[Illustration: THOMAS MUDGE _The first Horologist who successfully applied the Detached LeverEscapement to Watches. _ _Born 1715--Died 1794. _] AN ANALYSIS OF THE LEVER ESCAPEMENT BY H.  R. PLAYTNER. A LECTURE DELIVERED BEFORE THE CANADIAN WATCHMAKERS' AND RETAILJEWELERS' ASSOCIATION. ILLUSTRATED. CHICAGO: HAZLITT & WALKER, PUBLISHERS. 1910. PREFACE. Before entering upon our subject proper, we think it advisable toexplain a few points, simple though they are, which might causeconfusion to some readers. Our experience has shown us that as soon aswe use the words "millimeter" and "degree, " perplexity is the result. "What is a millimeter?" is propounded to us very often in the course ofa year; nearly every new acquaintance is interested in having the metricsystem of measurement, together with the fine gauges used, explained tohim. The metric system of measurement originated at the time of the FrenchRevolution, in the latter part of the 18th century; its divisions aredecimal, just the same as the system of currency we use in this country. A meter is the ten millionth part of an arc of the meridian of Paris, drawn from the equator to the north pole; as compared with the Englishinch there are 39+3708/10000 inches in a meter, and there are25. 4 millimeters in an inch. The meter is sub-divided into decimeters, centimeters and millimeters;1, 000 millimeters equal one meter; the millimeter is again divided into10ths and the 10ths into 100ths of a millimeter, which could becontinued indefinitely. The 1/100 millimeter is equal to the 1/2540 ofan inch. These are measurements with which the watchmaker is concerned. 1/100 millimeter, written . 01 mm. , is the side shake for a balancepivot; multiply it by 2¼ and we obtain the thickness for the springdetent of a pocket chronometer, which is about ⅓ the thickness of ahuman hair. The metric system of measurement is used in all the watch factories ofSwitzerland, France, Germany, and the United States, and nearly all thelathe makers number their chucks by it, and some of them cut the leadingscrews on their slide rests to it. In any modern work on horology of value, the metric system is used. Skilled horologists use it on account of its _convenience_. Themillimeter is a unit which can be handled on the small parts of a watch, whereas the inch must always be divided on anything smaller than theplates. Equally as fine gauges can be and are made for the inch as for themetric system, and the inch is decimally divided, but we require anotherdecimal point to express our measurement. Metric gauges can now be procured from the material shops; they consistof tenth measures, verniers and micrometers; the finer ones of thesecome from Glashutte, and are the ones mentioned by Grossmann in hisessay on the lever escapement. Any workman who has once used theseinstruments could not be persuaded to do without them. No one can comprehend the geometrical principles employed in escapementswithout a knowledge of angles and their measurements, therefore we deemit of sufficient importance to at least explain what a degree is, as weknow for a fact, that young workmen especially, often fail to see how toapply it. Every circle, no matter how large or small it may be, contains 360°; adegree is therefore the 360th part of a circle; it is divided intominutes, seconds, thirds, etc. To measure the _value_ of a degree of any circle, we must multiply thediameter of it by 3. 1416, which gives us the circumference, and thendivide it by 360. It will be seen that it depends on the size of thatcircle or its radius, as to the value of a degree in any _actual_measurement. To illustrate; a degree on the earth's circumferencemeasures 60 geographical miles, while measured on the circumference ofan escape wheel 7. 5 mm. In diameter, or as they would designate it in amaterial shop, No.  7½, it would be 7. 5 × 3. 1416 ÷ 360 = . 0655 mm. , whichis equal to the breadth of an ordinary human hair; it is a degree inboth cases, but the difference is very great, therefore a degree cannotbe associated with any actual measurement until the radius of thecircle is known. Degrees are generated from the center of the circle, and should be thought of as to ascension or direction and relativevalue. Circles contain four right angles of 90° each. Degrees arecommonly measured by means of the protractor, although the ordinaryinstruments of this kind leave very much to be desired. The lines can beverified by means of the compass, which is a good practical method. It may also be well to give an explanation of some of the terms used. _Drop_ equals the amount of freedom which is allowed for the action ofpallets and wheel. See Z, Fig.  1. _Primitive or Geometrical Diameter. _--In the ratchet tooth or Englishwheel, the primitive and real diameter are equal; in the club toothwheel it means across the locking corners of the teeth; in such a wheel, therefore, the primitive is _less_ than the real diameter by the heightof two impulse planes. _Lock_ equals the depth of locking, measured from the locking corner ofthe pallet at the moment the drop has occurred. _Run_ equals the amount of angular motion of pallets and fork to thebankings _after_ the drop has taken place. _Total Lock_ equals lock plus run. A _Tangent_ is a line which _touches_ a curve, but does not intersectit. AC and AD, Figs. 2 and 3, are tangents to the primitive circle GH atthe points of intersection of EB, AC, and GH and FB, AD and GH. _Impulse Angle_ equals the angular connection of the impulse or ruby pinwith the lever fork; or in other words, of the balance with theescapement. _Impulse Radius. _--From the face of the impulse jewel to the center ofmotion, which is in the balance staff, most writers assume the impulseangle and radius to be equal, and it is true that they must conform withone another. We have made a radical change in the radius and one whichdoes not affect the angle. We shall prove this in due time, and alsothat the wider the impulse pin the greater must the impulse radius be, although the angle will remain unchanged. Right here we wish to put in a word of advice to all young men, and thatis to learn to draw. No one can be a thorough watchmaker unless he candraw, because he cannot comprehend his trade unless he can do so. We know what it has done for us, and we have noticed the same resultswith others, therefore we speak from personal experience. Attend nightschools and mechanic's institutes and improve yourselves. The young workmen of Toronto have a great advantage in the TorontoTechnical School, but we are sorry to see that out of some 600 students, only five watchmakers attended last year. We can account for themajority of them, so it would seem as if the young men of the trade werenot much interested, or thought they could not apply the knowledge to begained there. This is a great mistake; we might almost say thatknowledge of any kind can be applied to horology. The young men who takeup these studies, will see the great advantage of them later on; oneworkman will labor intelligently and the other do blind "guess" work. We are now about to enter upon our subject and deem it well to say, wehave endeavored to make it as plain as possible. It is a deep subjectand is difficult to treat lightly; we will treat it in our own way, paying special attention to all these points which bothered us duringthe many years of painstaking study which we gave to the subject. Weespecially endeavor to point out how theory can be applied to practice;while we cannot expect that everyone will understand the subject withoutstudy, we think we have made it comparatively easy of comprehension. We will give our method of drafting the escapement, which happens insome respects to differ from others. We believe in making a drawingwhich we can reproduce in a watch. AN ANALYSIS OF THE LEVER ESCAPEMENT. The lever escapement is derived from Graham's dead-beat escapement forclocks. Thomas Mudge was the first horologist who successfully appliedit to watches in the detached form, about 1750. The locking faces of thepallets were arcs of circles struck from the pallet centers. Manyimprovements were made upon it until to-day it is the best form ofescapement for a general purpose watch, and when made on mechanicalprinciples is capable of producing first rate results. Our object will be to explain the whys and wherefores of thisescapement, and we will at once begin with the number of teeth in theescape wheel. It is not obligatory in the lever, as in the verge, tohave an uneven number of teeth in the wheel. While nearly all have 15teeth, we might make them of 14 or 16; occasionally we find some incomplicated watches of 12 teeth, and in old English watches, of 30, which is a clumsy arrangement, and if the pallets embrace only threeteeth in the latter, the pallet center cannot be pitched on a tangent. Although advisable from a timing standpoint that the teeth in the escapewheel should divide evenly into the number of beats made per minute in awatch with seconds hand, it is not, strictly speaking, necessary that itshould do so, as an example will show. We will take an ordinary watch, beating 300 times per minute; we will fit an escape wheel of 16 teeth;multiply this by 2, as there is a forward and then a return motion ofthe balance and consequently two beats for each tooth, making16 × 2 = 32 beats for each revolution of the escape wheel. 300 beats aremade per minute; divide this by the beats made on each revolution, andwe have the number of times in which the escape wheel revolves perminute, namely, 300 ÷ 32 = 9. 375. This number then is the proportionexisting for the teeth and pitch diameters of the 4th wheel and escapepinion. We must now find a suitable number of teeth for this wheel andpinion. Of available pinions for a watch, the only one which wouldanswer would be one of 8 leaves, as any other number would give afractional number of teeth for the 4th wheel, therefore 9. 375 × 8 = 75teeth in 4th wheel. Now as to the proof: as is well known, if wemultiply the number of teeth contained in 4th and escape wheels also by2, for the reason previously given, and divide by the leaves in theescape pinion, we get the number of beats made per minute; therefore(75 × 16 × 2)/8 = 300 beats per minute. Pallets can be made to embrace more than three teeth, but would be muchheavier and therefore the mechanical action would suffer. They can alsobe made to embrace fewer teeth, but the necessary side shake in thepivot holes would prove very detrimental to a total lifting angle of10°, which represents the angle of movement in modern watches. Some ofthe finest ones only make 8 or 9° of a movement; the smaller the anglethe greater will the effects of defective workmanship be; 10° is acommon-sense angle and gives a safe escapement capable of fine results. Theoretically, if a timepiece could be produced in which the balancewould vibrate without being connected with an escapement, we would havereached a step nearer the goal. Practice has shown this to be the propertheory to work on. Hence, the smaller the pallet and impulse angles theless will the balance and escapement be connected. The chronometer isstill more highly detached than the lever. The pallet embracing three teeth is sound and practical, and whenapplied to a 15 tooth wheel, this arrangement offers certain geometricaland mechanical advantages in its construction, which we will notice indue time. 15 teeth divide evenly into 360° leaving an interval of 24°from tooth to tooth, which is also the angle at which the locking facesof the teeth are inclined from the center, which fact will be foundconvenient when we come to cut our wheel. From locking to locking on the pallet scaping over three teeth, theangle is 60°, which is equal to 2½ spaces of the wheel. Fig.  1illustrates the lockings, spanning this arc. If the pallets embraced 4teeth, the angle would be 84°; or in case of a 16 tooth wheel scapingover three teeth, the angle would be 360 × 2. 5/16 = 56¼°. [Illustration: Fig.  1. ] Pallets may be divided into two kinds, namely: equidistant and circular. The equidistant pallet is so-called because the lockings are an equaldistance from the center; sometimes it is also called the tangentialescapement, on account of the unlocking taking place on the intersectionof tangent AC with EB, and FB with AD, the tangents, which is thevaluable feature of this form of escapement. [Illustration: Fig.  2. ] AC and AD, Fig.  2, are tangents to the primitive circle GH. ABE and ABFare angles of 30° each, together therefore forming the angle FBE of60°. The locking circle MN is struck from the pallet center A; theinterangles being equal, consequently the pallets must be equidistant. The weak point of this pallet is that the lifting is not performed sofavorably; by examining the lifting planes MO and NP, we see that thedischarging edge, O, is closer to the center, A, than the dischargingedge, P; consequently the lifting on the engaging pallet is performed ona shorter lever arm than on the disengaging pallet, also any inequalityin workmanship would prove more detrimental on the engaging than on thedisengaging pallet. The equidistant pallet requires fine workmanshipthroughout. We have purposely shown it of a width of 10°, which is thewidest we can employ in a 15 tooth wheel, and shows the defects of thisescapement more readily than if we had used a narrow pallet. A narrowerpallet is advisable, as the difference in the discharging edges will beless, and the lifting arms would, therefore, not show so much differencein leverage. [Illustration: Fig.  3. ] The circular pallet is sometimes appropriately called "the pallet withequal lifts, " as the lever arms AMO and ANP, Fig.  3, are equal lengths. It will be noticed by examining the diagram, that the pallets arebisected by the 30° lines EB and FB, one-half their width being placedon each side of these lines. In this pallet we have two locking circles, MP for the engaging pallet, and NO for the disengaging pallet. The weakpoints in this escapement are that the unlocking resistance is greateron the engaging than on the disengaging pallet, and that neither of themlock on the tangents AC and AD, at the points of intersection with EBand FB. The narrower the circular pallet is made, the nearer to thetangent will the unlocking be performed. In neither the equidistant orcircular pallets can the unlocking resistance be _exactly_ the same oneach pallet, as in the engaging pallet the friction takes place beforeAB, the line of centers, which is more severe than when this line hasbeen passed, as is the case with the disengaging pallet; this factproportionately increases the existing defects of the circular over theequidistant pallet, and _vice versa_, but for the same reason, thelifting in the equidistant is proportionately accompanied by morefriction than in the circular. Both equidistant and circular pallets have their adherents; the finestSwiss, French and German watches are made with equidistant escapements, while the majority of English and American watches contain the circular. In our opinion the English are wise in adhering to the circular form. Wethink a ratchet wheel should not be employed with equidistant pallets. By examining Fig.  2, we see an English pallet of this form. We haveshown its defects in such a wide pallet as the English (as we havebefore stated), because they are more readily perceived; also, onaccount of the shape of the teeth, there is danger of the dischargingedge, P, dipping so deep into the wheel, as to make considerable dropnecessary, or the pallets would touch on the backs of the teeth. In thecase of the club tooth, the latter is hollowed out, therefore, less dropis required. We have noticed that theoretically, it is advantageous tomake the pallets narrower than the English, both for the equidistant andcircular escapements. There is an escapement, Fig.  4, which is just theopposite to the English. The entire lift is performed by the wheel, while in the case of the ratchet wheel, the entire lifting angle is onthe pallets; also, the pallets being as narrow as they can be made, consistent with strength, it has the good points of both the equidistantand circular pallets, as the unlocking can be performed on the tangentand the lifting arms are of equal length. The wheel, however, is so muchheavier as to considerably increase the inertia; also, we have a metalsurface of quite an extent sliding over a thin jewel. For practicalreasons, therefore, it has been slightly altered in form and is onlyused in cheap work, being easily made. [Illustration: Fig.  4. ] We will now consider the drop, which is a clear loss of power, and, ifexcessive, is the cause of much irregularity. It should be as small aspossible consistent with perfect freedom of action. In so far as _angular_ measurements are concerned, no hard and fast rulecan be applied to it, the larger the escape wheel the smaller should bethe angle allowed for drop. Authorities on the subject allow 1½° dropfor the club and 2° for the ratchet tooth. It is a fact that escapewheels are not cut perfectly true; the teeth are apt to bend slightlyfrom the action of the cutters. The truest wheel can be made of steel, as each tooth can be successively ground after being hardened andtempered. Such a wheel would require less drop than one of any othermetal. Supposing we have a wheel with a primitive diameter of 7. 5 mm. , what is the amount of drop, allowing 1½° by angular measurement?7. 5 × 3. 1416 ÷ 360 × 1. 5 = . 0983 mm. , which is sufficient; a hair couldget between the pallet and tooth, and would not stop the watch. Evenafter allowing for imperfectly divided teeth, we require no greaterfreedom even if the wheel is larger. Now suppose we take a wheelwith a primitive diameter of 8. 5 mm. And find the amount of drop;8. 5 × 3. 1416 ÷ 360 × 1. 5 = . 1413 mm. , or . 1413 - . 0983 = . 043 mm. , more drop than the smaller wheel, if we take the same angle. This is awaste of force. The angular drop should, therefore, be proportionedaccording to the size of the wheel. We wish it to be understood thatcommon sense must always be our guide. When the horological student oncearrives at this standpoint, he can _intelligently_ apply himself to hiscalling. _The Draw. _--The draw or draft angle was added to the pallets in orderto draw the fork back against the bankings and the guard point from theroller whenever the safety action had performed its function. [Illustration: Fig.  5. ] Pallets with draw are more difficult to unlock than those without it, this is in the nature of a fault, but whenever there are two faults wemust choose the less. The rate of the watch will suffer less on accountof the recoil introduced than it would were the locking faces arcs ofcircles struck from the pallet center, in which case the guard pointwould often remain against the roller. The draw should be as light aspossible consistent with safety of action; some writers allow 15° on theengaging and 12° on the disengaging pallet; others again allow 12° oneach, which we deem sufficient. The draw is measured from the lockingedges M and N, Fig.  5. The locking planes _when locked_ are inclined 12°from EB, and FB. In the case of the engaging pallet it inclines towardthe center A. The draw is produced on account of MA being longer thanRA, consequently, when power is applied to the scape tooth S, the palletis drawn into the wheel. The disengaging pallet inclines in the samedirection but away from the center A; the reason is obvious from theformer explanation. Some people imagine that the greater the incline onthe locking edge of the escape teeth, the stronger the draw would be. This is not the case, but it is certainly necessary that the point ofthe tooth alone should touch the pallet. From this it follows that theangle on the teeth must be greater than on the pallets; examine thedisengaging pallet in Fig.  5, as it is from this pallet that theinclination of the teeth must be determined, as in the case of theengaging pallet the motion is toward the line of centers AB, andtherefore _away_ from the tooth, which partially explains why somepeople advocate 15° draw for this pallet. As illustrated in the case ofthe disengaging pallet, however, the motion is also towards the line ofcenters AB, and _towards_ the tooth as well, all of which will be seenby the dotted circles MM2 and NN2, representing the paths of thepallets. It will be noticed that UNF and BNB are opposite and equalangles of 12°. For practical reasons, from a manufacturing standpoint, the angle on the tooth is made just twice the amount, namely 24°; wecould make it a little less or a little more. If we made it less than20° too great a surface would be in contact with the jewel, involvinggreater friction in unlocking and an inefficient draw, but in the caseof an English lever with such an arrangement we could do with lessdrop, which advantage would be too dearly bought; or if the angle ismade over 28°, the point or locking edge of the tooth would rapidlybecome worn in case of a brass wheel. Also in an English lever more dropwould be required. _The Lock. _--What we have said in regard to drop also applies to thelock, which should be as small as possible, consistent with perfectsafety. The greater the drop the deeper must be the lock; 1½° is theangle generally allowed for the lock, but it is obvious that in a largeescapement it can be less. [Illustration: Fig.  6. ] _The Run. _--The run or, as it is sometimes called, "the slide, " shouldalso be as light as possible; from ¼° to ½° is sufficient. It followsthen, the bankings should be as close together as possible, consistentwith requisite freedom for escaping. Anything more than this increasesthe angular connection of the balance with the escapement, whichdirectly violates the theory under which it is constructed; also, agreater amount of work will be imposed upon the balance to meet theincreased unlocking resistance, resulting in a poor motion and accuratetime will be out of the question. It will be seen that those workmen whomake a practice of opening the banks, "to give the escapement morefreedom" simply jump from the frying pan into the fire. The bankingsshould be as far removed from the pallet center as possible, as thefurther away they are pitched the less run we require, according toangular measurement. Figure 6 illustrates this fact; the tooth S hasjust dropped on the engaging pallet, but the fork has not yet reachedthe bankings. At _a_ we have 1° of run, while if placed at _b_ we wouldonly have ½° of run, but still the same freedom for escaping, and lessunlocking resistance. The bankings should be placed towards the acting end of the fork asillustrated, as in case the watch "rebanks" there would be more strainon the lever pivots if they were placed at the other end of the fork. [Illustration: Fig.  7. ] _The Lift. _--The lift is composed of the actual lift on the teeth andpallets and the lock and run. We will suppose that from drop to drop weallow 10°; if the lock is 1½° then the actual lift by means of theinclined planes on teeth and pallets will be 8½°. We have seen that asmall lifting angle is advisable, so that the vibrations of the balancewill be as free as possible. There are other reasons as well. Fig.  7shows two inclined planes; we desire to lift the weight 2 a distanceequal to the angle at which the planes are inclined; it will be seen ata glance that we will have less friction by employing the smallerincline, whereas with the larger one the motive power is employedthrough a greater distance on the object to be moved. The smaller theangle the more energetic will the movement be; the grinding of theangles and fit of the pivots, etc. , also increases in importance. Anactual lift of 8½° satisfies the conditions imposed very well. We havebefore seen that both on account of the unlocking and the liftingleverage of the pallet arms, it would be advisable to make them narrowboth in the equidistant and circular escapement. We will now study thequestion from the standpoint of the lift, in so far as the wheel isconcerned. [Illustration: Fig.  8. ] It is self-evident that a narrow pallet requires a wide tooth, and awide pallet a narrow or thin tooth wheel; in the ratchet wheel we have ametal point passing over a jeweled plane. The friction is at itsminimum, because there is less adhesion than with the club tooth, but wemust emphasize the fact that we require a greater angle in proportion onthe pallets in this escapement than with the narrow pallets and widertooth. This seems to be a point which many do not thoroughly comprehend, and we would advise a close study of Fig.  8, which will make itperfectly clear, as we show both a wide and a narrow pallet. GH, represents the primitive, which in this figure is also the real diameterof the escape wheel. In measuring the lifting angles for the pallets, our starting point is _always_ from the tangents AC and AD. The tangentsare straight lines, but the wheel describes the circle GH, thereforethey must deviate from one another, and the closer to the center A thedischarging edge of the engaging pallet reaches, the greater does thisdifference become; and in the same manner the further the dischargingedge of the disengaging pallet is from the center A the greater it is. This shows that the loss is greater in the equidistant than in thecircular escapement. After this we will designate this difference asthe "loss. " In order to illustrate it more plainly we show the widestpallet--the English--in equidistant form. This gives another reason whythe English lever should only be made with circular pallets, as we haveseen that the wider the pallet the greater the loss. The loss ismeasured at the intersection of the path of the discharging edge OO, with the circle G H, and is shown through AC2, which intersects thesecircles at that point. In the case of the disengaging pallet, PPillustrates the path of the discharging edge; the loss is measured as inthe preceding case where GH is intersected as shown by AD2. It amountsto a different value on each pallet. Notice the loss between C and C2, on the engaging, and D and D2 on the disengaging pallet; it is greateron the engaging pallet, so much so that it amounts to 2°, which is equalto the entire lock; therefore if 8½° of work is to be accomplishedthrough this pallet, the lifting plane requires an angle of 10½° struckfrom AC. Let us now consider the lifting action of the club tooth wheel. This isdecidedly a complicated action, and requires some study to comprehend. In action with the engaging pallet the wheel moves _up_, or in thedirection of the motion of the pallets, but on the disengaging pallet itmoves _down_, and in a direction opposite to the pallets, and the heelof the tooth moves with greater velocity than the locking edge; also inthe case of the engaging pallet, the locking edge moves with greatervelocity than the discharging edge; in the disengaging pallet theopposite is the case, as the discharging edge moves with greatervelocity than the locking. These points involve factors which must beconsidered, and the drafting of a correct action is of paramountimportance; we therefore show the lift as it is accomplished in fourdifferent stages in a good action. Fig.  9 illustrates the engaging, andFig.  10 the disengaging pallet; by comparing the figures it will benoticed that the lift takes place on the point of the tooth similar tothe English, until the discharging edge of the pallet has been passed, when the heel gradually comes into play on the engaging, but morequickly on the disengaging pallet. We will also notice that during the first part of the lift the toothmoves faster along the engaging lifting plane than on the disengaging;on pallets 2 and 3 this difference is quite large; towards the latterpart of the lift the action becomes quicker on the disengaging palletand slower on the engaging. To obviate this difficulty some fine watches, notably those of A. Lange& Sons, have convex lifting planes on the engaging and concave on thedisengaging pallets; the lifting planes on the teeth are also curved. See Fig.  11. This is decidedly an ingenious arrangement, and is instrict accordance with scientific investigation. We should see many finewatches made with such escapements if the means for producing them couldfully satisfy the requirements of the scientific principles involved. [Illustration: Fig.  9. ] The distribution of the lift on tooth and pallet is a very importantmatter; the lifting angle on the tooth must be _less_ in proportion toits width than it is on the pallet. For the sake of making it perfectlyplain, we illustrate what should not be made; if we have 10½° for widthof tooth and pallet, and take half of it for a tooth, and the otherhalf for the pallet, making each of them 5¼° in width, and suppose wehave a lifting of 8½° to distribute between them, by allowing 4¼° oneach, the lift would take place as shown in Fig.  12, which is a veryunfavorable action. The edge of the engaging pallet scrapes on thelifting plane of the tooth, yet it is astonishing to find some otherwisevery fine watches being manufactured right along which contain thisfault; such watches can be stopped with the ruby pin in the fork and theengaging pallet in action, nor would they start when run down as soon asthe crown is touched, no matter how well they were finished and fitted. [Illustration: Fig.  10. ] The lever lengths of the club tooth are variable, while with the ratchetthey are constant, which is in its favor; in the latter it would alwaysbe as SB, Fig.  13. This is a shorter lever than QB, consequently morepowerful, although the greater velocity is at Q, which only comes intoaction after the inertia of wheel and pallets has been overcome, andwhen the greatest momentum during contact is reached. SB is theprimitive radius of the club tooth wheel, but both primitive and _real_radius of the ratchet wheel. The distance of centers of wheel and palletwill be alike in both cases; also the lockings will be the same distanceapart on both pallets; therefore, when horologists, even if they haveworldwide reputations, claim that the club tooth has an advantage overthe ratchet because it begins the lift with a shorter lever than thelatter, it does not make it so. We are treating the subject from apurely horological standpoint, and neither patriotism or prejudice hasanything to do with it. We wish to sift the matter thoroughly and arriveat a just conception of the merits and defects of each form ofescapement, and show _reasons_ for our conclusions. [Illustration: Fig.  11. ] [Illustration: Fig.  12. ] [Illustration: Fig.  13. ] Anyone who has closely followed our deductions must see that in so faras the wheel is concerned the ratchet or English wheel has severalpoints in its favor. Such a wheel is inseparable from a wide pallet; butwe have seen that a narrower pallet is advisable; also as little dropand lock as possible; clearly, we must effect a compromise. In otherwords, so far the balance of our reasoning is in favor of the club toothescapement and to effect an intelligent division of angles for tooth, pallet and lift is one of the great questions which confronts theintelligent horologist. Anyone who has ever taken the pains to draw pallet and tooth withdifferent angles, through every stage of the lift, with both wide andnarrow pallets and teeth, in circular and equidistant escapements, willhave received an eye-opener. We strongly advise all our readers who arepractical workmen to try it after studying what we have said. We arecertain it will repay them. [Illustration: Fig.  2. ] _The Center Distance of Wheel and Pallets. _ The direction of pressure ofthe wheel teeth should be through the pallet center by drawing thetangents AC and AD, Fig.  2 to the primitive circle GH, at theintersection of the angle FBE. This condition is realized in theequidistant pallet. In the circular pallet, Fig.  3, this conditioncannot exist, as in order _to lock_ on a tangent the center distanceshould be _greater_ for the engaging and _less_ for the disengagingpallet, therefore watchmakers aim to go between the two and plant themas before specified at A. When planted on the tangents the unlocking resistance will be less andthe impulse transmitted under favorable conditions, especially so inthe circular, as the direction of pressure coincides (close to thecenter of the lift), with the law of the parallelogram of forces. It is _impossible_ to plant pallets on the tangents in very smallescapements, as there would not be enough room for a pallet arbor ofproper strength, nor will they be found planted on the tangents in themedium size escapement with a long pallet arbor, nor in such a one witha very wide tooth (see Fig.  4) as the heel would come so close to thecenter A, that the solidity of pallets and arbor would suffer. We willgive an actual example. For a medium sized escape wheel with a primitivediameter of 7. 5 mm. , the center distance AB is 4. 33 mm. By using 3° of alifting angle on the teeth, the distance from the heel of the tooth tothe pallet center will be . 4691 mm. ; by allowing . 1 mm. Between wheeland pallet and . 15 mm. For stock on the pallets we find we will have apallet arbor as follows: . 4691 - (. 1 + . 15) × 2 = . 4382 mm. It would notbe practicable to make anything smaller. [Illustration: Fig.  3. ] It behooves us now to see that while a narrow pallet is advisable a verywide tooth is not; yet these two are inseparable. Here is another casefor a compromise, as, unquestionably the pallets ought to be planted onthe tangents. There is no difficulty about it in the English lever, andwe have shown in our example that a judiciously planned club toothescapement of medium size can be made with the center distance properlyplanted. [Illustration: Fig.  4. ] When considering the center distance we must of necessity consider thewidths of teeth and pallets and their lifting angles. We are now at apoint in which no watchmaker of intelligence would indicate one certaindivision for these parts and claim it to be "the best. " It is alwaysthose who do not thoroughly understand a subject who are the first tomake such claims. We will, however, give our opinion within certainlimits. The angle to be divided for tooth and pallet is 10½°. Let usdivide it by 2, which would be the most natural thing to do, and examinethe problem. We will have 5¼° each for width of tooth and pallet. We_must_ have a smaller lifting angle on the tooth than on the pallet, butthe wider the tooth the greater should its lifting angle be. It wouldnot be mechanical to make the tooth wide and the lifting angle small, asthe lifting plane on the pallets would be too steep on account of beingnarrow. A lifting angle on the tooth which would be _exactly_ suitablefor a given circular, would be _too great_ for a given equidistantpallet. It follows, therefore, taking 5¼° as a width for the tooth, thatwhile we could employ it in a fair sized escapement with equidistantpallets, we could not do so with circular pallets and still have thelatter pitched on the tangents. We see the majority of escapements madewith narrower teeth than pallets, and for a very good reason. In the example previously given, the 3° lift on the tooth is welladapted for a width of 4½°, which would require a pallet 6° in width. The tooth, therefore, would be ¾ the width of pallets, which is verygood indeed. From what we have said it follows that a large number of pallets are notplanted on the tangents at all. We have never noticed this question inprint before. Writers generally seem to, in fact do, assume that nomatter how large or small the escapement may be, or how the pallets andteeth are divided for width and lifting angle, no difficulty will befound in locating the pallets on the tangents. Theoretically there is nodifficulty, but in practice we find there is. _Equidistant vs. Circular. _ At this stage we are able to weigh thecircular against the equidistant pallet. In beginning this essay we hadto explain the difference between them, so the reader could follow ourdiscussion, and not until now, are we able to sum up our conclusions. The reader will have noticed that for such an important action as thelift, which supplies power to the balance, the circular pallet isfavored from every point of view. This is a very strong point in itsfavor. On the other hand, the unlocking resistance being less, and asnearly alike as possible on both pallets in the equidistant, it is aquestion if the total vibration of the balance will be greater with theone than the other, although it will receive the impulse under betterconditions from the circular pallet; but it expends more force inunlocking it. Escapement friction plays an important role in theposition and isochronal adjustments; the greater the frictionencountered the slower the vibration of the balance. The friction shouldbe constant. In unlocking, the equidistant comes nearer to fulfillingthis condition, while during the lift it is more nearly so in thecircular. The friction in unlocking, from a timing standpoint, overshadows that of the impulse, and the tooth can be a little wider inthe equidistant than the circular escapement with the pallet properlyplanted. Therefore for the _finest_ watches the equidistant escapementis well adapted, but for anything less than that the circular should beour choice. _The Fork and Roller Action. _ While the lifting action of the leverescapement corresponds to that of the cylinder, the fork and rolleraction corresponds to the impulse action in the chronometer and duplexescapements. Our experience leads us to believe that the action now underconsideration is but imperfectly understood by many workmen. It is acomplicated action, and when out of order is the cause of many annoyingstoppages, often characterized by the watch starting when taken from thepocket. The action is very important and is generally divided into impulse andsafety action, although we think we ought to divide it into three, namely, by adding that of the unlocking action. We will first of allconsider the impulse and unlocking actions, because we cannotintelligently consider the one without the other, as the ruby pin andthe slot in the fork are utilized in each. The ruby pin, or strictlyspeaking, the "impulse radius, " is a lever arm, whose length is measuredfrom the center of the balance staff to the face of the ruby pin, and isused, firstly, as a power or transmitting lever on the acting orgeometrical length of the fork (_i.  e. _, from the pallet center to thebeginning of the horn), and which at the moment is a resistance lever, to be utilized in unlocking the pallets. After the pallets are unlockedthe conditions are reversed, and we now find the lever fork, through thepallets, transmitting power to the balance by means of the impulseradius. In the first part of the action we have a short lever engaging alonger one, which is an advantage. See Fig.  14, where we have purposelysomewhat exaggerated the conditions. A′X represents the impulse radiusat present under discussion, and AW the acting length of the fork. Itwill be seen that the shorter the impulse radius, or in other words, thecloser the ruby pin is to the balance staff and the longer the fork, theeasier will the unlocking of the pallets be performed, but this entailsa great impulse angle, for the law applicable to the case is, that theangles are in the inverse ratio to the radii. In other words, theshorter the radius, the greater is the angle, and the smaller the anglethe greater is the radius. We know, though, that we must have as smallan impulse angle as possible in order that the balance should be highlydetached. Here is one point in favor of a short impulse radius, and oneagainst it. Now, let us turn to the impulse action. Here we have thelong lever AW acting on a short one, A′X, which is a disadvantage. Here, then, we ought to try and have a short lever acting on a long one, whichwould point to a short fork and a great impulse radius. Suppose AP, Fig.  14, is the length of fork, and A′P is the impulse radius; here, then, we favor the impulse, and it is directly in accordance with thetheory of the free vibration of the balance, for, as before stated, thelonger the radius the smaller the angle. The action at P is also closerto the line of centers than it is at W, which is another advantage. [Illustration: Fig.  14. ] We will notice that by employing a large impulse angle, and consequentlya short radius, the intersection _m_ of the two circles _ii_ and _cc_ isvery _safe_, whereas, with the conditions reversed in favor of theimpulse action, the intersection at _k_ is more delicate. We have nowseen enough to appreciate the fact that we favor one action at theexpense of another. By having a lifting angle on pallet and tooth of 8½°, a locking angle of1½°, and a run of ½°, we will have an angular movement of the fork of8½ + 1½ + ½ = 10½°. [Illustration: Fig.  15. ] Writers generally only consider the movement of the fork from drop todrop on the pallets, but we will be thoroughly practical in the matter. With a total motion of the fork of 10½° (JAW, Fig.  15), one-half, or 5¼°will be performed on each side of the line of centers. We are at libertyto choose any impulse angle which we may prefer; 3 to 1 is a goodproportion for an ordinary well-made watch. By employing it, the angleXA′Y would be equal to 31½°. The radius A′X Fig.  16, is also of the sameproportion, but the angle AA′X is greater because the fork angle WAA′ isgreater than the same angle in Fig.  15. We will notice that theintersection _k_ is much smaller in Fig.  15 than in Fig.  16. The actionin the latter begins much further from the line of centers than in theformer and outlines an action which should not be made. [Illustration: Fig.  16. ] To come back to the impulse angle, some might use a proportion of 3. 5, 4or even 5 to 1, while others for the finest of watches would only use2. 75 to 1. By having a total vibration of the balance of 1½ turns, whichis equal to 540° a fork angle of 10° and a proportion of 2. 75 for theimpulse angle which would be equal to 10 × 2. 75 = 27. 5°. The _free_vibration of the balance, or as this is called, "the supplemental arc, "is equal to 540° - 27. 5° = 512. 50°, while with a proportion of 5 to 1, making an impulse angle of 50°, it would be equal to 490°. To sum up, the finer the watch the lower the proportion, the closer the action tothe line of centers, the smaller the friction. On account of leveragethe more difficult the unlocking but the more energetic the impulse whenit does occur. The velocity of the ruby pin at P; Fig.  14, is muchgreater than at W, consequently it will not be overtaken as soon by thefork as at W. The velocity of the fork at the latter point is greaterthan at P; the intersection of _ii_ and _cc_ is also not as great;therefore the lower the proportion the finer and more exact must theworkmanship be. We will notice that the unlocking action has been overruled by theimpulse. The only point so far in which the former has been favored isin the diminished action before the line of centers, as previouslypointed out at P, Fig.  14. We will now consider the width of the ruby pin and to get a good insightinto the question, we will study Fig.  17. A is the pallet center, A′ thebalance center, the line AA′ being the line of centers; the angle WAAequals half the total motion of the fork, the other half, of course, taking place on the opposite side of the center line. WA is the _center_of the fork when it rests against the bank. The angle AA′X representshalf the impulse angle; the other half, the same as with the fork, isstruck on the other side of the center line. At the point ofintersection of these angles we will draw _cc_ from the pallet center A, which equals the acting length of the fork, and from the balance centerwe will draw _ii_, which equals the _theoretical_ impulse radius; somewriters use it as the _real_ radius. The wider the ruby pin the greaterwill the latter be, which we will explain presently. The ruby pin in entering the fork must have a certain amount of freedomfor action, from 1 to 1¼°. Should the watch receive a jar at the momentthe guard point enters the crescent or passing hollow in the roller, thefork would fly against the ruby pin. It is important that the angularfreedom between the fork and ruby pin at the moment it enters into theslot be _less_ than the total locking angle on the pallets. If we employa locking angle of 1½° and ½° run, we would have a total lock on thepallets of 2°. By allowing 1¼° of freedom for the ruby pin at the momentthe guard point enters the crescent, in case the fork should strike theface of the ruby pin, the pallets will still be locked ¾° and the forkdrawn back against the bankings through the draft angle. We will see what this shake amounts to for a given acting length offork, which describes an arc of a circle, therefore the acting length isonly the radius of that circle and must be multiplied by two in order toget the diameter. The acting length of fork = 4. 5 mm. , what is theamount of shake when the ruby pin passes the acting corner?4. 5 × 2 × 3. 1416 ÷ 360° = . 0785 × 1. 25 = . 0992 mm. The shake of the rubypin in the slot of the fork must be as slight as possible, consistentwith perfect freedom of action. It varies from ¼° to ½°, according tolength of fork and shape of ruby pin. A square ruby pin requires moreshake than any other kind; it enters the fork and receives the impulsein a diagonal direction on the jewel, in which position it isillustrated at Z, Fig.  20. This ruby pin acts on a knife edge, but forall that the engaging friction during the unlocking action isconsiderable. Our reasoning tells us it matters not if a ruby pin be wide or narrow, it must have _the same_ freedom in passing the acting edge of the fork, therefore, to have the impulse radius on the point of intersection ofA′X with AW, Fig.  17, we would require a _very_ narrow ruby pin. With 1°of freedom at the edge, and ½° in the slot, we could only have a rubypin of a width of 1½°. Applying it to the preceding example it wouldonly have an actual width of . 0785 × 1. 5 = . 1178 mm. , or the size of anordinary balance pivot. At _n_, Fig.  17, we illustrate such a ruby pin;the theoretical and real impulse radius coincide with one another. Theintersection of the circle _ii_ and _cc_ is very slight, while thefriction in unlocking begins within 1° of half the total movement of thefork from the line of centers; to illustrate, if the angular motion is11° the ruby pin under discussion will begin action 4½° before the lineof centers, being an engaging, or "uphill" friction of considerablemagnitude. [Illustration: Fig.  17. ] [Illustration: Fig.  18. ] [Illustration: Fig.  19. ] [Illustration: Fig.  20. ] The intersection with the fork is also much less than with the widerruby pin, making the impulse action very delicate. On the other hand thewidest ruby pin for which there is any occasion is one beginning theunlocking action on the line of centers, Fig.  17; this entails a widthof slot equal to the angular motion of the fork. We see here theadvantage of a wide ruby pin over a narrow one in the unlocking action. Let us now examine the question from the standpoint of the impulseaction. Fig.  18 illustrates the moment the impulse is transmitted; the fork hasbeen moved in the direction of the arrow by the ruby pin; the escapementhas been unlocked and the opposite side of the slot has just struck theruby pin. The exact position in which the impulse is transmitted varieswith the locking angle, the width of ruby pin, its shake in the slot, the length of fork, its weight, and the velocity of the ruby pin, whichis determined by the vibrations of the balance and the impulse radius. In an escapement with a total lock of 1¾° and 1¼ of shake in the slot, theoretically, the impulse would be transmitted 2° from the bankings. The narrow ruby pin n receives the impulse on the line _v_, which iscloser to the line of centers than the line _u_, on which the large rubypin receives the impulse. Here then we have an advantage of the narrowruby pin over a wide one; with a wider ruby pin the balance is also moreliable to rebank when it takes a long vibration. Also on account of thegreater angle at which the ruby pin stands to the slot when the impulsetakes place, the _drop_ of the fork against the jewel will amount tomore than its shake in the slot (which is measured when standing on theline of centers). On this account some watches have slots dovetailed inform, being wider at the bottom, others have ruby pins of this form. They require very exact execution; we think we can do without them byjudiciously selecting a width of ruby pin between the two extremes. Wewould choose a ruby pin of a width equal to half the angular motion ofthe fork. There is an ingenious arrangement of fork and roller whichaims to, and partially does, overcome the difficulty of choosing betweena wide and narrow ruby pin, it is known as the Savage pin rollerescapement. We intend to describe it later. If the face of the ruby pin were planted on the theoretical impulseradius _ii_, Fig.  19, the impulse would end in a butting action asshown; hence the great importance of distinguishing between thetheoretical and real impulse radius and establishing a reliable datafrom which to work. We feel that these actions have never been properlyand thoroughly treated in simple language; we have tried to make themplain so that anyone can comprehend them with a little study. Three good forms of ruby pins are the triangular, the oval and the flatfaced; for ordinary work the latter is as good as any, but for fine workthe triangular pin with the corners slightly rounded off is preferable. [Illustration: Fig.  21. ] [Illustration: Fig.  23. ] [Illustration: Fig.  22. ] English watches are met with having a cylindrical or round ruby pin. Such a pin should never be put into a watch. The law of theparallelogram of forces is completely ignored by using such a pin; thefriction during the unlocking and impulse actions is too severe, as itis, without the addition of so unmechanical an arrangement. Fig.  21illustrates the action of a round ruby pin; _ii_ is the path of the rubypin; _cc_ that of the acting length of the fork. It is shown at themoment the impulse is transmitted. It will be seen that the impact takesplace _below_ the center of the ruby pin, whereas it should take placeat the center, as the motion of the fork is _upwards_ and that of theruby pin _downwards_ until the line of the centers has been reached. The same rule applies to the flat-faced pin and it is important that theright quantity be ground off. We find that 3/7 is approximately theamount which should be ground away. Fig.  22 illustrates the forkstanding against the bank. The ruby pin touches the side of the slot buthas not as yet begun to act; _ri_ is the real impulse circle for whichwe allow 1¼° of freedom at the acting edge of the fork; the face of theruby pin is therefore on this line. The next thing to do is to find thecenter of the pin. From the side _n_ of the slot we construct the rightangle _o n t_; from _n_, we transmit ½ the width of the pin, and plantthe center _x_ on the line _n t_. We can have the center of the pinslightly below this line, but in no case above it; but if we put itbelow, the pin will be thinner and therefore more easily broken. [Illustration: Fig.  14. ] _The Safety Action. _ Although this action is separate from the impulseand unlocking actions, it is still very closely connected with them, much more so in the single than in the double roller escapement. If wewere to place the ruby pin at _X_, Fig.  14, we could have a muchsmaller roller than by placing it at _P_. With the small roller thesafety action is more secure, as the intersection at _m_ is greater thanat _k_. It is not as liable to "butt" and the friction is less when theguard point is thrown against the small roller. Suppose we take tworollers, one with a diameter of 2. 5 mm. , the other just twice thisamount, of 5 mm. By having the guard radius and pressure the same ineach case, if the guard point touched the larger roller it would notonly have twice, but four times more effect than on the smaller one. Wewill notice that the smaller the impulse angle the larger the roller, because the ruby pin is necessarily placed farther from the center. Theposition of the ruby pin should, therefore, govern the size of theroller, which should be as small as possible. There should only beenough metal left between the circumference of the roller and the faceof the jewel to allow for a crescent or passing hollow of sufficientdepth and an efficient setting for the jewel. For this reason, as wellas securing the correct impulse radius and therefore angle, whenreplacing the ruby pin, and having it set securely and mechanically inthe roller, it is necessary that the pin and the hole in the roller beof the same form, and a good fit. Fig.  23 illustrates the difference insize of rollers. In the smaller one the conditions imposed aresatisfied, while in the larger one they are not. In the single rollerthe safety action is at the mercy of the impulse and pallet angles. Wehave noticed that in order to favor the impulse we require a largeroller, and for the safety action a small one, therefore escapementsmade on fine principles are supplied with two rollers, one for eachaction. It may be well to say that in our opinion a proportion between the forkand impulse angles in 10° pallets of 3 or 3½ to 1, _depending_ upon thesize of the escapement, is the lowest which should be made in singleroller. We have seen them in proportions of 2 to 1 in single roller--ascientific principle foolishly applied--resulting in an action entirelyunsatisfactory. When the guard point is pressed against the roller the escape tooth muststill rest on the locking face of the pallet; if the total lock is 2°, byallowing 1¼° freedom for the guard point between the bank and the rollerthe escapement will still be locked ¾°. How much this shake actuallyamounts to depends upon the guard radius. Suppose this to be 4 mm. , then the freedom would equal 4 × 2 × 3. 1416 ÷ 360 × 1. 25 = . 0873 mm. [Illustration: Fig.  24. ] [Illustration: Fig.  25. ] _The Crescent_ in the roller must be large and deep enough so it will beimpossible for the guard point to touch in or on the corners of it; atthe same time it must not be too large, as it would necessitate a longerhorn on the fork than is necessary. Fig.  24 shows the slot _n_ of the fork standing at the bank. The rubypin _o_ touches it, but has not as yet acted on it; _s s_ illustrates asingle roller, while S2 illustrates the safety roller for a doubleroller escapement. In order to find the dimensions of the crescent inthe single roller we must proceed as follows: WA is in the center of thefork when it rests against the bank, and is, therefore, one of the sidesof the fork angle, and is drawn from the pallet center; V A W is anangle of 1¼°, which equals the freedom between the guard point and theroller; _g g_ represents the path of the guard pin _u_ for the singleroller, and is drawn at the intersection of VA with the roller A′ A2 isa line drawn from the balance center through that of the ruby pin, andtherefore also passes through the center of the crescent. By planting acompass on this line, where it cuts the periphery of the roller, andlocating the point of intersection of VA with the roller, will give usone-half the crescent, the remaining half being transferred to theopposite side of the line A′ A2. We will notice that the guard point hasentered the crescent 1¼° before the fork begins to move. The angle of opening for the crescent in the double roller escapement isgreater than in the single, because it is placed closer to the balancecenter, and the guard point or dart further from the pallet center, causing a greater intersection; also the velocity of the guard point hasincreased, while that of the safety roller has decreased. Fig.  24, at_ff_, shows the path of the dart _h_, which also has 1¼° freedom betweenbank and roller. From the balance center we draw A′ _d_ touching thecenter or point of the dart; from this point we construct at 5° angle_b_ A′ _d_. This is to ensure sufficient freedom for the dart whenentering the crescent. We plant a compass on the point of intersectionof A′ A2 with the safety roller, S2, and locating the point where A′_b_intersects it, have found one-half the opening for the crescent, theremaining half being constructed on the opposite side of the line A′ A2. _The Horn_ on the fork belongs to the safety action: more horn isrequired with the double than with the single roller, on account of thegreater angle of opening for the crescent. The horn should be of such a length that when the crescent has passedthe guard point, the end of the horn should point to at least the centerof the ruby pin. The dotted circle, _s s_, Fig.  25, represents a single roller. It willbe noticed that the corner of the crescent has passed the guard pin _u_by a considerable angle, and although this is so, in case of an accidentthe _acting edge_ of the fork would come in contact with the ruby pin;this proves that a well made single roller escapement really requiresbut little horn, only enough to ensure the safe entry of the ruby pin incase the guard point at that moment be thrown against the roller. Wewill now examine the question from the standpoint of the double roller;S2, Fig.  25, is the safety roller; the corner of the crescent has safelypassed the dart _h_; the centers of the ruby pin _o_ and of the crescentbeing on the line A′ A2, we plant the compass on the pallet center andthe center of the face of the ruby pin and draw _k k_, which will be thepath described by the horn. The end of the horn is therefore plantedupon it from 1½° to 1¾° from the ruby pin; this freedom at the end ofthe horn is therefore from ¼° to ½° more than we allow for the guardpoint; it depends upon the size of the escapement and locking angleswhich we would choose. It must in any case be less than the lock on thepallets, so that the fork will be drawn back against the bank in casethe horn be thrown against the ruby pin. When treating on the width of the ruby pin, we mentioned the Savage pinroller escapement, which we illustrate in Figs. 26 and 27. Thisingenious arrangement was designed with the view of combining theadvantages of both wide and narrow pins and at the same time without anyof their disadvantages. In Fig.  26 we show the unlocking pins _u_ beginning their action on theline of centers--the best possible point--in unlocking the escapement. These pins were made of gold in all which we examined, although it isrecorded that wide ruby pins and ruby rollers have been used in thisescapement, which would be preferable. The functions of the two pins in the roller are simply to unlock theescapement; the impulse is not transmitted to them as is the case in theordinary fork and roller action. In this action the guard pin _i_ alsoacts as the impulse pin. We will notice that the passing hollow in thisroller is a rectangular slot the same as in the ordinary fork. When theescapement is being unlocked the guard pin _i_ enters the hollow andwhen the escape tooth comes into contact with the lifting plane of thepallet the pin _i_, Fig.  27, transmits the impulse to the roller. [Illustration: Fig.  26. ] [Illustration: Fig.  28. ] The impulse is transmitted closer to the line of centers than could bedone with any ruby pin. If the pin _i_ were wider the impulse would betransmitted still closer to the line of centers, but the intersection ofit with the roller would be less. It is very delicate as it is, therefore from a practical standpoint it ought to be made thin butconsistent with solidity. If the pin is anyway large, it should beflattened on the sides, otherwise the friction would be similar to thatof the round ruby pin. It would also be preferable (on account of thepin _i_ being very easily bent) to make the impulse piece narrow but ofsuch a length that it could be screwed to the fork, the same as the dartin the double roller. The impulse radius is also the radius of theroller, because the impulse is transmitted to the roller itself; forthis reason the latter is smaller in this action than in the ordinaryone having the same angles; also a shorter lever is in contact with alonger one in the unlocking than in ordinary action of the same angles;but for all this the pins _u u_ should be pitched close to the edge ofthe roller, as the angular connection of the balance with the escapementwould be increased during the unlocking action. This escapement beingvery delicate requires a 12° pallet angle and a proportion betweenimpulse and pallet angles of not less than 3 to 1, which would mean animpulse angle of 36°; this, together with the first rate workmanshiprequired are two of the reasons why this action is not often met with. George Savage, of London, England, invented this action. He was awatchmaker who, in the early part of this century, did much to perfectthe lever escapement by good work and nice proportion, besides inventingthe two pin variety. He spent the early part of his life in Clerkenwell, but in his old days emigrated to Canada, and founded a flourishingretail business in Montreal, where he died. Some of George Savage'sdescendants are still engaged at the trade in Canada at the present day. The correct delineation of the lever escapement is a very importantmatter. We illustrate one which is so delineated that it can bepractically produced. We have not noticed a draft of the leverescapement, especially with equidistant pallets and club teeth, whichwould act correctly in a watch. We have been aggressive in our work and have sometimes found theoriespropounded and elongated which of themselves were not right; this mayhave something to do with it, that we so often hear workmen say, "Theoryis no use, because if you work according to it your machine will notrun. " We say, "No, sir, if your theory is not right in itself, then yourwork will certainly not be correct; but if your theory be correct thenyour work _must_ be correct. Why? it simply cannot be otherwise. " Wewill give it another name; let us say, apply sense, reason, thought, experience and study to your work, and what have you done? You havesimply applied theory. A theorem is a proposition to be proved, not being able to prove it, wemust simply change it according as our experience dictates, this isprecisely what we have done with the escapement after having followedthe deductions of recognized authorities with the result that we can nowillustrate an escapement which has been thoroughly subjected to animpartial analysis in every respect, and which is theoretically andpractically correct. We will not only give instructions for drafting the escapement now underconsideration, but will also make explanations how to draft it indifferent positions, also in circular pallet and single roller. We areconvinced that by so doing we will do a service to many, we also wish toavoid what we may call "the stereotyped" process, that is, one which maybe acquired by heart, but introduce any changes and perplexity is theresult. It is really not a difficult matter to draft escapements indifferent positions, as an example will show. Before making a draft we must know exactly what we wish to produce. Itis well in drafting escapements to make them as large as possible, saythirty to forty times larger than in the watch, in the present case thesize is immaterial, but we must have specifications for the proportionsof the angles. Our draft is to be the most difficult subject in leverescapements; it is to be represented just as if it were working in awatch; it is to represent a good and reliable action in every respect, one which can be applied without special difficulty to a good watch, andis to be "up to date" in every particular and to contain the majorityof the best points and conclusions reached in our analysis. _Specifications for Lever Escapement_: The pallets are to beequidistant; the wheel teeth of the "club" form; there are to be tworollers; wheel, pallet, and balance centers are to be in straight line. The lock is to be 1½°, the run ¼°, making a total lock of 1¾°; themovement of pallets from drop to drop is to be 10°, while the fork is tomove through 10¼° from bank to bank; the lift on the wheel teeth is tobe 3°, while the remainder is to be the lift on the pallets as follows:10¼ - (1¾ + 3) = 5½° for lift of pallets. The wheel is to have 15 teeth, with pallets spanning 3 teeth or 2½spaces, making the angle from lock to lock = 360 ÷ 15 × 2½ = 60°, theinterval from tooth to tooth is 360 ÷ 15 = 24°; divided by 2pallets = 24 ÷ 2 = 12° for width of tooth, pallet and drop; drop is tobe 1½°, the tooth is to be ¾ the width of the pallet, making a tooth ofa width of 4½° and a pallet of 6°. The draw is to be 12° on each pallet, while the locking faces of theteeth are to incline 24°. The acting length of fork is to be equal tothe distance of centers of scape wheel and pallets; the impulse angle isto be 28°; freedom from dart and safety, roller is to be 1¼°, and fordart and corner of crescent 5°; freedom for ruby pin and acting edge offork is to be 1¼°; width of slot is to be ½ the total motion, or10¼ ÷ 2 = 5⅛°; shake of ruby pin in slot = ¼°, leaving 5⅛ - ¼ = 4⅞° forwidth of ruby pin. Radius of safety roller to be 4/7 of the theoretical impulse radius. Thelength of horn is to be such that the end would point at least to thecenter of the ruby pin when the edge of the crescent passes the dart;space between the end of horn and ruby pin is to be 1½°. It is well to know that the angles for width of teeth, pallets and dropare measured from the wheel center, while the lifting and locking anglesare struck from the pallet center, the draw from the locking corners ofthe pallets, and the inclination of the teeth from the locking edge. In the fork and roller action, the angle of motion, the width of slot, the ruby pin and its shake, the freedom between dart and roller, of rubypin with acting edge of fork and end of horn are all measured from thepallet center, while the impulse angle and the crescent are measuredfrom the balance center. A sensible drawing board measures 17 × 24inches, we also require a set of good drawing instruments, the finer theinstruments the better; pay special attention to the compasses, pens andprotractor; add to this a straight ruler and set square. The best all-round drawing paper, both for India ink and colored workhas a rough surface; it must be fastened firmly and evenly to the boardby means of thumb tacks; the lines must be light and made with a hardpencil. Use Higgins' India ink, which dries rapidly. [Illustration] We will begin by drawing the center line A′ A B; use the point B for theescape center; place the compass on it and strike G H, the primitive orgeometrical circle of the escape wheel; set the center of the protractorat B and mark off an angle of 30° on each side of the line of centers;this will give us the angles A B E and A B F together, forming the angleF B E of 60°, which represents from lock to lock of the pallets. Sincethe chord of the angle of 60° is equal to the radius of the circle, thisgives us an easy means of verifying this angle by placing the compass atthe points of intersection of F B and E B with the primitive circle G H;this distance must be equal to the radius of the circle. At these pointswe will construct right angles to E B and F B, thus forming the tangentsC A and D A to the primitive circle G H. These tangents meet on the lineof centers at A, which will be the pallet center. Place the compass at Aand draw the locking circle M N at the points of intersection of E B andF B with the primitive circle G H. The locking edges of the pallets willalways stand on this circle no matter in what relation the palletsstand to the wheel. Place the center of the protractor at B and draw theangle of width of pallets of 6°; I B E being for the engaging and J B Ffor the disengaging pallet. In the equidistant pallet I B is drawn onthe side towards the center, while J B is drawn further from the center. If we were drawing a circular pallet, one-half the width of palletswould be placed on each side of E B and F B. At the points ofintersection of I B and J B with the primitive circle G H we draw thepath O for the discharging edge of the engaging and P for that of thedisengaging pallet. The total lock being 1¾°, we construct V′ A at thisangle from C A; the point of intersection of V′ A with the lockingcircle M N, is the position of the locking corner of the engagingpallet. The pallet having 12° draw when locked we place the center ofthe protractor on this corner and draw the angle Q M E. Q M will be thelocking face of the engaging pallet. If the face of the pallet were onthe line E B there would be no draw, and if placed to the opposite sideof E B the tooth would repel the pallet, forming what is known as therepellant escapement. [Illustration: Fig.  28. ] Having shown how to delineate the locking face of the engaging palletwhen locked, we will now consider how to draft both it and thedisengaging pallet in correct positions when unlocked; to do so wedirect our attention until further notice to Fig.  28. The locking facesQ M of the engaging and S N of the disengaging pallets are shown indotted lines _when locked_. We must now consider the relation which thelocking faces will bear to E B in the engaging, and to F B in thedisengaging pallets when unlocked. This is a question of someimportance; it is easy enough to represent the 12° from the 30° angleswhen locked; we must be certain that they would occupy exactly thatposition and yet show them unlocked; we shall take pains to do so. Indue time we shall show that there is no appreciable loss of lift on theengaging pallet in the escapement illustrated; the angle T A Vtherefore shows the total lift; we have not shown the correspondingangles on the disengaging side because the angles are somewhatdifferent, but the total lift is still the same. G H represents theprimitive circle of the escape wheel, and X Z that of the real, whileM N represents the circular course which the locking corners of thepallets take in an equidistant escapement. At a convenient position wewill construct the circle C C′ D from the pallet center A. Notice thepoints _e_ and _c_, where V A and T A intersect this circle; the spacebetween _e_ and _c_ represents the extent of the motion of the palletsat this particular distance from the center A; this being so, then letus apply it to the engaging pallet. At the point of intersection _o_ ofthe dotted line Q M (which is an extended line on which the face of thepallet lies when locked), with the circle C C′ D, we will plant ourdividers and transfer _e c_ to _o n_. By setting our dividers on _o_ Mand transferring to _n_ M′, we will obtain the location of Q′ M′, thelocking face when unlocked. Let us now turn our attention to thedisengaging pallet. The dotted line S N represents the location of thelocking face of the disengaging pallet when locked at an angle of 12°from F B. At the intersection of S N with the circle C C′ D we obtainthe point _j_. The motion of the two pallets being equal, we transferthe distance _e c_ with the dividers from _j_ and obtain the point _l_. By setting the dividers on _j_ N and transferring to _l_ N′ we draw theline S′ N′ on which the locking face of the disengaging pallet will belocated when unlocked. It will be perfectly clear to anyone that throughthese means we can correctly represent the pallets in any desiredposition. We will notice that the face Q′ M′ of the engaging pallet when unlockedstands at a greater angle to E B than it did when locked, while theopposite is the case on the disengaging pallet, in which the angleS′ N′ F is much less than S N F. This shows that the _deeper_ theengaging pallet locks, the lighter will the draw be, while the oppositeholds good with the disengaging pallet; also, that the draw increasesduring the unlocking of the engaging, and decreases during the unlockingof the disengaging pallet. These points show that the draw should bemeasured with the _fork standing against the bank_; not when the lockingcorner of the pallet stands on the primitive circle, as is so oftendone. The recoil of the wheel (which determines the draw), isillustrated by the difference between the locking circle M N and theface Q M for the engaging, and S N for the disengaging pallet, and alongthe _acting_ surface it is alike on each pallet, showing that the draftangle should be the same on each pallet. A number of years ago we constructed the escapement model which weherewith illustrate. All the parts are adjustable; the pallets can bemoved in any direction, the draft angles can be changed at will. Throughthis model we can practically demonstrate the points of which we havespoken. Such a model can be made by workmen after studying thesepapers. [Illustration] In both the equidistant and circular pallets the locking face S N of thedisengaging pallet deviates more from the locking circle M N than doesthe locking face Q M of the engaging pallet, as will be seen in thediagram. This is because the draft angle is struck from E B whichdeviates from the locking circle in such a manner, that if the face of apallet were planted on it and _locked deep enough_ to show it, thewheel would actually _repel_ the pallet, whereas with the disengagingpallet if it were planted on F B, it would actually produce draw iflocked very deep; this is on account of the natural deviation of the 30°lines from the locking circle. This difference is more pronounced in thecircular than in the equidistant pallet, because in the former we havetwo locking circles, the larger one being for the engaging pallet, andas an arc of a large circle does not deviate as much from a straightline as does that of a smaller circle, it will be easily understood thatthe natural difference before spoken of is only enhanced thereby. Forthis reason in order to produce an _actual_ draw of 12°, the engagingpallet may be set at a slightly greater angle from E B in the circularescapement; the amount depends upon the width of the pallets; therequirements are that the recoil of the wheel will be the same on eachpallet. We must, however, repeat that one of the most important pointsis to measure the draw when the fork stands against the bank, thereby_increasing_ the draw on the engaging and _decreasing_ that of thedisengaging pallet _during_ the unlocking action, thus _naturally_balancing one fault with another. We will again proceed with the delineation of the escapement hereillustrated. After having drawn the locking face Q M, we draw the angleof width of teeth of 4½°, by planting the protractor on the escapecenter B. We measure the angle E B K, from the locking face of thepallet; the line E B does not touch the locking face of the pallet atthe present time of contact with the tooth, therefore a line must bedrawn from the point of contact to the center B. We did so in ourdrawing but do not illustrate it, as in a reduced engraving of this kindit would be too close to E B and would only cause confusion. We will nowdraw in the lifting angle of 3° for the tooth. From the tangent C A wedraw T A at the required angle; at the point of intersection of T A withthe 30° line E B we have the real circumference of the escape wheel. Itwill only be necessary to connect the locking edge of the tooth with theline K B, where the real or outer circle intersects it. It must be drawnin the same manner in the circular escapement; if the tooth were drawnup to the intersection of K B with T A, the lift would be too great, asthat point is further from the center A than the points of contact are. If the real or outer circle of the wheel intersects both the lockingcircle M N and the path O of the discharging edge at the points whereT A intersects them, then there will be _no loss_ of lift on theengaging pallet. This is precisely how it is in the diagram; but ifthere is any deviation, then the angle of loss must be measured on the_real_ diameter of the wheel and not on the primitive, as is usuallydone, as the real diameter of the wheel, or in other words the heel ofthe tooth, forms the last point of contact. With a wider tooth and agreater lifting angle there will even be a _gain_ of lift on theengaging pallet; the pallet in such a case would actually require asmaller lifting angle, according to the amount of gain. We gave fulldirections for measuring the loss when describing its effects in Fig.  8. Whatever the loss amounts to, it is added to the lifting plane of thepallet. In the diagram under discussion there is no loss, consequentlythe lifting angle on the pallet is to be 5½°. From V′ A we draw V A atthe required angle; the point of intersection of V A with the path Owill be the discharging edge O. It will now only be necessary to connectthe locking corner M with it, and we have the lifting plane of thepallet; the discharging side of the pallet is then drawn parallel to thelocking face and made a suitable length. We will now draw the lockingedges of the tooth by placing the center of the protractor on thelocking edge M and construct the angle B M M′ of 24° and draw a circlefrom the scape center B, to which the line M M′ will be a tangent. Wewill utilize this circle in drawing in the faces of the other teethafter having spaced them off 24° apart, by simply putting a ruler onthe locking edges and on the periphery of the circle. We now construct W′ A as a tangent to the outer circle of the wheel, thus forming the lifting angle D A W′ of 3° for the teeth; thiscorresponds to the angle T A C on the engaging side. W′ A touches theouter circle of the wheel at the intersection of F B with it. We willnotice that there is considerable deviation of W′ A from the circle atthe intersection of J B with it. At the intersecting of this point wedraw U A; the angle U A W′ is the loss of lift. This angle must be addedto the lifting angle of the pallets; we see that in this action there isno loss on the engaging pallet, but on the disengaging the loss amountsto approximately ⅞° in the action illustrated. As we have allowed ¼° ofrun for the pallets, the discharging edge P is removed at this anglefrom U A; we do not illustrate it, as the lines would cause confusionbeing so close together. The lifting angle on the pallet is measuredfrom the point P and amounts to 5½° + the angle of the loss; the angleW A U embraces the above angles besides ¼° for run. If the locks areequal on each pallet, it proves that the lifts are also equal. Thisgives us a practical method of proving the correctness of the drawing;to do so, place the dividers on the locking circle M N at theintersection of T A and V A with it, as this is the extent of motion;transfer this measurement to N, if the _actual_ lift is the same on eachpallet, the dividers will locate the point which the locking corner Nwill occupy _when locked_; this, in the present case, will be at anangle of 1¾° below the tangent D A. By this simple method, thecorrectness of our proposition that the loss of lift should be measuredfrom the outside circle of the wheel, can be proven. We often see theloss measured for the engaging pallet on the primitive circumferenceG H, and on the real circumference for the disengaging; if one is rightthen the other must be wrong, as there is a noticeable deviation of thetangent C A from the primitive circle G H at the intersection of thelocking circle M N; had we added this amount to the lifting angle V′ A Vof the engaging pallet, the result would have been that the dischargingedge O would be over 1° below its present location, thus showing that bythe time the lift on the engaging pallet had been completed, the lockingcorner N of the disengaging pallet would be locked at an angle of 2¾°instead of only 1¾°. Many watches contain precisely this fault. If wewish to make a draft showing the pallets at any desired position, at thecenter of motion for instance, with the fork standing on the line ofcenters, we would proceed in the following manner: 10¼° being the totalmotion, one-half would equal 5⅛°; as the total lock equals 1¾°, wededuct this amount from it which leaves 5⅛ - 1¾ = 3⅜°, which is theangle at which the locking corner M should be shown above the tangentC A. Now let us see where the locking corner N should stand; M havingmoved up 5⅛°, therefore N moved down by that amount, the lift on thepallet being 5½° and on the tooth 3° (which is added to the tangentD A), it follows that N should stand 5½ + 3 - 5⅛ = 3⅜° above D A. We canprove it by the lock, namely: 3⅜° + 1¾ = 5⅛°, half the remaining motion. This shows how simple it is to draft pallets in various positions, remembering always to use the tangents to the primitive circle asmeasuring points. We have fully explained how to draw in the draft angleon the pallets when unlocked, and do not require to repeat it, except tosay, that most authorities draw a tangent R N to the locking circle M N, forming in other words, the right angle R N A, then construct an angleof 12° from R N. We have drawn ours in by our own method, which is thecorrect one. While we here illustrate S N R at an angle of 12° it is inreality _less_ than that amount; had we constructed S N at an angle of12° from R N, then the draw would be 12° from F B, when the primitivecircumference of the wheel is reached, but _more_ than 12° when thefork is against the bank. The space between the discharging edge P and the heel of the tooth formsthe angle of drop J B I of 1½°; the definition for drop is that it isthe freedom for wheel and pallet. This is not, strictly speaking, perfectly correct, as, during the unlocking action there will be arecoil of the wheel to the extent of the draft angle; the heel of thetooth will therefore approach the edge P, and the discharging side ofthe pallet approaches the tooth, as only the discharging edge moves onthe path P. A good length for the teeth is 1/10 the diameter of the wheel, measuredfrom the primitive diameter and from the locking edge of the tooth. The backs of the teeth are hollowed out so as not to interfere with thepallets, and are given a nice form; likewise the rim and arms are drawnin as light and as neat as possible, consistent with strength. Having explained the delineation of the wheel and pallet action we willnow turn our attention to that of the fork and roller. We tried toexplain these actions in such a manner that by the time we came todelineate them no difficulty would be found, as in our analysis wediscussed the subject sufficiently to enable any one of ordinaryintelligence to obtain a correct knowledge of them. The fork and rolleraction in straight line, right, or any other angle is delineated afterthe methods we are about to give. We specified that the acting length of fork was to be equal to thecenter distance of wheel and pallets; this gives a fork of a fairlength. Having drawn the line of centers A′ A we will construct an angle equalto half the angular motion of the pallets; the latter in the case underconsideration being 10¼°, therefore 5⅛° is spaced off on each side ofthe line of centers, forming the angles _m_ A _k_ of 10¼°. Placing ourdividers on A B the center distance of 'scape wheel and pallets, weplant them on A and construct _c c_; thus we will have the acting lengthof fork and its path. We saw in our analysis that the impulse angleshould be as small as possible. We will use one of 28° in our draft ofthe double roller; we might however remark that this angle should varywith the construction of the escapements in different watches; if toosmall, the balance may be stopped when the escapement is locked, whileif too great it can be stopped during the lift; both these defects areto be avoided. The angles being respectively 10¼° and 28° it followsthey are of the following proportions: 28° ÷ 10. 25 = 2. 7316. The impulseradius therefore bears this relation (but in the inverse ratio to theangles), to the acting length of fork. We will put it in the following proportion; let A_c_ equal acting lengthof fork, and _x_ the unknown quantity; 28:10. 25 :: A_c_:_x_; the answerwill be the theoretical impulse radius. Having found the required radiuswe plant one jaw of our measuring instrument on the point ofintersection of _c c_ with _k_ A or _m_ A and locate the other jaw onthe line of centers; we thus obtain A′ the balance center. Through thepoints of intersection before designated we will draft X A′ and Y A′forming the impulse angle X A′ Y of 28°. At the intersection of thisangle with the fork angle _k_ A′ _m_, we draw _i i_ from the center A;this gives us the theoretical impulse circle. The total lock being 1¾°it follows that the angle described by the balance in unlocking= 1¾ × 2. 7316 = 4. 788°. According to the specifications the width ofslot is to be 5⅛°; placing the center of the protractor on A weconstruct half of this angle on each side of _k_ A, which passes throughthe center of the fork when it rests against the bank; this gives us theangle _s_ A _n_ of 5⅛°. If the disengaging pallet were shown locked then_m_ A would represent the center of the fork. The slot is to be made ofsufficient depth so there will be no possibility of the ruby pintouching the bottom of it. The ruby pin is to have 1¼° freedom inpassing the acting edge of the fork; from the center A we construct theangle _t_ A _n_ of 1¼°; at the point of intersection of _t_ A with _c c_the acting radius of the fork, we locate the real impulse radius anddraw the arc _ri ri_ which describes the path made by the face of theruby pin. The ruby pin is to have ¼° of shake in the slot; it willtherefore have a width of 4⅞°; this width is drawn in with the ruby pinimagined as standing over the line of centers and is then transferred tothe position which the ruby pin is to occupy in the drawing. The radius of the safety roller was given as 4/7 of the theoreticalimpulse radius. They may be made of various proportions; thus ⅔ is oftenused. Remember that the smaller we make it, the less the friction duringaccidental contact with the guard pin, the greater must the passinghollow be and the horn of fork and guard point must be longer, whichincreases the weight of the fork. Having drawn in the safety roller, and having specified that the freedombetween the dart and safety roller was to be 1¼°, the dart being in thecenter of the fork, consequently _k_ A is the center of it; therefore weconstruct the angle _k_ A X of 1¼°. At the point of intersection of X Awith the safety roller we draw the arc _g g_; this locates the point ofthe dart which we will now draw in. We will next draw _d_ A′ from thebalance center and touching the point of the dart; we now construct_b_ A′ at an angle of 5° to it. This is to allow the necessary freedomfor the dart when entering the crescent; from A′ we draw a line throughthe center of the ruby pin. We do not show it in the drawing, as itwould be indiscernible, coming very close to A′ X. This line will alsopass through the center of the crescent. At the point of intersection ofA′ _b_ with the safety roller we have one of the edges of the crescent. Byplacing our compass at the center of the crescent on the periphery ofthe roller and on the edge which we have just found, it follows that ourcompass will span the radius of the crescent. We now sweep the arc forthe latter, thus also drawing in the remaining half of the crescent onthe other side of A′ X and bringing the crescent of sufficient depththat no possibility exists of the dart touching in or on the edges ofit. We will now draw in the impulse roller and make it as light aspossible consistent with strength. A hole is shown through the impulseroller to counterbalance the reduced weight at the crescent. Whendescribing Fig.  24, we gave instructions for finding the dimensions ofcrescent and position of guard pin for the single roller. We will findthe length of horn; to do so we must closely follow directions given forFig.  25. In locating the end of the horn, we must find the location ofthe center of the crescent and ruby pin _after_ the edge of the crescenthas passed the dart. From the point of intersection of A′ _b_ with thesafety roller we transfer the radius of the crescent on the periphery ofthe safety roller towards the side against the bank, then draw a linefrom A′ through the point so found. At point of intersection of thisline with the real impulse circle _r i r i_ we draw an arc radiatingfrom the pallet center; the end of the horn will be located on this arc. In our drawing the arc spoken of coincides with the dart radius _g g_. As before pointed out, we gave particulars when treating on Fig.  25, therefore considered it unnecessary to further complicate the draft bythe addition of all the constructional lines. We specified that thefreedom between ruby pin and end of horn was to be 1½°; these lines, (which we do not show) are drawn from the pallet center. Havinglocated the end of the horn on the side standing against the bank, weplace the dividers on it and on the point of intersection of _k_ A with_g g_--which in this case is on the point of the dart, --and transferthis measurement along _g g_ which will locate the end of the horn onthe opposite side. We have the acting edges of the fork on _cc_ and have also found theposition of the ends of the horns; their curvature is drawn in thefollowing manner: We place our compasses on A and _r i_, spanningtherefore the real impulse radius; the compass is now set on the actingedge of the fork and an arc swept with it which is then to beintersected by another arc swept from the end of the horn, on the sameside of the fork. At the point of intersection of the arcs the compassis planted and the curvature of the horn drawn in, the same operation isto be repeated with the other horn. We will now draw in the sides of thehorn of such a form that should the watch rebank, the side of the rubypin will squarely strike the fork. If the back of the ruby pin strikesthe fork there will be a greater tendency of breaking it and injuringthe pivots on account of acting like a wedge. The fork and pallets arenow drawn in as lightly as possible and of such form as to admit oftheir being readily poised. The banks are to be drawn at equal distancesfrom the line of centers. In delineating the fork and roller action inany desired position, it must be remembered that the points of locationof the real impulse radius, the end of horn, the dart or guard pin andcrescent, must _all_ be obtained _when standing against the bank_, andthe arcs drawn which they describe; the parts are then located accordingto the angle at which they are removed from the banks. We think the instructions given are ample to enable any one to masterthe subject. We may add that when one becomes well acquainted with theescapement, many of the angles radiating from a common center, may bedrawn in at once. We had intended describing the mechanical constructionof the escapement, which does unmistakably present some difficulties onaccount of the small dimensions of the parts, but nevertheless it can bemechanically executed true to the principles enumerated. We have evolveda method of so producing them that young men in a comparatively shortperiod have made them from their drafts (without automatic machinery)that their watches start off when run down the moment the crown istouched. Perhaps later on we will write up the subject. It is ourintention of doing so, as we make use of such explanations in ourregular work.