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   Chapter 2 THE CYLINDER ESCAPEMENT.

Watch and Clock Escapements By Anonymous Characters: 37447

Updated: 2017-12-06 00:03


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.

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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 25-1/2 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.

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