we believe most watchmakers will admit that in many instances it takes much longer to locate a fault than to remedy it after it has been found.



Let us now proceed to delineate a fork and roller. It is not imperative that we should draw the parts to any scale, but it is a rule among English makers to let the distance between the center of the pallet staff and the center of the balance staff equal in length the chord of ninety-six degrees of the pitch circle of the escape wheel, which, in case we employ a pitch circle of 5" radius, would make the distance between A and B, Fig. 55, approximately 71/2", which is a very fair scale for study drawings.

HOW TO DELINEATE A FORK AND ROLLER.

To arrive at the proper proportions of the several parts, we divide the space A B into four equal parts, as previously directed, and draw the circle a and short arc b. With our dividers set at 5", from B as a center we sweep the short arc c. From our arc of sixty degrees, with a 5" radius, we take five degrees, and from the intersection of the right line A B with the arc c we lay off on each side five degrees and establish the points d e; and from B as a center, through these points draw the lines B d' and B e'. Now the arc embraced between these lines represents the angular extent of our fork action.

From A as a center and with our dividers set at 5", we sweep the arc f. From the scale of degrees we just used we lay off fifteen degrees on each side of the line A B on the arc f, and establish the points g h. From A as a center, through the points just established we draw the radial lines A g' and A h'. The angular extent between these lines defines the limit of our roller action.

Now if we lay off on the arc f six degrees each side of its intersection with the line A B, we define the extent of the jewel pin; that is, on the arc f we establish the points l m at six degrees from the line A B, and through the points l m draw, from A as a center, the radial lines A l' and A m'. The extent of the space between the lines A l' and A m' on the circle a defines the size of our jewel pin.

TO DETERMINE THE SIZE OF A JEWEL PIN.



To make the situation better understood, we make an enlarged drawing of the lines defining the jewel pin at Fig. 56. At the intersection of the line A B with the arc a we locate the point k, and from it as a center we sweep the circle i so it passes through the intersection of the lines A l' and A m' with the arc a. We divide the radius of the circle i on the line A B into five equal parts, as shown by the vertical lines j. Of these five spaces we assume three as the extent of the jewel pin, cutting away that portion to the right of the heavy vertical line at k.



We will now proceed to delineate a fork and roller as the parts are related on first contact of jewel pin with fork and initial with the commencing of the act of unlocking a pallet. The position and relations are also the same as at the close of the act of impulse. We commence the drawing at Fig. 57, as before, by drawing the line A B and the arcs a and b to represent the pitch circles. We also sweep the arc f to enable us to delineate the line A g'. Next in order we draw our jewel pin as shown at D. In drawing the jewel pin we proceed as at Fig. 56, except we let the line A g', Fig. 57, assume the same relations to the jewel pin as A B in Fig. 56; that is, we delineate the jewel pin as if extending on the arc a six degrees on each side of the line A g', Fig. 57.

THE THEORY OF THE FORK ACTION.

To aid us in reasoning, we establish the point m, as in Fig. 55, at m, Fig. 57, and proceed to delineate another and imaginary jewel pin at D' (as we show in dotted outline). A brief reasoning will show that in allowing thirty degrees of contact of the fork with the jewel pin, the center of the jewel pin will pass through an arc of thirty degrees, as shown on the arcs a and f. Now here is an excellent opportunity to impress on our minds the true value of angular motion, inasmuch as thirty degrees on the arc f is of more than twice the linear extent as on the arc a.

Before we commence to draw the horn of the fork engaging the jewel pin D, shown at full line in Fig. 57, we will come to perfectly understand what mechanical relations are required. As previously stated, we assume the jewel pin, as shown at D, Fig. 57, is in the act of encountering the inner face of the horn of the fork for the end or purpose of unlocking the engaged pallet. Now if the inner face of the horn of the fork was on a radial line, such radial line would be p B, Fig. 57. We repeat this line at p, Fig. 56, where the parts are drawn on a larger scale.

To delineate a fork at the instant the last effort of impulse has been imparted to the jewel pin, and said jewel pin is in the act of separating from the inner face of the prong of the fork—we would also call attention to the fact that relations of parts are precisely the same as if the jewel pin had just returned from an excursion of vibration and was in the act of encountering the inner face of the prong of the fork in the act of unlocking the escapement.

We mentioned this matter previously, but venture on the repetition to make everything clear and easily understood. We commence by drawing the line A B and dividing it in four equal parts, as on previous occasions, and from A and B as centers draw the pitch circles c d. By methods previously described, we draw the lines A a and A a', also B b and B b' to represent the angular motion of the two mobiles, viz., fork and roller action. As already shown, the roller occupies twelve degrees of angular extent. To get at this conveniently, we lay off on the arc by which we located the lines A a and A a' six degrees above the line A a and draw the line A h.

Now the angular extent on the arc c between the lines A a and A h represents the radius of the circle defining the jewel pin. From the intersection of the line A a with the arc c as a center, and with the radius just named, we sweep the small circle D, Fig. 58, which represents our jewel pin; we afterward cut away two-fifths and draw the full line D, as shown. We show at Fig. 59 a portion of Fig. 58, enlarged four times, to show certain portions of our delineations more distinctly. If we give the subject a moment's consideration we will see that the length of the prong E of the lever fork is limited to such a length as will allow the jewel pin D to pass it.

HOW TO DELINEATE THE PRONGS OF A LEVER FORK.



To delineate this length, from B as a center we sweep the short arc f so it passes through the outer angle n, Fig. 59, of the jewel pin. This arc, carried across the jewel pin D, limits the length of the opposite prong of the fork. The outer face of the prong of the fork can be drawn as a line tangent to a circle drawn from A as a center through the angle n of the jewel pin. Such a circle or arc is shown at o, Figs. 58 and 59. There has been a good deal said as to whether the outer edge of the prong of a fork should be straight or curved.

To the writer's mind, a straight-faced prong, like from s to m, is what is required for a fork with a single roller, while a fork with a curved prong will be best adapted for a double roller. This subject will be taken up again when we consider double-roller action. The extent or length of the outer face of the prong is also an open subject, but as there is but one factor of the problem of lever escapement construction depending on it, when we name this and see this requirement satisfied we have made an end of this question. The function performed by the outer face of the prong of a fork is to prevent the engaged pallet from unlocking while the guard pin is opposite to the passing hollow.

The inner angle s of the horn of the fork must be so shaped and located that the jewel pin will just clear it as it passes out of the fork, or when it passes into the fork in the act of unlocking the escapement. In escapements with solid bankings a trifle is allowed, that is, the fork is made enough shorter than the absolute theoretical length to allow for safety in this respect.

THE PROPER LENGTH OF A LEVER.

We will now see how long a lever must be to perform its functions perfectly. Now let us determine at what point on the inner face of the prong E' the jewel pin parts from the fork, or engages on its return. To do this we draw a line from the center r (Fig. 59) of the jewel pin, so as to meet the line e at right angles, and the point t so established on the line e is where contact will take place between the jewel pin and fork.

It will be seen this point (t) of contact is some distance back of the angle u which terminates the inner face of the prong E'; consequently, it will be seen the prongs E E' of the fork can with safety be shortened enough to afford a safe ingress or egress to the jewel pin to the slot in the fork. As regards the length of the outer face of the prong of the fork, a good rule is to make it one and a half times the diameter of the jewel pin. The depth of the slot need be no more than to free the jewel in its passage across the ten degrees of fork action. A convenient rule as to the depth of the slot in a fork is to draw the line k, which, it will be seen, coincides with the circle which defines the jewel pin.

HOW TO DELINEATE THE SAFETY ACTION.



We will next consider a safety action of the single roller type. The active or necessary parts of such safety action consist of a roller or disk of metal, usually steel, shaped as shown in plan at A, Fig. 60. In the edge of this disk is cut in front of the jewel pin a circular recess shown at a called the passing hollow. The remaining part of the safety action is the guard pin shown at N Figs. 61 and 62, which is placed in the lever. Now it is to be understood that the sole function performed by the guard pin is to strike the edge of the roller A at any time when the fork starts to unlock the engaged pallet, except when the jewel pin is in the slot of the fork. To avoid extreme care in fitting up the passing hollow, the horns of the fork are arranged to strike the jewel pin and prevent unlocking in case the passing hollow is made too wide. To delineate the safety action we first draw the fork and jewel pin as previously directed and as shown at Fig. 63. The position of the guard pin should be as close to the bottom of the slot of the fork as possible and be safe. As to the size of the guard pin, it is usual to make it about one-third or half the diameter of the jewel pin. The size and position of the guard pin decided on and the small circle N drawn, to define the size and position of the roller we set our dividers so that a circle drawn from the center A will just touch the edge of the small circle N, and thus define the outer boundary of our roller, or roller table, as it is frequently called.



For deciding the angular extent of the passing hollow we have no fixed rule, but if we make it to occupy about half more angular extent on the circle y than will coincide with the angular extent of the jewel pin, it will be perfectly safe and effectual. We previously stated that the jewel pin should occupy about twelve degrees of angular extent on the circle c, and if we make the passing hollow occupy eighteen degrees (which is one and a half the angular extent of the jewel pin) it will do nicely. But if we should extend the width of the passing hollow to twenty-four degrees it would do no harm, as the jewel pin would be well inside the horn of the fork before the guard pin could enter the passing hollow.



We show in Fig. 61 the fork as separated from the roller, but in Fig. 62, which is a side view, we show the fork and jewel pin as engaged. When drawing a fork and roller action it is safe to show the guard pin as if in actual contact with the roller. Then in actual construction, if the parts are made to measure and agree with the drawing in the gray, that is, before polishing, the process of polishing will reduce the convex edge of the roller enough to free it.

It is evident if thought is given to the matter, that if the guard pin is entirely free and does not touch the roller in any position, a condition and relation of parts exist which is all we can desire. We are aware that it is usual to give a considerable latitude in this respect even by makers, and allow a good bit of side shake to the lever, but our judgment would condemn the practice, especially in high-grade watches.

RESTRICT THE FRICTIONAL SURFACES.

Grossmann, in his essay on the detached lever escapement, adopts one and a half degrees lock. Now, we think that one degree is ample; and we are sure that every workman experienced in the construction of the finer watches will agree with us in the assertion that we should in all instances seek to reduce the extent of all frictional surfaces, no matter how well jeweled. Acting under such advice, if we can reduce the surface friction on the lock from one and a half degrees to one degree or, better, to three-fourths of a degree, it is surely wise policy to do so. And as regards the extent of angular motion of the lever, if we reduce this to six degrees, exclusive of the lock, we would undoubtedly obtain better results in timing.

We shall next consider the effects of opening the bankings too wide, and follow with various conditions which are sure to come in the experience of the practical watch repairer. It is to be supposed in this problem that the fork and roller action is all right. The reader may say to this, why not close the banking? In reply we would offer the supposition that some workman had bent the guard pin forward or set a pallet stone too far out.

We have now instructed our readers how to draw and construct a lever escapement complete, of the correct proportions, and will next take up defective construction and consider faults existing to a lesser or greater degree in almost every watch. Faults may also be those arising from repairs by some workman not fully posted in the correct form and relation of the several parts which go to make up a lever escapement. It makes no difference to the artisan called upon to put a watch in perfect order as to whom he is to attribute the imperfection, maker or former repairer; all the workman having the job in hand has to do is to know positively that such a fault actually exists, and that it devolves upon him to correct it properly.

BE FEARLESS IN REPAIRS, IF SURE YOU ARE RIGHT.

Hence the importance of the workman being perfectly posted on such matters and, knowing that he is right, can go ahead and make the watch as it should be. The writer had an experience of this kind years ago in Chicago. A Jules Jurgensen watch had been in the hands of several good workmen in that city, but it would stop. It was then brought to him with a statement of facts given above. He knew there must be a fault somewhere and searched for it, and found it in the exit pallet—a certain tooth of the escape wheel under the right conditions would sometimes not escape. It might go through a great many thousand times and yet it might, and did sometimes, hold enough to stop the watch.

Now probably most of my fellow-workmen in this instance would have been afraid to alter a "Jurgensen," or even hint to the owner that such a thing could exist as a fault in construction in a watch of this justly-celebrated maker. The writer removed the stone, ground a little from the base of the offending pallet stone, replaced it, and all trouble ended—no stops from that on.

STUDY OF AN ESCAPEMENT ERROR.



Now let us suppose a case, and imagine a full-plate American movement in which the ingress or entrance pallet extends out too far, and in order to have it escape, the banking on that side is opened too wide. We show at Fig. 64 a drawing of the parts in their proper relations under the conditions named. It will be seen by careful inspection that the jewel pin D will not enter the fork, which is absolutely necessary. This condition very frequently exists in watches where a new pallet stone has been put in by an inexperienced workman. Now this is one of the instances in which workmen complain of hearing a "scraping" sound when the watch is placed to the ear. The remedy, of course, lies in warming up the pallet arms and pushing the stone in a trifle, "But how much?" say some of our readers. There is no definite rule, but we will tell such querists how they can test the matter.

Remove the hairspring, and after putting the train in place and securing the plates together, give the winding arbor a turn or two to put power on the train; close the bankings well in so the watch cannot escape on either pallet. Put the balance in place and screw down the cock. Carefully turn back the banking on one side so the jewel pin will just pass out of the slot in the fork. Repeat this process with the opposite banking; the jewel pin will now pass out on each side. Be sure the guard pin does not interfere with the fork action in any way. The fork is now in position to conform to the conditions required.

HOW TO ADJUST THE PALLETS TO MATCH THE FORK.

If the escapement is all right, the teeth will have one and a half degrees lock and escape correctly; but in the instance we are considering, the stone will not permit the teeth to pass, and must be pushed in until they will. It is not a very difficult matter after we have placed the parts together so we can see exactly how much the pallet protrudes beyond what is necessary, to judge how far to push it back when we have it out and heated. There is still an "if" in the problem we are considering, which lies in the fact that the fork we are experimenting with may be too short for the jewel pin to engage it for ten degrees of angular motion.

This condition a man of large experience will be able to judge of very closely, but the better plan for the workman is to make for himself a test gage for the angular movement of the fork. Of course it will be understood that with a fork which engages the roller for eight degrees of fork action, such fork will not give good results with pallets ground for ten degrees of pallet action; still, in many instances, a compromise can be effected which will give results that will satisfy the owner of a watch of moderate cost, and from a financial point of view it stands the repairer in hand to do no more work than is absolutely necessary to keep him well pleased.

We have just made mention of a device for testing the angular motion of the lever. Before we take up this matter, however, we will devote a little time and attention to the subject of jewel pins and how to set them. We have heretofore only considered jewel pins of one form, that is, a round jewel pin with two-fifths cut away. We assumed this form from the fact that experience has demonstrated that it is the most practicable and efficient form so far devised or applied. Subsequently we shall take up the subject of jewel pins of different shapes.

HOW TO SET A JEWEL PIN AS IT SHOULD BE.

Many workmen have a mortal terror of setting a jewel pin and seem to fancy that they must have a specially-devised instrument for accomplishing this end. Most American watches have the hole for the jewel pin "a world too wide" for it, and we have heard repeated complaints from this cause. Probably the original object of this accommodating sort of hole was to favor or obviate faults of pallet action. Let us suppose, for illustration, that we have a roller with the usual style of hole for a jewel pin which will take almost anything from the size of a No. 12 sewing needle up to a round French clock pallet.



We are restricted as regards the proper size of jewel pin by the width of the slot in the fork. Selecting a jewel which just fits the fork, we can set it as regards its relation to the staff so it will cause the pitch circle of the jewel pin to coincide with either of dotted circles a or a', Fig. 65. This will perhaps be better understood by referring to Fig. 66, which is a view of Fig. 65 seen in the direction of the arrow c. Here we see the roller jewel at D, and if we bring it forward as far as the hole in the roller will permit, it will occupy the position indicated at the dotted lines; and if we set it in (toward the staff) as far as the hole will allow, it will occupy the position indicated by the full outline.



Now such other condition might very easily exist, that bringing the jewel pin forward to the position indicated by the dotted lines at D, Fig. 66, would remedy the defect described and illustrated at Fig. 64 without any other change being necessary. We do not assert, understand, that a hole too large for the jewel pin is either necessary or desirable—what we wish to convey to the reader is the necessary knowledge so that he can profit by such a state if necessary. A hole which just fits the jewel pin so the merest film of cement will hold it in place is the way it should be; but we think it will be some time before such rollers are made, inasmuch as economy appears to be a chief consideration.

ABOUT JEWEL-PIN SETTERS.

To make a jewel-pin setter which will set a jewel pin straight is easy enough, but to devise any such instrument which will set a jewel so as to perfectly accord with the fork action is probably not practicable. What the workman needs is to know from examination when the jewel pin is in the proper position to perform its functions correctly, and he can only arrive at this knowledge by careful study and thought on the matter. If we make up our minds on examining a watch that a jewel pin is "set too wide," that is, so it carries the fork over too far and increases the lock to an undue degree, take out the balance, remove the hairspring, warm the roller with a small alcohol lamp, and then with the tweezers move the jewel pin in toward the staff.



No attempt should be made to move a jewel pin unless the cement which holds the jewel is soft, so that when the parts cool off the jewel is as rigid as ever. A very little practice will enable any workman who has the necessary delicacy of touch requisite to ever become a good watchmaker, to manipulate a jewel pin to his entire satisfaction with no other setter than a pair of tweezers and his eye, with a proper knowledge of what he wants to accomplish. To properly heat a roller for truing up the jewel pin, leave it on the staff, and after removing the hairspring hold the balance by the rim in a pair of tweezers, "flashing it" back and forth through the flame of a rather small alcohol lamp until the rim of the balance is so hot it can just be held between the thumb and finger, and while at this temperature the jewel pin can be pressed forward or backward, as illustrated in Fig. 66, and then a touch or two will set the pin straight or parallel with the staff. Figs. 68 and 69 are self-explanatory. For cementing in a jewel pin a very convenient tool is shown at Figs. 67 and 70. It is made of a piece of copper wire about 1/16" in diameter, bent to the form shown at Fig. 67. The ends b b of the copper wire are flattened a little and recessed on their inner faces, as shown in Fig. 70, to grasp the edges of the roller A. The heat of an alcohol lamp is applied to the loop of the wire at g until the small bit of shellac placed in the hole h melts. The necessary small pieces of shellac are made by warming a bit of the gum to near the melting point and then drawing the softened gum into a filament the size of horse hair. A bit of this broken off and placed in the hole h supplies the cement necessary to fasten the jewel pin. Figs. 68 and 69 will, no doubt, assist in a clear understanding of the matter.

HOW TO MAKE AN ANGLE-MEASURING DEVICE.

We will now resume the consideration of the device for measuring the extent of the angular motion of the fork and pallets. Now, before we take this matter up in detail we wish to say, or rather repeat what we have said before, which is to the effect that ten degrees of fork and lever action is not imperative, as we can get just as sound an action and precisely as good results with nine and a half or even nine degrees as with ten, if other acting parts are in unison with such an arc of angular motion. The chief use of such an angle-measuring device is to aid in comparing the relative action of the several parts with a known standard.



For use with full-plate movements about the best plan is a spring clip or clasp to embrace the pallet staff below the pallets. We show at Fig. 71 such a device. To make it, take a rather large size of sewing needle—the kind known as a milliner's needle is about the best. The diameter of the needle should be about No. 2, so that at b we can drill and put in a small screw. It is important that the whole affair should be very light. The length of the needle should be about 1-5/8", in order that from the notch a to the end of the needle A' should be 11/2". The needle should be annealed and flattened a little, to give a pretty good grasp to the notch a on the pallet staff.

Good judgment is important in making this clamp, as it is nearly impossible to give exact measurements. About 1/40" in width when seen in the direction of the arrow j will be found to be about the right width. The spring B can be made of a bit of mainspring, annealed and filed down to agree in width with the part A. In connection with the device shown at Fig. 71 we need a movement-holder to hold the movement as nearly a constant height as possible above the bench. The idea is, when the clamp A B is slipped on the pallet staff the index hand A' will extend outward, as shown in Fig. 72, where the circle C is supposed to represent the top plate of a watch, and A' the index hand.

HOW THE ANGULAR MOTION IS MEASURED.



Fig. 72 is supposed to be seen from above. It is evident that if we remove the balance from the movement shown at C, leaving power on the train, and with an oiling tool or hair broach move the lever back and forth, the index hand A' will show in a magnified manner the angular motion of the lever. Now if we provide an index arc, as shown at D, we can measure the extent of such motion from bank to bank.



To get up such an index arc we first make a stand as shown at E F, Fig. 73. The arc D is made to 11/2" radius, to agree with the index hand A', and is divided into twelve degree spaces, six each side of a zero, as shown at Fig. 74, which is an enlarged view of the index D in Fig. 72. The index arc is attached to a short bit of wire extending down into the support E, and made adjustable as to height by the set-screw l. Let us suppose the index arc is adjusted to the index hand A', and we move the fork as suggested; you see the hand would show exactly the arc passed through from bank to bank, and by moving the stand E F we can arrange so the zero mark on the scale stands in the center of such arc. This, of course, gives the angular motion from bank to bank. As an experiment, let us close the bankings so they arrest the fork at the instant the tooth drops from each pallet. If this arc is ten degrees, the pallet action is as it should be with the majority of modern watches.

TESTING LOCK AND DROP WITH OUR NEW DEVICE.

Let us try another experiment: We carefully move the fork away from the bank, and if after the index hand has passed through one and a half degrees the fork flies over, we know the lock is right. We repeat the experiment from the opposite bank, and in the same manner determine if the lock is right on the other pallets. You see we have now the means of measuring not only the angular motion of the lever, but the angular extent of the lock. At first glance one would say that if now we bring the roller and fork action to coincide and act in unison with the pallet action, we would be all right; and so we would, but frequently this bringing of the roller and fork to agree is not so easily accomplished.

It is chiefly toward this end the Waltham fork is made adjustable, so it can be moved to or from the roller, and also that we can allow the pallet arms to be moved, as we will try and explain. As we set the bankings the pallets are all right; but to test matters, let us remove the hairspring and put the balance in place. Now, if the jewel pin passes in and out of the fork, it is to be supposed the fork and roller action is all right. To test the fork and roller action we close the banking a little on one side. If the fork and jewel pin are related to each other as they should be, the jewel pin will not pass out of the fork, nor will the engaged tooth drop from that pallet. This condition should obtain on both pallets, that is, if the jewel pin will not pass out of the fork on a given bank the tooth engaged on its pallet should not drop.

We have now come to the most intricate and important problems which relate to the lever escapement. However, we promise our readers that if they will take the pains to follow closely our elucidations, to make these puzzles plain. But we warn them that they are no easy problems to solve, but require good, hard thinking. The readiest way to master this matter is by means of such a model escapement as we have described. With such a model, and the pallets made to clamp with small set-screws, and roller constructed so the jewel pin could be set to or from the staff, this matter can be reduced to object lessons. But study of the due relation of the parts in good drawings will also master the situation.

A FEW EXPERIMENTS WITH OUR ANGLE-MEASURING DEVICE.

In using the little instrument for determining angular motion that we have just described, care must be taken that the spring clamp which embraces the pallet staff does not slip. In order to thoroughly understand the methods of using this angle-measuring device, let us take a further lesson or two.

We considered measuring the amount of lock on each pallet, and advised the removal of the balance, because if we left the balance in we could not readily tell exactly when the tooth passed on to the impulse plane; but if we touch the fork lightly with an oiling tool or a hair broach, moving it (the fork) carefully away from the bank and watching the arc indicated by the hand A, Fig. 72, we can determine with great exactness the angular extent of lock. The diagram at Fig. 75 illustrates how this experiment is conducted. We apply the hair broach to the end of the fork M, as shown at L, and gently move the fork in the direction of the arrow i, watching the hand A and note the number of degrees, or parts of degrees, indicated by the hand as passed over before the tooth is unlocked and passes on to the impulse plane and the fork flies forward to the opposite bank. Now, the quick movement of the pallet and fork may make the hand mark more or less of an arc on the index than one of ten degrees, as the grasp may slip on the pallet staff; but the arc indicated by the slow movement in unlocking will be correct.



By taking a piece of sharpened pegwood and placing the point in the slot of the fork, we can test the fork to see if the drop takes place much before the lever rests against the opposite bank. As we have previously stated, the drop from the pallet should not take place until the lever almost rests on the banking pin. What the reader should impress on his mind is that the lever should pass through about one and a half degrees arc to unlock, and the remainder (eight and a half degrees) of the ten degrees are to be devoted to impulse. But, understand, if the impulse angle is only seven and a half degrees, and the jewel pin acts in accordance with the rules previously given, do not alter the pallet until you know for certain you will gain by it. An observant workman will, after a little practice, be able to determine this matter.

We will next take up the double roller and fork action, and also consider in many ways the effect of less angles of action than ten degrees. This matter now seems of more importance, from the fact that we are desirous to impress on our readers that there is no valid reason for adopting ten degrees of fork and roller action with the table roller, except that about this number of degrees of action are required to secure a reliable safety action. With the double roller, as low as six degrees fork and pallet action can be safely employed. In fork and pallet actions below six degrees of angular motion, side-shake in pivot holes becomes a dangerous factor, as will be explained further on. It is perfectly comprehending the action of the lever escapement and then being able to remedy defects, that constitute the master workman.

HOW TO MEASURE THE ANGULAR MOTION OF AN ESCAPE WHEEL.



We can also make use of our angle-testing device for measuring our escape-wheel action, by letting the clasp embrace the arbor of the escape wheel, instead of the pallet staff. We set the index arc as in our former experiments, except we place the movable index D, Fig. 76, so that when the engaged tooth rests on the locking face of a pallet, the index hand stands at the extreme end of our arc of twelve degrees. We next, with our pointed pegwood, start to move the fork away from the bank, as before, we look sharp and see the index hand move backward a little, indicating the "draw" on the locking face. As soon as the pallet reaches the impulse face, the hand A moves rapidly forward, and if the escapement is of the club-tooth order and closely matched, the hand A will pass over ten and a half degrees of angular motion before the drop takes place.



We will warn our readers in advance, that if they make such a testing device they will be astonished at the inaccuracy which they will find in the escapements of so-called fine watches. The lock, in many instances, instead of being one and a half degrees, will oftener be found to be from two to four degrees, and the impulse derived from the escape wheel, as illustrated at Fig. 76, will often fall below eight degrees. Such watches will have a poor motion and tick loud enough to keep a policeman awake. Trials with actual watches, with such a device as we have just described, in conjunction with a careful study of the acting parts, especially if aided by a large model, such as we have described, will soon bring the student to a degree of skill unknown to the old-style workman, who, if a poor escapement bothered him, would bend back the banking pins or widen the slot in the fork.

We hold that educating our repair workmen up to a high knowledge of what is required to constitute a high-grade escapement, will have a beneficial effect on manufacturers. When we wish to apply our device to the measurement of the escapement of three-quarter-plate watches, we will require another index hand, with the grasping end bent downward, as shown at Fig. 77. The idea with this form of index hand is, the bent-down jaws B', Fig. 77, grasp the fork as close to the pallet staff as possible, making an allowance for the acting center by so placing the index arc that the hand A will read correctly on the index D. Suppose, for instance, we place the jaws B' inside the pallet staff, we then place the index arc so the hand reads to the arc indicated by the dotted arc m, Fig. 78, and if set outside of the pallet staff, read by the arc o.



HOW A BALANCE CONTROLS THE TIMEKEEPING OF A WATCH.

We think a majority of the fine lever escapements made abroad in this day have what is termed double-roller safety action. The chief gains to be derived from this form of safety action are: (1) Reducing the arc of fork and roller action; (2) reducing the friction of the guard point to a minimum. While it is entirely practicable to use a table roller for holding the jewel pin with a double-roller action, still a departure from that form is desirable, both for looks and because as much of the aggregate weight of a balance should be kept as far from the axis of rotation as possible.

We might as well consider here as elsewhere, the relation the balance bears to the train as a controlling power. Strictly speaking, the balance and hairspring are the time measurers, the train serving only two purposes: (a) To keep the balance in motion; (b) to classify and record the number of vibrations of the balance. Hence, it is of paramount importance that the vibrations of the balance should be as untrammeled as possible; this is why we urge reducing the arc of connection between the balance and fork to one as brief as is consistent with sound results. With a double-roller safety action we can easily reduce the fork action to eight degrees and the roller action to twenty-four degrees.

Inasmuch as satisfactory results in adjustment depend very much on the perfection of construction, we shall now dwell to some extent on the necessity of the several parts being made on correct principles. For instance, by reducing the arc of engagement between the fork and roller, we lessen the duration of any disturbing influence of escapement action.

To resume the explanation of why it is desirable to make the staff and all parts near the axis of the balance as light as possible, we would say it is the moving portion of the balance which controls the regularity of the intervals of vibration. To illustrate, suppose we have a balance only 3/8" in diameter, but of the same weight as one in an ordinary eighteen-size movement. We can readily see that such a balance would require but a very light hairspring to cause it to give the usual 18,000 vibrations to the hour. We can also understand, after a little thought, that such a balance would exert as much breaking force on its pivots as a balance of the same weight, but 3/4" in diameter acting against a very much stronger hairspring. There is another factor in the balance problem which deserves our attention, which factor is atmospheric resistance. This increases rapidly in proportion to the velocity.

HOW BAROMETRIC PRESSURE AFFECTS A WATCH.

The most careful investigators in horological mechanics have decided that a balance much above 75/100" in diameter, making 18,000 vibrations per hour, is not desirable, because of the varying atmospheric disturbances as indicated by barometric pressure. A balance with all of its weight as near the periphery as is consistent with strength, is what is to be desired for best results. It is the moving matter composing the balance, pitted against the elastic force of the hairspring, which we have to depend upon for the regularity of the timekeeping of a watch, and if we can take two grains' weight of matter from our roller table and place them in the rim or screws of the balance, so as to act to better advantage against the hairspring, we have disposed of these two grains so as to increase the efficiency of the controlling power and not increase the stress on the pivots.



We have deduced from the facts set forth, two axioms: (a) That we should keep the weight of our balance as much in the periphery as possible, consistent with due strength; (b) avoid excessive size from the disturbing effect of the air. We show at A, Fig. 79, the shape of the piece which carries the jewel pin. As shown, it consists of three parts: (1) The socket A, which receives the jewel pin a; (2) the part A'' and hole b, which goes on the balance staff; (3) the counterpoise A''', which makes up for the weight of the jewel socket A, neck A' and jewel pin. This counterpoise also makes up for the passing hollow C in the guard roller B, Fig. 80. As the piece A is always in the same relation to the roller B, the poise of the balance must always remain the same, no matter how the roller action is placed on the staff. We once saw a double roller of nearly the shape shown at Fig. 79, which had a small gold screw placed at d, evidently for the purpose of poising the double rollers; but, to our thinking, it was a sort of hairsplitting hardly worth the extra trouble. Rollers for very fine watches should be poised on the staff before the balance is placed upon it.



We shall next give detailed instructions for drawing such a double roller as will be adapted for the large model previously described, which, as the reader will remember, was for ten degrees of roller action. We will also point out the necessary changes required to make it adapted for eight degrees of fork action. We would beg to urge again the advantages to be derived from constructing such a model, even for workmen who have had a long experience in escapements, our word for it they will discover a great many new wrinkles they never dreamed of previously.

It is important that every practical watchmaker should thoroughly master the theory of the lever escapement and be able to comprehend and understand at sight the faults and errors in such escapements, which, in the every-day practice of his profession, come to his notice. In no place is such knowledge more required than in fork and roller action. We are led to say the above chiefly for the benefit of a class of workmen who think there is a certain set of rules which, if they could be obtained, would enable them to set to rights any and all escapements. It is well to understand that no such system exists and that, practically, we must make one error balance another; and it is the "know how" to make such faults and errors counteract each other that enables one workman to earn more for himself or his employer in two days than another workman, who can file and drill as well as he can, will earn in a week.

PROPORTIONS OF THE DOUBLE-ROLLER ESCAPEMENT.

The proportion in size between the two rollers in a double-roller escapement is an open question, or, at least, makers seldom agree on it. Grossmann shows, in his work on the lever escapement, two sizes: (1) Half the diameter of the acting roller; (2) two-thirds of the size of the acting roller. The chief fault urged against a smaller safety roller is, that it necessitates longer horns to the fork to carry out the safety action. Longer horns mean more metal in the lever, and it is the conceded policy of all recent makers to have the fork and pallets as light as possible. Another fault pertaining to long horns is, when the horn does have to act as safety action, a greater friction ensues.

In all soundly-constructed lever escapements the safety action is only called into use in exceptional cases, and if the watch was lying still would theoretically never be required. Where fork and pallets are poised on their arbor, pocket motion (except torsional) should but very little affect the fork and pallet action of a watch, and torsional motion is something seldom brought to act on a watch to an extent to make it worthy of much consideration. In the double-roller action which we shall consider, we shall adopt three-fifths of the pitch diameter of the jewel-pin action as the proper size. Not but what the proportions given by Grossmann will do good service; but we adopt the proportions named because it enables us to use a light fork, and still the friction of the guard point on the roller is but little more than where a guard roller of half the diameter of the acting roller is employed.

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.



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.

HOW THE GUARD POINT IS MADE.



The guard point C', as shown at Fig. 82, is of extremely simple construction. Back of the slot of the fork, which is three-fifths of the diameter of the jewel pin in depth, is made a square hole, as shown at u, and the back end of the guard point C is fitted to this hole so that it is rigid in position. This manner of fastening the guard point is equally efficient as that of attaching it with a screw, and much lighter—a matter of the highest importance in escapement construction, as we have already urged. About the best material for such guard points is either aluminum or phosphor bronze, as such material is lighter than gold and very rigid and strong. At Fig. 83 we show a side view of the essential parts depicted in Fig. 82, as if seen in the direction of the arrow v, but we have added the piece which holds the jewel pin D. A careful study of the cut shown at Fig. 82 will soon give the horological student an excellent idea of the double-roller action.

We will now take up and consider at length why Saunier draws his entrance pallet with fifteen degrees draw and his exit pallet with only twelve degrees draw. To make ourselves more conversant with Saunier's method of delineating the lever escapement, we reproduce the essential features of his drawing, Fig. 1, plate VIII, of his "Modern Horology," in which he makes the draw of the locking face of the entrance pallet fifteen degrees and his exit pallet twelve degrees. In the cut shown at Fig. 84 we use the same letters of reference as he employs. We do not quote his description or directions for delineation because he refers to so much matter which he has previously given in the book just referred to. Besides we cannot entirely endorse his methods of delineations for many reasons, one of which appears in the drawing at Fig. 84.



MORE ABOUT TANGENTIAL LOCKINGS.

Most writers endorse the idea of tangential lockings, and Saunier speaks of the escapement as shown at Fig. 84 as having such tangential lockings, which is not the case. He defines the position of the pallet staff from the circle t, which represents the extreme length of the teeth; drawing the radial lines A D and A E to embrace an arc of sixty degrees, and establishing the center of his pallet staff C at the intersection of the lines D C and E C, which are drawn at right angles to the radial lines A D and A E, and tangential to the circle t.

Here is an error; the lines defining the center of the pallet staff should have been drawn tangent to the circle s, which represents the locking angle of the teeth. This would have placed the center of the pallet staff farther in, or closer to the wheel. Any person can see at a glance that the pallets as delineated are not tangential in a true sense.



We have previously considered engaging friction and also repeatedly have spoken of tangential lockings, but will repeat the idea of tangential lockings at Fig. 85. A tangential locking is neutral, or nearly so, as regards engaging friction. For illustration we refer to Fig. 85, where A represents the center of an escape wheel. We draw the radial lines A y and A z so that they embrace sixty degrees of the arcs s or t, which correspond to similar circles in Fig. 84, and represent the extreme extent of the teeth and likewise the locking angle of such teeth. In fact, with the club-tooth escapement all that part of a tooth which extends beyond the line s should be considered the same as the addendum in gear wheels. Consequently, a tangential locking made to coincide with the center of the impulse plane, as recommended by Saunier, would require the pallet staff to be located at C' instead of C, as he draws it. If the angle k' of the tooth k in Fig. 84 was extended outward from the center A so it would engage or rest on the locking face of the entrance pallet as shown at Fig. 84, then the draw of the locking angle would not be quite fifteen degrees; but it is evident no lock can take place until the angle a of the entrance pallet has passed inside the circle s. We would say here that we have added the letters s and t to the original drawings, as we have frequently to refer to these circles, and without letters had no means of designation. Before the locking angle k' of the tooth can engage the pallet, as shown in Fig. 84, the pallet must turn on the center C through an angular movement of at least four degrees. We show the situation in the diagram at Fig. 86, using the same letters of reference for similar parts as in Fig. 84.



As drawn in Fig. 84 the angle of draft G a I is equal to fifteen degrees, but when brought in a position to act as shown at G a' I', Fig. 86, the draw is less even than twelve degrees. The angle C a I remains constant, as shown at C a' I', but the relation to the radial A G changes when the pallet moves through the angle w C w', as it must when locked. A tangential locking in the true sense of the meaning of the phrase is a locking set so that a pallet with its face coinciding with a radial line like A G would be neutral, and the thrust of the tooth would be tangent to the circle described by the locking angle of the tooth. Thus the center C, Fig. 86, is placed on the line w' which is tangent to the circle s; said line w' also being at right angles to the radial line A G.

The facts are, the problems relating to the club-tooth lever escapement are very intricate and require very careful analysis, and without such care the horological student can very readily be misled. Faulty drawings, when studying such problems, lead to no end of errors, and practical men who make imperfect drawings lead to the popular phrase, "Oh, such a matter may be all right in theory, but will not work in practice." We should always bear in mind that theory, if right, must lead practice.

CORRECT DRAWING REQUIRED.

If we delineate our entrance pallet to have a draw of twelve degrees when in actual contact with the tooth, and then construct in exact conformity with such drawings, we will find our lever to "hug the banks" 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.



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 pass 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 space 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 illustration, 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 analyze 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 assume 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 analysis 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.



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 illustrating 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 assertion 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 (passing 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.



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 passes 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 passes 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 pass the arc k to give five degrees of angular motion to the lever. From A as a center we sweep the arc m, passing 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 assumed 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 illustration, 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 passed 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 substitute 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 passed through five degrees of angular motion and the inner angle s now lies on the pitch circle of the escape wheel, the angular space 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 space 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 illustrate, 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''.



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' passes 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. When contact ensues between the tooth D and pallet C the tooth D will attack the pallet at the point where the radial line A v crosses the tooth face. We have now explained how we can delineate a tooth or pallet at any point of its angular motion, and will next explain how to apply this knowledge in actual practice.

PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT.

To delineate our entrance pallet after one-half of the engaged tooth has passed the inner angle of the entrance pallet, we proceed, as in former illustrations, to establish the escape-wheel center at A, and from it sweep the arc b, to represent the pitch circle. We next sweep the short arcs p s, to represent the arcs through which the inner and outer angles of the entrance pallet move. Now, to comply with our statement as above, we must draw the tooth as if half of it has passed the arc s.

To do this we draw from A as a center the radial line A j, passing through the point s, said point s being located at the intersection of the arcs s and b. The tooth D is to be shown as if one half of it has passed the point s; and, consequently, if we lay off three degrees on each side of the point s and establish the points d m, we have located on the arc b the angular extent of the tooth to be drawn. To aid in our delineations we draw from the center A the radial lines A d' and A m', passing through the points d m. The arc a is next drawn as in former instructions and establishes the length of the addendum of the escape-wheel teeth, the outer angle of our escape-wheel tooth being located at the intersection of the arc a with the radial line A d'.

As shown in Fig. 92, the impulse planes of the tooth D and pallet C are in contact and, consequently, in parallel planes, as mentioned on page 91. It is not an easy matter to determine at exactly what degree of angular motion of the escape wheel such condition takes place; because to determine such relation mathematically requires a knowledge of higher mathematics, which would require more study than most practical men would care to bestow, especially as they would have but very little use for such knowledge except for this problem and a few others in dealing with epicycloidal curves for the teeth of wheels.

For all practical purposes it will make no difference whether such parallelism takes place after eight or nine degrees of angular motion of the escape wheel subsequent to the locking action. The great point, as far as practical results go, is to determine if it takes place at or near the time the escape wheel meets the greatest resistance from the hairspring. We find by analysis of our drawing that parallelism takes place about the time when the tooth has three degrees of angular motion to make, and the pallet lacks about two degrees of angular movement for the tooth to escape. It is thus evident that the relations, as shown in our drawing, are in favor of the train or mainspring power over hairspring resistance as three is to two, while the average is only as eleven to ten; that is, the escape wheel in its entire effort passes through eleven degrees of angular motion, while the pallets and fork move through ten degrees. The student will thus see we have arranged to give the train-power an advantage where it is most needed to overcome the opposing influence of the hairspring.