,illustration3 ,,thomas ,,mudge ,the first ,horologist who successfully applied the ,detached ,lever ,escapement to ,watches4 ,born #agae--;,died #agid4 ,,an ,,analysis ,,of ,,the ,,lever ,,escapement ,,by ,h4 ,r4 ,,playtner4 ,a ,,lecture ,,delivered ,,before ,,the ,,canadian ,,watchmakers' ,,and ,,retail ,,jewelers' ,,association4 ,,illustrated4 ,,chicago3 ,,hazlitt ,,walker1 ,,publishers4 #aiaj4 ,,preface4 ,before entering upon our subject proper1 we think it advisable to explain a few points1 simple though they are1 which might cause confusion to some readers4 ,our experience has shown us that as soon as we use the words millimeter and degree1 perplexity is the result4 ,what is a millimeter8 is propounded to us very often in the course of a year2 nearly every new acquaintance is interested in having the metric system of measurement1 together with the fine gauges used1 explained to him4 ,the metric system of measurement originated at the time of the ,french ,revolution1 in the latter part of the #ahth century2 its divisions are decimal1 just the same as the system of currency we use in this country4 ,a meter is the ten millionth part of an arc of the meridian of ,paris1 drawn from the equator to the north pole2 as compared with the ,english inch there are #cicgjh_/ajjjj inches in a meter1 and there are #be4d millimeters in an inch4 ,the meter is sub-divided into decimeters1 centimeters and millimeters2 #a1jjj millimeters equal one meter2 the millimeter is again divided into #ajths and the #ajths into #ajjths of a millimeter1 which could be continued indefinitely4 ,the #a_/ajj millimeter is equal to the #a_/bedj of an inch4 ,these are measurements with which the watchmaker is concerned4 #a_/ajj millimeter1 written 4#ja mm41 is the side shake for a balance pivot2 multiply it by #b and we obtain the thickness for the spring detent of a pocket chronometer1 which is about the thickness of a human hair4 ,the metric system of measurement is used in all the watch factories of ,switzerland1 ,france1 ,germany1 and the ,united ,states1 and nearly all the lathe makers number their chucks by it1 and some of them cut the leading screws on their slide rests to it4 ,in any modern work on horology of value1 the metric system is used4 ,skilled horologists use it on account of its convenience4 ,the millimeter is a unit which can be handled on the small parts of a watch1 whereas the inch must always be divided on anything smaller than the plates4 ,equally as fine gauges can be and are made for the inch as for the metric system1 and the inch is decimally divided1 but we require another decimal point to express our measurement4 ,metric gauges can now be procured from the material shops2 they consist of tenth measures1 verniers and micrometers2 the finer ones of these come from ,glashutte1 and are the ones mentioned by ,grossmann in his essay on the lever escapement4 ,any workman who has once used these instruments could not be persuaded to do without them4 ,no one can comprehend the geometrical principles employed in escapements without a knowledge of angles and their measurements1 therefore we deem it of sufficient importance to at least explain what a degree is1 as we know for a fact1 that young workmen especially1 often fail to see how to apply it4 ,every circle1 no matter how large or small it may be1 contains #cfj2 a degree is therefore the #cfjth part of a circle2 it is divided into minutes1 seconds1 thirds1 etc4 ,to measure the value of a degree of any circle1 we must multiply the diameter of it by #c4adaf1 which gives us the circumference1 and then divide it by #cfj4 ,it will be seen that it depends on the size of that circle or its radius1 as to the value of a degree in any actual measurement4 ,to illustrate2 a degree on the earth's circumference measures #fj geographical miles1 while measured on the circumference of an escape wheel #g4e mm4 in diameter1 or as they would designate it in a material shop1 ,no4 #g1 it would be #g4e #c4adaf #cfj 4#jfee mm41 which is equal to the breadth of an ordinary human hair2 it is a degree in both cases1 but the difference is very great1 therefore a degree cannot be associated with any actual measurement until the radius of the circle is known4 ,degrees are generated from the center of the circle1 and should be thought of as to ascension or direction and relative value4 ,circles contain four right angles of #ij each4 ,degrees are commonly measured by means of the protractor1 although the ordinary instruments of this kind leave very much to be desired4 ,the lines can be verified by means of the compass1 which is a good practical method4 ,it may also be well to give an explanation of some of the terms used4 ,drop equals the amount of freedom which is allowed for the action of pallets and wheel4 ,see ,z1 ,fig4 #a4 ,primitive or ,geometrical ,diameter4--,in the ratchet tooth or ,english wheel1 the primitive and real diameter are equal2 in the club tooth wheel it means across the locking corners of the teeth2 in such a wheel1 therefore1 the primitive is less than the real diameter by the height of two impulse planes4 ,lock equals the depth of locking1 measured from the locking corner of the pallet at the moment the drop has occurred4 ,run equals the amount of angular motion of pallets and fork to the bankings after the drop has taken place4 ,total ,lock equals lock plus run4 ,a ,tangent is a line which touches a curve1 but does not intersect it4 ,,ac and ,,ad1 ,figs4 #b and #c1 are tangents to the primitive circle ,,gh at the points of intersection of ,,eb1 ,,ac1 and ,,gh and ,,fb1 ,,ad and ,,gh4 ,impulse ,angle equals the angular connection of the impulse or ruby pin with the lever fork2 or in other words1 of the balance with the escapement4 ,impulse ,radius4--,from the face of the impulse jewel to the center of motion1 which is in the balance staff1 most writers assume the impulse angle and radius to be equal1 and it is true that they must conform with one another4 ,we have made a radical change in the radius and one which does not affect the angle4 ,we shall prove this in due time1 and also that the wider the impulse pin the greater must the impulse radius be1 although the angle will remain unchanged4 ,right here we wish to put in a word of advice to all young men1 and that is to learn to draw4 ,no one can be a thorough watchmaker unless he can draw1 because he cannot comprehend his trade unless he can do so4 ,we know what it has done for us1 and we have noticed the same results with others1 therefore we speak from personal experience4 ,attend night schools and mechanic's institutes and improve yourselves4 ,the young workmen of ,toronto have a great advantage in the ,toronto ,technical ,school1 but we are sorry to see that out of some #fjj students1 only five watchmakers attended last year4 ,we can account for the majority of them1 so it would seem as if the young men of the trade were not much interested1 or thought they could not apply the knowledge to be gained there4 ,this is a great mistake2 we might almost say that knowledge of any kind can be applied to horology4 ,the young men who take up these studies1 will see the great advantage of them later on2 one workman will labor intelligently and the other do blind guess work4 ,we are now about to enter upon our subject and deem it well to say1 we have endeavored to make it as plain as possible4 ,it is a deep subject and is difficult to treat lightly2 we will treat it in our own way1 paying special attention to all these points which bothered us during the many years of painstaking study which we gave to the subject4 ,we especially endeavor to point out how theory can be applied to practice2 while we cannot expect that everyone will understand the subject without study1 we think we have made it comparatively easy of comprehension4 ,we will give our method of drafting the escapement1 which happens in some respects to differ from others4 ,we believe in making a drawing which we can reproduce in a watch4 ,,an ,,analysis ,,of ,,the ,,lever ,,escapement4 ,the lever escapement is derived from ,graham's dead-beat escapement for clocks4 ,thomas ,mudge was the first horologist who successfully applied it to watches in the detached form1 about #agej4 ,the locking faces of the pallets were arcs of circles struck from the pallet centers4 ,many improvements were made upon it until to-day it is the best form of escapement for a general purpose watch1 and when made on mechanical principles is capable of producing first rate results4 ,our object will be to explain the whys and wherefores of this escapement1 and we will at once begin with the number of teeth in the escape wheel4 ,it is not obligatory in the lever1 as in the verge1 to have an uneven number of teeth in the wheel4 ,while nearly all have #ae teeth1 we might make them of #ad or #af2 occasionally we find some in complicated watches of #ab teeth1 and in old ,english watches1 of #cj1 which is a clumsy arrangement1 and if the pallets embrace only three teeth in the latter1 the pallet center cannot be pitched on a tangent4 ,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 hand1 it is not1 strictly speaking1 necessary that it should do so1 as an example will show4 ,we will take an ordinary watch1 beating #cjj times per minute2 we will fit an escape wheel of #af teeth2 multiply this by #b1 as there is a forward and then a return motion of the balance and consequently two beats for each tooth1 making #af #b #cb beats for each revolution of the escape wheel4 #cjj beats are made per minute2 divide this by the beats made on each revolution1 and we have the number of times in which the escape wheel revolves per minute1 namely1 #cjj #cb #i4cge4 ,this number then is the proportion existing for the teeth and pitch diameters of the #dth wheel and escape pinion4 ,we must now find a suitable number of teeth for this wheel and pinion4 ,of available pinions for a watch1 the only one which would answer would be one of #h leaves1 as any other number would give a fractional number of teeth for the #dth wheel1 therefore #i4cge #h #ge teeth in #dth wheel4 ,now as to the proof3 as is well known1 if we multiply the number of teeth contained in #dth and escape wheels also by #b1 for the reason previously given1 and divide by the leaves in the escape pinion1 we get the number of beats made per minute2 therefore 7#ge #af #b7_/h #cjj beats per minute4 ,pallets can be made to embrace more than three teeth1 but would be much heavier and therefore the mechanical action would suffer4 ,they can also be made to embrace fewer teeth1 but the necessary side shake in the pivot holes would prove very detrimental to a total lifting angle of #aj1 which represents the angle of movement in modern watches4 ,some of the finest ones only make #h or #i of a movement2 the smaller the angle the greater will the effects of defective workmanship be2 #aj is a common-sense angle and gives a safe escapement capable of fine results4 ,theoretically1 if a timepiece could be produced in which the balance would vibrate without being connected with an escapement1 we would have reached a step nearer the goal4 ,practice has shown this to be the proper theory to work on4 ,hence1 the smaller the pallet and impulse angles the less will the balance and escapement be connected4 ,the chronometer is still more highly detached than the lever4 ,the pallet embracing three teeth is sound and practical1 and when applied to a #ae tooth wheel1 this arrangement offers certain geometrical and mechanical advantages in its construction1 which we will notice in due time4 #ae teeth divide evenly into #cfj leaving an interval of #bd from tooth to tooth1 which is also the angle at which the locking faces of the teeth are inclined from the center1 which fact will be found convenient when we come to cut our wheel4 ,from locking to locking on the pallet scaping over three teeth1 the angle is #fj1 which is equal to #b spaces of the wheel4 ,fig4 #a illustrates the lockings1 spanning this arc4 ,if the pallets embraced #d teeth1 the angle would be #hd2 or in case of a #af tooth wheel scaping over three teeth1 the angle would be #cfj #b4e_/af #ef4 ,illustration3 ,fig4 #a4 ,pallets may be divided into two kinds1 namely3 equidistant and circular4 ,the equidistant pallet is so-called because the lockings are an equal distance from the center2 sometimes it is also called the tangential escapement1 on account of the unlocking taking place on the intersection of tangent ,,ac with ,,eb1 and ,,fb with ,,ad1 the tangents1 which is the valuable feature of this form of escapement4 ,illustration3 ,fig4 #b4 ,,ac and ,,ad1 ,fig4 #b1 are tangents to the primitive circle ,,gh4 ,,abe and ,,abf are angles of #cj each1 together therefore forming the angle ,,fbe of #fj4 ,the locking circle ,,mn is struck from the pallet center ,a2 the interangles being equal1 consequently the pallets must be equidistant4 ,the weak point of this pallet is that the lifting is not performed so favorably2 by examining the lifting planes ,,mo and ,,np1 we see that the discharging edge1 ,o1 is closer to the center1 ,a1 than the discharging edge1 ,p2 consequently the lifting on the engaging pallet is performed on a shorter lever arm than on the disengaging pallet1 also any inequality in workmanship would prove more detrimental on the engaging than on the disengaging pallet4 ,the equidistant pallet requires fine workmanship throughout4 ,we have purposely shown it of a width of #aj1 which is the widest we can employ in a #ae tooth wheel1 and shows the defects of this escapement more readily than if we had used a narrow pallet4 ,a narrower pallet is advisable1 as the difference in the discharging edges will be less1 and the lifting arms would1 therefore1 not show so much difference in leverage4 ,illustration3 ,fig4 #c4 ,the circular pallet is sometimes appropriately called the pallet with equal lifts1 as the lever arms ,,amo and ,,anp1 ,fig4 #c1 are equal lengths4 ,it will be noticed by examining the diagram1 that the pallets are bisected by the #cj lines ,,eb and ,,fb1 one-half their width being placed on each side of these lines4 ,in this pallet we have two locking circles1 ,,mp for the engaging pallet1 and ,,no for the disengaging pallet4 ,the weak points in this escapement are that the unlocking resistance is greater on the engaging than on the disengaging pallet1 and that neither of them lock on the tangents ,,ac and ,,ad1 at the points of intersection with ,,eb and ,,fb4 ,the narrower the circular pallet is made1 the nearer to the tangent will the unlocking be performed4 ,in neither the equidistant or circular pallets can the unlocking resistance be exactly the same on each pallet1 as in the engaging pallet the friction takes place before ,,ab1 the line of centers1 which is more severe than when this line has been passed1 as is the case with the disengaging pallet2 this fact proportionately increases the existing defects of the circular over the equidistant pallet1 and vice versa1 but for the same reason1 the lifting in the equidistant is proportionately accompanied by more friction than in the circular4 ,both equidistant and circular pallets have their adherents2 the finest ,swiss1 ,french and ,german watches are made with equidistant escapements1 while the majority of ,english and ,american watches contain the circular4 ,in our opinion the ,english are wise in adhering to the circular form4 ,we think a ratchet wheel should not be employed with equidistant pallets4 ,by examining ,fig4 #b1 we see an ,english pallet of this form4 ,we have shown its defects in such a wide pallet as the ,english 7as we have before stated71 because they are more readily perceived2 also1 on account of the shape of the teeth1 there is danger of the discharging edge1 ,p1 dipping so deep into the wheel1 as to make considerable drop necessary1 or the pallets would touch on the backs of the teeth4 ,in the case of the club tooth1 the latter is hollowed out1 therefore1 less drop is required4 ,we have noticed that theoretically1 it is advantageous to make the pallets narrower than the ,english1 both for the equidistant and circular escapements4 ,there is an escapement1 ,fig4 #d1 which is just the opposite to the ,english4 ,the entire lift is performed by the wheel1 while in the case of the ratchet wheel1 the entire lifting angle is on the pallets2 also1 the pallets being as narrow as they can be made1 consistent with strength1 it has the good points of both the equidistant and circular pallets1 as the unlocking can be performed on the tangent and the lifting arms are of equal length4 ,the wheel1 however1 is so much heavier as to considerably increase the inertia2 also1 we have a metal surface of quite an extent sliding over a thin jewel4 ,for practical reasons1 therefore1 it has been slightly altered in form and is only used in cheap work1 being easily made4 ,illustration3 ,fig4 #d4 ,we will now consider the drop1 which is a clear loss of power1 and1 if excessive1 is the cause of much irregularity4 ,it should be as small as possible consistent with perfect freedom of action4 ,in so far as angular measurements are concerned1 no hard and fast rule can be applied to it1 the larger the escape wheel the smaller should be the angle allowed for drop4 ,authorities on the subject allow #a drop for the club and #b for the ratchet tooth4 ,it is a fact that escape wheels are not cut perfectly true2 the teeth are apt to bend slightly from the action of the cutters4 ,the truest wheel can be made of steel1 as each tooth can be successively ground after being hardened and tempered4 ,such a wheel would require less drop than one of any other metal4 ,supposing we have a wheel with a primitive diameter of #g4e mm41 what is the amount of drop1 allowing #a by angular measurement8 #g4e #c4adaf #cfj #a4e 4#jihc mm41 which is sufficient2 a hair could get between the pallet and tooth1 and would not stop the watch4 ,even after allowing for imperfectly divided teeth1 we require no greater freedom even if the wheel is larger4 ,now suppose we take a wheel with a primitive diameter of #h4e mm4 and find the amount of drop2 #h4e #c4adaf #cfj #a4e 4#adac mm41 or 4#adac - 4#jihc 4#jdc mm41 more drop than the smaller wheel1 if we take the same angle4 ,this is a waste of force4 ,the angular drop should1 therefore1 be proportioned according to the size of the wheel4 ,we wish it to be understood that common sense must always be our guide4 ,when the horological student once arrives at this standpoint1 he can intelligently apply himself to his calling4 ,the ,draw4--,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 function4 ,illustration3 ,fig4 #e4 ,pallets with draw are more difficult to unlock than those without it1 this is in the nature of a fault1 but whenever there are two faults we must choose the less4 ,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 center1 in which case the guard point would often remain against the roller4 ,the draw should be as light as possible consistent with safety of action2 some writers allow #ae on the engaging and #ab on the disengaging pallet2 others again allow #ab on each1 which we deem sufficient4 ,the draw is measured from the locking edges ,m and ,n1 ,fig4 #e4 ,the locking planes when locked are inclined #ab from ,,eb1 and ,,fb4 ,in the case of the engaging pallet it inclines toward the center ,a4 ,the draw is produced on account of ,,ma being longer than ,,ra1 consequently1 when power is applied to the scape tooth ,s1 the pallet is drawn into the wheel4 ,the disengaging pallet inclines in the same direction but away from the center ,a2 the reason is obvious from the former explanation4 ,some people imagine that the greater the incline on the locking edge of the escape teeth1 the stronger the draw would be4 ,this is not the case1 but it is certainly necessary that the point of the tooth alone should touch the pallet4 ,from this it follows that the angle on the teeth must be greater than on the pallets2 examine the disengaging pallet in ,fig4 #e1 as it is from this pallet that the inclination of the teeth must be determined1 as in the case of the engaging pallet the motion is toward the line of centers ,,ab1 and therefore away from the tooth1 which partially explains why some people advocate #ae draw for this pallet4 ,as illustrated in the case of the disengaging pallet1 however1 the motion is also towards the line of centers ,,ab1 and towards the tooth as well1 all of which will be seen by the dotted circles ,,mm#b and ,,nn#b1 representing the paths of the pallets4 ,it will be noticed that ,,unf and ,,bnb are opposite and equal angles of #ab4 ,for practical reasons1 from a manufacturing standpoint1 the angle on the tooth is made just twice the amount1 namely #bd2 we could make it a little less or a little more4 ,if we made it less than #bj too great a surface would be in contact with the jewel1 involving greater friction in unlocking and an inefficient draw1 but in the case of an ,english lever with such an arrangement we could do with less drop1 which advantage would be too dearly bought2 or if the angle is made over #bh1 the point or locking edge of the tooth would rapidly become worn in case of a brass wheel4 ,also in an ,english lever more drop would be required4 ,the ,lock4--,what we have said in regard to drop also applies to the lock1 which should be as small as possible1 consistent with perfect safety4 ,the greater the drop the deeper must be the lock2 #a is the angle generally allowed for the lock1 but it is obvious that in a large escapement it can be less4 ,illustration3 ,fig4 #f4 ,the ,run4--,the run or1 as it is sometimes called1 the slide1 should also be as light as possible2 from to is sufficient4 ,it follows then1 the bankings should be as close together as possible1 consistent with requisite freedom for escaping4 ,anything more than this increases the angular connection of the balance with the escapement1 which directly violates the theory under which it is constructed2 also1 a greater amount of work will be imposed upon the balance to meet the increased unlocking resistance1 resulting in a poor motion and accurate time will be out of the question4 ,it will be seen that those workmen who make a practice of opening the banks1 to give the escapement more freedom simply jump from the frying pan into the fire4 ,the bankings should be as far removed from the pallet center as possible1 as the further away they are pitched the less run we require1 according to angular measurement4 ,figure #f illustrates this fact2 the tooth ,s has just dropped on the engaging pallet1 but the fork has not yet reached the bankings4 ,at a we have #a of run1 while if placed at b we would only have of run1 but still the same freedom for escaping1 and less unlocking resistance4 ,the bankings should be placed towards the acting end of the fork as illustrated1 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 fork4 ,illustration3 ,fig4 #g4 ,the ,lift4--,the lift is composed of the actual lift on the teeth and pallets and the lock and run4 ,we will suppose that from drop to drop we allow #aj2 if the lock is #a then the actual lift by means of the inclined planes on teeth and pallets will be #h4 ,we have seen that a small lifting angle is advisable1 so that the vibrations of the balance will be as free as possible4 ,there are other reasons as well4 ,fig4 #g shows two inclined planes2 we desire to lift the weight #b a distance equal to the angle at which the planes are inclined2 it will be seen at a glance that we will have less friction by employing the smaller incline1 whereas with the larger one the motive power is employed through a greater distance on the object to be moved4 ,the smaller the angle the more energetic will the movement be2 the grinding of the angles and fit of the pivots1 etc41 also increases in importance4 ,an actual lift of #h satisfies the conditions imposed very well4 ,we have before seen that both on account of the unlocking and the lifting leverage of the pallet arms1 it would be advisable to make them narrow both in the equidistant and circular escapement4 ,we will now study the question from the standpoint of the lift1 in so far as the wheel is concerned4 ,illustration3 ,fig4 #h4 ,it is self-evident that a narrow pallet requires a wide tooth1 and a wide pallet a narrow or thin tooth wheel2 in the ratchet wheel we have a metal point passing over a jeweled plane4 ,the friction is at its minimum1 because there is less adhesion than with the club tooth1 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 tooth4 ,this seems to be a point which many do not thoroughly comprehend1 and we would advise a close study of ,fig4 #h1 which will make it perfectly clear1 as we show both a wide and a narrow pallet4 ,,gh1 represents the primitive1 which in this figure is also the real diameter of the escape wheel4 ,in measuring the lifting angles for the pallets1 our starting point is always from the tangents ,,ac and ,,ad4 ,the tangents are straight lines1 but the wheel describes the circle ,,gh1 therefore they must deviate from one another1 and the closer to the center ,a the discharging edge of the engaging pallet reaches1 the greater does this difference become2 and in the same manner the further the discharging edge of the disengaging pallet is from the center ,a the greater it is4 ,this shows that the loss is greater in the equidistant than in the circular escapement4 ,after this we will designate this difference as the loss4 ,in order to illustrate it more plainly we show the widest pallet--the ,english--in equidistant form4 ,this gives another reason why the ,english lever should only be made with circular pallets1 as we have seen that the wider the pallet the greater the loss4 ,the loss is measured at the intersection of the path of the discharging edge ,,oo1 with the circle ,g ,h1 and is shown through ,,ac#b1 which intersects these circles at that point4 ,in the case of the disengaging pallet1 ,,pp illustrates the path of the discharging edge2 the loss is measured as in the preceding case where ,,gh is intersected as shown by ,,ad#b4 ,it amounts to a different value on each pallet4 ,notice the loss between ,c and ,c#b1 on the engaging1 and ,d and ,d#b on the disengaging pallet2 it is greater on the engaging pallet1 so much so that it amounts to #b1 which is equal to the entire lock2 therefore if #h of work is to be accomplished through this pallet1 the lifting plane requires an angle of #aj struck from ,,ac4 ,let us now consider the lifting action of the club tooth wheel4 ,this is decidedly a complicated action1 and requires some study to comprehend4 ,in action with the engaging pallet the wheel moves up1 or in the direction of the motion of the pallets1 but on the disengaging pallet it moves down1 and in a direction opposite to the pallets1 and the heel of the tooth moves with greater velocity than the locking edge2 also in the case of the engaging pallet1 the locking edge moves with greater velocity than the discharging edge2 in the disengaging pallet the opposite is the case1 as the discharging edge moves with greater velocity than the locking4 ,these points involve factors which must be considered1 and the drafting of a correct action is of paramount importance2 we therefore show the lift as it is accomplished in four different stages in a good action4 ,fig4 #i illustrates the engaging1 and ,fig4 #aj the disengaging pallet2 by comparing the figures it will be noticed that the lift takes place on the point of the tooth similar to the ,english1 until the discharging edge of the pallet has been passed1 when the heel gradually comes into play on the engaging1 but more quickly on the disengaging pallet4 ,we will also notice that during the first part of the lift the tooth moves faster along the engaging lifting plane than on the disengaging2 on pallets #b and #c this difference is quite large2 towards the latter part of the lift the action becomes quicker on the disengaging pallet and slower on the engaging4 ,to obviate this difficulty some fine watches1 notably those of ,a4 ,lange ,sons1 have convex lifting planes on the engaging and concave on the disengaging pallets2 the lifting planes on the teeth are also curved4 ,see ,fig4 #aa4 ,this is decidedly an ingenious arrangement1 and is in strict accordance with scientific investigation4 ,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 involved4 ,illustration3 ,fig4 #i4 ,the distribution of the lift on tooth and pallet is a very important matter2 the lifting angle on the tooth must be less in proportion to its width than it is on the pallet4 ,for the sake of making it perfectly plain1 we illustrate what should not be made2 if we have #aj for width of tooth and pallet1 and take half of it for a tooth1 and the other half for the pallet1 making each of them #e in width1 and suppose we have a lifting of #h to distribute between them1 by allowing #d on each1 the lift would take place as shown in ,fig4 #ab1 which is a very unfavorable action4 ,the edge of the engaging pallet scrapes on the lifting plane of the tooth1 yet it is astonishing to find some otherwise very fine watches being manufactured right along which contain this fault2 such watches can be stopped with the ruby pin in the fork and the engaging pallet in action1 nor would they start when run down as soon as the crown is touched1 no matter how well they were finished and fitted4 ,illustration3 ,fig4 #aj4 ,the lever lengths of the club tooth are variable1 while with the ratchet they are constant1 which is in its favor2 in the latter it would always be as ,,sb1 ,fig4 #ac4 ,this is a shorter lever than ,,qb1 consequently more powerful1 although the greater velocity is at ,q1 which only comes into action after the inertia of wheel and pallets has been overcome1 and when the greatest momentum during contact is reached4 ,,sb is the primitive radius of the club tooth wheel1 but both primitive and real radius of the ratchet wheel4 ,the distance of centers of wheel and pallet will be alike in both cases2 also the lockings will be the same distance apart on both pallets2 therefore1 when horologists1 even if they have worldwide reputations1 claim that the club tooth has an advantage over the ratchet because it begins the lift with a shorter lever than the latter1 it does not make it so4 ,we are treating the subject from a purely horological standpoint1 and neither patriotism or prejudice has anything to do with it4 ,we wish to sift the matter thoroughly and arrive at a just conception of the merits and defects of each form of escapement1 and show reasons for our conclusions4 ,illustration3 ,fig4 #aa4 ,illustration3 ,fig4 #ab4 ,illustration3 ,fig4 #ac4 ,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 favor4 ,such a wheel is inseparable from a wide pallet2 but we have seen that a narrower pallet is advisable2 also as little drop and lock as possible2 clearly1 we must effect a compromise4 ,in other words1 so far the balance of our reasoning is in favor of the club tooth escapement and to effect an intelligent division of angles for tooth1 pallet and lift is one of the great questions which confronts the intelligent horologist4 ,anyone who has ever taken the pains to draw pallet and tooth with different angles1 through every stage of the lift1 with both wide and narrow pallets and teeth1 in circular and equidistant escapements1 will have received an eye-opener4 ,we strongly advise all our readers who are practical workmen to try it after studying what we have said4 ,we are certain it will repay them4 ,illustration3 ,fig4 #b4 ,the ,center ,distance of ,wheel and ,pallets4 ,the direction of pressure of the wheel teeth should be through the pallet center by drawing the tangents ,,ac and ,,ad1 ,fig4 #b to the primitive circle ,,gh1 at the intersection of the angle ,,fbe4 ,this condition is realized in the equidistant pallet4 ,in the circular pallet1 ,fig4 #c1 this condition cannot exist1 as in order to lock on a tangent the center distance should be greater for the engaging and less for the disengaging pallet1 therefore watchmakers aim to go between the two and plant them as before specified at ,a4 ,when planted on the tangents the unlocking resistance will be less and the impulse transmitted under favorable conditions1 especially so in the circular1 as the direction of pressure coincides 7close to the center of the lift71 with the law of the parallelogram of forces4 ,it is impossible to plant pallets on the tangents in very small escapements1 as there would not be enough room for a pallet arbor of proper strength1 nor will they be found planted on the tangents in the medium size escapement with a long pallet arbor1 nor in such a one with a very wide tooth 7see ,fig4 #d7 as the heel would come so close to the center ,a1 that the solidity of pallets and arbor would suffer4 ,we will give an actual example4 ,for a medium sized escape wheel with a primitive diameter of #g4e mm41 the center distance ,,ab is #d4cc mm4 ,by using #c of a lifting angle on the teeth1 the distance from the heel of the tooth to the pallet center will be 4#dfia mm42 by allowing 4#a mm4 between wheel and pallet and 4#ae mm4 for stock on the pallets we find we will have a pallet arbor as follows3 4#dfia - 74#a 4#ae7 #b 4#dchb mm4 ,it would not be practicable to make anything smaller4 ,illustration3 ,fig4 #c4 ,it behooves us now to see that while a narrow pallet is advisable a very wide tooth is not2 yet these two are inseparable4 ,here is another case for a compromise1 as1 unquestionably the pallets ought to be planted on the tangents4 ,there is no difficulty about it in the ,english lever1 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 planted4 ,illustration3 ,fig4 #d4 ,when considering the center distance we must of necessity consider the widths of teeth and pallets and their lifting angles4 ,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 best4 ,it is always those who do not thoroughly understand a subject who are the first to make such claims4 ,we will1 however1 give our opinion within certain limits4 ,the angle to be divided for tooth and pallet is #aj4 ,let us divide it by #b1 which would be the most natural thing to do1 and examine the problem4 ,we will have #e each for width of tooth and pallet4 ,we must have a smaller lifting angle on the tooth than on the pallet1 but the wider the tooth the greater should its lifting angle be4 ,it would not be mechanical to make the tooth wide and the lifting angle small1 as the lifting plane on the pallets would be too steep on account of being narrow4 ,a lifting angle on the tooth which would be exactly suitable for a given circular1 would be too great for a given equidistant pallet4 ,it follows1 therefore1 taking #e as a width for the tooth1 that while we could employ it in a fair sized escapement with equidistant pallets1 we could not do so with circular pallets and still have the latter pitched on the tangents4 ,we see the majority of escapements made with narrower teeth than pallets1 and for a very good reason4 ,in the example previously given1 the #c lift on the tooth is well adapted for a width of #d1 which would require a pallet #f in width4 ,the tooth1 therefore1 would be the width of pallets1 which is very good indeed4 ,from what we have said it follows that a large number of pallets are not planted on the tangents at all4 ,we have never noticed this question in print before4 ,writers generally seem to1 in fact do1 assume that no matter how large or small the escapement may be1 or how the pallets and teeth are divided for width and lifting angle1 no difficulty will be found in locating the pallets on the tangents4 ,theoretically there is no difficulty1 but in practice we find there is4 ,equidistant vs4 ,circular4 ,at this stage we are able to weigh the circular against the equidistant pallet4 ,in beginning this essay we had to explain the difference between them1 so the reader could follow our discussion1 and not until now1 are we able to sum up our conclusions4 ,the reader will have noticed that for such an important action as the lift1 which supplies power to the balance1 the circular pallet is favored from every point of view4 ,this is a very strong point in its favor4 ,on the other hand1 the unlocking resistance being less1 and as nearly alike as possible on both pallets in the equidistant1 it is a question if the total vibration of the balance will be greater with the one than the other1 although it will receive the impulse under better conditions from the circular pallet2 but it expends more force in unlocking it4 ,escapement friction plays an important role in the position and isochronal adjustments2 the greater the friction encountered the slower the vibration of the balance4 ,the friction should be constant4 ,in unlocking1 the equidistant comes nearer to fulfilling this condition1 while during the lift it is more nearly so in the circular4 ,the friction in unlocking1 from a timing standpoint1 overshadows that of the impulse1 and the tooth can be a little wider in the equidistant than the circular escapement with the pallet properly planted4 ,therefore for the finest watches the equidistant escapement is well adapted1 but for anything less than that the circular should be our choice4 ,the ,fork and ,roller ,action4 ,while the lifting action of the lever escapement corresponds to that of the cylinder1 the fork and roller action corresponds to the impulse action in the chronometer and duplex escapements4 ,our experience leads us to believe that the action now under consideration is but imperfectly understood by many workmen4 ,it is a complicated action1 and when out of order is the cause of many annoying stoppages1 often characterized by the watch starting when taken from the pocket4 ,the action is very important and is generally divided into impulse and safety action1 although we think we ought to divide it into three1 namely1 by adding that of the unlocking action4 ,we will first of all consider the impulse and unlocking actions1 because we cannot intelligently consider the one without the other1 as the ruby pin and the slot in the fork are utilized in each4 ,the ruby pin1 or strictly speaking1 the impulse radius1 is a lever arm1 whose length is measured from the center of the balance staff to the face of the ruby pin1 and is used1 firstly1 as a power or transmitting lever on the acting or geometrical length of the fork 7i4 e41 from the pallet center to the beginning of the horn71 and which at the moment is a resistance lever1 to be utilized in unlocking the pallets4 ,after the pallets are unlocked the conditions are reversed1 and we now find the lever fork1 through the pallets1 transmitting power to the balance by means of the impulse radius4 ,in the first part of the action we have a short lever engaging a longer one1 which is an advantage4 ,see ,fig4 #ad1 where we have purposely somewhat exaggerated the conditions4 ,a,x represents the impulse radius at present under discussion1 and ,,aw the acting length of the fork4 ,it will be seen that the shorter the impulse radius1 or in other words1 the closer the ruby pin is to the balance staff and the longer the fork1 the easier will the unlocking of the pallets be performed1 but this entails a great impulse angle1 for the law applicable to the case is1 that the angles are in the inverse ratio to the radii4 ,in other words1 the shorter the radius1 the greater is the angle1 and the smaller the angle the greater is the radius4 ,we know1 though1 that we must have as small an impulse angle as possible in order that the balance should be highly detached4 ,here is one point in favor of a short impulse radius1 and one against it4 ,now1 let us turn to the impulse action4 ,here we have the long lever ,,aw acting on a short one1 ,a,x1 which is a disadvantage4 ,here1 then1 we ought to try and have a short lever acting on a long one1 which would point to a short fork and a great impulse radius4 ,suppose ,,ap1 ,fig4 #ad1 is the length of fork1 and ,a,p is the impulse radius2 here1 then1 we favor the impulse1 and it is directly in accordance with the theory of the free vibration of the balance1 for1 as before stated1 the longer the radius the smaller the angle4 ,the action at ,p is also closer to the line of centers than it is at ,w1 which is another advantage4 ,illustration3 ,fig4 #ad4 ,we will notice that by employing a large impulse angle1 and consequently a short radius1 the intersection m of the two circles ii and cc is very safe1 whereas1 with the conditions reversed in favor of the impulse action1 the intersection at k is more delicate4 ,we have now seen enough to appreciate the fact that we favor one action at the expense of another4 ,by having a lifting angle on pallet and tooth of #h1 a locking angle of #a1 and a run of 1 we will have an angular movement of the fork of #h #a #aj4 ,illustration3 ,fig4 #ae4 ,writers generally only consider the movement of the fork from drop to drop on the pallets1 but we will be thoroughly practical in the matter4 ,with a total motion of the fork of #aj 7,,jaw1 ,fig4 #ae71 one-half1 or #e will be performed on each side of the line of centers4 ,we are at liberty to choose any impulse angle which we may prefer2 #c to #a is a good proportion for an ordinary well-made watch4 ,by employing it1 the angle ,,xa,y would be equal to #ca4 ,the radius ,a,x ,fig4 #af1 is also of the same proportion1 but the angle ,,aa,x is greater because the fork angle ,,waa is greater than the same angle in ,fig4 #ae4 ,we will notice that the intersection k is much smaller in ,fig4 #ae than in ,fig4 #af4 ,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 made4 ,illustration3 ,fig4 #af4 ,to come back to the impulse angle1 some might use a proportion of #c4e1 #d or even #e to #a1 while others for the finest of watches would only use #b4ge to #a4 ,by having a total vibration of the balance of #a turns1 which is equal to #edj a fork angle of #aj and a proportion of #b4ge for the impulse angle which would be equal to #aj #b4ge #bg4e4 ,the free vibration of the balance1 or as this is called1 the supplemental arc1 is equal to #edj - #bg4e #eab4ej1 while with a proportion of #e to #a1 making an impulse angle of #ej1 it would be equal to #dij4 ,to sum up1 the finer the watch the lower the proportion1 the closer the action to the line of centers1 the smaller the friction4 ,on account of leverage the more difficult the unlocking but the more energetic the impulse when it does occur4 ,the velocity of the ruby pin at ,p2 ,fig4 #ad1 is much greater than at ,w1 consequently it will not be overtaken as soon by the fork as at ,w4 ,the velocity of the fork at the latter point is greater than at ,p2 the intersection of ii and cc is also not as great2 therefore the lower the proportion the finer and more exact must the workmanship be4 ,we will notice that the unlocking action has been overruled by the impulse4 ,the only point so far in which the former has been favored is in the diminished action before the line of centers1 as previously pointed out at ,p1 ,fig4 #ad4 ,we will now consider the width of the ruby pin and to get a good insight into the question1 we will study ,fig4 #ag4 ,a is the pallet center1 ,a the balance center1 the line ,,aa being the line of centers2 the angle ,,waa equals half the total motion of the fork1 the other half1 of course1 taking place on the opposite side of the center line4 ,,wa is the center of the fork when it rests against the bank4 ,the angle ,,aa,x represents half the impulse angle2 the other half1 the same as with the fork1 is struck on the other side of the center line4 ,at the point of intersection of these angles we will draw cc from the pallet center ,a1 which equals the acting length of the fork1 and from the balance center we will draw ii1 which equals the theoretical impulse radius2 some writers use it as the real radius4 ,the wider the ruby pin the greater will the latter be1 which we will explain presently4 ,the ruby pin in entering the fork must have a certain amount of freedom for action1 from #a to #a4 ,should the watch receive a jar at the moment the guard point enters the crescent or passing hollow in the roller1 the fork would fly against the ruby pin4 ,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 pallets4 ,if we employ a locking angle of #a and run1 we would have a total lock on the pallets of #b4 ,by allowing #a of freedom for the ruby pin at the moment the guard point enters the crescent1 in case the fork should strike the face of the ruby pin1 the pallets will still be locked and the fork drawn back against the bankings through the draft angle4 ,we will see what this shake amounts to for a given acting length of fork1 which describes an arc of a circle1 therefore the acting length is only the radius of that circle and must be multiplied by two in order to get the diameter4 ,the acting length of fork #d4e mm41 what is the amount of shake when the ruby pin passes the acting corner8 #d4e #b #c4adaf #cfj 4#jghe #a4be 4#jiib mm4 ,the shake of the ruby pin in the slot of the fork must be as slight as possible1 consistent with perfect freedom of action4 ,it varies from to 1 according to length of fork and shape of ruby pin4 ,a square ruby pin requires more shake than any other kind2 it enters the fork and receives the impulse in a diagonal direction on the jewel1 in which position it is illustrated at ,z1 ,fig4 #bj4 ,this ruby pin acts on a knife edge1 but for all that the engaging friction during the unlocking action is considerable4 ,our reasoning tells us it matters not if a ruby pin be wide or narrow1 it must have the same freedom in passing the acting edge of the fork1 therefore1 to have the impulse radius on the point of intersection of ,a,x with ,,aw1 ,fig4 #ag1 we would require a very narrow ruby pin4 ,with #a of freedom at the edge1 and in the slot1 we could only have a ruby pin of a width of #a4 ,applying it to the preceding example it would only have an actual width of 4#jghe #a4e 4#aagh mm41 or the size of an ordinary balance pivot4 ,at n1 ,fig4 #ag1 we illustrate such a ruby pin2 the theoretical and real impulse radius coincide with one another4 ,the intersection of the circle ii and cc is very slight1 while the friction in unlocking begins within #a of half the total movement of the fork from the line of centers2 to illustrate1 if the angular motion is #aa the ruby pin under discussion will begin action #d before the line of centers1 being an engaging1 or uphill friction of considerable magnitude4 ,illustration3 ,fig4 #ag4 ,illustration3 ,fig4 #ah4 ,illustration3 ,fig4 #ai4 ,illustration3 ,fig4 #bj4 ,the intersection with the fork is also much less than with the wider ruby pin1 making the impulse action very delicate4 ,on the other hand the widest ruby pin for which there is any occasion is one beginning the unlocking action on the line of centers1 ,fig4 #ag2 this entails a width of slot equal to the angular motion of the fork4 ,we see here the advantage of a wide ruby pin over a narrow one in the unlocking action4 ,let us now examine the question from the standpoint of the impulse action4 ,fig4 #ah illustrates the moment the impulse is transmitted2 the fork has been moved in the direction of the arrow by the ruby pin2 the escapement has been unlocked and the opposite side of the slot has just struck the ruby pin4 ,the exact position in which the impulse is transmitted varies with the locking angle1 the width of ruby pin1 its shake in the slot1 the length of fork1 its weight1 and the velocity of the ruby pin1 which is determined by the vibrations of the balance and the impulse radius4 ,in an escapement with a total lock of #a and #a of shake in the slot1 theoretically1 the impulse would be transmitted #b from the bankings4 ,the narrow ruby pin n receives the impulse on the line v1 which is closer to the line of centers than the line u1 on which the large ruby pin receives the impulse4 ,here then we have an advantage of the narrow ruby pin over a wide one2 with a wider ruby pin the balance is also more liable to rebank when it takes a long vibration4 ,also on account of the greater angle at which the ruby pin stands to the slot when the impulse takes place1 the drop of the fork against the jewel will amount to more than its shake in the slot 7which is measured when standing on the line of centers74 ,on this account some watches have slots dovetailed in form1 being wider at the bottom1 others have ruby pins of this form4 ,they require very exact execution2 we think we can do without them by judiciously selecting a width of ruby pin between the two extremes4 ,we would choose a ruby pin of a width equal to half the angular motion of the fork4 ,there is an ingenious arrangement of fork and roller which aims to1 and partially does1 overcome the difficulty of choosing between a wide and narrow ruby pin1 it is known as the ,savage pin roller escapement4 ,we intend to describe it later4 ,if the face of the ruby pin were planted on the theoretical impulse radius ii1 ,fig4 #ai1 the impulse would end in a butting action as shown2 hence the great importance of distinguishing between the theoretical and real impulse radius and establishing a reliable data from which to work4 ,we feel that these actions have never been properly and thoroughly treated in simple language2 we have tried to make them plain so that anyone can comprehend them with a little study4 ,three good forms of ruby pins are the triangular1 the oval and the flat faced2 for ordinary work the latter is as good as any1 but for fine work the triangular pin with the corners slightly rounded off is preferable4 ,illustration3 ,fig4 #ba4 ,illustration3 ,fig4 #bc4 ,illustration3 ,fig4 #bb4 ,english watches are met with having a cylindrical or round ruby pin4 ,such a pin should never be put into a watch4 ,the law of the parallelogram of forces is completely ignored by using such a pin2 the friction during the unlocking and impulse actions is too severe1 as it is1 without the addition of so unmechanical an arrangement4 ,fig4 #ba illustrates the action of a round ruby pin2 ii is the path of the ruby pin2 cc that of the acting length of the fork4 ,it is shown at the moment the impulse is transmitted4 ,it will be seen that the impact takes place below the center of the ruby pin1 whereas it should take place at the center1 as the motion of the fork is upwards and that of the ruby pin downwards until the line of the centers has been reached4 ,the same rule applies to the flat-faced pin and it is important that the right quantity be ground off4 ,we find that #c_/g is approximately the amount which should be ground away4 ,fig4 #bb illustrates the fork standing against the bank4 ,the ruby pin touches the side of the slot but has not as yet begun to act2 ri is the real impulse circle for which we allow #a of freedom at the acting edge of the fork2 the face of the ruby pin is therefore on this line4 ,the next thing to do is to find the center of the pin4 ,from the side n of the slot we construct the right angle o n t2 from n1 we transmit the width of the pin1 and plant the center x on the line n t4 ,we can have the center of the pin slightly below this line1 but in no case above it2 but if we put it below1 the pin will be thinner and therefore more easily broken4 ,illustration3 ,fig4 #ad4 ,the ,safety ,action4 ,although this action is separate from the impulse and unlocking actions1 it is still very closely connected with them1 much more so in the single than in the double roller escapement4 ,if we were to place the ruby pin at ,x1 ,fig4 #ad1 we could have a much smaller roller than by placing it at ,p4 ,with the small roller the safety action is more secure1 as the intersection at m is greater than at k4 ,it is not as liable to butt and the friction is less when the guard point is thrown against the small roller4 ,suppose we take two rollers1 one with a diameter of #b4e mm41 the other just twice this amount1 of #e mm4 ,by having the guard radius and pressure the same in each case1 if the guard point touched the larger roller it would not only have twice1 but four times more effect than on the smaller one4 ,we will notice that the smaller the impulse angle the larger the roller1 because the ruby pin is necessarily placed farther from the center4 ,the position of the ruby pin should1 therefore1 govern the size of the roller1 which should be as small as possible4 ,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 jewel4 ,for this reason1 as well as securing the correct impulse radius and therefore angle1 when replacing the ruby pin1 and having it set securely and mechanically in the roller1 it is necessary that the pin and the hole in the roller be of the same form1 and a good fit4 ,fig4 #bc illustrates the difference in size of rollers4 ,in the smaller one the conditions imposed are satisfied1 while in the larger one they are not4 ,in the single roller the safety action is at the mercy of the impulse and pallet angles4 ,we have noticed that in order to favor the impulse we require a large roller1 and for the safety action a small one1 therefore escapements made on fine principles are supplied with two rollers1 one for each action4 ,it may be well to say that in our opinion a proportion between the fork and impulse angles in #aj pallets of #c or #c to #a1 depending upon the size of the escapement1 is the lowest which should be made in single roller4 ,we have seen them in proportions of #b to #a in single roller--a scientific principle foolishly applied--resulting in an action entirely unsatisfactory4 ,when the guard point is pressed against the roller the escape tooth must still rest on the locking face of the pallet2 if the total lock is #b1 by allowing #a freedom for the guard point between the bank and the roller the escapement will still be locked 4 ,how much this shake actually amounts to depends upon the guard radius4 ,suppose this to be #d mm41 then the freedom would equal #d #b #c4adaf #cfj #a4be 4#jhgc mm4 ,illustration3 ,fig4 #bd4 ,illustration3 ,fig4 #be4 ,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 it2 at the same time it must not be too large1 as it would necessitate a longer horn on the fork than is necessary4 ,fig4 #bd shows the slot n of the fork standing at the bank4 ,the ruby pin o touches it1 but has not as yet acted on it2 s s illustrates a single roller1 while ,s#b illustrates the safety roller for a double roller escapement4 ,in order to find the dimensions of the crescent in the single roller we must proceed as follows3 ,,wa is in the center of the fork when it rests against the bank1 and is1 therefore1 one of the sides of the fork angle1 and is drawn from the pallet center2 ,v ,a ,w is an angle of #a1 which equals the freedom between the guard point and the roller2 g g represents the path of the guard pin u for the single roller1 and is drawn at the intersection of ,,va with the roller ,a ,a#b is a line drawn from the balance center through that of the ruby pin1 and therefore also passes through the center of the crescent4 ,by planting a compass on this line1 where it cuts the periphery of the roller1 and locating the point of intersection of ,,va with the roller1 will give us one-half the crescent1 the remaining half being transferred to the opposite side of the line ,a ,a#b4 ,we will notice that the guard point has entered the crescent #a before the fork begins to move4 ,the angle of opening for the crescent in the double roller escapement is greater than in the single1 because it is placed closer to the balance center1 and the guard point or dart further from the pallet center1 causing a greater intersection2 also the velocity of the guard point has increased1 while that of the safety roller has decreased4 ,fig4 #bd1 at ff1 shows the path of the dart h1 which also has #a freedom between bank and roller4 ,from the balance center we draw ,a d touching the center or point of the dart2 from this point we construct at #e angle b ,a d4 ,this is to ensure sufficient freedom for the dart when entering the crescent4 ,we plant a compass on the point of intersection of ,a ,a#b with the safety roller1 ,s#b1 and locating the point where ,ab intersects it1 have found one-half the opening for the crescent1 the remaining half being constructed on the opposite side of the line ,a ,a#b4 ,the ,horn on the fork belongs to the safety action3 more horn is required with the double than with the single roller1 on account of the greater angle of opening for the crescent4 ,the horn should be of such a length that when the crescent has passed the guard point1 the end of the horn should point to at least the center of the ruby pin4 ,the dotted circle1 s s1 ,fig4 #be1 represents a single roller4 ,it will be noticed that the corner of the crescent has passed the guard pin u by a considerable angle1 and although this is so1 in case of an accident the acting edge of the fork would come in contact with the ruby pin2 this proves that a well made single roller escapement really requires but little horn1 only enough to ensure the safe entry of the ruby pin in case the guard point at that moment be thrown against the roller4 ,we will now examine the question from the standpoint of the double roller2 ,s#b1 ,fig4 #be1 is the safety roller2 the corner of the crescent has safely passed the dart h2 the centers of the ruby pin o and of the crescent being on the line ,a ,a#b1 we plant the compass on the pallet center and the center of the face of the ruby pin and draw k k1 which will be the path described by the horn4 ,the end of the horn is therefore planted upon it from #a to #a from the ruby pin2 this freedom at the end of the horn is therefore from to more than we allow for the guard point2 it depends upon the size of the escapement and locking angles which we would choose4 ,it must in any case be less than the lock on the pallets1 so that the fork will be drawn back against the bank in case the horn be thrown against the ruby pin4 ,when treating on the width of the ruby pin1 we mentioned the ,savage pin roller escapement1 which we illustrate in ,figs4 #bf and #bg4 ,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 disadvantages4 ,in ,fig4 #bf we show the unlocking pins u beginning their action on the line of centers--the best possible point--in unlocking the escapement4 ,these pins were made of gold in all which we examined1 although it is recorded that wide ruby pins and ruby rollers have been used in this escapement1 which would be preferable4 ,the functions of the two pins in the roller are simply to unlock the escapement2 the impulse is not transmitted to them as is the case in the ordinary fork and roller action4 ,in this action the guard pin i also acts as the impulse pin4 ,we will notice that the passing hollow in this roller is a rectangular slot the same as in the ordinary fork4 ,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 i1 ,fig4 #bg1 transmits the impulse to the roller4 ,illustration3 ,fig4 #bf4 ,illustration3 ,fig4 #bh4 ,the impulse is transmitted closer to the line of centers than could be done with any ruby pin4 ,if the pin i were wider the impulse would be transmitted still closer to the line of centers1 but the intersection of it with the roller would be less4 ,it is very delicate as it is1 therefore from a practical standpoint it ought to be made thin but consistent with solidity4 ,if the pin is anyway large1 it should be flattened on the sides1 otherwise the friction would be similar to that of the round ruby pin4 ,it would also be preferable 7on account of the pin i being very easily bent7 to make the impulse piece narrow but of such a length that it could be screwed to the fork1 the same as the dart in the double roller4 ,the impulse radius is also the radius of the roller1 because the impulse is transmitted to the roller itself2 for this reason the latter is smaller in this action than in the ordinary one having the same angles2 also a shorter lever is in contact with a longer one in the unlocking than in ordinary action of the same angles2 but for all this the pins u u should be pitched close to the edge of the roller1 as the angular connection of the balance with the escapement would be increased during the unlocking action4 ,this escapement being very delicate requires a #ab pallet angle and a proportion between impulse and pallet angles of not less than #c to #a1 which would mean an impulse angle of #cf2 this1 together with the first rate workmanship required are two of the reasons why this action is not often met with4 ,george ,savage1 of ,london1 ,england1 invented this action4 ,he was a watchmaker who1 in the early part of this century1 did much to perfect the lever escapement by good work and nice proportion1 besides inventing the two pin variety4 ,he spent the early part of his life in ,clerkenwell1 but in his old days emigrated to ,canada1 and founded a flourishing retail business in ,montreal1 where he died4 ,some of ,george ,savage's descendants are still engaged at the trade in ,canada at the present day4 ,the correct delineation of the lever escapement is a very important matter4 ,we illustrate one which is so delineated that it can be practically produced4 ,we have not noticed a draft of the lever escapement1 especially with equidistant pallets and club teeth1 which would act correctly in a watch4 ,we have been aggressive in our work and have sometimes found theories propounded and elongated which of themselves were not right2 this may have something to do with it1 that we so often hear workmen say1 ,theory is no use1 because if you work according to it your machine will not run4 ,we say1 ,no1 sir1 if your theory is not right in itself1 then your work will certainly not be correct2 but if your theory be correct then your work must be correct4 ,why8 it simply cannot be otherwise4 ,we will give it another name2 let us say1 apply sense1 reason1 thought1 experience and study to your work1 and what have you done8 ,you have simply applied theory4 ,a theorem is a proposition to be proved1 not being able to prove it1 we must simply change it according as our experience dictates1 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 respect1 and which is theoretically and practically correct4 ,we will not only give instructions for drafting the escapement now under consideration1 but will also make explanations how to draft it in different positions1 also in circular pallet and single roller4 ,we are convinced that by so doing we will do a service to many1 we also wish to avoid what we may call the stereotyped process1 that is1 one which may be acquired by heart1 but introduce any changes and perplexity is the result4 ,it is really not a difficult matter to draft escapements in different positions1 as an example will show4 ,before making a draft we must know exactly what we wish to produce4 ,it is well in drafting escapements to make them as large as possible1 say thirty to forty times larger than in the watch1 in the present case the size is immaterial1 but we must have specifications for the proportions of the angles4 ,our draft is to be the most difficult subject in lever escapements2 it is to be represented just as if it were working in a watch2 it is to represent a good and reliable action in every respect1 one which can be applied without special difficulty to a good watch1 and is to be up to date in every particular and to contain the majority of the best points and conclusions reached in our analysis4 ,specifications for ,lever ,escapement3 ,the pallets are to be equidistant2 the wheel teeth of the club form2 there are to be two rollers2 wheel1 pallet1 and balance centers are to be in straight line4 ,the lock is to be #a1 the run 1 making a total lock of #a2 the movement of pallets from drop to drop is to be #aj1 while the fork is to move through #aj from bank to bank2 the lift on the wheel teeth is to be #c1 while the remainder is to be the lift on the pallets as follows3 #aj - 7#a #c7 #e for lift of pallets4 ,the wheel is to have #ae teeth1 with pallets spanning #c teeth or #b spaces1 making the angle from lock to lock #cfj #ae #b #fj1 the interval from tooth to tooth is #cfj #ae #bd2 divided by #b pallets #bd #b #ab for width of tooth1 pallet and drop2 drop is to be #a1 the tooth is to be the width of the pallet1 making a tooth of a width of #d and a pallet of #f4 ,the draw is to be #ab on each pallet1 while the locking faces of the teeth are to incline #bd4 ,the acting length of fork is to be equal to the distance of centers of scape wheel and pallets2 the impulse angle is to be #bh2 freedom from dart and safety1 roller is to be #a1 and for dart and corner of crescent #e2 freedom for ruby pin and acting edge of fork is to be #a2 width of slot is to be the total motion1 or #aj #b #e2 shake of ruby pin in slot 1 leaving #e - #d for width of ruby pin4 ,radius of safety roller to be #d_/g of the theoretical impulse radius4 ,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 dart2 space between the end of horn and ruby pin is to be #a4 ,it is well to know that the angles for width of teeth1 pallets and drop are measured from the wheel center1 while the lifting and locking angles are struck from the pallet center1 the draw from the locking corners of the pallets1 and the inclination of the teeth from the locking edge4 ,in the fork and roller action1 the angle of motion1 the width of slot1 the ruby pin and its shake1 the freedom between dart and roller1 of ruby pin with acting edge of fork and end of horn are all measured from the pallet center1 while the impulse angle and the crescent are measured from the balance center4 ,a sensible drawing board measures #ag #bd inches1 we also require a set of good drawing instruments1 the finer the instruments the better2 pay special attention to the compasses1 pens and protractor2 add to this a straight ruler and set square4 ,the best all-round drawing paper1 both for ,india ink and colored work has a rough surface2 it must be fastened firmly and evenly to the board by means of thumb tacks2 the lines must be light and made with a hard pencil4 ,use ,higgins' ,india ink1 which dries rapidly4 ,illustration ,we will begin by drawing the center line ,a ,a ,b2 use the point ,b for the escape center2 place the compass on it and strike ,g ,h1 the primitive or geometrical circle of the escape wheel2 set the center of the protractor at ,b and mark off an angle of #cj on each side of the line of centers2 this will give us the angles ,a ,b ,e and ,a ,b ,f together1 forming the angle ,f ,b ,e of #fj1 which represents from lock to lock of the pallets4 ,since the chord of the angle of #fj is equal to the radius of the circle1 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 ,h2 this distance must be equal to the radius of the circle4 ,at these points we will construct right angles to ,e ,b and ,f ,b1 thus forming the tangents ,c ,a and ,d ,a to the primitive circle ,g ,h4 ,these tangents meet on the line of centers at ,a1 which will be the pallet center4 ,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 ,h4 ,the locking edges of the pallets will always stand on this circle no matter in what relation the pallets stand to the wheel4 ,place the center of the protractor at ,b and draw the angle of width of pallets of #f2 ,i ,b ,e being for the engaging and ,j ,b ,f for the disengaging pallet4 ,in the equidistant pallet ,i ,b is drawn on the side towards the center1 while ,j ,b is drawn further from the center4 ,if we were drawing a circular pallet1 one-half the width of pallets would be placed on each side of ,e ,b and ,f ,b4 ,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 pallet4 ,the total lock being #a1 we construct ,v ,a at this angle from ,c ,a2 the point of intersection of ,v ,a with the locking circle ,m ,n1 is the position of the locking corner of the engaging pallet4 ,the pallet having #ab draw when locked we place the center of the protractor on this corner and draw the angle ,q ,m ,e4 ,q ,m will be the locking face of the engaging pallet4 ,if the face of the pallet were on the line ,e ,b there would be no draw1 and if placed to the opposite side of ,e ,b the tooth would repel the pallet1 forming what is known as the repellant escapement4 ,illustration3 ,fig4 #bh4 ,having shown how to delineate the locking face of the engaging pallet when locked1 we will now consider how to draft both it and the disengaging pallet in correct positions when unlocked2 to do so we direct our attention until further notice to ,fig4 #bh4 ,the locking faces ,q ,m of the engaging and ,s ,n of the disengaging pallets are shown in dotted lines when locked4 ,we must now consider the relation which the locking faces will bear to ,e ,b in the engaging1 and to ,f ,b in the disengaging pallets when unlocked4 ,this is a question of some importance2 it is easy enough to represent the #ab from the #cj angles when locked2 we must be certain that they would occupy exactly that position and yet show them unlocked2 we shall take pains to do so4 ,in due time we shall show that there is no appreciable loss of lift on the engaging pallet in the escapement illustrated2 the angle ,t ,a ,v therefore shows the total lift2 we have not shown the corresponding angles on the disengaging side because the angles are somewhat different1 but the total lift is still the same4 ,g ,h represents the primitive circle of the escape wheel1 and ,x ,z that of the real1 while ,m ,n represents the circular course which the locking corners of the pallets take in an equidistant escapement4 ,at a convenient position we will construct the circle ,c ,c ,d from the pallet center ,a4 ,notice the points e and c1 where ,v ,a and ,t ,a intersect this circle2 the space between e and c represents the extent of the motion of the pallets at this particular distance from the center ,a2 this being so1 then let us apply it to the engaging pallet4 ,at the point of intersection o of the dotted line ,q ,m 7which is an extended line on which the face of the pallet lies when locked71 with the circle ,c ,c ,d1 we will plant our dividers and transfer e c to o n4 ,by setting our dividers on o ,m and transferring to n ,m1 we will obtain the location of ,q ,m1 the locking face when unlocked4 ,let us now turn our attention to the disengaging pallet4 ,the dotted line ,s ,n represents the location of the locking face of the disengaging pallet when locked at an angle of #ab from ,f ,b4 ,at the intersection of ,s ,n with the circle ,c ,c ,d we obtain the point j4 ,the motion of the two pallets being equal1 we transfer the distance e c with the dividers from j and obtain the point l4 ,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 unlocked4 ,it will be perfectly clear to anyone that through these means we can correctly represent the pallets in any desired position4 ,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 locked1 while the opposite is the case on the disengaging pallet1 in which the angle ,s ,n ,f is much less than ,s ,n ,f4 ,this shows that the deeper the engaging pallet locks1 the lighter will the draw be1 while the opposite holds good with the disengaging pallet2 also1 that the draw increases during the unlocking of the engaging1 and decreases during the unlocking of the disengaging pallet4 ,these points show that the draw should be measured with the fork standing against the bank2 not when the locking corner of the pallet stands on the primitive circle1 as is so often done4 ,the recoil of the wheel 7which determines the draw71 is illustrated by the difference between the locking circle ,m ,n and the face ,q ,m for the engaging1 and ,s ,n for the disengaging pallet1 and along the acting surface it is alike on each pallet1 showing that the draft angle should be the same on each pallet4 ,a number of years ago we constructed the escapement model which we herewith illustrate4 ,all the parts are adjustable2 the pallets can be moved in any direction1 the draft angles can be changed at will4 ,through this model we can practically demonstrate the points of which we have spoken4 ,such a model can be made by workmen after studying these papers4 ,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 pallet1 as will be seen in the diagram4 ,this is because the draft angle is struck from ,e ,b which deviates from the locking circle in such a manner1 that if the face of a pallet were planted on it and locked deep enough to show it1 the wheel would actually repel the pallet1 whereas with the disengaging pallet if it were planted on ,f ,b1 it would actually produce draw if locked very deep2 this is on account of the natural deviation of the #cj lines from the locking circle4 ,this difference is more pronounced in the circular than in the equidistant pallet1 because in the former we have two locking circles1 the larger one being for the engaging pallet1 and as an arc of a large circle does not deviate as much from a straight line as does that of a smaller circle1 it will be easily understood that the natural difference before spoken of is only enhanced thereby4 ,for this reason in order to produce an actual draw of #ab1 the engaging pallet may be set at a slightly greater angle from ,e ,b in the circular escapement2 the amount depends upon the width of the pallets2 the requirements are that the recoil of the wheel will be the same on each pallet4 ,we must1 however1 repeat that one of the most important points is to measure the draw when the fork stands against the bank1 thereby increasing the draw on the engaging and decreasing that of the disengaging pallet during the unlocking action1 thus naturally balancing one fault with another4 ,we will again proceed with the delineation of the escapement here illustrated4 ,after having drawn the locking face ,q ,m1 we draw the angle of width of teeth of #d1 by planting the protractor on the escape center ,b4 ,we measure the angle ,e ,b ,k1 from the locking face of the pallet2 the line ,e ,b does not touch the locking face of the pallet at the present time of contact with the tooth1 therefore a line must be drawn from the point of contact to the center ,b4 ,we did so in our drawing but do not illustrate it1 as in a reduced engraving of this kind it would be too close to ,e ,b and would only cause confusion4 ,we will now draw in the lifting angle of #c for the tooth4 ,from the tangent ,c ,a we draw ,t ,a at the required angle2 at the point of intersection of ,t ,a with the #cj line ,e ,b we have the real circumference of the escape wheel4 ,it will only be necessary to connect the locking edge of the tooth with the line ,k ,b1 where the real or outer circle intersects it4 ,it must be drawn in the same manner in the circular escapement2 if the tooth were drawn up to the intersection of ,k ,b with ,t ,a1 the lift would be too great1 as that point is further from the center ,a than the points of contact are4 ,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 them1 then there will be no loss of lift on the engaging pallet4 ,this is precisely how it is in the diagram2 but if there is any deviation1 then the angle of loss must be measured on the real diameter of the wheel and not on the primitive1 as is usually done1 as the real diameter of the wheel1 or in other words the heel of the tooth1 forms the last point of contact4 ,with a wider tooth and a greater lifting angle there will even be a gain of lift on the engaging pallet2 the pallet in such a case would actually require a smaller lifting angle1 according to the amount of gain4 ,we gave full directions for measuring the loss when describing its effects in ,fig4 #h4 ,whatever the loss amounts to1 it is added to the lifting plane of the pallet4 ,in the diagram under discussion there is no loss1 consequently the lifting angle on the pallet is to be #e4 ,from ,v ,a we draw ,v ,a at the required angle2 the point of intersection of ,v ,a with the path ,o will be the discharging edge ,o4 ,it will now only be necessary to connect the locking corner ,m with it1 and we have the lifting plane of the pallet2 the discharging side of the pallet is then drawn parallel to the locking face and made a suitable length4 ,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 #bd and draw a circle from the scape center ,b1 to which the line ,m ,m will be a tangent4 ,we will utilize this circle in drawing in the faces of the other teeth after having spaced them off #bd apart1 by simply putting a ruler on the locking edges and on the periphery of the circle4 ,we now construct ,w ,a as a tangent to the outer circle of the wheel1 thus forming the lifting angle ,d ,a ,w of #c for the teeth2 this corresponds to the angle ,t ,a ,c on the engaging side4 ,w ,a touches the outer circle of the wheel at the intersection of ,f ,b with it4 ,we will notice that there is considerable deviation of ,w ,a from the circle at the intersection of ,j ,b with it4 ,at the intersecting of this point we draw ,u ,a2 the angle ,u ,a ,w is the loss of lift4 ,this angle must be added to the lifting angle of the pallets2 we see that in this action there is no loss on the engaging pallet1 but on the disengaging the loss amounts to approximately in the action illustrated4 ,as we have allowed of run for the pallets1 the discharging edge ,p is removed at this angle from ,u ,a2 we do not illustrate it1 as the lines would cause confusion being so close together4 ,the lifting angle on the pallet is measured from the point ,p and amounts to #e the angle of the loss2 the angle ,w ,a ,u embraces the above angles besides for run4 ,if the locks are equal on each pallet1 it proves that the lifts are also equal4 ,this gives us a practical method of proving the correctness of the drawing2 to do so1 place the dividers on the locking circle ,m ,n at the intersection of ,t ,a and ,v ,a with it1 as this is the extent of motion2 transfer this measurement to ,n1 if the actual lift is the same on each pallet1 the dividers will locate the point which the locking corner ,n will occupy when locked2 this1 in the present case1 will be at an angle of #a below the tangent ,d ,a4 ,by this simple method1 the correctness of our proposition that the loss of lift should be measured from the outside circle of the wheel1 can be proven4 ,we often see the loss measured for the engaging pallet on the primitive circumference ,g ,h1 and on the real circumference for the disengaging2 if one is right then the other must be wrong1 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 ,n2 had we added this amount to the lifting angle ,v ,a ,v of the engaging pallet1 the result would have been that the discharging edge ,o would be over #a below its present location1 thus showing that by the time the lift on the engaging pallet had been completed1 the locking corner ,n of the disengaging pallet would be locked at an angle of #b instead of only #a4 ,many watches contain precisely this fault4 ,if we wish to make a draft showing the pallets at any desired position1 at the center of motion for instance1 with the fork standing on the line of centers1 we would proceed in the following manner3 #aj being the total motion1 one-half would equal #e2 as the total lock equals #a1 we deduct this amount from it which leaves #e - #a #c1 which is the angle at which the locking corner ,m should be shown above the tangent ,c ,a4 ,now let us see where the locking corner ,n should stand2 ,m having moved up #e1 therefore ,n moved down by that amount1 the lift on the pallet being #e and on the tooth #c 7which is added to the tangent ,d ,a71 it follows that ,n should stand #e #c - #e #c above ,d ,a4 ,we can prove it by the lock1 namely3 #c #a #e1 half the remaining motion4 ,this shows how simple it is to draft pallets in various positions1 remembering always to use the tangents to the primitive circle as measuring points4 ,we have fully explained how to draw in the draft angle on the pallets when unlocked1 and do not require to repeat it1 except to say1 that most authorities draw a tangent ,r ,n to the locking circle ,m ,n1 forming in other words1 the right angle ,r ,n ,a1 then construct an angle of #ab from ,r ,n4 ,we have drawn ours in by our own method1 which is the correct one4 ,while we here illustrate ,s ,n ,r at an angle of #ab it is in reality less than that amount2 had we constructed ,s ,n at an angle of #ab from ,r ,n1 then the draw would be #ab from ,f ,b1 when the primitive circumference of the wheel is reached1 but more than #ab when the fork is against the bank4 ,the space between the discharging edge ,p and the heel of the tooth forms the angle of drop ,j ,b ,i of #a2 the definition for drop is that it is the freedom for wheel and pallet4 ,this is not1 strictly speaking1 perfectly correct1 as1 during the unlocking action there will be a recoil of the wheel to the extent of the draft angle2 the heel of the tooth will therefore approach the edge ,p1 and the discharging side of the pallet approaches the tooth1 as only the discharging edge moves on the path ,p4 ,a good length for the teeth is #a_/aj the diameter of the wheel1 measured from the primitive diameter and from the locking edge of the tooth4 ,the backs of the teeth are hollowed out so as not to interfere with the pallets1 and are given a nice form2 likewise the rim and arms are drawn in as light and as neat as possible1 consistent with strength4 ,having explained the delineation of the wheel and pallet action we will now turn our attention to that of the fork and roller4 ,we tried to explain these actions in such a manner that by the time we came to delineate them no difficulty would be found1 as in our analysis we discussed the subject sufficiently to enable any one of ordinary intelligence to obtain a correct knowledge of them4 ,the fork and roller action in straight line1 right1 or any other angle is delineated after the methods we are about to give4 ,we specified that the acting length of fork was to be equal to the center distance of wheel and pallets2 this gives a fork of a fair length4 ,having drawn the line of centers ,a ,a we will construct an angle equal to half the angular motion of the pallets2 the latter in the case under consideration being #aj1 therefore #e is spaced off on each side of the line of centers1 forming the angles m ,a k of #aj4 ,placing our dividers on ,a ,b the center distance of 'scape wheel and pallets1 we plant them on ,a and construct c c2 thus we will have the acting length of fork and its path4 ,we saw in our analysis that the impulse angle should be as small as possible4 ,we will use one of #bh in our draft of the double roller2 we might however remark that this angle should vary with the construction of the escapements in different watches2 if too small1 the balance may be stopped when the escapement is locked1 while if too great it can be stopped during the lift2 both these defects are to be avoided4 ,the angles being respectively #aj and #bh it follows they are of the following proportions3 #bh #aj4be #b4gcaf4 ,the impulse radius therefore bears this relation 7but in the inverse ratio to the angles71 to the acting length of fork4 ,we will put it in the following proportion2 let ,ac equal acting length of fork1 and x the unknown quantity2 #bh3aj4be 33 ,ac3x2 the answer will be the theoretical impulse radius4 ,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 centers2 we thus obtain ,a the balance center4 ,through the points of intersection before designated we will draft ,x ,a and ,y ,a forming the impulse angle ,x ,a ,y of #bh4 ,at the intersection of this angle with the fork angle k ,a m1 we draw i i from the center ,a2 this gives us the theoretical impulse circle4 ,the total lock being #a it follows that the angle described by the balance in unlocking #a #b4gcaf #d4ghh4 ,according to the specifications the width of slot is to be #e2 placing the center of the protractor on ,a we construct half of this angle on each side of k ,a1 which passes through the center of the fork when it rests against the bank2 this gives us the angle s ,a n of #e4 ,if the disengaging pallet were shown locked then m ,a would represent the center of the fork4 ,the slot is to be made of sufficient depth so there will be no possibility of the ruby pin touching the bottom of it4 ,the ruby pin is to have #a freedom in passing the acting edge of the fork2 from the center ,a we construct the angle t ,a n of #a2 at the point of intersection of t ,a with c c the acting radius of the fork1 we locate the real impulse radius and draw the arc ri ri which describes the path made by the face of the ruby pin4 ,the ruby pin is to have of shake in the slot2 it will therefore have a width of #d2 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 drawing4 ,the radius of the safety roller was given as #d_/g of the theoretical impulse radius4 ,they may be made of various proportions2 thus is often used4 ,remember that the smaller we make it1 the less the friction during accidental contact with the guard pin1 the greater must the passing hollow be and the horn of fork and guard point must be longer1 which increases the weight of the fork4 ,having drawn in the safety roller1 and having specified that the freedom between the dart and safety roller was to be #a1 the dart being in the center of the fork1 consequently k ,a is the center of it2 therefore we construct the angle k ,a ,x of #a4 ,at the point of intersection of ,x ,a with the safety roller we draw the arc g g2 this locates the point of the dart which we will now draw in4 ,we will next draw d ,a from the balance center and touching the point of the dart2 we now construct b ,a at an angle of #e to it4 ,this is to allow the necessary freedom for the dart when entering the crescent2 from ,a we draw a line through the center of the ruby pin4 ,we do not show it in the drawing1 as it would be indiscernible1 coming very close to ,a ,x4 ,this line will also pass through the center of the crescent4 ,at the point of intersection of ,a b with the safety roller we have one of the edges of the crescent4 ,by placing our compass at the center of the crescent on the periphery of the roller and on the edge which we have just found1 it follows that our compass will span the radius of the crescent4 ,we now sweep the arc for the latter1 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 it4 ,we will now draw in the impulse roller and make it as light as possible consistent with strength4 ,a hole is shown through the impulse roller to counterbalance the reduced weight at the crescent4 ,when describing ,fig4 #bd1 we gave instructions for finding the dimensions of crescent and position of guard pin for the single roller4 ,we will find the length of horn2 to do so we must closely follow directions given for ,fig4 #be4 ,in locating the end of the horn1 we must find the location of the center of the crescent and ruby pin after the edge of the crescent has passed the dart4 ,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 bank1 then draw a line from ,a through the point so found4 ,at point of intersection of this line with the real impulse circle r i r i we draw an arc radiating from the pallet center2 the end of the horn will be located on this arc4 ,in our drawing the arc spoken of coincides with the dart radius g g4 ,as before pointed out1 we gave particulars when treating on ,fig4 #be1 therefore considered it unnecessary to further complicate the draft by the addition of all the constructional lines4 ,we specified that the freedom between ruby pin and end of horn was to be #a2 these lines1 7which we do not show7 are drawn from the pallet center4 ,having located the end of the horn on the side standing against the bank1 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 dart1--and transfer this measurement along g g which will locate the end of the horn on the opposite side4 ,we have the acting edges of the fork on cc and have also found the position of the ends of the horns2 their curvature is drawn in the following manner3 ,we place our compasses on ,a and r i1 spanning therefore the real impulse radius2 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 horn1 on the same side of the fork4 ,at the point of intersection of the arcs the compass is planted and the curvature of the horn drawn in1 the same operation is to be repeated with the other horn4 ,we will now draw in the sides of the horn of such a form that should the watch rebank1 the side of the ruby pin will squarely strike the fork4 ,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 wedge4 ,the fork and pallets are now drawn in as lightly as possible and of such form as to admit of their being readily poised4 ,the banks are to be drawn at equal distances from the line of centers4 ,in delineating the fork and roller action in any desired position1 it must be remembered that the points of location of the real impulse radius1 the end of horn1 the dart or guard pin and crescent1 must all be obtained when standing against the bank1 and the arcs drawn which they describe2 the parts are then located according to the angle at which they are removed from the banks4 ,we think the instructions given are ample to enable any one to master the subject4 ,we may add that when one becomes well acquainted with the escapement1 many of the angles radiating from a common center1 may be drawn in at once4 ,we had intended describing the mechanical construction of the escapement1 which does unmistakably present some difficulties on account of the small dimensions of the parts1 but nevertheless it can be mechanically executed true to the principles enumerated4 ,we have evolved a method of so producing them that young men in a comparatively short period have made them from their drafts 7without automatic machinery7 that their watches start off when run down the moment the crown is touched4 ,perhaps later on we will write up the subject4 ,it is our intention of doing so1 as we make use of such explanations in our regular work4