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diff --git a/21978.txt b/21978.txt new file mode 100644 index 0000000..c6e066a --- /dev/null +++ b/21978.txt @@ -0,0 +1,2009 @@ +Project Gutenberg's An Analysis of the Lever Escapement, by H. R. Playtner + +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.org + + +Title: An Analysis of the Lever Escapement + +Author: H. R. Playtner + +Release Date: June 30, 2007 [EBook #21978] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK AN ANALYSIS OF THE LEVER *** + + + + +Produced by Sigal Alon, Fox in the Stars, Laura Wisewell +and the Online Distributed Proofreading Team at +http://www.pgdp.net + + + + + + + + + +[Illustration: THOMAS MUDGE + +_The first Horologist who successfully applied the Detached Lever +Escapement to Watches._ + +_Born 1715--Died 1794._] + + + + +AN ANALYSIS + +OF THE + +LEVER ESCAPEMENT + +BY H. R. PLAYTNER. + +A LECTURE DELIVERED BEFORE THE CANADIAN WATCHMAKERS' AND RETAIL +JEWELERS' ASSOCIATION. + +ILLUSTRATED. + +CHICAGO: + +HAZLITT & WALKER, PUBLISHERS. + +1910. + + + + +PREFACE. + + +Before entering upon our subject proper, we think it advisable to +explain a few points, simple though they are, which might cause +confusion to some readers. Our experience has shown us that as soon as +we use the words "millimeter" and "degree," perplexity is the result. +"What is a millimeter?" is propounded to us very often in the course of +a year; nearly every new acquaintance is interested in having the metric +system of measurement, together with the fine gauges used, explained to +him. + +The metric system of measurement originated at the time of the French +Revolution, in the latter part of the 18th century; its divisions are +decimal, 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 English +inch there are 39+3708/10000 inches in a meter, and there are +25.4 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 into +10ths and the 10ths into 100ths of a millimeter, which could be +continued indefinitely. The 1/100 millimeter is equal to the 1/2540 of +an inch. These are measurements with which the watchmaker is concerned. +1/100 millimeter, written .01 mm., is the side shake for a balance +pivot; multiply it by 2 1/4 and we obtain the thickness for the spring +detent of a pocket chronometer, which is about 1/3 the thickness of a +human hair. + +The metric system of measurement is used in all the watch factories of +Switzerland, France, Germany, and the United States, and nearly all the +lathe makers number their chucks by it, and some of them cut the leading +screws 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_. The +millimeter 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 the +plates. + +Equally as fine gauges can be and are made for the inch as for the +metric system, and the inch is decimally divided, but we require another +decimal point to express our measurement. + +Metric gauges can now be procured from the material shops; they consist +of tenth measures, verniers and micrometers; the finer ones of these +come from Glashutte, and are the ones mentioned by Grossmann in his +essay on the lever escapement. Any workman who has once used these +instruments could not be persuaded to do without them. + +No one can comprehend the geometrical principles employed in escapements +without a knowledge of angles and their measurements, therefore we deem +it of sufficient importance to at least explain what a degree is, as we +know for a fact, that young workmen especially, often fail to see how to +apply it. + +Every circle, no matter how large or small it may be, contains 360deg.; a +degree is therefore the 360th part of a circle; it is divided into +minutes, seconds, thirds, etc. + +To measure the _value_ of a degree of any circle, we must multiply the +diameter of it by 3.1416, which gives us the circumference, and then +divide it by 360. It will be seen that it depends on the size of that +circle or its radius, as to the value of a degree in any _actual_ +measurement. To illustrate; a degree on the earth's circumference +measures 60 geographical miles, while measured on the circumference of +an escape wheel 7.5 mm. in diameter, or as they would designate it in a +material shop, No. 7 1/2, it would be 7.5 x 3.1416 / 360 = .0655 mm., which +is equal to the breadth of an ordinary human hair; it is a degree in +both cases, but the difference is very great, therefore a degree cannot +be associated with any actual measurement until the radius of the +circle is known. Degrees are generated from the center of the circle, +and should be thought of as to ascension or direction and relative +value. Circles contain four right angles of 90deg. each. Degrees are +commonly measured by means of the protractor, although the ordinary +instruments of this kind leave very much to be desired. The lines can be +verified 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 of +pallets and wheel. See Z, Fig. 1. + +_Primitive or Geometrical Diameter._--In the ratchet tooth or English +wheel, the primitive and real diameter are equal; in the club tooth +wheel it means across the locking corners of the teeth; in such a wheel, +therefore, the primitive is _less_ than the real diameter by the height +of two impulse planes. + +_Lock_ equals the depth of locking, measured from the locking corner of +the pallet at the moment the drop has occurred. + +_Run_ equals the amount of angular motion of pallets and fork to the +bankings _after_ the drop has taken place. + +_Total Lock_ equals lock plus run. + +A _Tangent_ is a line which _touches_ a curve, but does not intersect +it. AC and AD, Figs. 2 and 3, are tangents to the primitive circle GH at +the points of intersection of EB, AC, and GH and FB, AD and GH. + +_Impulse Angle_ equals the angular connection of the impulse or ruby pin +with the lever fork; or in other words, of the balance with the +escapement. + +_Impulse Radius._--From the face of the impulse jewel to the center of +motion, which is in the balance staff, most writers assume the impulse +angle and radius to be equal, and it is true that they must conform with +one another. We have made a radical change in the radius and one which +does not affect the angle. We shall prove this in due time, and also +that 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 that +is to learn to draw. No one can be a thorough watchmaker unless he can +draw, 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 results +with others, therefore we speak from personal experience. Attend night +schools and mechanic's institutes and improve yourselves. + +The young workmen of Toronto have a great advantage in the Toronto +Technical School, but we are sorry to see that out of some 600 students, +only five watchmakers attended last year. We can account for the +majority of them, so it would seem as if the young men of the trade were +not much interested, or thought they could not apply the knowledge to be +gained there. This is a great mistake; we might almost say that +knowledge of any kind can be applied to horology. The young men who take +up these studies, will see the great advantage of them later on; one +workman 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, we +have endeavored to make it as plain as possible. It is a deep subject +and is difficult to treat lightly; we will treat it in our own way, +paying special attention to all these points which bothered us during +the many years of painstaking study which we gave to the subject. We +especially endeavor to point out how theory can be applied to practice; +while we cannot expect that everyone will understand the subject without +study, we think we have made it comparatively easy of comprehension. + +We will give our method of drafting the escapement, which happens in +some respects to differ from others. We believe in making a drawing +which we can reproduce in a watch. + + + + +AN ANALYSIS OF THE LEVER ESCAPEMENT. + + +The lever escapement is derived from Graham's dead-beat escapement for +clocks. Thomas Mudge was the first horologist who successfully applied +it to watches in the detached form, about 1750. The locking faces of the +pallets were arcs of circles struck from the pallet centers. Many +improvements were made upon it until to-day it is the best form of +escapement for a general purpose watch, and when made on mechanical +principles is capable of producing first rate results. + +Our object will be to explain the whys and wherefores of this +escapement, and we will at once begin with the number of teeth in the +escape wheel. It is not obligatory in the lever, as in the verge, to +have an uneven number of teeth in the wheel. While nearly all have 15 +teeth, we might make them of 14 or 16; occasionally we find some in +complicated watches of 12 teeth, and in old English watches, of 30, +which is a clumsy arrangement, and if the pallets embrace only three +teeth in the latter, the pallet center cannot be pitched on a tangent. + +Although advisable from a timing standpoint that the teeth in the escape +wheel should divide evenly into the number of beats made per minute in a +watch with seconds hand, it is not, strictly speaking, necessary that it +should 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 of +the balance and consequently two beats for each tooth, making +16 x 2 = 32 beats for each revolution of the escape wheel. 300 beats are +made per minute; divide this by the beats made on each revolution, and +we have the number of times in which the escape wheel revolves per +minute, namely, 300 / 32 = 9.375. This number then is the proportion +existing for the teeth and pitch diameters of the 4th wheel and escape +pinion. We must now find a suitable number of teeth for this wheel and +pinion. Of available pinions for a watch, the only one which would +answer would be one of 8 leaves, as any other number would give a +fractional number of teeth for the 4th wheel, therefore 9.375 x 8 = 75 +teeth in 4th wheel. Now as to the proof: as is well known, if we +multiply the number of teeth contained in 4th and escape wheels also by +2, for the reason previously given, and divide by the leaves in the +escape pinion, we get the number of beats made per minute; therefore +(75 x 16 x 2)/8 = 300 beats per minute. + +Pallets can be made to embrace more than three teeth, but would be much +heavier and therefore the mechanical action would suffer. They can also +be made to embrace fewer teeth, but the necessary side shake in the +pivot holes would prove very detrimental to a total lifting angle of +10deg., which represents the angle of movement in modern watches. Some of +the finest ones only make 8 or 9deg. of a movement; the smaller the angle +the greater will the effects of defective workmanship be; 10deg. is a +common-sense angle and gives a safe escapement capable of fine results. +Theoretically, if a timepiece could be produced in which the balance +would vibrate without being connected with an escapement, we would have +reached a step nearer the goal. Practice has shown this to be the proper +theory to work on. Hence, the smaller the pallet and impulse angles the +less will the balance and escapement be connected. The chronometer is +still more highly detached than the lever. + +The pallet embracing three teeth is sound and practical, and when +applied to a 15 tooth wheel, this arrangement offers certain geometrical +and mechanical advantages in its construction, which we will notice in +due time. 15 teeth divide evenly into 360deg. leaving an interval of 24deg. +from tooth to tooth, which is also the angle at which the locking faces +of the teeth are inclined from the center, which fact will be found +convenient when we come to cut our wheel. + +From locking to locking on the pallet scaping over three teeth, the +angle is 60deg., which is equal to 2 1/2 spaces of the wheel. Fig. 1 +illustrates the lockings, spanning this arc. If the pallets embraced 4 +teeth, the angle would be 84deg.; or in case of a 16 tooth wheel scaping +over three teeth, the angle would be 360 x 2.5/16 = 56 1/4deg. + +[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 equal +distance from the center; sometimes it is also called the tangential +escapement, on account of the unlocking taking place on the intersection +of tangent AC with EB, and FB with AD, the tangents, which is the +valuable feature of this form of escapement. + +[Illustration: Fig. 2.] + +AC and AD, Fig. 2, are tangents to the primitive circle GH. ABE and ABF +are angles of 30deg. each, together therefore forming the angle FBE of +60deg. The locking circle MN is struck from the pallet center A; the +interangles being equal, consequently the pallets must be equidistant. + +The weak point of this pallet is that the lifting is not performed so +favorably; by examining the lifting planes MO and NP, we see that the +discharging edge, O, is closer to the center, A, than the discharging +edge, P; consequently the lifting on the engaging pallet is performed on +a shorter lever arm than on the disengaging pallet, also any inequality +in workmanship would prove more detrimental on the engaging than on the +disengaging pallet. The equidistant pallet requires fine workmanship +throughout. We have purposely shown it of a width of 10deg., which is the +widest we can employ in a 15 tooth wheel, and shows the defects of this +escapement more readily than if we had used a narrow pallet. A narrower +pallet is advisable, as the difference in the discharging edges will be +less, and the lifting arms would, therefore, not show so much difference +in leverage. + +[Illustration: Fig. 3.] + +The circular pallet is sometimes appropriately called "the pallet with +equal lifts," as the lever arms AMO and ANP, Fig. 3, are equal lengths. +It will be noticed by examining the diagram, that the pallets are +bisected by the 30deg. lines EB and FB, one-half their width being placed +on 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 weak +points in this escapement are that the unlocking resistance is greater +on the engaging than on the disengaging pallet, and that neither of them +lock on the tangents AC and AD, at the points of intersection with EB +and FB. The narrower the circular pallet is made, the nearer to the +tangent will the unlocking be performed. In neither the equidistant or +circular pallets can the unlocking resistance be _exactly_ the same on +each pallet, as in the engaging pallet the friction takes place before +AB, the line of centers, which is more severe than when this line has +been passed, as is the case with the disengaging pallet; this fact +proportionately increases the existing defects of the circular over the +equidistant pallet, and _vice versa_, but for the same reason, the +lifting in the equidistant is proportionately accompanied by more +friction than in the circular. + +Both equidistant and circular pallets have their adherents; the finest +Swiss, 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. We +think a ratchet wheel should not be employed with equidistant pallets. +By examining Fig. 2, we see an English pallet of this form. We have +shown its defects in such a wide pallet as the English (as we have +before stated), because they are more readily perceived; also, on +account of the shape of the teeth, there is danger of the discharging +edge, P, dipping so deep into the wheel, as to make considerable drop +necessary, or the pallets would touch on the backs of the teeth. In the +case of the club tooth, the latter is hollowed out, therefore, less drop +is required. We have noticed that theoretically, it is advantageous to +make the pallets narrower than the English, both for the equidistant and +circular escapements. There is an escapement, Fig. 4, which is just the +opposite to the English. The entire lift is performed by the wheel, +while in the case of the ratchet wheel, the entire lifting angle is on +the pallets; also, the pallets being as narrow as they can be made, +consistent with strength, it has the good points of both the equidistant +and circular pallets, as the unlocking can be performed on the tangent +and the lifting arms are of equal length. The wheel, however, is so much +heavier as to considerably increase the inertia; also, we have a metal +surface of quite an extent sliding over a thin jewel. For practical +reasons, therefore, it has been slightly altered in form and is only +used in cheap work, being easily made. + +[Illustration: Fig. 4.] + +We will now consider the drop, which is a clear loss of power, and, if +excessive, is the cause of much irregularity. It should be as small as +possible consistent with perfect freedom of action. + +In so far as _angular_ measurements are concerned, no hard and fast rule +can be applied to it, the larger the escape wheel the smaller should be +the angle allowed for drop. Authorities on the subject allow 1 1/2deg. drop +for the club and 2deg. for the ratchet tooth. It is a fact that escape +wheels are not cut perfectly true; the teeth are apt to bend slightly +from the action of the cutters. The truest wheel can be made of steel, +as each tooth can be successively ground after being hardened and +tempered. Such a wheel would require less drop than one of any other +metal. Supposing we have a wheel with a primitive diameter of 7.5 mm., +what is the amount of drop, allowing 1 1/2deg. by angular measurement? +7.5 x 3.1416 / 360 x 1.5 = .0983 mm., which is sufficient; a hair could +get between the pallet and tooth, and would not stop the watch. Even +after allowing for imperfectly divided teeth, we require no greater +freedom even if the wheel is larger. Now suppose we take a wheel +with a primitive diameter of 8.5 mm. and find the amount of drop; +8.5 x 3.1416 / 360 x 1.5 = .1413 mm., or .1413 - .0983 = .043 mm., +more drop than the smaller wheel, if we take the same angle. This is a +waste of force. The angular drop should, therefore, be proportioned +according to the size of the wheel. We wish it to be understood that +common sense must always be our guide. When the horological student once +arrives at this standpoint, he can _intelligently_ apply himself to his +calling. + +_The Draw._--The draw or draft angle was added to the pallets in order +to draw the fork back against the bankings and the guard point from the +roller 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 we +must choose the less. The rate of the watch will suffer less on account +of the recoil introduced than it would were the locking faces arcs of +circles struck from the pallet center, in which case the guard point +would often remain against the roller. The draw should be as light as +possible consistent with safety of action; some writers allow 15deg. on the +engaging and 12deg. on the disengaging pallet; others again allow 12deg. on +each, which we deem sufficient. The draw is measured from the locking +edges M and N, Fig. 5. The locking planes _when locked_ are inclined 12deg. +from EB, and FB. In the case of the engaging pallet it inclines toward +the center A. The draw is produced on account of MA being longer than +RA, consequently, when power is applied to the scape tooth S, the pallet +is drawn into the wheel. The disengaging pallet inclines in the same +direction but away from the center A; the reason is obvious from the +former explanation. Some people imagine that the greater the incline on +the 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 of +the tooth alone should touch the pallet. From this it follows that the +angle on the teeth must be greater than on the pallets; examine the +disengaging pallet in Fig. 5, as it is from this pallet that the +inclination of the teeth must be determined, as in the case of the +engaging pallet the motion is toward the line of centers AB, and +therefore _away_ from the tooth, which partially explains why some +people advocate 15deg. draw for this pallet. As illustrated in the case of +the disengaging pallet, however, the motion is also towards the line of +centers AB, and _towards_ the tooth as well, all of which will be seen +by the dotted circles MM2 and NN2, representing the paths of the +pallets. It will be noticed that UNF and BNB are opposite and equal +angles of 12deg. For practical reasons, from a manufacturing standpoint, +the angle on the tooth is made just twice the amount, namely 24deg.; we +could make it a little less or a little more. If we made it less than +20deg. too great a surface would be in contact with the jewel, involving +greater friction in unlocking and an inefficient draw, but in the case +of an English lever with such an arrangement we could do with less +drop, which advantage would be too dearly bought; or if the angle is +made over 28deg., the point or locking edge of the tooth would rapidly +become worn in case of a brass wheel. Also in an English lever more drop +would be required. + +_The Lock._--What we have said in regard to drop also applies to the +lock, which should be as small as possible, consistent with perfect +safety. The greater the drop the deeper must be the lock; 1 1/2deg. is the +angle generally allowed for the lock, but it is obvious that in a large +escapement it can be less. + +[Illustration: Fig. 6.] + +_The Run._--The run or, as it is sometimes called, "the slide," should +also be as light as possible; from 1/4deg. to 1/2deg. is sufficient. It +follows then, the bankings should be as close together as possible, +consistent with requisite freedom for escaping. Anything more than this +increases the angular connection of the balance with the escapement, +which directly violates the theory under which it is constructed; also, +a greater amount of work will be imposed upon the balance to meet the +increased unlocking resistance, resulting in a poor motion and accurate +time will be out of the question. It will be seen that those workmen who +make a practice of opening the banks, "to give the escapement more +freedom" simply jump from the frying pan into the fire. The bankings +should be as far removed from the pallet center as possible, as the +further away they are pitched the less run we require, according to +angular measurement. Figure 6 illustrates this fact; the tooth S has +just dropped on the engaging pallet, but the fork has not yet reached +the bankings. At _a_ we have 1deg. of run, while if placed at _b_ we +would only have 1/2deg. of run, but still the same freedom for escaping, +and less unlocking resistance. + +The bankings should be placed towards the acting end of the fork as +illustrated, as in case the watch "rebanks" there would be more strain +on 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 and +pallets and the lock and run. We will suppose that from drop to drop we +allow 10deg.; if the lock is 1 1/2deg. then the actual lift by means of the +inclined planes on teeth and pallets will be 8 1/2deg. We have seen that a +small lifting angle is advisable, so that the vibrations of the balance +will be as free as possible. There are other reasons as well. Fig. 7 +shows two inclined planes; we desire to lift the weight 2 a distance +equal to the angle at which the planes are inclined; it will be seen at +a glance that we will have less friction by employing the smaller +incline, whereas with the larger one the motive power is employed +through a greater distance on the object to be moved. The smaller the +angle the more energetic will the movement be; the grinding of the +angles and fit of the pivots, etc., also increases in importance. An +actual lift of 8 1/2deg. satisfies the conditions imposed very well. We +have before seen that both on account of the unlocking and the lifting +leverage of the pallet arms, it would be advisable to make them narrow +both in the equidistant and circular escapement. We will now study the +question from the standpoint of the lift, in so far as the wheel is +concerned. + +[Illustration: Fig. 8.] + +It is self-evident that a narrow pallet requires a wide tooth, and a +wide pallet a narrow or thin tooth wheel; in the ratchet wheel we have a +metal point passing over a jeweled plane. The friction is at its +minimum, because there is less adhesion than with the club tooth, but we +must emphasize the fact that we require a greater angle in proportion on +the pallets in this escapement than with the narrow pallets and wider +tooth. 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 it +perfectly clear, as we show both a wide and a narrow pallet. GH, +represents the primitive, which in this figure is also the real diameter +of the escape wheel. In measuring the lifting angles for the pallets, +our starting point is _always_ from the tangents AC and AD. The tangents +are straight lines, but the wheel describes the circle GH, therefore +they must deviate from one another, and the closer to the center A the +discharging edge of the engaging pallet reaches, the greater does this +difference become; and in the same manner the further the discharging +edge 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 the +circular escapement. After this we will designate this difference as +the "loss." In order to illustrate it more plainly we show the widest +pallet--the English--in equidistant form. This gives another reason why +the English lever should only be made with circular pallets, as we have +seen that the wider the pallet the greater the loss. The loss is +measured at the intersection of the path of the discharging edge OO, +with the circle G H, and is shown through AC2, which intersects these +circles at that point. In the case of the disengaging pallet, PP +illustrates the path of the discharging edge; the loss is measured as in +the preceding case where GH is intersected as shown by AD2. It amounts +to 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 greater +on the engaging pallet, so much so that it amounts to 2deg., which is +equal to the entire lock; therefore if 8 1/2deg. of work is to be +accomplished through this pallet, the lifting plane requires an angle of +10 1/2deg. struck from AC. + +Let us now consider the lifting action of the club tooth wheel. This is +decidedly a complicated action, and requires some study to comprehend. +In action with the engaging pallet the wheel moves _up_, or in the +direction of the motion of the pallets, but on the disengaging pallet it +moves _down_, and in a direction opposite to the pallets, and the heel +of the tooth moves with greater velocity than the locking edge; also in +the case of the engaging pallet, the locking edge moves with greater +velocity than the discharging edge; in the disengaging pallet the +opposite is the case, as the discharging edge moves with greater +velocity than the locking. These points involve factors which must be +considered, and the drafting of a correct action is of paramount +importance; we therefore show the lift as it is accomplished in four +different stages in a good action. Fig. 9 illustrates the engaging, and +Fig. 10 the disengaging pallet; by comparing the figures it will be +noticed that the lift takes place on the point of the tooth similar to +the English, until the discharging edge of the pallet has been passed, +when the heel gradually comes into play on the engaging, but more +quickly on the disengaging pallet. + +We will also notice that during the first part of the lift the tooth +moves faster along the engaging lifting plane than on the disengaging; +on pallets 2 and 3 this difference is quite large; towards the latter +part of the lift the action becomes quicker on the disengaging pallet +and 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 the +disengaging pallets; the lifting planes on the teeth are also curved. +See Fig. 11. This is decidedly an ingenious arrangement, and is in +strict accordance with scientific investigation. We should see many fine +watches made with such escapements if the means for producing them could +fully satisfy the requirements of the scientific principles involved. + +[Illustration: Fig. 9.] + +The distribution of the lift on tooth and pallet is a very important +matter; the lifting angle on the tooth must be _less_ in proportion to +its width than it is on the pallet. For the sake of making it perfectly +plain, we illustrate what should not be made; if we have 10 1/2deg. for +width of tooth and pallet, and take half of it for a tooth, and the +other half for the pallet, making each of them 5 1/4deg. in width, and +suppose we have a lifting of 8 1/2deg. to distribute between them, by +allowing 4 1/4deg. on each, the lift would take place as shown in +Fig. 12, which is a very unfavorable action. The edge of the engaging +pallet scrapes on the lifting plane of the tooth, yet it is astonishing +to find some otherwise very fine watches being manufactured right along +which contain this fault; such watches can be stopped with the ruby pin +in the fork and the engaging pallet in action, nor would they start when +run down as soon as the 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 ratchet +they are constant, which is in its favor; in the latter it would always +be as SB, Fig. 13. This is a shorter lever than QB, consequently more +powerful, although the greater velocity is at Q, which only comes into +action after the inertia of wheel and pallets has been overcome, and +when the greatest momentum during contact is reached. SB is the +primitive radius of the club tooth wheel, but both primitive and _real_ +radius of the ratchet wheel. The distance of centers of wheel and pallet +will be alike in both cases; also the lockings will be the same distance +apart on both pallets; therefore, when horologists, even if they have +worldwide reputations, claim that the club tooth has an advantage over +the ratchet because it begins the lift with a shorter lever than the +latter, it does not make it so. We are treating the subject from a +purely horological standpoint, and neither patriotism or prejudice has +anything to do with it. We wish to sift the matter thoroughly and arrive +at a just conception of the merits and defects of each form of +escapement, 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 far +as the wheel is concerned the ratchet or English wheel has several +points in its favor. Such a wheel is inseparable from a wide pallet; but +we have seen that a narrower pallet is advisable; also as little drop +and lock as possible; clearly, we must effect a compromise. In other +words, so far the balance of our reasoning is in favor of the club tooth +escapement and to effect an intelligent division of angles for tooth, +pallet and lift is one of the great questions which confronts the +intelligent horologist. + +Anyone who has ever taken the pains to draw pallet and tooth with +different angles, through every stage of the lift, with both wide and +narrow pallets and teeth, in circular and equidistant escapements, will +have received an eye-opener. We strongly advise all our readers who are +practical workmen to try it after studying what we have said. We are +certain it will repay them. + +[Illustration: Fig. 2.] + +_The Center Distance of Wheel and Pallets._ The direction of pressure of +the wheel teeth should be through the pallet center by drawing the +tangents AC and AD, Fig. 2 to the primitive circle GH, at the +intersection of the angle FBE. This condition is realized in the +equidistant pallet. In the circular pallet, Fig. 3, this condition +cannot exist, as in order _to lock_ on a tangent the center distance +should be _greater_ for the engaging and _less_ for the disengaging +pallet, therefore watchmakers aim to go between the two and plant them +as before specified at A. + +When planted on the tangents the unlocking resistance will be less and +the impulse transmitted under favorable conditions, especially so in +the circular, as the direction of pressure coincides (close to the +center of the lift), with the law of the parallelogram of forces. + +It is _impossible_ to plant pallets on the tangents in very small +escapements, as there would not be enough room for a pallet arbor of +proper strength, nor will they be found planted on the tangents in the +medium size escapement with a long pallet arbor, nor in such a one with +a very wide tooth (see Fig. 4) as the heel would come so close to the +center A, that the solidity of pallets and arbor would suffer. We will +give an actual example. For a medium sized escape wheel with a primitive +diameter of 7.5 mm., the center distance AB is 4.33 mm. By using 3deg. of a +lifting angle on the teeth, the distance from the heel of the tooth to +the pallet center will be .4691 mm.; by allowing .1 mm. between wheel +and pallet and .15 mm. for stock on the pallets we find we will have a +pallet arbor as follows: .4691 - (.1 + .15) x 2 = .4382 mm. It would not +be practicable to make anything smaller. + +[Illustration: Fig. 3.] + +It behooves us now to see that while a narrow pallet is advisable a very +wide tooth is not; yet these two are inseparable. Here is another case +for a compromise, as, unquestionably the pallets ought to be planted on +the tangents. There is no difficulty about it in the English lever, and +we have shown in our example that a judiciously planned club tooth +escapement of medium size can be made with the center distance properly +planted. + +[Illustration: Fig. 4.] + +When considering the center distance we must of necessity consider the +widths of teeth and pallets and their lifting angles. We are now at a +point in which no watchmaker of intelligence would indicate one certain +division for these parts and claim it to be "the best." It is always +those who do not thoroughly understand a subject who are the first to +make such claims. We will, however, give our opinion within certain +limits. The angle to be divided for tooth and pallet is 10 1/2deg. Let us +divide it by 2, which would be the most natural thing to do, and examine +the problem. We will have 5 1/4deg. each for width of tooth and pallet. We +_must_ have a smaller lifting angle on the tooth than on the pallet, but +the wider the tooth the greater should its lifting angle be. It would +not be mechanical to make the tooth wide and the lifting angle small, as +the lifting plane on the pallets would be too steep on account of being +narrow. A lifting angle on the tooth which would be _exactly_ suitable +for a given circular, would be _too great_ for a given equidistant +pallet. It follows, therefore, taking 5 1/4deg. as a width for the +tooth, that while we could employ it in a fair sized escapement with +equidistant pallets, we could not do so with circular pallets and still +have the latter pitched on the tangents. We see the majority of +escapements made with narrower teeth than pallets, and for a very good +reason. + +In the example previously given, the 3deg. lift on the tooth is well +adapted for a width of 4 1/2deg., which would require a pallet 6deg. in +width. The tooth, therefore, would be 3/4 the width of pallets, which is +very good indeed. + +From what we have said it follows that a large number of pallets are not +planted on the tangents at all. We have never noticed this question in +print before. Writers generally seem to, in fact do, assume that no +matter how large or small the escapement may be, or how the pallets and +teeth are divided for width and lifting angle, no difficulty will be +found in locating the pallets on the tangents. Theoretically there is no +difficulty, but in practice we find there is. + +_Equidistant vs. Circular._ At this stage we are able to weigh the +circular against the equidistant pallet. In beginning this essay we had +to explain the difference between them, so the reader could follow our +discussion, and not until now, are we able to sum up our conclusions. + +The reader will have noticed that for such an important action as the +lift, which supplies power to the balance, the circular pallet is +favored from every point of view. This is a very strong point in its +favor. On the other hand, the unlocking resistance being less, and as +nearly alike as possible on both pallets in the equidistant, it is a +question if the total vibration of the balance will be greater with the +one than the other, although it will receive the impulse under better +conditions from the circular pallet; but it expends more force in +unlocking it. Escapement friction plays an important role in the +position and isochronal adjustments; the greater the friction +encountered the slower the vibration of the balance. The friction should +be constant. In unlocking, the equidistant comes nearer to fulfilling +this condition, while during the lift it is more nearly so in the +circular. The friction in unlocking, from a timing standpoint, +overshadows that of the impulse, and the tooth can be a little wider in +the equidistant than the circular escapement with the pallet properly +planted. Therefore for the _finest_ watches the equidistant escapement +is well adapted, but for anything less than that the circular should be +our choice. + +_The Fork and Roller Action._ While the lifting action of the lever +escapement corresponds to that of the cylinder, the fork and roller +action corresponds to the impulse action in the chronometer and duplex +escapements. + +Our experience leads us to believe that the action now under +consideration is but imperfectly understood by many workmen. It is a +complicated action, and when out of order is the cause of many annoying +stoppages, often characterized by the watch starting when taken from the +pocket. + +The action is very important and is generally divided into impulse and +safety action, although we think we ought to divide it into three, +namely, by adding that of the unlocking action. We will first of all +consider the impulse and unlocking actions, because we cannot +intelligently consider the one without the other, as the ruby pin and +the slot in the fork are utilized in each. The ruby pin, or strictly +speaking, the "impulse radius," is a lever arm, whose length is measured +from the center of the balance staff to the face of the ruby pin, and is +used, firstly, as a power or transmitting lever on the acting or +geometrical length of the fork (_i. e._, from the pallet center to the +beginning of the horn), and which at the moment is a resistance lever, +to be utilized in unlocking the pallets. After the pallets are unlocked +the conditions are reversed, and we now find the lever fork, through the +pallets, transmitting power to the balance by means of the impulse +radius. In the first part of the action we have a short lever engaging a +longer one, which is an advantage. See Fig. 14, where we have purposely +somewhat exaggerated the conditions. A'X represents the impulse radius +at present under discussion, and AW the acting length of the fork. It +will be seen that the shorter the impulse radius, or in other words, the +closer the ruby pin is to the balance staff and the longer the fork, the +easier will the unlocking of the pallets be performed, but this entails +a great impulse angle, for the law applicable to the case is, that the +angles are in the inverse ratio to the radii. In other words, the +shorter the radius, the greater is the angle, and the smaller the angle +the greater is the radius. We know, though, that we must have as small +an impulse angle as possible in order that the balance should be highly +detached. Here is one point in favor of a short impulse radius, and one +against it. Now, let us turn to the impulse action. Here we have the +long 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, which +would 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 the +theory of the free vibration of the balance, for, as before stated, the +longer the radius the smaller the angle. The action at P is also closer +to 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 consequently +a short radius, the intersection _m_ of the two circles _ii_ and _cc_ is +very _safe_, whereas, with the conditions reversed in favor of the +impulse action, the intersection at _k_ is more delicate. We have now +seen enough to appreciate the fact that we favor one action at the +expense of another. + +By having a lifting angle on pallet and tooth of 8 1/2deg., a locking +angle of 1 1/2deg., and a run of 1/2deg., we will have an angular +movement of the fork of 8 1/2 + 1 1/2 + 1/2 = 10 1/2deg. + +[Illustration: Fig. 15.] + +Writers generally only consider the movement of the fork from drop to +drop on the pallets, but we will be thoroughly practical in the matter. +With a total motion of the fork of 10 1/2deg. (JAW, Fig. 15), one-half, +or 5 1/4deg. will be performed on each side of the line of centers. We +are at liberty to choose any impulse angle which we may prefer; 3 to 1 +is a good proportion for an ordinary well-made watch. By employing it, +the angle XA'Y would be equal to 31 1/2deg. The radius A'X Fig. 16, is +also of the same proportion, but the angle AA'X is greater because the +fork angle WAA' is greater than the same angle in Fig. 15. We will +notice that the intersection _k_ is much smaller in Fig. 15 than in +Fig. 16. The action in the latter begins much further from the line of +centers than in the former 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, 4 +or even 5 to 1, while others for the finest of watches would only use +2.75 to 1. By having a total vibration of the balance of 1 1/2 turns, which +is equal to 540deg. a fork angle of 10deg. and a proportion of 2.75 for the +impulse angle which would be equal to 10 x 2.75 = 27.5deg. The _free_ +vibration of the balance, or as this is called, "the supplemental arc," +is equal to 540deg. - 27.5deg. = 512.50deg., while with a proportion of +5 to 1, making an impulse angle of 50deg., it would be equal to 490deg. +To sum up, the finer the watch the lower the proportion, the closer the +action to the line of centers, the smaller the friction. On account of +leverage the more difficult the unlocking but the more energetic the +impulse when it does occur. The velocity of the ruby pin at P; Fig. 14, +is much greater than at W, consequently it will not be overtaken as soon +by the fork as at W. The velocity of the fork at the latter point is +greater than at P; the intersection of _ii_ and _cc_ is also not as +great; therefore the lower the proportion the finer and more exact must +the workmanship be. + +We will notice that the unlocking action has been overruled by the +impulse. The only point so far in which the former has been favored is +in the diminished action before the line of centers, as previously +pointed out at P, Fig. 14. + +We will now consider the width of the ruby pin and to get a good insight +into the question, we will study Fig. 17. A is the pallet center, A' the +balance center, the line AA' being the line of centers; the angle WAA +equals 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 represents +half the impulse angle; the other half, the same as with the fork, is +struck on the other side of the center line. At the point of +intersection of these angles we will draw _cc_ from the pallet center A, +which equals the acting length of the fork, and from the balance center +we will draw _ii_, which equals the _theoretical_ impulse radius; some +writers use it as the _real_ radius. The wider the ruby pin the greater +will the latter be, which we will explain presently. + +The ruby pin in entering the fork must have a certain amount of freedom +for action, from 1 to 1 1/4deg. Should the watch receive a jar at the +moment the guard point enters the crescent or passing hollow in the +roller, the fork would fly against the ruby pin. It is important that +the angular freedom between the fork and ruby pin at the moment it +enters into the slot be _less_ than the total locking angle on the +pallets. If we employ a locking angle of 1 1/2deg. and 1/2deg. run, we +would have a total lock on the pallets of 2deg. By allowing 1 1/4deg. +of freedom for the ruby pin at the moment the guard point enters the +crescent, in case the fork should strike the face of the ruby pin, the +pallets will still be locked 3/4deg. and the fork drawn back against the +bankings through the draft angle. + +We will see what this shake amounts to for a given acting length of +fork, which describes an arc of a circle, therefore the acting length is +only the radius of that circle and must be multiplied by two in order to +get the diameter. The acting length of fork = 4.5 mm., what is the +amount of shake when the ruby pin passes the acting corner? +4.5 x 2 x 3.1416 / 360deg. = .0785 x 1.25 = .0992 mm. The shake of the ruby +pin in the slot of the fork must be as slight as possible, consistent +with perfect freedom of action. It varies from 1/4deg. to 1/2deg., +according to length of fork and shape of ruby pin. A square ruby pin +requires more shake than any other kind; it enters the fork and receives +the impulse in a diagonal direction on the jewel, in which position it +is illustrated at Z, Fig. 20. This ruby pin acts on a knife edge, but +for all that the engaging friction during the unlocking action is +considerable. + +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 of +A'X with AW, Fig. 17, we would require a _very_ narrow ruby pin. With +1deg. of freedom at the edge, and 1/2deg. in the slot, we could only +have a ruby pin of a width of 1 1/2deg. Applying it to the preceding +example it would only have an actual width of .0785 x 1.5 = .1178 mm., +or the size of an ordinary balance pivot. At _n_, Fig. 17, we illustrate +such a ruby pin; the theoretical and real impulse radius coincide with +one another. The intersection of the circle _ii_ and _cc_ is very +slight, while the friction in unlocking begins within 1deg. of half the +total movement of the fork from the line of centers; to illustrate, if +the angular motion is 11deg. the ruby pin under discussion will begin +action 4 1/2deg. before the line of centers, being an engaging, or +"uphill" friction of considerable magnitude. + +[Illustration: Fig. 17.] + +[Illustration: Fig. 18.] + +[Illustration: Fig. 19.] + +[Illustration: Fig. 20.] + +The intersection with the fork is also much less than with the wider +ruby pin, making the impulse action very delicate. On the other hand the +widest ruby pin for which there is any occasion is one beginning the +unlocking action on the line of centers, Fig. 17; this entails a width +of slot equal to the angular motion of the fork. We see here the +advantage of a wide ruby pin over a narrow one in the unlocking action. +Let us now examine the question from the standpoint of the impulse +action. + +Fig. 18 illustrates the moment the impulse is transmitted; the fork has +been moved in the direction of the arrow by the ruby pin; the escapement +has been unlocked and the opposite side of the slot has just struck the +ruby pin. The exact position in which the impulse is transmitted varies +with 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, which +is determined by the vibrations of the balance and the impulse radius. + +In an escapement with a total lock of 1 3/4deg. and 1 1/4 of shake in +the slot, theoretically, the impulse would be transmitted 2deg. from the +bankings. The narrow ruby pin n receives the impulse on the line _v_, +which is closer to the line of centers than the line _u_, on which the +large ruby pin receives the impulse. Here then we have an advantage of +the narrow ruby pin over a wide one; with a wider ruby pin the balance +is also more liable to rebank when it takes a long vibration. Also on +account of the greater angle at which the ruby pin stands to the slot +when the impulse takes place, the _drop_ of the fork against the jewel +will amount to more than its shake in the slot (which is measured when +standing on the line of centers). On this account some watches have +slots dovetailed in form, being wider at the bottom, others have ruby +pins of this form. They require very exact execution; we think we can do +without them by judiciously selecting a width of ruby pin between the +two extremes. We would choose a ruby pin of a width equal to half the +angular motion of the fork. There is an ingenious arrangement of fork +and roller which aims to, and partially does, overcome the difficulty of +choosing between a wide and narrow ruby pin, it is known as the Savage +pin roller escapement. We intend to describe it later. + +If the face of the ruby pin were planted on the theoretical impulse +radius _ii_, Fig. 19, the impulse would end in a butting action as +shown; hence the great importance of distinguishing between the +theoretical and real impulse radius and establishing a reliable data +from which to work. We feel that these actions have never been properly +and thoroughly treated in simple language; we have tried to make them +plain so that anyone can comprehend them with a little study. + +Three good forms of ruby pins are the triangular, the oval and the flat +faced; for ordinary work the latter is as good as any, but for fine work +the 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 the +parallelogram of forces is completely ignored by using such a pin; the +friction during the unlocking and impulse actions is too severe, as it +is, without the addition of so unmechanical an arrangement. Fig. 21 +illustrates the action of a round ruby pin; _ii_ is the path of the ruby +pin; _cc_ that of the acting length of the fork. It is shown at the +moment the impulse is transmitted. It will be seen that the impact takes +place _below_ the center of the ruby pin, whereas it should take place +at the center, as the motion of the fork is _upwards_ and that of the +ruby 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 the +right quantity be ground off. We find that 3/7 is approximately the +amount which should be ground away. Fig. 22 illustrates the fork +standing against the bank. The ruby pin touches the side of the slot but +has not as yet begun to act; _ri_ is the real impulse circle for which +we allow 1 1/4deg. of freedom at the acting edge of the fork; the face +of the ruby pin is therefore on this line. The next thing to do is to +find the center of the pin. From the side _n_ of the slot we construct +the right angle _o n t_; from _n_, we transmit 1/2 the width of the pin, +and plant the center _x_ on the line _n t_. We can have the center of +the pin slightly below this line, but in no case above it; but if we put +it below, the pin will be thinner and therefore more easily broken. + +[Illustration: Fig. 14.] + +_The Safety Action._ Although this action is separate from the impulse +and unlocking actions, it is still very closely connected with them, +much more so in the single than in the double roller escapement. If we +were to place the ruby pin at _X_, Fig. 14, we could have a much +smaller roller than by placing it at _P_. With the small roller the +safety action is more secure, as the intersection at _m_ is greater than +at _k_. It is not as liable to "butt" and the friction is less when the +guard point is thrown against the small roller. Suppose we take two +rollers, one with a diameter of 2.5 mm., the other just twice this +amount, of 5 mm. By having the guard radius and pressure the same in +each case, if the guard point touched the larger roller it would not +only have twice, but four times more effect than on the smaller one. We +will notice that the smaller the impulse angle the larger the roller, +because the ruby pin is necessarily placed farther from the center. The +position of the ruby pin should, therefore, govern the size of the +roller, which should be as small as possible. There should only be +enough metal left between the circumference of the roller and the face +of the jewel to allow for a crescent or passing hollow of sufficient +depth and an efficient setting for the jewel. For this reason, as well +as securing the correct impulse radius and therefore angle, when +replacing the ruby pin, and having it set securely and mechanically in +the roller, it is necessary that the pin and the hole in the roller be +of the same form, and a good fit. Fig. 23 illustrates the difference in +size of rollers. In the smaller one the conditions imposed are +satisfied, while in the larger one they are not. In the single roller +the safety action is at the mercy of the impulse and pallet angles. We +have noticed that in order to favor the impulse we require a large +roller, and for the safety action a small one, therefore escapements +made on fine principles are supplied with two rollers, one for each +action. + +It may be well to say that in our opinion a proportion between the fork +and impulse angles in 10deg. pallets of 3 or 3 1/2 to 1, _depending_ +upon the size of the escapement, is the lowest which should be made in +single roller. We have seen them in proportions of 2 to 1 in single +roller--a scientific principle foolishly applied--resulting in an action +entirely unsatisfactory. + +When the guard point is pressed against the roller the escape tooth +must still rest on the locking face of the pallet; if the total lock +is 2deg., by allowing 1 1/4deg. freedom for the guard point between +the bank and the roller the escapement will still be locked 3/4deg. +How much this shake actually amounts to depends upon the guard +radius. Suppose this to be 4 mm., then the freedom would equal +4 x 2 x 3.1416 / 360 x 1.25 = .0873 mm. + +[Illustration: Fig. 24.] + +[Illustration: Fig. 25.] + +_The Crescent_ in the roller must be large and deep enough so it will be +impossible for the guard point to touch in or on the corners of it; at +the same time it must not be too large, as it would necessitate a longer +horn on the fork than is necessary. + +Fig. 24 shows the slot _n_ of the fork standing at the bank. The ruby +pin _o_ touches it, but has not as yet acted on it; _s s_ illustrates a +single roller, while S2 illustrates the safety roller for a double +roller escapement. In order to find the dimensions of the crescent in +the single roller we must proceed as follows: WA is in the center of the +fork when it rests against the bank, and is, therefore, one of the sides +of the fork angle, and is drawn from the pallet center; V A W is an +angle of 1 1/4deg., which equals the freedom between the guard point and +the roller; _g g_ represents the path of the guard pin _u_ for the +single roller, and is drawn at the intersection of VA with the roller A' +A2 is a line drawn from the balance center through that of the ruby pin, +and therefore also passes through the center of the crescent. By +planting a compass on this line, where it cuts the periphery of the +roller, and locating the point of intersection of VA with the roller, +will give us one-half the crescent, the remaining half being transferred +to the opposite side of the line A' A2. We will notice that the guard +point has entered the crescent 1 1/4deg. before the fork begins to move. + +The angle of opening for the crescent in the double roller escapement is +greater than in the single, because it is placed closer to the balance +center, and the guard point or dart further from the pallet center, +causing a greater intersection; also the velocity of the guard point has +increased, while that of the safety roller has decreased. Fig. 24, at +_ff_, shows the path of the dart _h_, which also has 1 1/4deg. freedom +between bank and roller. From the balance center we draw A' _d_ touching +the center or point of the dart; from this point we construct at 5deg. +angle _b_ A' _d_. This is to ensure sufficient freedom for the dart when +entering the crescent. We plant a compass on the point of intersection +of 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, the +remaining half being constructed on the opposite side of the line A' A2. + +_The Horn_ on the fork belongs to the safety action: more horn is +required with the double than with the single roller, on account of the +greater angle of opening for the crescent. + +The horn should be of such a length that when the crescent has passed +the guard point, the end of the horn should point to at least the center +of the ruby pin. + +The dotted circle, _s s_, Fig. 25, represents a single roller. It will +be 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 accident +the _acting edge_ of the fork would come in contact with the ruby pin; +this proves that a well made single roller escapement really requires +but little horn, only enough to ensure the safe entry of the ruby pin in +case the guard point at that moment be thrown against the roller. We +will now examine the question from the standpoint of the double roller; +S2, Fig. 25, is the safety roller; the corner of the crescent has safely +passed the dart _h_; the centers of the ruby pin _o_ and of the crescent +being on the line A' A2, we plant the compass on the pallet center and +the center of the face of the ruby pin and draw _k k_, which will be the +path described by the horn. The end of the horn is therefore planted +upon it from 1 1/2deg. to 1 3/4deg. from the ruby pin; this freedom at +the end of the horn is therefore from 1/4deg. to 1/2deg. more than we +allow for the guard point; it depends upon the size of the escapement +and locking angles which we would choose. It must in any case be less +than the lock on the pallets, so that the fork will be drawn back +against the bank in case the horn be thrown against the ruby pin. + +When treating on the width of the ruby pin, we mentioned the Savage pin +roller escapement, which we illustrate in Figs. 26 and 27. This +ingenious arrangement was designed with the view of combining the +advantages of both wide and narrow pins and at the same time without any +of their disadvantages. + +In Fig. 26 we show the unlocking pins _u_ beginning their action on the +line of centers--the best possible point--in unlocking the escapement. +These pins were made of gold in all which we examined, although it is +recorded that wide ruby pins and ruby rollers have been used in this +escapement, which would be preferable. + +The functions of the two pins in the roller are simply to unlock the +escapement; the impulse is not transmitted to them as is the case in the +ordinary fork and roller action. In this action the guard pin _i_ also +acts as the impulse pin. We will notice that the passing hollow in this +roller is a rectangular slot the same as in the ordinary fork. When the +escapement is being unlocked the guard pin _i_ enters the hollow and +when the escape tooth comes into contact with the lifting plane of the +pallet 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 be +done with any ruby pin. If the pin _i_ were wider the impulse would be +transmitted still closer to the line of centers, but the intersection of +it with the roller would be less. It is very delicate as it is, +therefore from a practical standpoint it ought to be made thin but +consistent with solidity. If the pin is anyway large, it should be +flattened on the sides, otherwise the friction would be similar to that +of the round ruby pin. It would also be preferable (on account of the +pin _i_ being very easily bent) to make the impulse piece narrow but of +such a length that it could be screwed to the fork, the same as the dart +in the double roller. The impulse radius is also the radius of the +roller, because the impulse is transmitted to the roller itself; for +this reason the latter is smaller in this action than in the ordinary +one having the same angles; also a shorter lever is in contact with a +longer 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 of +the roller, as the angular connection of the balance with the escapement +would be increased during the unlocking action. This escapement being +very delicate requires a 12deg. pallet angle and a proportion between +impulse and pallet angles of not less than 3 to 1, which would mean an +impulse angle of 36deg.; this, together with the first rate workmanship +required are two of the reasons why this action is not often met with. + +George Savage, of London, England, invented this action. He was a +watchmaker who, in the early part of this century, did much to perfect +the lever escapement by good work and nice proportion, besides inventing +the two pin variety. He spent the early part of his life in Clerkenwell, +but in his old days emigrated to Canada, and founded a flourishing +retail business in Montreal, where he died. Some of George Savage's +descendants are still engaged at the trade in Canada at the present day. + +The correct delineation of the lever escapement is a very important +matter. We illustrate one which is so delineated that it can be +practically produced. We have not noticed a draft of the lever +escapement, especially with equidistant pallets and club teeth, which +would act correctly in a watch. + +We have been aggressive in our work and have sometimes found theories +propounded and elongated which of themselves were not right; this may +have something to do with it, that we so often hear workmen say, "Theory +is no use, because if you work according to it your machine will not +run." We say, "No, sir, if your theory is not right in itself, then your +work will certainly not be correct; but if your theory be correct then +your work _must_ be correct. Why? it simply cannot be otherwise." We +will give it another name; let us say, apply sense, reason, thought, +experience and study to your work, and what have you done? You have +simply applied theory. + +A theorem is a proposition to be proved, not being able to prove it, we +must simply change it according as our experience dictates, this is +precisely what we have done with the escapement after having followed +the deductions of recognized authorities with the result that we can now +illustrate an escapement which has been thoroughly subjected to an +impartial analysis in every respect, and which is theoretically and +practically correct. + +We will not only give instructions for drafting the escapement now under +consideration, but will also make explanations how to draft it in +different positions, also in circular pallet and single roller. We are +convinced that by so doing we will do a service to many, we also wish to +avoid what we may call "the stereotyped" process, that is, one which may +be acquired by heart, but introduce any changes and perplexity is the +result. It is really not a difficult matter to draft escapements in +different positions, as an example will show. + +Before making a draft we must know exactly what we wish to produce. It +is well in drafting escapements to make them as large as possible, say +thirty to forty times larger than in the watch, in the present case the +size is immaterial, but we must have specifications for the proportions +of the angles. Our draft is to be the most difficult subject in lever +escapements; it is to be represented just as if it were working in a +watch; it is to represent a good and reliable action in every respect, +one which can be applied without special difficulty to a good watch, and +is to be "up to date" in every particular and to contain the majority +of the best points and conclusions reached in our analysis. + +_Specifications for Lever Escapement_: The pallets are to be +equidistant; the wheel teeth of the "club" form; there are to be two +rollers; wheel, pallet, and balance centers are to be in straight line. +The lock is to be 1 1/2deg., the run 1/4deg., making a total lock of +1 3/4deg.; the movement of pallets from drop to drop is to be 10deg., +while the fork is to move through 10 1/4deg. from bank to bank; the lift +on the wheel teeth is to be 3deg., while the remainder is to be the lift +on the pallets as follows: 10 1/4 - (1 3/4 + 3) = 5 1/2deg. for lift of +pallets. + +The wheel is to have 15 teeth, with pallets spanning 3 teeth or 2 1/2 +spaces, making the angle from lock to lock = 360 / 15 x 2 1/2 = 60deg., +the interval from tooth to tooth is 360 / 15 = 24deg.; divided by 2 +pallets = 24 / 2 = 12deg. for width of tooth, pallet and drop; drop is +to be 1 1/2deg., the tooth is to be 3/4 the width of the pallet, making +a tooth of a width of 4 1/2deg. and a pallet of 6deg. + +The draw is to be 12deg. on each pallet, while the locking faces of the +teeth are to incline 24deg. The acting length of fork is to be equal to +the distance of centers of scape wheel and pallets; the impulse angle +is to be 28deg.; freedom from dart and safety, roller is to be +1 1/4deg., and for dart and corner of crescent 5deg.; freedom for ruby +pin and acting edge of fork is to be 1 1/4deg.; width of slot is to be +1/2 the total motion, or 10 1/4 / 2 = 5 1/8deg.; shake of ruby pin in +slot = 1/4deg., leaving 5 1/8 - 1/4 = 4 7/8deg. for width of ruby pin. + +Radius of safety roller to be 4/7 of the theoretical impulse radius. The +length of horn is to be such that the end would point at least to the +center 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 1 1/2deg. + +It is well to know that the angles for width of teeth, pallets and drop +are measured from the wheel center, while the lifting and locking angles +are struck from the pallet center, the draw from the locking corners of +the 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 ruby +pin with acting edge of fork and end of horn are all measured from the +pallet center, while the impulse angle and the crescent are measured +from the balance center. A sensible drawing board measures 17 x 24 +inches, we also require a set of good drawing instruments, the finer the +instruments the better; pay special attention to the compasses, pens and +protractor; add to this a straight ruler and set square. + +The best all-round drawing paper, both for India ink and colored work +has a rough surface; it must be fastened firmly and evenly to the board +by means of thumb tacks; the lines must be light and made with a hard +pencil. Use Higgins' India ink, which dries rapidly. + +[Illustration] + +We will begin by drawing the center line A' A B; use the point B for the +escape center; place the compass on it and strike G H, the primitive or +geometrical circle of the escape wheel; set the center of the protractor +at B and mark off an angle of 30deg. on each side of the line of centers; +this will give us the angles A B E and A B F together, forming the angle +F B E of 60deg., which represents from lock to lock of the pallets. Since +the chord of the angle of 60deg. is equal to the radius of the circle, this +gives us an easy means of verifying this angle by placing the compass at +the 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 points +we will construct right angles to E B and F B, thus forming the tangents +C A and D A to the primitive circle G H. These tangents meet on the line +of centers at A, which will be the pallet center. Place the compass at A +and draw the locking circle M N at the points of intersection of E B and +F B with the primitive circle G H. The locking edges of the pallets will +always stand on this circle no matter in what relation the pallets +stand to the wheel. Place the center of the protractor at B and draw the +angle of width of pallets of 6deg.; I B E being for the engaging and J B F +for the disengaging pallet. In the equidistant pallet I B is drawn on +the 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 pallets +would be placed on each side of E B and F B. At the points of +intersection of I B and J B with the primitive circle G H we draw the +path O for the discharging edge of the engaging and P for that of the +disengaging pallet. The total lock being 1 3/4deg., we construct V' A at +this angle from C A; the point of intersection of V' A with the locking +circle M N, is the position of the locking corner of the engaging +pallet. The pallet having 12deg. draw when locked we place the center of +the protractor on this corner and draw the angle Q M E. Q M will be the +locking face of the engaging pallet. If the face of the pallet were on +the line E B there would be no draw, and if placed to the opposite side +of E B the tooth would repel the pallet, forming what is known as the +repellant escapement. + +[Illustration: Fig. 28.] + +Having shown how to delineate the locking face of the engaging pallet +when locked, we will now consider how to draft both it and the +disengaging pallet in correct positions when unlocked; to do so we +direct our attention until further notice to Fig. 28. The locking faces +Q M of the engaging and S N of the disengaging pallets are shown in +dotted lines _when locked_. We must now consider the relation which the +locking faces will bear to E B in the engaging, and to F B in the +disengaging pallets when unlocked. This is a question of some +importance; it is easy enough to represent the 12deg. from the 30deg. +angles when locked; we must be certain that they would occupy exactly +that position and yet show them unlocked; we shall take pains to do so. +In due time we shall show that there is no appreciable loss of lift on +the engaging pallet in the escapement illustrated; the angle T A V +therefore shows the total lift; we have not shown the corresponding +angles on the disengaging side because the angles are somewhat +different, but the total lift is still the same. G H represents the +primitive circle of the escape wheel, and X Z that of the real, while +M N represents the circular course which the locking corners of the +pallets take in an equidistant escapement. At a convenient position we +will construct the circle C C' D from the pallet center A. Notice the +points _e_ and _c_, where V A and T A intersect this circle; the space +between _e_ and _c_ represents the extent of the motion of the pallets +at this particular distance from the center A; this being so, then let +us apply it to the engaging pallet. At the point of intersection _o_ of +the dotted line Q M (which is an extended line on which the face of the +pallet lies when locked), with the circle C C' D, we will plant our +dividers and transfer _e c_ to _o n_. By setting our dividers on _o_ M +and transferring to _n_ M', we will obtain the location of Q' M', the +locking face when unlocked. Let us now turn our attention to the +disengaging pallet. The dotted line S N represents the location of the +locking face of the disengaging pallet when locked at an angle of 12deg. +from F B. At the intersection of S N with the circle C C' D we obtain +the point _j_. The motion of the two pallets being equal, we transfer +the 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 the +line S' N' on which the locking face of the disengaging pallet will be +located when unlocked. It will be perfectly clear to anyone that through +these means we can correctly represent the pallets in any desired +position. + +We will notice that the face Q' M' of the engaging pallet when unlocked +stands at a greater angle to E B than it did when locked, while the +opposite is the case on the disengaging pallet, in which the angle +S' N' F is much less than S N F. This shows that the _deeper_ the +engaging pallet locks, the lighter will the draw be, while the opposite +holds good with the disengaging pallet; also, that the draw increases +during the unlocking of the engaging, and decreases during the unlocking +of the disengaging pallet. These points show that the draw should be +measured with the _fork standing against the bank_; not when the locking +corner of the pallet stands on the primitive circle, as is so often +done. The recoil of the wheel (which determines the draw), is +illustrated by the difference between the locking circle M N and the +face Q M for the engaging, and S N for the disengaging pallet, and along +the _acting_ surface it is alike on each pallet, showing that the draft +angle should be the same on each pallet. + +A number of years ago we constructed the escapement model which we +herewith illustrate. All the parts are adjustable; the pallets can be +moved in any direction, the draft angles can be changed at will. Through +this model we can practically demonstrate the points of which we have +spoken. Such a model can be made by workmen after studying these +papers. + +[Illustration] + +In both the equidistant and circular pallets the locking face S N of the +disengaging pallet deviates more from the locking circle M N than does +the locking face Q M of the engaging pallet, as will be seen in the +diagram. This is because the draft angle is struck from E B which +deviates from the locking circle in such a manner, that if the face of a +pallet were planted on it and _locked deep enough_ to show it, the +wheel would actually _repel_ the pallet, whereas with the disengaging +pallet if it were planted on F B, it would actually produce draw if +locked very deep; this is on account of the natural deviation of the 30deg. +lines from the locking circle. This difference is more pronounced in the +circular than in the equidistant pallet, because in the former we have +two locking circles, the larger one being for the engaging pallet, and +as an arc of a large circle does not deviate as much from a straight +line as does that of a smaller circle, it will be easily understood that +the natural difference before spoken of is only enhanced thereby. For +this reason in order to produce an _actual_ draw of 12deg., the engaging +pallet may be set at a slightly greater angle from E B in the circular +escapement; the amount depends upon the width of the pallets; the +requirements are that the recoil of the wheel will be the same on each +pallet. We must, however, repeat that one of the most important points +is to measure the draw when the fork stands against the bank, thereby +_increasing_ the draw on the engaging and _decreasing_ that of the +disengaging pallet _during_ the unlocking action, thus _naturally_ +balancing one fault with another. + +We will again proceed with the delineation of the escapement here +illustrated. After having drawn the locking face Q M, we draw the angle +of width of teeth of 4 1/2deg., by planting the protractor on the escape +center B. We measure the angle E B K, from the locking face of the +pallet; the line E B does not touch the locking face of the pallet at +the present time of contact with the tooth, therefore a line must be +drawn from the point of contact to the center B. We did so in our +drawing but do not illustrate it, as in a reduced engraving of this kind +it would be too close to E B and would only cause confusion. We will now +draw in the lifting angle of 3deg. for the tooth. From the tangent C A we +draw T A at the required angle; at the point of intersection of T A with +the 30deg. line E B we have the real circumference of the escape wheel. It +will only be necessary to connect the locking edge of the tooth with the +line K B, where the real or outer circle intersects it. It must be drawn +in the same manner in the circular escapement; if the tooth were drawn +up to the intersection of K B with T A, the lift would be too great, as +that 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 locking +circle M N and the path O of the discharging edge at the points where +T A intersects them, then there will be _no loss_ of lift on the +engaging pallet. This is precisely how it is in the diagram; but if +there 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 usually +done, as the real diameter of the wheel, or in other words the heel of +the tooth, forms the last point of contact. With a wider tooth and a +greater lifting angle there will even be a _gain_ of lift on the +engaging pallet; the pallet in such a case would actually require a +smaller lifting angle, according to the amount of gain. We gave full +directions for measuring the loss when describing its effects in Fig. 8. +Whatever the loss amounts to, it is added to the lifting plane of the +pallet. In the diagram under discussion there is no loss, consequently +the lifting angle on the pallet is to be 5 1/2deg. From V' A we draw V A at +the required angle; the point of intersection of V A with the path O +will be the discharging edge O. It will now only be necessary to connect +the locking corner M with it, and we have the lifting plane of the +pallet; the discharging side of the pallet is then drawn parallel to the +locking face and made a suitable length. We will now draw the locking +edges of the tooth by placing the center of the protractor on the +locking edge M and construct the angle B M M' of 24deg. and draw a circle +from the scape center B, to which the line M M' will be a tangent. We +will utilize this circle in drawing in the faces of the other teeth +after having spaced them off 24deg. apart, by simply putting a ruler on +the 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 3deg. for the teeth; this +corresponds to the angle T A C on the engaging side. W' A touches the +outer circle of the wheel at the intersection of F B with it. We will +notice that there is considerable deviation of W' A from the circle at +the intersection of J B with it. At the intersecting of this point we +draw U A; the angle U A W' is the loss of lift. This angle must be added +to the lifting angle of the pallets; we see that in this action there is +no loss on the engaging pallet, but on the disengaging the loss amounts +to approximately 7/8deg. in the action illustrated. As we have allowed +1/4deg. of run for the pallets, the discharging edge P is removed at +this angle from U A; we do not illustrate it, as the lines would cause +confusion being so close together. The lifting angle on the pallet is +measured from the point P and amounts to 5 1/2deg. + the angle of the +loss; the angle W A U embraces the above angles besides 1/4deg. for run. +If the locks are equal on each pallet, it proves that the lifts are also +equal. This gives us a practical method of proving the correctness of +the drawing; to do so, place the dividers on the locking circle M N at +the intersection 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 each pallet, the dividers will locate the point which the locking +corner N will occupy _when locked_; this, in the present case, will be +at an angle of 1 3/4deg. below the tangent D A. By this simple method, +the correctness of our proposition that the loss of lift should be +measured from the outside circle of the wheel, can be proven. We often +see the loss measured for the engaging pallet on the primitive +circumference G H, and on the real circumference for the disengaging; if +one is right then the other must be wrong, as there is a noticeable +deviation of the tangent C A from the primitive circle G H at the +intersection of the locking circle M N; had we added this amount to the +lifting angle V' A V of the engaging pallet, the result would have been +that the discharging edge O would be over 1deg. below its present +location, thus showing that by the time the lift on the engaging pallet +had been completed, the locking corner N of the disengaging pallet would +be locked at an angle of 2 3/4deg. instead of only 1 3/4deg. Many +watches contain precisely this fault. If we wish to make a draft showing +the pallets at any desired position, at the center of motion for +instance, with the fork standing on the line of centers, we would +proceed in the following manner: 10 1/4deg. being the total motion, +one-half would equal 5 1/8deg.; as the total lock equals 1 3/4deg., we +deduct this amount from it which leaves 5 1/8 - 1 3/4 = 3 3/8deg., which +is the angle at which the locking corner M should be shown above the +tangent C A. Now let us see where the locking corner N should stand; M +having moved up 5 1/8deg., therefore N moved down by that amount, the +lift on the pallet being 5 1/2deg. and on the tooth 3deg. (which is +added to the tangent D A), it follows that N should stand +5 1/2 + 3 - 5 1/8 = 3 3/8deg. above D A. We can prove it by the lock, +namely: 3 3/8deg. + 1 3/4 = 5 1/8deg., 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 as +measuring points. We have fully explained how to draw in the draft angle +on the pallets when unlocked, and do not require to repeat it, except to +say, 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 angle +of 12deg. from R N. We have drawn ours in by our own method, which is +the correct one. While we here illustrate S N R at an angle of 12deg. it +is in reality _less_ than that amount; had we constructed S N at an +angle of 12deg. from R N, then the draw would be 12deg. from F B, when +the primitive circumference of the wheel is reached, but _more_ than +12deg. when the fork is against the bank. + +The space between the discharging edge P and the heel of the tooth forms +the angle of drop J B I of 1 1/2deg.; the definition for drop is that it is +the freedom for wheel and pallet. This is not, strictly speaking, +perfectly correct, as, during the unlocking action there will be a +recoil of the wheel to the extent of the draft angle; the heel of the +tooth will therefore approach the edge P, and the discharging side of +the pallet approaches the tooth, as only the discharging edge moves on +the path P. + +A good length for the teeth is 1/10 the diameter of the wheel, measured +from 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 the +pallets, and are given a nice form; likewise the rim and arms are drawn +in as light and as neat as possible, consistent with strength. + +Having explained the delineation of the wheel and pallet action we will +now turn our attention to that of the fork and roller. We tried to +explain these actions in such a manner that by the time we came to +delineate them no difficulty would be found, as in our analysis we +discussed the subject sufficiently to enable any one of ordinary +intelligence to obtain a correct knowledge of them. The fork and roller +action in straight line, right, or any other angle is delineated after +the methods we are about to give. + +We specified that the acting length of fork was to be equal to the +center distance of wheel and pallets; this gives a fork of a fair +length. + +Having drawn the line of centers A' A we will construct an angle equal +to half the angular motion of the pallets; the latter in the case under +consideration being 10 1/4deg., therefore 5 1/8deg. is spaced off on +each side of the line of centers, forming the angles _m_ A _k_ of +10 1/4deg. Placing our dividers on A B the center distance of 'scape +wheel and pallets, we plant them on A and construct _c c_; thus we will +have the acting length of fork and its path. We saw in our analysis that +the impulse angle should be as small as possible. We will use one of +28deg. in our draft of the double roller; we might however remark that +this angle should vary with the construction of the escapements in +different watches; if too small, the balance may be stopped when the +escapement is locked, while if too great it can be stopped during the +lift; both these defects are to be avoided. The angles being +respectively 10 1/4deg. and 28deg. it follows they are of the following +proportions: 28deg. / 10.25 = 2.7316. The impulse radius therefore bears +this relation (but in the inverse ratio to the angles), to the acting +length of fork. + +We will put it in the following proportion; let A_c_ equal acting length +of fork, and _x_ the unknown quantity; 28:10.25 :: A_c_:_x_; the answer +will be the theoretical impulse radius. Having found the required radius +we plant one jaw of our measuring instrument on the point of +intersection of _c c_ with _k_ A or _m_ A and locate the other jaw on +the line of centers; we thus obtain A' the balance center. Through the +points of intersection before designated we will draft X A' and Y A' +forming the impulse angle X A' Y of 28deg. At the intersection of this +angle 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 +1 3/4deg. it follows that the angle described by the balance in +unlocking = 1 3/4 x 2.7316 = 4.788deg. According to the specifications +the width of slot is to be 5 1/8deg.; placing the center of the +protractor on A we construct half of this angle on each side of _k_ A, +which passes through the center of the fork when it rests against the +bank; this gives us the angle _s_ A _n_ of 5 1/8deg. If the disengaging +pallet were shown locked then _m_ A would represent the center of the +fork. The slot is to be made of sufficient depth so there will be no +possibility of the ruby pin touching the bottom of it. The ruby pin is +to have 1 1/4deg. freedom in passing the acting edge of the fork; from +the center A we construct the angle _t_ A _n_ of 1 1/4deg.; at the point +of intersection of _t_ A with _c c_ the acting radius of the fork, we +locate the real impulse radius and draw the arc _ri ri_ which describes +the path made by the face of the ruby pin. The ruby pin is to have +1/4deg. of shake in the slot; it will therefore have a width of +4 7/8deg.; this width is drawn in with the ruby pin imagined as standing +over the line of centers and is then transferred to the position which +the ruby pin is to occupy in the drawing. + +The radius of the safety roller was given as 4/7 of the theoretical +impulse radius. They may be made of various proportions; thus 2/3 is often +used. Remember that the smaller we make it, the less the friction during +accidental contact with the guard pin, the greater must the passing +hollow be and the horn of fork and guard point must be longer, which +increases the weight of the fork. + +Having drawn in the safety roller, and having specified that the freedom +between the dart and safety roller was to be 1 1/4deg., the dart being +in the center of the fork, consequently _k_ A is the center of it; +therefore we construct the angle _k_ A X of 1 1/4deg. At the point of +intersection of X A with the safety roller we draw the arc _g g_; this +locates the point of the dart which we will now draw in. We will next +draw _d_ A' from the balance center and touching the point of the dart; +we now construct _b_ A' at an angle of 5deg. to it. This is to allow the +necessary freedom for the dart when entering the crescent; from A' we +draw a line through the center of the ruby pin. We do not show it in the +drawing, as it would be indiscernible, coming very close to A' X. This +line will also pass through the center of the crescent. At the point of +intersection of A' _b_ with the safety roller we have one of the edges +of the crescent. By placing our compass at the center of the crescent on +the periphery of the roller and on the edge which we have just found, it +follows that our compass will span the radius of the crescent. We now +sweep the arc for the latter, thus also drawing in the remaining half of +the crescent on the other side of A' X and bringing the crescent of +sufficient depth that no possibility exists of the dart touching in or +on the edges of it. We will now draw in the impulse roller and make it +as light as possible consistent with strength. A hole is shown through +the impulse roller to counterbalance the reduced weight at the crescent. +When describing Fig. 24, we gave instructions for finding the dimensions +of crescent and position of guard pin for the single roller. We will +find the length of horn; to do so we must closely follow directions +given for Fig. 25. In locating the end of the horn, we must find the +location of the center of the crescent and ruby pin _after_ the edge of +the crescent has passed the dart. From the point of intersection of +A' _b_ with the safety roller we transfer the radius of the crescent on +the periphery of the safety roller towards the side against the bank, +then draw a line from A' through the point so found. At point of +intersection of this line with the real impulse circle _r i r i_ we draw +an arc radiating from 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 by the addition of all the constructional lines. We +specified that the freedom between ruby pin and end of horn was to be +1 1/2deg.; these lines, (which we do not show) are drawn from the pallet +center. Having located the end of the horn on the side standing against +the bank, we place 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 transfer this measurement along _g g_ which will locate the +end of the horn on the opposite side. + +We have the acting edges of the fork on _cc_ and have also found the +position of the ends of the horns; their curvature is drawn in the +following manner: We place our compasses on A and _r i_, spanning +therefore the real impulse radius; the compass is now set on the acting +edge of the fork and an arc swept with it which is then to be +intersected by another arc swept from the end of the horn, on the same +side of the fork. At the point of intersection of the arcs the compass +is planted and the curvature of the horn drawn in, the same operation is +to be repeated with the other horn. We will now draw in the sides of the +horn of such a form that should the watch rebank, the side of the ruby +pin will squarely strike the fork. If the back of the ruby pin strikes +the fork there will be a greater tendency of breaking it and injuring +the pivots on account of acting like a wedge. The fork and pallets are +now drawn in as lightly as possible and of such form as to admit of +their being readily poised. The banks are to be drawn at equal distances +from the line of centers. In delineating the fork and roller action in +any desired position, it must be remembered that the points of location +of the real impulse radius, the end of horn, the dart or guard pin and +crescent, must _all_ be obtained _when standing against the bank_, and +the arcs drawn which they describe; the parts are then located according +to the angle at which they are removed from the banks. + +We think the instructions given are ample to enable any one to master +the subject. We may add that when one becomes well acquainted with the +escapement, many of the angles radiating from a common center, may be +drawn in at once. We had intended describing the mechanical construction +of the escapement, which does unmistakably present some difficulties on +account of the small dimensions of the parts, but nevertheless it can be +mechanically executed true to the principles enumerated. We have evolved +a method of so producing them that young men in a comparatively short +period have made them from their drafts (without automatic machinery) +that their watches start off when run down the moment the crown is +touched. Perhaps later on we will write up the subject. It is our +intention of doing so, as we make use of such explanations in our +regular work. + + + + + +End of the Project Gutenberg EBook of An Analysis of the Lever Escapement, by +H. R. 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