The Project Gutenberg eBook, Watch and Clock Escapements, by Anonymous This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net Title: 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 Author: Anonymous Release Date: November 6, 2005 [eBook #17021] Language: English Character set encoding: ISO-8859-1 ***START OF THE PROJECT GUTENBERG EBOOK WATCH AND CLOCK ESCAPEMENTS*** E-text prepared by Robert Cicconetti, Janet Blenkinship, and the Project Gutenberg Online Distributed Proofreading Team (http://www.pgdp.net/). Book provided by the New York University Library. Note: Project Gutenberg also has an HTML version of this file which includes the original more than 180 illustrations. See 17021-h.htm or 17021-h.zip: (http://www.gutenberg.net/dirs/1/7/0/2/17021/17021-h/17021-h.htm) or (http://www.gutenberg.net/dirs/1/7/0/2/17021/17021-h.zip) 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. [Illustration: Fig. 1] 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 5½" long by 1¼" 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. [Illustration: Fig. 2] 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. [Illustration: Fig. 3] To make such a pair of small dividers, take a piece of hard sheet brass about 1/20" thick, ¼" wide, 1½" 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. [Illustration: Fig. 4] 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 5½" 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. [Illustration: Fig. 5] 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. [Illustration: Fig. 6] ESTABLISHING THE CENTER OF PALLET STAFF. [Illustration: Fig. 7] 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. [Illustration: Fig. 8] 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. [Illustration: Fig. 9] 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. [Illustration: Fig. 10] 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. [Illustration: Fig. 11] [Illustration: Fig. 12] [Illustration: Fig. 13] [Illustration: Fig. 14] 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. [Illustration: Fig. 15] 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. [Illustration: Fig. 16] 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_. [Illustration: Fig. 17] 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'_. [Illustration: Fig. 18] 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. [Illustration: Fig. 19] 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_. [Illustration: Fig. 20] 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. [Illustration: Fig. 21] 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_. [Illustration: Fig. 22] 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_. [Illustration: Fig. 23] 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. [Illustration: Fig. 24] 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. [Illustration: Fig. 25] 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 2½" 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. [Illustration: Fig. 26] 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 ½" in diameter and 1¼" 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 ½" high and ½" 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. [Illustration: Fig. 27] 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 ¼" in diameter and extend half through the plate, where they are held by screws, the same as in American movements. [Illustration: Fig. 28] 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. [Illustration: Fig. 29] 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. [Illustration: Fig. 30] [Illustration: Fig. 31] 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 ¼" 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. [Illustration: Fig. 32] [Illustration: Fig. 33] 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. [Illustration: Fig. 34] [Illustration: Fig. 35] 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. [Illustration: Fig. 36] 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. [Illustration: Fig. 37] [Illustration: Fig. 38] 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 1½" 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. [Illustration: Fig. 39] 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° 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. [Illustration: Fig. 40] 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. [Illustration: Fig. 41] To cut out sheet steel rapidly we take a piece of smooth clock mainspring about ¾" 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. [Illustration: Fig. 42] 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_. [Illustration: Fig. 43] 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 2½" by 3¼" 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. [Illustration: Fig. 44] [Illustration: Fig. 45] [Illustration: Fig. 46] 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 ¼"; second, flat zinc piece 3¼" by 3¼" by ¼"; 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. [Illustration: Fig. 47] 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. [Illustration: Fig. 48] [Illustration: Fig. 49] 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. [Illustration: Fig. 50] 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. [Illustration: Fig. 51] [Illustration: Fig. 52] 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. [Illustration: Fig. 53] 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. HOW TO FIND THE ROLLER DIAMETER FROM THE LENGTH OF THE FORK. To illustrate, let us imagine the small circles _A B_, Fig. 54, to represent the center of a pallet staff and balance staff in the order named. We divide this space into four equal parts, as shown, and the third space will represent the point at which the pitch circles of the fork and roller will intersect, as shown by the arc _a_ and circle _b_. Now if the length of the radii of these circles stand to each other as three to one, and the fork vibrates through an arc of ten degrees, the jewel pin engaging such fork must remain in contact with said fork for thirty degrees of angular motion of the balance. [Illustration: Fig. 54] Or, in other words, the ratio of angular motion of two _mobiles_ acting on each must be in the same ratio as the length of their radii at the point of contact. If we desire to give the jewel pin, or, in ordinary horological phraseology, have a greater arc of roller action, we would extend the length of fork (say) to the point _c_, which would be one-fifth of the space between _A_ and _B_, and the ratio of fork to roller action would be four to one, and ten degrees of fork action would give forty degrees of angular motion to the roller--and such escapements have been constructed. WHY THIRTY DEGREES OF ROLLER ACTION IS ABOUT RIGHT. Now we have two sound reasons why we should not extend the arc of vibration of the balance: (_a_) If there is an advantage to be derived from a detached escapement, it would surely be policy to have the arc of contact, that is, for the jewel pin to engage the fork, as short an arc as is compatible with a sound action. (_b_) It will be evident to any thinking mechanic that the acting force of a fork which would carry the jewel pin against the force exerted by the balance spring through an arc of fifteen degrees, or half of an arc of thirty degrees, would fail to do so through an arc of twenty degrees, which is the condition imposed when we adopt forty degrees of roller action. For the present we will accept thirty degrees of roller action as the standard. Before we proceed to delineate our fork and roller we will devote a brief consideration to the size and shape of a jewel pin to perform well. In this matter there has been a broad field gone over, both theoretically and in practical construction. Wide jewel pins, round jewel pins, oval jewel pins have been employed, but practical construction has now pretty well settled on a round jewel pin with about two-fifths cut away. And as regards size, if we adopt the linear extent of four degrees of fork or twelve degrees of roller action, we will find it about right. HOW TO SET A FORK AND ROLLER ACTION RIGHT. As previously stated, frequently the true place to begin to set a lever escapement right is with the roller and fork. But to do this properly we should know when such fork and roller action is right and safe in all respects. We will see on analysis of the actions involved that there are three important actions in the fork and roller functions: (_a_) The fork imparting perfect impulse through the jewel pin to the balance. (_b_) Proper unlocking action. (_c_) Safety action. The last function is in most instances sadly neglected and, we regret to add, by a large majority of even practical workmen it is very imperfectly understood. In most American watches we have ample opportunity afforded to inspect the pallet action, but the fork and roller action is placed so that rigid inspection is next to impossible. The Vacheron concern of Swiss manufacturers were acute enough to see the importance of such inspection, and proceeded to cut a circular opening in the lower plate, which permitted, on the removal of the dial, a careful scrutiny of the action of the roller and fork. While writing on this topic we would suggest the importance not only of knowing how to draw a correct fork and roller action, but letting the workman who desires to be _au fait_ in escapements delineate and study the action of a faulty fork and roller action--say one in which the fork, although of the proper form, is too short, or what at first glance would appear to amount to the same thing, a roller too small. Drawings help wonderfully in reasoning out not only correct actions, but also faulty ones, and our readers are earnestly advised to make such faulty drawings in several stages of action. By this course they will educate the eye to discriminate not only as to correct actions, but also to detect those which are imperfect, and we believe most watchmakers will admit that in many instances it takes much longer to locate a fault than to remedy it after it has been found. [Illustration: Fig. 55] Let us now proceed to delineate a fork and roller. It is not imperative that we should draw the parts to any scale, but it is a rule among English makers to let the distance between the center of the pallet staff and the center of the balance staff equal in length the chord of ninety-six degrees of the pitch circle of the escape wheel, which, in case we employ a pitch circle of 5" radius, would make the distance between _A_ and _B_, Fig. 55, approximately 7½", which is a very fair scale for study drawings. HOW TO DELINEATE A FORK AND ROLLER. To arrive at the proper proportions of the several parts, we divide the space _A B_ into four equal parts, as previously directed, and draw the circle _a_ and short arc _b_. With our dividers set at 5", from _B_ as a center we sweep the short arc _c_. From our arc of sixty degrees, with a 5" radius, we take five degrees, and from the intersection of the right line _A B_ with the arc _c_ we lay off on each side five degrees and establish the points _d e_; and from _B_ as a center, through these points draw the lines _B d'_ and _B e'_. Now the arc embraced between these lines represents the angular extent of our fork action. From _A_ as a center and with our dividers set at 5", we sweep the arc _f_. From the scale of degrees we just used we lay off fifteen degrees on each side of the line _A B_ on the arc _f_, and establish the points _g h_. From _A_ as a center, through the points just established we draw the radial lines _A g'_ and _A h'_. The angular extent between these lines defines the limit of our roller action. Now if we lay off on the arc _f_ six degrees each side of its intersection with the line _A B_, we define the extent of the jewel pin; that is, on the arc _f_ we establish the points _l m_ at six degrees from the line _A B_, and through the points _l m_ draw, from _A_ as a center, the radial lines _A l'_ and _A m'_. The extent of the space between the lines _A l'_ and _A m'_ on the circle _a_ defines the size of our jewel pin. TO DETERMINE THE SIZE OF A JEWEL PIN. [Illustration: Fig. 56] To make the situation better understood, we make an enlarged drawing of the lines defining the jewel pin at Fig. 56. At the intersection of the line _A B_ with the arc _a_ we locate the point _k_, and from it as a center we sweep the circle _i_ so it passes through the intersection of the lines _A l'_ and _A m'_ with the arc _a_. We divide the radius of the circle _i_ on the line _A B_ into five equal parts, as shown by the vertical lines _j_. Of these five spaces we assume three as the extent of the jewel pin, cutting away that portion to the right of the heavy vertical line at _k_. [Illustration: Fig. 57] We will now proceed to delineate a fork and roller as the parts are related on first contact of jewel pin with fork and initial with the commencing of the act of unlocking a pallet. The position and relations are also the same as at the close of the act of impulse. We commence the drawing at Fig. 57, as before, by drawing the line _A B_ and the arcs _a_ and _b_ to represent the pitch circles. We also sweep the arc _f_ to enable us to delineate the line _A g'_. Next in order we draw our jewel pin as shown at _D_. In drawing the jewel pin we proceed as at Fig. 56, except we let the line _A g'_, Fig. 57, assume the same relations to the jewel pin as _A B_ in Fig. 56; that is, we delineate the jewel pin as if extending on the arc _a_ six degrees on each side of the line _A g'_, Fig. 57. THE THEORY OF THE FORK ACTION. To aid us in reasoning, we establish the point _m_, as in Fig. 55, at _m_, Fig. 57, and proceed to delineate another and imaginary jewel pin at _D'_ (as we show in dotted outline). A brief reasoning will show that in allowing thirty degrees of contact of the fork with the jewel pin, the center of the jewel pin will pass through an arc of thirty degrees, as shown on the arcs _a_ and _f_. Now here is an excellent opportunity to impress on our minds the true value of angular motion, inasmuch as thirty degrees on the arc _f_ is of more than twice the linear extent as on the arc _a_. Before we commence to draw the horn of the fork engaging the jewel pin _D_, shown at full line in Fig. 57, we will come to perfectly understand what mechanical relations are required. As previously stated, we assume the jewel pin, as shown at _D_, Fig. 57, is in the act of encountering the inner face of the horn of the fork for the end or purpose of unlocking the engaged pallet. Now if the inner face of the horn of the fork was on a radial line, such radial line would be _p B_, Fig. 57. We repeat this line at _p_, Fig. 56, where the parts are drawn on a larger scale. To delineate a fork at the instant the last effort of impulse has been imparted to the jewel pin, and said jewel pin is in the act of separating from the inner face of the prong of the fork--we would also call attention to the fact that relations of parts are precisely the same as if the jewel pin had just returned from an excursion of vibration and was in the act of encountering the inner face of the prong of the fork in the act of unlocking the escapement. We mentioned this matter previously, but venture on the repetition to make everything clear and easily understood. We commence by drawing the line _A B_ and dividing it in four equal parts, as on previous occasions, and from _A_ and _B_ as centers draw the pitch circles _c d_. By methods previously described, we draw the lines _A a_ and _A a'_, also _B b_ and _B b'_ to represent the angular motion of the two mobiles, viz., fork and roller action. As already shown, the roller occupies twelve degrees of angular extent. To get at this conveniently, we lay off on the arc by which we located the lines _A a_ and _A a'_ six degrees above the line _A a_ and draw the line _A h_. Now the angular extent on the arc _c_ between the lines _A a_ and _A h_ represents the radius of the circle defining the jewel pin. From the intersection of the line _A a_ with the arc _c_ as a center, and with the radius just named, we sweep the small circle _D_, Fig. 58, which represents our jewel pin; we afterward cut away two-fifths and draw the full line _D_, as shown. We show at Fig. 59 a portion of Fig. 58, enlarged four times, to show certain portions of our delineations more distinctly. If we give the subject a moment's consideration we will see that the length of the prong _E_ of the lever fork is limited to such a length as will allow the jewel pin _D_ to pass it. HOW TO DELINEATE THE PRONGS OF A LEVER FORK. [Illustration: Fig. 58] [Illustration: Fig. 59] To delineate this length, from _B_ as a center we sweep the short arc _f_ so it passes through the outer angle _n_, Fig. 59, of the jewel pin. This arc, carried across the jewel pin _D_, limits the length of the opposite prong of the fork. The outer face of the prong of the fork can be drawn as a line tangent to a circle drawn from _A_ as a center through the angle _n_ of the jewel pin. Such a circle or arc is shown at _o_, Figs. 58 and 59. There has been a good deal said as to whether the outer edge of the prong of a fork should be straight or curved. To the writer's mind, a straight-faced prong, like from _s_ to _m_, is what is required for a fork with a single roller, while a fork with a curved prong will be best adapted for a double roller. This subject will be taken up again when we consider double-roller action. The extent or length of the outer face of the prong is also an open subject, but as there is but one factor of the problem of lever escapement construction depending on it, when we name this and see this requirement satisfied we have made an end of this question. The function performed by the outer face of the prong of a fork is to prevent the engaged pallet from unlocking while the guard pin is opposite to the passing hollow. The inner angle _s_ of the horn of the fork must be so shaped and located that the jewel pin will just clear it as it passes out of the fork, or when it passes into the fork in the act of unlocking the escapement. In escapements with solid bankings a trifle is allowed, that is, the fork is made enough shorter than the absolute theoretical length to allow for safety in this respect. THE PROPER LENGTH OF A LEVER. We will now see how long a lever must be to perform its functions perfectly. Now let us determine at what point on the inner face of the prong _E'_ the jewel pin parts from the fork, or engages on its return. To do this we draw a line from the center _r_ (Fig. 59) of the jewel pin, so as to meet the line _e_ at right angles, and the point _t_ so established on the line _e_ is where contact will take place between the jewel pin and fork. It will be seen this point (_t_) of contact is some distance back of the angle _u_ which terminates the inner face of the prong _E'_; consequently, it will be seen the prongs _E E'_ of the fork can with safety be shortened enough to afford a safe ingress or egress to the jewel pin to the slot in the fork. As regards the length of the outer face of the prong of the fork, a good rule is to make it one and a half times the diameter of the jewel pin. The depth of the slot need be no more than to free the jewel in its passage across the ten degrees of fork action. A convenient rule as to the depth of the slot in a fork is to draw the line _k_, which, it will be seen, coincides with the circle which defines the jewel pin. HOW TO DELINEATE THE SAFETY ACTION. [Illustration: Fig. 60] We will next consider a safety action of the single roller type. The active or necessary parts of such safety action consist of a roller or disk of metal, usually steel, shaped as shown in plan at _A_, Fig. 60. In the edge of this disk is cut in front of the jewel pin a circular recess shown at _a_ called the passing hollow. The remaining part of the safety action is the guard pin shown at _N_ Figs. 61 and 62, which is placed in the lever. Now it is to be understood that the sole function performed by the guard pin is to strike the edge of the roller _A_ at any time when the fork starts to unlock the engaged pallet, except when the jewel pin is in the slot of the fork. To avoid extreme care in fitting up the passing hollow, the horns of the fork are arranged to strike the jewel pin and prevent unlocking in case the passing hollow is made too wide. To delineate the safety action we first draw the fork and jewel pin as previously directed and as shown at Fig. 63. The position of the guard pin should be as close to the bottom of the slot of the fork as possible and be safe. As to the size of the guard pin, it is usual to make it about one-third or half the diameter of the jewel pin. The size and position of the guard pin decided on and the small circle _N_ drawn, to define the size and position of the roller we set our dividers so that a circle drawn from the center _A_ will just touch the edge of the small circle _N_, and thus define the outer boundary of our roller, or roller table, as it is frequently called. [Illustration: Fig. 61] [Illustration: Fig. 62] For deciding the angular extent of the passing hollow we have no fixed rule, but if we make it to occupy about half more angular extent on the circle _y_ than will coincide with the angular extent of the jewel pin, it will be perfectly safe and effectual. We previously stated that the jewel pin should occupy about twelve degrees of angular extent on the circle _c_, and if we make the passing hollow occupy eighteen degrees (which is one and a half the angular extent of the jewel pin) it will do nicely. But if we should extend the width of the passing hollow to twenty-four degrees it would do no harm, as the jewel pin would be well inside the horn of the fork before the guard pin could enter the passing hollow. [Illustration: Fig. 63] We show in Fig. 61 the fork as separated from the roller, but in Fig. 62, which is a side view, we show the fork and jewel pin as engaged. When drawing a fork and roller action it is safe to show the guard pin as if in actual contact with the roller. Then in actual construction, if the parts are made to measure and agree with the drawing in the gray, that is, before polishing, the process of polishing will reduce the convex edge of the roller enough to free it. It is evident if thought is given to the matter, that if the guard pin is entirely free and does not touch the roller in any position, a condition and relation of parts exist which is all we can desire. We are aware that it is usual to give a considerable latitude in this respect even by makers, and allow a good bit of side shake to the lever, but our judgment would condemn the practice, especially in high-grade watches. RESTRICT THE FRICTIONAL SURFACES. Grossmann, in his essay on the detached lever escapement, adopts one and a half degrees lock. Now, we think that one degree is ample; and we are sure that every workman experienced in the construction of the finer watches will agree with us in the assertion that we should in all instances seek to reduce the extent of all frictional surfaces, no matter how well jeweled. Acting under such advice, if we can reduce the surface friction on the lock from one and a half degrees to one degree or, better, to three-fourths of a degree, it is surely wise policy to do so. And as regards the extent of angular motion of the lever, if we reduce this to six degrees, exclusive of the lock, we would undoubtedly obtain better results in timing. We shall next consider the effects of opening the bankings too wide, and follow with various conditions which are sure to come in the experience of the practical watch repairer. It is to be supposed in this problem that the fork and roller action is all right. The reader may say to this, why not close the banking? In reply we would offer the supposition that some workman had bent the guard pin forward or set a pallet stone too far out. We have now instructed our readers how to draw and construct a lever escapement complete, of the correct proportions, and will next take up defective construction and consider faults existing to a lesser or greater degree in almost every watch. Faults may also be those arising from repairs by some workman not fully posted in the correct form and relation of the several parts which go to make up a lever escapement. It makes no difference to the artisan called upon to put a watch in perfect order as to whom he is to attribute the imperfection, maker or former repairer; all the workman having the job in hand has to do is to know positively that such a fault actually exists, and that it devolves upon him to correct it properly. BE FEARLESS IN REPAIRS, IF SURE YOU ARE RIGHT. Hence the importance of the workman being perfectly posted on such matters and, knowing that he is right, can go ahead and make the watch as it should be. The writer had an experience of this kind years ago in Chicago. A Jules Jurgensen watch had been in the hands of several good workmen in that city, but it would stop. It was then brought to him with a statement of facts given above. He knew there must be a fault somewhere and searched for it, and found it in the exit pallet--a certain tooth of the escape wheel under the right conditions would sometimes not escape. It might go through a great many thousand times and yet it might, and did sometimes, hold enough to stop the watch. Now probably most of my fellow-workmen in this instance would have been afraid to alter a "Jurgensen," or even hint to the owner that such a thing could exist as a fault in construction in a watch of this justly-celebrated maker. The writer removed the stone, ground a little from the base of the offending pallet stone, replaced it, and all trouble ended--no stops from that on. STUDY OF AN ESCAPEMENT ERROR. [Illustration: Fig. 64] Now let us suppose a case, and imagine a full-plate American movement in which the ingress or entrance pallet extends out too far, and in order to have it escape, the banking on that side is opened too wide. We show at Fig. 64 a drawing of the parts in their proper relations under the conditions named. It will be seen by careful inspection that the jewel pin _D_ will not enter the fork, which is absolutely necessary. This condition very frequently exists in watches where a new pallet stone has been put in by an inexperienced workman. Now this is one of the instances in which workmen complain of hearing a "scraping" sound when the watch is placed to the ear. The remedy, of course, lies in warming up the pallet arms and pushing the stone in a trifle, "But how much?" say some of our readers. There is no definite rule, but we will tell such querists how they can test the matter. Remove the hairspring, and after putting the train in place and securing the plates together, give the winding arbor a turn or two to put power on the train; close the bankings well in so the watch cannot escape on either pallet. Put the balance in place and screw down the cock. Carefully turn back the banking on one side so the jewel pin will just pass out of the slot in the fork. Repeat this process with the opposite banking; the jewel pin will now pass out on each side. Be sure the guard pin does not interfere with the fork action in any way. The fork is now in position to conform to the conditions required. HOW TO ADJUST THE PALLETS TO MATCH THE FORK. If the escapement is all right, the teeth will have one and a half degrees lock and escape correctly; but in the instance we are considering, the stone will not permit the teeth to pass, and must be pushed in until they will. It is not a very difficult matter after we have placed the parts together so we can see exactly how much the pallet protrudes beyond what is necessary, to judge how far to push it back when we have it out and heated. There is still an "if" in the problem we are considering, which lies in the fact that the fork we are experimenting with may be too short for the jewel pin to engage it for ten degrees of angular motion. This condition a man of large experience will be able to judge of very closely, but the better plan for the workman is to make for himself a test gage for the angular movement of the fork. Of course it will be understood that with a fork which engages the roller for eight degrees of fork action, such fork will not give good results with pallets ground for ten degrees of pallet action; still, in many instances, a compromise can be effected which will give results that will satisfy the owner of a watch of moderate cost, and from a financial point of view it stands the repairer in hand to do no more work than is absolutely necessary to keep him well pleased. We have just made mention of a device for testing the angular motion of the lever. Before we take up this matter, however, we will devote a little time and attention to the subject of jewel pins and how to set them. We have heretofore only considered jewel pins of one form, that is, a round jewel pin with two-fifths cut away. We assumed this form from the fact that experience has demonstrated that it is the most practicable and efficient form so far devised or applied. Subsequently we shall take up the subject of jewel pins of different shapes. HOW TO SET A JEWEL PIN AS IT SHOULD BE. Many workmen have a mortal terror of setting a jewel pin and seem to fancy that they must have a specially-devised instrument for accomplishing this end. Most American watches have the hole for the jewel pin "a world too wide" for it, and we have heard repeated complaints from this cause. Probably the original object of this accommodating sort of hole was to favor or obviate faults of pallet action. Let us suppose, for illustration, that we have a roller with the usual style of hole for a jewel pin which will take almost anything from the size of a No. 12 sewing needle up to a round French clock pallet. [Illustration: Fig. 65] We are restricted as regards the proper size of jewel pin by the width of the slot in the fork. Selecting a jewel which just fits the fork, we can set it as regards its relation to the staff so it will cause the pitch circle of the jewel pin to coincide with either of dotted circles _a_ or _a'_, Fig. 65. This will perhaps be better understood by referring to Fig. 66, which is a view of Fig. 65 seen in the direction of the arrow _c_. Here we see the roller jewel at _D_, and if we bring it forward as far as the hole in the roller will permit, it will occupy the position indicated at the dotted lines; and if we set it in (toward the staff) as far as the hole will allow, it will occupy the position indicated by the full outline. [Illustration: Fig. 66] Now such other condition might very easily exist, that bringing the jewel pin forward to the position indicated by the dotted lines at _D_, Fig. 66, would remedy the defect described and illustrated at Fig. 64 without any other change being necessary. We do not assert, understand, that a hole too large for the jewel pin is either necessary or desirable--what we wish to convey to the reader is the necessary knowledge so that he can profit by such a state if necessary. A hole which just fits the jewel pin so the merest film of cement will hold it in place is the way it should be; but we think it will be some time before such rollers are made, inasmuch as economy appears to be a chief consideration. ABOUT JEWEL-PIN SETTERS. To make a jewel-pin setter which will set a jewel pin straight is easy enough, but to devise any such instrument which will set a jewel so as to perfectly accord with the fork action is probably not practicable. What the workman needs is to know from examination when the jewel pin is in the proper position to perform its functions correctly, and he can only arrive at this knowledge by careful study and thought on the matter. If we make up our minds on examining a watch that a jewel pin is "set too wide," that is, so it carries the fork over too far and increases the lock to an undue degree, take out the balance, remove the hairspring, warm the roller with a small alcohol lamp, and then with the tweezers move the jewel pin in toward the staff. [Illustration: Fig. 67] [Illustration: Fig. 68] [Illustration: Fig. 69] [Illustration: Fig. 70] No attempt should be made to move a jewel pin unless the cement which holds the jewel is soft, so that when the parts cool off the jewel is as rigid as ever. A very little practice will enable any workman who has the necessary delicacy of touch requisite to ever become a good watchmaker, to manipulate a jewel pin to his entire satisfaction with no other setter than a pair of tweezers and his eye, with a proper knowledge of what he wants to accomplish. To properly heat a roller for truing up the jewel pin, leave it on the staff, and after removing the hairspring hold the balance by the rim in a pair of tweezers, "flashing it" back and forth through the flame of a rather small alcohol lamp until the rim of the balance is so hot it can just be held between the thumb and finger, and while at this temperature the jewel pin can be pressed forward or backward, as illustrated in Fig. 66, and then a touch or two will set the pin straight or parallel with the staff. Figs. 68 and 69 are self-explanatory. For cementing in a jewel pin a very convenient tool is shown at Figs. 67 and 70. It is made of a piece of copper wire about 1/16" in diameter, bent to the form shown at Fig. 67. The ends _b b_ of the copper wire are flattened a little and recessed on their inner faces, as shown in Fig. 70, to grasp the edges of the roller _A_. The heat of an alcohol lamp is applied to the loop of the wire at _g_ until the small bit of shellac placed in the hole _h_ melts. The necessary small pieces of shellac are made by warming a bit of the gum to near the melting point and then drawing the softened gum into a filament the size of horse hair. A bit of this broken off and placed in the hole _h_ supplies the cement necessary to fasten the jewel pin. Figs. 68 and 69 will, no doubt, assist in a clear understanding of the matter. HOW TO MAKE AN ANGLE-MEASURING DEVICE. We will now resume the consideration of the device for measuring the extent of the angular motion of the fork and pallets. Now, before we take this matter up in detail we wish to say, or rather repeat what we have said before, which is to the effect that ten degrees of fork and lever action is not imperative, as we can get just as sound an action and precisely as good results with nine and a half or even nine degrees as with ten, if other acting parts are in unison with such an arc of angular motion. The chief use of such an angle-measuring device is to aid in comparing the relative action of the several parts with a known standard. [Illustration: Fig. 71] For use with full-plate movements about the best plan is a spring clip or clasp to embrace the pallet staff below the pallets. We show at Fig. 71 such a device. To make it, take a rather large size of sewing needle--the kind known as a milliner's needle is about the best. The diameter of the needle should be about No. 2, so that at _b_ we can drill and put in a small screw. It is important that the whole affair should be very light. The length of the needle should be about 1-5/8", in order that from the notch _a_ to the end of the needle _A'_ should be 1½". The needle should be annealed and flattened a little, to give a pretty good grasp to the notch _a_ on the pallet staff. Good judgment is important in making this clamp, as it is nearly impossible to give exact measurements. About 1/40" in width when seen in the direction of the arrow _j_ will be found to be about the right width. The spring _B_ can be made of a bit of mainspring, annealed and filed down to agree in width with the part _A_. In connection with the device shown at Fig. 71 we need a movement-holder to hold the movement as nearly a constant height as possible above the bench. The idea is, when the clamp _A B_ is slipped on the pallet staff the index hand _A'_ will extend outward, as shown in Fig. 72, where the circle _C_ is supposed to represent the top plate of a watch, and _A'_ the index hand. HOW THE ANGULAR MOTION IS MEASURED. [Illustration: Fig. 72] Fig. 72 is supposed to be seen from above. It is evident that if we remove the balance from the movement shown at _C_, leaving power on the train, and with an oiling tool or hair broach move the lever back and forth, the index hand _A'_ will show in a magnified manner the angular motion of the lever. Now if we provide an index arc, as shown at _D_, we can measure the extent of such motion from bank to bank. [Illustration: Fig. 73] [Illustration: Fig. 74] To get up such an index arc we first make a stand as shown at _E F_, Fig. 73. The arc _D_ is made to 1½" radius, to agree with the index hand _A'_, and is divided into twelve degree spaces, six each side of a zero, as shown at Fig. 74, which is an enlarged view of the index _D_ in Fig. 72. The index arc is attached to a short bit of wire extending down into the support _E_, and made adjustable as to height by the set-screw _l_. Let us suppose the index arc is adjusted to the index hand _A'_, and we move the fork as suggested; you see the hand would show exactly the arc passed through from bank to bank, and by moving the stand _E F_ we can arrange so the zero mark on the scale stands in the center of such arc. This, of course, gives the angular motion from bank to bank. As an experiment, let us close the bankings so they arrest the fork at the instant the tooth drops from each pallet. If this arc is ten degrees, the pallet action is as it should be with the majority of modern watches. TESTING LOCK AND DROP WITH OUR NEW DEVICE. Let us try another experiment: We carefully move the fork away from the bank, and if after the index hand has passed through one and a half degrees the fork flies over, we know the lock is right. We repeat the experiment from the opposite bank, and in the same manner determine if the lock is right on the other pallets. You see we have now the means of measuring not only the angular motion of the lever, but the angular extent of the lock. At first glance one would say that if now we bring the roller and fork action to coincide and act in unison with the pallet action, we would be all right; and so we would, but frequently this bringing of the roller and fork to agree is not so easily accomplished. It is chiefly toward this end the Waltham fork is made adjustable, so it can be moved to or from the roller, and also that we can allow the pallet arms to be moved, as we will try and explain. As we set the bankings the pallets are all right; but to test matters, let us remove the hairspring and put the balance in place. Now, if the jewel pin passes in and out of the fork, it is to be supposed the fork and roller action is all right. To test the fork and roller action we close the banking a little on one side. If the fork and jewel pin are related to each other as they should be, the jewel pin will not pass out of the fork, nor will the engaged tooth drop from that pallet. This condition should obtain on both pallets, that is, if the jewel pin will not pass out of the fork on a given bank the tooth engaged on its pallet should not drop. We have now come to the most intricate and important problems which relate to the lever escapement. However, we promise our readers that if they will take the pains to follow closely our elucidations, to make these puzzles plain. But we warn them that they are no easy problems to solve, but require good, hard thinking. The readiest way to master this matter is by means of such a model escapement as we have described. With such a model, and the pallets made to clamp with small set-screws, and roller constructed so the jewel pin could be set to or from the staff, this matter can be reduced to object lessons. But study of the due relation of the parts in good drawings will also master the situation. A FEW EXPERIMENTS WITH OUR ANGLE-MEASURING DEVICE. In using the little instrument for determining angular motion that we have just described, care must be taken that the spring clamp which embraces the pallet staff does not slip. In order to thoroughly understand the methods of using this angle-measuring device, let us take a further lesson or two. We considered measuring the amount of lock on each pallet, and advised the removal of the balance, because if we left the balance in we could not readily tell exactly when the tooth passed on to the impulse plane; but if we touch the fork lightly with an oiling tool or a hair broach, moving it (the fork) carefully away from the bank and watching the arc indicated by the hand _A_, Fig. 72, we can determine with great exactness the angular extent of lock. The diagram at Fig. 75 illustrates how this experiment is conducted. We apply the hair broach to the end of the fork _M_, as shown at _L_, and gently move the fork in the direction of the arrow _i_, watching the hand _A_ and note the number of degrees, or parts of degrees, indicated by the hand as passed over before the tooth is unlocked and passes on to the impulse plane and the fork flies forward to the opposite bank. Now, the quick movement of the pallet and fork may make the hand mark more or less of an arc on the index than one of ten degrees, as the grasp may slip on the pallet staff; but the arc indicated by the slow movement in unlocking will be correct. [Illustration: Fig. 75] By taking a piece of sharpened pegwood and placing the point in the slot of the fork, we can test the fork to see if the drop takes place much before the lever rests against the opposite bank. As we have previously stated, the drop from the pallet should not take place until the lever _almost_ rests on the banking pin. What the reader should impress on his mind is that the lever should pass through about one and a half degrees arc to unlock, and the remainder (eight and a half degrees) of the ten degrees are to be devoted to impulse. But, understand, if the impulse angle is only seven and a half degrees, and the jewel pin acts in accordance with the rules previously given, do not alter the pallet until you know for certain you will gain by it. An observant workman will, after a little practice, be able to determine this matter. We will next take up the double roller and fork action, and also consider in many ways the effect of less angles of action than ten degrees. This matter now seems of more importance, from the fact that we are desirous to impress on our readers that _there is no valid reason for adopting ten degrees of fork and roller action with the table roller, except that about this number of degrees of action are required to secure a reliable safety action_. With the double roller, as low as six degrees fork and pallet action can be safely employed. In fork and pallet actions below six degrees of angular motion, side-shake in pivot holes becomes a dangerous factor, as will be explained further on. It is perfectly comprehending the action of the lever escapement and then being able to remedy defects, that constitute the master workman. HOW TO MEASURE THE ANGULAR MOTION OF AN ESCAPE WHEEL. [Illustration: Fig. 76] We can also make use of our angle-testing device for measuring our escape-wheel action, by letting the clasp embrace the arbor of the escape wheel, instead of the pallet staff. We set the index arc as in our former experiments, except we place the movable index _D_, Fig. 76, so that when the engaged tooth rests on the locking face of a pallet, the index hand stands at the extreme end of our arc of twelve degrees. We next, with our pointed pegwood, start to move the fork away from the bank, as before, we look sharp and see the index hand move backward a little, indicating the "draw" on the locking face. As soon as the pallet reaches the impulse face, the hand _A_ moves rapidly forward, and if the escapement is of the club-tooth order and closely matched, the hand _A_ will pass over ten and a half degrees of angular motion before the drop takes place. [Illustration: Fig. 77] We will warn our readers in advance, that if they make such a testing device they will be astonished at the inaccuracy which they will find in the escapements of so-called fine watches. The lock, in many instances, instead of being one and a half degrees, will oftener be found to be from two to four degrees, and the impulse derived from the escape wheel, as illustrated at Fig. 76, will often fall below eight degrees. Such watches will have a poor motion and tick loud enough to keep a policeman awake. Trials with actual watches, with such a device as we have just described, in conjunction with a careful study of the acting parts, especially if aided by a large model, such as we have described, will soon bring the student to a degree of skill unknown to the old-style workman, who, if a poor escapement bothered him, would bend back the banking pins or widen the slot in the fork. We hold that educating our repair workmen up to a high knowledge of what is required to constitute a high-grade escapement, will have a beneficial effect on manufacturers. When we wish to apply our device to the measurement of the escapement of three-quarter-plate watches, we will require another index hand, with the grasping end bent downward, as shown at Fig. 77. The idea with this form of index hand is, the bent-down jaws _B'_, Fig. 77, grasp the fork as close to the pallet staff as possible, making an allowance for the acting center by so placing the index arc that the hand _A_ will read correctly on the index _D_. Suppose, for instance, we place the jaws _B'_ inside the pallet staff, we then place the index arc so the hand reads to the arc indicated by the dotted arc _m_, Fig. 78, and if set outside of the pallet staff, read by the arc _o_. [Illustration: Fig. 78] HOW A BALANCE CONTROLS THE TIMEKEEPING OF A WATCH. We think a majority of the fine lever escapements made abroad in this day have what is termed double-roller safety action. The chief gains to be derived from this form of safety action are: (1) Reducing the arc of fork and roller action; (2) reducing the friction of the guard point to a minimum. While it is entirely practicable to use a table roller for holding the jewel pin with a double-roller action, still a departure from that form is desirable, both for looks and because as much of the aggregate weight of a balance should be kept as far from the axis of rotation as possible. We might as well consider here as elsewhere, the relation the balance bears to the train as a controlling power. Strictly speaking, _the balance and hairspring are the time measurers_, the train serving only two purposes: (_a_) To keep the balance in motion; (_b_) to classify and record the number of vibrations of the balance. Hence, it is of paramount importance that the vibrations of the balance should be as untrammeled as possible; this is why we urge reducing the arc of connection between the balance and fork to one as brief as is consistent with sound results. With a double-roller safety action we can easily reduce the fork action to eight degrees and the roller action to twenty-four degrees. Inasmuch as satisfactory results in adjustment depend very much on the perfection of construction, we shall now dwell to some extent on the necessity of the several parts being made on correct principles. For instance, by reducing the arc of engagement between the fork and roller, we lessen the duration of any disturbing influence of escapement action. To resume the explanation of why it is desirable to make the staff and all parts near the axis of the balance as light as possible, we would say it is the moving portion of the balance which controls the regularity of the intervals of vibration. To illustrate, suppose we have a balance only 3/8" in diameter, but of the same weight as one in an ordinary eighteen-size movement. We can readily see that such a balance would require but a very light hairspring to cause it to give the usual 18,000 vibrations to the hour. We can also understand, after a little thought, that such a balance would exert as much breaking force on its pivots as a balance of the same weight, but ¾" in diameter acting against a very much stronger hairspring. There is another factor in the balance problem which deserves our attention, which factor is atmospheric resistance. This increases rapidly in proportion to the velocity. HOW BAROMETRIC PRESSURE AFFECTS A WATCH. The most careful investigators in horological mechanics have decided that a balance much above 75/100" in diameter, making 18,000 vibrations per hour, is not desirable, because of the varying atmospheric disturbances as indicated by barometric pressure. A balance with all of its weight as near the periphery as is consistent with strength, is what is to be desired for best results. It is the moving matter composing the balance, pitted against the elastic force of the hairspring, which we have to depend upon for the regularity of the timekeeping of a watch, and if we can take two grains' weight of matter from our roller table and place them in the rim or screws of the balance, so as to act to better advantage against the hairspring, we have disposed of these two grains so as to increase the efficiency of the controlling power and not increase the stress on the pivots. [Illustration: Fig. 79] We have deduced from the facts set forth, two axioms: (_a_) That we should keep the weight of our balance as much in the periphery as possible, consistent with due strength; (_b_) avoid excessive size from the disturbing effect of the air. We show at _A_, Fig. 79, the shape of the piece which carries the jewel pin. As shown, it consists of three parts: (1) The socket _A_, which receives the jewel pin _a_; (2) the part _A''_ and hole _b_, which goes on the balance staff; (3) the counterpoise _A'''_, which makes up for the weight of the jewel socket _A_, neck _A'_ and jewel pin. This counterpoise also makes up for the passing hollow _C_ in the guard roller _B_, Fig. 80. As the piece _A_ is always in the same relation to the roller _B_, the poise of the balance must always remain the same, no matter how the roller action is placed on the staff. We once saw a double roller of nearly the shape shown at Fig. 79, which had a small gold screw placed at _d_, evidently for the purpose of poising the double rollers; but, to our thinking, it was a sort of hairsplitting hardly worth the extra trouble. Rollers for very fine watches should be poised on the staff before the balance is placed upon it. [Illustration: Fig. 80] We shall next give detailed instructions for drawing such a double roller as will be adapted for the large model previously described, which, as the reader will remember, was for ten degrees of roller action. We will also point out the necessary changes required to make it adapted for eight degrees of fork action. We would beg to urge again the advantages to be derived from constructing such a model, even for workmen who have had a long experience in escapements, our word for it they will discover a great many new wrinkles they never dreamed of previously. It is important that every practical watchmaker should thoroughly master the theory of the lever escapement and be able to comprehend and understand at sight the faults and errors in such escapements, which, in the every-day practice of his profession, come to his notice. In no place is such knowledge more required than in fork and roller action. We are led to say the above chiefly for the benefit of a class of workmen who think there is a certain set of rules which, if they could be obtained, would enable them to set to rights any and all escapements. It is well to understand that no such system exists and that, practically, we must make one error balance another; and it is the "know how" to make such faults and errors counteract each other that enables one workman to earn more for himself or his employer in two days than another workman, who can file and drill as well as he can, will earn in a week. PROPORTIONS OF THE DOUBLE-ROLLER ESCAPEMENT. The proportion in size between the two rollers in a double-roller escapement is an open question, or, at least, makers seldom agree on it. Grossmann shows, in his work on the lever escapement, two sizes: (1) Half the diameter of the acting roller; (2) two-thirds of the size of the acting roller. The chief fault urged against a smaller safety roller is, that it necessitates longer horns to the fork to carry out the safety action. Longer horns mean more metal in the lever, and it is the conceded policy of all recent makers to have the fork and pallets as light as possible. Another fault pertaining to long horns is, when the horn does have to act as safety action, a greater friction ensues. In all soundly-constructed lever escapements the safety action is only called into use in exceptional cases, and if the watch was lying still would theoretically never be required. Where fork and pallets are poised on their arbor, pocket motion (except torsional) should but very little affect the fork and pallet action of a watch, and torsional motion is something seldom brought to act on a watch to an extent to make it worthy of much consideration. In the double-roller action which we shall consider, we shall adopt three-fifths of the pitch diameter of the jewel-pin action as the proper size. Not but what the proportions given by Grossmann will do good service; but we adopt the proportions named because it enables us to use a light fork, and still the friction of the guard point on the roller is but little more than where a guard roller of half the diameter of the acting roller is employed. The fork action we shall consider at present is ten degrees, but subsequently we shall consider a double-roller action in which the fork and pallet action is reduced to eight degrees. We shall conceive the play between the guard point and the safety roller as one degree, which will leave half a degree of lock remaining in action on the engaged pallet. THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED. In the drawing at Fig. 81 we show a diagram of the action of the double-roller escapement. The small circle at _A_ represents the center of the pallet staff, and the one at _B_ the center of the balance staff. The radial lines _A d_ and _A d'_ represent the arc of angular motion of fork action. The circle _b b_ represents the pitch circle of the jewel pin, and the circle at _c c_ the periphery of the guard or safety roller. The points established on the circle _c c_ by intersection of the radial lines _A d_ and _A d'_ we will denominate the points _h_ and _h'_. It is at these points the end of the guard point of the fork will terminate. In construction, or in delineating for construction, we show the guard enough short of the points _h h'_ to allow the fork an angular motion of one degree, from _A_ as a center, before said point would come in contact with the safety roller. [Illustration: Fig. 81] We draw through the points _h h'_, from _B_ as a center, the radial lines _B g_ and _B g'_. We measure this angle by sweeping the short arc _i_ with any of the radii we have used for arc measurement in former delineations, and find it to be a trifle over sixty degrees. To give ourselves a practical object lesson, let us imagine that a real guard point rests on the circle _c_ at _h_. Suppose we make a notch in the guard roller represented by the circle _c_, to admit such imaginary guard point, and then commence to revolve the circle _c_ in the direction of the arrow _j_, letting the guard point rest constantly in such notch. When the notch _n_ in _c_ has been carried through thirty degrees of arc, counting from _B_ as a center, the guard point, as relates to _A_ as a center, would only have passed through an arc of five degrees. We show such a guard point and notch at _o n_. In fact, if a jewel pin was set to engage the fork on the pitch circle _b a_, the escapement would lock. To obviate such lock we widen the notch _n_ to the extent indicated by the dotted lines _n'_, allowing the guard point to fall back, so to speak, into the notch _n_, which really represents the passing hollow. It is not to be understood that the extended notch at _n_ is correctly drawn as regards position, because when the guard point was on the line _A f_ the point _o_ would be in the center of the extended notch, or passing hollow. We shall next give the details of drawing the double roller, but before doing so we deemed it important to explain the action of such guard points more fully than has been done heretofore. HOW TO DESIGN A DOUBLE-ROLLER ESCAPEMENT. We have already given very desirable forms for the parts of a double-roller escapement, consequently we shall now deal chiefly with acting principles as regards the rollers, but will give, at Fig. 82, a very well proportioned and practical form of fork. The pitch circle of the jewel pin is indicated by the dotted circle _a_, and the jewel pin of the usual cylindrical form, with two-fifths cut away. The safety roller is three-fifths of the diameter of the pitch diameter of the jewel-pin action, as indicated by the dotted circle _a_. The safety roller is shown in full outline at _B'_, and the passing hollow at _E_. It will be seen that the arc of intersection embraced between the radial lines _B c_ and _B d_ is about sixty-one and a half degrees for the roller, but the angular extent of the passing hollow is only a little over thirty-two degrees. The passing hollow _E_ is located and defined by drawing the radial line _B c_ from the center _B_ through the intersection of radial line _A i_ with the dotted arc _b_, which represents the pitch circle of the safety roller. We will name this intersection the point _l_. Now the end of the guard point _C_ terminates at the point _l_, and the passing hollow _E_ extends on _b_ sixteen degrees on each side of the radial line _B c_. [Illustration: Fig. 82] The roller action is supposed to continue through thirty degrees of angular motion of the balance staff, and is embraced on the circle _a_ between the radial line _B k_ and _B o_. To delineate the inner face of the horn _p_ of the fork _F_ we draw the short arc _g_, from _A_ as a center, and on said arc locate at two degrees from the center at _B_ the point _f_. We will designate the upper angle of the outer face of the jewel pin _D_ as the point _s_ and, from _A_ as a center, sweep through this point _s_ the short arc _n n_. Parallel with the line _A i_ and at the distance of half the diameter of the jewel pin _D_, we draw the short lines _t t'_, which define the inner faces of the fork. The intersection of the short line _t_ with the arc _n_ we will designate the point _r_. With our dividers set to embrace the space between the point _r_ and the point _f_, we sweep the arc which defines the inner face of the prong of the fork. The space we just made use of is practically the same as the radius of the circle _a_, and consequently of the same curvature. Practically, the length of the guard point _C'_ is made as long as will, with certainty, clear the safety roller _B_ in all positions. While we set the point _f_ at two degrees from the center _B_, still, in a well-constructed escapement, one and a half degrees should be sufficient, but the extra half degree will do no harm. If the roller _B'_ is accurately made and the guard point _C'_ properly fitted, the fork will not have half a degree of play. The reader will remember that in the escapement model we described we cut down the drop to one degree, being less by half a degree than advised by Grossmann and Saunier. We also advised only one degree of lock. In the perfected lever escapement, which we shall describe and give working drawings for the construction of, we shall describe a detached lever escapement with only eight degrees fork and pallet action, with only three-fourths of a degree drop and three-fourths of a degree lock, which we can assure our readers is easily within the limits of practical construction by modern machinery. HOW THE GUARD POINT IS MADE. [Illustration: Fig. 83] The guard point _C'_, as shown at Fig. 82, is of extremely simple construction. Back of the slot of the fork, which is three-fifths of the diameter of the jewel pin in depth, is made a square hole, as shown at _u_, and the back end of the guard point _C_ is fitted to this hole so that it is rigid in position. This manner of fastening the guard point is equally efficient as that of attaching it with a screw, and much lighter--a matter of the highest importance in escapement construction, as we have already urged. About the best material for such guard points is either aluminum or phosphor bronze, as such material is lighter than gold and very rigid and strong. At Fig. 83 we show a side view of the essential parts depicted in Fig. 82, as if seen in the direction of the arrow _v_, but we have added the piece which holds the jewel pin _D_. A careful study of the cut shown at Fig. 82 will soon give the horological student an excellent idea of the double-roller action. We will now take up and consider at length why Saunier draws his entrance pallet with fifteen degrees draw and his exit pallet with only twelve degrees draw. To make ourselves more conversant with Saunier's method of delineating the lever escapement, we reproduce the essential features of his drawing, Fig. 1, plate VIII, of his "Modern Horology," in which he makes the draw of the locking face of the entrance pallet fifteen degrees and his exit pallet twelve degrees. In the cut shown at Fig. 84 we use the same letters of reference as he employs. We do not quote his description or directions for delineation because he refers to so much matter which he has previously given in the book just referred to. Besides we cannot entirely endorse his methods of delineations for many reasons, one of which appears in the drawing at Fig. 84. [Illustration: Fig. 84] MORE ABOUT TANGENTIAL LOCKINGS. Most writers endorse the idea of tangential lockings, and Saunier speaks of the escapement as shown at Fig. 84 as having such tangential lockings, which is not the case. He defines the position of the pallet staff from the circle _t_, which represents the extreme length of the teeth; drawing the radial lines _A D_ and _A E_ to embrace an arc of sixty degrees, and establishing the center of his pallet staff _C_ at the intersection of the lines _D C_ and _E C_, which are drawn at right angles to the radial lines _A D_ and _A E_, and tangential to the circle _t_. Here is an error; the lines defining the center of the pallet staff should have been drawn tangent to the circle _s_, which represents the locking angle of the teeth. This would have placed the center of the pallet staff farther in, or closer to the wheel. Any person can see at a glance that the pallets as delineated are not tangential in a true sense. [Illustration: Fig. 85] We have previously considered engaging friction and also repeatedly have spoken of tangential lockings, but will repeat the idea of tangential lockings at Fig. 85. A tangential locking is neutral, or nearly so, as regards engaging friction. For illustration we refer to Fig. 85, where _A_ represents the center of an escape wheel. We draw the radial lines _A y_ and _A z_ so that they embrace sixty degrees of the arcs _s_ or _t_, which correspond to similar circles in Fig. 84, and represent the extreme extent of the teeth and likewise the locking angle of such teeth. In fact, with the club-tooth escapement all that part of a tooth which extends beyond the line _s_ should be considered the same as the addendum in gear wheels. Consequently, a tangential locking made to coincide with the center of the impulse plane, as recommended by Saunier, would require the pallet staff to be located at _C'_ instead of _C_, as he draws it. If the angle _k'_ of the tooth _k_ in Fig. 84 was extended outward from the center _A_ so it would engage or rest on the locking face of the entrance pallet as shown at Fig. 84, then the draw of the locking angle would not be quite fifteen degrees; but it is evident no lock can take place until the angle _a_ of the entrance pallet has passed inside the circle _s_. We would say here that we have added the letters _s_ and _t_ to the original drawings, as we have frequently to refer to these circles, and without letters had no means of designation. Before the locking angle _k'_ of the tooth can engage the pallet, as shown in Fig. 84, the pallet must turn on the center _C_ through an angular movement of at least four degrees. We show the situation in the diagram at Fig. 86, using the same letters of reference for similar parts as in Fig. 84. [Illustration: Fig. 86] As drawn in Fig. 84 the angle of draft _G a I_ is equal to fifteen degrees, but when brought in a position to act as shown at _G a' I'_, Fig. 86, the draw is less even than twelve degrees. The angle _C a I_ remains constant, as shown at _C a' I'_, but the relation to the radial _A G_ changes when the pallet moves through the angle _w C w'_, as it must when locked. A tangential locking in the true sense of the meaning of the phrase is a locking set so that a pallet with its face coinciding with a radial line like _A G_ would be neutral, and the thrust of the tooth would be tangent to the circle described by the locking angle of the tooth. Thus the center _C_, Fig. 86, is placed on the line _w'_ which is tangent to the circle _s_; said line _w'_ also being at right angles to the radial line _A G_. The facts are, the problems relating to the club-tooth lever escapement are very intricate and require very careful analysis, and without such care the horological student can very readily be misled. Faulty drawings, when studying such problems, lead to no end of errors, and practical men who make imperfect drawings lead to the popular phrase, "Oh, such a matter may be all right in theory, but will not work in practice." We should always bear in mind that _theory, if right, must lead practice_. CORRECT DRAWING REQUIRED. If we delineate our entrance pallet to have a draw of twelve degrees when in actual contact with the tooth, and then construct in exact conformity with such drawings, we will find our lever to "hug the banks" in every instance. It is inattention to such details which produces the errors of makers complained of by Saunier in section 696 of his "Modern Horology," and which he attempts to correct by drawing the locking face at fifteen degrees draw. We shall show that neither _C_ nor _C'_, Fig. 85, is the theoretically correct position for the pallet center for a tangential locking. We will now take up the consideration of a club-tooth lever escapement with circular pallets and tangential lockings; but previous to making the drawings we must decide several points, among which are the thickness of the pallet arms, which establishes the angular motion of the escape wheel utilized by such pallet arms, and also the angular motion imparted to the pallets by the impulse faces of the teeth. We will, for the present, accept the thickness of the arms as being equivalent to five degrees of angular extent of the pitch circle of the escape wheel. [Illustration: Fig. 87] [Illustration: Fig. 88] In making our drawings we commence, as on former occasions, by establishing the center of our escape wheel at _A_, Fig. 87, and sweeping the arc _a a_ to represent the pitch circle of such wheel. Through the center _A_ we draw the vertical line _A B_, which is supposed to also pass through the center of the pallet staff. The intersection of the line _A B_ with the arc _a_ we term the point _d_, and from this point we lay off on said arc _a_ thirty degrees each side of said intersection, and thus establish the points _c b_. From _A_, through the point _c_, we draw the line _A c c'_. On the arc _a a_ and two and a half degrees to the left of the point _c_ we establish the point _f_, which space represents half of the thickness of the entrance pallet. From _A_ we draw through the point _f_ the line _A f f'_. From _f_, and at right angles to said line _A f_, we draw the line _f e_ until it crosses the line _A B_. Now this line _f e_ is tangent to the arc _a_ from the point _f_, and consequently a locking placed at the point _f_ is a true tangential locking; and if the resting or locking face of a pallet was made to coincide with the line _A f'_, such locking face would be strictly "dead" or neutral. The intersection of the line _f e_ with the line _A B_ we call the point _C_, and locate at this point the center of our pallet staff. According to the method of delineating the lever escapement by Moritz Grossmann the tangent line for locating the center of the pallet staff is drawn from the point _c_, which would locate the center of the pallet staff at the point _h_ on the line _A B_. Grossmann, in delineating his locking face for the draw, shows such face at an angle of twelve degrees to the radial line _A f'_, when he should have drawn it twelve degrees to an imaginary line shown at _f i_, which is at right angles to the line _f h_. To the writer's mind this is not just as it should be, and may lead to misunderstanding and bad construction. We should always bear in mind the fact that the basis of a locking face is a neutral plane placed at right angles to the line of thrust, and the "draw" comes from a locking face placed at an angle to such neutral plane. A careful study of the diagram at Fig. 88 will give the reader correct ideas. If a tooth locks at the point _c_, the tangential thrust would be on the line _c h'_, and a neutral locking face would be on the line _A c_. NEUTRAL LOCKINGS. To aid in explanation, let us remove the pallet center to _D_; then the line of thrust would be _c D_ and a neutral locking face would coincide with the line _m m_, which is at right angles to the line _c D_. If we should now make a locking face with a "draw" and at an angle to the line _c D_, say, for illustration, to correspond to the line _c c'_ (leaving the pallet center at _D_), we would have a strong draw and also a cruel engaging friction. If, however, we removed the engaging tooth, which we have just conceived to be at _c_, to the point _k_ on the arc _a' a'_, Fig. 88, the pallet center _D_ would then represent a tangential locking, and a neutral pallet face would coincide with the radial line _A k'_; and a locking face with twelve degrees draw would coincide nearly with the line _l_. Let us next analyze what the effect would be if we changed the pallet center to _h'_, Fig. 88, leaving the engaging tooth still at _k_. In this instance the line _l l_ would then coincide with a neutral locking face, and to obtain the proper draw we should delineate the locking face to correspond to the line _k n_, which we assume to be twelve degrees from _k l_. It is not to be understood that we insist on precisely twelve degrees draw from a neutral plane for locking faces for lever pallets. What we do insist upon, however, is a "safe and sure draw" for a lever pallet which will hold a fork to the banks and will also return it to such banks if by accident the fork is moved away. We are well aware that it takes lots of patient, hard study to master the complications of the club-tooth lever escapement, but it is every watchmaker's duty to conquer the problem. The definition of "lock," in the detached lever escapement, is the stoppage or arrest of the escape wheel of a watch while the balance is left free or detached to perform the greater portion of its arc of vibration. "Draw" is a function of the locking parts to preserve the fork in the proper position to receive and act on the jewel pin of the balance. It should be borne in mind in connection with "lock" and "draw," that the line of thrust as projected from the locked tooth of the escape wheel should be as near tangential as practicable. This maxim applies particularly to the entrance pallet. We would beg to add that practically it will make but little odds whether we plant the center of our pallet staff at _C_ or _h_, Fig. 87, provided we modify the locking and impulse angles of our pallets to conform to such pallet center. But it will not do to arrange the parts for one center and then change to another. PRACTICAL HINTS FOR LEVER ESCAPEMENTS. Apparently there seems to be a belief with very many watchmakers that there is a set of shorthand rules for setting an escapement, especially in American watches, which, if once acquired, conquers all imperfections. Now we wish to disabuse the minds of our readers of any such notions. Although the lever escapement, as adopted by our American factories, is constructed on certain "lines," still these lines are subject to modifications, such as may be demanded for certain defects of construction. If we could duplicate every part of a watch movement perfectly, then we could have certain rules to go by, and fixed templets could be used for setting pallet stones and correcting other escapement faults. Let us now make an analysis of the action of a lever escapement. We show at Fig. 89 an ordinary eighteen-size full-plate lever with fork and pallets. The dotted lines _a b_ are supposed to represent an angular movement of ten degrees. Now, it is the function of the fork to carry the power of the train to the balance. How well the fork performs its office we will consider subsequently; for the present we are dealing with the power as conveyed to the fork by the pallets as shown at Fig. 89. [Illustration: Fig. 89] The angular motion between the lines _a c_ (which represents the lock) is not only absolutely lost--wasted--but during this movement the train has to retrograde; that is, the dynamic force stored in the momentum of the balance has to actually turn the train backward and against the force of the mainspring. True, it is only through a very short arc, but the necessary force to effect this has to be discounted from the power stored in the balance from a former impulse. For this reason we should make the angular motion of unlocking as brief as possible. Grossmann, in his essay, endorses one and a half degrees as the proper lock. In the description which we employed in describing the large model for illustrating the action of the detached lever escapement, we cut the lock to one degree, and in the description of the up-to-date lever escapement, which we shall hereafter give, we shall cut the lock down to three-quarters of a degree, a perfection easily to be attained by modern tools and appliances. We shall also cut the drop down to three-quarters of a degree. By these two economies we more than make up for the power lost in unlocking. With highly polished ruby or sapphire pallets ten degrees of draw is ample. But such draw must positively be ten degrees from a neutral locking face, not an escapement drawn on paper and called ten degrees, but when actually measured would only show eight and a half or nine degrees. THE PERFECTED LEVER ESCAPEMENT. With ten degrees angular motion of the lever and one and a half degrees lock, we should have eight and a half degrees impulse. The pith of the problem, as regards pallet action, for the practical workman can be embodied in the following question: What proportion of the power derived from the twelve degrees of angular motion of the escape wheel is really conveyed to the fork? The great leak of power as transmitted by the lever escapement to the balance is to be found in the pallet action, and we shall devote special attention to finding and stopping such leaks. WHEN POWER IS LOST IN THE LEVER ESCAPEMENT. If we use a ratchet-tooth escape wheel we must allow at least one and a half degrees drop to free the back of the tooth; but with a club-tooth escape wheel made as can be constructed by proper skill and care, the drop can be cut down to three-quarters of a degree, or one-half of the loss with the ratchet tooth. We do not wish our readers to imagine that such a condition exists in most of the so-called fine watches, because if we take the trouble to measure the actual drop with one of the little instruments we have described, it will be found that the drop is seldom less than two, or even three degrees. If we measure the angular movement of the fork while locked, it will seldom be found less than two or three degrees. Now, we can all understand that the friction of the locking surface has to be counted as well as the recoil of the draw. Locking friction is seldom looked after as carefully as the situation demands. Our factories make the impulse face of the pallets rounded, but leave the locking face flat. We are aware this condition is, in a degree, necessary from the use of exposed pallets. In many of the English lever watches with ratchet teeth, the locking faces are made cylindrical, but with such watches the pallet stones, as far as the writer has seen, are set "close"; that is, with steel pallet arms extending above and below the stone. There is another feature of the club-tooth lever escapement that next demands our attention which we have never seen discussed. We refer to arranging and disposing of the impulse of the escape wheel to meet the resistance of the hairspring. Let us imagine the dotted line _A d_, Fig. 89, to represent the center of action of the fork. We can readily see that the fork in a state of rest would stand half way between the two banks from the action of the hairspring, and in the pallet action the force of the escape wheel, one tooth of which rests on the impulse face of a pallet, would be exerted against the elastic force of the hairspring. If the force of the mainspring, as represented by the escape-wheel tooth, is superior to the power of the hairspring, the watch starts itself. The phases of this important part of the detached lever escapement will be fully discussed. ABOUT THE CLUB-TOOTH ESCAPEMENT. We will now take up a study of the detached lever escapement as relates to pallet action, with the point specially in view of constructing an escapement which cannot "set" in the pocket, or, in other words, an escapement which will start after winding (if run down) without shaking or any force other than that supplied by the train as impelled by the mainspring. In the drawing at Fig. 90 we propose to utilize eleven degrees of escape-wheel action, against ten and a half, as laid down by Grossmann. Of this eleven degrees we propose to divide the impulse arc of the escape wheel in six and five degrees, six to be derived from the impulse face of the club tooth and five from the impulse plane of the pallet. The pallet action we divide into five and four, with one degree of lock. Five degrees of pallet action is derived from the impulse face of the tooth and four from the impulse face of the pallet. The reader will please bear in mind that we do not give these proportions as imperative, because we propose to give the fullest evidence into the reader's hands and enable him to judge for himself, as we do not believe in laying down imperious laws that the reader must accept on our assertion as being correct. Our idea is rather to furnish the proper facts and put him in a situation to know for himself. The reader is urged to make the drawings for himself on a large scale, say, an escape wheel 10" pitch diameter. Such drawings will enable him to realize small errors which have been tolerated too much in drawings of this kind. The drawings, as they appear in the cut, are one-fourth the size recommended, and many of the lines fail to show points we desire to call attention to. As for instance, the pallet center at _B_ is tangential to the pitch circle _a_ from the point of tooth contact at _f_. To establish this point we draw the radial lines _A c_ and _A d_ from the escape-wheel center _A_, as shown, by laying off thirty degrees on each side of the intersection of the vertical line _i_ (passing through the centers _A B_) with the arc _a_, and then laying off two and a half degrees on _a_ and establishing the point _f_, and through _f_ from the center _A_ draw the radial line _A f'_. Through the point _f_ we draw the tangent line _b' b b''_, and at the intersection of the line _b_ with _i_ we establish the center of our pallet staff at _B_. At two and a half degrees from the point _c_ we lay off two and a half degrees to the right of said point and establish the point _n_, and draw the radial line _A n n'_, which establishes the extent of the arc of angular motion of the escape wheel utilized by the pallet arm. [Illustration: Fig. 90] We have now come to the point where we must exercise our reasoning powers a little. We know the locking angle of the escape-wheel tooth passes on the arc _a_, and if we utilize the impulse face of the tooth for five degrees of pallet or lever motion we must shape it to this end. We draw the short arc _k_ through the point _n_, knowing that the inner angle of the pallet stone must rest on this arc wherever it is situated. As, for instance, when the locking face of the pallet is engaged, the inner angle of the pallet stone must rest somewhere on this arc (_k_) inside of _a_, and the extreme outer angle of the impulse face of the tooth must part with the pallet on this arc _k_. HOW TO LOCATE THE PALLET ACTION. With the parts related to each other as shown in the cut, to establish where the inner angle of the pallet stone is located in the drawing, we measure down on the arc _k_ five degrees from its intersection with _a_, and establish the point _s_. The line _B b_, Fig. 90, as the reader will see, does not coincide with the intersection of the arcs _a_ and _k_, and to conveniently get at the proper location for the inner angle of our pallet stone, we draw the line _B b'_, which passes through the point _n_ located at the intersection of the arc _a_ with the arc _k_. From _B_ as a center we sweep the short arc _j_ with any convenient radius of which we have a sixty-degree scale, and from the intersection of _B b'_ with _j_ we lay off five degrees and draw the line _B s'_, which establishes the point _s_ on the arc _k_. As stated above, we allow one degree for lock, which we establish on the arc _o_ by laying off one degree on the arc _j_ below its intersection with the line _B b_. We do not show this line in the drawing, from the fact that it comes so near to _B b'_ that it would confuse the reader. Above the arc _a_ on the arc _k_ at five degrees from the point _n_ we establish the point _l_, by laying off five degrees on the arc _j_ above the intersection of the line _B b_ with _j_. The point _l_, Fig. 90, establishes where the outer angle of the tooth will pass the arc _k_ to give five degrees of angular motion to the lever. From _A_ as a center we sweep the arc _m_, passing through the point _l_. The intersection of the arc _m_ with the line _A h_ we call the point _r_, and by drawing the right line _r f_ we delineate the impulse face of the tooth. On the arc _o_ and one degree below its intersection with the line _B b_ we establish the point _t_, and by drawing a right line from _t_ to _s_ we delineate the impulse face of our entrance pallet. "ACTION" DRAWINGS. One great fault with most of our text books on horology lies in the fact that when dealing with the detached lever escapement the drawings show only the position of the pallets when locked, and many of the conditions assumed are arrived at by mental processes, without making the proper drawings to show the actual relation of the parts at the time such conditions exist. For illustration, it is often urged that there is a time in the action of the club-tooth lever escapement action when the incline on the tooth and the incline on the pallet present parallel surfaces, and consequently endure excessive friction, especially if the oil is a little thickened. We propose to make drawings to show the exact position and relation of the entrance pallet and tooth at three intervals viz: (1) Locked; (2) the position of the parts when the lever has performed one-half of its angular motion; (3) when half of the impulse face of the tooth has passed the pallet. The position of the entrance pallet when locked is sufficiently well shown in Fig. 90 to give a correct idea of the relations with the entrance pallet; and to conform to statement (2), as above. We will now delineate the entrance pallet, not in actual contact, however, with the pallet, because if we did so the lines we employed would become confused. The methods we use are such that _we can delineate with absolute correctness either a pallet or tooth at any point in its angular motion_. We have previously given instructions for drawing the pallet locked; and to delineate the pallet after five degrees of angular motion, we have only to conceive that we substitute the line _s'_ for the line _b'_. All angular motions and measurements for pallet actions are from the center of the pallet staff at _B_. As we desire to now delineate the entrance pallet, it has passed through five degrees of angular motion and the inner angle _s_ now lies on the pitch circle of the escape wheel, the angular space between the lines _b' s'_ being five degrees, the line _b''_ reducing the impulse face to four degrees. DRAWING AN ESCAPEMENT TO SHOW ANGULAR MOTION. To delineate our locking face we draw a line at right angles to the line _B b''_ from the point _t_, said point being located at the intersection of the arc _o_ with the line _B b''_. To draw a line perpendicular to _B b''_ from the point _t_, we take a convenient space in our dividers and establish on the line _B b''_ the points _x x'_ at equal distances from the point _t_. We open the dividers a little (no special distance) and sweep the short arcs _x'' x'''_, as shown at Fig. 91. Through the intersection of the short arcs _x'' x'''_ and to the point _t_ we draw the line _t y_. The reader will see from our former explanations that the line _t y_ represents the neutral plane of the locking face, and that to have the proper draw we must delineate the locking face of our pallet at twelve degrees. To do this we draw the line _t x'_ at twelve degrees to the line _t y_, and proceed to outline our pallet faces as shown. We can now understand, after a moment's thought, that we can delineate the impulse face of a tooth at any point or place we choose by laying off six degrees on the arc _m_, and drawing radial lines from _A_ to embrace such arc. To illustrate, suppose we draw the radial lines _w' w''_ to embrace six degrees on the arc _a_. We make these lines contiguous to the entrance pallet _C_ for convenience only. To delineate the impulse face of the tooth, we draw a line extending from the intersection of the radial line _A' w'_ with the arc _m_ to the intersection of the arc _a_ with the radial line _A w''_. [Illustration: Fig. 91] We next desire to know where contact will take place between the wheel-tooth _D_ and pallet _C_. To determine this we sweep, with our dividers set so one leg rests at the escape-wheel center _A_ and the other at the outer angle _t_ of the entrance pallet, the short arc _t' w_. Where this arc intersects the line _w_ (which represents the impulse face of the tooth) is where the outer angle _t_ of the entrance pallet _C_ will touch the impulse face of the tooth. To prove this we draw the radial line _A v_ through the point where the short arc _t t'_ passes through the impulse face _w_ of the tooth _D_. Then we continue the line _w_ to _n_, to represent the impulse face of the tooth, and then measure the angle _A w n_ between the lines _w n_ and _v A_, and find it to be approximately sixty-four degrees. We then, by a similar process, measure the angle _A t s'_ and find it to be approximately sixty-six degrees. When contact ensues between the tooth _D_ and pallet _C_ the tooth _D_ will attack the pallet at the point where the radial line _A v_ crosses the tooth face. We have now explained how we can delineate a tooth or pallet at any point of its angular motion, and will next explain how to apply this knowledge in actual practice. PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT. To delineate our entrance pallet after one-half of the engaged tooth has passed the inner angle of the entrance pallet, we proceed, as in former illustrations, to establish the escape-wheel center at _A_, and from it sweep the arc _b_, to represent the pitch circle. We next sweep the short arcs _p s_, to represent the arcs through which the inner and outer angles of the entrance pallet move. Now, to comply with our statement as above, we must draw the tooth as if half of it has passed the arc _s_. To do this we draw from _A_ as a center the radial line _A j_, passing through the point _s_, said point _s_ being located at the intersection of the arcs _s_ and _b_. The tooth _D_ is to be shown as if one half of it has passed the point _s_; and, consequently, if we lay off three degrees on each side of the point _s_ and establish the points _d m_, we have located on the arc _b_ the angular extent of the tooth to be drawn. To aid in our delineations we draw from the center _A_ the radial lines _A d'_ and _A m'_, passing through the points _d m_. The arc _a_ is next drawn as in former instructions and establishes the length of the addendum of the escape-wheel teeth, the outer angle of our escape-wheel tooth being located at the intersection of the arc _a_ with the radial line _A d'_. As shown in Fig. 92, the impulse planes of the tooth _D_ and pallet _C_ are in contact and, consequently, in parallel planes, as mentioned on page 91. It is not an easy matter to determine at exactly what degree of angular motion of the escape wheel such condition takes place; because to determine such relation mathematically requires a knowledge of higher mathematics, which would require more study than most practical men would care to bestow, especially as they would have but very little use for such knowledge except for this problem and a few others in dealing with epicycloidal curves for the teeth of wheels. For all practical purposes it will make no difference whether such parallelism takes place after eight or nine degrees of angular motion of the escape wheel subsequent to the locking action. The great point, as far as practical results go, is to determine if it takes place at or near the time the escape wheel meets the greatest resistance from the hairspring. We find by analysis of our drawing that parallelism takes place about the time when the tooth has three degrees of angular motion to make, and the pallet lacks about two degrees of angular movement for the tooth to escape. It is thus evident that the relations, as shown in our drawing, are in favor of the train or mainspring power over hairspring resistance as three is to two, while the average is only as eleven to ten; that is, the escape wheel in its entire effort passes through eleven degrees of angular motion, while the pallets and fork move through ten degrees. The student will thus see we have arranged to give the train-power an advantage where it is most needed to overcome the opposing influence of the hairspring. [Illustration: Fig. 92] As regards the exalted adhesion of the parallel surfaces, we fancy there is more harm feared than really exists, because, to take the worst view of the situation, such parallelism only exists for the briefest duration, in a practical sense, because theoretically these surfaces never slide on each other as parallel planes. Mathematically considered, the theoretical plane represented by the impulse face of the tooth approaches parallelism with the plane represented by the impulse face of the pallet, arrives at parallelism and instantly passes away from such parallelism. TO DRAW A PALLET IN ANY POSITION. As delineated in Fig. 92, the impulse planes of the tooth and pallet are in contact; but we have it in our power to delineate the pallet at any point we choose between the arcs _p s_. To describe and illustrate the above remark, we say the lines _B e_ and _B f_ embrace five degrees of angular motion of the pallet. Now, the impulse plane of the pallet occupies four of these five degrees. We do not draw a radial line from _B_ inside of the line _B e_ to show where the outer angle of the impulse plane commences, but the reader will see that the impulse plane is drawn one degree on the arc _p_ below the line _B e_. We continue the line _h h_ to represent the impulse face of the tooth, and measure the angle _B n h_ and find it to be twenty-seven degrees. Now suppose we wish to delineate the entrance pallet as if not in contact with the escape-wheel tooth--for illustration, say, we wish the inner angle of the pallet to be at the point _v_ on the arc _s_. We draw the radial line _B l_ through _v_; and if we draw another line so it passes through the point _v_ at an angle of twenty-seven degrees to _B l_, and continue said line so it crosses the arc _p_, we delineate the impulse face of our pallet. We measure the angle _i n B_, Fig. 92, and find it to be seventy-four degrees; we draw the line _v t_ to the same angle with _v B_, and we define the inner face of our pallet in the new position. We draw a line parallel with _v t_ from the intersection of the line _v y_ with the arc _p_, and we define our locking face. If now we revolve the lines we have just drawn on the center _B_ until the line _l B_ coincides with the line _f B_, we will find the line _y y_ to coincide with _h h_, and the line _v v'_ with _n i_. HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT. We have now instructed the reader how to delineate either tooth or pallet in any conceivable position in which they can be related to each other. Probably nothing has afforded more efficient aid to practical mechanics than has been afforded by the graphic solution of abstruce mathematical problems; and if we add to this the means of correction by mathematical calculations which do not involve the highest mathematical acquirements, we have approached pretty close to the actual requirements of the practical watchmaker. [Illustration: Fig. 93] To better explain what we mean, we refer the reader to Fig. 93, where we show preliminary drawings for delineating a lever escapement. We wish to ascertain by the graphic method the distance between the centers of action of the escape wheel and the pallet staff. We make our drawing very carefully to a given scale, as, for instance, the radius of the arc _a_ is 5". After the drawing is in the condition shown at Fig. 93 we measure the distance on the line _b_ between the points (centers) _A B_, and we thus by graphic means obtain a measure of the distance between _A B_. Now, by the use of trigonometry, we have the length of the line _A f_ (radius of the arc _a_) and all the angles given, to find the length of _f B_, or _A B_, or both _f B_ and _A B_. By adopting this policy we can verify the measurements taken from our drawings. Suppose we find by the graphic method that the distance between the points _A B_ is 5.78", and by trigonometrical computation find the distance to be 5.7762". We know from this that there is .0038" to be accounted for somewhere; but for all practical purposes either measurement should be satisfactory, because our drawing is about thirty-eight times the actual size of the escape wheel of an eighteen-size movement. HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED. Let us further suppose the diameter of our actual escape wheel to be .26", and we were constructing a watch after the lines of our drawing. By "lines," in this case, we mean in the same general form and ratio of parts; as, for illustration, if the distance from the intersection of the arc _a_ with the line _b_ to the point _B_ was one-fifteenth of the diameter of the escape wheel, this ratio would hold good in the actual watch, that is, it would be the one-fifteenth part of .26". Again, suppose the diameter of the escape wheel in the large drawing is 10" and the distance between the centers _A B_ is 5.78"; to obtain the actual distance for the watch with the escape wheel .26" diameter, we make a statement in proportion, thus: 10 : 5.78 :: .26 to the actual distance between the pivot holes of the watch. By computation we find the distance to be .15". These proportions will hold good in every part of actual construction. All parts--thickness of the pallet stones, length of pallet arms, etc.--bear the same ratio of proportion. We measure the thickness of the entrance pallet stone on the large drawing and find it to be .47"; we make a similar statement to the one above, thus: 10 : .47 :: .26 to the actual thickness of the real pallet stone. By computation we find it to be .0122". All angular relations are alike, whether in the large drawing or the small pallets to match the actual escape wheel .26" in diameter. Thus, in the pallet _D_, Fig. 93, the impulse face, as reckoned from _B_ as a center, would occupy four degrees. MAKE A LARGE ESCAPEMENT MODEL. Reason would suggest the idea of having the theoretical keep pace and touch with the practical. It has been a grave fault with many writers on horological matters that they did not make and measure the abstractions which they delineated on paper. We do not mean by this to endorse the cavil we so often hear--"Oh, that is all right in theory, but it will not work in practice." If theory is right, practice must conform to it. The trouble with many theories is, they do not contain all the elements or factors of the problem. [Illustration: Fig. 94] Near the beginning of this treatise we advised our readers to make a large model, and described in detail the complete parts for such a model. What we propose now is to make adjustable the pallets and fork to such a model, in order that we can set them both right and wrong, and thus practically demonstrate a perfect action and also the various faults to which the lever escapement is subject. The pallet arms are shaped as shown at _A_, Fig. 94. The pallets _B B'_ can be made of steel or stone, and for all practical purposes those made of steel answer quite as well, and have the advantage of being cheaper. A plate of sheet brass should be obtained, shaped as shown at _C_, Fig. 95. This plate is of thin brass, about No. 18, and on it are outlined the pallet arms shown at Fig. 94. [Illustration: Fig. 95] [Illustration: Fig. 96] [Illustration: Fig. 97] [Illustration: Fig. 98] To make the pallets adjustable, they are set in thick disks of sheet brass, as shown at _D_, Figs. 95, 96 and 97. At the center of the plate _C_ is placed a brass disk _E_, Fig. 98, which serves to support the lever shown at Fig. 99. This disk _E_ is permanently attached to the plate _C_. The lever shown at Fig. 99 is attached to the disk _E_ by two screws, which pass through the holes _h h_. If we now place the brass pieces _D D'_ on the plate _C_ in such a way that the pallets set in them correspond exactly to the pallets as outlined on the plate _C_, we will find the action of the pallets to be precisely the same as if the pallet arms _A A'_, Fig. 94, were employed. [Illustration: Fig. 99] To enable us to practically experiment with and to fully demonstrate all the problems of lock, draw, drop, etc., we make quite a large hole in _C_ where the screws _b_ come. To explain, if the screws _b b_ were tapped directly into _C_, as they are shown at Fig. 95, we could only turn the disk _D_ on the screw _b_; but if we enlarge the screw hole in _C_ to three or four times the natural diameter, and then place the nut _e_ under _C_ to receive the screw _b_, we can then set the disks _D D'_ and pallets _B B'_ in almost any relation we choose to the escape wheel, and clamp the pallets fast and try the action. We show at Fig. 97 a view of the pallet _B'_, disk _D'_ and plate _C_ (seen in the direction of the arrow _c_) as shown in Fig. 95. PRACTICAL LESSONS WITH FORK AND PALLET ACTION. It will be noticed in Fig. 99 that the hole _g_ for the pallet staff in the lever is oblong; this is to allow the lever to be shifted back and forth as relates to roller and fork action. We will not bother about this now, and only call attention to the capabilities of such adjustments when required. At the outset we will conceive the fork _F_ attached to the piece _E_ by two screws passing through the holes _h h_, Fig. 99. Such an arrangement will insure the fork and roller action keeping right if they are put right at first. Fig. 100 will do much to aid in conveying a clear impression to the reader. The idea of the adjustable features of our escapement model is to show the effects of setting the pallets wrong or having them of bad form. For illustration, we make use of a pallet with the angle too acute, as shown at _B'''_, Fig. 101. The problem in hand is to find out by mechanical experiments and tests the consequences of such a change. It is evident that the angular motion of the pallet staff will be increased, and that we shall have to open one of the banking pins to allow the engaging tooth to escape. To trace out _all_ the consequences of this one little change would require a considerable amount of study, and many drawings would have to be made to illustrate the effects which would naturally follow only one such slight change. [Illustration: Fig. 100] [Illustration: Fig. 101] Suppose, for illustration, we should make such a change in the pallet stone of the entrance pallet; we have increased the angle between the lines _k l_ by (say) one and a half degrees; by so doing we would increase the lock on the exit pallet to three degrees, provided we were working on a basis of one and a half degrees lock; and if we pushed back the exit pallet so as to have the proper degree of lock (one and a half) on it, the tooth which would next engage the entrance pallet would not lock at all, but would strike the pallet on the impulse instead of on the locking face. Again, such a change might cause the jewel pin to strike the horn of the fork, as indicated at the dotted line _m_, Fig. 99. Dealing with such and similar abstractions by mental process requires the closest kind of reasoning; and if we attempt to delineate all the complications which follow even such a small change, we will find the job a lengthy one. But with a large model having adjustable parts we provide ourselves with the means for the very best practical solution, and the workman who makes and manipulates such a model will soon master the lever escapement. QUIZ PROBLEMS IN THE DETACHED LEVER ESCAPEMENT. Some years ago a young watchmaker friend of the writer made, at his suggestion, a model of the lever escapement similar to the one described, which he used to "play with," as he termed it--that is, he would set the fork and pallets (which were adjustable) in all sorts of ways, right ways and wrong ways, so he could watch the results. A favorite pastime was to set every part for the best results, which was determined by the arc of vibration of the balance. By this sort of training he soon reached that degree of proficiency where one could no more puzzle him with a bad lever escapement than you could spoil a meal for him by disarranging his knife, fork and spoon. Let us, as a practical example, take up the consideration of a short fork. To represent this in our model we take a lever as shown at Fig. 99, with the elongated slot for the pallet staff at _g_. To facilitate the description we reproduce at Fig. 102 the figure just mentioned, and also employ the same letters of reference. We fancy everybody who has any knowledge of the lever escapement has an idea of exactly what a "short fork" is, and at the same time it would perhaps puzzle them a good deal to explain the difference between a short fork and a roller too small. [Illustration: Fig. 102] [Illustration: Fig. 103] In our practical problems, as solved on a large escapement model, say we first fit our fork of the proper length, and then by the slot _g_ move the lever back a little, leaving the bankings precisely as they were. What are the consequences of this slight change? One of the first results which would display itself would be discovered by the guard pin failing to perform its proper functions. For instance, the guard pin pushed inward against the roller would cause the engaged tooth to pass off the locking face of the pallet, and the fork, instead of returning against the banking, would cause the guard pin to "ride the roller" during the entire excursion of the jewel pin. This fault produces a scraping sound in a watch. Suppose we attempt to remedy the fault by bending forward the guard pin _b_, as indicated by the dotted outline _b'_ in Fig. 103, said figure being a side view of Fig. 102 seen in the direction of the arrow _a_. This policy would prevent the engaged pallet from passing off of the locking face of the pallet, but would be followed by the jewel pin not passing fully into the fork, but striking the inside face of the prong of the fork at about the point indicated by the dotted line _m_. We can see that if the prong of the fork was extended to about the length indicated by the outline at _c_, the action would be as it should be. To practically investigate this matter to the best advantage, we need some arrangement by which we can determine the angular motion of the lever and also of the roller and escape wheel. To do this, we provide ourselves with a device which has already been described, but of smaller size, for measuring fork and pallet action. The device to which we allude is shown at Figs. 104, 105 and 106. Fig. 104 shows only the index hand, which is made of steel about 1/20" thick and shaped as shown. The jaws _B''_ are intended to grasp the pallet staff by the notches _e_, and hold by friction. The prongs _l l_ are only to guard the staff so it will readily enter the notch _e_. The circle _d_ is only to enable us to better hold the hand _B_ flat. [Illustration: Fig. 104] HOW TO MEASURE ESCAPEMENT ANGLES. From the center of the notches _e_ to the tip of the index hand _B'_ the length is 2". This distance is also the radius of the index arc _C_. This index arc is divided into thirty degrees, with three or four supplementary degrees on each side, as shown. For measuring pallet action we only require ten degrees, and for roller action thirty degrees. The arc _C_, Fig. 105, can be made of brass and is about 1½" long by ¼" wide; said arc is mounted on a brass wire about 1/8" diameter, as shown at _k_, Fig. 106, which is a view of Fig. 105 seen in the direction of the arrow _i_. This wire _k_ enters a base shown at _D E_, Fig. 106, which is provided with a set-screw at _j_ for holding the index arc at the proper height to coincide with the hand _B_. [Illustration: Fig. 105] [Illustration: Fig. 106] A good way to get up the parts shown in Fig. 106 is to take a disk of thick sheet brass about 1" in diameter and insert in it a piece of brass wire about ¼" diameter and 3/8" long, through which drill axially a hole to receive the wire _k_. After the jaws _B''_ are clamped on the pallet staff, we set the index arc _C_ so the hand _B'_ will indicate the angular motion of the pallet staff. By placing the index hand _B_ on the balance staff we can get at the exact angular duration of the engagement of the jewel pin in the fork. Of course, it is understood that this instrument will also measure the angles of impulse and lock. Thus, suppose the entire angular motion of the lever from bank to bank is ten degrees; to determine how much of this is lock and how much impulse, we set the index arc _C_ so that the hand _B'_ marks ten degrees for the entire motion of the fork, and when the escapement is locked we move the fork from its bank and notice by the arc _C_ how many degrees the hand indicated before it passed of its own accord to the opposite bank. If we have more than one and a half degrees of lock we have too much and should seek to remedy it. How? It is just the answers to such questions we propose to give by the aid of our big model. DETERMINATION OF "RIGHT" METHODS. "Be sure you are right, then go ahead," was the advice of the celebrated Davie Crockett. The only trouble in applying this motto to watchmaking is to know when you are right. We have also often heard the remark that there was only one right way, but any number of wrong ways. Now we are inclined to think that most of the people who hold to but one right way are chiefly those who believe all ways but their own ways are wrong. Iron-bound rules are seldom sound even in ethics, and are utterly impracticable in mechanics. We have seen many workmen who had learned to draw a lever escapement of a given type, and lived firm in the belief that all lever escapements were wrong which were not made so as to conform to this certain method. One workman believes in equidistant lockings, another in circular pallets; each strong in the idea that their particular and peculiar method of designing a lever escapement was the only one to be tolerated. The writer is free to confess that he has seen lever escapements of both types, that is, circular pallets and equidistant lockings, which gave excellent results. Another mooted point in the lever escapement is, to decide between the merits of the ratchet and the club-tooth escape wheel. English makers, as a rule, hold to the ratchet tooth, while Continental and American manufacturers favor the club tooth. The chief arguments in favor of the ratchet tooth are: (_a_) It will run without oiling the pallets; (_b_) in case the escape wheel is lost or broken it is more readily replaced, as all ratchet-tooth escape wheels are alike, either for circular pallets or equidistant lockings. The objections urged against it are: (_a_) Excessive drop; (_b_) the escape wheel, being frail, is liable to be injured by incompetent persons handling it; (_c_) this escapement in many instances does require to have the pallets oiled. ESCAPEMENTS COMPARED. (_a_) That a ratchet-tooth escape wheel requires more drop than a club tooth must be admitted without argument, as this form of tooth requires from one-half to three-fourths of a degree more drop than a club tooth; (_b_) as regards the frailty of the teeth we hold this as of small import, as any workman who is competent to repair watches would never injure the delicate teeth of an escape wheel; (_c_) ratchet-tooth lever escapements will occasionally need to have the pallets oiled. The writer is inclined to think that this defect could be remedied by proper care in selecting the stone (ruby or sapphire) and grinding the pallets in such a way that the escape-wheel teeth will not act against the foliations with which all crystalline stones are built up. All workmen who have had an extended experience in repair work are well aware that there are some lever escapements in which the pallets absolutely require oil; others will seem to get along very nicely without. This applies also to American brass club-tooth escapements; hence, we have so much contention about oiling pallets. The writer does not claim to know positively that the pallet stones are at fault because some escapements need oiling, but the fact must admit of explanation some way, and is this not at least a rational solution? All persons who have paid attention to crystallography are aware that crystals are built up, and have lines of cleavage. In the manufacture of hole jewels, care must be taken to work with the axis of crystallization, or a smooth hole cannot be obtained. The advantages claimed for the club-tooth escapement are many; among them may be cited (_a_) the fact that it utilizes a greater arc of impulse of the escape wheel; (_b_) the impulse being divided between the tooth and the pallet, permits greater power to be utilized at the close of the impulse. This feature we have already explained. It is no doubt true that it is more difficult to match a set of pallets with an escape wheel of the club-tooth order than with a ratchet tooth; still the writer thinks that this objection is of but little consequence where a workman knows exactly what to do and how to do it; in other words, is sure he is right, and can then go ahead intelligently. It is claimed by some that all American escape wheels of a given grade are exact duplicates; but, as we have previously stated, this is not exactly the case, as they vary a trifle. So do the pallet jewels vary a little in thickness and in the angles. Suppose we put in a new escape wheel and find we have on the entrance pallet too much drop, that is, the tooth which engaged this pallet made a decided movement forward before the tooth which engaged the exit pallet encountered the locking face of said pallet. If we thoroughly understand the lever escapement we can see in an instant if putting in a thicker pallet stone for entrance pallet will remedy the defect. Here again we can study the effects of a change in our large model better than in an escapement no larger than is in an ordinary watch. HOW TO SET PALLET STONES. There have been many devices brought forward to aid the workman in adjusting the pallet stones to lever watches. Before going into the details of any such device we should thoroughly understand exactly what we desire to accomplish. In setting pallet stones we must take into consideration the relation of the roller and fork action. As has already been explained, the first thing to do is to set the roller and fork action as it should be, without regard in a great degree to pallet action. [Illustration: Fig. 107] To explain, suppose we have a pallet stone to set in a full-plate movement. The first thing to do is to close the bankings so that the jewel pin will not pass out of the slot in the fork on either side; then gradually open the bankings until the jewel pin will pass out. This will be understood by inspecting Fig. 107, where _A A'_ shows a lever fork as if in contact with both banks, and the jewel pin, represented at _B B''_, just passes the angle _a c'_ of the fork. The circle described by the jewel pin _B_ is indicated by the arc _e_. It is well to put a slight friction under the balance rim, in order that we can try the freedom of the guard pin. As a rule, all the guard pin needs is to be free and not touch the roller. The entire point, as far as setting the fork and bankings is concerned, is to have the fork and roller action sound. For all ordinary lever escapements the angular motion of the lever banked in as just described should be _about_ ten degrees. As explained in former examples, if the fork action is entirely sound and the lever only vibrates through an arc of nine degrees, it is quite as well to make the pallets conform to this arc as to make the jewel pin carry the fork through full ten degrees. Again, if the lever vibrates through eleven degrees, it is as well to make the pallets conform to this arc. The writer is well aware that many readers will cavil at this idea and insist that the workman should bring all the parts right on the basis of ten degrees fork and lever action. In reply we would say that no escapement is perfect, and it is the duty of the workman to get the best results he can for the money he gets for the job. In the instance given above, of the escapement with nine degrees of lever action, when the fork worked all right, if we undertook to give the fork the ten degrees demanded by the stickler for accuracy we would have to set out the jewel pin or lengthen the fork, and to do either would require more time than it would to bring the pallets to conform to the fork and roller action. It is just this knowing how and the decision to act that makes the difference in the workman who is worth to his employer twelve or twenty-five dollars per week. We have described instruments for measuring the angle of fork and pallet action, but after one has had experience he can judge pretty nearly and then it is seldom necessary to measure the angle of fork action as long as it is near the proper thing, and then bring the pallets to match the escape wheel after the fork and roller action is as it should be--that is, the jewel pin and fork work free, the guard pin has proper freedom, and the fork vibrates through an arc of about ten degrees. Usually the workman can manipulate the pallets to match the escape wheel so that the teeth will have the proper lock and drop at the right instant, and again have the correct lock on the next succeeding pallet. The tooth should fall but a slight distance before the tooth next in action locks it, because all the angular motion the escape wheel makes except when in contact with the pallets is just so much lost power, which should go toward giving motion to the balance. There seems to be a little confusion in the use of the word "drop" in horological phrase, as it is used to express the act of parting of the tooth with the pallet. The idea will be seen by inspecting Fig. 108, where we show the tooth _D_ and pallet _C_ as about parting or dropping. When we speak of "banking up to the drop" we mean we set the banking screws so that the teeth will just escape from each pallet. By the term "fall" we mean the arc the tooth passes through before the next pallet is engaged. This action is also illustrated at Fig. 108, where the tooth _D_, after dropping from the pallet _C_, is arrested at the position shown by the dotted outline. We designate this arc by the term "fall," and we measure this motion by its angular extent, as shown by the dotted radial lines _i f_ and _i g_. As we have explained, this fall should only extend through an arc of one and a half degrees, but by close escapement matching this arc can be reduced to one degree, or even a trifle less. [Illustration: Fig. 108] We shall next describe an instrument for holding the escape wheel and pallets while adjusting them. As shown at Fig. 107, the fork _A'_ is banked a little close and the jewel pin as shown would, in some portions, rub on _C'_, making a scraping sound. HOW TO MAKE AN ESCAPEMENT MATCHING TOOL. [Illustration: Fig. 109] A point has now been reached where we can use an escapement matcher to advantage. There are several good ones on the market, but we can make one very cheaply and also add our own improvements. In making one, the first thing to be provided is a movement holder. Any of the three-jaw types of such holders will answer, provided the jaws hold a movement plate perfectly parallel with the bed of the holder. This will be better understood by inspecting Fig. 109, which is a side view of a device of this kind seen edgewise in elevation. In this _B_ represents the bed plate, which supports three swing jaws, shown at _C_, Figs. 109 and 110. The watch plate is indicated by the parallel dotted lines _A_, Fig. 109. The seat _a_ of the swing jaws _C_ must hold the watch plate _A_ exactly parallel with the bed plate _B_. In the cheap movement holders these seats (_a_) are apt to be of irregular heights, and must be corrected for our purpose. We will take it for granted that all the seats _a_ are of precisely the same height, measured from _B_, and that a watch plate placed in the jaws _C_ will be held exactly parallel with the said bed _B_. We must next provide two pillars, shown at _D E_, Figs. 109 and 111. These pillars furnish support for sliding centers which hold the top pivots of the escape wheel and pallet staff while we are testing the depths and adjusting the pallet stones. It will be understood that these pillars _D E_ are at right angles to the plane of the bed _B_, in order that the slides like _G N_ on the pillars _D E_ move exactly vertical. In fact, all the parts moving up and down should be accurately made, so as not to destroy the depths taken from the watch plate _A_. Suppose, to illustrate, that we place the plate _A_ in position as shown, and insert the cone point _n_, Figs. 109 and 112, in the pivot hole for the pallet staff, adjusting the slide _G N_ so that the cone point rests accurately in said pivot hole. It is further demanded that the parts _I H F G N D_ be so constructed and adjusted that the sliding center _I_ moves truly vertical, and that we can change ends with said center _I_ and place the hollow cone end _m_, Fig. 112, so it will receive the top pivot of the pallet staff and hold it exactly upright. [Illustration: Fig. 110] [Illustration: Fig. 111] [Illustration: Fig. 112] The idea of the sliding center _I_ is to perfectly supply the place of the opposite plate of the watch and give us exactly the same practical depths as if the parts were in their place between the plates of the movement. The foot of the pillar _D_ has a flange attached, as shown at _f_, which aids in holding it perfectly upright. It is well to cut a screw on _D_ at _D'_, and screw the flange _f_ on such screw and then turn the lower face of _f_ flat to aid in having the pillar _D_ perfectly upright. DETAILS OF FITTING UP ESCAPEMENT MATCHER. It is well to fit the screw _D'_ loosely, so that the flange _f_ will come perfectly flat with the upper surface of the base plate _B_. The slide _G N_ on the pillar _D_ can be made of two pieces of small brass tube, one fitting the pillar _D_ and the other the bar _F_. The slide _G N_ is held in position by the set screw _g_, and the rod _F_ by the set screw _h_. [Illustration: Fig. 113] [Illustration: Fig. 114] The piece _H_ can be permanently attached to the rod _F_. We show separate at Figs. 113 and 114 the slide _G N_ on an enlarged scale from Fig. 109. Fig. 114 is a view of Fig. 113 seen in the direction of the arrow _e_. All joints and movable parts should work free, in order that the center _I_ may be readily and accurately set. The parts _H F_ are shown separate and enlarged at Figs. 115 and 116. The piece _H_ can be made of thick sheet brass securely attached to _F_ in such a way as to bring the V-shaped groove at right angles to the axis of the rod _F_. It is well to make the rod _F_ about 1/8" in diameter, while the sliding center _I_ need not be more than 1/16" in diameter. The cone point _n_ should be hardened to a spring temper and turned to a true cone in an accurately running wire chuck. [Illustration: Fig. 115] [Illustration: Fig. 116] The hollow cone end _m_ of _I_ should also be hardened, but this is best done after the hollow cone is turned in. The hardening of both ends should only be at the tips. The sliding center _I_ can be held in the V-shaped groove by two light friction springs, as indicated at the dotted lines _s s_, Fig. 115, or a flat plate of No. 24 or 25 sheet brass of the size of _H_ can be employed, as shown at Figs. 116 and 117, where _o_ represents the plate of No. 24 brass, _p p_ the small screws attaching the plate _o_ to _H_, and _k_ a clamping screw to fasten _I_ in position. It will be found that the two light springs _s s_, Fig. 115 will be the most satisfactory. The wire legs, shown at _L_, will aid in making the device set steady. The pillar _E_ is provided with the same slides and other parts as described and illustrated as attached to _D_. The position of the pillars _D_ and _E_ are indicated at Fig. 110. [Illustration: Fig. 117] [Illustration: Fig. 118] We will next tell how to flatten _F_ to keep _H_ exactly vertical. To aid in explanation, we will show (enlarged) at Fig. 118 the bar _F_ shown in Fig. 109. In flattening such pieces to prevent turning, we should cut away about two-fifths, as shown at Fig. 119, which is an end view of Fig. 118 seen in the direction of the arrow _c_. In such flattening we should not only cut away two-fifths at one end, but we must preserve this proportion from end to end. To aid in this operation we make a fixed gage of sheet metal, shaped as shown at _I_, Fig. 120. [Illustration: Fig. 119] ESCAPEMENT MATCHING DEVICE DESCRIBED. [Illustration: Fig. 120] In practical construction we first file away about two-fifths of _F_ and then grind the flat side on a glass slab to a flat, even surface and, of course, equal thickness from end to end. We reproduce the sleeve _G_ as shown at Fig. 113 as if seen from the left and in the direction of the axis of the bar _F_. To prevent the bar _F_ turning on its axis, we insert in the sleeve _G_ a piece of wire of the same size as _F_ but with three-fifths cut away, as shown at _y_, Fig. 121. This piece _y_ is soldered in the sleeve _G_ so its flat face stands vertical. To give service and efficiency to the screw _h_, we thicken the side of the sleeve _F_ by adding the stud _w_, through which the screw _h_ works. A soft metal plug goes between the screw _h_ and the bar _F_, to prevent _F_ being cut up and marred. It will be seen that we can place the top plate of a full-plate movement in the device shown at Fig. 109 and set the vertical centers _I_ so the cone points _n_ will rest in the pivot holes of the escape wheel and pallets. It is to be understood that the lower side of the top plate is placed uppermost in the movement holder. [Illustration: Fig. 121] If we now reverse the ends of the centers _I_ and let the pivots of the escape wheel and pallet staff rest in the hollow cones of these centers _I_, we have the escape wheel and pallets in precisely the same position and relation to each other as if the lower plate was in position. It is further to be supposed that the balance is in place and the cock screwed down, although the presence of the balance is not absolutely necessary if the banking screws are set as directed, that is, so the jewel pin will just freely pass in and out of the fork. HOW TO SET PALLET STONES. We have now come to setting or manipulating the pallet stones so they will act in exact conjunction with the fork and roller. To do this we need to have the shellac which holds the pallet stones heated enough to make it plastic. The usual way is to heat a piece of metal and place it in close proximity to the pallets, or to heat a pair of pliers and clamp the pallet arms to soften the cement. Of course, it is understood that the movement holder cannot be moved about while the stones are being manipulated. The better way is to set the movement holder on a rather heavy plate of glass or metal, so that the holder will not jostle about; then set the lamp so it will do its duty, and after a little practice the setting of a pair of pallet stones to perfectly perform their functions will take but a few minutes. In fact, if the stones will answer at all, three to five minutes is as much time as one could well devote to the adjustment. The reader will see that if the lever is properly banked all he has to do is to set the stones so the lock, draw and drop are right, when the entire escapement is as it should be, and will need no further trial or manipulating. CHAPTER II. THE CYLINDER ESCAPEMENT. There is always in mechanical matters an underlying combination of principles and relations of parts known as "theory." We often hear the remark made that such a thing may be all right in theory, but will not work in practice. This statement has no foundation in fact. If a given mechanical device accords strictly with theory, it will come out all right practically. _Mental conceptions_ of a machine are what we may term their theoretical existence. When we make drawings of a machine mentally conceived, we commence its mechanical construction, and if we make such drawings to scale, and add a specification stating the materials to be employed, we leave only the merest mechanical details to be carried out; the brain work is done and only finger work remains to be executed. With these preliminary remarks we will take up the consideration of the cylinder escapement invented by Robert Graham about the year 1720. It is one of the two so-called frictional rest dead-beat escapements which have come into popular use, the other being the duplex. Usage, or, to put it in other words, experience derived from the actual manufacture of the cylinder escapement, settled the best forms and proportions of the several parts years ago. Still, makers vary slightly on certain lines, which are important for a man who repairs such watches to know and be able to carry out, in order to put them in a condition to perform as intended by the manufacturers. It is not knowing these lines which leaves the average watchmaker so much at sea. He cuts and moves and shifts parts about to see if dumb luck will not supply the correction he does not know how to make. This requisite knowledge does not consist so much in knowing how to file or grind as it does in discriminating where such application of manual dexterity is to be applied. And right here let us make a remark to which we will call attention again later on. The point of this remark lies in the question--How many of the so-called practical watchmakers could tell you what proportion of a cylinder should be cut away from the half shell? How many could explain the difference between the "real" and "apparent" lift? Comparatively few, and yet a knowledge of these things is as important for a watchmaker as it is for a surgeon to understand the action of a man's heart or the relations of the muscles to the bones. ESSENTIAL PARTS OF THE CYLINDER ESCAPEMENT. The cylinder escapement is made up of two essential parts, viz.: the escape wheel and the cylinder. The cylinder escape wheel in all modern watches has fifteen teeth, although Saunier, in his "Modern Horology," delineates a twelve-tooth wheel for apparently no better reason than because it was more easily drawn. We, in this treatise, will consider both the theoretical action and the practical construction, but more particularly the repair of this escapement in a thorough and complete manner. At starting out, we will first agree on the names of the several parts of this escapement, and to aid us in this we will refer to the accompanying drawings, in which Fig. 122 is a side elevation of a cylinder complete and ready to have a balance staked on to it. Fig. 123 shows the cylinder removed from the balance collet. Figs. 124 and 125 show the upper and lower plugs removed from the cylinder. Fig. 126 is a horizontal section of Fig. 122 on the line _i_. Fig. 127 is a side view of one tooth of a cylinder escape wheel as if seen in the direction of the arrow _f_ in Fig. 126. Fig. 128 is a top view of two teeth of a cylinder escape wheel. The names of the several parts usually employed are as follows: _A._--Upper or Main Shell. _A'._--Half Shell. _A''._--Column. _A'''._--Small Shell. _B B' B''._--Balance Collet. _G._--Upper Plug. _H._--Lower Plug. _g._--Entrance Lip of Cylinder. _h._--Exit Lip of Cylinder. _c._--Banking Slot. _C._--Tooth. _D._--U arm. _E._--Stalk of Pillar. _I._--U space. _l._--Point of Tooth. _k._--Heel of Tooth. The cylinder escapement has two engagements or actions, during the passage of each tooth; that is, one on the outside of the cylinder and one on the inside of the shell. As we shall show later on, the cylinder escapement is the only positively dead-beat escapement in use, all others, even the duplex, having a slight recoil during the process of escaping. When the tooth of a cylinder escape wheel while performing its functions, strikes the cylinder shell, it rests dead on the outer or inner surface of the half shell until the action of the balance spring has brought the lip of the cylinder so that the impulse face of the tooth commences to impart motion or power to the balance. [Illustration: Fig. 122] [Illustration: Fig. 123] [Illustration: Fig. 124] [Illustration: Fig. 125] [Illustration: Fig. 126] [Illustration: Fig. 127] [Illustration: Fig. 128] Most writers on horological matters term this act the "lift," which name was no doubt acquired when escapements were chiefly confined to pendulum clocks. Very little thought on the matter will show any person who inspects Fig. 126 that if the tooth _C_ is released or escapes from the inside of the half shell of the cylinder _A_, said cylinder must turn or revolve a little in the direction of the arrow _j_, and also that the next succeeding tooth of the escape wheel will engage the cylinder on the outside of the half shell, falling on the dead or neutral portion of said cylinder, to rest until the hairspring causes the cylinder to turn in the opposite direction and permitting the tooth now resting on the outside of the cylinder to assume the position shown on the drawing. The first problem in our consideration of the theoretical action of the cylinder escapement, is to arrange the parts we have described so as to have these two movements of the escape wheel of like angular values. To explain what we mean by this, we must premise by saying, that as our escape wheel has fifteen teeth and we make each tooth give two impulses in alternate directions we must arrange to have these half-tooth movements exactly alike, or, as stated above, of equal angular values; and also each impulse must convey the same power or force to the balance. All escape wheels of fifteen teeth acting by half impulses must impel the balance during twelve degrees (minus the drop) of escape-wheel action; or, in other words, when a tooth passes out of the cylinder from the position shown at Fig. 126, the form of the impulse face of the tooth and the shape of the exit lip of the cylinder must be such during twelve degrees (less the drop) of the angular motion of the escape wheel. The entire power of such an escape wheel is devoted to giving impulse to the balance. The extent of angular motion of the balance during such impulse is, as previously stated, termed the "lifting angle." This "lifting angle" is by horological writers again divided into real and apparent lifts. This last division is only an imaginary one, as the real lift is the one to be studied and expresses the arc through which the impulse face of the tooth impels the balance during the act of escaping, and so, as we shall subsequently show, should no more be counted than in the detached lever escapement, where a precisely similar condition exists, but is never considered or discussed. We shall for the present take no note of this lifting angle, but confine ourselves to the problem just named, of so arranging and designing our escape-wheel teeth and cylinder that each half of the tooth space shall give equal impulses to the balance with the minimum of drop. To do this we will make a careful drawing of an escape-wheel tooth and cylinder on an enlarged scale; our method of making such drawings will be on a new and original system, which is very simple yet complete. DRAWING THE CYLINDER ESCAPEMENT. All horological--and for that matter all mechanical--drawings are based on two systems of measurements: (1) Linear extent; (2) angular movement. For the first measurement we adopt the inch and its decimals; for the second we adopt degrees, minutes and seconds. For measuring the latter the usual plan is to employ a protractor, which serves the double purpose of enabling us to lay off and delineate any angle and also to measure any angle obtained by the graphic method, and it is thus by this graphic method we propose to solve very simply some of the most abstruce problems in horological delineations. As an instance, we propose to draw our cylinder escapement with no other instruments than a steel straight-edge, showing one-hundredths of an inch, and a pair of dividers; the degree measurement being obtained from arcs of sixty degrees of radii, as will be explained further on. In describing the method for drawing the cylinder escapement we shall make a radical departure from the systems usually laid down in text-books, and seek to simplify the formulas which have heretofore been given for such delineations. In considering the cylinder escapement we shall pursue an analytical course and strive to build up from the underlying principles. In the drawings for this purpose we shall commence with one having an escape wheel of 10" radius, and our first effort will be the primary drawing shown at Fig. 129. Here we establish the point _A_ for the center of our escape wheel, and from this center sweep the short arc _a a_ with a 10" radius, to represent the circumference of our escape wheel. From _A_ we draw the vertical line _A B_, and from the intersection of said line with the arc _a a_ we lay off twelve degree spaces on each side of the line _A B_ on said arc _a_ and establish the points _b c_. From _A_ as a center we draw through the points _b c_ the radial lines _b' c'_. To define the face of the incline to the teeth we set our dividers to the radius of any of the convenient arcs of sixty degrees which we have provided, and sweep the arc _t t_. From the intersection of said arc with the line _A b'_ we lay off on said arc sixty-four degrees and establish the point _g_ and draw the line _b g_. Why we take sixty-four degrees for the angle _A b g_ will be explained later on, when we are discussing the angular motion of the cylinder. By dividing the eleventh degree from the point _b_ on the arc _a a_ into thirds and taking two of them, we establish the point _y_ and draw the radial line _A y'_. Where this line _A y'_ intersects the line _b g_ we name the point _n_, and in it is located the point of the escape-wheel tooth. That portion of the line _b g_ which lies between the points _b_ and _n_ represents the measure of the inner diameter of the cylinder, and also the length of the chord of the arc which rounds the impulse face of the tooth. We divide the space _b n_ into two equal portions and establish the point _e_, which locates the position of the center of the cylinder. From _A_ as a center and through the point _e_ we sweep the arc _e' e'_, and it is on this line that the points establishing the center of the cylinder will in every instance be located. From _A_ as a center, through the point _n_ we sweep the arc _k_, and on this line we locate the points of the escape-wheel teeth. For delineating the curved impulse faces of the escape-wheel teeth we draw from the point _e_ and at right angles to the line _b g_ the line _e o_. We next take in our dividers the radius of the arc _k_, and setting one leg at either of the points _b_ or _n_, establish with the other leg the point _p'_ on the line _e o_, and from the point _p'_ as a center we sweep the arc _b v n_, which defines the curve of the impulse faces of the teeth. From _A_ as a center through the point _p'_ we sweep the arc _p_, and in all instances where we desire to delineate the curved face of a tooth we locate either the position of the point or the heel of such tooth, and setting one leg of our dividers at such point, the other leg resting on the arc _p_, we establish the center from which to sweep the arc defining the face of said tooth. ADVANTAGES GAINED IN SHAPING. The reason for giving a curved form to the impulse face of the teeth of cylinder escape wheels are somewhat intricate, and the problem involves several factors. That there are advantages in so shaping the incline or impulse face is conceded, we believe, by all recent manufacturers. The chief benefit derived from such curved impulse faces will be evident after a little thought and study of the situation and relation of parts as shown in Fig. 129. It will be seen on inspection that the angular motion imparted to the cylinder by the impulse face of the tooth when curved as shown, is greater during the first half of the twelve degrees of escape-wheel action than during the last half, thus giving the escape wheel the advantage at the time the balance spring increases its resistance to the passage of the escape-wheel tooth across the lip of the cylinder. Or, in other words, as the ratio of resistance of the balance spring increases, in a like ratio the curved form of the impulse face of the tooth gives greater power to the escape-wheel action in proportion to the angular motion of the escape wheel. Hence, in actual service it is found that cylinder watches with curved impulse planes to the escape-wheel teeth are less liable to set in the pocket than the teeth having straight impulse faces. THE OUTER DIAMETER OF THE CYLINDER. [Illustration: Fig. 129] To define the remainder of the form of our escape-wheel tooth we will next delineate the heel. To do this we first define the outer diameter of our cylinder, which is the extent from the point _n_ to _c_, and after drawing the line _n c_ we halve the space and establish the point _x_, from which point as a center we sweep the circle _w w_, which defines the outer circumference of our cylinder. With our dividers set to embrace the extent from the point _n_ to the point _c_ we set one leg at the point _b_, and with the other leg establish on the arc _k_ the point _h_. We next draw the line _b h_, and from the point _b_ draw the line _b f_ at right angle to the line _b h_. Our object for drawing these lines is to define the heel of our escape-wheel tooth by a right angle line tangent to the circle _w_, from the point _b_; which circle _w_ represents the curve of the outer circumference of the cylinder. We shape the point of the tooth as shown to give it the proper stability, and draw the full line _j_ to a curve from the center _A_. We have now defined the form of the upper face of the tooth. How to delineate the U arms will be taken up later on, as, in the present case, the necessary lines would confuse our drawing. We would here take the opportunity to say that there is a great latitude taken by makers as regards the extent of angular impulse given to the cylinder, or, as it is termed, the "actual lift." This latitude governs to a great extent the angle _A b g_, which we gave as sixty-four degrees in our drawing. It is well to understand that the use of sixty-four degrees is based on no hard-and-fast rules, but varies back and forth, according as a greater or lesser angle of impulse or lift is employed. In practical workshop usage the impulse angle is probably more easily estimated by the ratio between the diameter of the cylinder and the measured (by lineal measure) height of the impulse plane. Or, to be more explicit, we measure the radial extent from the center _A_ between the arcs _a k_ on the line _A b_, and use this for comparison with the outer diameter of the cylinder. We can readily see that as we increase the height of the heel of the impulse face of our tooth we must also increase the angle of impulse imparted to the cylinder. With the advantages of accurate micrometer calipers now possessed by the horological student it is an easy matter to get at the angular extent of the real lift of any cylinder. The advantage of such measuring instruments is also made manifest in determining when the proper proportion of the cylinder is cut away for the half shell. [Illustration: Fig. 130] In the older methods of watchmaking it was a very common rule to say, let the height of the incline of the tooth be one-seventh of the outer diameter of the cylinder, and at the same time the trade was furnished with no tools except a clumsy douzieme gage; but with micrometer calipers which read to one-thousandths of an inch such rules can be definitely carried into effect and not left to guess work. Let us compare the old method with the new: Suppose we have a new cylinder to put in; we have the old escape wheel, but the former cylinder is gone. The old-style workman would take a round broach and calculate the size of the cylinder by finding a place where the broach would just go between the teeth, and the size of the broach at this point was supposed to be the outer diameter of the cylinder. By our method we measure the diameter of the escape wheel in thousandths of an inch, and from this size calculate exactly what the diameter of the new cylinder should be in thousandths of an inch. Suppose, to further carry out our comparison, the escape wheel which is in the watch has teeth which have been stoned off to permit the use of a cylinder which was too small inside, or, in fact, of a cylinder too small for the watch: in this case the broach system would only add to the trouble and give us a cylinder which would permit too much inside drop. DRAWING A CYLINDER. We have already instructed the pupil how to delineate a cylinder escape wheel tooth and we will next describe how to draw a cylinder. As already stated, the center of the cylinder is placed to coincide with the center of the chord of the arc which defines the impulse face of the tooth. Consequently, if we design a cylinder escape wheel tooth as previously described, and setting one leg of our compasses at the point _e_ which is situated at the center of the chord of the arc which defines the impulse face of the tooth and through the points _d_ and _b_ we define the inside of our cylinder. We next divide the chord _d b_ into eight parts and set our dividers to five of these parts, and from _e_ as a center sweep the circle _h_ and define the outside of our cylinder. From _A_ as a center we draw the radial line _A e'_. At right angles to the line _A e'_ and through the point _e_ we draw the line from _e_ as a center, and with our dividers set to the radius of any of the convenient arcs which we have divided into sixty degrees, we sweep the arc _i_. Where this arc intersects the line _f_ we term the point _k_, and from this point we lay off on the arc _i_ 220 degrees, and draw the line _l e l'_, which we see coincides with the chord of the impulse face of the tooth. We set our dividers to the same radius by which we sweep the arc _i_ and set one leg at the point _b_ for a center and sweep the arc _j'_. If we measure this arc from the point _j'_ to intersection of said arc _j'_ with the line _l_ we will find it to be sixty-four degrees, which accounts for our taking this number of degrees when we defined the face of our escape-wheel tooth, Fig. 129. There is no reason why we should take twenty-degrees for the angle _k e l_ except that the practical construction of the larger sizes of cylinder watches has established the fact that this is about the right angle to employ, while in smaller watches it frequently runs up as high as twenty-five. Although the cylinder is seemingly a very simple escapement, it is really a very abstruce one to follow out so as to become familiar with all of its actions. THE CYLINDER PROPER CONSIDERED. [Illustration: Fig. 131] We will now proceed and consider the cylinder proper, and to aid us in understanding the position and relation of the parts we refer to Fig. 131, where we repeat the circles _d_ and _h_, shown in Fig. 130, which represents the inside and outside of the cylinder. We have here also repeated the line _f_ of Fig. 130 as it cuts the cylinder in half, that is, divides it into two segments of 180 degrees each. If we conceive of a cylinder in which just one-half is cut away, that is, the lips are bounded by straight radial lines, we can also conceive of the relation and position of the parts shown in Fig. 130. The first position of which we should take cognizance is, the tooth _D_ is moved back to the left so as to rest on the outside of our cylinder. The cylinder is also supposed to stand so that the lips correspond to the line _f_. On pressing the tooth _D_ forward the incline of the tooth would attack the entrance lip of the cylinder at just about the center of the curved impulse face, imparting to the cylinder twenty degrees of angular motion, but the point of the tooth at _d_ would exactly encounter the inner angle of the exit lip, and of course the cylinder would afford no rest for the tooth; hence, we see the importance of not cutting away too much of the half shell of the cylinder. But before we further consider the action of the tooth _D_ in its action as it passes the exit lip of the cylinder we must finish with the action of the tooth on the entrance lip. A very little thought and study of Fig. 130 will convince us that the incline of the tooth as it enters the cylinder will commence at _t_, Fig. 130, but at the close of the action the tooth parts from the lip on the inner angle. Now it is evident that it would require greater force to propel the cylinder by its inner angle than by the outer one. To compensate for this we round the edge of the entrance lip so that the action of the tooth instead of commencing on the outer angle commences on the center of the edge of the entrance lip and also ends its action on the center of the entrance lip. To give angular extent enough to the shell of the cylinder to allow for rounding and also to afford a secure rest for the tooth inside the cylinder, we add six degrees to the angular extent of the entrance lip of the cylinder shell, as indicated on the arc _o'_, Fig. 131, three of these degrees being absorbed for rounding and three to insure a dead rest for the tooth when it enters the cylinder. WHY THE ANGULAR EXTENT IS INCREASED. Without rounding the exit lip the action of the tooth on its exit would be entirely on the inner angle of the shell. To obviate this it is the usual practice to increase the angular extent of the cylinder ten degrees, as shown on the arc _o'_ between the lines _f_ and _p_, Fig. 131. Why we should allow ten degrees on the exit lip and but six degrees on the entrance lip will be understood by observing Fig. 130, where the radial lines _s_ and _r_ show the extent of angular motion of the cylinder, which would be lost if the tooth commenced to act on the inner angle and ended on the outer angle of the exit lip. This arc is a little over six degrees, and if we add a trifle over three degrees for rounding we would account for the ten degrees between the lines _f_ and _p_, Fig. 131. It will now be seen that the angular extent is 196 degrees. If we draw the line _w_ we can see in what proportion the measurement should be made between the outer diameter of the cylinder and the measure of the half shell. It will be seen on measurement that the distance between the center _e_ and the line _w_ is about one-fifteenth part of the outer diameter of the cylinder and consequently with a cylinder which measures 45/1000 of an inch in diameter, now the half shell should measure half of the entire diameter of the cylinder plus one-fifteenth part of such diameter, or 25½ thousandths of an inch. After these proportions are understood and the drawing made, the eye will get accustomed to judging pretty near what is required; but much the safer plan is to measure, where we have the proper tools for doing so. Most workmen have an idea that the depth or distance at which the cylinder is set from the escape wheel is a matter of adjustment; while this is true to a certain extent, still there is really only one position for the center of the cylinder, and that is so that the center of the pivot hole coincides exactly with the center of the chord to the curve of the impulse face of the tooth or the point _e_, Fig. 130. Any adjustment or moving back and forth of the chariot to change the depth could only be demanded where there was some fault existing in the cylinder or where it had been moved out of its proper place by some genius as an experiment in cylinder depths. It will be evident on observing the drawing at Fig. 131 that when the cylinder is performing an arc of vibration, as soon as the entrance lip has passed the point indicated by the radial line _e x_ the point of the escape-wheel tooth will commence to act on the cylinder lip and continue to do so through an arc of forty degrees, or from the lines _x_ to _l_. MAKING A WORKING MODEL. To practically study the action of the cylinder escapement it is well to make a working model. It is not necessary that such a model should contain an entire escape wheel; all that is really required is two teeth cut out of brass of the proper forms and proportions and attached to the end of an arm 4-7/8" long with studs riveted to the U arms to support the teeth. This U arm is attached to the long arm we have just mentioned. A flat ring of heavy sheet brass is shaped to represent a short transverse section of a cylinder. This segment is mounted on a yoke which turns on pivots. In making such a model we can employ all the proportions and exact forms of the larger drawings made on a ten-inch radius. Such a model becomes of great service in learning the importance of properly shaping the lips of the cylinder. And right here we beg to call attention to the fact that in the ordinary repair shop the proper shape of cylinder lips is entirely neglected. PROPER SHAPE OF CYLINDER LIPS. The workman buys a cylinder and whether the proper amount is cut away from the half shell, or the lips, the correct form is entirely ignored, and still careful attention to the form of the cylinder lips adds full ten per cent. to the efficiency of the motive force as applied to the cylinder. In making study drawings of the cylinder escapement it is not necessary to employ paper so large that we can establish upon it the center of the arc which represents the periphery of our escape wheel, as we have at our disposal two plans by which this can be obviated. First, placing a bit of bristol board on our drawing-board in which we can set one leg of our dividers or compasses when we sweep the peripheral arc which we use in our delineations; second, making three arcs in brass or other sheet metal, viz.: the periphery of the escape wheel, the arc passing through the center of the chord of the arc of the impulse face of the tooth, and the arc passing through the point of the escape-wheel tooth. Of these plans we favor the one of sticking a bit of cardboard on the drawing board outside of the paper on which we are making our drawing. [Illustration: Fig. 132] At Fig. 132 we show the position and relation of the several parts just as the tooth passes into the shell of the cylinder, leaving the lip of the cylinder just as the tooth parted with it. The half shell of the cylinder as shown occupies 196 degrees or the larger arc embraced between the radial lines _k_ and _l_. In drawing the entrance lip the acting face is made almost identical with a radial line except to round the corners for about one-third the thickness of the cylinder shell. No portion, however, of the lip can be considered as a straight line, but might be described as a flattened curve. [Illustration: Fig. 133] A little study of what would be required to get the best results after making such a drawing will aid the pupil in arriving at the proper shape, especially when he remembers that the thickness of the cylinder shell of a twelve-line watch is only about five one-thousandths of an inch. But because the parts are small we should not shirk the problem of getting the most we possibly can out of a cylinder watch. The extent of arc between the radial lines _k f_, as shown in Fig. 132, is four degrees. Although in former drawings we showed the angular extent added as six degrees, as we show the lip _m_ in Fig. 132, two degrees are lost in rounding. The space _k f_ on the egress or exit side is intended to be about four degrees, which shows the extent of lock. We show at Fig. 133 the tooth _D_ just having passed out of the cylinder, having parted with the exit lip _p_. In making this drawing we proceed as with Fig. 132 by establishing a center for our radius of 10" outside of our drawing paper and drawing the line _A A_ to such center and sweeping the arcs _a b c_. We establish the point _e_, which represents the center of our cylinder, as before. We take the space to represent the radial extent of the outside of our cylinder in our dividers and from _e_ as a center sweep a fine pencil line, represented by the dotted line _t_ in our drawing; and where this circle intersects the arc _a_ we name it the point _s_; and it is at this point the heel of our escape-wheel tooth must part with the exit lip of the cylinder. From _e_ as a center and through the point _s_ we draw the line _e l''_. With our dividers set to the radius of any convenient arc which we have divided into degrees, we sweep the short arc _d'_. The intersection of this arc with the line _e l''_ we name the point _u_; and from _e_ as a center we draw the radial line _e u f'_. We place the letter _f''_ in connection with this line because it (the line) bears the same relations to the half shell of the cylinder shown in Fig. 133 that the line _f_ does to the half shell (_D_) shown in Fig. 132. We draw the line _f'' f'''_, Fig. 133, which divides the cylinder into two segments of 180 degrees each. We take the same space in our dividers with which we swept the interior of the cylinder in Fig. 132 and sweep the circle _v_, Fig. 133. From _e_ as a center we sweep the short arc _d''_, Fig. 133, and from its intersection of the line _f''_ we lay off six degrees on said arc _d''_ and draw the line _e' k''_, which defines the angular extent of our entrance lip to the half shell of the cylinder in Fig. 133. We draw the full lines of the cylinder as shown. We next delineate the heel of the tooth which has just passed out of the cylinder, as shown at _D'_, Fig. 133. We now have a drawing showing the position of the half shell of the cylinder just as the tooth has passed the exit lip. This drawing also represents the position of the half shell of the cylinder when the tooth rests against it on the outside. If we should make a drawing of an escape-wheel tooth shaped exactly as the one shown at Fig. 132 and the point of the tooth resting at _x_, we would show the position of a tooth encountering the cylinder after a tooth which has been engaged in the inside of the shell has passed out. By following the instructions now given, we can delineate a tooth in any of its relations with the cylinder shell. DELINEATING AN ESCAPE-WHEEL TOOTH WHILE IN ACTION. We will now go through the operation of delineating an escape-wheel tooth while in action. The position we shall assume is the one in which the cylinder and escape-wheel tooth are in the relation of the passage of half the impulse face of the tooth into the cylinder. To do this is simple enough: We first produce the arcs _a b c_, Fig. 133, as directed, and then proceed to delineate a tooth as in previous instances. To delineate our cylinder in the position we have assumed above, we take the space between the points _e d_ in our dividers and setting one leg at _d_ establish the point _g_, to represent the center of our cylinder. If we then sweep the circle _h_ from the center of _g_ we define the inner surface of the shell of our cylinder. Strictly speaking, we have not assumed the position we stated, that is, the impulse face of the tooth as passing half way into the cylinder. To comply strictly with our statement, we divide the chord of the impulse face of the tooth _A_ into eight equal spaces, as shown. Now as each of these spaces represent the thickness of the cylinder, if we take in our dividers four of these spaces and half of another, we have the radius of a circle passing the center of the cylinder shell. Consequently, if with this space in our dividers we set the leg at _d_, we establish on the arc _b_ the point _i_. We locate the center of our cylinder when one-half of an entering tooth has passed into the cylinder. If now from the new center with our dividers set at four of the spaces into which we have divided the line _e f_ we can sweep a circle representing the inner surface of the cylinder shell, and by setting our dividers to five of these spaces we can, from _i_ as a center, sweep an arc representing the outside of the cylinder shell. For all purposes of practical study the delineation we show at Fig. 133 is to be preferred, because, if we carry out all the details we have described, the lines would become confused. We set our dividers at five of the spaces on the line _e f_ and from _g_ as a center sweep the circle _j_, which delineates the outer surface of our cylinder shell. Let us now, as we directed in our former instructions, draw a flattened curve to represent the acting surface of the entrance lip of our cylinder as if it were in direct contact with the impulse face of the tooth. To delineate the exit lip we draw from the center _g_, Fig. 134, to the radial line _g k_, said line passing through the point of contact between the tooth and entrance lip of the cylinder. Let us next continue this line on the opposite side of the point _g_, as shown at _g k'_, and we thus bisect the cylinder shell into two equal parts of 180 degrees each. As we previously explained, the entire extent of the cylinder half shell is 196 degrees. We now set our dividers to the radius of any convenient arc which we have divided into degrees, and from _g_ as a center sweep the short arc _l l_, and from the intersection of this arc with the line _g k'_ we lay off sixteen degrees on the said arc _l_ and establish the point _n_, from _g_ as a center draw the radial line _g n'_. Take ten degrees from the same parent arc and establish the point _m_, then draw the line _g m'_. Now the arc on the circles _h j_ between the lines _g n'_ and _g m_ limits the extent of the exit lip of the cylinder and the arc between the lines _g k'_ and _g m'_ represents the locking surface of the cylinder shell. [Illustration: Fig. 134] To delineate the U arms we refer to Fig. 135. Here, again, we draw the arc _a b c_ and delineate a tooth as before. From the point _e_ located at the heel of the tooth we draw the radial line _e e'_. From the point _e_ we lay off on the arc _a_ five degrees and establish the point _p_; we halve this space and draw the short radial line _p' s'_ and _p s_. From the point _e_ on the arc _A_ we lay off twenty-four degrees and establish the point _t_, which locates the heel of the next tooth in advance of _A_. At two and a half degrees to the right of the point _t_ we locate the point _r_ and draw the short radial line _r s_. On the arc _b_ and half way between the lines _p s_ and _r s_, we establish the point _u_, and from it as a center we sweep the arc _v_ defining the curve of the U arms. We have now given minute instructions for drawing a cylinder escapement in all its details except the extent of the banking slot of the cylinder, which is usually made to embrace an angular extent of 270 degrees; consequently, the pillar of the cylinder will not measure more than ninety degrees of angular extent. There is no escapement constructed where carefully-made drawings tend more to perfect knowledge of the action than the cylinder. But it is necessary with the pupil to institute a careful analysis of the actions involved. In writing on a subject of this kind it is extremely perplexing to know when to stop; not that there is so much danger of saying too much as there is not having the words read with attention. As an illustration, let us consider the subject of depth between the cylinder and the escape wheel. As previously stated, 196 degrees of cylinder shell should be employed; but suppose we find a watch in which the half shell has had too much cut away, so the tooth on entering the half shell after parting with the entrance lip does not strike dead on the inside of the shell, but encounters the edge of the exit lip. In this case the impulse of the balance would cause the tooth to slightly retrograde and the watch would go but would lack a good motion. In such an instance a very slight advance of the chariot would remedy the fault--not perfectly remedy it, but patch up, so to speak--and the watch would run. [Illustration: Fig. 135] In this day, fine cylinder watches are not made, and only the common kind are met with, and for this reason the student should familiarize himself with all the imaginary faults which could occur from bad construction. The best way to do this is to delineate what he (the student) knows to be a faulty escapement, as, for instance, a cylinder in which too much of the half shell is cut away; but in every instance let the tooth be of the correct form. Then delineate an escapement in which the cylinder is correct but the teeth faulty; also change the thickness of the cylinder shell, so as to make the teeth too short. This sort of practice makes the pupil think and study and he will acquire a knowledge which will never be forgotten, but always be present to aid him in the puzzles to which the practical watchmaker is every day subject. The ability to solve these perplexing problems determines in a great degree the worth of a man to his employer, in addition to establishing his reputation as a skilled workman. The question is frequently asked, "How can I profitably employ myself in spare time?" It would seem that a watchmaker could do no better than to carefully study matters horological, striving constantly to attain a greater degree of perfection, for by so doing his earning capacity will undoubtedly be increased. CHAPTER III. THE CHRONOMETER ESCAPEMENT. Undoubtedly "the detent," or, as it is usually termed, "the chronometer escapement," is the most perfect of any of our portable time measurers. Although the marine chronometer is in a sense a portable timepiece, still it is not, like a pocket watch, capable of being adjusted to positions. As we are all aware, the detent escapement is used in fine pocket watches, still the general feeling of manufacturers is not favorable to it. Much of this feeling no doubt is owing to the mechanical difficulties presented in repairing the chronometer escapements when the detent is broken, and the fact that the spring detent could not be adjusted to position. We shall have occasion to speak of position adjustments as relate to the chronometer escapement later on. ADVANTAGES OF THE CHRONOMETER. We will proceed now to consider briefly the advantages the detent escapement has over all others. It was soon discovered in constructing portable timepieces, that to obtain the best results the vibrations of the balance should be as free as possible from any control or influence except at such times as it received the necessary impulse to maintain the vibrations at a constant arc. This want undoubtedly led to the invention of the detent escapement. The early escapements were all frictional escapements, i.e., the balance staff was never free from the influence of the train. The verge escapement, which was undoubtedly the first employed, was constantly in contact with the escape wheel, and was what is known as a "recoiling beat," that is, the contact of the pallets actually caused the escape wheel to recoil or turn back. Such escapements were too much influenced by the train, and any increase in power caused the timepiece to gain. The first attempt to correct this imperfection led to the invention and introduction of the fusee, which enabled the watchmaker to obtain from a coiled spring nearly equal power during the entire period of action. The next step in advance was the "dead-beat escapement," which included the cylinder and duplex. In these frictional escapements the balance staff locked the train while the balance performed its arc of vibration. FRICTIONAL ESCAPEMENTS IN HIGH FAVOR. These frictional escapements held favor with many eminent watchmakers even after the introduction of the detached escapements. It is no more than natural we should inquire, why? The idea with the advocates of the frictional rest escapements was, the friction of the tooth acted as a _corrective_, and led no doubt to the introduction of going-barrel watches. To illustrate, suppose in a cylinder watch we increase the motive power, such increase of power would not, as in the verge escapement, increase the rapidity of the vibrations; it might, in fact, cause the timepiece to run slower from the increased friction of the escape-wheel tooth on the cylinder; also, in the duplex escapement the friction of the locking tooth on the staff retards the vibrations. Dr. Hooke, the inventor of the balance spring, soon discovered it could be manipulated to isochronism, i.e., so arcs of different extent would be formed in equal time. Of course, the friction-rest escapement requiring a spring to possess different properties from one which would be isochronal with a perfectly detached escapement, these two frictional escapements also differing, the duplex requiring other properties from what would isochronize a spring for a cylinder escapement. Although pocket watches with duplex and cylinder escapements having balances compensated for heat and cold and balance springs adjusted to isochronism gave very good results, careful makers were satisfied that an escapement in which the balance was detached and free to act during the greater proportion of the arc of vibration and uncontrolled by any cause, would do still better, and this led to the detent escapement. FAULTS IN THE DETENT ESCAPEMENT. As stated previously, the detent escapement having pronounced faults in positions which held it back, it is probable it would never have been employed in pocket watches to any extent if it had not acquired such a high reputation in marine chronometers. Let us now analyze the influences which surround the detent escapement in a marine chronometer and take account of the causes which are combined to make it an accurate time measurer, and also take cognizance of other interfering causes which have a tendency to prevent desired results. First, we will imagine a balance with its spring such as we find in fine marine chronometers. It has small pivots running in highly-polished jewels; such pivots are perfectly cylindrical, and no larger than are absolutely necessary to endure the task imposed upon them--of carrying the weight of the balance and endure careful handling. To afford the necessary vibrations a spring is fitted, usually of a helical form, so disposed as to cause the balance to vibrate in arcs back and forth in equal time, _provided these arcs are of equal extent_. It is now to be taken note of that we have it at our disposal and option to make these arcs equal in time duration, i.e., to make the long or short arcs the quickest or to synchronize them. We can readily comprehend we have now established a very perfect measure of short intervals of time. We can also see if we provide the means of maintaining these vibrations and counting them we should possess the means of counting the flights of time with great accuracy. The conditions which surround our balance are very constant, the small pivots turning in fine hard jewels lubricated with an oil on which exposure to the action of the air has little effect, leaves but few influences which can interfere with the regular action of our balance. We add to the influences an adjustable correction for the disturbances of heat and cold, and we are convinced that but little could be added. ANTAGONISTIC INFLUENCES. In this combination we have pitted two antagonistic forces against each other, viz., the elasticity of the spring and the weight and inertia of the balance; both forces are theoretically constant and should produce constant results. The mechanical part of the problem is simply to afford these two forces perfect facilities to act on each other and compel each to realize its full effect. We must also devise mechanical means to record the duration of each conflict, that is, the time length of each vibration. Many years have been spent in experimenting to arrive at the best propositions to employ for the several parts to obtain the best practical results. Consequently, in designing a chronometer escapement we must not only draw the parts to a certain form, but consider the quality and weight of material to employ. To illustrate what we have just said, suppose, in drawing an escape wheel, we must not only delineate the proper angle for the acting face of the tooth, but must also take cognizance of the thickness of the tooth. By thickness we mean the measurement of extent of the tooth in the direction of the axis of the escape wheel. An escape-wheel tooth might be of the best form to act in conveying power to the balance and yet by being too thin soon wear or produce excessive friction. How thick an escape wheel should be to produce best results, is one of the many matters settled only by actual workshop experience. FACTORS THAT MUST BE CONSIDERED. Even this experience is in every instance modified by other influences. To illustrate: Let us suppose in the ordinary to-day marine chronometer the escape-wheel teeth exerted a given average force, which we set down as so many grains. Now, if we should employ other material than hammer-hardened brass for an escape wheel it would modify the thickness; also, if we should decrease the motive power and increase the arc of impulse. Or, if we should diminish the extent of the impulse arc and add to the motive force, every change would have a controlling influence. In the designs we shall employ, it is our purpose to follow such proportions as have been adopted by our best makers, in all respects, including form, size and material. We would say, however, there has been but little deviation with our principal manufacturers of marine chronometers for the last twenty years as regards the general principle on which they were constructed, the chief aim being to excel in the perfection of the several parts and the care taken in the several adjustments. Before we proceed to take up the details of constructing a chronometer escapement we had better master the names for the several parts. We show at Fig. 136 a complete plan of a chronometer escapement as if seen from the back, which is in reality the front or dial side of the "top plate." The chronometer escapement consists of four chief or principal parts, viz.: The escape wheel, a portion of which is shown at _A_; the impulse roller _B_; unlocking or discharging roller _C_, and the detent _D_. These principal parts are made up of sub-parts: thus, the escape wheel is composed of arms, teeth, recess and collet, the recess being the portion of the escape wheel sunk, to enable us to get wide teeth actions on the impulse pallet. The collet is a brass bush on which the wheel is set to afford better support to the escape wheel than could be obtained by the thinned wheel if driven directly on the pinion arbor. The impulse roller is composed of a cylindrical steel collet _B_, the impulse pallet _d_ (some call it the impulse stone), the safety recess _b b_. The diameter of the impulse collet is usually one-half that of the escape wheel. This impulse roller is staked directly on the balance staff, and its perfection of position assured by resting against the foot of the shoulder to which the balance is secured. This will be understood by inspecting Fig. 137, which is a vertical longitudinal section of a chronometer balance staff, the lower side of the impulse roller being cupped out at _c_ with a ball grinder and finished a ball polish. [Illustration: Fig. 136] [Illustration: Fig. 137] It will be seen the impulse roller is staked flat against the hub _E_ of the balance staff. The unlocking roller, or, as it is also called, the discharging roller, _C_, is usually thinner than the impulse roller and has a jewel similar to the impulse jewel _a_ shown at _f_. This roller is fitted by friction to the lower part of the balance staff and for additional security has a pipe or short socket _e_ which embraces the balance staff at _g_. The pipe _e_ is usually flattened on opposite sides to admit of employing a special wrench for turning the discharging roller in adjusting the jewel for opening the escapement at the proper instant to permit the escape wheel to act on the impulse jewel _a_. The parts which go to make up the detent _D_ consist of the "detent foot" _F_, the detent spring _h_, the detent blade _i_, the jewel pipe _j_, the locking jewel (or stone) _s_, the "horn" of the detent _k_, the "gold spring" (also called the auxiliary and lifting spring) _m_. This lifting or gold spring _m_ should be made as light and thin as possible and stand careful handling. We cannot impress on our readers too much the importance of making a chronometer detent light. Very few detents, even from the hands of our best makers, are as light as they might be. We should in such construction have very little care for clumsy workmen who may have to repair such mechanism. This feature should not enter into consideration. We should only be influenced by the feeling that we are working for best results, and it is acting under this influence that we devote so much time to establishing a correct idea of the underlying principles involved in a marine chronometer, instead of proceeding directly to the drawing of such an escapement and give empirical rules for the length of this or the diameter of that. As, for instance, in finishing the detent spring _h_, suppose we read in text books the spring should be reduced in thickness, so that a weight of one pennyweight suspended from the pipe _j_ will deflect the detent ¼". This is a rule well enough for people employed in a chronometer factory, but for the horological student such fixed rules (even if remembered) would be of small use. What the student requires is sound knowledge of the "whys," in order that he may be able to thoroughly master this escapement. FUNCTIONS OF THE DETENT. We can see, after a brief analysis of the principles involved, that the functions required of the detent _D_ are to lock the escape wheel _A_ and hold it while the balance performs its excursion, and that the detent or recovering spring _h_ must have sufficient strength and power to perform two functions: (1) Return the locking stone _s_ back to the proper position to arrest and hold the escape wheel; (2) the spring _h_ must also be able to resist, without buckling or cockling, the thrust of the escape wheel, represented by the arrows _p o_. Now we can readily understand that the lighter we make the parts _i j k m_, the weaker the spring _h_ can be. You say, perhaps, if we make it too weak it will be liable to buckle under the pressure of the escape wheel; this, in turn, will depend in a great measure on the condition of the spring _h_. Suppose we have it straight when we put it in position, it will then have no stress to keep it pressed to the holding, stop or banking screw, which regulates the lock of the tooth. To obtain this stress we set the foot _F_ of the detent around to the position indicated by the dotted lines _r_ and _n_, and we get the proper tension on the detent spring to effect the lock, or rather of the detent in time to lock the escape wheel; but the spring _h_, instead of being perfectly straight, is bent and consequently not in a condition to stand the thrust of the escape wheel, indicated by the arrows _o p_. OBTAINING THE BEST CONDITIONS. Now the true way to obtain the best conditions is to give the spring _h_ a set curvature before we put it in place, and then when the detent is in the proper position the spring _h_ will have tension enough on it to bring the jewel _s_ against the stop screw, which regulates the lock, and still be perfectly straight. This matter is of so much importance that we will give further explanation. Suppose we bend the detent spring _h_ so it is curved to the dotted line _t_, Fig. 136, and then the foot _F_ would assume the position indicated at the dotted line _r_. We next imagine the foot _F_ to be put in the position shown by the full lines, the spring _h_ will become straight again and in perfect shape to resist the thrust of the escape wheel. Little "ways and methods" like the above have long been known to the trade, but for some reason are never mentioned in our text books. A detent spring 2/1000" thick and 80/1000" wide will stand the thrust for any well-constructed marine chronometer in existence, and yet it will not require half a pennyweight to deflect it one-fourth of an inch. It is a good rule to make the length of the detent from the foot _F_ to the center of the locking jewel pipe _j_ equal to the diameter of the escape wheel, and the length of the detent spring _h_ two-sevenths of this distance. The length of the horn _k_ is determined by the graphic plan and can be taken from the plotted plan. The end, however, should approach as near to the discharging jewel as possible and not absolutely touch. The discharging (gold) spring _m_ is attached to the blade _i_ of the detent with a small screw _l_ cut in a No. 18 hole of a Swiss plate. While there should be a slight increase in thickness in the detent blade at _w_, where the gold spring is attached, still it should be no more than to separate the gold spring _m_ from the detent blade _i_. IMPORTANT CONSIDERATIONS. It is important the spring should be absolutely free and not touch the detent except at its point of attachment at _w_ and to rest against the end of the horn _k_, and the extreme end of _k_, where the gold spring rests, should only be what we may term a dull or thick edge. The end of the horn _k_ (shown at _y_) is best made, for convenience of elegant construction, square--that is, the part _y_ turns at right angles to _k_ and is made thicker than _k_ and at the same time deeper; or, to make a comparison to a clumsy article, _y_ is like the head of a nail, which is all on one side. Some makers bend the horn _k_ to a curve and allow the end of the horn to arrest or stop the gold spring; but as it is important the entire detent should be as light as possible, the square end best answers this purpose. The banking placed at _j_ should arrest the detent as thrown back by the spring _h_ at the "point of percussion." This point of percussion is a certain point in a moving mass where the greatest effort is produced and would be somewhere near the point _x_, in a bar _G_ turning on a pivot at _z_, Fig. 138. It will be evident, on inspection of this figure, if the bar _G_ was turning on the center _z_ it would not give the hardest impact at the end _v_, as parts of its force would be expended at the center _z_. [Illustration: Fig. 138] DECISIONS ARRIVED AT BY EXPERIENCE. Experience has decided that the impulse roller should be about half the diameter of the escape wheel, and experience has also decided that an escape wheel of fifteen teeth has the greatest number of advantages; also, that the balance should make 14,400 vibrations in one hour. We will accept these proportions and conditions as best, from the fact that they are now almost universally adopted by our best chronometer makers. Although it would seem as if these proportions should have established themselves earlier among practical men, we shall in these drawings confine ourselves to the graphic plan, considering it preferable. In the practical detail drawing we advise the employment of the scale given, i.e., delineating an escape wheel 10" in diameter. The drawings which accompany the description are one-fourth of this size, for the sake of convenience in copying. With an escape wheel of fifteen teeth the impulse arc is exactly twenty-four degrees, and of course the periphery of the impulse roller must intersect the periphery of the escape wheel for this arc (24°). The circles _A B_, Fig. 139, represent the peripheries of these two mobiles, and the problem in hand is to locate and define the position of the two centers _a c_. These, of course, are not separated, the sum of the two radii, i.e., 5" + 2½" (in the large drawing), as these circles intersect, as shown at _d_. Arithmetically considered, the problem is quite difficult, but graphically, simple enough. After we have swept the circle _A_ with a radius of 5", we draw the radial line _a f_, said line extending beyond the circle _A_. LOCATING THE CENTER OF THE BALANCE STAFF. Somewhere on this line is located the center of the balance staff, and it is the problem in hand to locate or establish this center. Now, it is known the circles which define the peripheries of the escape wheel and the impulse roller intersect at _e e^2_. We can establish on our circle _A_ where these intersections take place by laying off twelve degrees, one-half of the impulse arc on each side of the line of centers _a f_ on this circle and establishing the points _e e^2_. These points _e e^2_ being located at the intersection of the circles _A_ and _B_, must be at the respective distances of 5" and 2½" distance from the center of the circles _A B_; consequently, if we set our dividers at 2½" and place one leg at _e_ and sweep the short arc _g^2_, and repeat this process when one leg of the dividers is set at _e^2_, the intersection of the short arcs _g_ and _g^2_ will locate the center of our balance staff. We have now our two centers established, whose peripheries are in the relation of 2 to 1. To know, in the chronometer which we are supposed to be constructing, the exact distance apart at which to plant the hole jewels for our two mobiles, i.e., escape wheel and balance staff, we measure carefully on our drawing the distance from _a_ to _c_ (the latter we having just established) and make our statement in the rule of three, as follows: As (10) the diameter of drawn escape wheel is to our real escape wheel so is the measured distance on our drawing to the real distance in the chronometer we are constructing. It is well to use great care in the large drawing to obtain great accuracy, and make said large drawing on a sheet of metal. This course is justified by the degree of perfection to which measuring tools have arrived in this day. It will be found on measurement of the arc of the circle _B_, embraced between the intersections _e e^2_, that it is about forty-eight degrees. How much of this we can utilize in our escapement will depend very much on the perfection and accuracy of construction. [Illustration: Fig. 139] We show at Fig. 140 three teeth of an escape wheel, together with the locking jewel _E_ and impulse jewel _D_. Now, while theoretically we could commence the impulse as soon as the impulse jewel _D_ was inside of the circle representing the periphery of the escape wheel, still, in practical construction, we must allow for contingencies. Before it is safe for the escape wheel to attack the impulse jewel, said jewel must be safely inside of said escape wheel periphery, in order that the attacking tooth shall act with certainty and its full effect. A good deal of thought and study can be bestowed to great advantage on the "action" of a chronometer escapement. Let us examine the conditions involved. We show in Fig. 140 the impulse jewel _D_ just passing inside the circle of the periphery of the escape wheel. Now the attendant conditions are these: The escape wheel is locked fast and perfectly dead, and in the effort of unlocking it has to first turn backward against the effort of the mainspring; the power of force required for this effort is derived from the balance in which is stored up, so to speak, power from impulses imparted to the balance by former efforts of the escape wheel. In actual fact, the balance at the time the unlocking takes place is moving with nearly its greatest peripheral velocity and, as stated above, the escape wheel is at rest. Here comes a very delicate problem as regards setting the unlocking or discharging jewel. Let us first suppose we set the discharging jewel so the locking jewel frees its tooth at the exact instant the impulse jewel is inside the periphery of the escape wheel. As just stated, the escape wheel is not only dead but actually moving back at the time the release takes place. Now, it is evident that the escape wheel requires an appreciable time to move forward and attack the impulse jewel, and during this appreciable time the impulse jewel has been moving forward inside of the arc _A A_, which represents the periphery of the escape wheel. The proper consideration of this problem is of more importance in chronometer making than we might at first thought have imagined, consequently, we shall dwell upon it at some length. HOW TO SET THE DISCHARGING JEWEL. [Illustration: Fig. 140] Theoretically, the escape-wheel tooth should encounter the impulse jewel at the time--instant--both are moving with the same velocity. It is evident then that there can be no special rule given for this, i.e., how to set the discharging jewel so it will free the tooth at exactly the proper instant, from the fact that one chronometer train may be much slower in getting to move forward from said train being heavy and clumsy in construction. Let us make an experiment with a real chronometer in illustration of our problem. To do so we remove our balance spring and place the balance in position. If we start the balance revolving in the direction of the arrow _y_, Fig. 140, it will cause the escapement to be unlocked and the balance to turn rapidly in one direction and with increasing velocity until, in fact, the escape wheel has but very little effect on the impulse jewel; in fact, we could, by applying some outside source of power--like blowing with a blow pipe on the balance--cause the impulse jewel to pass in advance of the escape wheel; that is, the escape-wheel tooth would not be able to catch the impulse jewel during the entire impulse arc. Let us suppose, now, we set our unlocking or discharging jewel in advance, that is, so the escapement is really unlocked a little before the setting parts are in the positions and relations shown in Fig. 141. Under the new conditions the escape wheel would commence to move and get sufficient velocity on it to act on the impulse jewel as soon as it was inside of the periphery of the escape wheel. If the balance was turned slowly now the tooth of the escape wheel would not encounter the impulse jewel at all, but fall into the passing hollow _n_; but if we give the balance a high velocity, the tooth would again encounter and act upon the jewel in the proper manner. Experienced adjusters of chronometers can tell by listening if the escape-wheel tooth attacks the impulse jewel properly, i.e., when both are moving with similar velocities. The true sound indicating correct action is only given when the balance has its maximum arc of vibration, which should be about 1¼ revolutions, or perform an arc of 225 degrees on each excursion. Fig. 142 is a side view of Fig. 141 seen in the direction of the arrow _y_. We have mentioned a chariot to which the detent is attached, but we shall make no attempt to show it in the accompanying drawings, as it really has no relation to the problem in hand; i.e., explaining the action of the chronometer escapement, as the chariot relates entirely to the convenience of setting and adjusting the relation of the second parts. The size, or better, say, the inside diameter of the pipe at _C_, Fig. 143, which holds the locking jewel, should be about one-third of a tooth space, and the jewel made to fit perfectly. Usually, jewelmakers have a tendency to make this jewel too frail, cutting away the jewel back of the releasing angle (_n_, Fig. 143) too much. A GOOD FORM OF LOCKING STONE. A very practical form for a locking stone is shown in transverse section at Fig. 143. In construction it is a piece of ruby, or, better, sapphire cut to coincide to its axis of crystallization, into first a solid cylinder nicely fitting the pipe _C_ and finished with an after-grinding, cutting away four-tenths of the cylinder, as shown at _I_, Fig. 143. Here the line _m_ represents the locking face of the jewel and the line _o_ the clearance to free the escaping tooth, the angle at _n_ being about fifty-four degrees. This angle (_n_) should leave the rounding of the stone intact, that is, the rounding of the angle should be left and not made after the flat faces _m o_ are ground and polished. The circular space at _I_ is filled with an aluminum pin. The sizes shown are of about the right relative proportions; but we feel it well to repeat the statement made previously, to the effect that the detent to a chronometer cannot well be made too light. [Illustration: Fig. 141] [Illustration: Fig. 142] [Illustration: Fig. 143] The so-called gold spring shown at _H_, Figs. 141 and 142, should also be as light as is consistent with due strength and can be made of the composite metal used for gold filled goods, as the only real benefit to be derived from employing gold is to avoid the necessity of applying oil to any part of the escapement. If such gold metal is employed, after hammering to obtain the greatest possible elasticity to the spring, the gold is filed away, except where the spring is acted upon by the discharging jewel _h_. We have previously mentioned the importance of avoiding wide, flat contacts between all acting surfaces, like where the gold spring rests on the horn of the detent at _p_; also where the detent banks on the banking screw, shown at _G_, Fig. 142. Under this principle the impact of the face of the discharging jewel with the end of the gold spring should be confined to as small a surface as is consistent with what will not produce abrasive action. The gold spring is shaped as shown at Fig. 142 and loses, in a measure, under the pipe of the locking jewel, a little more than one-half of the pipe below the blade of the detent being cut away, as shown in Fig. 143, where the lines _r r_ show the extent of the part of the pipe which banks against the banking screw _G_. In this place even, only the curved surface of the outside of the pipe touches the screw _G_, again avoiding contact of broad surfaces. We show the gold spring separate at Fig. 144. A slight torsion or twist is given to the gold spring to cause it to bend with a true curvature in the act of allowing the discharging pallet to pass back after unlocking. If the gold spring is filed and stoned to the right flexure, that is, the thinnest point properly placed or, say, located, the gold spring will not continue in contact with the discharging pallet any longer time or through a greater arc than during the process of unlocking. To make this statement better understood, let us suppose the weakest part of the gold spring _H_ is opposite the arrow _y_, Fig. 141, it will readily be understood the contact of the discharging stone _h_ would continue longer than if the point of greatest (or easiest) flexure was nearer to the pipe _C_. If the end _D^2_ of the horn of the detent is as near as it should be to the discharging stone there need be no fear but the escapement will be unlocked. The horn _D^2_ of the detent should be bent until five degrees of angular motion of the balance will unlock the escape, and the contact of discharging jewel _h_ should be made without engaging friction. This condition can be determined by observing if the jewel seems to slide up (toward the pipe _C_) on the gold spring after contact. Some adjusters set the jewel _J_, Figs. 143 and 141, in such a way that the tooth rests close to the base; such adjusters claiming this course has a tendency to avoid cockling or buckling of the detent spring _E_. Such adjusters also set the impulse jewel slightly oblique, so as to lean on the opposite angle of the tooth. Our advice is to set both stones in places corresponding to the axis of the balance staff, and the escape-wheel mobiles. THE DETENT SPRING. [Illustration: Fig. 144] It will be noticed we have made the detent spring _E_ pretty wide and extended it well above the blade of the detent. By shaping the detent in this way nearly all the tendency of the spring _E_ to cockle is annulled. We would beg to add to what we said in regard to setting jewels obliquely. We are unable to understand the advantage of wide-faced stones and deep teeth when we do not take advantage of the wide surfaces which we assert are important. We guarantee that with a detent and spring made as we show, there will be no tendency to cockle, or if there is, it will be too feeble to even display itself. Those who have had extended experience with chronometers cannot fail to have noticed a gummy secretion which accumulates on the impulse and discharging stones of a chronometer, although no oil is ever applied to them. We imagine this coating is derived from the oil applied to the pivots, which certainly evaporates, passes into vapor, or the remaining oil could not become gummy. We would advise, when setting jewels (we mean the locking, impulse and discharging jewels), to employ no more shellac than is absolutely necessary, depending chiefly on metallic contact for security. DETAILS OF CONSTRUCTION. We will now say a few words about the number of beats to the hour for a box or marine chronometer to make to give the best results. Experience shows that slow but most perfect construction has settled that 14,400, or four vibrations of the balance to a second, as the proper number, the weight of balance, including balance proper and movable weights, to be about 5½ pennyweights, and the compensating curb about 1-2/10" in diameter. The escape wheel, 55/100" in diameter and recessed so as to be as light as possible, should have sufficient strength to perform its functions properly. The thickness or, more properly, the face extent of the tooth, measured in the direction of the axis of the escape wheel, should be about 1/20". The recessing should extend half way up the radial back of the tooth at _t_. The curvature of the back of the teeth is produced with the same radii as the impulse roller. To locate the center from which the arc which defines the back of the teeth is swept, we halve the space between the teeth _A^2_ and _a^4_ and establish the point _n_, Fig. 141, and with our dividers set to sweep the circle representing the impulse roller, we sweep an arc passing the point of the tooth _A^3_ and _u_, thus locating the center _w_. From the center _k_ of the escape wheel we sweep a complete circle, a portion of which is represented by the arc _w v_. For delineating other teeth we set one leg of our dividers to agree with the point of the tooth and the other leg on the circle _w v_ and produce an arc like _z u_. ORIGINAL DESIGNING OF THE ESCAPEMENT. On delineating our chronometer escapement shown at Fig. 141 we have followed no text-book authority, but have drawn it according to such requirements as are essential to obtain the best results. An escapement of any kind is only a machine, and merely requires in its construction a combination of sound mechanical principles. Neither Saunier nor Britten, in their works, give instructions for drawing this escapement which will bear close analysis. It is not our intention, however, to criticise these authors, except we can present better methods and give correct systems. TANGENTIAL LOCKINGS. It has been a matter of great contention with makers of chronometer and also lever escapements as to the advantages of "tangential lockings." By this term is meant a locking the same as is shown at _C_, Fig. 141, and means a detent planted at right angles to a line radial to the escape-wheel axis, said radial line passing through the point of the escape-wheel tooth resting on the locking jewel. In escapements not set tangential, the detent is pushed forward in the direction of the arrow _x_ about half a tooth space. Britten, in his "Hand-Book," gives a drawing of such an escapement. We claim the chief advantage of tangential locking to lie in the action of the escape-wheel teeth, both on the impulse stone and also on the locking stone of the detent. Saunier, in his "Modern Horology," gives the inclination of the front fan of the escape-wheel teeth as being at an angle of twenty-seven degrees to a radial line. Britten says twenty degrees, and also employs a non-tangential locking. Our drawing is on an angle of twenty-eight degrees, which is as low as is safe, as we shall proceed to demonstrate. For establishing the angle of an escape-wheel tooth we draw the line _C d_, from the point of the escape-wheel tooth resting on the locking stone shown at _C_ at an angle of twenty-eight degrees to radial line _C k_. We have already discussed how to locate and plant the center of the balance staff. We shall not show in this drawing the angular motion of the escape wheel, but delineate at the radial lines _c e_ and _c f_ of the arc of the balance during the extent of its implication with the periphery of the escape wheel, which arc is one of about forty-eight degrees. Of this angle but forty-three degrees is attempted to be utilized for the purpose of impulse, five degrees being allowed for the impulse jewel to pass inside of the arc of periphery of the escape wheel before the locking jewel releases the tooth of the escape wheel resting upon it. At this point it is supposed the escape wheel attacks the impulse jewel, because, as we just explained, the locking jewel has released the tooth engaging it. Now, if the train had no weight, no inertia to overcome, the escape wheel tooth _A^2_ would move forward and attack the impulse pallet instantly; but, in fact, as we have already explained, there will be an appreciable time elapse before the tooth overtakes the rapidly-moving impulse jewel. It will, of course, be understood that the reference letters used herein refer to the illustrations that have appeared on preceding pages. If we reason carefully on the matter, we will readily comprehend that we can move the locking jewel, i.e., set it so the unlocking will take place in reality before the impulse jewel has passed through the entire five degrees of arc embraced between the radial lines _c e_ and _c g_, Fig. 141, and yet have the tooth attack the jewel after the five degrees of arc. In practice it is safe to set the discharging jewel _h_ so the release of the held tooth _A^1_ will take place as soon as the tooth _A^2_ is inside the principal line of the escape wheel. As we previously explained, the contact between _A^2_ and the impulse jewel _i_ would not in reality occur until the said jewel _i_ had fully passed through the arc (five degrees) embraced between the radial lines _c e_ and _c g_. At this point we will explain why we drew the front fan of the escape-wheel teeth at the angle of twenty-eight degrees. If the fan of impulse jewel _i_ is set radial to the axis of the balance, the engagement of the tooth _A^2_ would be at a disadvantage if it took place prior to this jewel passing through an arc of five degrees inside the periphery of the escape wheel. It will be evident on thought that if an escape-wheel tooth engaged the impulse stone before the five-degrees angle had passed, the contact would not be on its flat face, but the tooth would strike the impulse jewel on its outer angle. A continued inspection will also reveal the fact that in order to have the point of the tooth engage the flat surface of the impulse pallet the impulse jewel must coincide with the radial line _c g_. If we seek to remedy this condition by setting the impulse jewel so the face is not radial, but inclined backward, we encounter a bad engaging friction, because, during the first part of the impulse action, the tooth has to slide up the face of the impulse jewel. All things considered, the best action is obtained with the impulse jewel set so the acting face is radial to the balance staff and the engagement takes place between the tooth and the impulse jewel when both are moving with equal velocities, i.e., when the balance is performing with an arc (or motion) of 1¼ revolutions or 225 degrees each way from a point of rest. Under such conditions the actual contact will not take place before some little time after the impulse jewel has passed the five-degree arc between the lines _c e_ and _c g_. THE DROP AND DRAW CONSIDERED. Exactly how much drop must be allowed from the time the tooth leaves the impulse jewel before the locking tooth engages the locking jewel will depend in a great measure on the perfection of workmanship, but should in no instance be more than what is absolutely required to make the escapement safe. The amount of draw given to the locking stone _c_ is usually about twelve degrees to the radial line _k a_. Much of the perfection of the chronometer escapement will always depend on the skill of the escapement adjuster and not on the mechanical perfection of the parts. The jewels all have to be set by hand after they are made, and the distance to which the impulse jewel protrudes beyond the periphery of the impulse roller is entirely a matter for hand and eye, but should never exceed 2/1000". After the locking jewel _c_ is set, we can set the foot _F_ of the detent _D_ forward or back, to perfect and correct the engagement of the escape-wheel teeth with the impulse roller _B_. If we set this too far forward, the tooth _A^3_ will encounter the roller while the tooth _A^2_ will be free. We would beg to say here there is no escape wheel made which requires the same extreme accuracy as the chronometer, as the tooth spaces and the equal radial extent of each tooth should be only limited by our powers toward perfection. It is usual to give the detent a locking of about two degrees; that is, it requires about two degrees to open it, counting the center of fluxion of the detent spring _E_ and five degrees of balance arc. FITTING UP OF THE FOOT. Several attempts have been made by chronometer makers to have the foot _F_ adjustable; that is, so it could be moved back and forth with a screw, but we have never known of anything satisfactory being accomplished in this direction. About the best way of fitting up the foot _F_ seems to be to provide it with two soft iron steady pins (shown at _j_) with corresponding holes in the chariot, said holes being conically enlarged so they (the pins) can be bent and manipulated so the detent not only stands in the proper position as regards the escape wheel, but also to give the detent spring _E_ the proper elastic force to return in time to afford a secure locking to the arresting tooth of the escape wheel after an impulse has been given. If these pins _j_ are bent properly by the adjuster, whoever afterwards cleans the chronometer needs only to gently push the foot _F_ forward so as to cause the pins _j_ to take the correct positions as determined by the adjuster and set the screw _l_ up to hold the foot _F_ when all the other relations are as they should be, except such as we can control by the screw _G_, which prevents the locking jewel from entering too deeply into the escape wheel. In addition to being a complete master of the technical part of his business, it is also desirable that the up-to-date workman should be familiar with the subject from a historical point of view. To aid in such an understanding of the matter we have translated from "L'Almanach de l'Horologerie et de la Bijouterie" the matter contained in the following chapter. CHAPTER IV. HISTORY OF ESCAPEMENTS. It could not have been long after man first became cognizant of his reasoning faculties that he began to take more or less notice of the flight of time. The motion of the sun by day and of the moon and stars by night served to warn him of the recurring periods of light and darkness. By noting the position of these stellar bodies during his lonely vigils, he soon became proficient in roughly dividing up the cycle into sections, which he denominated the hours of the day and of the night. Primitive at first, his methods were simple, his needs few and his time abundant. Increase in numbers, multiplicity of duties, and division of occupation began to make it imperative that a more systematic following of these occupations should be instituted, and with this end in view he contrived, by means of burning lights or by restricting the flowing of water or the falling of weights, to subdivide into convenient intervals and in a tolerably satisfactory manner the periods of light. These modest means then were the first steps toward the exact subdivisions of time which we now enjoy. Unrest, progress, discontent with things that be, we must acknowledge, have, from the appearance of the first clock to the present hour, been the powers which have driven on the inventive genius of watch and clockmakers to designate some new and more acceptable system for regulating the course of the movement. In consequence of this restless search after the best, a very considerable number of escapements have been invented and made up, both for clocks and watches; only a few, however, of the almost numberless systems have survived the test of time and been adopted in the manufacture of the timepiece as we know it now. Indeed, many such inventions never passed the experimental stage, and yet it would be very interesting to the professional horologist, the apprentice and even the layman to become more intimately acquainted with the vast variety of inventions made upon this domain since the inception of horological science. Undoubtedly, a complete collection of all the escapements invented would constitute a most instructive work for the progressive watchmaker, and while we are waiting for a competent author to take such an exhaustive work upon his hands, we shall endeavor to open the way and trust that a number of voluntary collaborators will come forward and assist us to the extent of their ability in filling up the chinks. PROBLEMS TO BE SOLVED. The problem to be solved by means of the escapement has always been to govern, within limits precise and perfectly regular, if it be possible, the flow of the motive force; that means the procession of the wheel-work and, as a consequence, of the hands thereto attached. At first blush it seems as if a continually-moving governor, such as is in use on steam engines, for example, ought to fulfil the conditions, and attempts have accordingly been made upon this line with results which have proven entirely unsatisfactory. Having thoroughly sifted the many varieties at hand, it has been finally determined that the only means known to provide the most regular flow of power consists in intermittently interrupting the procession of the wheel-work, and thereby gaining a periodically uniform movement. Whatever may be the system or kind of escapement employed, the functioning of the mechanism is characterized by the suspension, at regular intervals, of the rotation of the last wheel of the train and in transmitting to a regulator, be it a balance or a pendulum, the power sent into that wheel. ESCAPEMENT THE MOST ESSENTIAL PART. Of all the parts of the timepiece the escapement is then the most essential; it is the part which assures regularity in the running of the watch or clock, and that part of parts that endows the piece with real value. The most perfect escapement would be that one which should perform its duty with the least influence upon the time of oscillation or vibration of the regulating organ. The stoppage of the train by the escapement is brought about in different ways, which may be gathered under three heads or categories. In the two which we shall mention first, the stop is effected directly upon the axis of the regulator, or against a piece which forms a part of that axis; the tooth of the escape wheel at the moment of its disengagement remains supported upon or against that stop. In the first escapement invented and, indeed, in some actually employed to-day for certain kinds of timekeepers, we notice during the locking a retrograde movement of the escape wheel; to this kind of movement has been given the name of _recoil escapement_. It was recognized by the fraternity that this recoil was prejudicial to the regularity of the running of the mechanism and, after the invention of the pendulum and the spiral, inventive makers succeeded in replacing this sort of escapement with one which we now call the _dead-beat escapement_. In this latter the wheel, stopped by the axis of the regulator, remains immovable up to the instant of its disengagement or unlocking. In the third category have been collected all those forms of escapement wherein the escape wheel is locked by an intermediate piece, independent of the regulating organ. This latter performs its vibrations of oscillation quite without interference, and it is only in contact with the train during the very brief moment of impulse which is needful to keep the regulating organ in motion. This category constitutes what is known as the _detached escapement_ class. Of the _recoil escapement_ the principal types are: the _verge escapement_ or _crown-wheel escapement_ for both watches and clocks, and the _recoil anchor escapement_ for clocks. The _cylinder_ and _duplex escapements_ for watches and the _Graham anchor escapement_ for clocks are styles of the _dead-beat escapement_ most often employed. Among the _detached escapements_ we have the _lever_ and _detent_ or _chronometer escapements_ for watches; for clocks there is no fixed type of detached lever and it finds no application to-day. THE VERGE ESCAPEMENT. The _verge escapement_, called also the _crown-wheel escapement_, is by far the simplest and presents the least difficulty in construction. We regret that the world does not know either the name of its originator nor the date at which the invention made its first appearance, but it seems to have followed very closely upon the birth of mechanical horology. Up to 1750 it was employed to the exclusion of almost all the others. In 1850 a very large part of the ordinary commercial watches were still fitted with the verge escapement, and it is still used under the form of _recoil anchor_ in clocks, eighty years after the invention of the cylinder escapement, or in 1802. Ferdinand Berthoud, in his "History of the Measurement of Time," says of the balance-wheel escapement: "Since the epoch of its invention an infinite variety of escapements have been constructed, but the one which is employed in ordinary watches for every-day use is still the best." In referring to our illustrations, we beg first to call attention to the plates marked Figs. 145 and 146. This plate gives us two views of a verge escapement; that is, a balance wheel and a verge formed by its two opposite pallets. The views are intentionally presented in this manner to show that the verge _V_ may be disposed either horizontally, as in Fig. 146, or vertically, as in Fig. 145. [Illustration: Figs. 145 and 146] [Illustration: Fig. 147] Let us imagine that our drawing is in motion, then will the tooth _d_, of the crown wheel _R_, be pushing against the pallet _P_, and just upon the point of slipping by or escaping, while the opposite tooth _e_ is just about to impinge upon the advancing pallet _P'_. This it does, and will at first, through the impulse received from the tooth _d_ be forced back by the momentum of the pallet, that is, suffer a recoil; but on the return journey of the pallet _P'_, the tooth _e_ will then add its impulse to the receding pallet. The tooth _e_ having thus accomplished its mission, will now slip by and the tooth _c_ will come in lock with the pallet _P_ and, after the manner just described for _e_, continue the escapement. Usually these escape wheels are provided with teeth to the number of 11, 13 or 15, and always uneven. A great advantage possessed by this form of escapement is that it does not require any oil, and it may be made to work even under very inferior construction. OLDEST ARRANGEMENT OF A CROWN-WHEEL ESCAPEMENT. [Illustration: Fig. 148] Plate 147 shows us the oldest known arrangement of a crown-wheel escapement in a clock. _R_ is the crown wheel or balance wheel acting upon the pallets _P_ and _P'_, which form part of the verge _V_. This verge is suspended as lightly as possible upon a pliable cord _C_ and carries at its upper end two arms, _B_ and _B_, called adjusters, forming the balance. Two small weights _D D_, adapted to movement along the rules or adjusters serve to regulate the duration of a vibration. In Fig. 148 we have the arrangement adopted in small timepieces and watches: _B_ represents the regulator in the form of a circular balance, but not yet furnished with a spiral regulating spring; _c_ is the last wheel of the train and called the _fourth wheel_, it being that number distant from the great wheel. As will be seen, the verge provided with its pallets is vertically placed, as in the preceding plate. [Illustration: Fig. 149] Here it will quickly be seen that regarded from the standpoint of regularity of motion, this arrangement can be productive of but meager results. Subjected as it is to the influence of the slightest variation in the motive power and of the least jar or shaking, a balance wheel escapement improvided with a regulator containing within itself a regulating force, could not possibly give forth anything else than an unsteady movement. However, mechanical clocks fitted with this escapement offer indisputable advantages over the ancient clepsydra; in spite of their imperfections they rendered important services, especially after the striking movement had been added. For more than three centuries both this crude escapement and the cruder regulator were suffered to continue in this state without a thought of improvement; even in 1600, when Galileo discovered the law governing the oscillation of the pendulum, they did not suspect how important this discovery was for the science of time measurement. GALILEO'S EXPERIMENTS. [Illustration: Fig. 150] Galileo, himself, in spite of his genius for investigation, was so engrossed in his researches that he could not seem to disengage the simple pendulum from the compound pendulums to which he devoted his attention; besides, he attributed to the oscillation an absolute generality of isochronism, which they did not possess; nor did he know how to apply his famous discovery to the measurement of time. In fact, it was not till after more than half a century had elapsed, in 1657, to be exact, that the celebrated Dutch mathematician and astronomer, Huygens, published his memoirs in which he made known to the world the degree of perfection which would accrue to clocks if the pendulum were adopted to regulate their movement. [Illustration: Fig. 151] An attempt was indeed made to snatch from Huygens and confer upon Galileo the glory of having first applied the pendulum to a clock, but this attempt not having been made until some time after the publication of "Huygens' Memoirs," it was impossible to place any faith in the contention. If Galileo had indeed solved the beautiful problem, both in the conception and the fact, the honor of the discovery was lost to him by the laziness and negligence of his pupil, Viviani, upon whom he had placed such high hopes. One thing is certain, that the right of priority of the discovery and the recognition of the entire world has been incontestably bestowed upon Huygens. The escapement which Galileo is supposed to have conceived and to which he applied the pendulum, is shown in Fig. 149. The wheel _R_ is supplied with teeth, which lock against the piece _D_ attached to a lever pivoted at _a_, and also with pins calculated to impart impulses to the pendulum through the pallet _P_. The arm _L_ serves to disengage or unlock the wheel by lifting the lever _D_ upon the return oscillation of the pendulum. [Illustration: Fig. 152] [Illustration: Fig. 153] A careful study of Fig. 150 will discover a simple transposition which it became necessary to make in the clocks, for the effectual adaptation of the pendulum to their regulation. The verge _V_ was set up horizontally and the pendulum _B_, suspended freely from a flexible cord, received the impulses through the intermediation of the forked arm _F_, which formed a part of the verge. At first this forked arm was not thought of, for the pendulum itself formed a part of the verge. A far-reaching step had been taken, but it soon became apparent that perfection was still a long way off. The crown-wheel escapement forcibly incited the pendulum to wider oscillations; these oscillations not being as Galileo had believed, of unvaried durations, but they varied sensibly with the intensity of the motive power. THE ATTAINMENT OF ISOCHRONISM BY HUYGENS. Huygens rendered his pendulum _isochronous_; that is, compelled it to make its oscillations of equal duration, whatever might be the arc described, by suspending the pendulum between two metallic curves _c c'_, each one formed by an arc of a cycloid and against which the suspending cord must lie upon each forward or backward oscillation. We show this device in Fig. 151. In great oscillations, and by that we mean oscillations under a greater impulse, the pendulum would thus be shortened and the shortening would correct the time of the oscillation. However, the application of an exact cycloidal arc was a matter of no little difficulty, if not an impossibility in practice, and practical men began to grope about in search of an escapement which would permit the use of shorter arcs of oscillation. At London the horologist, G. Clement, solved the problem in 1675 with his rack escapement and recoil anchor. In the interval other means were invented, especially the addition of a second pendulum to correct the irregularities of the first. Such an escapement is pictured in Fig. 152. The verge is again vertical and carries near its upper end two arms _D D_, which are each connected by a cord with a pendulum. The two pendulums oscillate constantly in the inverse sense the one to the other. [Illustration: Fig. 154] [Illustration: Fig. 155] ANOTHER TWO-PENDULUM ESCAPEMENT. We show another escapement with two pendulums in Fig. 153. These are fixed directly upon two axes, each one carrying a pallet _P P'_ and a segment of a toothed wheel _D D_, which produces the effect of solidarity between them. The two pendulums oscillate inversely one to the other, and one after the other receives an impulse. This escapement was constructed by Jean Baptiste Dutertre, of Paris. Fig. 154 shows another disposition of a double pendulum. While the pendulum here is double, it has but one bob; it receives the impulse by means of a double fork _F_. _C C_ represents the cycloidal curves and are placed with a view of correcting the inequality in the duration of the oscillations. In watches the circular balances did not afford any better results than the regulating rods or rules of the clocks, and the pendulum, of course, was out of the question altogether; it therefore became imperative to invent some other regulating system. [Illustration: Fig. 156] [Illustration: Fig. 157] It occured to the Abbé d'Hautefeuille to form a sort of resilient mechanism by attaching one end of a hog's bristle to the plate and the other to the balance near the axis. Though imperfect in results, this was nevertheless a brilliant idea, and it was but a short step to replace the bristle with a straight and very flexible spring, which later was supplanted by one coiled up like a serpent; but in spite of this advancement, the watches did not keep much better time. Harrison, the celebrated English horologist, had recourse to two artifices, of which the one consisted in giving to the pallets of the escapement such a curvature that the balance could be led back with a velocity corresponding to the extension of the oscillation; the second consisted of an accessory piece, the resultant action of which was analogous to that of the cycloidal curves in connection with the pendulum. CORRECTING IRREGULARITIES IN THE VERGE ESCAPEMENT. Huygens attempted to correct these irregularities in the verge escapement in watches by amplifying the arc of oscillation of the balance itself. He constructed for that purpose a pirouette escapement shown in Fig. 155, in which a toothed wheel _A_ adjusted upon the verge _V_ serves as an intermediary between that and the balance _B_, upon the axis of which was fixed a pinion _D_. By this method he obtained extended arcs of vibration, but the vibrations were, as a consequence, very slow, and they still remained subject to all the irregularities arising from the variation in the motive power as well as from shocks. A little later, but about the same epoch, a certain Dr. Hook, of the Royal Society of London, contrived another arrangement by means of which he succeeded, so it appeared to him at least, in greatly diminishing the influence of shock upon the escapement; but many other, perhaps greater, inconveniences caused his invention to be speedily rejected. We shall give our readers an idea of what Dr. Hook's escapement was like. [Illustration: Fig. 158] [Illustration: Fig. 159] On looking at Fig. 156 we see the escape wheel _R_, which was flat and in the form of a ratchet; it was provided with two balances. _B B_ engaging each other in teeth, each one carrying a pallet _P P'_ upon its axis; the axes of the three wheels being parallel. Now, in our drawing, the tooth _a_ of the escape wheel exerts its lift upon the pallet _P'_; when this tooth escapes the tooth _b_ will fall upon the pallet _P'_ on the opposite side, a recoil will be produced upon the action of the two united balances, then the tooth _b_ will give its impulse in the contrary direction. Considerable analogy exists between this form of escapement and that shown in Fig. 153 and intended for clocks. This was the busy era in the watchmaker's line. All the great heads were pondering upon the subject and everyone was on the _qui vive_ for the newest thing in the art. In 1674 Huygens brought out the first watch having a regulating spring in the form of a spiral; the merit of this invention was disputed by the English savant, Dr. Hook, who pretended, as did Galileo, in the application of the pendulum, to have priority in the idea. Huygens, who had discovered and corrected the irregularities in the oscillations of the pendulum, did not think of those of the balance with the spiral spring. And it was not until the close of the year 1750 that Pierre Le Roy and Ferdinand Berthoud studied the conditions of isochronism pertaining to the spiral. AN INVENTION THAT CREATED MUCH ENTHUSIASM. However that may be, this magnificent invention, like the adaptation of the pendulum, was welcomed with general enthusiasm throughout the scientific world: without spiral and without pendulum, no other escapement but the recoil escapement was possible; a new highway was thus opened to the searchers. The water clocks (clepsydrę) and the hour glasses disappeared completely, and the timepieces which had till then only marked the hours, having been perfected up to the point of keeping more exact time, were graced with the addition of another hand to tell off the minutes. [Illustration: Fig. 160] [Illustration: Fig. 161] It was not until 1695 that the first _dead-beat escapement_ appeared upon the scene; during the interval of over twenty years all thought had been directed toward the one goal, viz.: the perfecting of the _verge escapement_; but practice demonstrated that no other arrangement of the parts was superior to the original idea. For the benefit of our readers we shall give a few of these attempts at betterment, and you may see for yourselves wherein the trials failed. Fig. 157 represents a _verge escapement_ with a ratchet wheel, the pallets _P P'_ being carried upon separate axes. The two axes are rigidly connected, the one to the other, by means of the arms _o o'_. One of the axes carries besides the fork _F_, which transmits the impulse to the pendulum _B_. In the front view, at the right of the plate, for the sake of clearness the fork and the pendulum are not shown, but one may easily see the jointure of the arms _o o'_ and their mode of operation. Another very peculiar arrangement of the _verge escapement_ we show at Fig. 158. In this there are two wheels, one, _R'_, a small one in the form of a ratchet; the other, _R_, somewhat larger, called the balance wheel, but being supplied with straight and slender teeth. The verge _V_ carrying the two pallets is pivoted in the vertical diameter of the larger wheel. The front view shows the _modus operandi_ of this combination, which is practically the same as the others. The tooth _a_ of the large wheel exerts its force upon the pallet _P_, and the tooth _b_ of the ratchet will encounter the pallet _P'_. This pallet, after suffering its recoil, will receive the impulse communicated by the tooth _b_. This escapement surely could not have given much satisfaction, for it offers no advantage over the others, besides it is of very difficult construction. [Illustration: Fig. 162] [Illustration: Fig. 163] INGENIOUS ATTEMPTS AT SOLUTION OF A DIFFICULT PROBLEM. Much ingenuity to a worthy end, but of little practical value, is displayed in these various attempts at the solution of a very difficult problem. In Fig. 159 we have a mechanism combining two escape wheels engaging each other in gear; of the two wheels, _R R'_, one alone is driven directly by the train, the other being turned in the opposite direction by its comrade. Both are furnished with pins _c c'_, which act alternately upon the pallets _P P'_ disposed in the same plane upon the verge _V_ and pivoted between the wheels. Our drawing represents the escapement at the moment when the pin _C'_ delivers its impulse, and this having been accomplished, the locking takes place upon the pin _C_ of the other wheel upon the pallet _P'_. Another system of two escape wheels is shown in Fig. 160, but in this case the two wheels _R R_ are driven in a like direction by the last wheel _A_ of the train. The operation of the escapement is the same as in Fig. 159. [Illustration: Fig. 164] [Illustration: Fig. 165] In Fig. 161 we have a departure from the road ordinarily pursued. Here we see an escapement combining two levers, invented by the Chevalier de Béthune and applied by M. Thiout, master-horologist, at Paris in 1727. _P P'_ are the two levers or pallets separately pivoted. Upon the axis _V_, of the lever _P_, is fixed a fork which communicates the motion to the pendulum. The two levers are intimately connected by the two arms _B B'_, of which the former carries an adjusting screw, a well-conceived addition for regulating the opening between the pallets. The counter-weight _C_ compels constant contact between the arms _B B'_. The function is always the same, the recoil and the impulsion operate upon the two pallets simultaneously. This escapement enjoyed a certain degree of success, having been employed by a number of horologists who modified it in various ways. VARIOUS MODIFICATIONS Some of these modifications we shall show. For the first example, then, let Fig. 162 illustrate. In this arrangement the fork is carried upon the axis of the pallet _P'_, which effectually does away with the counter-weight _C_, as shown. Somewhat more complicated, but of the same intrinsic nature, is the arrangement displayed in Fig. 163. We should not imagine that it enjoyed a very extensive application. Here the two levers are completely independent of each other; they act upon the piece _B B_ upon the axis _V_ of the fork. The counter-weights _C C'_ maintain the arms carrying the rollers _D D'_ in contact with the piece _B B'_ which thus receives the impulse from the wheel _R_. Two adjusting screws serve to place the escapement upon the center. By degrees these fantastic constructions were abandoned to make way for the anchor recoil escapement, which was invented, as we have said, in 1675, by G. Clement, a horologist, of London. In Fig. 164 we have the disposition of the parts as first arranged by this artist. Here the pallets are replaced by the inclines _A_ and _B_ of the anchor, which is pivoted at _V_ upon an axis to which is fixed also the fork. The tooth _a_ escapes from the incline or lever _A_, and the tooth _b_ immediately rests upon the lever _B_; by the action of the pendulum the escape wheel suffers a recoil as in the pallet escapement, and on the return of the pendulum the tooth _c_ gives out its impulse in the contrary direction. With this new system it became possible to increase the weight of the bob and at the same time lessen the effective motor power. The travel of the pendulum, or arc of oscillation, being reduced in a marked degree, an accuracy of rate was obtained far superior to that of the crown-wheel escapement. However, this new application of the recoil escapement was not adopted in France until 1695. [Illustration: Fig. 166] [Illustration: Fig. 167] The travel of the pendulum, though greatly reduced, still surpassed in breadth the arc in which it is isochronous, and repeated efforts were made to give such shape to the levers as would compel its oscillation within the arc of equal time; a motion which is, as was recognized even at that epoch, the prime requisite to a precise rating. Thus, in 1720, Julien Leroy occupied himself working out the proper shapes for the inclines to produce this desired isochronism. Searching along the same path, Ferd. Berthoud constructed an escapement represented by the Fig. 165. In it we see the same inclines _A B_ of the former construction, but the locking is effected against the slides _C_ and _D_, the curved faces of which produce isochronous oscillations of the pendulum. The tooth _b_ imparts its lift and the tooth _c_ will lock against the face _C_; after having passed through its recoil motion this tooth _c_ will butt against the incline _A_ and work out its lift or impulse upon it. THE GABLE ESCAPEMENT. [Illustration: Fig. 168] [Illustration: Fig. 169] The _gable escapement_, shown in Fig. 166, allows the use of a heavier pendulum, at the same time the anchor embraces within its jaws a greater number of the escape-wheel teeth; an arrangement after this manner leads to the conclusion that with these long levers of the anchor the friction will be considerably increased and the recoil faces will, as a consequence, be quickly worn away. Without doubt, this was invented to permit of opening and closing the contact points of the anchor more easily. Under the name of the _English recoil anchor_ there came into use an escapement with a _reduced gable_, which embraced fewer teeth between the pallets or inclines; we give a representation of this in Fig. 167. This system seems to have been moderately successful. The anchor recoil escapement in use in Germany to-day is demonstrated in Fig. 168; this arrangement is also found in the American clocks. As we see, the anchor is composed of a single piece of curved steel bent to the desired curves. Clocks provided with this escapement keep reasonably good time; the resistance of the recoils compensate in a measure for the want of isochronism in the oscillations of the pendulum. Ordinary clocks require considerably more power to drive them than finer clocks and, as a consequence, their ticking is very noisy. Several means have been employed to dampen this noise, one of which we show in Fig. 169. [Illustration: Fig. 170] Here the anchor is composed of two pieces, _A B_, screwed upon a plate _H_ pivoting at _V_. In their arrangement the two pieces represent, as to distance and curvature, the counterpart of Fig. 168. At the moment of impact their extreme ends recoil or spring back from the shock of the escape teeth, but the resiliency of the metal is calculated to be strong enough to return them immediately to the contact studs _e e_. As a termination to this chapter, we shall mention the use made at the present day of the recoil lever escapement in repeating watches. We give a diagram of this construction in Fig. 170. The lever here is intended to restrain and regulate the motion of the small striking work. It is pivoted at _V_ and is capable of a very rapid oscillatory motion, the arc of which may, however, be fixed by the stud or stop _D_, which limits the swing of the fly _C_. This fly is of one piece with the lever and, together with the stud _D_, determines the angular motion of the lever. If the angle be large that means the path of the fly be long, then the striking train will move slowly; but if the teeth of the escape wheel _R_ can just pass by without causing the lever to describe a supplementary or extended arc, the striking work will run off rapidly. CHAPTER V. PUTTING IN A NEW CYLINDER. Putting in a new cylinder is something most watchmakers fancy they can do, and do well; but still it is a job very few workmen can do and fulfill all the requirements a job of this kind demands under the ever-varying conditions and circumstances presented in repairs of this kind. It is well to explain somewhat at this point: Suppose we have five watches taken in with broken cylinders. Out of this number probably two could be pivoted to advantage and make the watches as good as ever. As to the pivoting of a cylinder, we will deal with this later on. The first thing to do is to make an examination of the cylinder, not only to see if it is broken, but also to determine if pivoting is going to bring it out all right. Let us imagine that some workman has, at some previous time, put in a new cylinder, and instead of putting in one of the proper size he has put one in too large or too small. Now, in either case he would have to remove a portion of the escape-wheel tooth, that is, shorten the tooth: because, if the cylinder was too large it would not go in between the teeth, and consequently the teeth would have to be cut or stoned away. If the cylinder was too small, again the teeth would have to be cut away to allow them to enter the cylinder. All workmen have traditions, rules some call them, that they go by in relation to the right way to dress a cylinder tooth; some insisting that the toe or point of the tooth is the only place which should be tampered with. Other workmen insist that the heel of the tooth is the proper place. Now, with all due consideration, we would say that in ninety-nine cases out of a hundred the proper thing to do is to let the escape-wheel teeth entirely alone. As we can understand, after a moment's thought, that it is impossible to have the teeth of the escape wheel too long and have the watch run at all; hence, the idea of stoning a cylinder escape-wheel tooth should not be tolerated. ESCAPE-WHEEL TEETH _vs._ CYLINDER. It will not do, however, to accept, and take it for granted that the escape-wheel teeth are all right, because in many instances they have been stoned away and made too short; but if we accept this condition as being the case, that is, that the escape-wheel teeth are too short, what is the workman going to do about it? The owner of the watch will not pay for a new escape wheel as well as a new cylinder. The situation can be summed up about in this way, that we will have to make the best we can out of a bad job, and pick out and fit a cylinder on a compromise idea. In regard to picking out a new cylinder, it may not do to select one of the same size as the old one, from the fact that the old one may not have been of the proper size for the escape wheel, because, even in new, cheap watches, the workmen who "run in" the escapement knew very well the cylinder and escape wheel were not adapted for each other, but they were the best he had. Chapter II, on the cylinder escapement, will enable our readers to master the subject and hence be better able to judge of allowances to be made in order to permit imperfect material to be used. In illustration, let us imagine that we have to put in a new cylinder, and we have none of precisely the proper size, but we have them both a mere trifle too large and too small, and the question is which to use. Our advice is to use the smaller one if it does not require the escape-wheel teeth to be "dressed," that is, made smaller. Why we make this choice is based on the fact that the smaller cylinder shell gives less friction, and the loss from "drop"--that is, side play between the escape-wheel teeth and the cylinder--will be the same in both instances except to change the lost motion from inside to outside drop. In devising a system to be applied to selecting a new cylinder, we meet the same troubles encountered throughout all watchmakers' repair work, and chief among these are good and convenient measuring tools. But even with perfect measuring tools we would have to exercise good judgment, as just explained. In Chapter II we gave a rule for determining the outside diameter of a cylinder from the diameter of the escape wheel; but such rules and tables will, in nine instances out of ten, have to be modified by attendant circumstances--as, for instance, the thickness of the shell of the cylinder, which should be one-tenth of the outer diameter of the shell, but the shell is usually thicker. A tolerably safe practical rule and one also depending very much on the workman's good judgment is, when the escape-wheel teeth have been shortened, to select a cylinder giving ample clearance inside the shell to the tooth, but by no means large enough to fill the space between the teeth. After studying carefully the instructions just given we think the workman will have no difficulty in selecting a cylinder of the right diameter. MEASURING THE HEIGHTS. The next thing is to get the proper heights. This is much more easily arrived at: the main measurement being to have the teeth of the escape wheel clear the upper face of the lower plug. In order to talk intelligently we will make a drawing of a cylinder and agree on the proper names for the several parts to be used in this chapter. Such drawing is shown at Fig. 171. The names are: The hollow cylinder, made up of the parts _A A' A'' A'''_, called the shell--_A_ is the great shell, _A'_ the half shell, _A''_ the banking slot, and _A'''_ the small shell. The brass part _D_ is called the collet and consists of three parts--the hairspring seat _D_, the balance seat _D'_ and the shoulder _D''_, against which the balance is riveted. [Illustration: Fig. 171] The first measurement for fitting a new cylinder is to determine the height of the lower plug face, which corresponds to the line _x x_, Fig. 171. The height of this face is such as to permit the escape wheel to pass freely over it. In selecting a new cylinder it is well to choose one which is as wide at the banking slot _A''_ as is consistent with safety. The width of the banking slot is represented by the dotted lines _x u_. The dotted line _v_ represents the length to which the lower pivot _y_ is to be cut. [Illustration: Fig. 172] [Illustration: Fig. 173] There are several little tools on the market used for making the necessary measurements, but we will describe a very simple one which can readily be made. To do so, take about a No. 5 sewing needle and, after annealing, cut a screw thread on it, as shown at Fig, 172, where _E_ represents the needle and _t t_ the screw cut upon it. After the screw is cut, the needle is again hardened and tempered to a spring temper and a long, thin pivot turned upon it. The needle is now shaped as shown at Fig. 173. The pivot at _s_ should be small enough to go easily through the smallest hole jewel to be found in cylinder watches, and should be about 1/16" long. The part at _r_ should be about 3/16" long and only reduced in size enough to fully remove the screw threads shown at _t_. [Illustration: Fig. 174] [Illustration: Fig. 175] [Illustration: Fig. 176] [Illustration: Fig. 177] We next provide a sleeve or guard for our gage. To do this we take a piece of hard brass bushing wire about ½" long and, placing it in a wire chuck, center and drill it nearly the entire length, leaving, say, 1/10" at one end to be carried through with a small drill. We show at _F_, Fig. 174, a magnified longitudinal section of such a sleeve. The piece _F_ is drilled from the end _l_ up to the line _q_ with a drill of such a size that a female screw can be cut in it to fit the screw on the needle, and _F_ is tapped out to fit such a screw from _l_ up to the dotted line _p_. The sleeve _F_ is run on the screw _t_ and now appears as shown at Fig. 175, with the addition of a handle shown at _G G'_. It is evident that we can allow the pivot _s_ to protrude from the sleeve _F_ any portion of its length, and regulate such protrusion by the screw _t_. To employ this tool for getting the proper length to which to cut the pivot _y_, Fig. 171, we remove the lower cap jewel to the cylinder pivot and, holding, the movement in the left hand, pass the pivot _s_, Fig. 175, up through the hole jewel, regulate the length by turning the sleeve _F_ until the arm of the escape wheel _I_, Fig. 176, will just turn free over it. Now the length of the pivot _s_, which protrudes beyond the sleeve _F_, coincides with the length to which we must cut the pivot _y_, Fig. 171. To hold a cylinder for reducing the length of the pivot _y_, we hold said pivot in a pair of thin-edged cutting pliers, as shown at Fig. 177, where _N N'_ represent the jaws of a pair of cutting pliers and _y_ the pivot to be cut. The measurement is made by putting the pivot _s_ between the jaws _N N'_ as they hold the pivot. The cutting is done by simply filing back the pivot until of the right length. TURNING THE PIVOTS. We have now the pivot _y_ of the proper length, and what remains to be done is to turn it to the right size. We do not think it advisable to try to use a split chuck, although we have seen workmen drive the shell _A A'''_ out of the collet _D_ and then turn up the pivots _y z_ in said wire chuck. To our judgment there is but one chuck for turning pivots, and this is the cement chuck provided with all American lathes. Many workmen object to a cement chuck, but we think no man should lay claim to the name of watchmaker until he masters the mystery of the cement chuck. It is not such a very difficult matter, and the skill once acquired would not be parted with cheaply. One thing has served to put the wax or cement chuck into disfavor, and that is the abominable stuff sold by some material houses for lathe cement. The original cement, made and patented by James Bottum for his cement chuck, was made up of a rather complicated mixture; but all the substances really demanded in such cement are ultramarine blue and a good quality of shellac. These ingredients are compounded in the proportion of 8 parts of shellac and 1 part of ultramarine--all by weight. HOW TO USE A CEMENT CHUCK. The shellac is melted in an iron vessel, and the ultramarine added and stirred to incorporate the parts. Care should be observed not to burn the shellac. While warm, the melted mass is poured on to a cold slab of iron or stone, and while plastic made into sticks about ½" in diameter. [Illustration: Fig. 178] [Illustration: Fig. 179] We show at Fig. 178 a side view of the outer end of a cement chuck with a cylinder in position. We commence to turn the lower pivot of a cylinder, allowing the pivot _z_ to rest at the apex of the hollow cone _a_, as shown. There is something of a trick in turning such a hollow cone and leaving no "tit" or protuberance in the center, but it is important it should be done. A little practice will soon enable one to master the job. A graver for this purpose should be cut to rather an oblique point, as shown at _L_, Fig. 179. The slope of the sides to the recess _a_, Fig. 178, should be to about forty-five degrees, making the angle at _a_ about ninety degrees. The only way to insure perfect accuracy of centering of a cylinder in a cement chuck is center by the shell, which is done by cutting a piece of pegwood to a wedge shape and letting it rest on the T-rest; then hold the edge of the pegwood to the cylinder as the lathe revolves and the cement soft and plastic. A cylinder so centered will be absolutely true. The outline curve at _c_, Fig. 178, represents the surface of the cement. The next operation is turning the pivot to the proper size to fit the jewel. This is usually done by trial, that is, trying the pivot into the hole in the jewel. A quicker way is to gage the hole jewel and then turn the pivot to the right size, as measured by micrometer calipers. In some cylinder watches the end stone stands at some distance from the outer surface of the hole jewel; consequently, if the measurement for the length of the pivot is taken by the tool shown at Fig. 175, the pivot will apparently be too short. When the lower end stone is removed we should take note if any allowance is to be made for such extra space. The trouble which would ensue from not providing for such extra end shake would be that the lower edge of the half shell, shown at _e_, Fig. 171, would strike the projection on which the "stalk" of the tooth is planted. After the lower pivot is turned to fit the jewel the cylinder is to be removed from the cement chuck and the upper part turned. The measurements to be looked to now are, first, the entire length of the cylinder, which is understood to be the entire distance between the inner faces of the two end stones, and corresponds to the distance between the lines _v d_, Fig. 171. This measurement can be got by removing both end stones and taking the distance with a Boley gage or a douzieme caliper. A CONVENIENT TOOL FOR LENGTH MEASUREMENT. [Illustration: Fig. 180] A pair of common pinion calipers slightly modified makes as good a pair of calipers for length measurement as one can desire. This instrument is made by inserting a small screw in one of the blades--the head on the inner side, as shown at _f_, Fig. 180. The idea of the tool is, the screw head _f_ rests in the sink of the cap jewel or end stone, while the other blade rests on the cock over the balance. After the adjusting screw to the caliper is set, the spring of the blades allows of their removal. The top pivot _z_ of the cylinder is next cut to the proper length, as indicated by the space between the screwhead _f_ and the other blade of the pinion caliper. The upper pinion _z_ is held in the jaws of the cutting pliers, as shown in Fig. 177, the same as the lower one was held, until the proper length between the lines _d v_, Fig. 171, is secured, after which the cylinder is put back into the cement chuck, as shown at Fig. 178, except this time the top portion of the cylinder is allowed to protrude so that we can turn the top pivot and the balance collet _D_, Fig. 171. The sizes we have now to look to is to fit the pivot _z_ to the top hole jewel in the cock, also the hairspring seat _D_ and balance seat _D'_. These are turned to diameters, and are the most readily secured by the use of the micrometer calipers to be had of any large watchmakers' tool and supply house. In addition to the diameters named, we must get the proper height for the balance, which is represented by the dotted line _b_. The measurement for this can usually be obtained from the old cylinder by simply comparing it with the new one as it rests in the cement chuck. The true tool for such measurements is a height gage. We have made no mention of finishing and polishing the pivots, as these points are generally well understood by the trade. REMOVING THE LATHE CEMENT. One point perhaps we might well say a few words on, and this is in regard to removing the lathe cement. Such cement is usually removed by boiling in a copper dish with alcohol. But there are several objections to the practice. In the first place, it wastes a good deal of alcohol, and also leaves the work stained. We can accomplish this operation quicker, and save alcohol, by putting the cylinder with the wax on it in a very small homeopathic bottle and corking it tight. The bottle is then boiled in water, and in a few seconds the shellac is dissolved away. The balance to most cylinder watches is of red brass, and in some instances of low karat gold; in either case the balance should be repolished. To do this dip in a strong solution of cyanide of potassium dissolved in water; one-fourth ounce of cyanide in half pint of water is about the proper strength. Dip and rinse, then polish with a chamois buff and rouge. [Illustration: Fig. 181] In staking on the balance, care should be observed to set the banking pin in the rim so it will come right; this is usually secured by setting said pin so it stands opposite to the opening in the half shell. The seat of the balance on the collet _D_ should be undercut so that there is only an edge to rivet down on the balance. This will be better understood by inspecting Fig. 181, where we show a vertical section of the collet _D_ and cylinder _A_. At _g g_ is shown the undercut edge of the balance seat, which is folded over as the balance is rivetted fast. About all that remains now to be done is to true up the balance and bring it to poise. The practice frequently adopted to poise a plain balance is to file it with a half-round file on the inside, in order not to show any detraction when looking at the outer edge of the rim. A better and quicker plan is to place the balance in a split chuck, and with a diamond or round-pointed tool scoop out a little piece of metal as the balance revolves. In doing this, the spindle of the lathe is turned by the hand grasping the pulley between the finger and thumb. The so-called diamond and round-pointed tools are shown at _o o'_, Fig. 182. The idea of this plan of reducing the weight of a balance is, one of the tools _o_ is rested on the T-rest and pressed forward until a chip is started and allowed to enter until sufficient metal is engaged, then, by swinging down on the handle of the tool, the chip is taken out. [Illustration: Fig. 182] [Illustration: Fig. 183] In placing a balance in a step chuck, the banking pin is caused to enter one of the three slots in the chuck, so as not to be bent down on to the rim of the balance. It is seldom the depth between the cylinder and escape wheel will need be changed after putting in a new cylinder; if such is the case, however, move the chariot--we mean the cock attached to the lower plate. Do not attempt to change the depth by manipulating the balance cock. Fig. 183 shows, at _h h_, the form of chip taken out by the tool _o o'_, Fig. 182. INDEX A Acid frosting, 46 "Action" drawings, 90 Action of a chronometer escapement, 142 Acting surface of entrance lip, 127 Actions of cylinder escapement, 112 Adhesion of parallel surfaces, 94 Adjustable pallets, 98 Adjusting screw for drawing instruments, 21 Analysis of principles involved in detent, 137 Analysis of the action of a lever escapement, 86 Angle-measuring device, 68 Angular extent of shell of cylinder, 122 Angular motion, drawing an escapement to show, 91 How measured, 69 Of escape wheel, 37 Antagonistic influences, 133 Arc of degrees, 9 Atmospheric disturbances, 74 Attainment of isochronism, 159 B Balance, how it controls timekeeping, 73 Weight and inertia of, 133 Balance spring, inventor of, 132 Banking slot of cylinder, 112 Bankings, effect of opening too wide, 63 Bar compasses, 21 Barometric pressure, 74 Basis for close measurements, 96 C Cement chuck, how to use, 173 Chronometer detent, importance of light construction, 136 Chronometer escapement, 131, 155 Four principal parts of, 134 Circular pallets, 27 Club-tooth escapement, 30, 34 Club-tooth lever escapement with circular pallets and tangential lockings, 83 Crown-wheel escapement, 155 Cylinder, drawing a, 120 Outer diameter of, 116 Putting in a new, 169 Cylinder escapement, 155 Date of invention, etc., 111 Forms and proportions of several parts of, 111 Names of various parts, 112 Cylinder lips, proper shape of, 124 D Dead-beat escapement, 131, 135 Only one true, 112 Depth, between cylinder and escape wheel, 129 Effect of changing, 176 Designing a double roller, 77 Detached escapement, 155 Detent, functions of the, 137 Detent escapement, 131, 155 Faults in, 132 Detent spring dimensions, 138 Detent springs, width of, 147 Discharging jewel, setting the, 142 Discharging roller, 136 Dividers, 9 Making, 10 Double pendulum, 160 Double-roller escapement, 75 Draw defined, 85 Drawing-board, 11 Drawing instruments, 9 Drawings, advantage of large, 29 Drop and draw, 150 Duplex escapement, 131, 155 E Elasticity of spring, 133 Engaging friction, 81 English recoil anchor, 167 Entrance lip of cylinder escapement, 125 Escapement angles, measuring, 101 Escapement error, study of, 64 Escapement matching tool, 106 Escapement model, 40 Balance, 42 Balance staff, 44 Bridges, 41, 42 Escape wheel, 43 Extra balance cock, 45 "Frosting", 46 Hairspring, 42 Jewel for, 43 Lower plate, 41 Main plate, 41 Movement for, 41 Pallet staff, 42 Pillars, 43 Regulator, 46 Uses of, 44 Wood base for, 41 Escapements compared, 103 Escapement of Dutertre, 160 Escape-wheel action, 30 Escape-wheel, delineating an, 11 Escape-wheel teeth vs. cylinder, 169 Escape-wheel tooth in action, delineating an, 126 Exit pallet, 26 Experiments of Galileo, 158 Experiments with a chronometer, 142 Extent of angular impulse, 118 F "Fall" defined, 106 Faults in the detent escapement, 132 Fixed rules, of little value to student, 137 Flexure of gold spring, 146 Foot, fitting up the, 151 Fork, testing the, 71 Fork action, 30 Theory of, 59 Fork and roller action, 54 Formulas for delineating cylinder escapement, 115 Frictions, 24 Frictional escapement, 131, 132 Frictional surfaces, 63 Fusee, 131 G Gable escapement, 167 Gage, a new, 172 Graham anchor escapement, 155 Gold spring, 146 Guard point, 79 Material for, 79 Gummy secretion on impulse and discharging stones, 147 H Heights in cylinders, how obtained, 171 Hole jewels, distance apart, 140 I Imaginary faults in cylinders, 129 Impulse angle, 118 Impulse arc, extent of, 134 Impulse jewel set oblique, 147 Impulse planes, locating outer angle of, 39 Impulse roller, 136 Incline of teeth, 122 Inertia of balance, 133 Inventions of Berthoud, 163 Béthune, 165 Clement, 166 Dr. Hook, 162 Harrison, 161 Hautefeuille, 161 Huygens, 158 Leroy, 163 Thiout, 165 J Jewel pin, determining size, 58 Cementing in, 67 Settings, 66 Jewel-pin setters, 67 L Lathe cement, 173 Removing, 175 Lever, proper length of, 61 Lever fork, horn of, 61 prongs of, 60 Lift, real and apparent, 112 Lifting angle, 114 Lock, amount of, 28 Defined, 85 Lock and drop testing, 69 Locking jewel, moving the, 149 Locking stone, good form of, 144 Lower plate, circular opening in, 56 M Marine chronometer, number of beats to hour, 148 Mathematics, 95 Measuring tools, 171 Metal drawings, advantages of, 140 Motion, how obtained, 16 Movement holder, 110 N Neutral lockings, 84 O Original designing, 148 P Pallet action, locating the, 90 Pallet-and-fork action, 12, 13, 17, 18 Pallet stones, how to set, 104 Pallets, adjusting to match the fork, 65 Paper for drawing, 11 Parts, relations of the, 32 Passing hollow, 62 Perfected lever escapement, 87 Pivots, turning, 172 Point of percussion, 139 Points for drawing instruments, 20 Polishing materials, 52 Power leaks, 16 Power lost in lever escapement, 87 Practical problems in the lever escapement, 98 R Radial extent of outside of cylinder, 125 Ratchet-tooth escape wheel, 12 Recoil anchor escapement, 155 Recoil escapement, 154 Reduced gable escapement, 167 Retrograde motion, 36 Roller action, why 30 degrees, 55 Of double roller, 78 Roller diameter, determining the, 55 Ruling pen, 9 S Safety action, 56 Scale of inches, 9 Screws, making extra large, 45 Screwheads, fancy, 45 Selecting new cylinder, 170 Shaping, advantages gained in, 116 Sheet steel, cutting, 48 Short fork, 100 Sound as indicator of correct action, 144 Spring, elasticity of, 133 Staking on a balance, 175 Steel, polishing, 49 Tempering, 49 Study drawings, 124 Systems of measurements, 114 T Tangential lockings, 80, 148 Test gage for angular movement, 65 Theoretical action of double roller, 76 Timekeeping, controlled by balance, 73 Tool for length measurement, 174 Tools, measuring, 171 Triangle, 18 T-square, 9 U Unlocking action, 56 Unlocking roller, 136 V Verge escapement, 131, 155 W Weight and inertia of balance, 133 Working model of cylinder escapement, 123 * * * * * * THE WATCH ADJUSTER'S MANUAL [Illustration] A Complete and Practical Guide for Watchmakers in Adjusting Watches and Chronometers for Isochronism, Position, Heat and Cold. BY CHARLES EDGAR FRITTS (EXCELSIOR), Author of "Practical Hints on Watch Repairing," "Practical Treatise on Balance Spring," "Electricity and Magnetism for Watchmakers," etc., etc. This well-known work is now recognized as the standard authority on the adjustments and kindred subjects, both here and in England. It contains an exhaustive consideration of the various theories proposed, the mechanical principles on which the adjustments are based, and the different methods followed in actual practice, giving all that is publicly known in the trade, with a large amount of entirely new practical matter not to be found elsewhere, obtained from the best manufacturers and workmen, as well as from the author's own studies and experiences. Sent postpaid to any part of the world on receipt of $2.50 (10s. 5d.) THE KEYSTONE (SOLE AGENT), 19TH AND BROWN STREETS, PHILADELPHIA, U.S.A. * * * * * THE ART OF ENGRAVING [Illustration] A Complete Treatise on the Engraver's Art, with Special Reference to Letter and Monogram Engraving. Specially Compiled as a Standard Text-Book for Students and a Reliable Reference Book for Engravers. This work is the only thoroughly reliable and exhaustive treatise published on this important subject. It is an ideal text-book, beginning with the rudiments and leading the student step by step to a complete and practical mastery of the art. Back of the authorship is a long experience as a successful engraver, also a successful career as an instructor in engraving. These qualifications ensure accuracy and reliability of matter, and such a course of instruction as is best for the learner and qualified engraver. The most notable feature of the new treatise is the instructive character of the illustrations. There are over 200 original illustrations by the author. A very complete index facilitates reference to any required topic. Bound in Silk Cloth--208 Pages and 216 Illustrations. Sent postpaid to any part of the world on receipt of price, $1.50 (6s. 3d.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH & BROWN STS., PHILADELPHIA, U.S.A. * * * * * THE KEYSTONE PORTFOLIO OF MONOGRAMS [Illustration: C.B.R.] [Illustration: A.O.U.W] [Illustration: I.R.C.] [Illustration: G.H.I.] This portfolio contains 121 combination designs. These designs were selected from the best of those submitted in a prize competition held by The Keystone, and will be found of value to every one doing engraving. The designs are conceded to be the best in the market, excelling in art and novelty of combination and skill in execution. They are printed from steel plates on stiff, durable paper, and contain sample monograms in a variety of combinations. The portfolio is a bench requirement that no jeweler can afford to be without. It is a necessary supplement to any text-book on letter engraving. Price, 50 Cents (2s.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH & BROWN STS., PHILADELPHIA, U.S.A. * * * * * THE OPTICIAN'S MANUAL VOL. I. BY C.H. BROWN, M.D. Graduate University of Pennsylvania; Professor of Optics and Refraction; formerly Physician in Philadelphia Hospital; Member of Philadelphia County, Pennsylvania State and American Medical Societies. [Illustration] The Optician's Manual, Vol. I., has proved to be the most popular work on practical refraction ever published. The knowledge it contains has been more effective in building up the optical profession than any other educational factor. A study of it is essential to an intelligent appreciation of Vol. II., for it lays the foundation structure of all optical knowledge, as the titles of its ten chapters show: Chapter I.--Introductory Remarks. Chapter II.--The Eye Anatomically. Chapter III.--The Eye Optically; or, The Physiology of Vision. Chapter IV.--Optics. Chapter V.--Lenses. Chapter VI.--Numbering of Lenses. Chapter VII.--The Use and Value of Glasses. Chapter VIII.--Outfit Required. Chapter IX.--Method of Examination. Chapter X.--Presbyopia. The Optician's Manual, Vol. I., is complete in itself, and has been the entire optical education of many successful opticians. For student and teacher it is the best treatise of its kind, being simple in style, accurate in statement and comprehensive in its treatment of refractive procedure and problems. It merits the place of honor beside Vol. II. in every optical library. Bound in Cloth--422 pages--colored plates and Illustrations. Sent postpaid on receipt of $2.00 (8s. 4d.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH & BROWN STS., PHILADELPHIA, U.S.A. * * * * * THE OPTICIAN'S MANUAL VOL. II. BY C.H. BROWN, M.D. Graduate University of Pennsylvania; Professor of Optics and Refraction; formerly Physician in Philadelphia Hospital; Member of Philadelphia County, Pennsylvania State and American Medical Societies. [Illustration] The Optician's Manual, Vol. II., is a direct continuation of The Optician's Manual, Vol. I., being a much more advanced and comprehensive treatise. It covers in minutest detail the four great subdivisions of practical eye refraction, viz: Myopia. Hypermetropia. Astigmatism. Muscular Anomalies. It contains the most authoritative and complete researches up to date on these subjects, treated by the master hand of an eminent oculist and optical teacher. It is thoroughly practical, explicit in statement and accurate as to fact. All refractive errors and complications are clearly explained, and the methods of correction thoroughly elucidated. This book fills the last great want in higher refractive optics, and the knowledge contained in it marks the standard of professionalism. Bound in Cloth--408 pages--with illustrations. Sent postpaid on receipt of $2.00 (8s. 4d.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH & BROWN STS., PHILADELPHIA, U.S.A. * * * * * SKIASCOPY AND THE USE OF THE RETINOSCOPE [Illustration] A Treatise on the Shadow Test in its Practical Application to the Work of Refraction, with an Explanation in Detail of the Optical Principles on which the Science is Based. This new work, the sale of which has already necessitated a second edition, far excels all previous treatises on the subject in comprehensiveness and practical value to the refractionist. It not only explains the test, but expounds fully and explicitly the principles underlying it--not only the phenomena revealed by the test, but the why and wherefore of such phenomena. It contains a full description of skiascopic apparatus, including the latest and most approved instruments. In depth of research, wealth of illustration and scientific completeness this work is unique. Bound in cloth; contains 231 pages and 73 illustrations and colored plates. Sent postpaid to any part of the world on receipt of $1.00 (4s. 2d.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH AND BROWN STS., PHILADELPHIA, U.S.A. * * * * * PHYSIOLOGIC OPTICS Ocular Dioptrics--Functions of the Retina--Ocular Movements and Binocular Vision BY DR. M. TSCHERNING Adjunct-Director of the Laboratory of Ophthalmology at the Sorbonne, Paris AUTHORIZED TRANSLATION BY CARL WEILAND, M.D. Former Chief of Clinic in the Eye Department of the Jefferson College Hospital, Philadelphia, Pa. This is the crowning work on physiologic optics, and will mark a new era in optical study. Its distinguished author is recognized in the world of science as the greatest living authority on this subject, and his book embodies not only his own researches, but those of the several hundred investigators who, in the past hundred years, made the eye their specialty and life study. Tscherning has sifted the gold of all optical research from the dross, and his book, as now published in English with many additions, is the most valuable mine of reliable optical knowledge within reach of ophthalmologists. It contains 380 pages and 212 illustrations, and its reference list comprises the entire galaxy of scientists who have made the century famous in the world of optics. The chapters on Ophthalmometry, Ophthalmoscopy, Accommodation, Astigmatism, Aberration and Entoptic Phenomena, etc.--in fact, the entire book contains so much that is new, practical and necessary that no refractionist can afford to be without it. Bound in Cloth. 380 Pages, 212 Illustrations. Price, $3.50 (14s. 7d.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH & BROWN STS., PHILADELPHIA, U.S.A. * * * * * OPHTHALMIC LENSES Dioptric Formulę for Combined Cylindrical Lenses, The Prism-Dioptry and Other Original Papers BY CHARLES F. PRENTICE, M.E. A new and revised edition of all the original papers of this noted author, combined in one volume. In this revised form, with the addition of recent research, these standard papers are of increased value. Combined for the first time in one volume, they are the greatest compilation on the subject of lenses extant. This book of over 200 pages contains the following papers: Ophthalmic Lenses. Dioptric Formulę for Combined Cylindrical Lenses. The Prism-Dioptry. A Metric System of Numbering and Measuring Prisms. The Relation of the Prism-Dioptry to the Meter Angle. The Relation of the Prism-Dioptry to the Lens-Dioptry. The Perfected Prismometer. The Prismometric Scale. On the Practical Execution of Ophthalmic Prescriptions involving Prisms. A Problem in Cemented Bi-Focal Lenses, Solved by the Prism-Dioptry. Why Strong Contra-Generic Lenses of Equal Power Fail to Neutralize Each Other. The Advantages of the Sphero-Toric Lens. The Iris, as Diaphragm and Photostat. The Typoscope. The Correction of Depleted Dynamic Refraction (Presbyopia). _Press Notices on the Original Edition:_ OPHTHALMIC LENSES. "The work stands alone, in its present form, a compendium of the various laws of physics relative to this subject that are so difficult of access in scattered treatises."--_New England Medical Gazette._ "It is the most complete and best illustrated book on this special subject ever published."--_Horological Review_, New York. "Of all the simple treatises on the properties of lenses that we have seen, this is incomparably the best.... The teacher of the average medical student will hail this little work as a great boon."--_Archives of Ophthalmology, edited by H. Knapp, M.D._ DIOPTRIC FORMULĘ FOR COMBINED CYLINDRICAL LENSES. "This little brochure solves the problem of combined cylinders in all its aspects, and in a manner simple enough for the comprehension of the average student of ophthalmology. The author is to be congratulated upon the success that has crowned his labors, for nowhere is there to be found so simple and yet so complete an explanation as is contained in these pages."--_Archives of Ophthalmology, edited by H. Knapp, M.D._ "This exhaustive work of Mr. Prentice is a solution of one of the most difficult problems in ophthalmological optics. Thanks are due to Mr. Prentice for the excellent manner in which he has elucidated a subject which has not hitherto been satisfactorily explained."--_The Ophthalmic Review_, London. The book contains 110 Original Diagrams. Bound in cloth. Price, $1.50 (6s. 3d.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH & BROWN STS., PHILADELPHIA, U.S.A. * * * * * OPTOMETRIC RECORD BOOK A record book, wherein to record optometric examinations, is an indispensable adjunct of an optician's outfit. The Keystone Optometric Record Book was specially prepared for this purpose. It excels all others in being not only a record book, but an invaluable guide in examination. The book contains two hundred record forms with printed headings, suggesting, in the proper order, the course of examination that should be pursued to obtain most accurate results. Each book has an index, which enables the optician to refer instantly to the case of any particular patient. The Keystone Record Book diminishes the time and labor required for examinations, obviates possible oversights from carelessness and assures a systematic and thorough examination of the eye, as well as furnishes a permanent record of all examinations. Sent postpaid on receipt of $1.00 (4s. 2d.) PUBLISHED BY THE KEYSTONE, THE ORGAN OF THE JEWELRY AND OPTICAL TRADES, 19TH & BROWN STS., PHILADELPHIA, U.S.A. * * * * * THE KEYSTONE BOOK OF MONOGRAMS This book contains 2400 designs and over 6000 different combinations of two and three letters. Is an essential to every jeweler's outfit. It is not only necessary for the jeweler's own use and guidance, but also to enable customers to indicate exactly what they want, thus saving time and possible dissatisfaction. The Monograms are purposely left in outline, in order to show clearly how the letters are intertwined or woven together. This permits such enlargement or reduction of the Monogram as may be desired, and as much shading, ornamentation and artistic finish as the jeweler may wish to add. This comprehensive compilation of Monograms is especially available as a reference book in busy seasons. Its use saves time, thought and labor, and ensures quick and satisfactory work. 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