As regards the exalted adhesion of the parallel surfaces, we fancy there is more harm feared than really exists, because, to take the worst view of the situation, such parallelism only exists for the briefest duration, in a practical sense, because theoretically these surfaces never slide on each other as parallel planes. Mathematically considered, the theoretical plane represented by the impulse face of the tooth approaches parallelism with the plane represented by the impulse face of the pallet, arrives at parallelism and instantly passes away from such parallelism.

TO DRAW A PALLET IN ANY POSITION.

As delineated in Fig. 92, the impulse planes of the tooth and pallet are in contact; but we have it in our power to delineate the pallet at any point we choose between the arcs p s. To describe and illustrate the above remark, we say the lines B e and B f embrace five degrees of angular motion of the pallet. Now, the impulse plane of the pallet occupies four of these five degrees. We do not draw a radial line from B inside of the line B e to show where the outer angle of the impulse plane commences, but the reader will see that the impulse plane is drawn one degree on the arc p below the line B e. We continue the line h h to represent the impulse face of the tooth, and measure the angle B n h and find it to be twenty-seven degrees. Now suppose we wish to delineate the entrance pallet as if not in contact with the escape-wheel tooth—for illustration, say, we wish the inner angle of the pallet to be at the point v on the arc s. We draw the radial line B l through v; and if we draw another line so it passes through the point v at an angle of twenty-seven degrees to B l, and continue said line so it crosses the arc p, we delineate the impulse face of our pallet.

We measure the angle i n B, Fig. 92, and find it to be seventy-four degrees; we draw the line v t to the same angle with v B, and we define the inner face of our pallet in the new position. We draw a line parallel with v t from the intersection of the line v y with the arc p, and we define our locking face. If now we revolve the lines we have just drawn on the center B until the line l B coincides with the line f B, we will find the line y y to coincide with h h, and the line v v' with n i.

HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT.

We have now instructed the reader how to delineate either tooth or pallet in any conceivable position in which they can be related to each other. Probably nothing has afforded more efficient aid to practical mechanics than has been afforded by the graphic solution of abstruce mathematical problems; and if we add to this the means of correction by mathematical calculations which do not involve the highest mathematical acquirements, we have approached pretty close to the actual requirements of the practical watchmaker.



To better explain what we mean, we refer the reader to Fig. 93, where we show preliminary drawings for delineating a lever escapement. We wish to ascertain by the graphic method the distance between the centers of action of the escape wheel and the pallet staff. We make our drawing very carefully to a given scale, as, for instance, the radius of the arc a is 5". After the drawing is in the condition shown at Fig. 93 we measure the distance on the line b between the points (centers) A B, and we thus by graphic means obtain a measure of the distance between A B. Now, by the use of trigonometry, we have the length of the line A f (radius of the arc a) and all the angles given, to find the length of f B, or A B, or both f B and A B. By adopting this policy we can verify the measurements taken from our drawings. Suppose we find by the graphic method that the distance between the points A B is 5.78", and by trigonometrical computation find the distance to be 5.7762". We know from this that there is .0038" to be accounted for somewhere; but for all practical purposes either measurement should be satisfactory, because our drawing is about thirty-eight times the actual size of the escape wheel of an eighteen-size movement.

HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED.

Let us further suppose the diameter of our actual escape wheel to be .26", and we were constructing a watch after the lines of our drawing. By "lines," in this case, we mean in the same general form and ratio of parts; as, for illustration, if the distance from the intersection of the arc a with the line b to the point B was one-fifteenth of the diameter of the escape wheel, this ratio would hold good in the actual watch, that is, it would be the one-fifteenth part of .26". Again, suppose the diameter of the escape wheel in the large drawing is 10" and the distance between the centers A B is 5.78"; to obtain the actual distance for the watch with the escape wheel .26" diameter, we make a statement in proportion, thus: 10 : 5.78 :: .26 to the actual distance between the pivot holes of the watch. By computation we find the distance to be .15". These proportions will hold good in every part of actual construction.

All parts—thickness of the pallet stones, length of pallet arms, etc.—bear the same ratio of proportion. We measure the thickness of the entrance pallet stone on the large drawing and find it to be .47"; we make a similar statement to the one above, thus: 10 : .47 :: .26 to the actual thickness of the real pallet stone. By computation we find it to be .0122". All angular relations are alike, whether in the large drawing or the small pallets to match the actual escape wheel .26" in diameter. Thus, in the pallet D, Fig. 93, the impulse face, as reckoned from B as a center, would occupy four degrees.

MAKE A LARGE ESCAPEMENT MODEL.

Reason would suggest the idea of having the theoretical keep pace and touch with the practical. It has been a grave fault with many writers on horological matters that they did not make and measure the abstractions which they delineated on paper. We do not mean by this to endorse the cavil we so often hear—"Oh, that is all right in theory, but it will not work in practice." If theory is right, practice must conform to it. The trouble with many theories is, they do not contain all the elements or factors of the problem.



Near the beginning of this treatise we advised our readers to make a large model, and described in detail the complete parts for such a model. What we propose now is to make adjustable the pallets and fork to such a model, in order that we can set them both right and wrong, and thus practically demonstrate a perfect action and also the various faults to which the lever escapement is subject. The pallet arms are shaped as shown at A, Fig. 94. The pallets B B' can be made of steel or stone, and for all practical purposes those made of steel answer quite as well, and have the advantage of being cheaper. A plate of sheet brass should be obtained, shaped as shown at C, Fig. 95. This plate is of thin brass, about No. 18, and on it are outlined the pallet arms shown at Fig. 94.



To make the pallets adjustable, they are set in thick disks of sheet brass, as shown at D, Figs. 95, 96 and 97. At the center of the plate C is placed a brass disk E, Fig. 98, which serves to support the lever shown at Fig. 99. This disk E is permanently attached to the plate C. The lever shown at Fig. 99 is attached to the disk E by two screws, which pass through the holes h h. If we now place the brass pieces D D' on the plate C in such a way that the pallets set in them correspond exactly to the pallets as outlined on the plate C, we will find the action of the pallets to be precisely the same as if the pallet arms A A', Fig. 94, were employed.



To enable us to practically experiment with and to fully demonstrate all the problems of lock, draw, drop, etc., we make quite a large hole in C where the screws b come. To explain, if the screws b b were tapped directly into C, as they are shown at Fig. 95, we could only turn the disk D on the screw b; but if we enlarge the screw hole in C to three or four times the natural diameter, and then place the nut e under C to receive the screw b, we can then set the disks D D' and pallets B B' in almost any relation we choose to the escape wheel, and clamp the pallets fast and try the action. We show at Fig. 97 a view of the pallet B', disk D' and plate C (seen in the direction of the arrow c) as shown in Fig. 95.

PRACTICAL LESSONS WITH FORK AND PALLET ACTION.

It will be noticed in Fig. 99 that the hole g for the pallet staff in the lever is oblong; this is to allow the lever to be shifted back and forth as relates to roller and fork action. We will not bother about this now, and only call attention to the capabilities of such adjustments when required. At the outset we will conceive the fork F attached to the piece E by two screws passing through the holes h h, Fig. 99. Such an arrangement will insure the fork and roller action keeping right if they are put right at first. Fig. 100 will do much to aid in conveying a clear impression to the reader.

The idea of the adjustable features of our escapement model is to show the effects of setting the pallets wrong or having them of bad form. For illustration, we make use of a pallet with the angle too acute, as shown at B''', Fig. 101. The problem in hand is to find out by mechanical experiments and tests the consequences of such a change. It is evident that the angular motion of the pallet staff will be increased, and that we shall have to open one of the banking pins to allow the engaging tooth to escape. To trace out all the consequences of this one little change would require a considerable amount of study, and many drawings would have to be made to illustrate the effects which would naturally follow only one such slight change.



Suppose, for illustration, we should make such a change in the pallet stone of the entrance pallet; we have increased the angle between the lines k l by (say) one and a half degrees; by so doing we would increase the lock on the exit pallet to three degrees, provided we were working on a basis of one and a half degrees lock; and if we pushed back the exit pallet so as to have the proper degree of lock (one and a half) on it, the tooth which would next engage the entrance pallet would not lock at all, but would strike the pallet on the impulse instead of on the locking face. Again, such a change might cause the jewel pin to strike the horn of the fork, as indicated at the dotted line m, Fig. 99.

Dealing with such and similar abstractions by mental process requires the closest kind of reasoning; and if we attempt to delineate all the complications which follow even such a small change, we will find the job a lengthy one. But with a large model having adjustable parts we provide ourselves with the means for the very best practical solution, and the workman who makes and manipulates such a model will soon master the lever escapement.

QUIZ PROBLEMS IN THE DETACHED LEVER ESCAPEMENT.

Some years ago a young watchmaker friend of the writer made, at his suggestion, a model of the lever escapement similar to the one described, which he used to "play with," as he termed it—that is, he would set the fork and pallets (which were adjustable) in all sorts of ways, right ways and wrong ways, so he could watch the results. A favorite pastime was to set every part for the best results, which was determined by the arc of vibration of the balance. By this sort of training he soon reached that degree of proficiency where one could no more puzzle him with a bad lever escapement than you could spoil a meal for him by disarranging his knife, fork and spoon.

Let us, as a practical example, take up the consideration of a short fork. To represent this in our model we take a lever as shown at Fig. 99, with the elongated slot for the pallet staff at g. To facilitate the description we reproduce at Fig. 102 the figure just mentioned, and also employ the same letters of reference. We fancy everybody who has any knowledge of the lever escapement has an idea of exactly what a "short fork" is, and at the same time it would perhaps puzzle them a good deal to explain the difference between a short fork and a roller too small.



In our practical problems, as solved on a large escapement model, say we first fit our fork of the proper length, and then by the slot g move the lever back a little, leaving the bankings precisely as they were. What are the consequences of this slight change? One of the first results which would display itself would be discovered by the guard pin failing to perform its proper functions. For instance, the guard pin pushed inward against the roller would cause the engaged tooth to pass off the locking face of the pallet, and the fork, instead of returning against the banking, would cause the guard pin to "ride the roller" during the entire excursion of the jewel pin. This fault produces a scraping sound in a watch. Suppose we attempt to remedy the fault by bending forward the guard pin b, as indicated by the dotted outline b' in Fig. 103, said figure being a side view of Fig. 102 seen in the direction of the arrow a. This policy would prevent the engaged pallet from passing off of the locking face of the pallet, but would be followed by the jewel pin not passing fully into the fork, but striking the inside face of the prong of the fork at about the point indicated by the dotted line m. We can see that if the prong of the fork was extended to about the length indicated by the outline at c, the action would be as it should be.

To practically investigate this matter to the best advantage, we need some arrangement by which we can determine the angular motion of the lever and also of the roller and escape wheel. To do this, we provide ourselves with a device which has already been described, but of smaller size, for measuring fork and pallet action. The device to which we allude is shown at Figs. 104, 105 and 106. Fig. 104 shows only the index hand, which is made of steel about 1/20" thick and shaped as shown. The jaws B'' are intended to grasp the pallet staff by the notches e, and hold by friction. The prongs l l are only to guard the staff so it will readily enter the notch e. The circle d is only to enable us to better hold the hand B flat.



HOW TO MEASURE ESCAPEMENT ANGLES.

From the center of the notches e to the tip of the index hand B' the length is 2". This distance is also the radius of the index arc C. This index arc is divided into thirty degrees, with three or four supplementary degrees on each side, as shown. For measuring pallet action we only require ten degrees, and for roller action thirty degrees. The arc C, Fig. 105, can be made of brass and is about 11/2" long by 1/4" wide; said arc is mounted on a brass wire about 1/8" diameter, as shown at k, Fig. 106, which is a view of Fig. 105 seen in the direction of the arrow i. This wire k enters a base shown at D E, Fig. 106, which is provided with a set-screw at j for holding the index arc at the proper height to coincide with the hand B.



A good way to get up the parts shown in Fig. 106 is to take a disk of thick sheet brass about 1" in diameter and insert in it a piece of brass wire about 1/4" diameter and 3/8" long, through which drill axially a hole to receive the wire k. After the jaws B'' are clamped on the pallet staff, we set the index arc C so the hand B' will indicate the angular motion of the pallet staff. By placing the index hand B on the balance staff we can get at the exact angular duration of the engagement of the jewel pin in the fork.

Of course, it is understood that this instrument will also measure the angles of impulse and lock. Thus, suppose the entire angular motion of the lever from bank to bank is ten degrees; to determine how much of this is lock and how much impulse, we set the index arc C so that the hand B' marks ten degrees for the entire motion of the fork, and when the escapement is locked we move the fork from its bank and notice by the arc C how many degrees the hand indicated before it passed of its own accord to the opposite bank. If we have more than one and a half degrees of lock we have too much and should seek to remedy it. How? It is just the answers to such questions we propose to give by the aid of our big model.

DETERMINATION OF "RIGHT" METHODS.

"Be sure you are right, then go ahead," was the advice of the celebrated Davie Crockett. The only trouble in applying this motto to watchmaking is to know when you are right. We have also often heard the remark that there was only one right way, but any number of wrong ways. Now we are inclined to think that most of the people who hold to but one right way are chiefly those who believe all ways but their own ways are wrong. Iron-bound rules are seldom sound even in ethics, and are utterly impracticable in mechanics.

We have seen many workmen who had learned to draw a lever escapement of a given type, and lived firm in the belief that all lever escapements were wrong which were not made so as to conform to this certain method. One workman believes in equidistant lockings, another in circular pallets; each strong in the idea that their particular and peculiar method of designing a lever escapement was the only one to be tolerated. The writer is free to confess that he has seen lever escapements of both types, that is, circular pallets and equidistant lockings, which gave excellent results.

Another mooted point in the lever escapement is, to decide between the merits of the ratchet and the club-tooth escape wheel. English makers, as a rule, hold to the ratchet tooth, while Continental and American manufacturers favor the club tooth. The chief arguments in favor of the ratchet tooth are: (a) It will run without oiling the pallets; (b) in case the escape wheel is lost or broken it is more readily replaced, as all ratchet-tooth escape wheels are alike, either for circular pallets or equidistant lockings. The objections urged against it are: (a) Excessive drop; (b) the escape wheel, being frail, is liable to be injured by incompetent persons handling it; (c) this escapement in many instances does require to have the pallets oiled.

ESCAPEMENTS COMPARED.

(a) That a ratchet-tooth escape wheel requires more drop than a club tooth must be admitted without argument, as this form of tooth requires from one-half to three-fourths of a degree more drop than a club tooth; (b) as regards the frailty of the teeth we hold this as of small import, as any workman who is competent to repair watches would never injure the delicate teeth of an escape wheel; (c) ratchet-tooth lever escapements will occasionally need to have the pallets oiled. The writer is inclined to think that this defect could be remedied by proper care in selecting the stone (ruby or sapphire) and grinding the pallets in such a way that the escape-wheel teeth will not act against the foliations with which all crystalline stones are built up.

All workmen who have had an extended experience in repair work are well aware that there are some lever escapements in which the pallets absolutely require oil; others will seem to get along very nicely without. This applies also to American brass club-tooth escapements; hence, we have so much contention about oiling pallets. The writer does not claim to know positively that the pallet stones are at fault because some escapements need oiling, but the fact must admit of explanation some way, and is this not at least a rational solution? All persons who have paid attention to crystallography are aware that crystals are built up, and have lines of cleavage. In the manufacture of hole jewels, care must be taken to work with the axis of crystallization, or a smooth hole cannot be obtained.

The advantages claimed for the club-tooth escapement are many; among them may be cited (a) the fact that it utilizes a greater arc of impulse of the escape wheel; (b) the impulse being divided between the tooth and the pallet, permits greater power to be utilized at the close of the impulse. This feature we have already explained. It is no doubt true that it is more difficult to match a set of pallets with an escape wheel of the club-tooth order than with a ratchet tooth; still the writer thinks that this objection is of but little consequence where a workman knows exactly what to do and how to do it; in other words, is sure he is right, and can then go ahead intelligently.

It is claimed by some that all American escape wheels of a given grade are exact duplicates; but, as we have previously stated, this is not exactly the case, as they vary a trifle. So do the pallet jewels vary a little in thickness and in the angles. Suppose we put in a new escape wheel and find we have on the entrance pallet too much drop, that is, the tooth which engaged this pallet made a decided movement forward before the tooth which engaged the exit pallet encountered the locking face of said pallet. If we thoroughly understand the lever escapement we can see in an instant if putting in a thicker pallet stone for entrance pallet will remedy the defect. Here again we can study the effects of a change in our large model better than in an escapement no larger than is in an ordinary watch.

HOW TO SET PALLET STONES.

There have been many devices brought forward to aid the workman in adjusting the pallet stones to lever watches. Before going into the details of any such device we should thoroughly understand exactly what we desire to accomplish. In setting pallet stones we must take into consideration the relation of the roller and fork action. As has already been explained, the first thing to do is to set the roller and fork action as it should be, without regard in a great degree to pallet action.



To explain, suppose we have a pallet stone to set in a full-plate movement. The first thing to do is to close the bankings so that the jewel pin will not pass out of the slot in the fork on either side; then gradually open the bankings until the jewel pin will pass out. This will be understood by inspecting Fig. 107, where A A' shows a lever fork as if in contact with both banks, and the jewel pin, represented at B B'', just passes the angle a c' of the fork. The circle described by the jewel pin B is indicated by the arc e. It is well to put a slight friction under the balance rim, in order that we can try the freedom of the guard pin. As a rule, all the guard pin needs is to be free and not touch the roller. The entire point, as far as setting the fork and bankings is concerned, is to have the fork and roller action sound. For all ordinary lever escapements the angular motion of the lever banked in as just described should be about ten degrees. As explained in former examples, if the fork action is entirely sound and the lever only vibrates through an arc of nine degrees, it is quite as well to make the pallets conform to this arc as to make the jewel pin carry the fork through full ten degrees. Again, if the lever vibrates through eleven degrees, it is as well to make the pallets conform to this arc.

The writer is well aware that many readers will cavil at this idea and insist that the workman should bring all the parts right on the basis of ten degrees fork and lever action. In reply we would say that no escapement is perfect, and it is the duty of the workman to get the best results he can for the money he gets for the job. In the instance given above, of the escapement with nine degrees of lever action, when the fork worked all right, if we undertook to give the fork the ten degrees demanded by the stickler for accuracy we would have to set out the jewel pin or lengthen the fork, and to do either would require more time than it would to bring the pallets to conform to the fork and roller action. It is just this knowing how and the decision to act that makes the difference in the workman who is worth to his employer twelve or twenty-five dollars per week.

We have described instruments for measuring the angle of fork and pallet action, but after one has had experience he can judge pretty nearly and then it is seldom necessary to measure the angle of fork action as long as it is near the proper thing, and then bring the pallets to match the escape wheel after the fork and roller action is as it should be—that is, the jewel pin and fork work free, the guard pin has proper freedom, and the fork vibrates through an arc of about ten degrees.

Usually the workman can manipulate the pallets to match the escape wheel so that the teeth will have the proper lock and drop at the right instant, and again have the correct lock on the next succeeding pallet. The tooth should fall but a slight distance before the tooth next in action locks it, because all the angular motion the escape wheel makes except when in contact with the pallets is just so much lost power, which should go toward giving motion to the balance.

There seems to be a little confusion in the use of the word "drop" in horological phrase, as it is used to express the act of parting of the tooth with the pallet. The idea will be seen by inspecting Fig. 108, where we show the tooth D and pallet C as about parting or dropping. When we speak of "banking up to the drop" we mean we set the banking screws so that the teeth will just escape from each pallet. By the term "fall" we mean the arc the tooth passes through before the next pallet is engaged. This action is also illustrated at Fig. 108, where the tooth D, after dropping from the pallet C, is arrested at the position shown by the dotted outline. We designate this arc by the term "fall," and we measure this motion by its angular extent, as shown by the dotted radial lines i f and i g. As we have explained, this fall should only extend through an arc of one and a half degrees, but by close escapement matching this arc can be reduced to one degree, or even a trifle less.



We shall next describe an instrument for holding the escape wheel and pallets while adjusting them. As shown at Fig. 107, the fork A' is banked a little close and the jewel pin as shown would, in some portions, rub on C', making a scraping sound.

HOW TO MAKE AN ESCAPEMENT MATCHING TOOL.



A point has now been reached where we can use an escapement matcher to advantage. There are several good ones on the market, but we can make one very cheaply and also add our own improvements. In making one, the first thing to be provided is a movement holder. Any of the three-jaw types of such holders will answer, provided the jaws hold a movement plate perfectly parallel with the bed of the holder. This will be better understood by inspecting Fig. 109, which is a side view of a device of this kind seen edgewise in elevation. In this B represents the bed plate, which supports three swing jaws, shown at C, Figs. 109 and 110. The watch plate is indicated by the parallel dotted lines A, Fig. 109. The seat a of the swing jaws C must hold the watch plate A exactly parallel with the bed plate B. In the cheap movement holders these seats (a) are apt to be of irregular heights, and must be corrected for our purpose. We will take it for granted that all the seats a are of precisely the same height, measured from B, and that a watch plate placed in the jaws C will be held exactly parallel with the said bed B. We must next provide two pillars, shown at D E, Figs. 109 and 111. These pillars furnish support for sliding centers which hold the top pivots of the escape wheel and pallet staff while we are testing the depths and adjusting the pallet stones. It will be understood that these pillars D E are at right angles to the plane of the bed B, in order that the slides like G N on the pillars D E move exactly vertical. In fact, all the parts moving up and down should be accurately made, so as not to destroy the depths taken from the watch plate A. Suppose, to illustrate, that we place the plate A in position as shown, and insert the cone point n, Figs. 109 and 112, in the pivot hole for the pallet staff, adjusting the slide G N so that the cone point rests accurately in said pivot hole. It is further demanded that the parts I H F G N D be so constructed and adjusted that the sliding center I moves truly vertical, and that we can change ends with said center I and place the hollow cone end m, Fig. 112, so it will receive the top pivot of the pallet staff and hold it exactly upright.



The idea of the sliding center I is to perfectly supply the place of the opposite plate of the watch and give us exactly the same practical depths as if the parts were in their place between the plates of the movement. The foot of the pillar D has a flange attached, as shown at f, which aids in holding it perfectly upright. It is well to cut a screw on D at D', and screw the flange f on such screw and then turn the lower face of f flat to aid in having the pillar D perfectly upright.

DETAILS OF FITTING UP ESCAPEMENT MATCHER.

It is well to fit the screw D' loosely, so that the flange f will come perfectly flat with the upper surface of the base plate B. The slide G N on the pillar D can be made of two pieces of small brass tube, one fitting the pillar D and the other the bar F. The slide G N is held in position by the set screw g, and the rod F by the set screw h.



The piece H can be permanently attached to the rod F. We show separate at Figs. 113 and 114 the slide G N on an enlarged scale from Fig. 109. Fig. 114 is a view of Fig. 113 seen in the direction of the arrow e. All joints and movable parts should work free, in order that the center I may be readily and accurately set. The parts H F are shown separate and enlarged at Figs. 115 and 116. The piece H can be made of thick sheet brass securely attached to F in such a way as to bring the V-shaped groove at right angles to the axis of the rod F. It is well to make the rod F about 1/8" in diameter, while the sliding center I need not be more than 1/16" in diameter. The cone point n should be hardened to a spring temper and turned to a true cone in an accurately running wire chuck.



The hollow cone end m of I should also be hardened, but this is best done after the hollow cone is turned in. The hardening of both ends should only be at the tips. The sliding center I can be held in the V-shaped groove by two light friction springs, as indicated at the dotted lines s s, Fig. 115, or a flat plate of No. 24 or 25 sheet brass of the size of H can be employed, as shown at Figs. 116 and 117, where o represents the plate of No. 24 brass, p p the small screws attaching the plate o to H, and k a clamping screw to fasten I in position. It will be found that the two light springs s s, Fig. 115 will be the most satisfactory. The wire legs, shown at L, will aid in making the device set steady. The pillar E is provided with the same slides and other parts as described and illustrated as attached to D. The position of the pillars D and E are indicated at Fig. 110.



We will next tell how to flatten F to keep H exactly vertical. To aid in explanation, we will show (enlarged) at Fig. 118 the bar F shown in Fig. 109. In flattening such pieces to prevent turning, we should cut away about two-fifths, as shown at Fig. 119, which is an end view of Fig. 118 seen in the direction of the arrow c. In such flattening we should not only cut away two-fifths at one end, but we must preserve this proportion from end to end. To aid in this operation we make a fixed gage of sheet metal, shaped as shown at I, Fig. 120.



ESCAPEMENT MATCHING DEVICE DESCRIBED.



In practical construction we first file away about two-fifths of F and then grind the flat side on a glass slab to a flat, even surface and, of course, equal thickness from end to end. We reproduce the sleeve G as shown at Fig. 113 as if seen from the left and in the direction of the axis of the bar F. To prevent the bar F turning on its axis, we insert in the sleeve G a piece of wire of the same size as F but with three-fifths cut away, as shown at y, Fig. 121. This piece y is soldered in the sleeve G so its flat face stands vertical. To give service and efficiency to the screw h, we thicken the side of the sleeve F by adding the stud w, through which the screw h works. A soft metal plug goes between the screw h and the bar F, to prevent F being cut up and marred. It will be seen that we can place the top plate of a full-plate movement in the device shown at Fig. 109 and set the vertical centers I so the cone points n will rest in the pivot holes of the escape wheel and pallets. It is to be understood that the lower side of the top plate is placed uppermost in the movement holder.



If we now reverse the ends of the centers I and let the pivots of the escape wheel and pallet staff rest in the hollow cones of these centers I, we have the escape wheel and pallets in precisely the same position and relation to each other as if the lower plate was in position. It is further to be supposed that the balance is in place and the cock screwed down, although the presence of the balance is not absolutely necessary if the banking screws are set as directed, that is, so the jewel pin will just freely pass in and out of the fork.

HOW TO SET PALLET STONES.

We have now come to setting or manipulating the pallet stones so they will act in exact conjunction with the fork and roller. To do this we need to have the shellac which holds the pallet stones heated enough to make it plastic. The usual way is to heat a piece of metal and place it in close proximity to the pallets, or to heat a pair of pliers and clamp the pallet arms to soften the cement.

Of course, it is understood that the movement holder cannot be moved about while the stones are being manipulated. The better way is to set the movement holder on a rather heavy plate of glass or metal, so that the holder will not jostle about; then set the lamp so it will do its duty, and after a little practice the setting of a pair of pallet stones to perfectly perform their functions will take but a few minutes. In fact, if the stones will answer at all, three to five minutes is as much time as one could well devote to the adjustment. The reader will see that if the lever is properly banked all he has to do is to set the stones so the lock, draw and drop are right, when the entire escapement is as it should be, and will need no further trial or manipulating.



CHAPTER II.

THE CYLINDER ESCAPEMENT.

There is always in mechanical matters an underlying combination of principles and relations of parts known as "theory." We often hear the remark made that such a thing may be all right in theory, but will not work in practice. This statement has no foundation in fact. If a given mechanical device accords strictly with theory, it will come out all right practically. Mental conceptions of a machine are what we may term their theoretical existence.

When we make drawings of a machine mentally conceived, we commence its mechanical construction, and if we make such drawings to scale, and add a specification stating the materials to be employed, we leave only the merest mechanical details to be carried out; the brain work is done and only finger work remains to be executed.

With these preliminary remarks we will take up the consideration of the cylinder escapement invented by Robert Graham about the year 1720. It is one of the two so-called frictional rest dead-beat escapements which have come into popular use, the other being the duplex. Usage, or, to put it in other words, experience derived from the actual manufacture of the cylinder escapement, settled the best forms and proportions of the several parts years ago. Still, makers vary slightly on certain lines, which are important for a man who repairs such watches to know and be able to carry out, in order to put them in a condition to perform as intended by the manufacturers. It is not knowing these lines which leaves the average watchmaker so much at sea. He cuts and moves and shifts parts about to see if dumb luck will not supply the correction he does not know how to make. This requisite knowledge does not consist so much in knowing how to file or grind as it does in discriminating where such application of manual dexterity is to be applied. And right here let us make a remark to which we will call attention again later on. The point of this remark lies in the question—How many of the so-called practical watchmakers could tell you what proportion of a cylinder should be cut away from the half shell? How many could explain the difference between the "real" and "apparent" lift? Comparatively few, and yet a knowledge of these things is as important for a watchmaker as it is for a surgeon to understand the action of a man's heart or the relations of the muscles to the bones.

ESSENTIAL PARTS OF THE CYLINDER ESCAPEMENT.

The cylinder escapement is made up of two essential parts, viz.: the escape wheel and the cylinder. The cylinder escape wheel in all modern watches has fifteen teeth, although Saunier, in his "Modern Horology," delineates a twelve-tooth wheel for apparently no better reason than because it was more easily drawn. We, in this treatise, will consider both the theoretical action and the practical construction, but more particularly the repair of this escapement in a thorough and complete manner.

At starting out, we will first agree on the names of the several parts of this escapement, and to aid us in this we will refer to the accompanying drawings, in which Fig. 122 is a side elevation of a cylinder complete and ready to have a balance staked on to it. Fig. 123 shows the cylinder removed from the balance collet. Figs. 124 and 125 show the upper and lower plugs removed from the cylinder. Fig. 126 is a horizontal section of Fig. 122 on the line i. Fig. 127 is a side view of one tooth of a cylinder escape wheel as if seen in the direction of the arrow f in Fig. 126. Fig. 128 is a top view of two teeth of a cylinder escape wheel. The names of the several parts usually employed are as follows:

A.—Upper or Main Shell. A'.—Half Shell. A''.—Column. A'''.—Small Shell. B B' B''.—Balance Collet. G.—Upper Plug. H.—Lower Plug. g.—Entrance Lip of Cylinder. h.—Exit Lip of Cylinder. c.—Banking Slot. C.—Tooth. D.—U arm. E.—Stalk of Pillar. I.—U space. l.—Point of Tooth. k.—Heel of Tooth.

The cylinder escapement has two engagements or actions, during the passage of each tooth; that is, one on the outside of the cylinder and one on the inside of the shell. As we shall show later on, the cylinder escapement is the only positively dead-beat escapement in use, all others, even the duplex, having a slight recoil during the process of escaping.

When the tooth of a cylinder escape wheel while performing its functions, strikes the cylinder shell, it rests dead on the outer or inner surface of the half shell until the action of the balance spring has brought the lip of the cylinder so that the impulse face of the tooth commences to impart motion or power to the balance.



Most writers on horological matters term this act the "lift," which name was no doubt acquired when escapements were chiefly confined to pendulum clocks. Very little thought on the matter will show any person who inspects Fig. 126 that if the tooth C is released or escapes from the inside of the half shell of the cylinder A, said cylinder must turn or revolve a little in the direction of the arrow j, and also that the next succeeding tooth of the escape wheel will engage the cylinder on the outside of the half shell, falling on the dead or neutral portion of said cylinder, to rest until the hairspring causes the cylinder to turn in the opposite direction and permitting the tooth now resting on the outside of the cylinder to assume the position shown on the drawing.

The first problem in our consideration of the theoretical action of the cylinder escapement, is to arrange the parts we have described so as to have these two movements of the escape wheel of like angular values. To explain what we mean by this, we must premise by saying, that as our escape wheel has fifteen teeth and we make each tooth give two impulses in alternate directions we must arrange to have these half-tooth movements exactly alike, or, as stated above, of equal angular values; and also each impulse must convey the same power or force to the balance. All escape wheels of fifteen teeth acting by half impulses must impel the balance during twelve degrees (minus the drop) of escape-wheel action; or, in other words, when a tooth passes out of the cylinder from the position shown at Fig. 126, the form of the impulse face of the tooth and the shape of the exit lip of the cylinder must be such during twelve degrees (less the drop) of the angular motion of the escape wheel. The entire power of such an escape wheel is devoted to giving impulse to the balance.

The extent of angular motion of the balance during such impulse is, as previously stated, termed the "lifting angle." This "lifting angle" is by horological writers again divided into real and apparent lifts. This last division is only an imaginary one, as the real lift is the one to be studied and expresses the arc through which the impulse face of the tooth impels the balance during the act of escaping, and so, as we shall subsequently show, should no more be counted than in the detached lever escapement, where a precisely similar condition exists, but is never considered or discussed.

We shall for the present take no note of this lifting angle, but confine ourselves to the problem just named, of so arranging and designing our escape-wheel teeth and cylinder that each half of the tooth space shall give equal impulses to the balance with the minimum of drop. To do this we will make a careful drawing of an escape-wheel tooth and cylinder on an enlarged scale; our method of making such drawings will be on a new and original system, which is very simple yet complete.

DRAWING THE CYLINDER ESCAPEMENT.

All horological—and for that matter all mechanical—drawings are based on two systems of measurements: (1) Linear extent; (2) angular movement. For the first measurement we adopt the inch and its decimals; for the second we adopt degrees, minutes and seconds. For measuring the latter the usual plan is to employ a protractor, which serves the double purpose of enabling us to lay off and delineate any angle and also to measure any angle obtained by the graphic method, and it is thus by this graphic method we propose to solve very simply some of the most abstruce problems in horological delineations. As an instance, we propose to draw our cylinder escapement with no other instruments than a steel straight-edge, showing one-hundredths of an inch, and a pair of dividers; the degree measurement being obtained from arcs of sixty degrees of radii, as will be explained further on.

In describing the method for drawing the cylinder escapement we shall make a radical departure from the systems usually laid down in text-books, and seek to simplify the formulas which have heretofore been given for such delineations. In considering the cylinder escapement we shall pursue an analytical course and strive to build up from the underlying principles. In the drawings for this purpose we shall commence with one having an escape wheel of 10" radius, and our first effort will be the primary drawing shown at Fig. 129. Here we establish the point A for the center of our escape wheel, and from this center sweep the short arc a a with a 10" radius, to represent the circumference of our escape wheel. From A we draw the vertical line A B, and from the intersection of said line with the arc a a we lay off twelve degree spaces on each side of the line A B on said arc a and establish the points b c. From A as a center we draw through the points b c the radial lines b' c'.

To define the face of the incline to the teeth we set our dividers to the radius of any of the convenient arcs of sixty degrees which we have provided, and sweep the arc t t. From the intersection of said arc with the line A b' we lay off on said arc sixty-four degrees and establish the point g and draw the line b g. Why we take sixty-four degrees for the angle A b g will be explained later on, when we are discussing the angular motion of the cylinder. By dividing the eleventh degree from the point b on the arc a a into thirds and taking two of them, we establish the point y and draw the radial line A y'. Where this line A y' intersects the line b g we name the point n, and in it is located the point of the escape-wheel tooth. That portion of the line b g which lies between the points b and n represents the measure of the inner diameter of the cylinder, and also the length of the chord of the arc which rounds the impulse face of the tooth. We divide the space b n into two equal portions and establish the point e, which locates the position of the center of the cylinder. From A as a center and through the point e we sweep the arc e' e', and it is on this line that the points establishing the center of the cylinder will in every instance be located. From A as a center, through the point n we sweep the arc k, and on this line we locate the points of the escape-wheel teeth. For delineating the curved impulse faces of the escape-wheel teeth we draw from the point e and at right angles to the line b g the line e o. We next take in our dividers the radius of the arc k, and setting one leg at either of the points b or n, establish with the other leg the point p' on the line e o, and from the point p' as a center we sweep the arc b v n, which defines the curve of the impulse faces of the teeth. From A as a center through the point p' we sweep the arc p, and in all instances where we desire to delineate the curved face of a tooth we locate either the position of the point or the heel of such tooth, and setting one leg of our dividers at such point, the other leg resting on the arc p, we establish the center from which to sweep the arc defining the face of said tooth.

ADVANTAGES GAINED IN SHAPING.

The reason for giving a curved form to the impulse face of the teeth of cylinder escape wheels are somewhat intricate, and the problem involves several factors. That there are advantages in so shaping the incline or impulse face is conceded, we believe, by all recent manufacturers. The chief benefit derived from such curved impulse faces will be evident after a little thought and study of the situation and relation of parts as shown in Fig. 129. It will be seen on inspection that the angular motion imparted to the cylinder by the impulse face of the tooth when curved as shown, is greater during the first half of the twelve degrees of escape-wheel action than during the last half, thus giving the escape wheel the advantage at the time the balance spring increases its resistance to the passage of the escape-wheel tooth across the lip of the cylinder. Or, in other words, as the ratio of resistance of the balance spring increases, in a like ratio the curved form of the impulse face of the tooth gives greater power to the escape-wheel action in proportion to the angular motion of the escape wheel. Hence, in actual service it is found that cylinder watches with curved impulse planes to the escape-wheel teeth are less liable to set in the pocket than the teeth having straight impulse faces.

THE OUTER DIAMETER OF THE CYLINDER.



To define the remainder of the form of our escape-wheel tooth we will next delineate the heel. To do this we first define the outer diameter of our cylinder, which is the extent from the point n to c, and after drawing the line n c we halve the space and establish the point x, from which point as a center we sweep the circle w w, which defines the outer circumference of our cylinder. With our dividers set to embrace the extent from the point n to the point c we set one leg at the point b, and with the other leg establish on the arc k the point h. We next draw the line b h, and from the point b draw the line b f at right angle to the line b h. Our object for drawing these lines is to define the heel of our escape-wheel tooth by a right angle line tangent to the circle w, from the point b; which circle w represents the curve of the outer circumference of the cylinder. We shape the point of the tooth as shown to give it the proper stability, and draw the full line j to a curve from the center A. We have now defined the form of the upper face of the tooth. How to delineate the U arms will be taken up later on, as, in the present case, the necessary lines would confuse our drawing.

We would here take the opportunity to say that there is a great latitude taken by makers as regards the extent of angular impulse given to the cylinder, or, as it is termed, the "actual lift." This latitude governs to a great extent the angle A b g, which we gave as sixty-four degrees in our drawing. It is well to understand that the use of sixty-four degrees is based on no hard-and-fast rules, but varies back and forth, according as a greater or lesser angle of impulse or lift is employed.

In practical workshop usage the impulse angle is probably more easily estimated by the ratio between the diameter of the cylinder and the measured (by lineal measure) height of the impulse plane. Or, to be more explicit, we measure the radial extent from the center A between the arcs a k on the line A b, and use this for comparison with the outer diameter of the cylinder.

We can readily see that as we increase the height of the heel of the impulse face of our tooth we must also increase the angle of impulse imparted to the cylinder. With the advantages of accurate micrometer calipers now possessed by the horological student it is an easy matter to get at the angular extent of the real lift of any cylinder. The advantage of such measuring instruments is also made manifest in determining when the proper proportion of the cylinder is cut away for the half shell.



In the older methods of watchmaking it was a very common rule to say, let the height of the incline of the tooth be one-seventh of the outer diameter of the cylinder, and at the same time the trade was furnished with no tools except a clumsy douzieme gage; but with micrometer calipers which read to one-thousandths of an inch such rules can be definitely carried into effect and not left to guess work. Let us compare the old method with the new: Suppose we have a new cylinder to put in; we have the old escape wheel, but the former cylinder is gone. The old-style workman would take a round broach and calculate the size of the cylinder by finding a place where the broach would just go between the teeth, and the size of the broach at this point was supposed to be the outer diameter of the cylinder. By our method we measure the diameter of the escape wheel in thousandths of an inch, and from this size calculate exactly what the diameter of the new cylinder should be in thousandths of an inch. Suppose, to further carry out our comparison, the escape wheel which is in the watch has teeth which have been stoned off to permit the use of a cylinder which was too small inside, or, in fact, of a cylinder too small for the watch: in this case the broach system would only add to the trouble and give us a cylinder which would permit too much inside drop.

DRAWING A CYLINDER.

We have already instructed the pupil how to delineate a cylinder escape wheel tooth and we will next describe how to draw a cylinder. As already stated, the center of the cylinder is placed to coincide with the center of the chord of the arc which defines the impulse face of the tooth. Consequently, if we design a cylinder escape wheel tooth as previously described, and setting one leg of our compasses at the point e which is situated at the center of the chord of the arc which defines the impulse face of the tooth and through the points d and b we define the inside of our cylinder. We next divide the chord d b into eight parts and set our dividers to five of these parts, and from e as a center sweep the circle h and define the outside of our cylinder. From A as a center we draw the radial line A e'. At right angles to the line A e' and through the point e we draw the line from e as a center, and with our dividers set to the radius of any of the convenient arcs which we have divided into sixty degrees, we sweep the arc i. Where this arc intersects the line f we term the point k, and from this point we lay off on the arc i 220 degrees, and draw the line l e l', which we see coincides with the chord of the impulse face of the tooth. We set our dividers to the same radius by which we sweep the arc i and set one leg at the point b for a center and sweep the arc j'. If we measure this arc from the point j' to intersection of said arc j' with the line l we will find it to be sixty-four degrees, which accounts for our taking this number of degrees when we defined the face of our escape-wheel tooth, Fig. 129.

There is no reason why we should take twenty-degrees for the angle k e l except that the practical construction of the larger sizes of cylinder watches has established the fact that this is about the right angle to employ, while in smaller watches it frequently runs up as high as twenty-five. Although the cylinder is seemingly a very simple escapement, it is really a very abstruce one to follow out so as to become familiar with all of its actions.

THE CYLINDER PROPER CONSIDERED.



We will now proceed and consider the cylinder proper, and to aid us in understanding the position and relation of the parts we refer to Fig. 131, where we repeat the circles d and h, shown in Fig. 130, which represents the inside and outside of the cylinder. We have here also repeated the line f of Fig. 130 as it cuts the cylinder in half, that is, divides it into two segments of 180 degrees each. If we conceive of a cylinder in which just one-half is cut away, that is, the lips are bounded by straight radial lines, we can also conceive of the relation and position of the parts shown in Fig. 130. The first position of which we should take cognizance is, the tooth D is moved back to the left so as to rest on the outside of our cylinder. The cylinder is also supposed to stand so that the lips correspond to the line f. On pressing the tooth D forward the incline of the tooth would attack the entrance lip of the cylinder at just about the center of the curved impulse face, imparting to the cylinder twenty degrees of angular motion, but the point of the tooth at d would exactly encounter the inner angle of the exit lip, and of course the cylinder would afford no rest for the tooth; hence, we see the importance of not cutting away too much of the half shell of the cylinder.

But before we further consider the action of the tooth D in its action as it passes the exit lip of the cylinder we must finish with the action of the tooth on the entrance lip. A very little thought and study of Fig. 130 will convince us that the incline of the tooth as it enters the cylinder will commence at t, Fig. 130, but at the close of the action the tooth parts from the lip on the inner angle. Now it is evident that it would require greater force to propel the cylinder by its inner angle than by the outer one. To compensate for this we round the edge of the entrance lip so that the action of the tooth instead of commencing on the outer angle commences on the center of the edge of the entrance lip and also ends its action on the center of the entrance lip. To give angular extent enough to the shell of the cylinder to allow for rounding and also to afford a secure rest for the tooth inside the cylinder, we add six degrees to the angular extent of the entrance lip of the cylinder shell, as indicated on the arc o', Fig. 131, three of these degrees being absorbed for rounding and three to insure a dead rest for the tooth when it enters the cylinder.

WHY THE ANGULAR EXTENT IS INCREASED.

Without rounding the exit lip the action of the tooth on its exit would be entirely on the inner angle of the shell. To obviate this it is the usual practice to increase the angular extent of the cylinder ten degrees, as shown on the arc o' between the lines f and p, Fig. 131. Why we should allow ten degrees on the exit lip and but six degrees on the entrance lip will be understood by observing Fig. 130, where the radial lines s and r show the extent of angular motion of the cylinder, which would be lost if the tooth commenced to act on the inner angle and ended on the outer angle of the exit lip. This arc is a little over six degrees, and if we add a trifle over three degrees for rounding we would account for the ten degrees between the lines f and p, Fig. 131. It will now be seen that the angular extent is 196 degrees. If we draw the line w we can see in what proportion the measurement should be made between the outer diameter of the cylinder and the measure of the half shell. It will be seen on measurement that the distance between the center e and the line w is about one-fifteenth part of the outer diameter of the cylinder and consequently with a cylinder which measures 45/1000 of an inch in diameter, now the half shell should measure half of the entire diameter of the cylinder plus one-fifteenth part of such diameter, or 251/2 thousandths of an inch.

After these proportions are understood and the drawing made, the eye will get accustomed to judging pretty near what is required; but much the safer plan is to measure, where we have the proper tools for doing so. Most workmen have an idea that the depth or distance at which the cylinder is set from the escape wheel is a matter of adjustment; while this is true to a certain extent, still there is really only one position for the center of the cylinder, and that is so that the center of the pivot hole coincides exactly with the center of the chord to the curve of the impulse face of the tooth or the point e, Fig. 130. Any adjustment or moving back and forth of the chariot to change the depth could only be demanded where there was some fault existing in the cylinder or where it had been moved out of its proper place by some genius as an experiment in cylinder depths. It will be evident on observing the drawing at Fig. 131 that when the cylinder is performing an arc of vibration, as soon as the entrance lip has passed the point indicated by the radial line e x the point of the escape-wheel tooth will commence to act on the cylinder lip and continue to do so through an arc of forty degrees, or from the lines x to l.

MAKING A WORKING MODEL.

To practically study the action of the cylinder escapement it is well to make a working model. It is not necessary that such a model should contain an entire escape wheel; all that is really required is two teeth cut out of brass of the proper forms and proportions and attached to the end of an arm 4-7/8" long with studs riveted to the U arms to support the teeth. This U arm is attached to the long arm we have just mentioned. A flat ring of heavy sheet brass is shaped to represent a short transverse section of a cylinder. This segment is mounted on a yoke which turns on pivots. In making such a model we can employ all the proportions and exact forms of the larger drawings made on a ten-inch radius. Such a model becomes of great service in learning the importance of properly shaping the lips of the cylinder. And right here we beg to call attention to the fact that in the ordinary repair shop the proper shape of cylinder lips is entirely neglected.

PROPER SHAPE OF CYLINDER LIPS.

The workman buys a cylinder and whether the proper amount is cut away from the half shell, or the lips, the correct form is entirely ignored, and still careful attention to the form of the cylinder lips adds full ten per cent. to the efficiency of the motive force as applied to the cylinder. In making study drawings of the cylinder escapement it is not necessary to employ paper so large that we can establish upon it the center of the arc which represents the periphery of our escape wheel, as we have at our disposal two plans by which this can be obviated. First, placing a bit of bristol board on our drawing-board in which we can set one leg of our dividers or compasses when we sweep the peripheral arc which we use in our delineations; second, making three arcs in brass or other sheet metal, viz.: the periphery of the escape wheel, the arc passing through the center of the chord of the arc of the impulse face of the tooth, and the arc passing through the point of the escape-wheel tooth. Of these plans we favor the one of sticking a bit of cardboard on the drawing board outside of the paper on which we are making our drawing.



At Fig. 132 we show the position and relation of the several parts just as the tooth passes into the shell of the cylinder, leaving the lip of the cylinder just as the tooth parted with it. The half shell of the cylinder as shown occupies 196 degrees or the larger arc embraced between the radial lines k and l. In drawing the entrance lip the acting face is made almost identical with a radial line except to round the corners for about one-third the thickness of the cylinder shell. No portion, however, of the lip can be considered as a straight line, but might be described as a flattened curve.



A little study of what would be required to get the best results after making such a drawing will aid the pupil in arriving at the proper shape, especially when he remembers that the thickness of the cylinder shell of a twelve-line watch is only about five one-thousandths of an inch. But because the parts are small we should not shirk the problem of getting the most we possibly can out of a cylinder watch.

The extent of arc between the radial lines k f, as shown in Fig. 132, is four degrees. Although in former drawings we showed the angular extent added as six degrees, as we show the lip m in Fig. 132, two degrees are lost in rounding. The space k f on the egress or exit side is intended to be about four degrees, which shows the extent of lock. We show at Fig. 133 the tooth D just having passed out of the cylinder, having parted with the exit lip p.

In making this drawing we proceed as with Fig. 132 by establishing a center for our radius of 10" outside of our drawing paper and drawing the line A A to such center and sweeping the arcs a b c. We establish the point e, which represents the center of our cylinder, as before. We take the space to represent the radial extent of the outside of our cylinder in our dividers and from e as a center sweep a fine pencil line, represented by the dotted line t in our drawing; and where this circle intersects the arc a we name it the point s; and it is at this point the heel of our escape-wheel tooth must part with the exit lip of the cylinder. From e as a center and through the point s we draw the line e l''. With our dividers set to the radius of any convenient arc which we have divided into degrees, we sweep the short arc d'. The intersection of this arc with the line e l'' we name the point u; and from e as a center we draw the radial line e u f'. We place the letter f'' in connection with this line because it (the line) bears the same relations to the half shell of the cylinder shown in Fig. 133 that the line f does to the half shell (D) shown in Fig. 132. We draw the line f'' f''', Fig. 133, which divides the cylinder into two segments of 180 degrees each. We take the same space in our dividers with which we swept the interior of the cylinder in Fig. 132 and sweep the circle v, Fig. 133. From e as a center we sweep the short arc d'', Fig. 133, and from its intersection of the line f'' we lay off six degrees on said arc d'' and draw the line e' k'', which defines the angular extent of our entrance lip to the half shell of the cylinder in Fig. 133. We draw the full lines of the cylinder as shown.

We next delineate the heel of the tooth which has just passed out of the cylinder, as shown at D', Fig. 133. We now have a drawing showing the position of the half shell of the cylinder just as the tooth has passed the exit lip. This drawing also represents the position of the half shell of the cylinder when the tooth rests against it on the outside. If we should make a drawing of an escape-wheel tooth shaped exactly as the one shown at Fig. 132 and the point of the tooth resting at x, we would show the position of a tooth encountering the cylinder after a tooth which has been engaged in the inside of the shell has passed out. By following the instructions now given, we can delineate a tooth in any of its relations with the cylinder shell.

DELINEATING AN ESCAPE-WHEEL TOOTH WHILE IN ACTION.

We will now go through the operation of delineating an escape-wheel tooth while in action. The position we shall assume is the one in which the cylinder and escape-wheel tooth are in the relation of the passage of half the impulse face of the tooth into the cylinder. To do this is simple enough: We first produce the arcs a b c, Fig. 133, as directed, and then proceed to delineate a tooth as in previous instances. To delineate our cylinder in the position we have assumed above, we take the space between the points e d in our dividers and setting one leg at d establish the point g, to represent the center of our cylinder. If we then sweep the circle h from the center of g we define the inner surface of the shell of our cylinder.

Strictly speaking, we have not assumed the position we stated, that is, the impulse face of the tooth as passing half way into the cylinder. To comply strictly with our statement, we divide the chord of the impulse face of the tooth A into eight equal spaces, as shown. Now as each of these spaces represent the thickness of the cylinder, if we take in our dividers four of these spaces and half of another, we have the radius of a circle passing the center of the cylinder shell. Consequently, if with this space in our dividers we set the leg at d, we establish on the arc b the point i. We locate the center of our cylinder when one-half of an entering tooth has passed into the cylinder. If now from the new center with our dividers set at four of the spaces into which we have divided the line e f we can sweep a circle representing the inner surface of the cylinder shell, and by setting our dividers to five of these spaces we can, from i as a center, sweep an arc representing the outside of the cylinder shell. For all purposes of practical study the delineation we show at Fig. 133 is to be preferred, because, if we carry out all the details we have described, the lines would become confused. We set our dividers at five of the spaces on the line e f and from g as a center sweep the circle j, which delineates the outer surface of our cylinder shell.

Let us now, as we directed in our former instructions, draw a flattened curve to represent the acting surface of the entrance lip of our cylinder as if it were in direct contact with the impulse face of the tooth. To delineate the exit lip we draw from the center g, Fig. 134, to the radial line g k, said line passing through the point of contact between the tooth and entrance lip of the cylinder. Let us next continue this line on the opposite side of the point g, as shown at g k', and we thus bisect the cylinder shell into two equal parts of 180 degrees each. As we previously explained, the entire extent of the cylinder half shell is 196 degrees. We now set our dividers to the radius of any convenient arc which we have divided into degrees, and from g as a center sweep the short arc l l, and from the intersection of this arc with the line g k' we lay off sixteen degrees on the said arc l and establish the point n, from g as a center draw the radial line g n'. Take ten degrees from the same parent arc and establish the point m, then draw the line g m'. Now the arc on the circles h j between the lines g n' and g m limits the extent of the exit lip of the cylinder and the arc between the lines g k' and g m' represents the locking surface of the cylinder shell.



To delineate the U arms we refer to Fig. 135. Here, again, we draw the arc a b c and delineate a tooth as before. From the point e located at the heel of the tooth we draw the radial line e e'. From the point e we lay off on the arc a five degrees and establish the point p; we halve this space and draw the short radial line p' s' and p s. From the point e on the arc A we lay off twenty-four degrees and establish the point t, which locates the heel of the next tooth in advance of A. At two and a half degrees to the right of the point t we locate the point r and draw the short radial line r s. On the arc b and half way between the lines p s and r s, we establish the point u, and from it as a center we sweep the arc v defining the curve of the U arms.

We have now given minute instructions for drawing a cylinder escapement in all its details except the extent of the banking slot of the cylinder, which is usually made to embrace an angular extent of 270 degrees; consequently, the pillar of the cylinder will not measure more than ninety degrees of angular extent.

There is no escapement constructed where carefully-made drawings tend more to perfect knowledge of the action than the cylinder. But it is necessary with the pupil to institute a careful analysis of the actions involved. In writing on a subject of this kind it is extremely perplexing to know when to stop; not that there is so much danger of saying too much as there is not having the words read with attention.

As an illustration, let us consider the subject of depth between the cylinder and the escape wheel. As previously stated, 196 degrees of cylinder shell should be employed; but suppose we find a watch in which the half shell has had too much cut away, so the tooth on entering the half shell after parting with the entrance lip does not strike dead on the inside of the shell, but encounters the edge of the exit lip. In this case the impulse of the balance would cause the tooth to slightly retrograde and the watch would go but would lack a good motion. In such an instance a very slight advance of the chariot would remedy the fault—not perfectly remedy it, but patch up, so to speak—and the watch would run.



In this day, fine cylinder watches are not made, and only the common kind are met with, and for this reason the student should familiarize himself with all the imaginary faults which could occur from bad construction. The best way to do this is to delineate what he (the student) knows to be a faulty escapement, as, for instance, a cylinder in which too much of the half shell is cut away; but in every instance let the tooth be of the correct form. Then delineate an escapement in which the cylinder is correct but the teeth faulty; also change the thickness of the cylinder shell, so as to make the teeth too short. This sort of practice makes the pupil think and study and he will acquire a knowledge which will never be forgotten, but always be present to aid him in the puzzles to which the practical watchmaker is every day subject.

The ability to solve these perplexing problems determines in a great degree the worth of a man to his employer, in addition to establishing his reputation as a skilled workman. The question is frequently asked, "How can I profitably employ myself in spare time?" It would seem that a watchmaker could do no better than to carefully study matters horological, striving constantly to attain a greater degree of perfection, for by so doing his earning capacity will undoubtedly be increased.



CHAPTER III.

THE CHRONOMETER ESCAPEMENT.

Undoubtedly "the detent," or, as it is usually termed, "the chronometer escapement," is the most perfect of any of our portable time measurers. Although the marine chronometer is in a sense a portable timepiece, still it is not, like a pocket watch, capable of being adjusted to positions. As we are all aware, the detent escapement is used in fine pocket watches, still the general feeling of manufacturers is not favorable to it. Much of this feeling no doubt is owing to the mechanical difficulties presented in repairing the chronometer escapements when the detent is broken, and the fact that the spring detent could not be adjusted to position. We shall have occasion to speak of position adjustments as relate to the chronometer escapement later on.

ADVANTAGES OF THE CHRONOMETER.

We will proceed now to consider briefly the advantages the detent escapement has over all others. It was soon discovered in constructing portable timepieces, that to obtain the best results the vibrations of the balance should be as free as possible from any control or influence except at such times as it received the necessary impulse to maintain the vibrations at a constant arc. This want undoubtedly led to the invention of the detent escapement. The early escapements were all frictional escapements, i.e., the balance staff was never free from the influence of the train. The verge escapement, which was undoubtedly the first employed, was constantly in contact with the escape wheel, and was what is known as a "recoiling beat," that is, the contact of the pallets actually caused the escape wheel to recoil or turn back. Such escapements were too much influenced by the train, and any increase in power caused the timepiece to gain. The first attempt to correct this imperfection led to the invention and introduction of the fusee, which enabled the watchmaker to obtain from a coiled spring nearly equal power during the entire period of action. The next step in advance was the "dead-beat escapement," which included the cylinder and duplex. In these frictional escapements the balance staff locked the train while the balance performed its arc of vibration.

FRICTIONAL ESCAPEMENTS IN HIGH FAVOR.

These frictional escapements held favor with many eminent watchmakers even after the introduction of the detached escapements. It is no more than natural we should inquire, why? The idea with the advocates of the frictional rest escapements was, the friction of the tooth acted as a corrective, and led no doubt to the introduction of going-barrel watches. To illustrate, suppose in a cylinder watch we increase the motive power, such increase of power would not, as in the verge escapement, increase the rapidity of the vibrations; it might, in fact, cause the timepiece to run slower from the increased friction of the escape-wheel tooth on the cylinder; also, in the duplex escapement the friction of the locking tooth on the staff retards the vibrations.

Dr. Hooke, the inventor of the balance spring, soon discovered it could be manipulated to isochronism, i.e., so arcs of different extent would be formed in equal time. Of course, the friction-rest escapement requiring a spring to possess different properties from one which would be isochronal with a perfectly detached escapement, these two frictional escapements also differing, the duplex requiring other properties from what would isochronize a spring for a cylinder escapement. Although pocket watches with duplex and cylinder escapements having balances compensated for heat and cold and balance springs adjusted to isochronism gave very good results, careful makers were satisfied that an escapement in which the balance was detached and free to act during the greater proportion of the arc of vibration and uncontrolled by any cause, would do still better, and this led to the detent escapement.

FAULTS IN THE DETENT ESCAPEMENT.

As stated previously, the detent escapement having pronounced faults in positions which held it back, it is probable it would never have been employed in pocket watches to any extent if it had not acquired such a high reputation in marine chronometers. Let us now analyze the influences which surround the detent escapement in a marine chronometer and take account of the causes which are combined to make it an accurate time measurer, and also take cognizance of other interfering causes which have a tendency to prevent desired results. First, we will imagine a balance with its spring such as we find in fine marine chronometers. It has small pivots running in highly-polished jewels; such pivots are perfectly cylindrical, and no larger than are absolutely necessary to endure the task imposed upon them—of carrying the weight of the balance and endure careful handling.

To afford the necessary vibrations a spring is fitted, usually of a helical form, so disposed as to cause the balance to vibrate in arcs back and forth in equal time, provided these arcs are of equal extent. It is now to be taken note of that we have it at our disposal and option to make these arcs equal in time duration, i.e., to make the long or short arcs the quickest or to synchronize them. We can readily comprehend we have now established a very perfect measure of short intervals of time. We can also see if we provide the means of maintaining these vibrations and counting them we should possess the means of counting the flights of time with great accuracy. The conditions which surround our balance are very constant, the small pivots turning in fine hard jewels lubricated with an oil on which exposure to the action of the air has little effect, leaves but few influences which can interfere with the regular action of our balance. We add to the influences an adjustable correction for the disturbances of heat and cold, and we are convinced that but little could be added.

ANTAGONISTIC INFLUENCES.

In this combination we have pitted two antagonistic forces against each other, viz., the elasticity of the spring and the weight and inertia of the balance; both forces are theoretically constant and should produce constant results. The mechanical part of the problem is simply to afford these two forces perfect facilities to act on each other and compel each to realize its full effect. We must also devise mechanical means to record the duration of each conflict, that is, the time length of each vibration. Many years have been spent in experimenting to arrive at the best propositions to employ for the several parts to obtain the best practical results. Consequently, in designing a chronometer escapement we must not only draw the parts to a certain form, but consider the quality and weight of material to employ.

To illustrate what we have just said, suppose, in drawing an escape wheel, we must not only delineate the proper angle for the acting face of the tooth, but must also take cognizance of the thickness of the tooth. By thickness we mean the measurement of extent of the tooth in the direction of the axis of the escape wheel. An escape-wheel tooth might be of the best form to act in conveying power to the balance and yet by being too thin soon wear or produce excessive friction. How thick an escape wheel should be to produce best results, is one of the many matters settled only by actual workshop experience.

FACTORS THAT MUST BE CONSIDERED.

Even this experience is in every instance modified by other influences. To illustrate: Let us suppose in the ordinary to-day marine chronometer the escape-wheel teeth exerted a given average force, which we set down as so many grains. Now, if we should employ other material than hammer-hardened brass for an escape wheel it would modify the thickness; also, if we should decrease the motive power and increase the arc of impulse. Or, if we should diminish the extent of the impulse arc and add to the motive force, every change would have a controlling influence. In the designs we shall employ, it is our purpose to follow such proportions as have been adopted by our best makers, in all respects, including form, size and material. We would say, however, there has been but little deviation with our principal manufacturers of marine chronometers for the last twenty years as regards the general principle on which they were constructed, the chief aim being to excel in the perfection of the several parts and the care taken in the several adjustments.

Before we proceed to take up the details of constructing a chronometer escapement we had better master the names for the several parts. We show at Fig. 136 a complete plan of a chronometer escapement as if seen from the back, which is in reality the front or dial side of the "top plate." The chronometer escapement consists of four chief or principal parts, viz.: The escape wheel, a portion of which is shown at A; the impulse roller B; unlocking or discharging roller C, and the detent D. These principal parts are made up of sub-parts: thus, the escape wheel is composed of arms, teeth, recess and collet, the recess being the portion of the escape wheel sunk, to enable us to get wide teeth actions on the impulse pallet. The collet is a brass bush on which the wheel is set to afford better support to the escape wheel than could be obtained by the thinned wheel if driven directly on the pinion arbor. The impulse roller is composed of a cylindrical steel collet B, the impulse pallet d (some call it the impulse stone), the safety recess b b. The diameter of the impulse collet is usually one-half that of the escape wheel. This impulse roller is staked directly on the balance staff, and its perfection of position assured by resting against the foot of the shoulder to which the balance is secured. This will be understood by inspecting Fig. 137, which is a vertical longitudinal section of a chronometer balance staff, the lower side of the impulse roller being cupped out at c with a ball grinder and finished a ball polish.



It will be seen the impulse roller is staked flat against the hub E of the balance staff. The unlocking roller, or, as it is also called, the discharging roller, C, is usually thinner than the impulse roller and has a jewel similar to the impulse jewel a shown at f. This roller is fitted by friction to the lower part of the balance staff and for additional security has a pipe or short socket e which embraces the balance staff at g. The pipe e is usually flattened on opposite sides to admit of employing a special wrench for turning the discharging roller in adjusting the jewel for opening the escapement at the proper instant to permit the escape wheel to act on the impulse jewel a. The parts which go to make up the detent D consist of the "detent foot" F, the detent spring h, the detent blade i, the jewel pipe j, the locking jewel (or stone) s, the "horn" of the detent k, the "gold spring" (also called the auxiliary and lifting spring) m. This lifting or gold spring m should be made as light and thin as possible and stand careful handling.

We cannot impress on our readers too much the importance of making a chronometer detent light. Very few detents, even from the hands of our best makers, are as light as they might be. We should in such construction have very little care for clumsy workmen who may have to repair such mechanism. This feature should not enter into consideration.

We should only be influenced by the feeling that we are working for best results, and it is acting under this influence that we devote so much time to establishing a correct idea of the underlying principles involved in a marine chronometer, instead of proceeding directly to the drawing of such an escapement and give empirical rules for the length of this or the diameter of that. As, for instance, in finishing the detent spring h, suppose we read in text books the spring should be reduced in thickness, so that a weight of one pennyweight suspended from the pipe j will deflect the detent 1/4". This is a rule well enough for people employed in a chronometer factory, but for the horological student such fixed rules (even if remembered) would be of small use. What the student requires is sound knowledge of the "whys," in order that he may be able to thoroughly master this escapement.

FUNCTIONS OF THE DETENT.

We can see, after a brief analysis of the principles involved, that the functions required of the detent D are to lock the escape wheel A and hold it while the balance performs its excursion, and that the detent or recovering spring h must have sufficient strength and power to perform two functions: (1) Return the locking stone s back to the proper position to arrest and hold the escape wheel; (2) the spring h must also be able to resist, without buckling or cockling, the thrust of the escape wheel, represented by the arrows p o. Now we can readily understand that the lighter we make the parts i j k m, the weaker the spring h can be. You say, perhaps, if we make it too weak it will be liable to buckle under the pressure of the escape wheel; this, in turn, will depend in a great measure on the condition of the spring h. Suppose we have it straight when we put it in position, it will then have no stress to keep it pressed to the holding, stop or banking screw, which regulates the lock of the tooth. To obtain this stress we set the foot F of the detent around to the position indicated by the dotted lines r and n, and we get the proper tension on the detent spring to effect the lock, or rather of the detent in time to lock the escape wheel; but the spring h, instead of being perfectly straight, is bent and consequently not in a condition to stand the thrust of the escape wheel, indicated by the arrows o p.

OBTAINING THE BEST CONDITIONS.

Now the true way to obtain the best conditions is to give the spring h a set curvature before we put it in place, and then when the detent is in the proper position the spring h will have tension enough on it to bring the jewel s against the stop screw, which regulates the lock, and still be perfectly straight. This matter is of so much importance that we will give further explanation. Suppose we bend the detent spring h so it is curved to the dotted line t, Fig. 136, and then the foot F would assume the position indicated at the dotted line r. We next imagine the foot F to be put in the position shown by the full lines, the spring h will become straight again and in perfect shape to resist the thrust of the escape wheel.

Little "ways and methods" like the above have long been known to the trade, but for some reason are never mentioned in our text books. A detent spring 2/1000" thick and 80/1000" wide will stand the thrust for any well-constructed marine chronometer in existence, and yet it will not require half a pennyweight to deflect it one-fourth of an inch. It is a good rule to make the length of the detent from the foot F to the center of the locking jewel pipe j equal to the diameter of the escape wheel, and the length of the detent spring h two-sevenths of this distance. The length of the horn k is determined by the graphic plan and can be taken from the plotted plan. The end, however, should approach as near to the discharging jewel as possible and not absolutely touch. The discharging (gold) spring m is attached to the blade i of the detent with a small screw l cut in a No. 18 hole of a Swiss plate. While there should be a slight increase in thickness in the detent blade at w, where the gold spring is attached, still it should be no more than to separate the gold spring m from the detent blade i.

IMPORTANT CONSIDERATIONS.

It is important the spring should be absolutely free and not touch the detent except at its point of attachment at w and to rest against the end of the horn k, and the extreme end of k, where the gold spring rests, should only be what we may term a dull or thick edge. The end of the horn k (shown at y) is best made, for convenience of elegant construction, square—that is, the part y turns at right angles to k and is made thicker than k and at the same time deeper; or, to make a comparison to a clumsy article, y is like the head of a nail, which is all on one side. Some makers bend the horn k to a curve and allow the end of the horn to arrest or stop the gold spring; but as it is important the entire detent should be as light as possible, the square end best answers this purpose. The banking placed at j should arrest the detent as thrown back by the spring h at the "point of percussion." This point of percussion is a certain point in a moving mass where the greatest effort is produced and would be somewhere near the point x, in a bar G turning on a pivot at z, Fig. 138. It will be evident, on inspection of this figure, if the bar G was turning on the center z it would not give the hardest impact at the end v, as parts of its force would be expended at the center z.