WATCH AND CLOCK ESCAPEMENTS

A Complete Study in Theory and Practice of the Lever, Cylinder and Chronometer Escapements, Together with a Brief Account of the Origin and Evolution of the Escapement in Horology

Compiled from the well-known Escapement Serials published in The Keystone

Nearly Two Hundred Original Illustrations



Published by The Keystone The Organ of the Jewelry and Optical Trades 19th & Brown Sts., Philadelphia, U.S.A.

1904

All Rights Reserved Copyright, 1904, By B. Thorpe, Publisher of the Keystone.



PREFACE

Especially notable among the achievements of The Keystone in the field of horology were the three serials devoted to the lever, cylinder and chronometer escapements. So highly valued were these serials when published that on the completion of each we were importuned to republish it in book form, but we deemed it advisable to postpone such publication until the completion of all three, in order that the volume should be a complete treatise on the several escapements in use in horology. The recent completion of the third serial gave us the opportunity to republish in book form, and the present volume is the result. We present it to the trade and students of horology happy in the knowledge that its contents have already received their approval. An interesting addition to the book is the illustrated story of the escapements, from the first crude conceptions to their present perfection.



CONTENTS

CHAPTER I.

THE DETACHED LEVER ESCAPEMENT 9

CHAPTER II.

THE CYLINDER ESCAPEMENT 111

CHAPTER III.

THE CHRONOMETER ESCAPEMENT 131

CHAPTER IV.

HISTORY OF ESCAPEMENTS 153

CHAPTER V.

PUTTING IN A NEW CYLINDER 169

INDEX 177



WATCH AND CLOCK ESCAPEMENTS



CHAPTER I.

THE DETACHED LEVER ESCAPEMENT.

In this treatise we do not propose to go into the history of this escapement and give a long dissertation on its origin and evolution, but shall confine ourselves strictly to the designing and construction as employed in our best watches. By designing, we mean giving full instructions for drawing an escapement of this kind to the best proportions. The workman will need but few drawing instruments, and a drawing-board about 15" by 18" will be quite large enough. The necessary drawing-instruments are a T-square with 15" blade; a scale of inches divided into decimal parts; two pairs dividers with pen and pencil points—one pair of these dividers to be 5" and the other 6"; one ruling pen. Other instruments can be added as the workman finds he needs them. Those enumerated above, however, will be all that are absolutely necessary.



We shall, in addition, need an arc of degrees, which we can best make for ourselves. To construct one, we procure a piece of No. 24 brass, about 51/2" long by 11/4" wide. We show such a piece of brass at A, Fig. 1. On this piece of brass we sweep two arcs with a pair of dividers set at precisely 5", as shown (reduced) at a a and b b. On these arcs we set off the space held in our dividers—that is 5"—as shown at the short radial lines at each end of the two arcs. Now it is a well-known fact that the space embraced by our dividers contains exactly sixty degrees of the arcs a a and b b, or one-sixth of the entire circle; consequently, we divide the arcs a a and b b into sixty equal parts, to represent degrees, and at one end of these arcs we halve five spaces so we can get at half degrees.



Before we take up the details of drawing an escapement we will say a few words about "degrees," as this seems to be something difficult to understand by most pupils in horology when learning to draw parts of watches to scale. At Fig. 2 we show several short arcs of fifteen degrees, all having the common center g. Most learners seem to have an idea that a degree must be a specific space, like an inch or a foot. Now the first thing in learning to draw an escapement is to fix in our minds the fact that the extent of a degree depends entirely on the radius of the arc we employ. To aid in this explanation we refer to Fig. 2. Here the arcs c, d, e and f are all fifteen degrees, although the linear extent of the degree on the arc c is twice that of the degree on the arc f. When we speak of a degree in connection with a circle we mean the one-three-hundred-and-sixtieth part of the periphery of such a circle. In dividing the arcs a a and b b we first divide them into six spaces, as shown, and each of these spaces into ten minor spaces, as is also shown. We halve five of the degree spaces, as shown at h. We should be very careful about making the degree arcs shown at Fig. 1, as the accuracy of our drawings depends a great deal on the perfection of the division on the scale A. In connection with such a fixed scale of degrees as is shown at Fig. 1, a pair of small dividers, constantly set to a degree space, is very convenient.

MAKING A PAIR OF DIVIDERS.



To make such a pair of small dividers, take a piece of hard sheet brass about 1/20" thick, 1/4" wide, 11/2" long, and shape it as shown at Fig. 3. It should be explained, the part cut from the sheet brass is shown below the dotted line k, the portion above (C) being a round handle turned from hard wood or ivory. The slot l is sawn in, and two holes drilled in the end to insert the needle points i i. In making the slot l we arrange to have the needle points come a little too close together to agree with the degree spaces on the arcs a a and b b. We then put the small screw j through one of the legs D'', and by turning j, set the needle points i i to exactly agree with the degree spaces. As soon as the points i i are set correctly, j should be soft soldered fast.

The degree spaces on A are set off with these dividers and the spaces on A very carefully marked. The upper and outer arc a a should have the spaces cut with a graver line, while the lower one, b b is best permanently marked with a carefully-made prick punch. After the arc a a is divided, the brass plate A is cut back to this arc so the divisions we have just made are on the edge. The object of having two arcs on the plate A is, if we desire to get at the number of degrees contained in any arc of a 5" radius we lay the scale A so the edge agrees with the arc a a, and read off the number of degrees from the scale. In setting dividers we employ the dotted spaces on the arc b b.

DELINEATING AN ESCAPE WHEEL.



We will now proceed to delineate an escape wheel for a detached lever. We place a piece of good drawing-paper on our drawing-board and provide ourselves with a very hard (HHH) drawing-pencil and a bottle of liquid India ink. After placing our paper on the board, we draw, with the aid of our T-square, a line through the center of the paper, as shown at m m, Fig. 4. At 51/2" from the lower margin of the paper we establish the point p and sweep the circle n n with a radius of 5". We have said nothing about stretching our paper on the drawing-board; still, carefully-stretched paper is an important part of nice and correct drawing. We shall subsequently give directions for properly stretching paper, but for the present we will suppose the paper we are using is nicely tacked to the face of the drawing-board with the smallest tacks we can procure. The paper should not come quite to the edge of the drawing-board, so as to interfere with the head of the T-square. We are now ready to commence delineating our escape wheel and a set of pallets to match.

The simplest form of the detached lever escapement in use is the one known as the "ratchet-tooth lever escapement," and generally found in English lever watches. This form of escapement gives excellent results when well made; and we can only account for it not being in more general use from the fact that the escape-wheel teeth are not so strong and capable of resisting careless usage as the club-tooth escape wheel.

It will be our aim to convey broad ideas and inculcate general principles, rather than to give specific instructions for doing "one thing one way." The ratchet-tooth lever escapements of later dates have almost invariably been constructed on the ten-degree lever-and-pallet-action plan; that is, the fork and pallets were intended to act through this arc. Some of the other specimens of this escapement have larger arcs—some as high as twelve degrees.

PALLET-AND-FORK ACTION.



We illustrate at Fig. 5 what we mean by ten degrees of pallet-and-fork action. If we draw a line through the center of the pallet staff, and also through the center of the fork slot, as shown at a b, Fig. 5, and allow the fork to vibrate five degrees each side of said lines a b, to the lines a c and a c', the fork has what we term ten-degree pallet action. If the fork and pallets vibrate six degrees on each side of the line a b—that is, to the lines a d and a d'—we have twelve degrees pallet action. If we cut the arc down so the oscillation is only four and one-quarter degrees on each side of a b, as indicated by the lines a s and a s', we have a pallet-and-fork action of eight and one-half degrees; which, by the way, is a very desirable arc for a carefully-constructed escapement.

The controlling idea which would seem to rule in constructing a detached lever escapement, would be to make it so the balance is free of the fork; that is, detached, during as much of the arc of the vibration of the balance as possible, and yet have the action thoroughly sound and secure. Where a ratchet-tooth escapement is thoroughly well-made of eight and one-half degrees of pallet-and-fork action, ten and one-half degrees of escape-wheel action can be utilized, as will be explained later on.

We will now resume the drawing of our escape wheel, as illustrated at Fig. 4. In the drawing at Fig. 6 we show the circle n n, which represents the periphery of our escape wheel; and in the drawing we are supposed to be drawing it ten inches in diameter.

We produce the vertical line m passing through the center p of the circle n. From the intersection of the circle n with the line m at i we lay off thirty degrees on each side, and establish the points e f; and from the center p, through these points, draw the radial lines p e' and p f'. The points f e, Fig. 6, are, of course, just sixty degrees apart and represent the extent of two and one-half teeth of the escape wheel. There are two systems on which pallets for lever escapements are made, viz., equidistant lockings and circular pallets. The advantages claimed for each system will be discussed subsequently. For the first and present illustration we will assume we are to employ circular pallets and one of the teeth of the escape wheel resting on the pallet at the point f; and the escape wheel turning in the direction of the arrow j. If we imagine a tooth as indicated at the dotted outline at D, Fig. 6, pressing against a surface which coincides with the radial line p f, the action would be in the direction of the line f h and at right angles to p f. If we reason on the action of the tooth D, as it presses against a pallet placed at f, we see the action is neutral.



ESTABLISHING THE CENTER OF PALLET STAFF.



With a fifteen-tooth escape wheel each tooth occupies twenty-four degrees, and from the point f to e would be two and one-half tooth-spaces. We show the dotted points of four teeth at D D' D''D'''. To establish the center of the pallet staff we draw a line at right angles to the line p e' from the point e so it intersects the line f h at k. For drawing a line at right angles to another line, as we have just done, a hard-rubber triangle, shaped as shown at C, Fig. 7, can be employed. To use such a triangle, we place it so the right, or ninety-degrees angle, rests at e, as shown at the dotted triangle C, Fig. 6, and the long side coincides with the radial line p e'. If the short side of the hard-rubber triangle is too short, as indicated, we place a short ruler so it rests against the edge, as shown at the dotted line g e, Fig. 7, and while holding it securely down on the drawing we remove the triangle, and with a fine-pointed pencil draw the line e g, Fig. 6, by the short rule. Let us imagine a flat surface placed at e so its face was at right angles to the line g e, which would arrest the tooth D'' after the tooth D resting on f had been released and passed through an arc of twelve degrees. A tooth resting on a flat surface, as imagined above, would also rest dead. As stated previously, the pallets we are considering have equidistant locking faces and correspond to the arc l l, Fig. 6.

In order to realize any power from our escape-wheel tooth, we must provide an impulse face to the pallets faced at f e; and the problem before us is to delineate these pallets so that the lever will be propelled through an arc of eight and one-half degrees, while the escape wheel is moving through an arc of ten and one-half degrees. We make the arc of fork action eight and one-half degrees for two reasons—(1) because most text-books have selected ten degrees of fork-and-pallet action; (2) because most of the finer lever escapements of recent construction have a lever action of less than ten degrees.

LAYING OUT ESCAPE-WHEEL TEETH.

To "lay out" or delineate our escape-wheel teeth, we continue our drawing shown at Fig. 6, and reproduce this cut very nearly at Fig. 8. With our dividers set at five inches, we sweep the short arc a a' from f as a center. It is to be borne in mind that at the point f is located the extreme point of an escape-wheel tooth. On the arc a a we lay off from p twenty-four degrees, and establish the point b; at twelve degrees beyond b we establish the point c. From f we draw the lines f b and f c; these lines establishing the form and thickness of the tooth D. To get the length of the tooth, we take in our dividers one-half a tooth space, and on the radial line p f establish the point d and draw circle d' d'.

To facilitate the drawing of the other teeth, we draw the circles d' c', to which the lines f b and f c are tangent, as shown. We divide the circle n n, representing the periphery of our escape wheel, into fifteen spaces, to represent teeth, commencing at f and continued as shown at o o until the entire wheel is divided. We only show four teeth complete, but the same methods as produced these will produce them all. To briefly recapitulate the instructions for drawing the teeth for the ratchet-tooth lever escapement: We draw the face of the teeth at an angle of twenty-four degrees to a radial line; the back of the tooth at an angle of thirty-six degrees to the same radial line; and make teeth half a tooth-space deep or long.



We now come to the consideration of the pallets and how to delineate them. To this we shall add a careful analysis of their action. Let us, before proceeding further, "think a little" over some of the factors involved. To aid in this thinking or reasoning on the matter, let us draw the heavy arc l extending from a little inside of the circle n at f to the circle n at e. If now we imagine our escape wheel to be pressed forward in the direction of the arrow j, the tooth D would press on the arc l and be held. If, however, we should revolve the arc l on the center k in the direction of the arrow i, the tooth D would escape from the edge of l and the tooth D'' would pass through an arc (reckoning from the center p) of twelve degrees, and be arrested by the inside of the arc l at e. If we now should reverse the motion and turn the arc l backward, the tooth at e would, in turn, be released and the tooth following after D (but not shown) would engage l at f. By supplying motive to revolve the escape wheel (E) represented by the circle n, and causing the arc l to oscillate back and forth in exact intervals of time, we should have, in effect, a perfect escapement. To accomplish automatically such oscillations is the problem we have now on hand.

HOW MOTION IS OBTAINED.

In clocks, the back-and-forth movement, or oscillating motion, is obtained by employing a pendulum; in a movable timepiece we make use of an equally-poised wheel of some weight on a pivoted axle, which device we term a balance; the vibrations or oscillations being obtained by applying a coiled spring, which was first called a "pendulum spring," then a "balance spring," and finally, from its diminutive size and coil form, a "hairspring." We are all aware that for the motive power for keeping up the oscillations of the escaping circle l we must contrive to employ power derived from the teeth D of the escape wheel. About the most available means of conveying power from the escape wheel to the oscillating arc l is to provide the lip of said arc with an inclined plane, along which the tooth which is disengaged from l at f to slide and move said arc l through—in the present instance an arc of eight and one-half degrees, during the time the tooth D is passing through ten and one-half degrees. This angular motion of the arc l is represented by the radial lines k f' and k r, Fig. 8. We desire to impress on the reader's mind the idea that each of these angular motions is not only required to be made, but the motion of one mobile must convey power to another mobile.

In this case the power conveyed from the mainspring to the escape wheel is to be conveyed to the lever, and by the lever transmitted to the balance. We know it is the usual plan adopted by text-books to lay down a certain formula for drawing an escapement, leaving the pupil to work and reason out the principles involved in the action. In the plan we have adopted we propose to induct the reader into the why and how, and point out to him the rules and methods of analysis of the problem, so that he can, if required, calculate mathematically exactly how many grains of force the fork exerts on the jewel pin, and also how much (or, rather, what percentage) of the motive power is lost in various "power leaks," like "drop" and lost motion. In the present case the mechanical result we desire to obtain is to cause our lever pivoted at k to vibrate back and forth through an arc of eight and one-half degrees; this lever not only to vibrate back and forth, but also to lock and hold the escape wheel during a certain period of time; that is, through the period of time the balance is performing its excursion and the jewel pin free and detached from the fork.

We have spoken of paper being employed for drawings, but for very accurate delineations we would recommend the horological student to make drawings on a flat metal plate, after perfectly smoothing the surface and blackening it by oxidizing.

PALLET-AND-FORK ACTION.

By adopting eight and one-half degrees pallet-and-fork action we can utilize ten and one-half degrees of escape-wheel action. We show at A A', Fig. 9, two teeth of a ratchet-tooth escape wheel reduced one-half; that is, the original drawing was made for an escape wheel ten inches in diameter. We shall make a radical departure from the usual practice in making cuts on an enlarged scale, for only such parts as we are talking about. To explain, we show at Fig. 10 about one-half of an escape wheel one eighth the size of our large drawing; and when we wish to show some portion of such drawing on a larger scale we will designate such enlargement by saying one-fourth, one-half or full size.



At Fig. 9 we show at half size that portion of our escapement embraced by the dotted lines d, Fig. 10. This plan enables us to show very minutely such parts as we have under consideration, and yet occupy but little space. The arc a, Fig. 9, represents the periphery of the escape wheel. On this line, ten and one-half degrees from the point of the tooth A, we establish the point c and draw the radial line c c'. It is to be borne in mind that the arc embraced between the points b and c represents the duration of contact between the tooth A and the entrance pallet of the lever. The space or short arc c n represents the "drop" of the tooth.

This arc of one and one-half degrees of escape-wheel movement is a complete loss of six and one-fourth per cent. of the entire power of the mainspring, as brought down to the escapement; still, up to the present time, no remedy has been devised to overcome it. All the other escapements, including the chronometer, duplex and cylinder, are quite as wasteful of power, if not more so. It is usual to construct ratchet-tooth pallets so as to utilize but ten degrees of escape-wheel action; but we shall show that half a degree more can be utilized by adopting the eight and one-half degree fork action and employing a double-roller safety action to prevent over-banking.



From the point e, which represents the center of the pallet staff, we draw through b the line e f. At one degree below e f we draw the line e g, and seven and one-half degrees below the line e g we draw the line e h. For delineating the lines e g, etc., correctly, we employ a degree-arc; that is, on the large drawing we are making we first draw the line e b f, Fig. 10, and then, with our dividers set at five inches, sweep the short arc i, and on this lay off first one degree from the intersection of f e with the arc i, and through this point draw the line e g.

From the intersection of the line f e with the arc i we lay off eight and one-half degrees, and through this point draw the line e h. Bear in mind that we are drawing the pallet at B to represent one with eight and one-half degrees fork-and-pallet action, and with equidistant lockings. If we reason on the matter under consideration, we will see the tooth A and the pallet B, against which it acts, part or separate when the tooth arrives at the point c; that is, after the escape wheel has moved through ten and one-half degrees of angular motion, the tooth drops from the impulse face of the pallet and falls through one and one-half degrees of arc, when the tooth A'', Fig. 10, is arrested by the exit pallet.

To locate the position of the inner angle of the pallet B, sweep the short arc l by setting the dividers so one point or leg rests at the center e and the other at the point c. Somewhere on this arc l is to be located the inner angle of our pallet. In delineating this angle, Moritz Grossman, in his "Prize Essay on the Detached Lever Escapement," makes an error, in Plate III of large English edition, of more than his entire lock, or about two degrees. We make no apologies for calling attention to this mistake on the part of an authority holding so high a position on such matters as Mr. Grossman, because a mistake is a mistake, no matter who makes it.

We will say no more of this error at present, but will farther on show drawings of Mr. Grossman's faulty method, and also the correct method of drawing such a pallet. To delineate the locking face of our pallet, from the point formed by the intersection of the lines e g b b', Fig. 9, as a center, we draw the line j at an angle of twelve degrees to b b''. In doing this we employ the same method of establishing the angle as we made use of in drawing the lines e g and e h, Fig. 10. The line j establishes the locking face of the pallet B. Setting the locking face of the pallet at twelve degrees has been found in practice to give a safe "draw" to the pallet and keep the lever secure against the bank. It will be remembered the face of the escape-wheel tooth was drawn at twenty-four degrees to a radial line of the escape wheel, which, in this instance, is the line b b', Fig. 9. It will now be seen that the angle of the pallet just halves this angle, and consequently the tooth A only rests with its point on the locking face of the pallet. We do not show the outlines of the pallet B, because we have not so far pointed out the correct method of delineating it.

METHODS OF MAKING GOOD DRAWING INSTRUMENTS.

Perhaps we cannot do our readers a greater favor than to digress from the study of the detached lever escapement long enough to say a few words about drawing instruments and tablets or surfaces on which to delineate, with due precision, mechanical designs or drawings. Ordinary drawing instruments, even of the higher grades, and costing a good deal of money, are far from being satisfactory to a man who has the proper idea of accuracy to be rated as a first-class mechanic. Ordinary compasses are obstinate when we try to set them to the hundredth of an inch; usually the points are dull and ill-shapen; if they make a puncture in the paper it is unsightly.

Watchmakers have one advantage, however, because they can very easily work over a cheap set of drawing instruments and make them even superior to anything they can buy at the art stores. To illustrate, let us take a cheap pair of brass or German-silver five-inch dividers and make them over into needle points and "spring set." To do this the points are cut off at the line a a, Fig 11, and a steel tube is gold-soldered on each leg. The steel tube is made by taking a piece of steel wire which will fit a No. 16 chuck of a Whitcomb lathe, and drilling a hole in the end about one-fourth of an inch deep and about the size of a No. 3 sewing needle. We Show at Fig. 12 a view of the point A', Fig. 11, enlarged, and the steel tube we have just drilled out attached at C. About the best way to attach C is to solder. After the tube C is attached a hole is drilled through A' at d, and the thumb-screw d inserted. This thumb-screw should be of steel, and hardened and tempered. The use of this screw is to clamp the needle point. With such a device as the tube C and set-screw d, a No. 3 needle is used for a point; but for drawings on paper a turned point, as shown at Fig 13, is to be preferred. Such points can be made from a No. 3 needle after softening enough to be turned so as to form the point c. This point at the shoulder f should be about 12/1000 of an inch, or the size of a fourth-wheel pivot to an eighteen size movement.



The idea is, when drawing on paper the point c enters the paper. For drawing on metal the form of the point is changed to a simple cone, as shown at B' c, Fig. 13. such cones can be turned carefully, then hardened and tempered to a straw color; and when they become dull, can be ground by placing the points in a wire chuck and dressing them up with an emery buff or an Arkansas slip. The opposite leg of the dividers is the one to which is attached the spring for close setting of the points.

In making this spring, we take a piece of steel about two and one-fourth inches long and of the same width as the leg of the divider, and attach it to the inside of the leg as shown at Fig. 14, where D represents the spring and A the leg of the dividers. The spring D has a short steel tube C'' and set-screw d'' for a fine point like B or B'. In the lower end of the leg A, Fig. 14, is placed the milled-head screw g, which serves to adjust the two points of the dividers to very close distances. The spring D is, of course, set so it would press close to the leg A if the screw g did not force it away.

SPRING AND ADJUSTING SCREW FOR DRAWING INSTRUMENTS.



It will be seen that we can apply a spring D and adjusting screw opposite to the leg which carries the pen or pencil point of all our dividers if we choose to do so; but it is for metal drawing that such points are of the greatest advantage, as we can secure an accuracy very gratifying to a workman who believes in precision. For drawing circles on metal, "bar compasses" are much the best, as they are almost entirely free from spring, which attends the jointed compass. To make (because they cannot be bought) such an instrument, take a piece of flat steel, one-eighth by three-eighths of an inch and seven inches long, and after turning and smoothing it carefully, make a slide half an inch wide, as shown at Fig. 15, with a set-screw h on top to secure it at any point on the bar E. In the lower part of the slide F is placed a steel tube like C, shown in Figs. 12 and 14, with set-screw for holding points like B B', Fig. 13. At the opposite end of the bar E is placed a looped spring G, which carries a steel tube and point like the spring D, Fig. 14. Above this tube and point, shown at j, Fig. 15, is placed an adjustment screw k for fine adjustment. The inner end of the screw k rests against the end of the bar E. The tendency of the spring G is to close upon the end of E; consequently if we make use of the screw k to force away the lower end of G, we can set the fine point in j to the greatest exactness.

The spring G is made of a piece of steel one-eighth of an inch square, and secured to the bar E with a screw and steady pins at m. A pen and pencil point attachment can be added to the spring G; but in case this is done it would be better to make another spring like G without the point j, and with the adjusting screw placed at l. In fitting pen and pencil points to a spring like G it would probably be economical to make them outright; that is, make the blades and screw for the ruling pen and a spring or clamping tube for the pencil point.

CONSIDERATION OF DETACHED LEVER ESCAPEMENT RESUMED.

We will now, with our improved drawing instruments, resume the consideration of the ratchet-tooth lever escapement. We reproduce at Fig. 16 a portion of diagram III, from Moritz Grossmann's "Prize Essay on the Detached Lever Escapement," in order to point out the error in delineating the entrance pallet to which we previously called attention. The cut, as we give it, is not quite one-half the size of Mr. Grossmann's original plate.

In the cut we give the letters of reference employed the same as on the original engraving, except where we use others in explanation. The angular motion of the lever and pallet action as shown in the cut is ten degrees; but in our drawing, where we only use eight and one-half degrees, the same mistake would give proportionate error if we did not take the means to correct it. The error to which we refer lies in drawing the impulse face of the entrance pallet. The impulse face of this pallet as drawn by Mr. Grossmann would not, from the action of the engaging tooth, carry this pallet through more than eight degrees of angular motion; consequently, the tooth which should lock on the exit pallet would fail to do so, and strike the impulse face.

We would here beg to add that nothing will so much instruct a person desiring to acquire sound ideas on escapements as making a large model. The writer calls to mind a wood model of a lever escapement made by one of the "boys" in the Elgin factory about a year or two after Mr. Grossmann's prize essay was published. It went from hand to hand and did much toward establishing sound ideas as regards the correct action of the lever escapement in that notable concern.

If a horological student should construct a large model on the lines laid down in Mr. Grossmann's work, the entrance pallet would be faulty in form and would not properly perform its functions. Why? perhaps says our reader. In reply let us analyze the action of the tooth B as it rests on the pallet A. Now, if we move this pallet through an angular motion of one and one-half degrees on the center g (which also represents the center of the pallet staff), the tooth B is disengaged from the locking face and commences to slide along the impulse face of the pallet and "drops," that is, falls from the pallet, when the inner angle of the pallet is reached.



This inner angle, as located by Mr. Grossmann, is at the intersection of the short arc i with the line g n, which limits the ten-degree angular motion of the pallets. If we carefully study the drawing, we will see the pallet has only to move through eight degrees of angular motion of the pallet staff for the tooth to escape, because the tooth certainly must be disengaged when the inner angle of the pallet reaches the peripheral line a. The true way to locate the position of the inner angle of the pallet, is to measure down on the arc i ten degrees from its intersection with the peripheral line a and locate a point to which a line is drawn from the intersection of the line g m with the radial line a c, thus defining the inner angle of the entrance pallet. We will name this point the point x.

It may not be amiss to say the arc i is swept from the center g through the point u, said point being located ten degrees from the intersection of the radial a c with the peripheral line a. It will be noticed that the inner angle of the entrance pallet A seems to extend inward, beyond the radial line a j, that is, toward the pallet center g, and gives the appearance of being much thicker than the exit pallet A'; but we will see on examination that the extreme angle x of the entrance pallet must move on the arc i and, consequently, cross the peripheral line a at the point u. If we measure the impulse faces of the two pallets A A', we will find them nearly alike in linear extent.

Mr. Grossmann, in delineating his exit pallet, brings the extreme angle (shown at 4) down to the periphery of the escape, as shown in the drawing, where it extends beyond the intersection of the line g f with the radial line a 3. The correct form for the entrance pallet should be to the dotted line z x y.



We have spoken of engaging and disengaging frictions; we do not know how we can better explain this term than by illustrating the idea with a grindstone. Suppose two men are grinding on the same stone; each has, say, a cold chisel to grind, as shown at Fig. 17, where G represents the grindstone and N N' the cold chisels. The grindstone is supposed to be revolving in the direction of the arrow. The chisels N and N' are both being ground, but the chisel N' is being cut much the more rapidly, as each particle of grit of the stone as it catches on the steel causes the chisel to hug the stone and bite in deeper and deeper; while the chisel shown at N is thrust away by the action of the grit. Now, friction of any kind is only a sort of grinding operation, and the same principles hold good.

THE NECESSITY FOR GOOD INSTRUMENTS.

It is to be hoped the reader who intends to profit by this treatise has fitted up such a pair of dividers as those we have described, because it is only with accurate instruments he can hope to produce drawings on which any reliance can be placed. The drawing of a ratchet-tooth lever escapement of eight and one-half degrees pallet action will now be resumed. In the drawing at Fig. 18 is shown a complete delineation of such an escapement with eight and one-half degrees of pallet action and equidistant locking faces. It is, of course, understood the escape wheel is to be drawn ten inches in diameter, and that the degree arcs shown in Fig. 1 will be used.

We commence by carefully placing on the drawing-board a sheet of paper about fifteen inches square, and then vertically through the center draw the line a' a''. At some convenient position on this line is established the point a, which represents the center of the escape wheel. In this drawing it is not important that the entire escape wheel be shown, inasmuch as we have really to do with but a little over sixty degrees of the periphery of the escape wheel. With the dividers carefully set at five inches, from a, as a center, we sweep the arc n n, and from the intersection of the perpendicular line a' a'' with the arc n we lay off on each side thirty degrees from the brass degree arc, and through the points thus established are drawn the radial lines a b' and a d'.



The point on the arc n where it intersects with the line b' is termed the point b. At the intersection of the radial line a d' is established the point d. We take ten and one-half degrees in the dividers, and from the point b establish the point c, which embraces the arc of the escape wheel which is utilized by the pallet action. Through the point b the line h' h is drawn at right angles to the line a b'. The line j j' is also drawn at right angles to the line a d' through the point d. We now have an intersection of the lines just drawn in common with the line a a' at the point g, said point indicating the center of the pallet action.

The dividers are now set to embrace the space between the points b and g on the line h' h, and the arc f f is swept; which, in proof of the accuracy of the work, intersects the arc n at the point d. This arc coincides with the locking faces of both pallets. To lay out the entrance pallet, the dividers are set to five inches, and from g as a center the short arc o o is swept. On this arc one degree is laid off below the line h' h, and the line g i drawn. The space embraced between the lines h and i on the arc f represents the locking face of the entrance pallet, and the point formed at the intersection of the line g i with the arc f is called the point p. To give the proper lock to the face of the pallet, from the point p as a center is swept the short arc r r, and from its intersection with the line a b' twelve degrees are laid off and the line b s drawn, which defines the locking face of the entrance pallet. From g as a center is swept the arc c' c', intersecting the arc n n at c. On this arc (c) is located the inner angle of the entrance pallet. The dividers are set to embrace the space on the arc c' between the lines g h' and g k. With this space in the dividers one leg is set at the point c, measuring down on the arc c' and establishing the point t. The points p and t are then connected, and thus the impulse face of the entrance pallet B is defined. From the point t is drawn the line t t', parallel to the line b s, thus defining the inner face of the entrance pallet.

DELINEATING THE EXIT PALLET.

To delineate the exit pallet, sweep the short arc u u (from g as a center) with the dividers set at five inches, and from the intersection of this arc with the line g j' set off eight and one-half degrees and draw the line g l. At one degree below this line is drawn the line g m. The space on the arc f between these lines defines the locking face of the exit pallet. The point where the line g m intersects the arc f is named the point x. From the point x is erected the line x w, perpendicular to the line g m. From x as a center, and with the dividers set at five inches, the short arc y y is swept, and on this arc are laid off twelve degrees, and the line x z is drawn, which line defines the locking face of the exit pallet.

Next is taken ten and one-half degrees from the brass degree-scale, and from the point d on the arc n the space named is laid off, and thus is established the point v; and from g as a center is swept the arc v' v' through the point v. It will be evident on a little thought, that if the tooth A' impelled the exit pallet to the position shown, the outer angle of the pallet must extend down to the point v, on the arc v' v'; consequently, we define the impulse face of this pallet by drawing a line from point x to v. To define the outer face of the exit pallet, we draw the line v e parallel to the line x z.

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

DELINEATING CIRCULAR PALLETS.

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

We erect from the point a a perpendicular to the line A a, and, as previously explained, establish the pallet center at B. Inasmuch as we are to employ circular pallets, we lay off to the left on the arc m, from the point a, five degrees, said five degrees being half of the angular motion of the escape wheel utilized in the present drawing, and thus establish the point c, and from A as a center draw through this point the radial line A c'. To the right of the point a we lay off five degrees and establish the point d. To illustrate the underlying principle of our circular pallets: with one leg of the dividers set at B we sweep through the points c a d the arcs c'' a'' d''.

From B as a center, we continue the line B a to f, and with the dividers set at five inches, sweep the short arc e e. From the intersection of this arc with the line B f we lay off one and a half degrees and draw the line B g, which establishes the extent of the lock on the entrance pallet. It will be noticed the linear extent of the locking face of the entrance pallet is greater than that of the exit, although both represent an angle of one and a half degrees. Really, in practice, this discrepancy is of little importance, as the same side-shake in banking would secure safety in either case.



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

THE AMOUNT OF LOCK.

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

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

ADVANTAGE OF MAKING LARGE DRAWINGS.

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

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

THE CLUB-TOOTH LEVER ESCAPEMENT.

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

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

It will be noticed that the pallets here are comparatively thin to those in general use; this condition is accomplished by deriving the principal part of the impulse from driving planes placed on the teeth. As relates to the escape-wheel action of the ten and one-half degrees, which gives impulse to the escapement, five and one-half degrees are utilized by the driving planes on the teeth and five by the impulse face of the pallet. Of the ten degrees of fork action, four and a half degrees relate to the impulse face of the teeth, one and a half degrees to lock, and four degrees to the driving plane of the pallets.

In delineating such a club-tooth escapement, we commence, as in former examples, by first assuming the center of the escape wheel at A, and with the dividers set at five inches sweeping the arc a a. Through A we draw the vertical line A B'. On the arc a a, and each side of its intersection with the line A B', we lay off thirty degrees, as in former drawings, and through the points so established on the arc a a we draw the radial lines A b and A c. From the intersection of the radial line A b with the arc a we draw the line h h at right angles to A b. Where the line h intersects the radial lines A B' is located the center of the pallet staff, as shown at B. Inasmuch as we decided to let the pallet utilize five degrees of escape-wheel action, we take a space of two and a half degrees in the dividers, and on the arc a a lay off the said two and a half degrees to the left of this intersection, and through the point so established draw the radial line A g. From B as a center we sweep the arc d d so it passes through the point of intersection of the arc a with the line A g.



We again lay off two and a half degrees from the intersection of the line A b with the arc a, but this time to the right of said intersection, and through the point so established, and from B as a center, we sweep the arc e. From the intersection of the radial line A g with the arc a we lay off to the left five and a half degrees on said arc, and through the point so established draw the radial line A f. With the dividers set at five inches we sweep the short arc m from B as a center. From the intersection of the line h B h' with the arc m we lay off on said arc and above the line h' four and a half degrees, and through the point so established draw the line B j.

We next set the dividers so they embrace the space on the radial line A b between its intersection with the line B j and the center A, and from A as a center sweep the arc i, said arc defining the addendum of the escape-wheel teeth. We draw a line from the intersection of the radial line A f with the arc i to the intersection of the radial line A g with the arc a, and thus define the impulse face of the escape-wheel tooth D. For defining the locking face of the tooth we draw a line at an angle of twenty-four degrees to the line A g, as previously described. The back of the tooth is defined with a curve swept from some point on the addendum circle i, such as our judgment will dictate.

In the drawing shown at Fig. 20 the radius of this curve was obtained by taking eleven and a half degrees from the degree arc of 5" radius in the dividers, and setting one leg at the intersection of the radial line A f with the arc i, and placing the other on the line i, and allowing the point so established to serve as a center, the arc was swept for the back of the tooth, the small circle at n denoting one of the centers just described. The length for the face of the tooth was obtained by taking eleven degrees from the degree arc just referred to and laying that space off on the line p, which defined the face of the tooth. The line B k is laid off one and a half degrees below B h on the arc m. The extent of this arc on the arc d defines the locking face of the entrance pallet. We set off four degrees on the arc m below the line B k, and through the point so established draw the line B l. We draw a line from the intersection of the line A g with the line c h to the intersection of the arc e with the line c l, and define the impulse face of the entrance pallet.

RELATIONS OF THE SEVERAL PARTS.

Before we proceed to delineate the exit pallet of our escapement, let us reason on the relations of the several parts.

The club-tooth lever escapement is really the most complicated escapement made. We mean by this that there are more factors involved in the problem of designing it correctly than in any other known escapement. Most—we had better say all, for there are no exceptions which occur to us—writers on the lever escapement lay down certain empirical rules for delineating the several parts, without giving reasons for this or that course. For illustration, it is an established practice among escapement makers to employ tangential lockings, as we explained and illustrated in Fig. 16.

Now, when we adopt circular pallets and carry the locking face of the entrance pallet around to the left two and a half degrees, the true center for the pallet staff, if we employ tangent lockings, would be located on a line drawn tangent to the circle a a from its intersection with the radial line A k, Fig. 21. Such a tangent is depicted at the line s l'. If we reason on the situation, we will see that the line A k is not at right angles to the line s l; and, consequently, the locking face of the entrance pallet E has not really the twelve-degree lock we are taught to believe it has.



We will not discuss these minor points further at present, but leave them for subsequent consideration. We will say, however, that we could locate the center of the pallet action at the small circle B' above the center B, which we have selected as our fork-and-pallet action, and secure a perfectly sound escapement, with several claimed advantages.

Let us now take up the delineation of the exit pallet. It is very easy to locate the outer angle of this pallet, as this must be situated at the intersection of the addendum circle i and the arc g, and located at o. It is also self-evident that the inner or locking angle must be situated at some point on the arc h. To determine this location we draw the line B c from B (the pallet center) through the intersection of the arc h with the pitch circle a.

Again, it follows as a self-evident fact, if the pallet we are dealing with was locked, that is, engaged with the tooth D'', the inner angle n of the exit pallet would be one and a half degrees inside the pitch circle a. With the dividers set at 5", we sweep the short arc b b, and from the intersection of this arc with the line B c we lay off ten degrees, and through the point so established, from B, we draw the line B d. Below the point of intersection of the line B d with the short arc b b we lay off one and a half degrees, and through the point thus established we draw the line B e.

LOCATING THE INNER ANGLE OF THE EXIT PALLET.

The intersection of the line B e with the arc h, which we will term the point n, represents the location of the inner angle of the exit pallet. We have already explained how we located the position of the outer angle at o. We draw the line n o and define the impulse face of the exit pallet. If we mentally analyze the problem in hand, we will see that as the exit pallet vibrates through its ten degrees of arc the line B d and B c change places, and the tooth D'' locks one and a half degrees. To delineate the locking face of the exit pallet, we erect a perpendicular to the line B e from the point n, as shown by the line n p.

From n as a center we sweep the short arc t t, and from its intersection with the line n p we lay off twelve degrees, and through the point so established we draw the line n u, which defines the locking face of the exit pallet. We draw the line o o' parallel with n u and define the outer face of said pallet. In Fig. 21 we have not made any attempt to show the full outline of the pallets, as they are delineated in precisely the same manner as those previously shown.

We shall next describe the delineation of a club-tooth escapement with pallets having equidistant locking faces; and in Fig. 22 we shall show pallets with much wider arms, because, in this instance, we shall derive more of the impulse from the pallets than from the teeth. We do this to show the horological student the facility with which the club-tooth lever escapement can be manipulated. We wish also to impress on his mind the facts that the employment of thick pallet arms and thin pallet arms depends on the teeth of the escape wheel for its efficiency, and that he must have knowledge enough of the principles of action to tell at a glance on what lines the escapement was constructed.

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

CLUB-TOOTH LEVER WITH EQUIDISTANT LOCKING FACES.

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

From the intersection of the radial line A b with the arc a lay off three and a half degrees to the left of said intersection on the arc a, and through the point so established draw the radial line A e. From the intersection of the radial line A b with the arc a erect the perpendicular line f, and at the crossing or intersection of said line with the vertical line A k establish the center of the pallet staff, as indicated by the small circle B. From B as a center sweep the short arc l with a 5" radius; and from the intersection of the radial line A b with the arc a continue the line f until it crosses the short arc l, as shown at f'. Lay off one and a half degrees on the arc l below its intersection with the line f', and from B as a center draw the line B i through said intersection. From B as a center, through the intersection of the radial line A b and the arc a, sweep the arc g.

The space between the lines B f' and B i on the arc g defines the extent of the locking face of the entrance pallet C. The intersection of the line B f' with the arc g we denominate the point o, and from this point as a center sweep the short arc p with a 5" radius; and on this arc, from its intersection with the radial line A b, lay off twelve degrees, and through the point so established, from o as a center, draw the radial line o m, said line defining the locking face of the entrance pallet C.



It will be seen that this gives a positive "draw" of twelve degrees to the entrance pallet; that is, counting to the line B f'. In this escapement as delineated there is perfect tangential locking. If the locking face of the entrance-pallet stone at C was made to conform to the radial line A b, the lock of the tooth D at o would be "dead"; that is, absolutely neutral. The tooth D would press the pallet C in the direction of the arrow x, toward the center of the pallet staff B, with no tendency on the part of the pallet to turn on its axis B. Theoretically, the pallet with the locking face cut to coincide with the line A b would resist movement on the center B in either direction indicated by the double-headed arrow y.

A pallet at C with a circular locking face made to conform to the arc g, would permit movement in the direction of the double-headed arrow y with only mechanical effort enough to overcome friction. But it is evident on inspection that a locking face on the line A b would cause a retrograde motion of the escape wheel, and consequent resistance, if said pallet was moved in either direction indicated by the double-headed arrow y. Precisely the same conditions obtain at the point u, which holds the same relations to the exit pallet as the point o does to the entrance pallet C.

ANGULAR MOTION OF ESCAPE WHEEL DETERMINED.

The arc (three and a half degrees) of the circle a embraced between the radial lines A b and A e determines the angular motion of the escape wheel utilized by the escape-wheel tooth. To establish and define the extent of angular motion of the escape wheel utilized by the pallet, we lay off seven degrees on the arc a from the point o and establish the point n, and through the point n, from B as a center, we sweep the short arc n'. Now somewhere on this arc n' will be located the inner angle of the entrance pallet. With a carefully-made drawing, having the escape wheel 10" in diameter, it will be seen that the arc a separates considerably from the line, B f' where it crosses the arc n'.

It will be remembered that when drawing the ratchet-tooth lever escapement a measurement of eight and a half degrees was made on the arc n' down from its intersection with the pitch circle, and thus the inner angle of the pallet was located. In the present instance the addendum line w becomes the controlling arc, and it will be further noticed on the large drawing that the line B h at its intersection with the arc n' approaches nearer to the arc w than does the line B f' to the pitch circle a; consequently, the inner angle of the pallet should not in this instance be carried down on the arc n' so far to correct the error as in the ratchet tooth.

Reason tells us that if we measure ten degrees down on the arc n' from its intersection with the addendum circle w we must define the position of the inner angle of the entrance pallet. We name the point so established the point r. The outer angle of this pallet is located at the intersection of the radial line A b with the line B i; said intersection we name the point v. Draw a line from the point v to the point r, and we define the impulse face of the entrance pallet; and the angular motion obtained from it as relates to the pallet staff embraces six degrees.

Measured on the arc l, the entire ten degrees of angular motion is as follows: Two and a half degrees from the impulse face of the tooth, and indicated between the lines B h and B f; one and a half degrees lock between the lines B f' and B i; six degrees impulse from pallet face, entrance between the lines B i and B j.

A DEPARTURE FROM FORMER PRACTICES.

Grossmann and Britten, in all their delineations of the club-tooth escapement, show the exit pallet as disengaged. To vary from this beaten track we will draw our exit pallet as locked. There are other reasons which prompt us to do this, one of which is, pupils are apt to fall into a rut and only learn to do things a certain way, and that way just as they are instructed.

To illustrate, the writer has met several students of the lever escapement who could make drawings of either club or ratchet-tooth escapement with the lock on the entrance pallet; but when required to draw a pallet as illustrated at Fig. 23, could not do it correctly. Occasionally one could do it, but the instances were rare. A still greater poser was to request them to delineate a pallet and tooth when the action of escaping was one-half or one-third performed; and it is easy to understand that only by such studies the master workman can thoroughly comprehend the complications involved in the club-tooth lever escapement.

AN APT ILLUSTRATION.

As an illustration: Two draughtsmen, employed by two competing watch factories, each designs a club-tooth escapement. We will further suppose the trains and mainspring power used by each concern to be precisely alike. But in practice the escapement of the watches made by one factory would "set," that is, if you stopped the balance dead still, with the pin in the fork, the watch would not start of itself; while the escapement designed by the other draughtsman would not "set"—stop the balance dead as often as you choose, the watch would start of itself. Yet even to experienced workmen the escape wheels and pallets looked exactly alike. Of course, there was a difference, and still none of the text-books make mention of it.

For the present we will go on with delineating our exit pallet. The preliminaries are the same as with former drawings, the instructions for which we need not repeat. Previous to drawing the exit pallet, let us reason on the matter. The point r in Fig. 23 is located at the intersection of pitch circle a and the radial line A c; and this will also be the point at which the tooth C will engage the locking face of the exit pallet.

This point likewise represents the advance angle of the engaging tooth. Now if we measure on the arc k (which represents the locking faces of both pallets) downward one and a half degrees, we establish the lock of the pallet E. To get this one and a half degrees defined on the arc k, we set the dividers at 5", and from B as a center sweep the short arc i, and from the intersection of the arc i with the line B e we lay off on said arc i one and a half degrees, and through the point so established draw the line B f.

Now the space on the arc k between the lines B e and B f defines the angular extent of the locking face. With the dividers set at 5" and one leg resting at the point r, we sweep the short arc t, and from the intersection of said arc with the line A c we draw the line n p; but in doing so we extend it (the line) so that it intersects the line B f, and at said intersection is located the inner angle of the exit pallet. This intersection we will name the point n.



From the intersection of the line B e with the arc i we lay off two and a half degrees on said arc, and through the point so established we draw the line B g. The intersection of this line with the arc k we name the point z. With one leg of our dividers set at A we sweep the arc l so it passes through the point z. This last arc defines the addendum of the escape-wheel teeth. From the point r on the arc a we lay off three and a half degrees, and through the point so established draw the line A j.

LOCATING THE OUTER ANGLE OF THE IMPULSE PLANES.

The intersection of this line with the addendum arc l locates the outer angle of the impulse planes of the teeth, and we name it the point x. From the point r we lay off on the arc a seven degrees and establish the point v, which defines the extent of the angular motion of the escape wheel utilized by pallet. Through the point v, from B as a center, we sweep the short arc m. It will be evident on a moment's reflection that this arc m must represent the path of movement of the outer angle of the exit pallet, and if we measure down ten degrees from the intersection of the arc l with the arc m, the point so established (which we name the point s) must be the exact position of the outer angle of the pallet during locking. We have a measure of ten degrees on the arc m, between the lines B g and B h, and by taking this space in the dividers and setting one leg at the intersection of the arc l with the arc m, and measuring down on m, we establish the point s. Drawing a line from point n to point s we define the impulse face of the pallet.

MAKING AN ESCAPEMENT MODEL.



It is next proposed we apply the theories we have been considering and make an enlarged model of an escapement, as shown at Figs. 24 and 25. This model is supposed to have an escape wheel one-fifth the size of the 10" one we have been drawing. In the accompanying cuts are shown only the main plate and bridges in full lines, while the positions of the escape wheel and balance are indicated by the dotted circles I B. The cuts are to no precise scale, but were reduced from a full-size drawing for convenience in printing. We shall give exact dimensions, however, so there will be no difficulty in carrying out our instructions in construction.



Perhaps it would be as well to give a general description of the model before taking up the details. A reduced side view of the complete model is given at Fig. 26. In this cut the escapement model shown at Figs. 24 and 25 is sketched in a rough way at R, while N shows a glass cover, and M a wooden base of polished oak or walnut. This base is recessed on the lower side to receive an eight-day spring clock movement, which supplies the motive power for the model. This base is recessed on top to receive the main plate A, Fig. 24, and also to hold the glass shade N in position. The base M is 21/2" high and 8" diameter. The glass cover N can have either a high and spherical top, as shown, or, as most people prefer, a flattened oval.



The main plate A is of hard spring brass, 1/10" thick and 6" in diameter; in fact, a simple disk of the size named, with slightly rounded edges. The top plate, shown at C, Figs. 24 and 25, is 1/8" thick and shaped as shown. This plate (C) is supported on two pillars 1/2" in diameter and 11/4" high. Fig. 25 is a side view of Fig. 24 seen in the direction of the arrow p. The cock D is also of 1/8" spring brass shaped as shown, and attached by the screw f and steady pins s s to the top plate C. The bridge F G carries the top pivots of escape wheel and pallet staff, and is shaped as shown at the full outline. This bridge is supported on two pillars 1/2" high and 1/2" in diameter, one of which is shown at E, Fig. 25, and both at the dotted circles E E', Fig. 24.

To lay out the lower plate we draw the line a a so it passes through the center of A at m. At 1.3" from one edge of A we establish on the line a the point d, which locates the center of the escape wheel. On the same line a at 1.15" from d we establish the point b, which represents the center of the pallet staff. At the distance of 1.16" from b we establish the point c, which represents the center of the balance staff. To locate the pillars H, which support the top plate C, we set the dividers at 2.58", and from the center m sweep the arc n.

From the intersection of this arc with the line a (at r) we lay off on said arc n 2.1" and establish the points g g', which locate the center of the pillars H H. With the dividers set so one leg rests at the center m and the other leg at the point d, we sweep the arc t. With the dividers set at 1.33" we establish on the arc t, from the point d, the points e e', which locate the position of the pillars E E'. The outside diameter of the balance B is 3-5/8" with the rim 3/16" wide and 5/16" deep, with screws in the rim in imitation of the ordinary compensation balance.

Speaking of a balance of this kind suggests to the writer the trouble he experienced in procuring material for a model of this kind—for the balance, a pattern had to be made, then a casting made, then a machinist turned the casting up, as it was too large for an American lathe. A hairspring had to be specially made, inasmuch as a mainspring was too short, the coils too open and, more particularly, did not look well. Pallet jewels had to be made, and lapidists have usually poor ideas of close measurements. Present-day conditions, however, will, no doubt, enable the workman to follow our instructions much more readily.

MAKING THE BRIDGES.

In case the reader makes the bridges C and F, as shown in Fig. 27, he should locate small circles on them to indicate the position of the screws for securing these bridges to the pillars which support them, and also other small circles to indicate the position of the pivot holes d b for the escape wheel and pallet staff. In practice it will be well to draw the line a a through the center of the main plate A, as previously directed, and also establish the point d as therein directed.

The pivot hole d' for the escape wheel, and also the holes at e e and b, are now drilled in the bridge F. These holes should be about 1/16" in diameter. The same sized hole is also drilled in the main plate A at d. We now place a nicely-fitting steel pin in the hole d' in the bridge F and let it extend into the hole d in the main plate. We clamp the bridge F to A so the hole b comes central on the line a, and using the holes e e in F as guides, drill or mark the corresponding holes e' e' and b in the main plate for the pillars E E' and the pallet staff.



This plan will insure the escape wheel and pallet staff being perfectly upright. The same course pursued with the plate C will insure the balance being upright. The pillars which support the bridges are shaped as shown at Fig. 28, which shows a side view of one of the pillars which support the top plate or bridge C. The ends are turned to 1/4" in diameter and extend half through the plate, where they are held by screws, the same as in American movements.



The pillars (like H) can be riveted in the lower plate A, but we think most workmen will find it more satisfactory to employ screws, as shown at Fig. 29. The heads of such screws should be about 3/8" in diameter and nicely rounded, polished and blued. We would not advise jeweling the pivot holes, because there is but slight friction, except to the foot of the balance pivot, which should be jeweled with a plano-convex garnet.



IMITATION RUBIES FOR CAPPING THE TOP PIVOTS.

The top pivots to the escape wheel should be capped with imitation rubies for appearance sake only, letting the cap settings be red gold, or brass red gilded. If real twelve-karat gold is employed the cost will not be much, as the settings are only about 3/8" across and can be turned very thin, so they will really contain but very little gold. The reason why we recommend imitation ruby cap jewels for the upper holes, is that such jewels are much more brilliant than any real stone we can get for a moderate cost. Besides, there is no wear on them.

The pallet jewels are also best made of glass, as garnet or any red stone will look almost black in such large pieces. Red carnelian has a sort of brick-red color, which has a cheap appearance. There is a new phosphorus glass used by optical instrument makers which is intensely hard, and if colored ruby-red makes a beautiful pallet jewel, which will afford as much service as if real stones were used; they are no cheaper than carnelian pallets, but much richer looking. The prettiest cap for the balance is one of those foilback stones in imitation of a rose-cut diamond.



In turning the staffs it is the best plan to use double centers, but a piece of Stubs steel wire that will go into a No. 40 wire chuck, will answer; in case such wire is used, a brass collet must be provided. This will be understood by inspecting Fig. 30, where L represents the Stubs wire and B N the brass collet, with the balance seat shown at k. The escape-wheel arbor and pallet staff can be made in the same way. The lower end of the escape wheel pivot is made about 1/4" long, so that a short piece of brass wire can be screwed upon it, as shown in Fig. 31, where h represents the pivot, A the lower plate, and the dotted line at p the brass piece screwed on the end of the pivot. This piece p is simply a short bit of brass wire with a female screw tapped into the end, which screws on to the pivot. An arm is attached to p, as shown at T. The idea is, the pieces T p act like a lathe dog to convey the power from one of the pivots of an old eight-day spring clock movement, which is secured by screws to the lower side of the main plate A. The plan is illustrated at Fig. 32, where l represents pivot of the eight-day clock employed to run the model. Counting the escape-wheel pivot of the clock as one, we take the third pivot from this in the clock train, placing the movement so this point comes opposite the escape-wheel pivot of the model, and screw the clock movement fast to the lower side of the plate A. The parts T, Fig. 33, are alike on both pivots.



PROFITABLE FOR EXPLAINING TO A CUSTOMER.

To fully appreciate such a large escapement model as we have been describing, a person must see it with its great balance, nearly 4" across, flashing and sparkling in the show window in the evening, and the brilliant imitation ruby pallets dipping in and out of the escape wheel. A model of this kind is far more attractive than if the entire train were shown, the mystery of "What makes it go?" being one of the attractions. Such a model is, further, of great value in explaining to a customer what you mean when you say the escapement of his watch is out of order. Any practical workman can easily make an even $100 extra in a year by making use of such a model.

For explaining to customers an extra balance cock can be used to show how the jewels (hole and cap) are arranged. Where the parts are as large as they are in the model, the customer can see and understand for himself what is necessary to be done.

It is not to be understood that our advice to purchase the jewels for an extra balance cock conflicts with our recommending the reader not to jewel the holes of his model. The extra cock is to be shown, not for use, and is employed solely for explaining to a customer what is required when a pivot or jewel is found to be broken.

HOW LARGE SCREWS ARE MADE.

The screws which hold the plates in place should have heads about 3/8" in diameter, to be in proportion to the scale on which the balance and escape wheel are gotten up. There is much in the manner in which the screw heads are finished as regards the elegance of such a model. A perfectly flat head, no matter how highly polished, does not look well, neither does a flattened conehead, like Fig. 35. The best head for this purpose is a cupped head with chamfered edges, as shown at Fig. 34 in vertical section. The center b is ground and polished into a perfect concave by means of a metal ball. The face, between the lines a a, is polished dead flat, and the chamfered edge a c finished a trifle convex. The flat surface at a is bright, but the concave b and chamfer at c are beautifully blued. For a gilt-edged, double extra head, the chamfer at c can be "snailed," that is, ground with a suitable lap before bluing, like the stem-wind wheels on some watches.



FANCY SCREWHEADS.

There are two easy methods of removing the blue from the flat part of the screwhead at a. (1) Make a special holder for the screw in the end of a cement brass, as shown at E, Fig. 36, and while it is slowly revolving in the lathe touch the flat surface a with a sharpened pegwood wet with muriatic acid, which dissolves the blue coating of oxide of iron. (2) The surface of the screwhead is coated with a very thin coating of shellac dissolved in alcohol and thoroughly dried, or a thin coating of collodion, which is also dried. The screw is placed in the ordinary polishing triangle and the flat face at a polished on a tin lap with diamantine and oil. In polishing such surfaces the thinnest possible coating of diamantine and oil is smeared on the lap—in fact, only enough to dim the surface of the tin. It is, of course, understood that it is necessary to move only next to nothing of the material to restore the polish of the steel. The polishing of the other steel parts is done precisely like any other steel work.



The regulator is of the Howard pattern. The hairspring stud is set in the cock like the Elgin three-quarter-plate movement. The richest finish for such a model is frosted plates and bridges. The frosting should not be a fine mat, like a watch movement, but coarse-grained—in fact, the grain of the frosting should be proportionate to the size of the movement. The edges of the bridges and balance cock can be left smooth. The best process for frosting is by acid. Details for doing the work will now be given.



To do this frosting by acid nicely, make a sieve by tacking and gluing four pieces of thin wood together, to make a rectangular box without a bottom. Four pieces of cigar-box wood, 8" long by 11/2" wide, answer first rate. We show at A A A A, Fig. 37, such a box as if seen from above; with a side view, as if seen in the direction of the arrow a, at Fig. 38. A piece of India muslin is glued across the bottom, as shown at the dotted lines b b. By turning up the edges on the outside of the box, the muslin bottom can be drawn as tight as a drum head.

HOW TO DO ACID FROSTING.

To do acid frosting, we procure two ounces of gum mastic and place in the square sieve, shown at Fig. 37. Usually more than half the weight of gum mastic is in fine dust, and if not, that is, if the gum is in the shape of small round pellets called "mastic tears," crush these into dust and place the dust in A. Let us next suppose we wish to frost the cock on the balance, shown at Fig. 39. Before we commence to frost, the cock should be perfectly finished, with all the holes made, the regulator cap in position, the screw hole made for the Howard regulator and the index arc engraved with the letters S and F.



It is not necessary the brass should be polished, but every file mark and scratch should be stoned out with a Scotch stone; in fact, be in the condition known as "in the gray." It is not necessary to frost any portion of the cock C, except the upper surface. To protect the portion of the cock not to be frosted, like the edges and the back, we "stop out" by painting over with shellac dissolved in alcohol, to which a little lampblack is added. It is not necessary the coating of shellac should be very thick, but it is important it should be well dried.

HOW TO PREPARE THE SURFACE.

For illustration, let us suppose the back and edges of the cock at Fig. 39 are coated with shellac and it is laid flat on a piece of paper about a foot square to catch the excess of mastic. Holes should be made in this paper and also in the board on which the paper rests to receive the steady pins of the cock. We hold the sieve containing the mastic over the cock and, gently tapping the box A with a piece of wood like a medium-sized file handle, shake down a little snowstorm of mastic dust over the face of the cock C.

Exactly how much mastic dust is required to produce a nice frosting is only to be determined by practice. The way to obtain the knack is to frost a few scraps to "get your hand in." Nitric acid of full strength is used, dipping the piece into a shallow dish for a few seconds. A good-sized soup plate would answer very nicely for frosting the bottom plate, which, it will be remembered, is 6" in diameter.

HOW TO ETCH THE SURFACE.

After the mastic is sifted on, the cock should be heated up to about 250 deg. F., to cause the particles of mastic to adhere to the surface. The philosophy of the process is, the nitric acid eats or dissolves the brass, leaving a little brass island the size of the particle of mastic which was attached to the surface. After heating to attach the particles of mastic, the dipping in nitric acid is done as just described. Common commercial nitric acid is used, it not being necessary to employ chemically pure acid. For that matter, for such purposes the commercial acid is the best.

After the acid has acted for fifteen or twenty seconds the brass is rinsed in pure water to remove the acid, and dried by patting with an old soft towel, and further dried by waving through the air. A little turpentine on a rag will remove the mastic, but turpentine will not touch the shellac coating. The surface of the brass will be found irregularly acted upon, producing a sort of mottled look. To obtain a nice frosting the process of applying the mastic and etching must be repeated three or four times, when a beautiful coarse-grain mat or frosting will be produced.

The shellac protection will not need much patching up during the three or four bitings of acid, as the turpentine used to wash off the mastic does not much affect the shellac coating. All the screw holes like s s and d, also the steady pins on the back, are protected by varnishing with shellac. The edges of the cocks and bridges should be polished by rubbing lengthwise with willow charcoal or a bit of chamois skin saturated with oil and a little hard rouge scattered upon it. The frosting needs thorough scratch-brushing.



At Fig. 40 we show the balance cock of our model with modified form of Howard regulator. The regulator bar A and spring B should be ground smooth on one side and deeply outlined to perfect form. The regulator cap C is cut out to the correct size. These parts are of decarbonized cast steel, annealed until almost as soft as sheet brass. It is not so much work to finish these parts as one might imagine. Let us take the regulator bar for an example and carry it through the process of making. The strip of soft sheet steel on which the regulator bar is outlined is represented by the dotted outline b, Fig. 41.



To cut out sheet steel rapidly we take a piece of smooth clock mainspring about 3/4" and 10" long and double it together, softening the bending point with the lamp until the piece of mainspring assumes the form shown at Fig. 42, where c represents the piece of spring and H H the bench-vise jaws. The piece of soft steel is placed between the limbs of c c' of the old mainspring up to the line a, Fig. 41, and clamped in the vise jaws. The superfluous steel is cut away with a sharp and rather thin cold chisel.



The chisel is presented as shown at G, Fig. 43 (which is an end view of the vise jaws H H and regulator bar), and held to cut obliquely and with a sort of shearing action, as illustrated in Fig. 42, where A'' represents the soft steel and G the cold chisel. We might add that Fig. 42 is a view of Fig. 43 seen in the direction of the arrow f. It is well to cut in from the edge b on the line d, Fig. 41, with a saw, in order to readily break out the surplus steel and not bend the regulator bar. By setting the pieces of steel obliquely in the vise, or so the line e comes even with the vise jaws, we can cut to more nearly conform to the circular loop A'' of the regulator A.



The smooth steel surface of the bent mainspring c prevents the vise jaws from marking the soft steel of the regulator bar. A person who has not tried this method of cutting out soft steel would not believe with what facility pieces can be shaped. Any workman who has a universal face plate to his lathe can turn out the center of the regulator bar to receive the disk C, and also turn out the center of the regulator spring B. What we have said about the regulator bar applies also to the regulator spring B. This spring is attached to the cock D by means of two small screws at n.

The micrometer screw F is tapped through B'' as in the ordinary Howard regulator, and the screw should be about No. 6 of a Swiss screw-plate. The wire from which such screw is made should be 1/10" in diameter. The steel cap C is fitted like the finer forms of Swiss watches. The hairspring stud E is of steel, shaped as shown, and comes outlined with the other parts.

TO TEMPER AND POLISH STEEL.

The regulator bar should be hardened by being placed in a folded piece of sheet iron and heated red hot, and thrown into cold water. The regulator bar A A' is about 3" long; and for holding it for hardening, cut a piece of thin sheet iron 21/2" by 31/4" and fold it through the middle lengthwise, as indicated by the dotted line g, Fig. 44. The sheet iron when folded will appear as shown at Fig. 45. A piece of flat sheet metal of the same thickness as the regulator bar should be placed between the iron leaves I I, and the leaves beaten down with a hammer, that the iron may serve as a support for the regulator during heating and hardening. A paste made of castile soap and water applied to the regulator bar in the iron envelope will protect it from oxidizing much during the heating. The portions of the regulator bar marked h are intended to be rounded, while the parts marked m are intended to be dead flat. The rounding is carefully done, first with a file and finished with emery paper. The outer edge of the loop A'' is a little rounded, also the inner edge next the cap C. This will be understood by inspecting Fig. 46, where we show a magnified vertical section of the regulator on line l, Fig. 40. The curvature should embrace that portion of A'' between the radial lines o o', and should, on the model, not measure more than 1/40". It will be seen that the curved surface of the regulator is sunk so it meets only the vertical edge of the loop A''. For the average workman, polishing the flat parts m is the most difficult to do, and for this reason we will give entire details. It is to be expected that the regulator bar will spring a little in hardening, but if only a little we need pay no attention to it.



HOW FLAT STEEL POLISHING IS DONE.

Polishing a regulator bar for a large model, such as we are building, is only a heavy job of flat steel work, a little larger but no more difficult than to polish a regulator for a sixteen-size watch. We would ask permission here to say that really nice flat steel work is something which only a comparatively few workmen can do, and, still, the process is quite simple and the accessories few and inexpensive. First, ground-glass slab 6" by 6" by 1/4"; second, flat zinc piece 31/4" by 31/4" by 1/4"; third, a piece of thick sheet brass 3" by 2" by 1/8"; and a bottle of Vienna lime. The glass slab is only a piece of plate glass cut to the size given above. The zinc slab is pure zinc planed dead flat, and the glass ground to a dead surface with another piece of plate glass and some medium fine emery and water, the whole surface being gone over with emery and water until completely depolished. The regulator bar, after careful filing and dressing up on the edges with an oilstone slip or a narrow emery buff, is finished as previously described. We would add to the details already given a few words on polishing the edges.



It is not necessary that the edges of steelwork, like the regulator bar B, Fig. 47, should be polished to a flat surface; indeed, they look better to be nicely rounded. Perhaps we can convey the idea better by referring to certain parts: say, spring to the regulator, shown at D, Fig. 40, and also the hairspring stud E. The edges of these parts look best beveled in a rounded manner.



It is a little difficult to convey in words what is meant by "rounded" manner. To aid in understanding our meaning, we refer to Figs. 48 and 49, which are transverse sections of D, Fig. 50, on the line f. The edges of D, in Fig. 48, are simply rounded. There are no rules for such rounding—only good judgment and an eye for what looks well. The edges of D as shown in Fig. 49 are more on the beveled order. In smoothing and polishing such edges, an ordinary jeweler's steel burnish can be used.



SMOOTHING AND POLISHING.

The idea in smoothing and polishing such edges is to get a fair gloss without much attention to perfect form, inasmuch as it is the flat surface d on top which produces the impression of fine finish. If this is flat and brilliant, the rounded edges, like g c can really have quite an inferior polish and still look well. For producing the flat polish on the upper surface of the regulator bar B and spring D, the flat surface d, Figs. 48, 49, 51 and 52, we must attach the regulator bar to a plate of heavy brass, as shown at Fig. 47, where A represents the brass plate, and B the regulator bar, arranged for grinding and polishing flat.



For attaching the regulator bar B to the brass plate A, a good plan is to cement it fast with lathe wax; but a better plan is to make the plate A of heavy sheet iron, something about 1/8" thick, and secure the two together with three or four little catches of soft solder. It is to be understood the edges of the regulator bar or the regulator spring are polished, and all that remains to be done is to grind and polish the flat face.

Two pieces a a of the same thickness as the regulator bar are placed as shown and attached to A to prevent rocking. After B is securely attached to A, the regulator should be coated with shellac dissolved in alcohol and well dried. The object of this shellac coating is to keep the angles formed at the meeting of the face and side clean in the process of grinding with oilstone dust and oil. The face of the regulator is now placed on the ground glass after smearing it with oil and oilstone dust. It requires but a very slight coating to do the work.

The grinding is continued until the required surface is dead flat, after which the work is washed with soap and water and the shellac dissolved away with alcohol. The final polish is obtained on the zinc lap with Vienna lime and alcohol. Where lathe cement is used for securing the regulator to the plate A, the alcohol used with the Vienna lime dissolves the cement and smears the steel. Diamantine and oil are the best materials for polishing when the regulator bar is cemented to the plate A.

KNOWLEDGE THAT IS MOST ESSENTIAL.

The knowledge most important for a practical working watchmaker to possess is how to get the watches he has to repair in a shape to give satisfaction to his customers. No one will dispute the truth of the above italicised statement. It is only when we seek to have limits set, and define what such knowledge should consist of, that disagreement occurs.

One workman who has read Grossmann or Saunier, or both, would insist on all watches being made to a certain standard, and, according to their ideas, all such lever watches as we are now dealing with should have club-tooth escapements with equidistant lockings, ten degrees lever and pallet action, with one and one-half degrees lock and one and one-half degrees drop. Another workman would insist on circular pallets, his judgment being based chiefly on what he had read as stated by some author. Now the facts of the situation are that lever escapements vary as made by different manufacturers, one concern using circular pallets and another using pallets with equidistant lockings.

WHAT A WORKMAN SHOULD KNOW TO REPAIR A WATCH.

One escapement maker will divide the impulse equally between the tooth and pallet; another will give an excess to the tooth. Now while these matters demand our attention in the highest degree in a theoretical sense, still, for such "know hows" as count in a workshop, they are of but trivial importance in practice.

We propose to deal in detail with the theoretical consideration of "thick" and "thin" pallets, and dwell exhaustively on circular pallets and those with equidistant locking faces; but before we do so we wish to impress on our readers the importance of being able to free themselves of the idea that all lever escapements should conform to the rigid rules of any dictum.

EDUCATE THE EYE TO JUDGE OF ANGULAR AS WELL AS LINEAR EXTENT.

For illustration: It would be easy to design a lever escapement that would have locking faces which were based on the idea of employing neither system, but a compromise between the two, and still give a good, sound action. All workmen should learn to estimate accurately the extent of angular motion, so as to be able to judge correctly of escapement actions. It is not only necessary to know that a club-tooth escapement should have one and one-half degrees drop, but the eye should be educated, so to speak, as to be able to judge of angular as well as linear extent.



Most mechanics will estimate the size of any object measured in inches or parts of inches very closely; but as regards angular extent, except in a few instances, we will find mechanics but indifferent judges. To illustrate, let us refer to Fig. 53. Here we have the base line A A' and the perpendicular line a B. Now almost any person would be able to see if the angle A a B was equal to B a A'; but not five in one hundred practical mechanics would be able to estimate with even tolerable accuracy the measure the angles made to the base by the lines b c d; and still watchmakers are required in the daily practice of their craft to work to angular motions and movements almost as important as to results as diameters.

What is the use of our knowing that in theory an escape-wheel tooth should have one and one-half degrees drop, when in reality it has three degrees? It is only by educating the eye from carefully-made drawings; or, what is better, constructing a model on a large scale, that we can learn to judge of proper proportion and relation of parts, especially as we have no convenient tool for measuring the angular motion of the fork or escape wheel. Nor is it important that we should have, if the workman is thoroughly "booked up" in the principles involved.

As we explained early in this treatise, there is no imperative necessity compelling us to have the pallets and fork move through ten degrees any more than nine and one-half degrees, except that experience has proven that ten degrees is about the right thing for good results. In this day, when such a large percentage of lever escapements have exposed pallets, we can very readily manipulate the pallets to match the fork and roller action. For that matter, in many instances, with a faulty lever escapement, the best way to go about putting it to rights is to first set the fork and roller so they act correctly, and then bring the pallets to conform to the angular motion of the fork so adjusted.

FORK AND ROLLER ACTION.

Although we could say a good deal more about pallets and pallet action, still we think it advisable to drop for the present this particular part of the lever escapement and take up fork and roller action, because, as we have stated, frequently the fork and roller are principally at fault. In considering the action and relation of the parts of the fork and roller, we will first define what is considered necessary to constitute a good, sound construction where the fork vibrates through ten degrees of angular motion and is supposed to be engaged with the roller by means of the jewel pin for thirty degrees of angular motion of the balance.

There is no special reason why thirty degrees of roller action should be employed, except that experience in practical construction has come to admit this as about the right arc for watches of ordinary good, sound construction. Manufacturers have made departures from this standard, but in almost every instance have finally come back to pretty near these proportions. In deciding on the length of fork and size of roller, we first decide on the distance apart at which to place the center of the balance and the center of the pallet staff. These two points established, we have the length of the fork and diameter of the roller defined at once.