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PREFACE 
 
 |fi[E DETACHED LEVER ESCAPEMENT forms one of the most interesting and important subjects for study 
 in the whole range of the horological art, and is at the same time one of the most ditticult to treat fully, com- 
 preliensively, and in such manner as to be easily understood. Realizing the paramount impdrtance to the work- 
 ing watchmalier of a thorough comprehension of tlie Detached Lever Escapement, the principles of its construc- 
 tion, the relation of its several parts and the methods of calculation Ijy which its relative proportions may be 
 varied to produce certain results, the subscribers to the Prize Fund of the British Horological Institute resolved, 
 in tlie month of January, 1864, that its first prize should be offered for the best treatise on this sul)j(jct. This 
 prize, of the sum of thirty guineas, or about $150, was promptly announced in a circular issued to the members 
 of the Institute, and at once attracted the attention of Muritz Grossmanu, then as now a resident of Glashutte, Saxony, a mem- 
 ber of the Institute of many years standing, and a careful, painstaking, scientific horologist. He at once determined to com- 
 pete for th» prize, the more readily arriving at this determination from the fact that he had long contemplated writing a series 
 of works upon the several branches of practical horology, embodying the result of his experience and study, and the reception 
 accorded this essay would serve as an index to the measure of success likely to attend such publications. 
 
 Having been awarded the prize, Mr. Grossmaun, encouraged by many eminent horologists, concluded to publish the work 
 in book form, preparatory to which he greatly elaljorated many portions of it and added the chapters on "Measuring Instru- 
 ments," and "Materials Employed in Making Lever Escapements," thus increasing it to nearly double its original size. 
 
 In April, 1866, it was published, and immediately assumed the importance of a standard text-book upon the sub- 
 ject of which it treats. It has been widely read and consulted in this country as well as in Europe, the superior intelligence of 
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 workman in the profitable and pleasant pursuit of his calling. 
 
 THE JEWELERS' PUBLISHING COMPANY, 
 Chicago, March 1, 1884. H. A. PiiatCE, PresU 
 
TABLE OFCONTENTS. 
 
 PNDEX. 
 
 Page. 
 Chapter I. Historical Notices of the Origin of the Detached Lever 
 
 Escapement . 21 
 
 Chapter n. Preliminary Kemarks 23 
 
 Chapter m. General Observatioue on the Detached Lever Escape- 
 ment 25 
 
 Chapter IV. Analysis of the Detached Lever Escapement — Its Parts 
 
 and Their Various Coustruction— Classification 26 
 
 Chapter V. The Action of Wheel and Pallet 27 
 
 Chapter VI. The Action of Fork and Roller 30 
 
 Chapter VII, Combination of the Actions ^itj 
 
 Chapter VIII. Description of Two Excellent Arrangements of the De- 
 tached Lever Escapement 37 
 
 Chapter IX. Description of Some Special Constructions on Different 
 
 Principles 40 
 
 Chapter X. Inetructious for Drawing Correct Escapements 43 
 
 Chapter XI. On the Respective Proportions of the Parts of the De- 
 tached Lever Escapement and the Effects of Varia- 
 tions in these Proportions 49 
 
 Chapter XII. Tables of Proportions 57 
 
 Chapter Xin. Procedure of Making a Correct Lever Escapement 89 
 
 Chapter XIV. On the Materials Employed for Making Lever Escape- 
 ments 92 
 
 Chapter XV. On the Points to which the Examiner Should Direct his 
 
 Attention lOU 
 
 Chapter XVI. On the System of Measurement and the Measuring In- 
 struments—Tables of Reduction lo:f 
 
 DIAGRAMS. 
 
 1. A. Mudge's Lever Escapement. 
 B. Rack Lever Escapement. 
 
 2. Lever Escapement with Ratchet Wheel and Circular Pallet. 
 
 3. Lever Escapement with Ratchet Wheel and Equidistant Lockings, 
 
 4. Pin Anchor. 
 
 5. A. Pin Anchor, jeweled. 
 
 B. Pin Anchor, soUd jewels. 
 
 6. Lever Escapement with Club Wheel and Circular Pallet, visible 
 jewels. 
 
 7. Lever Escapement with Club Wheel and Circular Pallet, improved. 
 
 8. Lever Escapement with Club Wheel and Equidistant Lockings. 
 
 9. Table Roller. 
 
 10. Double Roller and Spring Fork. 
 
 11. A. Two Pin Lever. 
 
 B. Solid Impulse Lever. 
 
 C. Jewel Roller Lever. 
 
 12. Enghfih Lever Escapement. 
 
 13. Lange's Lever Escapement with Analytical Construction of Lange's 
 Improvement. 
 
 14. Resilient Lever Escapement. 
 
 15. Repellent Lever Escapement. 
 
 16. Pallet, 'Scaping over 2—5 teeth. 
 
 17. Pallet of C*' and 15° Lifting. 
 
 18. Illustration of the Procedure of Making Correct Escapements. 
 
 19. Measuring Instruments. 
 
 20. Measuring Instruments. 
 
THE DETACHED LEVER ESCAPEMENT. 
 
 CHAPTER I. 
 
 HISTOEICAI, NOTICKS OF THE ORIGIN OF THE DETACHED 
 fST^^%a LEVER ESCAPEMENT. 
 
 iJHE first trace of time-keeping by purely me- 
 chanical means dates back to the Tenth centu- 
 ry, when Gerbert, Bishop of Magdeburg (subse- 
 quently Pope Sylvester II), is said to have 
 constructed a clock going by weights and wheels. 
 About the year 1370 Henry Vick, whom 
 King Charles V of France called from Germany 
 for this purpose, made a turret-clock, the first 
 one of which we possess complete and positive information. 
 Since the time of these first clocks the progress of horo- 
 logy has been very great, but what has been done in this 
 way has been chiefly in perfecting the escapement and the 
 regulating parts, while the wheelwork of the train ha.s suf- 
 fered but very little and comparatively unessential altera- 
 tions. The invention of the pendulum as the regulating 
 part of clocks and of the pendulum spring for portable 
 timekeepers were the principal sources of transformation 
 in the means employed for time-measuring. 
 
 Any one who sees the clocks and watches of our day, 
 would be inclined to suppose that the first clocks were con- 
 structed with a pendulum as regulator, because this is evi- 
 dently the most simple and certain system for clocks, and 
 that the employment of the balance as a regulator has been 
 
 suggested by the necessity of producing portable timekeep- 
 ers, for which the pendulum would not answer. 
 
 This is, however, not the case, for the first clocks we 
 have any historical notices of had a verge escapement with 
 a kind of rudimentary balance as a regulator, and the employ- 
 ment of the pendulum for measuring the time was discov- 
 ered nearly three centuries after the construction of Vick's 
 clock, by Galileo. From this time clocks were made with 
 the pendulum, but always with the verge escapement, this 
 being the only one known at this period. 
 
 This progress, important as it was, became much more 
 so by another invention ensuing from it. 
 
 The old vertical or verge escapement was very soon 
 found unsatisfactory for clocks, by requiring too large an 
 arc of oscillation. This circumstance led to the invention 
 of the anchor pallets for clocks, by Hooke, about 16-50. 
 From that time the possibility existed of employing a long, 
 heavy pendulum with small arcs of vibration. 
 
 An improvement of great value on Hooke's anchor pal- 
 lets was Graham's dead-beat escapement, invented about 
 the end of the Seventeenth century. Though the compara- 
 tive value of Hooke's recoiling anchor and Graham's dead- 
 beat escapement was a matter of earnest doubt among the 
 most competent horologists of that time, the latter has de- 
 cidedly superseded its rival, and is even now, in spite of all 
 inventions of later date, the very best escapement for a good 
 astronomical clock. 
 
 21 
 
While these important imjjrovements were made on the 
 ■escapement of clocks, watches were constructed mostly with 
 the old vertical escapement. The great inaccuracy in the 
 timekeeping of such watches, though amended as much 
 as possible by the insertion of the fusee, created many 
 contrivances of escapements with the principal view of 
 giving more extension to the vibrations, and by doing so, 
 making them more independent of the variable effect of the 
 moving force and less liable to be disturbed by the external 
 motion which a portable timekeeper is exposed to. 
 
 Among these experiments we find a contrivance of Huy- 
 ghens, in which the verge escapement is kept as it is, with 
 the only difierence that the verge, instead of carrying the 
 balance, has a wheel riveted on its axis, pitching into a pin- 
 ion, which carries the balance. This was the first rough 
 embodiment of the idea of increasing the arc of vibration 
 by intervening mechanism. 
 
 Another escapement witli this multiplication of vibra- 
 tory movement is the rack-lever, invented by the Abbe 
 Hautefeuille. It is almost identical with Hooke's recoiling 
 anchor, but on the anchor axis is mounted a toothed rack, 
 which pitches into a pinion forming the balance staS". This 
 method, however, was soon abandoned, after the horizontal 
 and the duplex escapements had been invented by Gral^ara 
 and Dutertre. 
 
 In these two dead-beat escapements the possibility oi 
 larger vibrations was obtained, but during the excursions 
 of the balance the tooth of the escape wheel was resting 
 against a circular part of the balance axis. These escape- 
 ments are very little influenced by the variations of the mo- 
 tive force, but the tooth resting against the axis produces 
 necessarily a considerable friction, increasing with the diam- 
 eter of that circular part and with the extent of the vibra- 
 tions. This friction, although diminished to the smallest 
 
 amount po.ssible inthe duplex escapement, necessitates the 
 application of oil on these parts, thus making the rate of the 
 watch dependent on the quality of the oil and on all the 
 changes by time and atmospheric influence to which even 
 the best oil is subject. This occasioned the most earnest ef- 
 forts to make the vibrations of the balance more independ- 
 ent of the train and of the variable condition of the oil. Es- 
 capements were constructed effecting this purpose more or 
 less perfectly, one of which originated through taking up 
 the idea of Huyghens and Hautefeuille of multiplying the 
 arc of vibration by transmitting it to the balance through 
 a-Iever. The recoiling anchor employed by Hautefeuille 
 was converted into a reposing or dead-beat anchor. By the 
 lever on the anchor axis the very small lifting arc of this 
 latter was transferred to the balance in such a way as to 
 multiply it considerably and to make all connection between 
 these two parts cease immediately after the small arc of in- 
 tersection had been performed, leaving the balance quite 
 free for all the rest of its vibration. This escapement is the 
 detached lever egcapement; it was invented by Mudge, about 
 1750, and it has served as prototype to all sorts of detached 
 lever escapements known in our day. 
 
 A description of Mudge's detached lever escapement will 
 be given in Chapter V, with a diagram of its original form. 
 This escapement was at the time of its invention not fully 
 appreciated, for Mudge himself applied it to but two of his 
 watches. Even at the beginning of our century it was 
 but very little known, and the horizontal and duplex 
 escapements prevailed for first-class watches. Since that 
 time it has been more and more employed for better classes 
 of watches, and has now got the better of its former rivals. 
 
 Many modifications and improvements have been made 
 on it, the most important of which will be described in the 
 fifth and ninth chapters. 
 
 22 
 
CHAPTER II. 
 
 PRELIMINARY REMARKS. 
 
 Before entering into tlie practical description and expla- 
 nation of the lever escapement and its varieties, I think it 
 right to say some words indicating the points of view from 
 which I intend to treat the subject. 
 
 In the first place, I deem it necessary to assume a neu- 
 tral and cosmopolitan position, not merely dwelling on the 
 inventions and contrivances in the lever escapement origi- 
 nated in England and by English horologists, but describ- 
 ing any construction of this escapement, no matter where it 
 has been invented or kept in use. 
 
 With respect to the order in which to describe the dif- 
 ferent varieties of the lever escapement, I have thought it 
 best to follow the historical arrangement as much as possi- 
 ble, always fully describing and explaining those peculiari- 
 ties which are good and commendable, and only indicating 
 by a short description and diagram those which are of a 
 merely historical value, and have not shown any practical 
 advantage. 
 
 In all the points where construction and calculation are 
 concerned, I intend to take a quite different course from 
 that hitherto in use. This deviation from the common way 
 will be perceived through the whole extent of this treatise, 
 and as I think this reformation of the method of measuring 
 aind calculating the most important and useful part of it, I 
 beg to explain here the motives that make me think so. 
 
 The manufacture of clocks and watches, especially the 
 latter, presents a peculiar difficulty by the reduced dimen- 
 sions in which the parts of a watch must be constructed. 
 The necessity of portability restrains the size allowed to a 
 
 watch within very small limits, and even those horological i 
 struments for which no such I'estriction would be imposed — 
 for instance, box chronometers — are, for good reasons, very 
 rarely made beyond a certain conventional size, which does 
 not obviate the difficulty above mentioned. 
 
 Now it is easy enough to draw any individual jiart of a 
 watch on a large scale perfectly, according as scientific rules 
 and good symmetry and harmony between the different 
 parts may demand. But it is very difficult to transmit the 
 exact proportions found in this way to the real dimensions 
 of our work, without any essential alteration. 
 
 Every oiher mechanician has the advantage that he 
 may draw his work to the real size, and very often he is 
 even obliged to draw on a smaller scale. Besides this, he 
 has at his disposal measuring instruments of sufficient accu- 
 racy to execute his work with the necessary exactness. But 
 the watchmaker, on the contrary, cannot draw the objects 
 of his manufacture except on a magnified scale, and those 
 especially for which the greatest accuracy is required can 
 only be drawn on a scale of 20 or '60 to 1, if the distinct 
 illustration of all the particulars would be attained. The 
 way and means of transferring the correct proportions of a 
 good drawing to the real working size of watch-work are 
 problems of great importance, though very little has been 
 done till now to obtain a satisfactory result in this direction. 
 
 The measuring instruments, gauges, calipers and tables 
 for every special purpose, such as are resorted to by the 
 majority of horologists and escapement makers, are very 
 imperfect means. The measuring instruments are for the 
 greater part not even of a sufficient accuracy and delicacy 
 in their construction, and are in most cases quite independ- 
 ent of any certain standard measure ; therefore they could 
 not be used as a vehicle of mutual understanding on ques- 
 tions of sizes and proportions, nor could they be employed 
 
 23 
 
for any calculation or reduction of these sizes. The eccen- 
 tric gauge of Roberts, for instance, though described and 
 recomraended twice in the British Horological Journal, 
 would be quite useless tor the two cases just mentioned. 
 For iutercoiujaarison it would not do because it would 
 prove a very difficult thing to construct a number of these 
 gauges to give an identical measurement, for the slightest 
 deviation from the true ditterence of centers, here one-tenth 
 inch, would always produce a difference of twice the extent. 
 For calculation or reduction it would not answer, because 
 there is not the slightest connection with any standard meas- 
 ure, and because the sizes measured by it are progressing in 
 an increasing and decreasing ratio, so that it would be a very 
 dangerous error to suppose, for instance, that the size 20 on 
 this gauge would be a third of 60 or a half of 40. Besides, 
 the range of sizes encompassed by this gauge is very limited, 
 and will hardly exceed three or four millimetres when the 
 f' '-^ion is extended up to 100 parts, and the delicacy of the 
 division is not very great, for one degree of it corresponds 
 to an average size of 0.04 m. The instrument is also not of 
 a nature to be used for measuring very small and frail ob- 
 jects, such as the ruby roller of a duplex escapement, etc., 
 and altogether it is not to be recommended because the ec- 
 centric principle is entirely defective for this purpose. Most 
 of the gauges and tables now in use are made only for a 
 certain number of cases and sizes, and leave the workman 
 quite helpless when it is required to make an escapement 
 with different numbers of teeth, uncommon angles of lifting 
 and in larger or smaller sizes than usual. Besides, they are 
 very seldom based upon scientific principles, and it is a 
 question whether many of them are not altogether incorrect. 
 As the Museum Committee of the British Horological 
 Institute, by its announcement of March 20th, 1861, asked 
 for information on the subject of a good and uniform sys- 
 tem of measurement, beiug a member and a warm friend 
 
 of the Institute, I thought it would be wrong not to give 
 the description of a system known to me by many years' 
 experience, and which I was sure would prove very useful 
 when introduced into English watch manufacturing. I 
 therefore sent in a paper, giving complete details on this 
 subject, and for better illustration I also forwarded two nl 
 the measuring instruments, as a donation for the museum. 
 The paj)fr was puljlished in the Horological Journal, No. 
 55, March 2nd, 1863. I demonstrated in it that the pro- 
 posed system was not only very suitable as a universal 
 Standard of measuring in the watch trade, but more than 
 chat, would at the same time be the means of applying 
 mathematical principles directly to the practical execution 
 of watchwork. 
 
 Nobody will deny that though the advantages of a uni- 
 form measurement are very imjiortant, the possibility of 
 <»iui<!ferring exact proportions to escapements, etc., is much 
 more so ; and I had not the slightest doubt that the system 
 proposed by me, uniting these two great objects, would soon 
 make friends in England. 
 
 The publication of the above mentioned paper was fol- 
 lowed by a warm recommendation of the Museum Commit- 
 tee to introduce and employ universally the metric system. 
 It is strange to say that this opinion of the Museum Com- 
 mittee has not found any adhereuts, and I conclude by this 
 unexpected fact that I have not been successful in my en" 
 deavors to prove the applicability of the metric system to 
 the solution of every problem in horology, or that perhaps 
 a great number of practical men liave gained an unfavor- 
 able impression by the calculations which for greater com- 
 pleteness I gave in the paper. 
 
 I think the present opportunity very favorable for show- 
 ing to what extent this way of measuring and calculating 
 is capable of application in constructing a correct lever ea- 
 
 24 
 
eapement. For the double purpose of being useful to the 
 practical workman as well as to the scientific horologist, I 
 shall describe, in the first place, the simple graphic method ; 
 that is, the way to make a drawing on a large scale, and to 
 reduce and transmit the sizes from the drawing to the real 
 working proportions. At the same time I shall give the 
 shortest and easiest forms of calculation by which the pro- 
 portions are developed in a mathematical way. 
 
 Thus, I hope, every one will be able to avail himself of 
 the advantages of this system. The practical workman 
 who does not like to be troubled by mathematical disserta- 
 tions may leave the calculutive part aside and proceed in 
 the practical way to make a drawing, which, in most cases, 
 will not prove a great difficulty to him. 
 
 In the diagrams I have deemed it advisable to make the 
 angle of movement of wheel and pallet 10° from drop to 
 drop, and that on the balance 30°, these being about the 
 average angles of all those in use. 
 
 j; 
 
 . L 
 
 CHAPTER III. 
 
 GENERAL OBSERVATIONS ON THE DETACIIEn LEVER. 
 
 The detached lever escapement shows at the first glance 
 a very ditterent feature from all the escapements now in use 
 for watchwork. This diHerence is perceptible even to the 
 eye of the least experienced observer, and consists chiefly 
 iu the intervening action of a lever between the escape 
 wheel and the balance, while in all other escapements for 
 watches (except the remontoir escapement) the escape 
 wheel gives its impulse directly to the balance. 
 
 It might be considerad a matter of doubt whether per- 
 fection ought to besought by creating an additional part of the 
 escapement, and thus making it a more complicated mechan- 
 ism. Still, the experience of more than half a century con- 
 firms the truly good performance of the lever escapement, 
 and we must acknowledge on close examination that of all 
 the escapements for watches only the duplex and detent 
 escapements might enter into competition with it. The 
 duplex, however, is of a I'ather ii'ail nature, and very much 
 exposed to injury by rough use of the watch and sudden 
 movements in wearing it. The detent escapement, though 
 of very valuable time-keeping properties, and apparently 
 more simple, by admitting a direct impulse of the balance 
 roller, is, by its locking and dt^tent-spring at least as com- 
 plicated, and at any rate much more difficult to execute and 
 to keep in good order, than the lever escapement. , 
 
 There is another circumstance which speaks strongly 
 m favor of the lever escapement. The balance in this latter 
 
 25 
 
receives an imjnilse for each vibration, while the duplex 
 and detent escapements have but one impulse for each two 
 vibrations. 
 
 The lever escapement does not admit of constructing 
 such very flat watches as the Swiss manufacturers produce 
 with the horizontal escapement ; but hai)pily the predilec- 
 tion for such flat watches is now declining, and for watches 
 of a more substantial size the lever escapement, of all the 
 escapements known, is certainly the most valuable, its parts 
 being comparatively strong and not easily injured by vio- 
 lent external motion, or by being repaired or cleaned by 
 unskilled workmen. 
 
 Another and most important advantage of the lever 
 escapement is, that, supposing a proper construction and 
 right proportions of the weight and diameter of the balance 
 and the force of the mainspring, it will not set on the lock- 
 ing, nor on the lifting, but go on immediately by itself as 
 soon as the motive force is in action. This cannot be said 
 of the dujjlex or detent escapements, though this quality 
 must be highly a]iprecinl('(l in a portable timekeeper. 
 
 CHAPTER IV. 
 
 ANAIA'SIS OF THE DETACHED LEVEE ESCAPEMENT.- 
 PARTS AND THEIR VARIOUS CONSTRUCTIONS. 
 
 -ITS 
 
 A complete lever escapement is composed of and contains 
 two distinct actions : First, the action of the wheel and pal- 
 let. Second, the action of the lever or fork and roller. 
 These two actions are produced each by two acting parts, so 
 that the number of those parts in the lever escapement is 
 four. They are: The wheel, the pallet, the lever and the 
 roller. 
 
 The wheel is flat, its teeth projecting in its own plane. 
 The tcc4Ji are of various shapes, corresponding to the way 
 in which the lifting is performed, and vary from a sharp 
 pointed form to a full inclined plane. The wheel is mounted 
 upon the escape-pinion, by which it is connected with the 
 train. 
 
 The pallet is also of very different shape and proportion. 
 In most cases its body lies in a tangential direction to the 
 circle of the wheel, and shows on its extremities two pro- 
 jecting parts, directed towards the wheel-teeth, on w'hich the 
 action of these latter takes place. The parts are called the 
 arms of the pallet. In most cases, the parts operated on by 
 the wheel-teeth are jeweled with hard stones, to provide for 
 greater resistance against wearing. The pallet has a hole 
 in its centre by which it is fixed on the pallet-axis or pallet- 
 stafl, and moves with this axis. 
 
 •26 
 
The lever is a bar of metal, fitted by its hole on the 
 pallet-axis, and fastened at a certain angle to the lougitudi- 
 ual direction of the pallet. This angle is quite arbitrary 
 and depends entirely upon the intended arrangement of the 
 escapement. (Chapt. VII.) If there are two arms of the 
 lever, one of them serves merely to establish the equipoise, 
 while the other is the acting arm. This latter has in the 
 greatest number of lever escapements a notch cut into its 
 extremity, wherefore it has been called the fork. 
 
 The roller, in the ordinary ci instruction of lever escape- 
 ments, carries the impulse pin, commonly made of a ruby, 
 workine into the notch of the fork. It is a round disc, fitted 
 by its centre-hole on the balance-st;itf. 
 
 These four parts have have three centres of motion, the 
 pallet and lever moving together on the same axis. They 
 are made in manifold ways, thus constituting an indefinite 
 number or diflerent lever-escapements, the whole of which 
 it would be a very tedious task to describe. 
 
 But as all these varieties result from different combina- 
 tions of the various kinds of the two before-mentioned 
 .actions forming the lever-escapement, and which, being en- 
 tirely separate actions, may be combined in every possible 
 way, it will simplify the treatment of the subject, to estab- 
 lish a classification of these t\V(} actions, according to the 
 various ways in which they take place, and then to explain 
 what is required for their combination. 
 
 ThercfVjre the various constructions of the lever escape- 
 ment may be classified from two principal points of view; 
 first, with regard to the way in which the lifting of the 
 ■wheel on the pallet takes place; second, with regard to the 
 means by which the impulsion is transferred to the balance. 
 
 CHArTER V. 
 
 THE ACTION OF WHEEL AND PALLET. 
 
 This action consists in an alternate lifting, imparting a 
 small vibratory motion to the pallet, by means of a diagonal 
 driving-jjlane on each arm of the pallet. This lifting is not 
 permanent, because the two driving-planes are intcn-upted 
 by two planes nearly concentric to the pallet centre, so as 
 to arrest or lock the wheel-tooth dropping against them. By 
 the interposing of these locking-faces, the lifting of every 
 tooth, ending with the drop of this tooth from the edge of 
 the lifting plane on one pallet-arm, is succeeded by the rest- 
 ing of the corresponding tooth on the locking face of the 
 other arm. There it remains locked, until released by an 
 action which shall be spukeu of later. 
 
 The locking-faces must have a slight dc%iation ■^'-om the 
 line adapted for the mere resting or locking of the wheel 
 tooth. This deviation serves to produce a tendency of the 
 pallet-arm to be drawn forward towards the centre of the 
 wheel, thus securing the detaclinient of the vibrations of the 
 balance by preventing the jjallet from leaving its position 
 of rest by the slightest movement of the watch. This ten- 
 dency of the locking-faces is commonly called the " draw. " 
 
 The lifting of the pallet, which coustitutes the princijtal 
 part of the wheel and pallet-action, can be produced in tliree 
 different ways : 
 
 1. The inclined planes being on the pallet and the 
 wheel-te^'th having a simply pointed form. (Ratchet-teeth.) 
 
 2. The inclined planes being on the wheel-teeth aad 
 the pallet presenting two thin pins or edges. 
 
 27 
 
^. The inclined planes being partly on the pallet and 
 partly on the wheel teeth. (Club-teeth.) 
 
 The system of making the inclined planes only on 
 the pallet arms seems to be the oldest plan ot lever escape- 
 ment for watches. Mudge, who, according to our opinion, 
 executed the first detached lever escapement, made his pal- 
 let in that way, and the same system, with very trifling 
 alterations, is still in use in our day in almost all English 
 lever watches. 
 
 Mudge's pallet was made to embrace five teeth (of a 
 wheel of twenty teeth) (Diagram 1), which number has been 
 reduced to three, with a view of having the pallet of as 
 little weight as possible, and to reduce the friction of the 
 acting parts to a smaller amount. The locking faces of 
 Mudge's pallet were merely arcs of circles concentric to 
 the pallet centre, the "draw" being an improvement of 
 later date. 
 
 Diagrams 2 and 3 show two different kinds of lever es- 
 capements with the lifting planes on the pallet. In Diagram 
 2, the arms of the pallet are of equal length, and conse- 
 quently the action of the wheel teeth takes place at the 
 same centre distance on both of them. (Circular pallet.) 
 But the resistance in unlocking is with this construction 
 very diSerent, and much less on the second arm than on 
 the fii-st, or entrance arm, owing to the diflerent radii of the 
 locking circles. This is a very serious obstacle to a regular 
 performance of the watch, and therefore all the better es- 
 capements are made in the way shown by Diagram 3. Here 
 are the two locking faces at the same distance from the 
 centre of pallet, and the unlocking will consequently be 
 done on each side with the same amount of force. 
 
 The lever escapement with pointed or ratchet teeth has 
 the considerable advantage of going with the least possible 
 amount of friction, the point of the tooth sliding along a 
 
 polished surface, generally made of hard stone, to diminish 
 friction and prevent wearing of the acting parts. Besides 
 it has not so much to suffer under the pernicious influence 
 of the adhesion of thickening oil, which exemption makes 
 it keep a very steady rate. Almost all English watches 
 have ratchet wheels. Still, it may be said against this sys- 
 tem that there must be necessarily a certain quantity of 
 drop, which in this dead-beat escapement is a complete loss, 
 of power. The very delicate points of the ratchet wheel 
 teeth are also very liable to being spoiled by unskillful hands. 
 The lever escapement with the lifting planes on the 
 wheel teeth is, from a theoretical point of view, a very per- 
 fect action, because its lifting and locking are performed 
 exactly at the same centre distance and under the same 
 angles. 
 
 This variety of the lever escapement has been adopted 
 in a certain kind of German watches, but has been hither- 
 to very little used and known. 
 
 The most simple form of it is shown in Diagram 4. The 
 pallet consists of two arms of brass, carrying each a very 
 thin, hard-tempered steel pin, standing upright out of its 
 upper surface. The pallet and lever are one and the same 
 piece. The lifting faces on the wheel teeth are rounded, and 
 must be carefully polished, as well as the locking faces of 
 the teeth. The draw in this escapement is efiected by a 
 slight deviation of the locking faces (on the foreside of the 
 wheel-teeth) from the straight line towards the centre of the 
 wheel. Watches with this escapement perform very well. 
 There may be objection to the acting parts not being jew- 
 eled, and consequently liable to wear from use, but it is a 
 fact that such escapements, with an escape-wheel of tempered 
 st^el, snow no symptoms of deterioration of the pins afler 
 many j-ears of service ; and even if such a thing should 
 happen, it is a very easy matter to insert new pins. 
 
 28 
 
A lever of this kind can be made in very delicate 
 proportions, and weighing less than any pallet and lever of 
 another kind. This escapement ought to be more generally 
 known, for, requiring no jewels, it can be made so cheaply, 
 and with the tools to be found in every watchmaker's 
 workshop, that it might prove very useful, especially in 
 cases where economy in construction is an object. 
 
 Nevertheless, the wish to produce an escapement possess- 
 ing the valuable theoretical advantages of this system with- 
 out being exposed to the acting parts wearing away, has 
 originated some attempts to supply the pin anchor \rith jewels. 
 
 This has been done by taking the same lever and pal- 
 let-piece, merely having a little larger holes to fix ruby-pins 
 into, in the shape of the locking-stone in the detent-spring 
 of a chronometer. These pins can also be fastened by in- 
 serting them into a notch cut into the lever arm and shut- 
 ting the notch by a slight pressure, so as to hold the jewel 
 in its place. Diagram -5, A, shows both meth<jds, the one 
 on the first arm and the other on the second. 
 
 Diagram -5, B illustrates another plan on the same prin- 
 ciple, approaching very nearly to the common construction. 
 The pallet is made independent of the lever, and carries two 
 jewels, presenting a thin edge to the lifting-planes on the 
 wheel-teeth. 
 
 This construction is certainly not so frail and delicate 
 as the former, but the pallet and lever must necessarily be 
 much heavier. 
 
 Escapements of this kind have been made by some 
 Swiss manufacturers, and according to Mr. J. F. Cole's de- 
 scription of his clock {Horological Jmimal I, p. 134), the 
 escapement of this latter must be identical with it 
 
 The lever escapement with the inclined planes partly 
 on the anchor pallet and partly on the wheel-teeth is 
 almost exclusively in use in the Swiss watches. It 
 
 29 
 
 has the advantage of admitting the closest scaping and 
 requiring the least pf/saible amount of drop, because its teeth 
 are hollowed out on their back part in order t/j secure suf- 
 ficient freedom for the delivery-edge. The wheel of this 
 escapement, with its little dri\Tng-plane8 on the ends of its 
 teeth (club-teeth), is certainly much less expf>sed U> injury, 
 when falling into inexperienced hands, than the wheel with 
 pointed teeth. 
 
 Most of the ordinary escapements of this kind are made 
 with a circular pallet; that is, the pallet-arms of e^^ual length, 
 and the driving-planes at equal centre distances. There are 
 the same reasoas for speaking agaiast this construction as 
 already mentioned when treating of the escapement ^rith 
 the ratchet wheel Still, the breadth of pallet-arms being 
 considerably smaller, ajmpared to those of a ratchet-wheel 
 escapement, the incorrectness of a circular pallet to a club- 
 wheel escapement is comparatively less, and reduces itself 
 in proportion to the part of the total lifting ailotte<l to the 
 wheel-teeth. 
 
 Diagram 7 represents a circular pallet with a club- 
 wheel, of the proportions' usually executed. 
 
 Diagram 8 shows a circular pallet with a dub-wheel, 
 the total lifting of which is divided equally between the 
 pallet and wheel, for the reason above mentioned. 
 
 Diagram 9 iUostrates an escapement with equidistant 
 lockings and the total lifting .distributed between pallet and 
 wheel in the proportion in which it is u-sually done. 
 
 The escapement with the club-wheel, though superior in 
 the economical use of the moving power, is still objection- 
 able from another point of view. The inclined planes of 
 the pallet-arm and wheel-tooth are so very little diverging, 
 that with thick and glutinous oil there is much adhe- 
 sion between them, which may produce under unfavorable 
 circumstances a very disadvantageous infiueace on the p«- 
 fbrmance of the watch. 
 
CHAPTER VI. « 
 
 fTHE ACTION OF FOBK AND ROLLER. 
 ? HE parts which transfer the motion created by the 
 \ action of the wheel and pallet to the balance, have 
 also been constructed in a variety of different ways ; 
 and their action is commonly called the fork and roller 
 action, because in almost all lever escapements the interven- 
 ing lever is, at the extremity turned towards the balance, 
 worked out into a notch, which gives it some resemblance 
 to a fork. The roller in most of the lever escapements is 
 a steel disc, carrying a pin to fit the notch in the fork. This 
 pin is commonly made of a ruby, in order to diminish fric- 
 tion and give greater duraliility to the acting parts. 
 
 The fork and roller action can be divided into two dis- 
 tinct functions, in which the two parts act alternately the 
 one upon the other. These functions are the lifting and the 
 unlocking. In the lifting, the lever-fork impels the ruby- 
 pin in the roller, being impelled itself by the lifting of the 
 wheel-tooth on the pallet, which latter is solidly joined to 
 the lever, so as to form but one piece with it. This impul- 
 sion of the wheel on the pallet, and the impulse of the fork 
 on the roller arising from it, continues until the wheel-tooth 
 dyops from the edge of the driving-jilane, which causes the 
 eorrespondiug tooth to fall against the locking face of the 
 other pallet-arm. The pallet and fork are kept in that 
 position while the balance makes its excursion to the same 
 side. On its return, effectuated by the tension of the pen- 
 dulum-spring, the ruby-pin has to perform the other func- 
 tion, in which it plays the active part, the function of 
 unlocking. As soon as in this returning vibration the ruby- 
 
 pin touches the fork, the latter (and also the pallet) follows 
 the impulse a little way, thus withdrawing the locking- 
 face against which the wheel-tooth is resting. The tooth, 
 immediately after having left the edge of the locking-face, 
 begins its lifting on the driving plane, which is transferred 
 by the pallet and lever to the roller and balance ; this lift- 
 ing continues until the tooth has slidden across the driving- 
 plane and dropped from the edge of it, after which the 
 corresponding tooth rests against the locking face of the 
 opposite pallet-arm. This play of the escapement is con- 
 stantly repeated, so that the ruby-pin is driving a short way 
 at each vibration, and is driven immediately afterward. 
 
 It is a peculiar feature of this part of the escapement, 
 that it is quite out of action during the greater part of the 
 vibration of the balance, and but a very little arc of the 
 whole vibration keeps the roller in connexion with the fork. 
 This circumstance on the one side constitutes the lever es- 
 capement a detached one, and endows it with all the valu- 
 able qualities of such escapements. But, on the other side, 
 it produces a tendency to frequent disturbances in a portable 
 time-keeper, which must be prevented by an arrangement 
 of the parts, called the safety action. 
 
 It has already been mentioned in the description of the 
 wheel and pallet action, that the locking-faces of the pallet 
 cannot be made circular, or at least not concentric circles to 
 the centre of the pallet, but must deviate from that circle so 
 much as to produce a locking tendeucj , by which the pres- 
 sure of the wheel-tooth on the locking face draws the pallet 
 farther into the wheel. But this alone would not be suffi- 
 cient to prevent the pallet leaving its state of rest in case 
 of the watch being exposed to sudden external motions. 
 The results of such uncontrolled motion of the pallet and 
 lever would be that the lever would not present its fork to 
 the ruby pin of the balance roller when returning from its 
 
 30 
 
excursion, but the pin would fall against the outside of the 
 fork and tlie watch would stop immediately, requiring the 
 aid of a watchmaker to put it right again. It is therefore 
 of the greatest importance to secure continuous motion in 
 watches with the lever escapement, by a careful safety 
 action. 
 
 There is still another function which the lever performs 
 in all the usual constructions. It has already lieen observed 
 that the deviation of the locking faces from the concentric 
 circle produces a tendency of the wheel to draw the pallet- 
 arm towards its centre. This tendency would of oourse 
 draw the palkt-arm in, until arrested by the circular rim 
 of the wheel between the teeth ; and this excess of drawing 
 motion would occasion a great loss of power in unlocking, 
 or even cause a butting of the ruby pin against some part 
 of the lever not prepared for its reception. For this reason 
 it is indispensable to reduce the motion of the lever and 
 pallet to the amount required for the safe escapement of the 
 wheel. This limitation is technically called the banking, 
 and can be attained in dift'erent ways. In many watches, 
 especially in the English ones, there are two upright pins 
 planted into the plate at convenient distances from and on 
 each side of the lever, near the fork end of it. (Banking 
 pins.) 
 
 In the greater part of the Swiss lever watches the lever 
 and wheel are sunk into the plate, and the frtrk end of the 
 lever is banked against two projecting corners produced by 
 the intersection of the sinks for the balance roller and the 
 lever. In some watches we also find the banking-pins near 
 the other end of the lever. 
 
 The banking of the lever, though indispensable for the 
 good performance of the escapement, is at the same time a 
 source of very disagreeable irregularities. When by a sud- 
 den cu-cular motion of the watch in the plane of the balance 
 
 (a very frequent occurrence when wearing the watch, or 
 winding it up in a careless way), the vil^ration increases to 
 more than two full turns, the impulse-pin strikes against the 
 outside of the fork, which cannot yield, because it is leaning 
 against the banking-pin or edge. By the violence of this 
 percussion there is some danger of injury, not only to the 
 ruby-pin, but also to the balance pivots, which are often bent 
 or broken by the reaction. But more than that, all such 
 cases are accompanied by a considerable acceleration of the 
 rate of the watch, producing under unfavorable circum- 
 stances great differences in its timekeeping. t 
 
 Of the three described modes, the banking between two 
 pins is decidedly the best, provided the pins are not too 
 thick and are as near the fork end as possible, thereby avoid- 
 ing any essential part of the shock being communicated to 
 the pallet axis. The elasticity of thin and hard pins proves 
 to be a tolerable safeguard against the danger of any injury 
 to the ruby-pin or balance pivots. But such pins are very 
 easily bent when cleaning or repairing the watch, and then 
 the banking will be too wide, or, still worse, too narrow, 
 producing a want of freedom in the action of fork and 
 roller, or in the safety action, or not allowing the wheel- 
 teeth to drop freely from the driving planes. 
 
 The banking against solid corners of the sinks in the 
 plate is not liable to such disturbances, and with such solid 
 bankings the balance will not continue to strike against 
 them so long as it does with the elastic banking-pins ; but 
 at the same time the danger of injury to the delicate parts 
 of the escapement is greater. Besides, it is advisable to 
 make these banking corners sharp, and not obtuse or flatted, 
 as is often seen in such cases, where the banking was orig- 
 inally not wide enough. The consequence of such flattened 
 corners is aii adhesion between fork and corner when the 
 
 31 
 
parts are not perfectly clean, and this adhesion is an increase 
 of resistance to the unlocking. 
 
 The worst system is that of banking the other extremity 
 of the lever, bet^Yeen two pins or otherwise, because by this 
 arraiTgemeut the lever transmits about double the banking 
 shock" to the pallet axis; and indeed, if a machine were 
 wanted for the express purpose of breaking the anchor 
 pivots, a better construction than this could not be devised, 
 with a pair of thick pins and a strong unelastic lever. 
 
 By the preceding general remarks on the fork and roller 
 action it will be seen that an investigation into the difterent 
 constructions of these parts of the lever escapement must 
 include their four different functions ; the lifting, unlocking 
 and safety action, and the banking. 
 
 DESCRIPTION OF SEVEKAL FORK AND ROLLER ACTIONS. 
 
 1 Rack Lever.— The oldest method of transferrmg the 
 impulse of the wheel and pallet to the balance was the 
 rack lever. Its invention succeeded that of the application 
 of the pendulum spring to the balance at a very short 
 interval of time. The inventor of it was the Abbe Haute- 
 feuille, who published it in 1722. His pallet is a recoiling 
 one, though dead beat escapements existed long before that 
 time. The balance axis is a pinion of six leaves, into which 
 is pitched a toothed rack, fastened on the pallet arbor. 
 
 Though the employment of the rack lever deprives the 
 escapement of the character of detachment, still, it com- 
 bined with a dead beat wheel and pallet action, it has its 
 decided advantages, and is even now resorted to in those 
 constructions where extreme simplicity is desirable. It re- 
 quires no safety action, because the rack and pinion cannot 
 be disturbed in their connexion by any external motion. 
 For the same reason the locking faces of the pallet can be 
 made concentric circles to the centre of the pallet, thus 
 avoiding the recoil and unlocking resistance arising from 
 
 the draw. The rack lever also does nos require banking; 
 and it is an advantage of this construction that it is free from 
 all the inconveniences and risks connected with the safety 
 action and banking. It is true the lever and pallet are 
 compelled to follow the balance, even in its widest vibrations, 
 and therefore the tooth on the locking face is running farther 
 in than required, thus creating more friction; but this dis- 
 advantage is nearly made up by the absence of the draw 
 and the unlocking resistance connected therewith. 
 
 The system of producing a large vibration of the balance 
 by a rack and pinion is of very old date, and has been em- 
 ployed in other escapements, long before the lever escape- 
 ment was known. (See Chapter I.) 
 
 The very easy anil simple construction of the rack lever 
 escapement is shown in Diagram 1 
 
 2 Mudge'& Escapement— Th^ fork and roller action m 
 Mudge's escapement shows a very curious complication, 
 having the two prongs of the fork in different planes, the 
 one a little lower than the other. It is evident that this 
 arrangement has been made with a view of completing the 
 safety action. We give the whole escapement of Mudge m 
 its original shape (Diagram 1). a and h are the two 
 pron-8 of the fork; c and d are two small impulse pieces 
 on the balance-staff, the one over the other, and correspond- 
 ing to the planes of the prongs. The acting edges of these 
 two impulse pieces are rounded off so as to complete each 
 other's form to that of a cylindrical impulse pin, and when 
 the balance in its vibration comes to the point of intersec- 
 tion, the unlocking of the wheel is performed by one of the 
 impulse pieces, while the other one receives its impulse im- 
 mediately afterward. 
 
 The safety action of Mudge's escapement consists m a 
 small disc of steel on the balance axis, with a shallow notch 
 in it. A small and pointed piece of steel, e, is screwed upon 
 
 32 
 
Diagram I. 
 
DlAQEAM II. 
 
Diagram III. 
 
Diagram IV. 
 
the fork end of the lever in the same plane as the small 
 disc or roller on the balance staff. When the balance in 
 its vibration crosses the line of centres, the little index, e, 
 passes through the notch in the roller and stands at a little 
 distance from its circumference during the free vibration of 
 the balance. This safety action is a very good one, but if not 
 constructed with the greatest accuracy, there would be some 
 danger of failing at those points where the impulse pieces 
 leave the^fork, because this latter has no horns. For this 
 reason a complement to the safety action is given by the 
 two impulse pieces each having a circular part, detaining 
 the edge of the prong it has been actuated by from falling 
 back by external disturbances during the period that the 
 little safety roller is passing the centre line. 
 
 3. The Table Roller. — This is the name of a fork and 
 roller action which has been employed more than any other. 
 The greater ])s.xi of the English and Swiss lever watches 
 have the table roller. The roller is a disc of steel, carrying 
 the impulse pin. The part of its circumference next the 
 pin is filed out a little to form the passing hollow. The 
 fork has on its extremity a notch to receive the impulse 
 pin, which must pass through it freely and with a little 
 shake. The safety action is effected in the English watches 
 by an upright jiin (guard pin) projecting from the surface 
 of the leve]' very near the bottom of the fork, and corres- 
 ponding to the passing hollow in the roller, which allows of 
 its passing the centre line. During the free vibration of the 
 balance the guard pin stands at a very little distance from 
 the roller edge. The Swiss escapements have instead of the 
 guard pin a projecting edge on the lever, near the bottom 
 of the fork. (Diagram 9.) 
 
 To complete the safety action, which would be rather 
 deficient at the time when the impulse pin leaves the fork, 
 this latter has two horns projecting beyond the acting- 
 
 edges. The inner sides of these horns, or the sides turned 
 toward the impulse pin, are formed by two eccentric circles. 
 The impulse pin, when the lever is resting against the bank- 
 ing, passes these inner circles at a very little distance, thus 
 preventing the fork from falling back to the other side until 
 the guard pin is safely out of the passing hollow. 
 
 The edge of the roller must be carefully rounded and 
 polished, to reduce friction to the smallest possible amount 
 in those cases when the pallet may happen to leave its 
 place of rest. The edge of the roller should not extend be- 
 yond the circle of the impulse pin more than is required 
 for making a hollow deep enough for the passage of the 
 guard pin. An unnecessarily large disc causes the guard 
 pin to travel farther than the proper arc of escapement 
 action in order to get safety hold, thereby causing a run of 
 the wheel teeth on the locking faces. Diagram 9 shows the 
 table roller in its different positions. 
 
 It may be here observed that the form of the impulse 
 pin has been made very differently, though it is of the 
 greatest importance to give it a good and proper shape. In 
 many English watches we find full cylindrical pins, which 
 is decidedly a very bad system. A cylindrical pin will not 
 admit an advantageous transmission of movement; one con- 
 sequence of this is a loss of power, both in the unlocking 
 and in the lifting action. Besides, it is a source of other 
 irregularities, the pin very often touching the bottom of the 
 notch in certain positions of the watch, if the notch is not 
 very deep and if the pivots of anchor and balance have 
 much shake in their holes. In many Swiss watches the im- 
 pulse pins have an elliptical form, which is much better 
 than the cylindrical form. A cylindrical pin flattened down 
 one-third of its diameter is very appropriate for economi- 
 cally transmitting the moving power without any loss by 
 useless drop, In diagram 9 the flattened cylindrical pin is 
 
 33 
 
shown. In the same diagram the dotted lines (Figure B) 
 illustrate the disadvantageous action of a full cylindrical 
 pin. The disadvantage increases with the diameter of the 
 pin. • 
 
 The triangular form of the impulse pin is also very good, 
 and admits, as well as the preceding, of the most profitable 
 application of the moving force. Yet it may be observed 
 that the flatted cylindrical pin is stronger, and consequently 
 may be expected to oppose a greater resistance to the shocks 
 it has to sustain, when striking violently against the bank- 
 ings. 
 
 4. The Double Roller Escapement. — Under tliis desig- 
 nation is known an improved safety action which is now 
 very much made use of in the better English and Swiss 
 watches. The fork and roller action shows no difierence 
 to that of the table roller. For the safety action there is a 
 steel disc or roller fitted on the lower part of the balance 
 staff, and in corresponding height to it a pointed index 
 piece or guard pin is screwed or fastened to the lower side 
 of the lever on its fork end, and projecting toward the bal- 
 ance. The small disc is merely for the safety action, and 
 has a hollow of sufficient size to allow the index to pass 
 freely. It is strange enough that this method, originally 
 employed by Mudge, has been laid aside for so long a time, 
 and is now again resorted to and considered an improve- 
 ment. 
 
 A comparison of the respective value of these two sys- 
 tems most in use speaks strongly in favor of the double 
 roller. Diagram 9 of the table roller shows clearly that 
 the arc and angle of intersection of the roller edge with 
 the guard pin circle h I is much smaller than that of the 
 impulse pin in the circle laid through the acting edges of 
 the fork e /, the former being about four- fifths of the latter. 
 This disproportion is of less consequence in escapements 
 
 with large lifting arcs. But in our time the better horolo- 
 gists have aimed at giving more freedom and greater detach- 
 ment to the vibrations of the balance by diminishing the 
 lifting angles, and in such escapements, when made with 
 the table roller, the intersection of the guard pin and roller 
 edge would be so shallow that the least side shake of the 
 balance and pallet pivots would make the detaining action 
 a very doubtful one. This caused the return to Mudge's 
 original plan. The double roller admits of a much greater 
 arc of intersection for the safety action than that of the 
 fork and roller. The double roller is not only preferable 
 for giving a greater efficiency and soundness to the safety- 
 action ; it has still another and very important advantage 
 in all those cases in which, by external influences, the pallet 
 leaves its state of rest and the guard pin or index nuist be 
 detained by the roller edge. Then the small roller will not 
 experience so much friction on its circumference as the table 
 roller. The effect of this friction will be still more dimin- 
 ished, because it is applied at a smaller distance from the 
 balance center, and transmitted by a greater length of 
 lever, compared to the table roller. For these reasons, the 
 vibrations of the balance will be much less disturbed by the 
 detaining action when the escapement is a double roller one. 
 .5. The Two-pin Lever. — This is quite an original con- 
 trivance, and is doubtless, especially in its improved and 
 jeweled form, the best fork and roller action that exists. 
 It is based upon a separation of the unlocking and impulse 
 functions, effecting both in a very advantageous way. The 
 end of the lever is a fork with a wide notch, in which it 
 receives the unlocking action by two upright pins fixed in 
 the roller near it's edge. Between these two pins there is a 
 small notch in the circumference of the roller, which is to 
 receive the impulse by an upright pin fixed into the lever 
 very near the bottom of the fork. This pin at the same 
 
 34 
 
time serves as guard pin, passing tlu-dugli Uie notch in the 
 roller and resting at a very small distance from the roller 
 edge during the free vibration. The distance of the two 
 pins from each other embraces tlie whole arc of lifting of 
 the roller, and by this arrangement the unlocking takes 
 place in the Hue of centres, and consequently under the 
 most favorable circumstances. Diagram 11 shows the jiosi- 
 tiou of the parts in their difterent functions. 
 
 The impulse action of the two-jiin lever shows an inver- 
 sion of the common principle, as the notch is in the roller 
 instead of in tlie lever, and the lever carries the impulse 
 pin, instead of the roller. The effect is the same a.s that of 
 the common fork, excejst the mechanical advantage of the 
 impulse obtained by the thinness of the pin (See Chapter 
 XI.), and besides there is a complementary impulse, which 
 is given by the prong of the fork opposite to that on which 
 the unlocking has been performed, to the pin that did not 
 unlock. This secondary impulsion, if the parts are proper- 
 ly made and pitched, avoids all loss of power arising out of 
 the necessary drop, and thus we see in the two-pin lever 
 system the greatest economy of moving power, both in ilie 
 unlocking and impelling action. 
 
 The two-pin lever escapement was invented by George 
 Savage, of London. 
 
 A fork and roller of this kiiid must be made very care- 
 fully and of correct proportions, and they would hardly do 
 any service at all if constructed in such a careless way as 
 the fork and roller parts of the lower kinds of lever watches 
 are generally made. The above consideration of the super- 
 iority of this system -Hill not, however, remove the appre- 
 hension that the acting parts, being not jeweled, might be 
 worn out in a rather short time, or that those thin pins might 
 be bent accidentally, when cleaning or repairing the watch. 
 These circumstances created the desire to contrive a form of 
 
 the two-pin lever possessing all the valuable qualities above 
 mentioned, united with the durability and sound \ess of jew- 
 eled acting parts. Thia led to several improvemsnts, and 
 it seems that the inventor, George Savage, himself made a 
 step in that direction, jeweling the notch by inserting two 
 very small rubies in it and replacing the two unlocking 
 pins in the roller by one broad ruby pm. Still the thin im- 
 pulse pin was kept, with its liability to bending and to wear. 
 
 6. The Solid Impulse Lever removes this deficiency by 
 making the impulse pin of a sharp triangular shape, worked 
 out of the substance of the lever, or riveted into it This 
 impulse pin is often replaced by a ruby pin of the same 
 shape, while the notch of the roller is not jeweled. The 
 unlocking is produced by the broad face of a triangular 
 gold plug or ruby in the roller. 
 
 7. The Jewel Holler Escapement is another improvement 
 on the two-pin lever. Its roller is made out of a solid stone, 
 with a well-polished notch in it. The centre hole in the 
 roller is large enough to receive a steel collet, on which it is 
 fixed by a little shellac. This collet is fitted at a convenient 
 height on the balance staff, and has a shoulder covering the 
 greater part of the roller's lower surface, thus protecting it 
 against injury. This collet carries near to its edge a broad 
 and thin ruby pin for the unlocking. The impulse pin is 
 the same as in the original escapement of Savage. 
 
 8. The Spring Fori-. — This construction has been made 
 for the purpose of avoiding all danger arising from violent 
 banking, and all irregularities of rate resulting from the 
 same. It is a common table roller or double roller esca^-e- 
 meut, with only the difference that the prongs of the fork 
 are not made from the solid of the lever, but are rej^laced 
 by two small sj'riug^ fastened on the surface of the lever 
 and projecting beyond its end. These projecting ends of 
 the two springs form the prongs of tlie fork, and have the 
 
 35 
 
common shajse of these latter. They are kept at convenient 
 distance from each other by two thin upright [ins in the 
 lever, near the end of it. 
 
 A lever watch with this spring fork may be subjected to 
 sudden and violent movements without any fear of damage 
 to the balance pivots or impulse pin, for if the vibration 
 exceeds two full turns, the impulse pin will strike against 
 the outside of one prong of the ^si-i, which, by its elastic 
 nature, yields to the shock ant allows the iiK pulse pin to 
 pass. This play continues until the vibration has settled to 
 a regular extent. Diagram 10 shows the spring fork and 
 its action. 
 
 CHAPTER VII. 
 
 COMBINATION OF THE ACTIONS. _ 
 
 ^NY one of all the fork and roller actions just de- 
 scribed may be combined with any kind of wheel and 
 pallet action before mentioned, thus forming a great 
 variety of lever escapements. As the particular qualities 
 of these dift'erent actions are not at all altered by any such 
 combination, I have thought it best to refrain from enumer- 
 ating all the varieties to be obtained, which would have been 
 a very tedious proceeding, without auy practical use. But 
 before leaving the descriptive part of this treatise, I deem 
 it right to say a word about the arrangement of the parts of 
 the lever escapement. 
 
 The respective positions of the three pieces of the lever 
 escapement, the wheel, anchor and balance, are not the 
 same in all watches. There are two principal modes to be 
 observed: The escapement in straight line, and the escape- 
 ment in right angle. The latter is the usual plan resorted 
 to in all English, and in the lower kinds of Swiss lever 
 watches. The line from the wheel to the pallet centre makes 
 a right angle, or nearly so, to the line from the centre of 
 the pallet to that of the balance. 
 
 The Swiss manufacturers make their better qualities of 
 lever watches with the escapement in straight line. 
 
 It might appear almost superfluous to state here that the 
 performance of the escapement in either of these two ar- 
 rangements, or in any other angle, is entirely the same, 
 because, as is shown in the preceding chapters, the two 
 
 36 
 
actions of the lever escapement are perfectly independent 
 mechanisms, and their nature cannot be altered by making 
 them perform in any special angularity to each other. 
 Therefore it is quite unjustifiable to consider a straight Ime 
 escapement as an indispensable attribute of a first-rate Isver 
 watch ; an opinion very much prevailing among the Swiss 
 manufacturers and those connected with their manufacture. 
 The escapement at right angle allows a greater economy 
 of space in the watch, and therefore is very appropriate for 
 fusee watches. The straight line escapement, especially in 
 f plate watches, makes a better display of the acting parts. 
 Another apparent difference consists in the way of jew- 
 eling the paUet arms. This is done with visible or covered 
 jewels. The covered jewels are fixstened in a slit made in 
 the middle of the substance of the pallet arm, horizontally 
 or parallel to the surface of the pallet. The visible jewels 
 are cut into the pallet vertically, (Diagram 6) so that the 
 whole pallet-arm is a solid jewel. The Swiss manufacturers 
 choose this plan for their first-class watches. The greater 
 part of Swiss watches and all English lever watches are 
 made with covered jewels. The action is in both cases the 
 same, if the locking and lifting faces are properly made 
 and if not, the one is as bad as the other. Therefore it is 
 erroneous to consider the visible jewels as an essential and 
 characteristic feature of a good lever watch, as many people 
 in France and Switzerland do. The whole difierence lies 
 in the effect to the eye, and it cannot be denied that a well- 
 made lever escapement with visible jewels is a very good- 
 looking thing. Anyhow, the covered jewels are superior 
 in point of solidity, because they can be fixed more firmly, 
 owing to the large surfaces which they ofter to the slit in 
 the anchor; besides, those surfaces are rough, which makes 
 the fastening more than efficient. 
 
 CHAPTER VIII. 
 
 DESCRIPTION OP TWO EXCELLENT ARRANGE:. ^NTS OF THE 
 DETACHED LEVER ESC.U>EMENT. 
 
 As a sequel to the contents of the preceding chapters, 
 we give here a description of the most advantageous con- 
 structions of complete detached lever escapements, for the 
 purpose of serving as a base for the following chapters, ex- 
 plaining the respective proportions of the various parts of 
 the escapement and the efiects of alterations in the same. 
 
 The detached lever escapement, as it is made in the bet- 
 ter English lever watches, is decidedly one of the best com- 
 binations. We give in Diagram 12 an illustration of an 
 escapement of this kind, standing at right angles. The 
 escape wheel with ratchet teeth is made cf very good and 
 hard hammered brass, and is usually polished. It would 
 not be advisable to gild it, because by the common proce- 
 Jure of gilding the brass would lose its hardness and elas- 
 ticity. But even when merely electro-gilt, the thic cover 
 of precipitated gold cannot give as hard and durable a 
 surface as that of carefully hammered brass; and besides, 
 nobody can be sure that the difierent chemical ingredients 
 employed by the gilders for the processes of gilding and 
 brushing may not be retained to some extent by the gold 
 in such a loose state, and produce a pernicious influ'^nce on 
 
 the oil. 
 
 The pallet is made of steel, tempered, and has covered 
 jewels. The lifting angle on the pallet varies from 8° to 12°. 
 
 In the better English lever escapements of later days, 
 
 37 
 
the lifting angle very seldom exceeds 10° from drop to drop, 
 and this is the angle represented in all our diagrams. The 
 lever is made of a thin, flat piece of steel, filed out on its 
 sides merely to diminish its weight and give it a nice shape. 
 The fork is the common fork of the doable roller already 
 described, and carries on its lower side an index for the 
 safety action, fixed to it by a screw and a steady pin. The 
 lever is joined to the pallet by a plain staff, forming the 
 axis of both, and by a pin fitted in a hole drilled through 
 the lever and pallet near to the extremity of one arm of 
 the latter. This j>iu prevents any displacement of the parts, 
 which would, of '-'ourse, place the whole escapement out of 
 going order. • 
 
 The lever and index are tempered and the surfaces 
 carefully polished, especially the acting parts of the fork. 
 
 The balance staff has a shoulder, on which the balance 
 is fitted and rivitcd. On the lower part of the balance staff 
 and next to the balance a steel disc or roller with a collet 
 projecting towards the balance is fitted, carrying the im- 
 pulse pin. This latter firojects from the lower surface of 
 the roller, is cylindrical, and flattened away one-third. 
 
 The small detaining roller is fitted -jii the balance staff, 
 a liitle lower than the lower extremity of the impulse pin, 
 just to agree with the height of the index on the lever. 
 
 The play of the lever is limited by two banking pins, 
 whose place is near the fork end of the lever. 
 
 In full plate watches, the pallet staff and escape pinion 
 have their pivot holes in the tw .» plates, and may be of the 
 full length allowed by the height of the frame. The bal- 
 ance is hung between two cocks on the upper arid lower 
 side of the upper plate. 
 
 In i plate watches, the pallet staff and escape pinion 
 must be brought under a small cock, to allow the balance 
 above it the necessary freedom. Tiiey must then be very 
 
 short, which is not advantageous, because the necessary side 
 shake in the pivot holes has too much influence on the 
 steadiness of the action. Therefore, it would be desirable 
 to set the escapement in J plate movements in straight line 
 because this arrangement allows a greater length of the es- 
 cape pinion, while in full plate watches the escapement may 
 be set in right angle just as well. 
 
 This escapement, as it is used in England, may serve as 
 a fundamental type in all the following chapters treating 
 of the drawing, execution and proportions of the lever es- 
 capement, and, in fact, all that can be said of this kind of 
 lever escapement is in the same way more or less applicable 
 to any other variety. 
 
 Another arrangement of the lever escapement seems well 
 deserving of a short description here, because it has a very 
 good tendency to facilitate the manufacturing process and 
 to make the parts of the least possible weight, without any 
 prejudice to their solidity. This escapement is devised by 
 A. Lange, and is found in almost all lever watches manu- 
 factured in Glasshutte. (Saxony.) The escapement etands 
 in straight line. The escape wheel is made of very hard 
 hammered gold or aluminium-bronze, and has club teeth. 
 The pallet and lever are but one piece, and of the same 
 material as the wheel. The arm of the lever, opposite the 
 fork end, which generally serves to establish the equipose, 
 is suppressed here, and the fork arm made so thin aS to be 
 counterpoised by the weight of the pallet. The fork end 
 has the usual form, and the guard pin is formed by a thin 
 pin of hard gold or aluminium-bronze \Nire, fixed into a 
 very small square hole next to the bottom of the notch in 
 the fork, and bent in a right angle towards the balance. The 
 pallet has its locking faces at equal centre distances and in 
 equal angles. 
 
 The balance is compensated and hollowod out on both 
 
 38 
 
sides to allow a little more height for the pallet arbor. On 
 the upper side, tlie hollow is uot turned out close to the 
 centre hole, thus leaving a pipe round this latter, to fit the 
 pendulum collet on. 'j'^e hole, iu consequence of this, is 
 rather long, but small ; and the balance staff is but a straight 
 arbor fitted tightly into this hole. This saves the troul)le 
 of turning a shoulder on both sides and riviting the balance 
 upon it, besi'.lcs leaving the ])0ssibility of little alterations 
 in the height of the balance staff by driving this latter a 
 trifle further in or out. Every practical man who knows 
 by experience the vexati jn of a balance not being Ii» proper 
 height in an English watch, will agree that with this ar- 
 rangement the detect is very easily removed, while in an 
 English escapement another staff would be required. On 
 the lower side of the balance the hollow is also not continued 
 up to the centre liole, leaving a thicker part of the balance 
 arm iu convenient length from the centre to receive the 
 impulse pin, which has a triangular form. By these means 
 the roller which in the other lever escapements carries the 
 impulse pin, is dispensed with, and consequently the dead 
 weight of the balance staff and the manufacturing expenses 
 diminished A. small detaining roller completes* the ar- 
 rangement. The banking is etiected by a pin projecting 
 from the lower surface of the short or entrance arm, estab- 
 lishing at the same time the equipoise between the short and 
 long pallet arm. This pin plays iu a hole in the cock under 
 the dial, or in the pillar plate, and the hole must be of just 
 the size to allow the necessary freedom of escaping. This 
 way of banking might be thought objectionalilo for the 
 reasons mentioned in Chapter VI, but the lever in this es- 
 capement being very thin and elastic, there is hardly any 
 danger for the pivots and impulse pin. Besides, it has the 
 advantage of not being liable to derangement by careless 
 workmen, for the banking inn in the pallet is so strong as 
 
 not to be easily bent. Diagram 1.3 gives an illustration of 
 Lange's lever escapement. 
 
 Mr. Lange has lately perfected the escapement in a way 
 which deserves mention here. It is a natural defect of all 
 lever escapements with inclined planes on the [)allet, that 
 during the lifting action, l)y the gradual movement of the 
 pallet, the angle in which the lifting plane stands to the 
 wheel tooth is altered in every movement of the action. The 
 result of this alteration is an unequal distribution of the 
 lifting along the length of the lifting plane. When we 
 suppose this length divided into a certain number of equal 
 parts, the angularity performed by one of these parts will 
 not be equal to that produced by any of the other parts. 
 This change of position of the lifting planes would be less 
 objectionable if it were of the same nature for both arms of 
 the pallet; but this is uot the case. On the contrary, the 
 angle of the lifting plane of the first arm increases coutiu- 
 ually during the lifting action, while that of the second arm 
 is gradually diminishing. The intended angle of lifting is 
 performed, nevertheless, but is not equally distributed 
 within the length of the lifting plane. The inclination of 
 the lifting plane on the first arm will be the least at the 
 beu'inniue of the lifting action, and that on the second arm 
 will be greatest when the action begins. 
 
 This defect may be noticed by the circumstance that in 
 well-made lever watches, iu cases where the moving force is 
 not suflicient, or its effect lessened by thickened oil and in- 
 creased frictional resistance, the escapement has a tendency 
 to set on the lifting face of the entrance arm when the pen- 
 dulum spring is so adjusted that the balance stands right 
 in the middle of action. To remove this defect, the ad- 
 justment of the pendulum spring must be slightly altered. 
 
 For better illustration, Diagram i:> shows an analytical 
 sketch of the form which would be required for the two 
 
 39 
 
driving planes to produce an equal distribution of the lift- 
 ing action For tliis purpose, the angle of lifting, as well 
 as the breadth of pallet, is divided into a certain number 
 of equal parts, and corresponding to the curvature of the 
 wheel circle, the parts of the lifting angle are delineated by 
 arcs described with the radius of the wheel, but from cen- 
 tres of increasing distance from the centre of the wheel. 
 The points of intersection of the corresponding arcs indi- 
 cate the form of the lifting faces, the first of which must 
 be a convex curve, while the second must have a concave 
 form. 
 
 It is difficult to execute such curved lifting faces practi- 
 cally, but the difficulties are happily sui'mounted, and it is 
 a merit due to Mr. Lange to have invented and perfected 
 this valuable improvement of the lever escapement. 
 
 CHAPTER IX. 
 
 DESCRIPTION OF SOME SPECIAL CONSTRUCTIONS ON DIF- 
 
 fFEKENT PRINCIPLES. 
 HE Resilient lever escapement is an invention of J. F. 
 ^^ Cole, and may be considered as a successful solution 
 of the problem of removing all the disagreeable even- 
 tualities connected with the banking. Its principle consists 
 in limiting the lockiug-faces on the wheel or pallet to a 
 very small extent, just sufficient for a sound locking. The 
 continuation of this locking iace stands at an angle to it, 
 similar to the lifting angle, and this secondary lifting angle 
 is for the purpose of leading the pallet back to its place of 
 rest, if, in the case of banking, it has been pushed beyond its 
 escaping arc. It is evident that an escapement" of this kind 
 needs no banking pins, because by the elastic recoil pro- 
 duced b/ the secondary lifting, the pallet and lever always 
 return to the right place. Diagram 14, A and B illustrate 
 the applications of the resilient princijjle most in use, the 
 one with a ratchet wheel and the other with a club wheel. 
 However, I do not think that these two ways of apply- 
 ing the resilient system are the most commendable, because 
 the inclined planes on the foresides of the teeth giving the 
 resilient action, and the driving planes of the pallet, touch 
 each other with very little divergence. This must result in 
 a very detrimental influence upon the rate of a watch, be- 
 cause if the oil is getting thick and glutinous, every approach 
 of these nearly coinciding planes will produce a strong ad- 
 hesion, thereby augmenting the unlocking resistance. This 
 
 40 
 
disadvantage can be avoided by placing the resilient action 
 in the pallet instead of the wheel teeth, in the \\'ay shown 
 by Diagram 14 C, if a ratchet wheel is in question. With 
 a club wheel, however, it would not be gaining anything, 
 because the small inclined planes on the top of the wheel- 
 teeth ^,'ould nearly coincide with the resilient faces of the 
 anchor, thus creating the same danger of adhesion. 
 
 Escapements with the lifting planes only on the wheel- 
 teeth admit a very good resilient action if the foresides of 
 their teeth are shaped in the way shown by Diagram 14, D. 
 
 Watches with a good resilient escapement may be 
 brought to strike violently against the banking by strong 
 motions of the watch, or by an excess of moving power, 
 and still there will not be the slightest exposure to any in- 
 jury on the pivots or impulse pin, nor will they show any 
 essential deviation in their rate, after having banked for 
 some time. 
 
 The repellent or anti-detached lever escapement of J. F. 
 Cole is, as may be concluded by its name, quite a rever- 
 sion of the ordinary principle. Tlie pallet of this escape- 
 ment has the same lifting planes as any other, but the 
 locking faces are different. They have no draw, nor are 
 they concentric circles to the pallet centre, so as to give a 
 dead rest ; they have on the contrary a small angularity, 
 with a tendency to throw the pallet off, so that the escape- 
 ment will run down if the balance be taken out. Instead 
 of a fork, the lever has a thin pointed end, resting against 
 the circumference of a jewel roller and giving the intpulse 
 fo the balance, on the staff of which this roller is fixed by 
 passing through a notch in the roller (Diagram 15) Tt is 
 a great advantage of this escapement that it does not re- 
 quire any safety parts or banking, and consequently it is 
 nee of all the sources of error and failure connected there- 
 •viih. 
 
 41 
 
 At first sight it causes a strange impression to see the 
 greatest virtue of the lever escapement, the independence 
 of its vibrations, thrown overboard so readily, with a view 
 to perfecting it. Still, on close investigation, the idea is in 
 many respects commendable, and well worth reflecting upon. 
 The simplicity of this mechanism, and the removal of 
 the danger of any external disturbance, are very important 
 qualifications for its employment in pocket watches. 
 
 The unlocking without any resistance is also a very val- 
 uable economy of power, and must be esteemed so much 
 the more, as in the detached lever escapement the unlock- 
 ing resistance, which is one of the weak parts of it, cannot 
 be removed. 
 
 The repellent lever escapement requires also a much 
 smaller amount of drop than the detached lever escapement, 
 with the same safety of action, because it does not require 
 the teeth of the escape wheel being undercut, thereby al- 
 lowing the back slope of the teeth to be cut in a direction 
 to leave sufficient liberty to the entering pallet arm. The 
 only objectionable point is the friction on the roller during 
 the excursion of the balanoe. This friction is very similar 
 to that in the duplex escapement, but in this latter it is not 
 supposed an impediment to good performance. On the con- 
 trary, many watchmakers believe that a part of the super- 
 iority of the duplex escapement is chiefly due to this fric- 
 tion, which augments in the same rate as the moving force 
 increases, and thus forms a kind of compensation of power. 
 Apart from the fragility of the duplex escapement insep- 
 arable from its nature, it would be the most resorted to of 
 all the escapements ; and it seems that the repellent lever 
 removes that natural defect. The chief object is to decide 
 whether the friction of the repellent lever escapement is not 
 greater than that of the duplex. 
 
 The roller of the repellent lever must certainly be much 
 
larger thau the duplex roller, or the lifting angle would be 
 disproportioually large. But in the repellent escapement 
 the pressure of the lever end on the roller is but a small 
 fraction of the force of the escape wheel, while the duplex 
 wheel is pressing on its roller with the whole power trans- 
 mitted by the train, only diminished by the greater diameter 
 of the star wheel. 
 
 A simple calculation will be sufficient to show tliat a 
 comparison between the friction of both these escapements 
 does not turn to the disadvantage of the repellent lever. 
 
 To establish equal conditions for both, I will compare a 
 duplex escapement, the imjjulse wheel of which has a di- 
 ameter of 10 millimeters, and a repellent lever escapement 
 with a wheel of the same size. 
 
 The star wheel of the dujslex escapement of this size 
 has a diameter of 13.0 m. and consequently, as the force is 
 in the inverse ratio of the radius, the force with which tlie 
 star tooth acts against the circumference of the roller is to 
 the force of the upright teeth as 10-13, or supposing the 
 force of the impulse wheel = 1, the pressure on the roller 
 
 10 
 is = rrr == 0.769. Tlie ruby roller in a duplex escapement 
 
 of that size has a diameter of 0.77 m. 
 
 The repellent escapement with a wheel of 10 m. diam- 
 eter will have a middle length of pallet arm = 2.885 m. 
 Supposing now the length of lever arm to be 3.08 m. and 
 the lifting intended on the balance roller 40°, the diameter 
 of this latter would be 1.54 m. or the double of the roller 
 in the before mentioned duplex escapement. The pressure 
 of the lever end is now to be ascertained, and we suppose 
 the angle of the locking faces to be 10°, which ought to be 
 sufficient for the repulsion. 
 
 Tie pressure, being in the ratio of the sine of the angle, 
 is in this case =: sin. 10° = 0.1736 (the force of the wheel 
 
 always supposed =: 1). This amount is further diminished 
 in the inverse ratio of the length of the pallet arm to the 
 length of the lever arm. This latter being 2.885 m. and 
 the former 3.08 m., the pressure of the lever end acting on 
 
 , . , , , „ 0.1736 2.885 
 the circumference of the roller is = ttj^ = 0.162. 
 
 Thus the pressure on the duplex roller is to that on the 
 repellent roller as 0.769 to 0.162. 
 
 The friction on both these rollei-s can be supposed in the 
 ratio of the squares of the diameters, and as the roller of 
 the repellent scapement is double the size of that of the 
 duplex, is as 1-4. Therefore the frictional coefficient of the 
 repellent roller must be multiplied by 4 to give the whole 
 amount of comparative friction, 0.162 X 4 = 0.648 This 
 number, compared to that of the duplex, shows clearly that 
 the rei^ellent lever of the proportions supposed in this case 
 is by no means at a disadvantage in point of friction. 
 
 I have thought it not a«iiss to give this calculation here, 
 because the comparison without it would be very uncertain, 
 and might easily lead the student to underrate this inven- 
 tion. 
 
 When we consider, finally, that the repellent lever es- 
 capement has not so much loss of power by the diminished 
 drop of both the wheel and pallet action and that of lever 
 and roller, and besides no loss of power by unlocking re- 
 sistence, it may be considered as a rival to the detached 
 lever escapement, even without taking into consideration 
 the constructive advantage, and soundness of action. 
 
 Comparing it to the duplex, and leaving the settled 
 question of friction aside, the repellent lever has the advan- 
 tage of giving an impulse at each vibration ; and though 
 the transmission of the impulse in the direct way, as we 
 have it in the duplex, be superior to that by the diagonal 
 driving planes and intervening lever, the circumstance that 
 
 42 
 
the duplex impulse requires fur the safety of its action a 
 drop of about 10° before falling on the duplex pallet may 
 be considered to make up for that deficiency. 
 
 By omitting the fork and guard pin, the lever of tliis 
 escapement may be constructed of very little weight, but it 
 is necessary to establish carefully an exact equipoise of the 
 pallet and lever, lest the escapement might go entirely out 
 of action. 
 
 There is one drawback, however, to this escapement. 
 Though it will never set on the lifting, when properly made 
 and kept in good order, it will not go on by itself when the 
 notch in the roller stands in the centre line and the lever 
 end is lying on the right or left side of the roller. This 
 happens very easily, when the watch has gone down. In 
 such cases, tlie watch requires, as well as the duplex watch, 
 a small motion to make the balance vibrate. 
 
 Diagram 15 B shows a pin anchor escapement upoa 
 the repellent principle. 
 
 CHAPTER X. 
 
 INSTKUCTIONS FOK DRAWING CORRECT ESCAPEJIENTS. 
 
 The correct way to draw the escapement is a very im- 
 portant desideratum, especially for those who would like to 
 give a solid and rational base to their endeavors in this part 
 of watchmaking, because, for reasons best known to them- 
 selves, practical working men do not like to undergo the 
 trouble of developing the sizes and angles they require by 
 mathematical calculations. For these persons the graphic 
 way is the most convenient when any uncommon construc- 
 tion or size of escapement is required, while for problems 
 of frequent occurrence they may find it more convenient to 
 go by the tables which will be found in Chapter XII 
 
 For making a good and accurate drawing of a lever es- 
 capement it is necessary to adopt a rather large scale, be- 
 cause the lines of very small angles, as for instance 1° or 
 li°, would nearly coincide if not diawn up to a certain 
 length. Most of the before-mentioned diagrams are made 
 with a radius of the escape wheel = 100 m., which is con- 
 venient for drawing, and for the reduction of sizes. 
 
 THE LEVER ESCAPEMENT WITH THE RATCHET WHEEL. 
 
 Draw a circle with a radius of 100 m. in which the 
 points of the wheel teeth are lying, and trace the line of 
 centres a b. From this line set out to each side 30° with 
 the aid of the protractor, and draw radii c and d to embrace 
 this angle. 
 
 These 60° form the escaping angle of the wheel, and 
 correspond to 2* spaces between the teeth. (The wheel is 
 
 43 
 
ahva3's supposcil to liave 15 teeth, though it might have any 
 other number, and as the wliole circumference of a circle 
 
 is — ^G0°, the space between two teeth is = -^^ — 24°). 
 
 Tlu'ougli tlie two points of locking found by the intersection 
 of the radii c and d with the circumlerence of the wheel, 
 draw rectangular lines e and / to the radii, which of course 
 are tangents to the circle, that is, lines touching the circum- 
 ference but in one jjoiut. The point g, in which the tv,o 
 tangents are crossing each other, falls into the centre line, 
 and is the centre of motion for the pallet. The nest tiling 
 to do is to mark the breadth of the pallet arms. This would 
 in theory be equal to half the space between two teeth, or 
 taking the space as 1-15 of the circumference of the wheel, 
 12° from the wheel centre. But in practice it is impossible 
 to give this breadth to the arms, because no wheel can be 
 made mathematically true in its division, and every moving 
 part of the watch must have for the free movement of its 
 pivots a certain shake. The points of the teeth, too, cannot 
 be made perfectly sharp edges, nor can the slope on the 
 back part of the teeth be hollowed out for the free passage 
 of the delivery edge of the pallet. 
 
 For all these reasons, a suiEcient quantity of drop is in- 
 dispensable for the good and safe action of the escapement, 
 and it will prove a good proportion to employ for this pur- 
 pose 2° of the wheel's circumference, thus leaving but 10° 
 of the 12° for the breadth of pallet arm. 
 
 If a circular pallet is required (Diagram 2), tLdse 10° 
 must be marked as 5° on each side of the radii c d. For 
 forming an escapement with e-.juidistant lockings (Diagram 
 3), the 10° must be aj^plied to the right side of both the 
 radii c and d. 
 
 Through the points iu which the lines of these angles 
 intersect the circumference of the wheel, the cii'cles /( and i, 
 
 k and I, must be traced from the pallet centre, giving the 
 theoretical outlines of the pallet arms. 
 
 To form the driving planes, it is necessary to indi cate 
 the angles of locking and lifting. Of the whole angle of 
 movement (which, in all these drawings, we suppose to be 
 10°, though it might be more or less than that), li* must 
 be reckoned for the locking, and the remaining 8^° serve 
 for the driving action. Supposing the tooth on the outside 
 of the pallet to be on the locking (which for the sake of 
 uniformity will be so in all the drawings), the li° of the 
 .yoking angle, as well as the 8}° of the lifting angle, must 
 be taken towards the wheel centre on the entrance side. 
 The lines m and n are drawn so as to embrace these angles. 
 Pcrresponding to this position of the first pallet-arm, the 
 d«>livery edge of the other arm must be in the periphery of 
 the wheel, where the circle I is intersecting it. A line o 
 must be drawn from the pallet centre to this point, and out- 
 side from tlie tangent /the lines j) and q embracing the an- 
 gles of 82 and li". The points where the lines m and n, 
 and p, are crossing the circles h and i, k and /, when joined 
 by straight lines, give the direction of the driving planes of 
 the pallet. 
 
 For the j^urpose of creating the draw, it is necessary to 
 make the locking faces of tlie pallet deviate from the the- 
 oretical circles h and k, which would only give a dead rest. 
 Therefore a straight line r from the outer edge of the en- 
 trance arm must be drawn, standing at an angle of 12° to 
 the tangent of the circle h, which tangent is in this case 
 identical with the radius c. The same angle of draw being 
 required for the locking face of the other arm, a tangent s 
 must be laid to the circle k in the inner edge of the driving 
 plane on this arm (/ The locking face is drawn by a straight 
 line t. in the angle of 12° to the tangent, from the inner 
 edge of the driving plane. 
 
 44 
 
To promote this drawing action and diminish friction on 
 the lockings, it is necessary to give an inclination to the 
 foreside of the teeth. An angle of about 24° to the radius 
 will be what is required for this purjiose. The sloped back- 
 face of the tooth must be made so as to give a solid tooth, 
 and the lower part of the tooth may have any shape what- 
 ever. The only thing rerpiired is to have the extremity of 
 the tooth thin enough to enable the pallet to escape freely. 
 For saving the trouble of marking these angles for each 
 tooth separately', the following method is very convenient: 
 Prolong the straight line forming the foreside of one tooth, 
 and draw a circle from the centre of the wheel, to which 
 this line is a tangent. Then draw from all the points of 
 teeth straight lines touching this circle in but one point, and 
 these are the foresides of the teeth and all in the same 
 angle to the radial direction. The back lines of the teeth 
 may be drawn in the same way. 
 
 The delivery faces of the pallet arms are made parallel 
 lines to the locking faces, and the rest of the outline of the 
 pallet, which has nothing to do with the action, requires but 
 a convenient shape. 
 
 THE ESCAPEMENT WITH THE CLUB TEETH. 
 
 Diagram 7 shows a club tooth escapement with circular 
 pallet. Draw a circle with a radius of 100 m., in which 
 the fore edges of the teeth are lying, and a line of centres 
 a b, on each side of which set out 30° as before ; then trace 
 the radii c and d and the tangents e and /. From the cross- 
 ing point of these tangents, ff, which must he in the line of 
 centres a b, draw a line v in an angle of 42° to one of the 
 tangents, outside of the circle. These 4^° form the lifting 
 angle for the inclined planes of the wheel teeth, and the 
 remainder of the total lifting angle of 82° is assigned with 
 4° to the pallet. The outer edges of the teeth lie in a cir- 
 cle drawn tlu'ough the crossing point of the lines v and c. 
 
 The 12°, or half the s]>ace between two teeth after a 
 subtraction of I3? of drop (Chapter V shows why with the 
 club wheel a smaller quantity of drop is sufficient), equal 
 to 105°, must be divided between the brcadtli of tooth and 
 that of the pallet arm. Corresponding to their respective 
 lifting angles, they might be made, the tooth 52" and the 
 pallet arm 5". But this projiortion is not obligatory, and 
 might be altered in any direction. 
 
 The 5° of the l)readth of pallet arm must be set out 
 with 21° ou each side of the radii c and d and the circles h 
 and i, k and I drawn, as already described. 
 
 The angle of total movement = 10°, leaves after the 
 subtraction of l2° of locking, a total lifting of 8^°, divided 
 so between wheel and pallet that the former performs 4J8 
 and the latter 4°. 
 
 At first, the locking angle = 1J°, must be marked in- 
 ward of the tangent e by the line m, and then the 4° of 
 lifting by the line n. In the same way these two angles 
 are marked on the other pallet arm outside the line 0, drawn 
 through the crossing point of the circle I with the circum- 
 ference of the wheel. The driving planes are drawn in the 
 way already described. 
 
 The locking faces of the pallet are made with the same 
 drawing angle and in the same way as formerly mentioned 
 when speaking of the ratchet wheel. The foreside of the 
 teeth, too, is nuide witli the angle of 24" to the radius. 
 
 To form the inclined planes of the teeth, set out the 
 breadth of tooth = 5^°, to the left of the radius c; take 
 the resulting size with the compass and mark it on each 
 tooth to the left side. By drawing straight lines between 
 the outer and the fore edges the inclined planes on the teeth 
 are defined. The back of the teeth must be hollowed out 
 in a suitable way for the free passage of the delivery edge 
 
 45 
 
of the pallet, and the shape of the pallet made in the usual 
 manner. (Diagram 7.) 
 
 The pallet with equidistant lockings does not require 
 this particular distribution of the lifting action, and in most 
 cases the lifting angle is so divided that only about one- 
 third of the total lifting is performed by the wheel teeth. 
 
 In this case, the lifting will be 2it on the wheel and 6° 
 on the pallet, and the respective breadths will be, for the 
 tooth 3i° and for the pallet arm 7?. 
 
 Draw the line v at an angle of 2}° to the tangent e, and 
 the circle from the wheel centre passing through the cross- 
 ing point of the line v and the radius c is the circle of the 
 outer edges. Mark the inclined planes and fore sides of 
 teeth in the way already described. 
 
 Mark the 7° for the pallet arm to the right side of the 
 two radii c and d. set out the locking angle = IP and the 
 lifting angle of the pallet = 6°, and draw the circles and 
 lines as already described. (Diagram 8.) 
 
 Diagram 6 is an illustration of the circular pallet with 
 the club wheel and the usual repartition of the lifting angle 
 for better comparison of this way of executing with the one 
 indicated by Diagram 7. 
 
 THE PIN ANCHOR — DIAGRAM 4. 
 
 Draw a circle of 100 m radius for the fore edges of the 
 teeth, trace the line of centres, a h, and mark out on each 
 side of it 30? ; draw the radii c and d and the tangents e 
 and /, as before. Mark on each side of one of the radii 
 li", double which, 25°, is the diameter of the pin. The 
 tooth outside being supposed to be on the locking, the lock- 
 ing angle of 1J° must be marked inside the circle by the 
 line m, and the circle of the pin drawn from the crossing 
 point of this line with the radius c. This done, the half of 
 the space of 24" between two teeth must be divided. After 
 subtraction of 2h° for the thickness of the pin and \l° for 
 
 the drop, the remainder = 8? is the breadth of the tooth, 
 Mark this angle on the circumference of the wheel to the 
 left of the pin, and divide the wheel to give teeth in equal 
 spaces and of equal breadth. 
 
 The total angle of lifting is composed of two parts: the 
 lifting on the inner half of the pin, and that on the inclined 
 planes of the wheel teeth. The thickness of the jsin sup- 
 posed to be equal to 2*° of the wheel, a lifting angle of 
 about 2? on the anchor results from it, and the whole lift- 
 ing angle being appointed = 8*°, the remaining 6i° must 
 be performed by the wheel teeth. Mark this angle outside 
 of the tangent e by the line v, and lay a circle from the 
 centre of the wheel through the point where this line crosses 
 the radius c. This circle embraces the outer edges of the 
 teeth. Draw the inclined plane of one tooth, prolong the 
 line of it, trace a circle to which this line is a tangent, and 
 draw through all the fore edges of the teeth tangents to 
 that circle, which give the inclined planes all in the same 
 angle. 
 
 The pin of the entrance arm standing at the locking, 
 the pin of the other arm must accordingly be outside of the 
 circle of the outer edges of the teeth. To mark this pin 
 draw an arc from the crossing point of the radius d with 
 the tangent /and set out half the thickness of the pin = 
 li° on this arc, just outside of the outer circle of the wheel. 
 This gives the centre of the pin. 
 
 The foresides of the wheel teeth must now be drawn 
 with the angles of draw = 15?, which is done in the way 
 already indicated. 
 
 The back lines of the teeth are made parallel to the 
 locking face of the second following tooth, to give the an- 
 chor pins freedom to enter into the space. The parallelism 
 of the two lines mentioned is not essential, but it affords a 
 
 46 
 
convenience in cutting the Avheel. To iinish the drawing, 
 give a suitable shape to the anchor arms. 
 
 THE JEWELED PIN ANCHOR. 
 
 This escapement is to be draAvn in a very similar way, 
 with the only exception that in this case the edge of the 
 ruby pin can be made sufficiently thin as to produce no 
 supplementary lifting angle, as the round pins in the pin 
 anchor do. (Diagram 6, A and B). 
 
 Draw the radii c and d and the tangents e and /, and 
 inside of one tangent the locking angle = IJ", and outside 
 of it the lifting angle = 82° by the lines m and n. Draw 
 a circle through the crossing point of the line m and the 
 radius c. Then set out 10° to the left of the locking radius 
 for the breadth of tooth, leaving 2° for the drop. Draw the 
 inclined planes of the teeth, give the foresides of the teeth 
 the drawing angle of 15°, and shape the reverse in the way 
 already explained. Trace the locking faces of the pallet 
 jewels in a drawing angle of 10°, and shape the rest of the 
 pallet and jewels appropriately. (In Figure B visible 
 jewels are supposed, though they might be made as well 
 covered in the usual way.) 
 
 THE RESILIENT LEVEE ESCAPEMENT. 
 
 The drawing of the resilient escapement, after what has 
 been said, requires no further explanation. (Diagram 14, 
 A— D.) 
 
 THE REPELLENT LEVEE ESCAPEMENT. 
 
 For drawing the repellent escapement trace the line of 
 centres a b, and the radii c and d, in angles of 30° on each 
 side of it. Mark the breadth of pallet arm = 101° on the 
 right side of the radii c and d, and draw the circles h, i, k, 
 and I. Mark the angle of locking =21° and that of lift- 
 ing = 82° inside the tangent e and outside of the tangent 
 /, and draw the driving planes of the pallet. Then mark 
 an angle of 10° for the repulsion, outside of the tangent of 
 
 circle h and inside of that of the circle Tc, and shape the 
 pallet as usual (Diagram 15). The foresides of the teeth 
 may be radial and the back slope just sufficient to give a 
 solid tooth. 
 
 THE TABLE ROLLER — DIAGRAM 9. 
 
 Draw the line of centres, a b, and to the right and left 
 side of it the lines e and d, at an angle of 5°, the sum of 
 these angles being 10°, the total movement of pallet and 
 lever which we suppose in all the diagrams. Mark on each 
 of these lines the acting length of the lever by the points e 
 and /, representing the edges of the notch in the fork. Take 
 one-third of this length as radius and draw two arcs from 
 the jjoints e and /. These two arcs cross in the line of cen- 
 tres, and their crossing point </ is the centre of the balance. 
 From this centre g draw two straight lines to the points e 
 and /, which in this case embrace an angle of S0°, the lift- 
 ing angle of the roller. The distance between the centre g 
 and the points e and / is the acting radius of the roller, and 
 the outer edges of the ruby pin must coincide with a circle 
 drawn through these points. The pin has commonly abreadth 
 of about 5°, measured from the pallet centre. Mark this 
 size with 21° on each side of the centre line, and draw the 
 form of the ruby pin, by which the size of the notch in the 
 fork is given, which must have a sufficient width to allow 
 the necessary shake to the pin. 
 
 The horns of the fork must be made parts of circles, so 
 as to admit free passage of. the ruby pin when it has gone 
 through the are of intersection. To provide for any want 
 of accuracy in the execution, this fi-eedom is generally made 
 to increase a little towards the ends of the horns, and for 
 that reason the centres of these circles are not adopted in 
 the points of intersection of the lines e and / with the circle 
 drawn out of the centre a, through the balance centre g, 
 
 47 
 
but a trifle towards this centre on the same circle^ See 
 Diagram 9, points h and i). 
 
 The edge of the disc still remains, and the passing hol- 
 low in it. The diameter of the disc must be taken as small 
 as can be, just to hold the ruby pin with solidity after the 
 passing hollow has been made. This latter can be a little 
 smaller than the breadth of the ruby pin, and the guard 
 pin must be put in the lever so as to give the lever IS of 
 play between the banking pin and the roller edge. 
 
 All the rest is merely a matter of form and elegance, 
 keeping in view the practical importance of making the 
 parts as light as soundness and solidity of action will permit. 
 
 THE DOUBLE ROLLER — DIAGRAM 10. 
 
 The drawing of the fork, roller and ruby pin of the 
 angles and respective lengths are the same as those of the 
 table roller When all this is done, draw the circle of the 
 small roller for the safety action. The diameter of this 
 roller varies in the greater part of escapements between f 
 and J of the acting size of the impulse roller. Diagram 10 
 A shows the first-mentioned proportion, while in B the 
 safety roller is half the size of the impulse circle The 
 length of the index piece is such as to have 1? of play to 
 the roller edge when the lever is resting against the bank- 
 ing. 
 
 Tne passing hollow in the impulse roller is no more re- 
 quired, but that in the small roller must be larger than that 
 in the table roller, corresponding to the greater arc of in- 
 tei-seetion in this safety action, which in A ;= 51? and in 
 B = 76°. 
 
 In consequence of this larger arc performed by the safety 
 action, the horns of the fork in a double roller escapement 
 must be longer than those of a table roller escapement. 
 
 THE TWO PIN ESCAPEIMENT. 
 
 Draw the same lines and angles as before described. A 
 
 circle drawn through the points e and / from the centre g 
 represents the impulse roller. In the middle of the arc e f 
 draw the impulse pin and the notch to receive this pin, with 
 a shake of 1 to li°. 
 
 At the distance of 4-5 of the radius of the impulse roller 
 draw the circle for the two unlocking pins, which must be 
 set so that theu' outsides are exactly embraced by the arc of 
 lifting, here supposed to be 30°. The acting (inner) sides 
 of the fork coincide with the prolongation of the lines c and 
 d. The fork has no horns, because in cases where the es- 
 capement would tend to unlock, it would not be possible 
 that the prong of the fork, standing outside, could fall as 
 much inward as to pass or to butt against the corresjjonding 
 unlocking pin. The bottom of the notch in the fork must 
 be made a little slanting from its middle towards the jsrongs, 
 for the purpose of procuring sufficient strength for the hole 
 in which the impulse pin is fitted, without making the notch 
 in the fork too shallow. 
 
 The drawing of the impulse pin and jewel roller escape- 
 ment, as well as that of the spring ibrk, requires no further 
 explanation, because in flmdamental principles they are 
 quite identical with those constructions the drawing of 
 which has already been described. 
 
 48 
 
a- 
 
 Diagram V. 
 
?! 
 
 . / 
 
 Diagram VI. 
 
DiAGEAM VII. 
 
Diagram VIII. 
 
CHAPTER XI, 
 
 ON THE PROPORTIONS OP THE PARTS OF THE LEVDR ES- 
 
 OAPKMEXT, AND THE EFFECTS OF VARIATIONS 
 
 IN THESE PROPORTIONS. 
 
 ,'NE of the most important essentials to a thorough 
 Icnowledge of the detached lever escapement is to 
 ascertain the best respective proportions of its parts. 
 The nature of this escapement, being composed of two dis- 
 tinctly separate actions, admits a greater variety of propor- 
 tions than any other. This circumstance accounts for the 
 fact that an indefinite number of very divergent opinions 
 on this matter are to be found among horologists, and it must 
 be well understood that many of the questions bearing in 
 this direction cannot be answered absolutely and positively, 
 because the different proportions of the moving force to the 
 weight and diaiueter of the balance and to the required 
 speed of its vibrations, as well as the amount of care which 
 can be bestowed on the execution of the escapement, and 
 many other considerations, essentially influence the matter. 
 Nevertheless, we must try to establish at least some general 
 principles which will, if discreetly adhered to, secure a good 
 performance of the escapement under common circum- 
 stances, and be a safeguard against extremes in any direc- 
 tion. 
 
 To begin with the wheel, the number of its teeth is 
 generally fifteen. This number, however, is by no means 
 essential, nor need it be an odd number, as many are in- 
 clined to suppose. We should see many wheels with other 
 
 numbers if the greater part of lever watches were not re- 
 quired to show seconds, and for this purpose the number of 
 15, being contained without remainder in 60, is the most 
 convenient. Therefore, and because a wheel of a different 
 number is a very rare occurrence, in all the diagrams, cal- 
 • culatious and tables this number of teeth will be supposed. 
 Any increa,se of this number without alteration of the 
 number of teeth embraced by the pallet would diminish 
 the augle of the wheel scaped over, and vicfi versa, as shown 
 by the following table:* 
 
 Number of 
 wheel teeth. 
 
 10 
 
 11 
 
 12 
 13 
 14 
 
 1.5 
 
 Arc of wheel 
 scaped over. 
 
 .90° 
 , 81° 48' 
 . 7."i° 
 
 69° i.y 
 
 . H4° 16' 
 60° 
 
 Nniuber of 
 
 Arc of wheel 
 
 wheel teeth. 
 
 scaped eyer. 
 
 16 . . 
 
 . . 56° 1.5' 
 
 17 . . . 
 
 . 62° 55' 
 
 18 . . 
 
 . . 50° 
 
 19 . . . 
 
 . 47° 22' 
 
 20 . . 
 
 . . 45° 
 
 The number of wheel teeth embraced by the pallet, 
 though universally three, is also not a mechanical necessity, 
 and with perfect analogy to the anchor of Graham's dead 
 beat escapement, which generally embraces from six to 
 twelve teeth, the pallet of the detached lever escapement 
 might just as well be made to scape over two, or four, or 
 even more teeth. Therefore the effects of variation in this 
 particular must be examined, to ascertain which number is 
 the best. 
 
 For better illustration of these effects, Diagram 16 shows 
 with one and the same wheel of fifteen teeth four different 
 pallets, the entrance arm of all of which is locking at the 
 same tooth. The first pallet, scaping over two teeth, is 
 drawn with all its auxiliaries and outlines marked with the 
 number 2. The next one, scaping over three teeth, is 
 marked 3 in all its lines. The following, over four teeth, 
 
 ♦The pallet i3 supposed to embrace 2!^ spaces ot teeth. 
 
 49 
 
has the number 4, and the last one, em' racing five teeth, 
 shows the number 5 on all lines belonging to it. 
 
 It will be very easily perceived by this combination that 
 every increase of the number of teeth scaped over makes 
 the driving planes more diverging from the tangent, or from 
 the direction in which the force of the wheel acts, and more 
 approaching to the direction of the radius — the direction 
 which would absolutely oppose any action of the wheel. It 
 will further be seen that the arc of locking becomes more 
 extended and that the pallet arms and driving planes grow 
 longer with every increase of the number of teeth scaped 
 over. 
 
 It might appear that the increase of length of the pal- 
 let arms would be a mechanical advantage — an increase of 
 power ; but such it really is not, because the effect of it, the 
 work performed by the lever and the force employed to this 
 purpose are the same. 
 
 On the other side, there are considerable mechanical 
 disadvantages connected with a pallet of large dimensions. 
 The greater length of the driving planes, together with the 
 unl'avorable diagonal direction of the same, are attended 
 with greater friction, and what is the worst of all, the un- 
 locking resistance increases in the ratio of the squares of 
 centre distance, while the gain of power, if such could be 
 obtained by the longer arms of the pallet, would only be in 
 the ratio of the simple centre distance. • 
 
 It must also not be overlooked that a pallet scaping 
 over five teeth would necessarily be a rather heavy object, 
 the inertia of which would require to be overcome at every 
 beat of the escapement, and that an escapement with such 
 a pallet would require more space than could be well af- 
 forded in a watch. 
 
 If, therefore, a pallet scaping over five or four teeth 
 does not work with any mechanical ad vantage, and better 
 
 conditions can be obtained by scaping over a smaller num- 
 ber of teeth, it might be asked whether three, teeth would 
 not be also objectionable to a certain degree, and whether 
 we had not better make all our pallets scape over two teetk. 
 This is a point which must be thoroughly examined, 
 and the same considerations decided here in favor of the 
 usual system will apply to many other particulars in the 
 lever escapement, so that it is preferable to treat this matter 
 more amply. When it is asked what number of teeth 
 scaped over will be the best system, and whether three are 
 preferable, or more, or less, it must be considered that there 
 are reasons for and against any of the two extremes. We 
 have already mentioned the considerations that make a pal- 
 let scaping over more than three teeth appear objectionable. 
 The pallet scaping over two teeth is certainly not so heavy 
 as that over a larger number of teeth; the driving planes, 
 being less divergent from the direction of the wheel's action, 
 admit a more perfect transmission of power; the action on 
 the driving planes is shorter, but more energetic, and occa- 
 sions less friction ; the locking arc and unlocking resistance 
 is reduced to the smallest amount possible. Still, there are 
 considerations obliging us to keep within certain limits also 
 on this point. 
 
 A glance at Diagram 16 shows that the arcs of motion, 
 though the angle be the same for all the four pallets, exhibit 
 a great difference, arising from the different lengths of pal- 
 let arms or radiL The lengths of these arcs are, measured 
 fi-om the diagram: 
 
 For the pallet over two teeth, . . . 5.6 m. 
 
 " " " " three "... 9.9 " 
 
 " " " " four " ... 15.8 " 
 
 " " " " five "... 24.0 " 
 
 It cannot be doubted that the real effect of all these 
 
 lifting movements will be a little less than it was intended 
 
 50 
 
to be, because in reality the shake which must be granted 
 for the freedom of the pivots in their holes will produce by 
 the reaction on the inclined planes a tendency of the acting 
 parts to take the widest distance possible. This loss in the 
 mechanical effect is of much more consequence than it is 
 usually esteemed to be. Therefore it will be advisable to 
 deduce its extent by a little calculation. For common size 
 escapement pivots a shake in the holes of 0.015 m. is an 
 absolute necessity. This shake of the escape pinion and 
 the pallet axis make together an increase of the pitched 
 distance of 0.03 m., when both pans are taken in an un- 
 favorable direction, as will be ^mostly the case when the 
 parts are in action. 
 
 The size <>t the wheel in this diagram is to that of a 
 common size escape whtfei about as ?0 : 1. Cousequently 
 the eSect of this increase of distance will be for a wheel of 
 the size in the diagram = 0.9 m. 
 
 When we compare now the diiference of 0.9 m. with 
 the total extent of the arc of movement in the pallet over 
 two teeth = 5.6 m. (See the table), we shall find that it is 
 a loss of about i-6, or 16 per cent, of the intended total 
 lifting effect. 
 
 Escapements with a pallet scaping over three and more 
 teeth, requiring exactly the same conditions for the freedom 
 of their pivots, suffer of course under the same loss i.. 
 nieclianical effect, but not so much to their disadvantage, 
 for the alteration of 0.9 m. in the pitched distance is but 9 
 per cent, of the whole arc of movement of the pallet over 
 three ^eth. The pallet over four teeth has under the same 
 circumstances but a loss of 6 per cent., and that over five 
 teeth li ses only 3.7 per cent, of the total amount of intended 
 motion, by the same shake of the pivots. 
 
 This diminution of the lifting eflect is, however, not so 
 detriflaeatal as the loss on the locking. The extent of the 
 
 locking arc when measured on the drawing is only 0.9 m. 
 with the pallet scaping over two teeth, and consequently 
 the whole locking action would be annihilated by the indis- 
 pensable shake of the parts, and the necessity would urge a 
 greater angle of locking. Thus the gain obtained on one 
 side would be lost on the other. 
 
 In all this, we have merely spoken of carefully sized 
 pivot holes and carefully pitched pallets, and it must be 
 perceived by the examples given that for a pallet over two 
 teeth the slightest excess of shake in the holes, or the smallest 
 deviation from the true pitch, would immediately produce 
 the greatest irregularities in the action of the escapement, 
 while the same defect would be of little consequence to a 
 pallet over three teeth. In short, the pallet over three teeth 
 is preferable, because those over more than three teeth wor k 
 under mechanical disadvantages, further augmented by 
 thickening oil, etc., and because the pallet over two teeth 
 requires a greater accuracy of execution than could be af- 
 forded under common cu'cumstances. 
 
 The angle of lifting on the pallet is another very im- 
 portant point, on which, nevertheless, opinions are very 
 different. We see escapements with lifting angles varying 
 from 6"^ to 12", and even more, and the question which of 
 these angles is the best is a very natural one. 
 
 Diagram 17 is intended to illustrate the effects of differ- 
 ent lifting angles. One and the same pallet is represented 
 with an angle of total movement of 6? from drop to drop, 
 and with an angle of 15°. For the lifting of 6^ a locking 
 angle of 1** has been adopted, while that of 15? shows a 
 locking angle of li°. The lines belonging particularly to 
 the angle of 6" are marked 1, and those referring to the 
 angle of 15° are marked 2. 
 
 The effects produced by these two extreme angularities 
 are the foUowing: 
 
 51 
 
The driving planes increase in length with the lifting 
 angle, and at the same time they become more divergent 
 from the direction in which the wheel acts. In both cases 
 the whole power of the wheel is acting, but as the pallet 
 with the longer arc is made to go through a wider distance, 
 it is quite plain that the action at each point of this dis- 
 tance cannot have the same energy, according to the great 
 rule of mechanics that the force is in the inverse ratio to 
 the velocity or to the distance to be })assed over. Besides, 
 the friction on these hjuger and mure diagonal driving planes 
 is also a disadvantage. 
 
 On the other- hand, the reasons already mentioned wi'l 
 apply here to prevent the construction of pallets with too 
 short arcs. A pallet with 8? of total movement will re- 
 quire the utmost rastriction of the locking angle, else th^s 
 latter would form too great a part of the whole movement ; 
 in consequence of which, this pallet would necessitate a 
 very exact pitching and a most careful sizing of the pivot 
 holes, because the least imperfection in these points would 
 make the lockings unsafe and occasion considerable loss in 
 the real eflect of the lifting. We liud the long arcs of 
 movement in all the inferior classes of watches, and with 
 good reason, especially when there are no jewel holes for 
 the escape pinion and pallet axis, in which case a greater 
 shake must be granted, because the brass holes cannot, for 
 durability, be made so short or be rounded off, as a jewel 
 hole may be. Short arcs, down to 8°, are em25loyed only 
 in the very best and most carefully constructed watches. 
 
 For escapements with the table roller it is not advisa- 
 ble to emjjloy a pallet moving less than 10?, because the 
 arc of intersection for the safety action is then too small 
 to admit a perfect performance. 
 
 The shape of the teeth may also be made an object of 
 consideration. An alteration of this shape would be possi- 
 
 ble by making the acting faces less inclined, and altering 
 the back slopes accordingly. This would produce a shape 
 similar t(> that in Mudge's escapemen' {See Diagram 1), 
 and would be desirable by diminishing the drop which 
 must necessarily be given to a ratchet wheel to make the 
 delivery edges of the pallet pass freely the back slope of 
 the tooth. But a very serious objection to such shape of 
 teeth is that the friction on the locking would be considera- 
 bly increased, because there would not be the point of the 
 tooth, but a part of the acting face of it, lying against the 
 locking face. The drawing action of the pallet would also 
 be annihilated by approaching the acting face of the teeth 
 to the radial direction. For this reason it is not advisable 
 to make the inclination of the teeth less than 24° to the 
 radius. 
 
 The length of tho teeth, if the ILfting angle of the pal- 
 let is not an uncommonly large one, may be 1-10 of the 
 wheel's diameter. Any excess of length, especially with 
 a ratchet wheel, would be of no use, and would put the 
 durability of the wheel in danger. 
 
 With respect to the form of the club teeth, the same 
 considerations demand a sufficient inclination of their fore- 
 sides. The objection of any loss of power by too much 
 drop does not apply to the club wheel, because the possibil- 
 ity of hollowing the back part of the tooth allows as close 
 scaping as possible. The small inclined planes on the club 
 teeth should be of such angle that the lifting on the pallet 
 would be performed first, and that of the wheel tooth take 
 place fifterwards, at the delivery edge. When the total 
 lifting angle is divided so that its greatest part is assigned 
 to the wheel, without giving at the same time more breadth 
 to the teeth, the result will be that the lifting of the wheel 
 tooth is performed first, by the inclined plane of the tooth 
 
 52 
 
at the entrance edge, which is not so favorable as in the first 
 method. 
 
 The wheel teeth'of the pin anchor, and siraliar construc- 
 tions, are bound, as to tlie forms of their fore faces, to the 
 necessary drawing angle. The back part must be undercut 
 to allow free passage to the pin during the slight recoil pro- 
 duced by the drawing angle at the moment of unlocking. 
 The lifting faces of the teeth may be made in dift'ereut 
 ways. Some of these escapements have straight lifting faces, 
 .some of them curves, although there seems no reason for 
 a<li)pting this latter system, as the lifting angle of this kind 
 of wheels, diiferent from all other kinds, is regular from 
 beginning to end, so that any part of the length of the lift- 
 ing face sliows the same lifting efl'ect as any other part of 
 the same length, '.vhich cannot be said of the club wheel' 
 and less still of the ratchet wheel. In fact, if it were of 
 any importance to give to a ratchet or club wheel escajie- 
 ment this regularity of lifting, the lifting faces of the two 
 arms would require to be curved, and differently curved, 
 too, the one on the entrance arm convex, and the other con- 
 cave. This complication has not been thouglit essential for 
 regularity of performance ; but when the pin anchor afibrds 
 by its nature this correct progression of tlie lifting, we can 
 see no reason for destroying it. Therefore the straight line 
 seems to be the best shape hr the lifting faces of the wheel 
 teeth in the pin anchor escapement. 
 
 The length of the lever, in its proportion to the length 
 of the pallet arms, e.xhibits the greatest variation of all the 
 proportions in the lever escapement. This is explained by 
 the fact that the fork and roller action is entirely indei)en- 
 dent of the action of the wheel and pallet. The length of 
 lever may be in any proportion to the diameter of the wheel, 
 or, which is the same, to the length of the pallet arms, with- 
 out prejudice to the mechanical effect. We find escape- 
 
 ments with levers whose acting length is more than three 
 times the length of the pallet arm. Swiss manufacturers 
 have gone very far indeed in that direction, for the purpose, 
 probably, of making a fine display of the escapement, this 
 idea evidently prevailing in all their manufactures. But 
 to the practical horologist this is but a secondary considera- 
 tion, and we must ask in the first place, what are the effects 
 of increased length of the lever on the performance of the 
 escapement? 
 
 The answer to this question is very similar to those al- 
 ready given when speaking of the proportions of the pallet. 
 Any increased length of lever will require a greater radius 
 of impulse, or a greater distance of the impulse pin from 
 the balance centre, if the angle of lifting remains the same, 
 and conse(iuently the arc of intersection will be longer, and 
 the friction of the acting parts must increase in the same 
 ratio. The force transmitted both in the unlocking and the 
 impulse action is the same whether the lever be long or 
 short, provided the angles performed and the proportions of 
 lever length and impulse radius remain tlie same in both 
 cases, and the only difference consists in the greater breadth 
 of intersection and the increased friction connected with the 
 long lever. 
 
 These considerations would lead to employing as short 
 levers as possible; but it must be observed here that the 
 diminution of the intended effect of the movement by the 
 necessary side shake in the pivot holes must be taken nonce 
 of, because the loss arising from this circumstance, tbough 
 an absolute quantity, is in very different proportion to the 
 extent of the distance to be performed by the fork and roller 
 action. Therefore it is advisable not to go too far in either 
 direction, and it may be esteemed a good proportion to make 
 the lever not so long as to allow its arbor to stand beyond 
 the circumference of the balance. 
 
One consequence of the short lever in all three-fourths 
 plate watches will be that the pallet arbor must be 
 made very short and the escape pinion too, if the es- 
 capement is not set iu straight line ; but the advantages of 
 diminished friction outweigh this minor defect of construc- 
 tion so much that we see all the better lever watches of our 
 day, and the English lever watches without exception, with 
 short levers of about 0.55 to 0.6 of the diameter of wheel. 
 
 The angle of lifting on the roller depends entirely upon 
 the proportion of the length of the lever to the centre dis- 
 tance of the impulse pin (impulse radius), and the angle 
 produced at the roller is in the inverse ratio of these lengths 
 to the angle performed by the lever. 
 
 If, for instance, the length of the lever be 4.2 m. and 
 its angle of movement 10° and the angle of lifting on the 
 roller is intended to be 30°, the acting length or radius of 
 impulse will be: ^ g m. 10 
 
 30 
 
 1.4 m. 
 
 = 1.05 m. 
 
 For a lifting angle of 35^ it would be: 
 
 4.2 m. 10 , „ 
 
 = 1.2 m. 
 
 35 
 
 and for a lifting angle of 40^^ : 
 4.2 m. 10 
 40 
 
 When we try to ascertain which lifting angle is best 
 suited to a good performance of a lever escapement, we must 
 in the tir.st place examine the effects produced by changing 
 the extent of this angle. The consequence of a large lift- ' 
 ing angle is a longer arc of intersection, attended with in- 
 creased friction and diminished energy of imjjulse at each 
 point of its path, because the same force must be spent to 
 perform a longer course. The consequences of a small lift- 
 ing angle are the unfavorable extent of the loss of move- 
 
 ment by shake of the parts, and the greater influence of 
 alterations of intended effect by impropm- ;iiiching or 
 wearing out of the pivot holes and pivots. All these con- 
 siderations are nearly the same a.s before mentioned, and 
 their result is that any excess in both these directions ought 
 to be avoided, but that within certain limits, and especially 
 in escapements made and pitched iu a very careful way, 
 the performance of the smaller angle ought to be preferred 
 for the greater detachment of the vii)rations of the balance 
 afforded by it. 
 
 But there is still another reason against the large angle 
 of lifting. This is the very imfavorable action of the un- 
 locking, which takes place at the two extremes of the lifting- 
 arc. It is evident that this action will be the easiest when 
 performed as near the centre-line as can be, and will cause 
 more loss of power the farther it takes place from this line. 
 This loss of power finds no comjjensation in any other part 
 of such construction, and consequently it should be avoided 
 as much as possible. 
 
 One circumstance is also of great influence upon the de- 
 cision of this question, and it must be indicated here, though 
 falling beyond the reach intended for this treatise. The 
 unlocking action has to be performed by the returning vi- 
 bration of the balance, and this vibration is effected by the 
 tension of the pendulum spring. This tension, supposing 
 all other circumstances to be the same, will be stronger if 
 the unlocking takes place farther from the centre line, and 
 will diminish the nearer it comes to that line, on which 
 there is no tension at all. In such cases, when the balance 
 is small and not heavy enough, the vibrations slow and the 
 pendulum spring weak, the balance will stand a bad chance 
 of overcoming the unlocking resistance, especially when, 
 for obtaining a large vibration, a mainspring of proportion- 
 ately great strength is applied to the watch Under such 
 
 54 
 
circumstances the escapement will have a tendency to set on 
 the lockings and not to go on, except by an external motion 
 of the watch. Therefore, in all cases in which these pro- 
 portions are not established with the utmost accuracy, and 
 the greatest care in making and pitching the escapement 
 cannot be bestowed, it is not advisable to give a lifting angle 
 of less than 30°. 
 
 The respective proportions between the lifting angle at 
 the pallet ind at the roller are also not dictated liy any 
 general rules of mechanics, and escapements might possibly 
 be constructed with a small angle at the pallet and a large 
 one at the roller, and vice versa. It is also by no means es- 
 sential that the angle at the roller l)e such that the angle 
 at the pallet be contained in it without any fraction. This 
 proportion is quite arbitrary, and will not influence the 
 mechanical effect. Nevertheless, as the considerations which 
 make us choose certain angles as the best suited under cer- 
 tain given circumstances are the same for both the angles 
 in question, it is very unlikely that anybody, except in some 
 particular case, should execute a lever escapement with a 
 very small angle for one and a very large angle for the 
 other action. 
 
 The size or breadth of the impulse pin is also a matter 
 deserving some attention. Many people prefer a broad pin 
 for the impulse, to facilitate the unlocking action. This is 
 quite correct, because a broad pin requires a wide notch in 
 the fork, and consequently brings the unlocking action 
 nearer to the line of centres, which is the most favorable 
 place for it. 
 
 But it must not be overlooked that every gain on this 
 side is a loss on the side of the impulse action, because in 
 the same proportion as the unlocking is approaching the 
 centre line, the impelling action is removing from it. There- 
 fore the solidity of the pin itself must be the principal con- 
 
 sideration, and it may be called a suitable dimension if a 
 flatted cylindrical pin has a breadth of 0.06 to 0.07 of the 
 diameter of the escape wheel. 
 
 The above mentioned circumstances have led to the in- 
 genious invention of the two-pin lever by George Bavage, 
 the essence of which, as it has been already indicated in 
 Chapter VI, is a complete separation of impulse and un- 
 locking, by which the possibility is attained of employing 
 a thin pin for the former and n broad one, or two pins at 
 suitable distance from each other, for the latter. 
 
 For escapements with the two-pin lever the smallest pos- 
 sible angles of lifting will be practicable, because it offers 
 the most favorable conditions for both the actions, and the 
 most economical trausmis.sion of moving force. 
 
 With respect to the two-]iin lever especially, the propor- 
 tion of the unlocking radius to the radius of impulse is 
 6ubject to variations, which in all other fork and roller 
 actions are im[!ossible by their nature. It seems to be of 
 great advantage for an easy unlocking to place the unlock- 
 ing pins as near the centre of the balance as possible, be- 
 cause by forming a shorter lever and acting upon a greater 
 length of the fork lever, the unlocking resistance may be 
 better overcome. But this would be a very great mistake, 
 because in the first place it would require a much larger arc 
 of balance motion for the unlocking, and besides the con- 
 siderable difference of speed with which the unlocking pins 
 would move, compared to the outer edge of the roller, would 
 have the effect that the notch would have nearly passed the 
 impulse pin before the unlocking was completely over. To 
 prevent the butting of these parts, a much wider notch 
 would then be required, and the drop arising from it would 
 consume more than the power saved (jn the unlocking. The 
 best plan, therefore, seems to be to plant the unlocking pins 
 as near the edge of the roller as can be, and four-fifths of 
 
 55 
 
the radius of the roller may be considered a very good pro- 
 portion of the unlocking radius of the two-pin lever. 
 
 The size of the detaining roller is of no great conse- 
 quence for the action of the lever escapement, because 
 the parts belonging to the safety action are not acting parts, 
 as all the rest of the escapement, but on the contrary are 
 quite out of action during the common, regular performance 
 of the e.sca|ienient, and in well made escapements are 
 acting only in very exceptional cases, when by some external 
 uiiluence an iriv,^ulurity in tlw functions of wheoi and pal- 
 let happens. Their action is also of very short duration, 
 because the next vibration must necessarily re-establish the 
 regular state of things. For the soundness of the safety 
 action it is sufficient to give the detaining roller just the size 
 of the impulse circle, so as to make its angle of intersection 
 equal to that of the impulse pin. But in those exceptional 
 cases where the detaining roller plays the active part it li 
 intended for, it is im})ortant to diminish the friction arising 
 out of the pressure of the index or guard pin against the 
 circumference of the roller to the smallest amount possible, 
 which, supposing the surfaces of the parts to be polished 
 very smoothly, can only be eilected by giving the roller the 
 smallest size permitted without prejudice to the soundness 
 of the safety action. In good watches with double roller 
 escapements, the detaining roller is about half the size of 
 the circle of impulse, which size admits still a very effica- 
 cious safety action, with an arc of intersection amounting 
 under the other circumstances supposed here to about 80°. 
 The length to be given to the horns of the fork is not 
 the same for all escapements; it is dependent on the angle 
 of intersection ot the safety action, and on the form and 
 breadth of the impulse pin. Thus, the fork of the table 
 roller escapement may be made with much shorter horns 
 than another one with a double roller, and this latter will 
 
 require a greater length of horns in the same proportion in 
 which the diameter of the safety roller is made smaller 
 compared to the circle of impulse. A very broad impulse 
 pin, the foreside of which is made to agree with the impulse 
 circle, admits the total admission of the horns, and we would 
 see escapements of this construction more frequently if, be- 
 sides the unfavorable action of lifting caused by such breadth 
 of the impulse pin (See the paragraph treating of the size 
 of the impulse pin), there were not an objection to be raised 
 against it because it restrains the total space allowed for 
 the vibration of the balance to less than two full turns, thus 
 creating a tendency to banking. This objection, however, 
 being removed by the resilient escapement, the broad pin 
 and the fork without horns have been employed for escape- 
 ments of this class. 
 
 This chapter is one of the most important of this treatise. 
 I am perfectly aware that the reader who takes it in hand 
 with the hope of finding here brief and definite instructions 
 how to make the parts of a good lever escapement in certain 
 proportions will be much disappointed. The nature of this 
 matter, however, would not permit such a course, and it 
 would be indeed something like arrogance on my part if I 
 could have expected to dictate to the horological world cer- 
 tain proportions as the only ones fit for a good lever escape- 
 ment. Such a way of proceeding would have been very 
 convenient, but this is not the purpose for which this chap- 
 ter is written. It is my object to stimulate thought by its 
 contents, in order that each one may find the proportions 
 best suited to the kind of work he is making. 
 
 The assistance in practical execution which might have 
 been expected here will be furnished by the following chap- 
 ter, after having chosen, according to the contents of the 
 present one, the most appropriate lifting angles and pro- 
 portions for the given circumstances. 
 
 56 
 
CHAPTER XII. 
 
 f TABLES OF PEOPOETIONS. 
 
 HE following tables have been prepared for the express 
 purpose of facilitating the construction of correct lever 
 ^^ escapements upon a truly scientific basis, and without 
 experiments or testing instruments, with the aid of the uni- 
 versal measuring system mentioned in Chapter II, which 
 will be completely described and explained in Chapter XVI. 
 
 The tables are arranged, not only to provide for the 
 common procedi'.re of making an escajaement to a wheel of 
 a given size and pitching it afterwards, but they may also 
 be applied in those cases in which any part of the escape- 
 ment must be replaced to fit exactly to the other parts and 
 to the pitched distance. I think tables of this kind have 
 not previously existed, and I hope they will prove very use- 
 Jiil to the practical workman, who does not like making 
 calculations. 
 
 The tables refer only to escapements with wheels of 15 
 teeth and pallets scaping over 3 teeth, because deviations 
 from these proportions are of very rare occurrence, and the 
 enumeration of all such excejjtional cases would extremely 
 complicate the tables, without being of any real use. In all 
 cases in which it might be desirable to construct an escape- 
 ment, or to replace parts of one, having any deviation from 
 these generally adopted suppositions, the type of calculation 
 given to each table will indicate the shortest way to calcu- 
 late the required proportions, while for those who are not 
 accustomed or not inclined to calculations, the explanations 
 given in Chapter X will be sufficient to enable them to make 
 
 a correct drawing of the escapement to be made, and the 
 proportions taken from a drawing of the proposed size will 
 aflbrd all the accuracy that could be wished for, attainable 
 by human hands. 
 
 The tables of proportions for the wheel and pallet action 
 are made under the supposition of three different angles of 
 total movement: 8°, 10° and 12°. For the first case, a 
 locking angle of 1*^ is adoi)ted, while those of the two others 
 are H", so that after subtraction of the locking angle there 
 remains a real lifting of 7", 8i° and 101°. For any lift- 
 ing angle between these three, if it should be required, the 
 numbers will be easily found by interpolation, as their pro- 
 gression is merely an arithmetical one. 
 
 EXPLANATION OF THE DIFFERENT COLUMNS IN TABLES I 
 AND II. 
 
 It must be mentioned in the first place that these tables 
 purposely give the diameters of all circles and not their 
 radii, though the latter are the real acting lengths. This 
 has been found preferable with a view of making the tables 
 more handy and convenient to the practical workman, who 
 always measures the diameters, because the radii cannot be 
 measured in a direct way. 
 
 The second column contains the sizes of the wheels, 
 when measured. These sizes do not exactly equal the dia- 
 meter of the wheel, because the odd number of teeth does 
 not admit of measuring two opposite teeth, but always one 
 tooth and the space opposite to it. This makes a difference 
 equal to the height of arc of an angle of 24° from the wheel 
 centre, amounting to 0.0109 or 1-100 of the diameter of the 
 wheel, and thus a wheel measuring 9.9 m. has a real diame- 
 ter of 10 m. For all cases where wheels must be made to 
 fit to a certain given centre distance or pallet, I have thought 
 it useful to take this difi'erence into consideration. 
 
 67 
 

 
 TABLE I. 
 
 CiRC0LAR Pallet. Ratchet Wheel. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 
 
 
 
 Lifting circles for total angle of pallet 
 
 Height of seg- 
 
 Breadth of 
 
 Distance of 
 
 Diameter of wheel. 
 
 Circles ol pallet. 
 
 movement. 
 
 ment. 
 
 pallet arm. 
 
 centres. 
 
 
 Measured 
 
 Outflr 
 
 luner 
 
 8» 
 
 109 
 
 128 
 
 1.0 
 
 0.99 
 
 0.li647 
 
 0.4901 
 
 0.211 
 
 0.248 
 
 0.292 
 
 0.502 
 
 0.0873 
 
 0.6774 
 
 5.0 
 
 4.95 
 
 333 
 
 2.45 
 
 1 .06 
 
 1.24 
 
 1.46 
 
 2.51 
 
 0.44 
 
 2.89 
 
 5.2 
 
 5.15 
 
 3.46 
 
 2.55 
 
 1.10 
 
 1.29 
 
 1.52 
 
 2.61 
 
 0.46 
 
 3.00 
 
 5.4 
 
 5.;55 
 
 3.59 
 
 2.(!5 
 
 1.14 
 
 \M 
 
 1.58 
 
 2.71 
 
 0.47 
 
 3.12 
 
 5.6 
 
 5.54 
 
 3.72 
 
 2.74 
 
 1.18 
 
 1.39 
 
 1.64 
 
 2.81 
 
 0.49 
 
 3.23 
 
 5.8 
 
 5.74 
 
 3.86 
 
 2.84. 
 
 1.22 
 
 1.44 
 
 1.69 
 
 2.91 
 
 0.51 
 
 3.35 
 
 6.0 
 
 5.94 
 
 3.99 
 
 2.94 
 
 1.27 
 
 1.49 
 
 1.75 
 
 3.01 
 
 0.53 
 
 3.46 
 
 6.2 
 
 6.14 
 
 4.12 
 
 3.04 
 
 1.31 
 
 1..54 
 
 1.81 
 
 3.11 
 
 0.54 
 
 3.58 
 
 6.4 
 
 6.84 
 
 4.25 
 
 3.14 
 
 1.35 
 
 1.59 
 
 1.87 
 
 3.21 
 
 0.56 
 
 3.70 
 
 6.6 
 
 6.53 
 
 4.38 
 
 3.24 
 
 1.39 
 
 1.64 
 
 1.93 
 
 3.31 
 
 0.58 
 
 3.81 
 
 6.8 
 
 6.73 
 
 4.52 
 
 3.33 
 
 1.44 
 
 1.69 
 
 1.99 
 
 3.41 
 
 0.60 
 
 3.93 
 
 7.0 
 
 6.93 
 
 4.65 
 
 3.43 
 
 1.48 
 
 1.74 
 
 2.04 
 
 3.51 
 
 0.61 
 
 4.04 
 
 7.2 
 
 7.13 
 
 4.79 
 
 3.53 
 
 1.52 
 
 1.79 
 
 2.10 
 
 3.61 
 
 0.63 
 
 4.16 
 
 7.4 
 
 7.33 
 
 4.92 
 
 3.63 
 
 1.56 
 
 1.84 
 
 2.16 
 
 3.71 
 
 0.65 
 
 4.27 
 
 7.6 
 
 7.52 
 
 5.05 
 
 3.73 
 
 1.61 
 
 1.89 
 
 2.22 
 
 3.82 
 
 0.67 
 
 4.39 
 
 7.8 
 
 7.72 
 
 5.18 
 
 3.82 
 
 1.65 
 
 1.93 
 
 2.28 
 
 3.92 
 
 0.68 
 
 4.50 
 
 8.0 
 
 7.92 
 
 5.32 
 
 3.92 
 
 1.69 
 
 1.98 
 
 2.34 
 
 4.02 
 
 0.70 
 
 4,62 
 
 8.2 
 
 8.12 
 
 5.45 
 
 4.02 
 
 1.73 
 
 2.03 
 
 2.39 
 
 4.12 
 
 0.72 
 
 4.73 
 
 8.4 
 
 8.32 
 
 5.59 
 
 4.12 
 
 1.77 
 
 2.08 
 
 2.45 
 
 4.22 
 
 0.74 
 
 4.85 
 
 8.6 
 
 8.51 
 
 5.72 
 
 4.22 
 
 1.82 
 
 2.13 
 
 2.51 
 
 4.32 
 
 0.76 
 
 4.97 
 
 8.8 
 
 8.71 
 
 5.85 
 
 4.31 
 
 1.86 
 
 2.18 
 
 2.57 
 
 4.42 
 
 0.77 
 
 5.08 
 
 9.0 
 
 8.91 
 
 5.99 
 
 4.41 
 
 1.90 
 
 2.23 
 
 2.63 
 
 4.52 
 
 0.79 
 
 5.20 
 
 9.2 
 
 9.11 
 
 6.12 
 
 4.51 
 
 1.94 
 
 2.28 
 
 2.69 
 
 4.62 
 
 0.81 
 
 5.31 
 
 9.4 
 
 9.31 
 
 6.25 
 
 4,61 
 
 1.98 
 
 2.33 
 
 2.74 
 
 4.72 
 
 0.83 
 
 5.43 
 
 9.6 
 
 9.50 
 
 6.38 
 
 4.71 
 
 2.03 
 
 2.38 
 
 2.80 
 
 4.82 
 
 0.85 
 
 5.54 
 
 9.8 
 
 9.70 
 
 6.52 
 
 4.S0 
 
 2.07 
 
 2.43 
 
 2.86 
 
 4.92 
 
 0.86 
 
 5.66 
 
 10.0 
 
 9.90 
 
 6.65 
 
 4.90 
 
 2.11 
 
 2.43 
 
 2.92 
 
 5.02 
 
 0.88 
 
 5.77 
 
 58- 
 
\ 
 
 H 
 
 
 
 
 TABLE 
 
 II. Pa 
 
 LLET WITH ElJUI DISTANT 
 
 Lockings. Rah 
 
 'CHf;T W 
 
 'heel. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 ! 
 
 8 
 
 9 
 
 10 
 
 11 
 
 
 
 
 
 
 
 
 
 
 
 
 Height 
 
 Breailtb 
 
 Distance 
 
 Diameter of wiieel. j 
 
 Circles of pallet. 
 
 Circles of lifting for the total angle ( 
 
 f movement. 
 
 of 
 
 of 
 
 of 
 
 
 
 
 
 
 
 
 
 
 
 
 segment. 
 
 pallet arm. 
 
 centres. 
 
 Seal 
 
 Measured 
 
 Locking 
 
 Outer 
 
 Inner 
 
 8° 
 
 10, 
 
 12° 
 
 l.U 
 
 0.99 
 
 0.5774 
 
 0.7519 
 
 0.40t>9 
 
 0.1 343 
 
 0.2753 
 
 0.1823 
 
 0.3'310 
 
 0.2107 
 
 0.3730 
 
 0.5425 
 
 0.087S 
 
 0.6774 
 
 5.0 
 
 4.95 
 
 2.89 
 
 3.76 
 
 2.01 
 
 0.77 
 
 1.38 
 
 0.01 
 
 !.(;() 
 
 l.os 
 
 1.87 
 
 2.71 
 
 0.44 
 
 2.89 
 
 a.l 
 
 5.15 
 
 3.00 
 
 3.91 
 
 2.10 
 
 0.80 
 
 1.43 
 
 (i.:t.") 
 
 I.(i7 
 
 1.13 
 
 l.!)4 
 
 2.82 
 
 0.46 
 
 3.00 
 
 5.4 
 
 5.35 
 
 3.12 
 
 4.06 
 
 2.18 
 
 0.83 
 
 1.49 
 
 O.'.IS 
 
 1.73 
 
 1.17 
 
 2.01 
 
 2.93 
 
 0.47 
 
 3.12 
 
 o.G 
 
 5.54 
 
 3.23 
 
 4.21 
 
 2.26 
 
 0.86 
 
 1.54 
 
 1.02 
 
 l.Sii 
 
 1.21 
 
 2.00 
 
 3.04 
 
 0.40 
 
 3.23 
 
 5.8 
 
 5.74 
 
 3.35 
 
 4.36 
 
 2.34 
 
 0.89 
 
 1.60 
 
 i.(k; 
 
 l..S(i 
 
 1.26 
 
 2.1 1; 
 
 3.15 
 
 0.51 
 
 3.35 
 
 6.0 
 
 5.94 
 
 3.46 
 
 4..-.1 
 
 2.42 
 
 0.93 
 
 1.65 
 
 l.O'.l 
 
 1.93 
 
 ] M 
 
 2.24 
 
 3.26 
 
 0.53 
 
 3.46 
 
 6.2 
 
 6.14 
 
 3.58 
 
 4.G6 
 
 2.50 
 
 0.96 
 
 1.71 
 
 1.13 
 
 i.:i!i 
 
 1.34 
 
 2.31 
 
 3.36 
 
 0.54 
 
 3.58 
 
 6.4 
 
 6.34 
 
 3.70 
 
 4.81 
 
 2.58 
 
 0.99 
 
 1.76 
 
 1.17 
 
 2.05 
 
 1.39 
 
 2.39 
 
 :;.47 
 
 0.5li 
 
 3.70 
 
 6.6 
 
 6.53 
 
 3.81 
 
 4.96 
 
 2.66 
 
 1.02 
 
 1.82 
 
 1.2(1 
 
 2.12 
 
 1.43 
 
 2.46 
 
 3.58 
 
 0.58 
 
 3.81 
 
 0.8 
 
 6.73 
 
 3.93 
 
 5.11 
 
 2.74 
 
 1.05 
 
 1.87 
 
 1.24 
 
 2.18 
 
 1.47 
 
 2.54 
 
 3.69 
 
 0.60 
 
 3.93 
 
 7.0 
 
 6.93 
 
 4.04 
 
 5.26 
 
 2.82 
 
 1.08 
 
 1.93 
 
 1.28 
 
 2.25 
 
 1 ..52 
 
 2.61 
 
 3.80 
 
 0.61 
 
 4.C'4 
 
 7.2 
 
 7.13 
 
 4.16 
 
 5.41 
 
 2.90 
 
 1.11 
 
 1.98 
 
 1.31 
 
 2.31 
 
 1.56 
 
 2.69 
 
 3.91 
 
 o.o;; 
 
 4.16 
 
 7.4 
 
 7.33 
 
 4.27 
 
 5.56 
 
 2.98 
 
 1.14 
 
 2.04 
 
 1.35 
 
 2.38 
 
 1.60 
 
 2.76 
 
 4.01 
 
 0.05 
 
 4.27 
 
 7.6 
 
 7.52 
 
 4.39 
 
 5.71 
 
 3.06 
 
 1.17 
 
 2.09 
 
 1.39 
 
 2.44 
 
 1.65 
 
 2.84 
 
 4.12 
 
 0.(.. 
 
 4.39 
 
 7.8 
 
 7.72_ 
 
 4.50 
 
 5.86 
 
 3,14 
 
 1.20 
 
 2.15 
 
 1.42 
 
 2.51 
 
 1.69 
 
 2.91 
 
 4.23 
 
 0.68 
 
 4.50 
 
 8.0 
 
 7.92 
 
 4.62 
 
 6.02 
 
 3.22 
 
 1.23 
 
 2.20 
 
 1.46 
 
 2.57 
 
 1.73 
 
 2.98 
 
 4.34 
 
 0.70 
 
 4,62 
 
 8.2 
 
 8.12 
 
 4.73 
 
 6.17 
 
 3.30 
 
 1.27 
 
 2.26 
 
 1.49 
 
 2.63 
 
 1.78 
 
 3.06 
 
 4.45 
 
 0.72 
 
 4.73 
 
 8.4 
 
 8.32 
 
 4.85 
 
 6.32 
 
 3.38 
 
 1.30 
 
 2.31 
 
 1.53 
 
 2.70 
 
 1.82 
 
 3.13 
 
 4.56 
 
 0.74 
 
 4.85 
 
 8.6 
 
 8.51 
 
 4.97 
 
 6.47 
 
 3.46 
 
 1.33 
 
 2.37 
 
 1.57 
 
 2.76 
 
 1.86 
 
 3.21 
 
 4.67 
 
 0.76 
 
 4.97 
 
 8.8 
 
 8.71 
 
 5.08 
 
 6.62 
 
 3.54 
 
 1.36 
 
 2.42 
 
 l.(!0 
 
 2.83 
 
 1.91 
 
 3.28 
 
 4.77 
 
 0.77 
 
 5.08 
 
 9.0 
 
 8.91 
 
 5.20 
 
 6.77 
 
 3.63 
 
 1.39 
 
 2.48 
 
 1.64 
 
 2,89 
 
 1.95 
 
 3.36 
 
 4,88 
 
 0.79 
 
 5.20 
 
 9.2 
 
 9.11 
 
 5.31 
 
 6.92 
 
 3.71 
 
 1.42 
 
 2.53 
 
 1.68 
 
 2.95 
 
 1.99 
 
 3.43 
 
 4.99 
 
 0.81 
 
 5.31 
 
 9.4 
 
 9.31 
 
 5.43 
 
 7.07 
 
 3.79 
 
 1.45 
 
 2.59 
 
 1.71 
 
 3.02 
 
 2,04 
 
 3.51 
 
 5.10 
 
 0.83 
 
 5.43 
 
 9.6 
 
 9.50 
 
 5.54 
 
 7 22 
 
 3.87 
 
 1.48 
 
 2.64 
 
 1.75 
 
 3.08 
 
 2.08 
 
 3.58 
 
 5.21 
 
 0.85 
 
 5.54 
 
 9.8 
 10.0 
 
 9.70 
 
 5.56 
 
 7^37 
 
 3.95 
 
 1.51 
 
 2.70 
 
 1.79 
 
 3.15 
 
 2.12 
 
 3.66 
 
 5.32 
 
 0.86 
 
 5,66 
 
 9.90 
 
 5.77 
 
 7.52 
 
 4.03 
 
 1.54 
 
 2.75 
 
 1.82 
 
 3.21 
 
 2.17 
 
 3.73 
 
 5.43 
 
 0.88 
 
 5.77 
 
 59 
 
The columns containing the circles of pallets require no 
 explanation, after what has been said in Chapter V. 
 
 The columns 5, 6 and 7 in Table I and 6, 7 and 8 in 
 Table II indicate the lifting cireks. These circles will re- 
 quire some explanation. 
 
 The exact angle of inclination for the driving planes to 
 give the intended lii'ting etteet can be very conveniently 
 measured by the diameters of circles to which the prolong- 
 ations of the driving planes are tangents, and in the next 
 chapter it will be shown how to use these circles. In the 
 tables they are for the sake of brevity called lifting circles, 
 and their diameters are calculated for the three angles of 
 movement: S'^, 10° and 12", as already mentioned. In 
 Table II there are two diameters given in every column, 
 because for a pallet with equidistant lockings the lifting 
 circles for each pallet arm are not equal, as is the case w ith 
 those of the circular pallet. 
 
 The column 8 in Table I and 9 in Table II indicate the 
 height of a segment, serving to determine the outer corners 
 of the pallet. The diameter for the circle of this segment 
 is that of the largest circle of pallet, and it must be imag- 
 ined to be flattened away by a straight line, to show the 
 height indicated in the table. 
 
 The two last columns contain the breadth of pallet arms, 
 which is the same for both the tables, and the distance of 
 pitch for which the parts are intended, and which cannot 
 be altered without making the escapement defective. • 
 
 The following explanations may serve for the use of 
 those who take an interest in the method of establishing 
 these tables , but it may be repeated here that for the use of 
 {he tables themselves it is by no means necessary to go 
 through these calculations, because the tables are the results 
 of them, and may be used by a person who knows nothing 
 at all of mathematics. Another reason for giving these de- 
 
 tailed explanations is to facilitate, to those who have had a 
 good education, the solution of problems which are out of 
 the common way. Besides, he who writes a book must be 
 aware that it is dedicated to future times and to coming 
 generations, and from all that has been said by the most 
 competent English horologists there prevails the conviction 
 that superiority in our time cannot be secured by mere 
 practical skill, but on the contrary the task of our days 
 must be to give to every workman p. good and thorough 
 education, in order to enable him to apjily the aid of science 
 directly to his practical pursuits. 
 
 The calculations were originally made with live and six 
 decimals, and the result shortened down to the more con- 
 venient length of four decimals. Tliis will account for small 
 differences that may be observed in the last decimals. All 
 the angles in the following calculations have been rounded 
 off, so that differences of less than 5' have been dropped, as 
 they are too minute to perceptibly influence the working 
 sizes. The woodcut diagrams accompanying these calcula- 
 tions are merely meant to facilitate the understanding of 
 the lines and augles spoken of. They serve for very dif- 
 ferent angles and proportions, and it must be remarked here 
 that the}' are not intended to give the proportions and 
 angularities of each special case, but only to give a general 
 impression of the part of the escapement just in question. 
 
 TABLE I. COLUMNS ONE AND TWO. 
 
 The column 2 contains the measured diameter of the 
 escape wheel. This measured diameter is = the real 
 diameter less the height of arc of the central angle of 
 24°, contained between two points of teeth. (See the dia- 
 gram.) 
 
 60 
 
Por a diameter of the. 
 circle =n l,tlie height of 
 arc of the angle of 24? 
 is = 0.0109, of which 
 number the last two 
 decimals may be omit- 
 ted. 
 
 Consequently, the 
 measured diameter of a 
 wheel is =: the real dia- 
 meter less 0.01, or in this 
 case - 1—0.01=0.99. 
 This is the ])ro]jortioiial 
 number at tLe head of 
 column 2. 
 
 P'lir wheels of any greater or smaller number of teeth, 
 the diHerence between measured and real diameter is dif- 
 ferent, because the angle of 24° belongs only to the wheel 
 of 15 teeth. 
 
 d g = a d tang 
 A. =0.5. taug- 
 30°. = 0.5. 
 0.5774.*) = 
 0.2887. 
 
 f/(/is the radius 
 of the locking 
 ' circle, and con- 
 seijuently the 
 diameter of this 
 circle must i)e: 
 
 0.2882=0.5774. 
 
 The diameter of outer circle, as it has been previously 
 explained, is= : 
 
 0.5774+0.0873 = 0.HH47. 
 
 COLUMN THREE. 
 
 The diameter of the outer circle of the (circular) ])allet 
 is the sum of the diameter of the locking circle -|- the 
 breadth of j)allet arm. This latter, equal to an arc of 10° 
 of the wheel's circumference, would be for the diameter of 
 wheel = 1 : 
 
 1 ■ :j.l41fi . 10 _3.1416 
 360 ~ 36 
 
 = 0.08727. 
 
 The diameter of the lucking circle is found in the fol- 
 lowing way: Given the diameter of wheel = 1. 
 The radius a f? =0.5 
 
 coLUJix foi;k. 
 The diameter of the inner pallet circle is, by the con- 
 structiim of the escapement ( Diagram 2) equal to the dia- 
 meter of locking circle less the breadth of pallet arm : 
 0.5774 — 0.0873 = 0.4901. 
 
 COLUMNS FIVE, SIX AND SEVEN. 
 
 The calculation of the lifting circles corresponding to 
 the lifting angles 7", 8i° and 101° is the following. 
 
 *The value of this tangent and of all trigonometric functions will be 
 found in any good handbook of mathematica or navigation. 
 
 61 
 
Of tlic triangle a h c the known jiarls are: 
 
 a=^-- — = 0.3323 (nidiiis of outer circle) 
 
 , 0.4901 „.,,- ,. ,. . . , 
 
 0= — - = (1.^-1.) ( radius ol inner circle) 
 
 0=7", or 8A" or 10]^. 
 
 5) < 0= 7' 
 
 ^ ^^ I "^ " —90" _: := MO^ — 
 
 2 2 ■ 
 
 3° 30' = 86° 30' 
 
 ^-«-(^H5^— «-5 
 
 0.3323 — 0.245 
 = 0J«23T():245'^"^'"'«- 
 
 30' 
 
 0.087:! 
 
 cotano;. 3" 30' 
 
 0.5773 
 log. 873= 2.!)410* 
 + log. c.tang. 3° 30' =11.2135 
 14,1545 
 — log. 5773 = 3.7fi]4 
 
 •In all tbesB caloulatious the oapitol letters siguify angles and the lower 
 case letters, lines. 
 
 log. tang. (A-^) = 
 
 < 
 
 A 
 
 10.3931 
 68° 
 
 <^ +^ = 86° 30' 
 2 
 
 Hence follows: 
 A — 86° 30' + OS" -= 15^° 30' 
 £ = 86^ 30' — 68" = 18° 30' 
 C(already known) = 7° — ' 
 180°—' 
 (,The .sum of the three angles in each triangle.) 
 This calculation was made for the purpose of finding 
 the value of the angled. This angle serves now to de- 
 tiriiiiiie the lino ;/ d in the rectangular triangle g df, of 
 which is known : 
 
 The hypotheuuse ;/ f ^0.3323. 
 
 and<7?" =18° 30' 
 
 yd- <jj sin. B = 0.3323 sin. 18° 30' 
 ^ 0.3323.0.3173 = 0.1054 
 The line 7 '/ is the radius of the lifting circle, and ac- 
 cordingly the diameter of it is 
 
 = 0.1054 . 2 = 0.2108 
 
 62 
 
6) <0=8J° 
 
 -^+-^ = 90'>__^= 91) 
 2 2 
 
 4" l.V = S.-)° 4o 
 
 log. 873 = 2.9410 
 + log. cotang. 4-" 1 -V = 1 1.129 
 14.0700 
 — log. 5773 = 3.76 14 
 
 log. tang./^Lzj?) = 10.3080 
 
 A—B 
 
 = fi3° .")()' 
 
 2 
 
 B = 85" 45' — 63° 50' = 21° 55' 
 g(l = f/f sm B = 0..S32:: . sin 21" 5.5' 
 = 0.3323 . 0.3733 = 0.124047. 
 Diameter of lifting circle - 2 . 0.124 
 = 0.248 
 7) <C'= 10i°. 
 -'^+^ . = 90° ^ = 90° — 5° 15' = 84° 4S 
 
 9 o 
 
 IA—B\ 0.0873 , -o 1 V 
 "\ 2 /- 0.5773 
 
 log. 873 = 2.9410 
 
 + log. cotang. 5" 15' = 11.0368 
 
 13.9778 
 
 — log. 5773 = 3..7614 
 
 log. tang, 
 
 d=^ :^ 58^ 45' 
 2 
 
 i^)- 
 
 = 10.2164 
 
 B = 84° 45' — 58° 45' = 26° 
 d g = fffam B = 0.3323 . 0. 4384 = 0.146. 
 
 Diameter of lifting circle -■ 2 . 0.146 
 
 0.292 
 Tliu.s the diameters oi' the lifting circles for the three 
 lifting angles are: 
 
 Diam. of\ 7°. 8r 10i° 
 
 wheel = 1./ 0.211 0.248 0.292 
 
 f:OLUMN EKiliT. 
 
 The eighth column indicates the height of a segment of 
 the outer circle of pallet (diameter = 0.t;(;47), which serves 
 to find the outer corners of the pallet. 
 
 This height is calculated in the following way: 
 
 Of the triangle h 17 i the known i)arts are: 
 
 (J h = g ; 77= 0.3323 (radius of (jutei- circle.) 
 
 Of the two rectangular triangles a <■ ;/ and a il g the 
 two angles in a are by construction 30" each, and conse- 
 ((uently the two other angles in g must be G0° each. 
 The sum of the two angles in the angle h .'/ / =^ 1 i^O"- 
 
 The angle h g ii>< ^ < hg I — < I g 1= i 20° — 1° 30' 
 (locking angle) = 118° 30'. 
 
 The sides gh and g i being e(|ual, tli.> angles opjjosite to 
 them must be equal too : 
 
 ]80°— 118° 30' 
 < g h I = < gili=^ ^ 
 
 61" 30' 
 
 = 30" 45' 
 
 A perpendicular line drawn from the point g to the line 
 ///divides the triangle y /i / in two equal rectangular tri- 
 angles. This perpendicular line does not coincide com- 
 pletely with the line of centres (/ a, but as the divergence 
 of the.se two lines is but ii°, it may be neglected altogether 
 
 68 
 
in the drawing. We suppose then the point h to be the 
 point of intersection, and the two rectangular triangles axe: 
 ghk and gik. 
 
 COLUMN NINE. 
 
 The breadth of pallet arm has already been intlieated 
 as being equal to the opening of an angle of 10° at the 
 wheel's centre, measured at the circumference of the wheel. 
 This breadth is = 0.0873 for the diameter of the wheel = 1. 
 
 COLUMN TEN. 
 
 The distance 
 of centres can 
 be found by the 
 rectangular tri- 
 angle a c g, of 
 which we know: 
 *" ac= 0.5 < 
 cag = ZO° (by 
 construction.) 
 
 ac 
 ay ^= 
 
 cos. cag 
 
 0.5 
 
 cos. 30" 
 
 0.5 
 0:866 
 
 =0.5774. 
 
 TABLE TI. COLUMNS one .and two. 
 The real and nie.isiued diameters of wheel are unaltered. 
 
 In tliese two triannles we kmnv: 
 g h =z gi =0.3:!23. 
 <ghi= <gih = ^Q°-i^' 
 gk = gi.sm.gih= 0.3Ci3 . sin . 30" 45' 
 = 0.3323 . 0.5112 = 0.1699 
 The sum of the radius of the outer circle = 0.3323 
 and the line^i = 0/1099 
 0.5022 
 is the height of segment required. 
 
 column three. 
 The circle of locking i^ the same as it has been foun' 
 when calculating Table 1 ; its diameter is = 0.5774. 
 
 COLUMN FOUR, 
 
 The diameter of the outer circle is the sum of 
 
 the diameter of locking circle — 0.57 1 4. 
 
 + double the breadth of pallet arm — OAJio^ 
 
 0.7519. 
 
 64 
 
Diagram XII. 
 
COLUMN FIVE. 
 
 The diameter of the iimer pallet circle is the difference of 
 tlie diameter of locking circle = 0.5774. 
 
 — double the breadth of pallet arm = 0.1745 . 
 
 0.4029. 
 
 COLUMNS SIX, SEVEN AND EIGHT. 
 
 The diameters of lifting circles are, for a pallet with 
 equi-distant lockings, different for tlie driving plane of each 
 pallet arm, therefore the column for each lifting angle con- 
 tains two numbers, the lower of which is the diameter of 
 lifting circle for the first driving plane, and the higher 
 number that for the driving plane of the second pallet arm. 
 
 The way of calculating these numbers is the same as 
 before described, only substituting the different radii. 
 
 .''<5 
 
 ^,- COLUMN SIX. 
 
 C= 7°. First arm. 
 Of the triangle ab c vne know : 
 
 o = 0.2887. (radius of locking circle) 
 6= 0.2015. (radius of inner circle) 
 
 C=7?. 
 
 A+B 
 
 = 90° _ -^ = 90O — 3° 30' = 86° 30' 
 2 
 
 IA—B\ a—b , 
 
 30' 
 
 C 
 
 2 
 
 0.2887—0.2015 , oo "iv 
 
 =: cotang. 3r oO 
 
 0.2887+0.2015 " 
 
 0.0873 , 
 
 = 0:4902-*°''^"^-'' 
 
 log. 873= 2.9410 
 
 + log. cotang. 3° 30'= 11.2135. 
 
 14.1gi6. 
 
 — log. 4902 = 3.69037. 
 
 log. tang. / "^"~^ \ = 10.46413. 
 
 A—B 
 
 = 71' 
 
 B = 86" 30' — 71° = 15° 30' 
 gd = gf sin B = 0.2887. . 0.2672 
 
 = 0.07713 
 Diameter of lifting circle for the first pallet arm 
 2.gd = 2. 0.07713 
 = 0.543. 
 Second Arm. — Known parts of the triangle abc: 
 
 '/ ~ ^ 
 
 a = 0.3759 (radius of outer circle) 
 i = 0.2887 (radius of locking circle) 
 
 0=7° 
 
 65 
 
A+B 
 
 90° 
 
 tang.(:i^) = 
 
 — ■- =00° — 3^ 30' = 86® 30' 
 
 2 
 
 0.3759—0.2887 , C 
 
 cotang. — 
 
 0.8759+0,2887- ^ 2 
 
 '^•^- ^'^ cotang. 3° 30' 
 
 0.664«- 
 
 log. 873 2.9410. 
 + log. cotang. 3" 30' = 11.2135 
 
 log. 664fi 
 
 14.1545 
 3.82256 
 
 A—B 
 
 log. tang. (^~^\ = 10.33194 
 05° B = 86= 30' — 65° = 21 ° 30' 
 
 r/ ,1 = r/f sin. B = 0.3759 . 0.36{i5. 
 = 0.1378. 
 Diameter of the lifting circle of the second pallet arm 
 = 2 . r/r/ = 2 .0.1378 
 = 0.2755. 
 
 / 
 
 ./ 
 
 '-2? 
 
 ^ -■ COLUMN SEVEN. 
 
 < C'=8i°. First arm. 
 « ^ 0.2887 
 b = 0.2015 
 
 ('= 8.1? 
 
 A+B 
 2 
 
 C 
 
 90° —±' = 90" —4" 15' = 85° 45' 
 
 66 
 
 tant 
 
 A—B\ a—h , C 0.0873 , ,„,., 
 
 — T— J = T cotang — = cotang. 4° 15 
 
 , 2 / a-\-b ^ 2 0.4902- 
 
 log. 873 = 2.9410 
 
 + log. cotang. 4° 15' = 11.12894 • 
 
 147)6994 ■ 
 
 — log. 4902 = 3.09037. 
 
 tang. /iL^\ ... 10.37957 
 
 A—B 
 
 ; 07° 20' 
 
 B = 85° 45' — 67" 20' = 18° 25' 
 gd^-gf sin. . £ = 0.2887 . 0.3158 = 0.09117 
 Diameter of lifting circle of the first pallet arm 
 =z2 . r/d = 2 . 0.09117 = 0.1823. 
 
 SECOND ARM. 
 
 a = 0.3759 
 
 h = 0.2887 
 A+B 
 
 r=8i° 
 
 90° —J: 
 
 tsillg- ("^T")- 
 
 = 90 
 
 a — /; 
 
 4° 15': 
 
 c 
 
 85° 45' 
 
 cotang. 
 
 a+h "^ 2 
 
 0.0873 
 
 cotang. 4° 15' 
 
 0.6647- 
 log. 873 = 2.9410 
 + log. cotang. 4° 15' = 11.12894 
 UM99i 
 — log. 6647 = .3.82256 
 
 log. tang. / ^~^ \ = 10.24738 
 
 A—B 
 
 = 00° 30' 
 
 B = 85° 45' — 60" 30' = 25° 15' 
 
 gd = .9/ sin. B= 0.3759 . sin. 25° 15' 
 ^ 0.3759 . 0.4267 
 = 0.10035 
 
Diameter of lifting circle of the second pallet arm 
 = 2 ..^fZ = 2 . 0.16035 
 = 0.3207 
 
 COLUMN EI(4H'l'. 
 
 C = 10*°. First arm. 
 a = 0.2887. 
 h = 0.2015. 
 
 C = 102 30' 
 
 A+B 
 
 = 90" 
 lA—B\ 
 
 C 
 
 90° _ 5" 15' ^- 8-1° 4.V 
 
 /A—B\ __ a 
 
 6 , G 
 cotaug. — 
 
 0.0873 , -o 1 V 
 
 = cotaug. .T lo 
 
 0.4902- ^ 
 
 log. 873 = 2.0410. 
 
 -(- log. cotang. .5° ].")' — 11 03(i74 
 
 13.97774 
 
 — log. 4902 z= 3.69037 
 
 ,^ taug. (-.,-') = 10.28737 
 
 'Izi^— 02" 40' 
 2 
 
 B = 84° 45' — ;ti2° 40' = 22" 5' 
 
 rid =. ^/sin. . B = 0.2887 . 0.3758. 
 
 = 0.10837 
 
 Diameter of lifting circle of the first pallet arm 
 
 z= 2 . r/rf = 2 . 0.10837 
 
 = 0.267, 
 
 tSECOND ARM. 
 
 a = 0.3759 
 /) =;0.2S87 
 A^B „„o C 
 
 90° 
 
 C'=10J° 
 = 90" — 5" 15' = 84° 45' 
 
 iA—B\ a—b , C 
 
 tang.^— -j=__^.cotang._ 
 
 log. 873 
 
 1+6' 
 
 0.0873 
 
 ■ 0.664C' 
 
 cotang. 5° 15' 
 = 2.9410 
 
 67 
 
A—B 
 
 + lug. cotang. 5" ].")' I 1. (13118 
 
 i:r.;»778^ 
 
 — log. I)(i47 ^ :!.S22.')6 
 log. taug. (^i^j = 1< 1. 15524 
 
 rz: 55" 
 
 B = 84° 45' — 55" = 29° 45' 
 ;/ d = gfslu. . B = 0.3759 . 0.4963 
 = 0.18650. 
 Diameter of lil'tiug circle of the second pallet arm 
 = 2. r/f? = 2. 0.18656 
 = 0.373 
 
 COI.t'MN NINE. 
 
 The height of segment in tlii.s case is not quite as easily 
 to lie found as that for the circular jiallot, because of the 
 triangle (/ h i the two sides r/ h and g i, and conseciueutly ihe 
 angles opposite to them, are not ecjual ; so that the known 
 parts are only: 
 
 f/ i (radius of locking circle) = 0.2887. 
 </ h (radius of outer circle) ::= 0.3759. 
 < i,jh z=\18° 30' 
 To shorten the formulse, we substitute for 
 g h — ({ 
 gi — b 
 hi — c 
 and call the angles opposite to these sides A, B and C 
 
 A + B_ 
 
 -90' 
 
 /A—B\ a—h , 
 
 0.376—0.2887 ^ kooir- 
 : •cotang. 59° 15 
 
 (1.376+0.2887 ^ 
 
 0.0873 
 
 ■cotaug. 59'-' 15' 
 
 ~ 0.6647 
 log. 873 — 2.9410 
 
 4- log. cotang. 59° 15' = 9.77447. 
 
 log. 6647 
 
 log. taug. (^-^Y^ ^ ^" 
 
 12.71547 
 = 3.82262 
 
 ,89285 
 
 A—B 
 
 = 4° 28' and 
 
 A + B 
 
 = 30° 45' 
 
 68 
 
 B — -^ + ^' — ^~^ = 30^' 45' 
 2 2 
 
 = 26° 17' 
 
 • 4'* 28' 
 
The angle B hemg foiiml, we have in the rectangular 
 triangle <j h /■ 
 
 the hypothenuse c/ h = O.o7(! 
 <r//)/t=B =26° 17' 
 
 gk = gh sin. B. = 0.37G . sin. 20° 17 
 = 0,376. 0,4428 
 = 0.1665. 
 The sum of the radius of outer pallet circle = 0.376 
 + the linear/- =0.1665 
 
 i.f the required height nf segment = 0.5425 
 
 Explanations of the Columns in Tables III and IV. 
 
 Column One. — The primitive circle of wheel is the 
 circle laW through the fore edges of the teeth. This circle 
 is called the primitive circle because it serves as base for 
 the construction, the locking being performed in it. 
 
 In all the calculations the diameter of primitive circle 
 is supposed = 1 . 
 
 Column Two.— This column indicates the diameter of 
 the theoretical circle embracing the outer edges of the teeth. 
 
 Column three contains the measured size of the outer 
 circle, as e.Kplained when treating th 3 ratchet wheel. 
 
 The columns four and five in Table III, and four, five 
 and six in Table IV give the circles of ])allet correspond- 
 ing to those of the ratchet wheel pallet. 
 
 The columns for the lifting circles, height of segment, 
 breadth of pallet arm and distance of centres are quite 
 analogous to those in the ratchet wheel tables. 
 
 There is .still the column indicating the breadth of wheel 
 teeth before making the inclined plane. This serves for 
 making the cutter for the wheel of the right breadth. 
 
 Finally, the tangent circles serve to draw the inclined 
 planes on the wheel teeth with the proper angularity. 
 
 Table III. Calculations. 
 Columns Two and Three. — The outer diameter is to 
 be calculated in this way : 
 
 The lifting angle to be performed by the wheel teeth is sup 
 
 posed to be 2° for a pallet of 8° of total movement, an 
 
 for those of U". and 
 
 12° of total movement. \ 
 
 For these latter the '\ 
 
 projection of the m- '•, ,-.'^ 
 
 clined end of the tooth 
 beyond the primitive 
 diameter is: 
 o. = b tang. yl. 
 6=(rad. of locking 
 circle) 
 = 0.2887. 
 A = 2i° 
 «= 0.2887 
 
 = 0.2887 
 
 = 0.0126 
 
 tang. A 
 (1.0437 
 
 dsr 
 
 Outer diameter = 1 + 2 . 0.0126 
 
 = 1 4- 0.252 = 1.0252 
 Measured diameter = 1.0252 , 0.99 = 1.0149 
 For the pallet of 8°, A . .2°, and consequently: 
 n = b tang. ^ =0.2887 . tang. 2° 
 = (1.2887 . 0.0.349. 
 =: (1.01 0075 
 Outer diameter = 1 + 2 . 0.010075 
 = 1 -f 0.0201 5 
 = 1.02015 
 This number presents so very small a difference to that 
 referring to the angle of 25°, that we refrain from forming 
 a separate column for it, which would only complicaio the 
 
 Gl) 
 
TABLE III. Circular Pallet — (Jluk Wheel. 
 
 1 1 2 1 3 
 
 4 1 5 
 
 6 1 7 1 8 
 
 9 
 
 10 
 
 11 
 
 12 1 13 
 
 14 
 
 Diameter of wheel circle 
 
 Circles of pallet 
 
 Lifting circles for the total 
 angle of movement : 
 
 Height 
 
 of 
 segment 
 
 0.482.'-. 
 
 Breadth 
 
 of 
 
 pallet 
 
 arm 
 
 0.06108 
 
 Breadth 
 
 of 
 
 wheelteeth 
 
 before 
 
 inclining 
 
 0.0305 
 
 Tangent circles 
 for the inclined 
 planes of teeth 
 
 Distance 
 
 of: 
 
 centres 
 
 
 Outer 
 
 1 I 
 Outer Inner 
 0.(i385 0.S163 1 
 
 8" 10° 
 0.2183 0.2537 
 
 100 
 
 0.3144 
 
 8° 
 0.9088 
 
 10° and 12° 
 0.9476 
 
 
 1.00. 
 
 Real ; Measured 
 1.012G 1 l.OU'25 
 
 0.5774 
 
 5.0 
 5.2 
 5.4 
 5.6 
 
 5.8 
 
 6.0 
 6.2 
 6.4 
 6.6 
 
 6.« 
 
 7.0 
 7.2 
 7.4 
 7.6 
 
 7.8 
 
 8.0 
 
 8.2 
 8.4 
 8.(5 
 8.8 
 
 9.0 
 9.2 
 9.4 
 9.6 
 9.8 
 
 10.0 
 
 5.06 
 
 5.01 
 
 5.27 
 
 6.21 
 
 5.47 
 
 5.41 
 
 5.67 
 
 5.61 
 
 5.87 
 
 5.81 
 
 6.0S 
 
 6.02 
 
 6.28 
 
 6.22 
 
 6.48 
 
 6.42 
 
 6.68 
 
 6.62 
 
 6.89 
 
 6.82 
 
 7.09 
 
 7.02 
 
 7.29 
 
 7.22 
 
 7.49 
 
 7.42 
 
 7.70 
 
 7.62 
 
 7.90 
 
 7.82 
 
 8.10 
 
 8.02 
 
 8.30 
 
 8.22 
 
 8.51 
 
 8.42 
 
 8.71 
 
 8.62 
 
 8.91 
 
 8.82 
 
 9.11 
 
 9.02 
 
 9.32 
 
 9.22 ' 
 
 9.52 
 
 9.42 
 
 9.72 
 
 9.62 
 
 9.92 
 
 9.82 
 
 0.120 
 
 10.025 j 
 
 3.19 
 3.32 
 3.45 
 3.58 
 
 3.70 
 
 3.83 
 3.96 
 4.09 
 4.21 
 4.34 
 
 4.47 
 
 4.60 
 4.72 
 4.85 
 4.98 
 
 5.11 
 5.24 
 5.36 
 5.49 
 5.62 
 
 5.75 
 5.87 
 6.00 
 6.13 
 6.2G 
 
 6.3851 5.163 
 
 2.58 
 2.69 
 2.79 
 2.89 
 3.00 
 
 3.10 
 3.20 
 3.30 
 3.41 
 3.51 
 
 3.61 
 3.72 
 3.82 
 3.92 
 4.03 
 
 4.13 
 4.23 
 4.34 
 4.44 
 4.54 
 
 1.09 
 1.14 
 1.18 
 1.22 
 1.27 
 
 1.31 
 1.35 
 1.40 
 1.44 
 
 1.48 
 
 1.53 
 1.57 
 1.62 
 1.66 
 1.70 
 
 1.75 
 
 1.79 
 1.83 
 1.88 
 1,92 
 
 4.6;) 
 
 1.96 
 
 4.75 
 
 2.01 
 
 4.85 
 
 2.05 
 
 496 
 
 2.10 
 
 5.06 
 
 2.14 
 
 .18:; 
 
 1.27 
 
 1.57 
 
 2.41 
 
 1.32 
 
 1.63 
 
 2.51 
 
 1.37 
 
 1.70 
 
 2.61 
 
 1.42 
 
 1.76 
 
 2.70 
 
 1.47 
 
 1.82 
 
 2.80 
 
 1.52 
 
 1.89 
 
 2.90 
 
 1.57 
 
 1.95 
 
 2.99 
 
 1.62 
 
 2.01 
 
 3.09 
 
 1.67 
 
 2.08 
 
 3.18 
 
 1.73 
 
 2.14 
 
 3.28 
 
 1.78 
 
 2.20 
 
 3.38 
 
 1.83 
 
 2.26 
 
 3.47 
 
 1.88 
 
 2.33 
 
 3.57 
 
 1.93 
 
 2.39 
 
 3.67 
 
 1.98 
 
 2.45 
 
 3.76 
 
 2.03 
 
 2.52 
 
 3.86 
 
 2.08 
 
 2.58 
 
 3.96 
 
 2.13 
 
 2.64 
 
 4.05 
 
 2.18 
 
 2.70 
 
 4.15 
 
 2.23 
 
 2.77 
 
 4.25 
 
 2.28 
 
 2.83 
 
 4.34 
 
 2.33 
 
 2.89 
 
 4.44 
 
 2.38 
 
 2.96 
 
 4.54 
 
 2.44 
 
 3.02 
 
 4.63 
 
 2.49 
 
 3.08 
 
 4.73 
 
 2.537 
 
 3.144 
 
 4.825 
 
 0.31 
 0.32 
 0.33 
 0.34 
 0.35 
 
 0.37 
 0.38 
 0.39 
 0.40 
 0.42 
 
 0.43 
 0.44 
 0.45 
 0.46 
 
 0.48 
 
 0.49 
 0.50 
 0.51 
 0.53 
 0.54 
 
 0.55 
 0.56 
 0.57 
 0.59 
 '0.60 
 
 0.6108 
 
 0.15 
 0.16 
 0.16 
 0.17 
 0.18 
 
 0.18 
 0.19 
 0.20 
 0.20 
 0.21 
 
 0.21 
 0.22 
 0.23 
 0.23 
 0.24 
 
 0.24 
 0.25 
 0.26 
 0.26 
 0.27 
 
 0.27 
 0.28 
 0.29 
 0.29 
 0.30 
 
 0.305 
 
 4.84 
 
 5.04 
 
 5.23 
 
 5.43 
 
 5,62 
 
 5.81 
 
 6.01 
 
 6.20 
 
 6.39 
 
 (!.59 
 
 6.78 
 
 6.98 
 
 7.17 
 
 7.36 
 
 7.56 
 
 7.75 
 
 7.94 
 
 8.14 
 
 8.33 
 
 8.53 
 
 8.72 
 
 8.91 
 
 9.11 
 
 9.30 
 
 9.49 
 
 9.688 
 
 4.74 
 
 2.89 
 
 4.93 
 
 3.00 
 
 5.12 
 
 3.12 
 
 5.31 
 
 3.23 
 
 5.50 
 
 3.35 
 
 5.69 
 
 3.46 
 
 5.88 
 
 3.58 
 
 6.06 
 
 S'JO 
 
 6.25 
 
 3.81 
 
 6.44 
 
 3.93 
 
 6.63 
 
 4.04 
 
 6.82 
 
 4.16 
 
 7.01 
 
 4.27 
 
 7.20 
 
 4.39 
 
 7.39 
 
 4.50 
 
 7.58 
 
 4.62 
 
 7.77 
 
 4.73 
 
 7.96 
 
 4.85 
 
 8.15 
 
 4.97 
 
 8.34 
 
 5.08 
 
 8.53 
 
 5.20 
 
 8.72 
 
 5.31 
 
 8.91 
 
 5.43 
 
 9.10 
 
 5.54 
 
 9.29 
 
 5.66 
 
 9.476 
 
 5.774 
 
 70 
 

 
 
 TABLE IV. Pallet 
 
 WITH 
 
 Equidistant Lockin'gs 
 
 — Cf,ur. Wheel. 
 
 
 
 
 1 
 
 ! 2 
 
 3 
 
 4 1 5 
 
 6 
 
 7 1 8*1 9 
 
 10 1 11 
 
 12 
 
 13 
 
 1 14 
 
 15 
 
 Diameter of wlieel circle. 
 
 Circles of pallet. 
 
 Lifting circles for the total angle of 
 movement. 
 
 Height 
 of Bes- 
 meut. 
 
 Breadth 
 of pallet- 
 arm. 
 
 Breadth 
 of wheel- 
 teeth be 
 fore in- 
 clining. 
 
 Tangent circles 
 for the inclina- 
 tion of teeth. 
 
 Distance 
 
 of 
 centers. 
 
 Primi- 
 
 Outer 
 
 Locli- 
 mg. 
 
 Outer. 
 
 Inuer 
 
 8° 
 
 10" 
 
 12" 
 
 8° 
 
 10 & 12" 
 
 
 tive 
 
 Eeal 
 
 Mens'd 
 
 
 1,00. 
 
 1.(1120 
 
 1.0112.-, 
 
 5.or 
 
 0.5774 
 2.S9 
 
 0.6995G 
 
 0.4.^.124 
 
 0. 17G 0.2e21 
 
 0.20G1 0,304 
 
 0.2.';84 0.3724 
 
 0.5113 O.ric.108 
 
 0.030.5 
 0.15 
 
 0.9688 
 
 4.84 
 
 0.9476 
 4.74 
 
 0.5774 
 
 5.0 
 
 5.06 
 
 3.50 
 
 2.28 
 
 0.88 
 
 1.31 
 
 1.03 
 
 1.52 
 
 1.29 
 
 1.86 
 
 2.56 
 
 0.31 
 
 2.89 
 
 5.2 
 
 5.27 
 
 5.21 
 
 3.00 
 
 3.64 
 
 2.37 
 
 0.92 
 
 1.36 
 
 1.07 
 
 1..58 
 
 1.34 
 
 1.94 
 
 2.66 
 
 0.32 
 
 0.16 
 
 5.04 
 
 4.93 
 
 3.00 
 
 5.4 
 
 5.47 
 
 5.41 
 
 3.12 
 
 3.78 
 
 2.46 
 
 0.95 
 
 1.42 
 
 1.11 
 
 ].G4 
 
 1.40 
 
 2.01 
 
 2.70 
 
 0.33 
 
 0.1 G 
 
 5.23 
 
 5.12 
 
 3.12 
 
 5.6 
 
 5.r.7 
 
 5.61 
 
 3.23 
 
 .3.92 
 
 2.55 
 
 0.99 
 
 1.47 
 
 1.15 
 
 1.70 
 
 1.45 
 
 2.09 
 
 2.86 
 
 0.34 
 
 0.17 
 
 5,43 
 
 5.31 
 
 3.23 
 
 fcS 
 
 5.87 
 
 5.S1 
 
 3.35 
 
 4.06 
 
 2.64 
 
 1.02 
 
 1.52 
 
 1.20 
 
 1.76 
 
 1.50 
 
 2.16 
 
 2.97 
 
 0.35 
 
 0.18 
 
 5.62 
 
 5.50 
 
 3.35 
 
 6.0 
 
 6.08 
 
 6,02 
 
 3.46 
 
 4.20 
 
 2.73 
 
 1.06 
 
 1.57 
 
 1.24 
 
 1.82 
 
 1.55 
 
 2.23 
 
 3.07 
 
 0.37 
 
 0.18 
 
 5.81 
 
 5.69 
 
 3.46 
 
 6.2 
 
 6.28 
 
 6.22 
 
 3.58 
 
 4.34 
 
 2.82 
 
 1.09 
 
 1.C3 
 
 1.28 
 
 1.88 
 
 1.60 
 
 2.31 
 
 3.17 
 
 38 
 
 0.19 
 
 6.01 
 
 5.88 
 
 3.58 
 
 6.4 
 
 6.48 
 
 6.42 
 
 3.70 
 
 4.48 
 
 2.91 
 
 1.13 
 
 l.C.S 
 
 1.32 
 
 1.95 
 
 1.65 
 
 2.38 
 
 3.27 
 
 0.39 
 
 0.20 
 
 G.20 
 
 6.06 
 
 3.70 
 
 6.6 
 
 6.68 
 
 6.62 
 
 3.81 
 
 4.62 
 
 3.00 
 
 I.IG 
 
 1.73 
 
 1.36 
 
 2.01 
 
 1.71 
 
 2.46 
 
 3.37 
 
 0.40 
 
 0.20 
 
 G.39 
 
 6.25 
 
 3.81 
 
 6.8 
 
 6.89 
 
 6.82 
 
 3.93 
 
 4.76 
 
 3.10 
 
 1.20 
 
 1.78 
 
 1.40 
 
 2.07 
 
 1.76 
 
 2.53 
 
 3.48 
 
 0.42 
 
 0.21 
 
 G.59 
 
 6.44 
 
 3.93 
 
 7.0 
 
 7.09 
 
 7.02 
 
 4.04 
 
 4.90 
 
 3.19 
 
 1.23 
 
 1.83 
 
 1.44 
 
 2.13 
 
 1.81 
 
 2.61 
 
 3.58 
 
 0.43 
 
 0.21 
 
 6.78 
 
 6.63 
 
 4.04 
 
 7.2 
 
 7.29 
 
 7.22 
 
 4.16 
 
 5.04 
 
 3.28 
 
 1.27 
 
 1.89 
 
 1.48 
 
 2.19 
 
 1.8G 
 
 2.68 
 
 3.68 
 
 0.44 
 
 22 
 
 6.98 
 
 6.82 
 
 4.16 
 
 7.4 
 
 7.49 
 
 7.42 
 
 4.27 
 
 5.18 
 
 3.37 
 
 1..30 
 
 1.94 
 
 1..53 
 
 2.25 
 
 1.91 
 
 2.76 
 
 3.78 
 
 0.45 
 
 0.23 
 
 7.17 
 
 7.01 
 
 4.27 
 
 7.6 
 
 7.70 
 
 7.62 
 
 4.39 
 
 5.32 
 
 3.46 
 
 1.34 
 
 1.99 
 
 1..57 
 
 2.31 
 
 1.96 
 
 2.83 
 
 3.89 
 
 0.46 
 
 0.23 
 
 7.36 
 
 7.20 
 
 4.39 
 
 .7.8 
 
 7.90 
 
 7.82 
 
 4.50 
 
 5.46 
 
 3.55 
 
 1.37 
 
 2.04 
 
 1.61 
 
 2.37 
 
 2.02 
 
 2.90 
 
 3.99 
 
 0.48 
 
 0.24 
 
 7.56 
 
 7.39 
 
 4.50 
 
 8.0 
 
 8.10 
 
 8.02 
 
 4.62 
 
 5.60 
 
 3.64 
 
 1.41 
 
 2.10 
 
 1.65 
 
 2.43 
 
 2.07 
 
 2.98 
 
 4.09 
 
 0.49 
 
 0.24 
 
 7.75 
 
 7..58 
 
 4.62 
 
 8.2 
 
 8.30 
 
 8.22 
 
 4.73 
 
 5.74 
 
 3.73 
 
 1.44 
 
 2.15 
 
 1.69 
 
 2.49 
 
 212 
 
 3.05 
 
 4.19 
 
 0.50 
 
 0.25 
 
 7.94 
 
 7.77 
 
 4.73 
 
 8.4 
 
 8.51 
 
 8.42 
 
 4.85 
 
 5.88 
 
 3.82 
 
 1.48 
 
 2 20 
 
 1.73 
 
 2.55 
 
 2.17 
 
 3.13 
 
 4.29 
 
 0.51 
 
 0.26 
 
 8.14 
 
 7.96 
 
 4.85 
 
 8.6 
 
 8.71 
 
 8.62 
 
 4.97 
 
 6.02 
 
 3.92 
 
 1,51 
 
 2.^5 
 2.31 
 
 1.77 
 
 2.61 
 
 2.22 
 
 3.20 
 
 4.40 
 
 0.53 
 
 0.2G 
 
 8.33 
 
 8.15 
 
 4.97 
 
 8.8 
 
 8.91 
 
 8.82 
 
 5.08 
 
 6.16 
 
 4.01 
 
 1,55 
 
 1.81 
 
 2.68 
 
 2.27 
 
 3.28 
 
 4.50 
 
 0.54 
 
 0.27 
 
 8.53 
 
 8.34 
 
 5.08 
 
 9.0 
 
 9.11 
 
 9.02 
 
 5.20 
 
 6.30 
 
 4.10 
 
 1.58 
 
 2.36 
 
 1.85 
 
 2.74 
 
 2.33 
 
 3.35 
 
 4.60 
 
 0.55 
 
 0.27 
 
 8.72 
 
 8.53 
 
 5.20 
 
 9.2 
 
 9.32 
 
 9.22 
 
 5.31 
 
 6.44 
 
 4.19 
 
 1.62 
 
 2.41 
 
 1.90 
 
 2.80 
 
 2.38 
 
 3.43 
 
 4.70 
 
 0.56 
 
 0.28 
 
 8.91 
 
 8.72 
 
 5.31 
 
 9.4 
 
 9.52 
 
 9.42 
 
 5.43 
 
 6.58 
 
 4.28 
 
 1.65 
 
 2.46 
 
 1.94 
 
 2.86 
 
 2.43 
 
 3.50 
 
 4.81 
 
 0.57 
 
 0.29 
 
 9.11 
 
 8.91 
 
 5.43 
 
 9.6 
 
 9.72 
 
 9.62 
 
 5.54 
 
 6.72 
 
 4.37 
 
 1.69 
 
 2.52 
 
 1.98 
 
 2.92 
 
 2.48 
 
 3.58 
 
 4.91 
 
 0.59 
 
 0.29 
 
 9.30 
 
 9.10 
 
 5.54 
 
 9.8 
 
 9.92 
 
 9.82 
 
 5.66 
 
 6.86 
 
 4.46 
 
 1.72 
 
 2.57 
 
 2.02 
 
 2.98 
 
 2.53 
 
 3.65 
 
 5.01 
 
 0.60 
 
 0.30 
 
 9.49 
 
 9.29 
 
 5.66 
 
 10.0 
 
 10.126 
 
 10.025 
 
 5.774 
 
 6.9956 
 
 4.5524 
 
 1.76 
 
 2.621 
 
 2.061 
 
 3.04 
 
 2.584 
 
 3.724 
 
 5.113 
 
 0.6108 
 
 0.305 
 
 9.688 
 
 9.476 
 
 5.774 
 
 71 
 
tables without presenting any difference that could be meas- 
 ured with even v^ry delicate instruments. 
 
 LOCKING CIRCLK. 
 
 The calculation of the locking circle is the same as for 
 the ratchet wheel pallet, and based upon the same diameter 
 of wheel = 1 and the same angle of 30" ; the size of the 
 circle is also the same = '•.5774. 
 
 OUTER AND INNER CIRCLE OF PALLET. 
 
 These sizes differ from those in Tables I and II, because 
 the half of the space between two teeth is divided into IJ" 
 of drop, SJ" breadth of wheel tooth and 7° breadth of pal- 
 let arm. This latter must be calculated first, before finding 
 the numbers of outer and inner circle. 
 
 The circumference of the primitive circle of the wheel is : 
 1 . 3.141(3 = 3.1416. 
 
 The arc of 7'' of this circunifereuce is 
 
 3 1416 7 21 091'^ 
 = ™^ = -^i^- ^ 0.06108. 
 360 360 
 
 In Table III the diameter of outer circle is 
 
 = the diameter of locking circle = 0.5774 
 
 + the breadth of pallet arm 
 
 and the diameter of inner circle is 
 := the diameter of locking circle 
 
 — the breadth of pallet arm = 
 
 0.51 63i 
 In Table IV the diameter of the outer circle is 
 = the diameter of locking circle = 0.5774 
 -f double the breadth of pallet arm = 0.12216 
 
 o:6!:)956 
 and the diameter of inner circle 
 
 = the diameter of locking circle = 0.5774 
 
 — double the breadth of pallet arm = 0,1221 6 
 
 = 0.45524 
 
 = 0^6108 
 063848 
 
 = 0.5774 
 
 = o.oeiof 
 
 LIFTING CIRCLES. CIRCULAR PALLET. 
 
 Total angle of movement 8° 
 
 Locking angle ^1" 
 
 Lifting angle of wheel tooth = 2° 
 
 Lifting angle of pallet = 5° 
 
 a = 0.3192 (radius of outer circle) 
 
 b = 0.2582 (radius of inner circle) 
 
 (7=5" 
 
 A+B_ 
 
 : 'M° 
 
 C 
 
 = 90'' 
 
 2" 30' = 87° 30' 
 
 /A—B\ a—b , C 
 tang.(_^)=--.cotang._ 
 
 " --. 
 
 0.3192 — 0.2582 
 
 A—B 
 
 ' 0.3192+ 0.2582 - "°^""g" 
 ^■^^^ cotang.2°30' 
 
 2.4187 
 
 30' 
 
 "0.5774 
 = 0.1056 . 2.2904 
 
 = 67° 30' 
 
 £= 87° 30' — 67° 30' = 20" 
 ,j<l=-(i . sin />' = (1.3192 . sin 20° 
 = 11.3192.0.342 
 = 0.109166 
 
 72 
 
Diameter of lifting circle = 
 
 2 . ffd=r.2 . 0.10916(5 = ((.2188. 
 
 Diameter of lilting circle = 2 . gd 
 = 2 . 0.157174 = 0.31-14 
 
 .1- 
 
 2 
 tang. 
 
 Total angle of movement = 10" 
 Locking angle = 1 2 ? 
 Lifting angle of wheel = 2i° 
 Lifting angle of pallet = 6° 
 
 : 90" — 3" = 87'^ 
 
 b 
 
 --S^90°_£ 
 
 i^-l 
 
 _ . cotang. I 
 
 = 0.1056 . cotang. 3° = 0.105(J . 1.9081 = 2.0149a 
 
 till^ = 63° 35' 
 2 
 
 £ = 87° — 63" 35' = 23° 25' 
 
 5, £« = a. sin 5 =0.3192 .sin 23" 25' 
 
 = 0.3192 . 0.3974 = 0.12685 
 
 Diameter of lifting circle = 2 . jr rf 
 
 = 2 . 0.12685 = 0.2537 
 
 A+B 
 
 Total angle of movement =^ 12b 
 Locking angle =l-i° 
 
 Lifting angle of wheel = 25" 
 Lifting angle of pallet = 8° 
 
 C 
 
 ■ 40 = 86' 
 
 90° _ _= 902,- 
 
 2 2 
 
 U—B\ a—h , C 
 
 tang.(_^)=— cotang.^ 
 
 = 0.1056 . cotang . 4" 
 = 0.1056 . 14.301 = 1.5102 
 
 :^~^_ 56° 30' 
 
 2 - 
 
 B = 86" — 56° 30' ^ 29" 30' 
 
 gd = a. sin B = 0.3192 . sin 29" 30' 
 
 = 0.3192 . 0,4924. = 0.157174. 
 
 Lifting-Circles, Table IV.— Pallet with Equidistant 
 Lockings. 
 For greater simplification of the matter, we shall calculate 
 the lifting circles of the first arm for all the three angles at 
 first, because the greater part of the coefficients are the 
 same for all. 
 
 lifting circles of the first pallet arm. 
 
 Angle of movement = 8" 
 
 Lifting angle of pallet = 5° 
 
 a ■= 0,2887 (radius of locking-circle) 
 
 h ^ 0,2279 (radius of inner circle) 
 
 C=5° 
 
 A ^ B C 
 
 — 2^ _ 90° _ 2 = 90" — 2° 30' = 87° 30' 
 
 tang / A — ^ \ ^^ a — b C 
 
 \ 2 / a + b' cotang. 2 
 
 0,2887 — 0,2276 
 ■ ((,2887 + 0,2276' 
 
 cotang. 2° 30' 
 
 73 
 
"-"tin . 90 on' 
 
 = 0,1183.22,904 =2.7095 
 ^i— ^ = 09"^ 45' 
 
 B -.= 86" _ 59^ 25' = 26° 35' 
 gd=a. sin 5 = 0,2887 . 0,4475 :^- 0,12919 
 Diameter of lifting-circle ^= 1 g d 
 = 2 . 0,12919 = 0,2584 . 
 
 B — S7° 30' — 69" 45' = 17° 45' 
 r/ (/ = a . sin £ . = 0,2887 . 0,3040 
 
 = 0,088025 
 Diameter of lifting- circle = 2 g d 
 =2 . 0,088025 = 0,176 
 
 A+ B 
 
 90° 
 
 Angle of movement = 10° 
 Lifting-angle of pallet = 6° 
 
 ^= 90" _ 3" = 87? 
 
 tang . \ 2 /= 0,1183 . cotang. 3" 
 
 = 0,1183 . 19,081 . = 2,2573. 
 
 ^^ P^ 66'' 5' 
 2 
 
 5 = 872 — 66? 5' = 20° 55' . 
 
 g d= a .sm B . = 0,2887 . 0,357 .■ = 0,10307 . 
 
 Diameter of lifting-circle ^ 2 . g d 
 
 ^ 2 . 0,1030 < = 0,2061 
 
 Angle of movement = 12°, 
 Lifting-angle of the pallet = 8° 
 
 :£±^= 90°— ~- 90" 
 t.u^A-B^^^ 
 
 4° = 86"'- 
 
 1183 . cotang. 4° 
 )1 = 
 = 59° 25' 
 
 = 0,1183.14,301 = 1,6918 . 
 
 9 
 
 LIFTING CIRCLKS OF SECOND PALLET ARM. 
 
 Angle of movement = 8° 
 a =^ 0,34978 (radius of outer circle) 
 b = 0,2887 (radius of locking circle) 
 C=5" 
 
 4_+j?.= 90° — 4^ = 2° 30' = 87° 30' 
 
 tang 
 
 / .4 -^i; \ u,: 
 V --i I 0,: 
 
 0,34978 — 0,2887 , O 
 
 ' ' cotang. — 
 
 34978 + 0,2887 ^ 2 
 
 0,06108 , .,o ..„' 
 
 cotang. 2" 30 
 
 A—B 
 
 0,63848 
 = 0,09568 . 22.904 
 = 2,19145 . 
 
 = 65° 30' 
 
 B = 87° 30' — 65° 30' = 22° 
 gd = a.iim B = 0,34978 . 0,3746 . = 0,131028 
 
 74 
 
Diameter of lifting circle = 2 . g d 
 = 2 .0,131028 = 0,2621 .' 
 
 CIRCULAR PALLET — HEIGHT OV KKtJMENT. 
 
 Angle of movement =10° 
 Lifting angle of the pallet = <!'^ 
 
 A^ B 
 
 C 
 
 = 90° — _ = 90° — 3° = 87° . 
 2 2 
 
 tang/^ ~ ^\ = 0,09568 . cOtang3° 
 = 0,09568 . 19,081 = 1,82557 . 
 
 "^~~-^ = 61° 15' 
 2 
 
 £ = 87° — 61° UV = 25° 45' 
 (ld = a.f^\n B . = 0,34978 . 0,4345 . = 0,151979 
 Diameter of lifting circle ^ 2 . {/ d 
 = 2 . 0,151979 = 0,304 
 
 Angle of movement ^12° 
 Lifting angle of the pallet = 8° 
 
 A + B 
 
 = 90° 
 
 C 
 
 ^ i)(|o _ 4° 
 
 80° 
 
 tang i'i----Ji\ = 0,09568 . cotang 4° 
 1,3683 
 = 53° 50' 
 
 = 0,09568 . 14,301 
 A — B 
 
 B . = 86° — 53° 50' = 32° 10' 
 rt . sin . 5 . = 0,34978 . 0,5324 . = 0,1862 
 Diameter of lifting circle = 2 . (j d 
 — 2 11,1862 = 0,3724. 
 
 fj h = 9 ?! = 0.31925 (radius of outer circle) 
 < h(, i = 118° 30' (by construction) 
 
 180° — 11 8° 30' 61° 30' 
 
 =30° 45' 
 
 < ff'i i = <f/ ' h 2 2" 
 
 Of the rectangular triangle g h k we know ■ 
 J/ /i = 0.31925 . 
 "< r/ /( i = 30° 45' 
 
 gk = (/h.s\n.g h i = 0.31925 , sin 30° 45' 
 = 0.31925 . 0.5113 = 0.16323 . 
 The sum of the radius of outer circle = 0.31925 
 and the line f/ Z- =0.16323. 
 
 is the height of segment = 0.48248 
 
 75 
 
Table IV. — pallet with equidistant lockings. 
 
 (J i = radius of locking circle = 0.2887 . 
 jr /i = radius of outer circle = 0.34978 . 
 
 <i^^ = 118°30' 
 For brevity we call : 
 
 (J h — a and the angles opposite to them : 
 
 g i — h A, B and C. 
 
 h i — f. 
 
 '2 ■ 2 
 
 A -y h (jQo ^ 
 
 = 90° — 59^^ 15' = 30° 45' 
 
 tang(^^) 
 
 n — b , C 
 
 -^^.cotang.- 
 
 0.3498—0.2887 
 0.3498+0.2887 
 0.0611 
 
 cotang. 59° 15' 
 
 0,595 
 
 0.(3385 
 
 0.09568 . 0.595 = 0.0.5C93 
 
 A —B_ 
 
 3° 15' 
 
 30' 
 
 B = 30° 45' — 3° 15' = 
 In the rectangle ghlc there is : 
 gli = 0.3498 
 B = 27° 30' 
 g k== g h .sin B .= 0.3498 . sin 
 = 0..349S . 0.4fil7 = 0.1 CI 5 . 
 The sum of the radius of outer circle = 
 + the line g k = 
 
 is the height of segment -= 0.5113 
 
 The breadth of pallet arms is the same for both tables, 
 and it has already been mentioned that it is = 7° of the 
 wheel's circumference : 
 1 . 3.1416 
 
 . 27° 30' 
 
 0.3498 
 0.1615 
 
 360 
 
 = 0.06108 . 
 
 The breadth of wheel teeth (before inclining) having 
 been fixed to 02° of the wheel circle, is accordingly half 
 the breadth of pallet arm = 0.0305-1 
 
 The tangent circles for the inclined planes of the teeth 
 are also the same iu both the tables, but it must be remem- 
 bered here, that for the sake of better respective propor- 
 tion, it has been found advisable to make the teeth for an 
 escapement of 8° movement lift only 2°, while the 2 other 
 angles spokeu of in these tables will be better arranged with 
 p lifting of 21° at the teeth. 
 
 76 
 
Therefore there are two columns of tangent circles in 
 each table. It may be observed here, that it would not 
 derange the other proportions, if an escapement should be 
 executed to give 8°, as the table prescribes it, giving to the 
 teeth a lifting angle of 2i°. The only effect of the change 
 would be an augmentation of the total angle of movement 
 from 8 to 82° For escapements of 10 and 12" of move- 
 ment, it is also allowed to give the wheel teeth a lifting 
 angle of but 2°, without altering in any way the correct- 
 ness of the other proportions, so that the only effect of the 
 change will be a diminishing of the total lifting angle by 
 i degree. 
 
 The calculation of the tangent circles in question is the 
 following : 
 
 The inclined part of the tooth, projecting beyond the 
 primitive radius, presents a small rectangular triangle, of 
 which we know: 
 b = 0.030O-1 (breadth of wheel tooth) 
 
 g^ 
 
 a ^_ 0.01 26 (difference of outer and primitive radius of 
 wheel) 
 
 tang. 5.=1=0:^'3054_ 
 a 0.0r2(j 
 £ = 67° 35' 
 
 We prolong the line c and draw a perpendicular line to 
 it passing through the centre of the wheel. 
 
 The rectangular triangle d g f contains the known 
 parts: 
 
 d g ^ radius of outer wheel circle = 0.5126. 
 < ^ = 67° 35' 
 
 ^/= rfjr . sin 5 . = 0.5126 . 0.9244 = 0.4738 
 Diameter of tangent circle = 2 . gf 
 l^ 2 . 0.4738 = 0.9476 
 For the angle of lifting = 2°, there is: 
 b = 0.03054 
 a = 0,010075' 
 tane;. 
 
 ^.=^=^'03054 = 
 
 a 0.001075 ^■"^^^^• 
 
 5 . = 71° 45' 
 gf=gd.sm B = 0.510075 . 0.9497 = 0.4844 
 Diameter of tangent circle = 2 g f 
 = 2 . 0.4S44 = 0.9688 
 
 The primitive diameter of the club-wheel being the 
 same (1,00) as in Tables 1 and 2, the wheel having the same 
 number of teeth and consequently the same scaping angl e, 
 the distance of centres must be the same as in those tables 
 = 0-5774. 
 
 JiXPLANATION OF TabLE V. 
 
 This table gives the proportions for the improved club 
 wheel escapement with circular pallet, proposed in Chap- 
 ter V and illustrated in Diagram VIII. 
 
 There are many escapement makers who are very fond 
 of circular pallets, though they are defective in principle. 
 
 77 
 
TABLE V. Improved Circular Pallet Escapement with Club Wheel. (Diagram 8.) 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 Diameter of wheel circle. 1 
 
 Circles of pallet. 
 
 Lifting-circle 
 
 for the angle 
 
 of movement 
 
 10" 
 
 0.243 
 
 Height 
 
 of 
 
 segment. 
 
 0.4693 
 
 Breadth 
 
 of 
 
 pallet-arm. 
 
 0.0436 
 
 Breadth 
 of 
 
 wheel-teeth 
 
 before 
 
 inclining. 
 
 0.048 
 
 Tangent-circle 
 
 for 
 
 inclined 
 
 planes 
 
 of teeth. 
 
 0.9448 
 
 Distance 
 of 
 
 
 Outer. 
 
 
 centres. 
 
 Primitive. 
 1.00 
 
 Real 
 1.0454 
 
 Measured 
 1.0349 
 
 Outer 
 0.6210 
 
 Inner 
 0.5338 
 
 0.5774 
 
 5.00 
 
 5.23 
 
 5.17 
 
 3.11 
 
 2.67 
 
 1.22 
 
 2.35 
 
 0.22 
 
 0.24 
 
 4.72 
 
 2.89 
 
 5.2 
 
 5.44 
 
 5.38 
 
 3.23 
 
 2.78 
 
 1.26 
 
 2.44 
 
 0.23 
 
 0.25 
 
 4.91 
 
 3.00 
 
 5.4 
 
 5.65 
 
 5.58 
 
 3.35 
 
 2.88 
 
 1.31 
 
 2.53 
 
 0.24 
 
 0.20 
 
 5.10 
 
 3.12 
 
 5.6 
 
 5.85 
 
 5.79 
 
 3.48 
 
 2.99 
 
 1.36 
 
 2.63 
 
 0.24 
 
 0.27 
 
 5.29 
 
 3.23 
 
 5.8 
 
 6.06 
 
 6.00 
 
 3.60 
 
 3.10 
 
 1.41 
 
 2.72 
 
 0.25 
 
 0.28 
 
 5.48 
 
 3.35 
 
 6.0 
 
 6.27 
 
 6.21 
 
 3.73 
 
 3.20 
 
 1.46 
 
 2.82 
 
 0.26 
 
 0.29 
 
 5.67 
 
 3.46 
 
 6.2 
 
 6.48 
 
 6.42 
 
 3.85 
 
 3.31 
 
 1.51 
 
 2.91 
 
 0.27 
 
 0.30 
 
 5.86 
 
 3.58 
 
 6.4 
 
 6.69 
 
 6.62 
 
 3.97 
 
 3.42 
 
 1.56 
 
 3.00 
 
 0.28 
 
 0.31 
 
 6.05 
 
 3.70 
 
 6.6 
 
 6.90 
 
 6.83 
 
 4.10 
 
 3.52 
 
 1.61 
 
 3.10 
 
 0.29 
 
 0.32 
 
 6.24 
 
 3.81 
 
 6.8 
 
 7.11 
 
 7.04 
 
 4.22 
 
 3.63 
 
 1.65 
 
 3.19 
 
 0.30 
 
 0.33 
 
 6.42 
 
 3.93 
 
 7.0 
 
 7.32 
 
 7.24 
 
 4.35 
 
 3.74 
 
 1.70 
 
 3.29 
 
 0.31 
 
 0.34 
 
 6.61 
 
 4.04 
 
 7.2 
 
 7.53 
 
 7.45 
 
 4.47 
 
 3.84 
 
 1.75 
 
 3.38 
 
 0.31 
 
 0.35 
 
 6.80 
 
 4.16 
 
 7.4 I 7.74 
 
 7.66 
 
 4.60 
 
 3.95 
 
 1.80 
 
 3.47 
 
 0.32 
 
 0.36 
 
 6.99 
 
 4.27 
 
 7.6 
 
 7.95 
 
 7.87 
 
 4.72 
 
 4.06 
 
 1.85 
 
 3.57 
 
 0.33 
 
 0.36 
 
 7.18 
 
 4.39 
 
 7.8 
 
 8.15 
 
 8.07 
 
 4.84 
 
 4.16 
 
 1.90 
 
 3.66 
 
 0.34 
 
 0.37 
 
 7.37 
 
 4.50 
 
 8.0 
 
 8.36 
 
 8.28 
 
 4.97 
 
 4.27 
 
 1.94 
 
 3.75 
 
 0.35 
 
 0.38 
 
 7.56 
 
 4,62 
 
 8.2 
 
 8.57 
 
 8.49 
 
 5.09 
 
 4.38 
 
 1.99 
 
 3.85 
 
 0.36 
 
 0.39 
 
 7.75 
 
 4.73 
 
 8.4 
 
 8.78 
 
 8.69 
 
 5.22 
 
 4.48 
 
 2.04 
 
 3.94 
 
 0.37 
 
 0.40 
 
 7.94 
 
 4.85 
 
 8.6 
 
 8.99 
 
 8.90 
 
 5.34 
 
 4.59 
 
 2.09 
 
 4.04 
 
 0.37 
 
 0.41 
 
 8.13 
 
 4.97 
 
 8.8 
 
 9.20 
 
 9.11 
 
 5.46 
 
 4.70 
 
 2.14 
 
 4.13 
 
 0.38 
 
 0.42 
 
 8.31 
 
 5.08 
 
 y.o 
 
 9.41 
 
 9.31 
 
 5.59 
 
 4.80 
 
 2.19 
 
 4.22 
 
 0.39 
 
 0,43 
 
 8.50 
 
 5.20 
 
 9.2 
 
 9.62 
 
 9.52 
 
 5.71 
 
 4.91 
 
 2.24 
 
 4.32 
 
 0.40 
 
 0.44 
 
 8.69 
 
 5.31 
 
 9.4 
 
 9.83 
 
 9.73 
 
 5.84 
 
 5.02 
 
 2.28 
 
 4.41 
 
 0.41 
 
 0.45 
 
 8.88 
 
 5.43 
 
 9.6 
 
 10.04 
 
 9.94 
 
 5.96 
 
 5.12 
 
 2.33 
 
 4.51 
 
 0.42 
 
 0.46 
 
 9.07 
 
 5.54 
 
 9.8 
 
 10.24 
 
 10.14 
 
 6.09 
 
 5.23 
 
 2.38 
 
 5.60 
 
 0.43 
 
 0.47 
 
 9.26 
 
 5.66 
 
 10.0 
 
 10.454 
 
 10.349 
 
 6.21 
 
 5.338 
 
 1 2.43 
 
 4.693 
 
 0.436 
 
 0.48 
 
 9.448 
 
 5.774 
 
 78 
 
When a ratchei, wheel is employed, there is nothing to be 
 done against this deficiency, but with the club wheel the 
 possibility of diminishing it exists, and thus I see no reason 
 why this should not be done. The pallet arms becoming 
 much smaller by this arrangement, the locking-circles, ac- 
 cordingly, are but very little out of their natural place, and 
 this circular pallet is nearly as con-ect as one with equidis- 
 tant lockings. 
 
 The arrangement illustrated by Diagram VII has an 
 angle of movement of 10° from drop to drop, leaving after 
 subtraction of the locking-angle of 1]° a lifting-angle of 
 82°, of which 42? are performed by the wheel-teeth, and 4'? 
 by the pallet. The space of 12° at the wheel's primitive 
 circumference is divided accordingly, so that the breadth 
 of the tooth is S^" and that of the pallet arm 5'^, thus leav- 
 ing li° of drop. 
 
 CALCULATIONS — COLUMN ONE. 
 
 Diameter of the primitive circle of the wheel = 1. 
 
 COLUMN TWO. 
 
 Diameter of the outer circle of wheel. 
 
 /> =0.2887 (radius of 
 locking-circle) 
 
 ^=4° .30' 
 
 a =h . tang. A 
 =0.2887. tang. 4i° 
 =0.2887 . 0.0787 . 
 =0.0227 . 
 
 Outer diameter =. 
 1+2 « 
 
 
 = H-2 . 0,0227 =1+0,0454 = 1,0454 
 
 fOLUJIN •'!. 
 
 Measured diameter = 1.0454 . 0.09 
 = 1 .0.349 . 
 
 COLUMN FOUR. 
 
 The diameter of outer circle of pallet = 
 the diameter of the locking-circle = 0.5774 . 
 -f the breadth of pallet-arm = 0.0436 . 
 
 0.G210 
 
 COLUMN FIVE. 
 
 The diameter of inner pallet-circle = 
 the r.idius of the locking-circle ^ 0.5774 
 — the breadth of pallet-arm = 0.0436 , 
 
 0..5338 
 
 COLUMN SIX. 
 
 The lifting-circle has been calculated merely for the 
 angle of movement of 10°, in order to simplify the table. 
 
 79 
 
a = 0.8105 (radius of outer circle) 
 b = 0.2669 (radius of inner circle.) 
 C= 4° 
 
 A + £ 
 
 2 
 
 =90° — 
 
 £= 90'= 
 
 2 
 
 — 2° = 
 
 = 88° 
 
 tang. 
 
 (^ 
 
 7^. 
 
 a—b 
 
 a + b 
 
 cotang. 
 
 C 
 
 2 
 
 
 
 
 0.3105 - 
 0.3105 
 
 - 0.2669 
 
 + 0.2669 
 
 . cotang 
 
 
 
 
 0.0436 
 ~ 0.5774' 
 
 cotang. 
 
 2° 
 
 
 
 
 =0,0755. 28,636. = 
 
 = 2.162 
 
 A — 
 
 ^_ 
 
 = 65° 
 
 10' 
 
 
 
 no 
 
 B = 88° — 65° 10' = 22° 50' 
 gd = a . sin B. = 0.3105.9.3881. = 0.1215. 
 Diameter of lifting-circle = 2 . gd. 
 =■2.0.1215=0.243. 
 
 COLUMN SEVEN. 
 
 The height of segment is to be found in the same way 
 as it has been done in the corresponding cases referring to 
 Tables I and IV. 
 
 gh = gi = 0.3105 (radius of outer circle.) 
 < ghi =-118° 30' (by construction.) 
 
 180"— 118° 30' 61° 30' 
 
 < ghi = < gih = 
 
 In the rectangular triangle ghk we know : 
 gh = 0.31 05. 
 < ghi = 30° 45' 
 
 gk = gh . sin . 30° 45' = 0.3105. 0.5113. =0.1588. 
 
 The sum of the radius of the outer pallet circle=0.3105 
 
 + the line gk ' =0.1588. 
 
 is the height of segment=^0.4693. 
 
 COLUMN EIGHT. 
 
 Breadth of pallet arm = 5° of the primitive circle oi 
 uheel, 
 
 3.141G.5 0.1416 
 
 = 30° 45' 
 
 360 
 
 -= 0.0430. 
 
 80 
 
Diagram XIII. 
 
 \rr 
 
 \H1 
 
DiAGEAM XIV 
 
Diagram XV 
 
^ 
 
 t/\ 
 
 • i 
 
 ■ > 
 ' 1 
 
 X 
 
 ■1 .' 
 
 \ \ 
 
 '_ . i 
 
 Vv\i 
 
 
 
 Diagram XVI. 
 
COLUMN NINE. 
 
 The breadth of the wheel teeth before making the in- 
 clined planes, measured at the primitive circle of the wheel, 
 is 
 
 3.1416.5.5° 3.1416.1.1 3.4.5576 
 
 360 
 
 72 
 
 72 
 
 . = 0.048 . 
 
 COLUMN TEN. 
 
 The tangent circle for the inclined planes on the wheel 
 teeth. 
 
 \\ 
 
 \ \i 
 
 a = 0.0227. 
 b = 0.048. 
 
 
 0.048 
 
 = 2.1146. 
 
 tang. B. = - 
 
 * a 0.0227 
 
 jB = 64° 40' 
 In the rectangular triangle dc/f there is: 
 dg = 0.5227 . (radius of outer wheel circle) 
 < B=-. (M" 40' 
 (jf = d(j.m\ . B. = 0.5227. sin 64° 40' 
 
 = 0.5227. 0.9038 
 = 0.4724. 
 Diameter of tangent circle = 2. (/f 
 
 = 2.0.4724 == 0.9448. 
 
 COLUMN ELEVEN. 
 
 The distance of centres is equal to that of Tables I and 
 
 IV. 
 
 Explanation of Table VI. 
 
 Thi& table refers to the pin anchor, and though this 
 construction is very rarely employed, and, I may say, very 
 little known, I think it likely that some who have read the 
 particulars of it in the fifth chapter might be desirous to 
 try it for such purpose as it may be suitable. Therefore, 
 and for greater completeness, a table of proportions of the 
 pin anchor might be useful. Still, I have executed it in a 
 simplified way, only referring to the angle of movement of 
 10°, this being about the average of the angles in use. 
 
 With the aid of this table an anchor of this kind will 
 not be an object of difficult execution, as it requires no 
 jewels, nor anything beyond the reach of every watch- 
 maker's workshop. 
 
 COLUMNS one, two AND THREE. 
 
 The primitive diameter is, as well as in all the preced- 
 ing calculations, supposed to be^ 1. 
 
 The outer diameter must be calculated according to the 
 
 81 
 

 
 TABLE VI. Pallet with I 
 
 Equidistant Lockings 
 
 . Ratche' 
 
 r Wheel. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 Diameter of wheel circle. 1 
 
 Thickness 
 
 Breadth of 
 
 Tangent. 
 
 Distance 
 
 Distance 
 
 Diameter 
 
 Height 
 
 Distance 
 
 
 
 of the 
 pics. 
 
 teetli moa- 
 Burttl at the 
 
 circle for 
 the 
 
 between 
 the pins. 
 
 measured 
 across the 
 
 of 
 pin-circle 
 
 of 
 triangle. 
 
 of 1 
 centres. ( 
 
 
 Outer. 
 
 
 
 
 primitive 
 
 inclined 
 
 
 outt.r sides 
 
 (locking- 
 
 
 
 Primitive. 
 I.UO 
 
 Beat 
 
 Measured 
 
 
 circle. 
 
 planes. 
 
 
 of the pins. 
 
 circle.) 
 
 
 
 
 1.0658 
 
 1.055 
 
 0.0218 
 
 0.0698 
 
 0.9369 
 
 0.5171 
 
 0.5389 
 
 0.5774 
 
 0.1393 
 
 0.5774 
 
 5.0 
 
 5.33 
 
 .5.28 
 
 0.11 
 
 0.35 
 
 4.68 
 
 2.59 
 
 2.70 
 
 2.89 
 
 0.70 
 
 2.S9 
 
 5.2 
 
 5.54 
 
 5.49 
 
 0.11 
 
 0.36 
 
 4.87 
 
 2.69 
 
 2.80 
 
 3.00 
 
 0.72 
 
 3.00 
 
 5.4 
 
 5.76 
 
 5.70 
 
 0.12 
 
 0.38 
 
 5.06 
 
 2.79 
 
 2.91 
 
 3.12 
 
 0.75 
 
 3.12 
 
 5.6 
 
 5.97 
 
 5.91 
 
 0.12 
 
 0.39 
 
 5.25 
 
 2.90 
 
 3.02 
 
 3.23 
 
 0.78 
 
 3.23 
 
 5.8 
 
 6.18 
 
 6.12 
 
 0.13 
 
 0.40 
 
 5.43 
 
 3.00 
 
 3.13 
 
 3.35 
 
 0.81 
 
 3.35 
 
 6.0 
 
 6..39 
 
 6.33 
 
 0.13 
 
 0.42 
 
 5.62 
 
 3.10 
 
 3.23 
 
 3.46 
 
 0.84 
 
 3.46 
 
 6.2 
 
 6.61 
 
 6.54 
 
 0.14 
 
 0.43 
 
 5.81 
 
 3.21 
 
 3.34 
 
 3.58 
 
 0.86 
 
 3.58 
 
 6.4 
 
 6.82 
 
 6.75 
 
 0.14 
 
 0.45 
 
 6.00 
 
 3.31 
 
 .3.45 
 
 3.70 
 
 0.89 
 
 3.70 
 
 6.6 
 
 7.03 
 
 6.96 
 
 0.14 
 
 0.46 
 
 6.18 
 
 3.41 
 
 3.56 
 
 3.81 
 
 0.92 
 
 3.81 
 
 6.8 
 
 7.25 
 
 7.17 
 
 0.15 
 
 0.47 
 
 6.37 
 
 3..52 
 
 3.67 
 
 3.93 
 
 0.95 
 
 3.93 
 
 7.0 
 
 7.46 
 
 7.39 
 
 0.15 
 
 0.49 
 
 6.56 
 
 3.62 
 
 .3.77 
 
 4.04 
 
 0.98 
 
 4.04 
 
 7.2 
 
 T ii7 
 
 7.60 
 
 0.16 
 
 0.50 
 
 6.75 
 
 3.72 
 
 3.88 • 
 
 4.16 
 
 1.00 
 
 4.16 
 
 7.4 
 
 7.8!) 
 
 7.81 
 
 0.16 
 
 0.52 
 
 6.93 
 
 3.83 
 
 3.99 
 
 4.27 
 
 1.03 
 
 4.27 
 
 7.6 
 
 8.10 
 
 8.02 
 
 0.17 
 
 0.53 
 
 7.12 
 
 3.93 
 
 4.10 
 
 4.39 
 
 1.06 
 
 4.39 
 
 7.8 
 
 8.31 
 
 8.23 
 
 0.17 
 
 0.54 
 
 7.31 
 
 4.03 
 
 4.20 
 
 4.50 
 
 1.09 
 
 4.50 
 
 8.0 
 
 «..53 
 
 8.44 
 
 0.17 
 
 0.56 
 
 7.50 
 
 4.14 
 
 4.31 
 
 4.62 
 
 1.11 
 
 4,62 
 
 8.2 
 
 8.74 
 
 8.65 
 
 0.18 
 
 0.57 
 
 7.68 
 
 4.24 
 
 4.42 
 
 4.73 
 
 1.14 
 
 4.73 
 
 8.4 
 
 8.95 
 
 8.S6 
 
 0.18 
 
 0.59 
 
 7.87 
 
 4.34 
 
 4.53 
 
 4.85 
 
 1.17 
 
 4.85 
 
 8.6 
 
 9.17 
 
 9.07 
 
 0.19 
 
 0.60 
 
 8.06 
 
 4.45 
 
 4.64 
 
 4.97 
 
 1.20 
 
 4.97 
 
 8.8 
 
 9.38 
 
 9.28 
 
 0.19 
 
 0.61 
 
 8.24 
 
 4.55 - 
 
 4.74 
 
 5.08 
 
 1.23 
 
 5.08 
 
 9.0 
 
 9.59 
 
 9.50 
 
 0.20 
 
 0.(!3 
 
 8.43 
 
 4.65 
 
 4.85 
 
 5,20 
 
 1.25 
 
 5.20 
 
 9.2 
 
 9.S1 
 
 9.71 
 
 0.20 
 
 0.(>4 
 
 8.62 
 
 4.76 
 
 4.96 
 
 5.31 
 
 1.28 
 
 5.31 
 
 9.4 
 
 10.(1.; 
 
 !).'.)2 
 
 0.20 
 
 0.66 
 
 8.81 
 
 4.86 
 
 5.07 
 
 5.43 
 
 1.31 
 
 5.43 
 
 ' 9.6 
 
 10.2:; 
 
 10.13 
 
 0.21 
 
 0.67 
 
 8.99 
 
 4.96 
 
 5.17 
 
 5.54 
 
 1.34 
 
 5.54 
 
 9.8 
 
 10.44 
 
 10.34 
 
 0.21 
 
 0.68 
 
 9.18 
 
 5.07 
 
 5.28 
 
 5.66 
 
 1.37 
 
 5.00 
 
 10.0 
 
 10.658 
 
 10.55 
 
 0.218 
 
 0.698 
 
 9.369 
 
 5.171 
 
 5..389 
 
 5.774 
 
 1.393 
 
 5.774 
 
 82 
 
lifting angle peif(jriiiL'd by tlic wheel teeth, which is for an 
 angle of 10°=6J°. 
 
 /) = 0.2887 (radius 
 of locking circle) 
 ; A - IJ° 30' 
 «= b. tang. A. 
 = 0.2887. tang. 6° 30' 
 = 0.2887.0.1139 
 = 0.03288 . 
 Outer diam. =1+-" 
 = 1+2.0.03288 
 = 1+0.0658. 
 = 1.0658. 
 
 Measured diameter = 1.0658.0.99 = 1.055142. 
 
 COLUMN HIX. 
 
 The tangent circle for the inclined planes of the wheel 
 teeth. For such a considerable angle (8°) as is given here 
 for the breadth of wheel tooth, the triangle a b c cannot be 
 KUjii)osed to be a rectangular one. The angle at tlie wheel 
 centre for the tooth being 8°, the two radii enclosing it 
 form with the line b an isosceles triangle, of which the value 
 
 >. \ i 
 
 COLUMN FOUR. 
 
 The thickness of the anchor pins is 
 the primitive circle of the wheel : 
 3.1416.2.5 3.1416 
 
 2i°, measured at 
 
 360 
 
 144. 
 
 -= 0.02182. 
 
 COLUMN FIVE. 
 
 The breadth of teeth, measured at the primitive circle, 
 is = 8° of this circle : 
 
 3.1416.8 3.1416 
 
 360 
 
 45 
 
 0.0698. 
 
 83 
 
 of any of the two other angles is ^ 
 
 180°— 8° 172° 
 
 =86' 
 
 2 2 
 
 Accordingly, the angle Cin the small triangle of tooth a h r 
 being the supplement to this former, is = 180° — 86° = 
 94°. Thus we know of the triangle a h <■ : 
 
 (I = 0.03288 (difference ot outer and primitive radius 
 of wheel.) 
 
 fc = 0.0698 (breadth of tooth.) 
 
 C=94° 
 
 R — ^ • «ia C* _ 0.0698 . 0.9976 
 
 tang. i> — ^^_^ ^^^ ^ 0.03288 + 0.0698 . 0.0698 
 
0.00963 
 
 0.06068 
 0.03775 ' 
 
 : 1.844556. 
 
 0.03288 + 0.00487 ' 
 5 = 61° 30' 
 In the rectangular triangle dfi f, we know : 
 
 dg = 0.53288 (radius of outer wheel circle) 
 i=61°30' 
 
 r/f =d(/.s\D.B= 0.53288 . 0.8791 = 0.46845 
 Diameter of tangent circle 2 . f/f 
 = 2.0.46845 = 0.9369. 
 
 COLUMN SEVEN. 
 
 The distance of the jjiu.s — that is, the distance from one 
 centre of pin to the other, is found in the following way : 
 
 The triangle «7c/ is by the construction an isosceles tri- 
 angle, the sides g c and gf, and consequently the angles op- 
 posite to them, being equal. 
 
 \ i / 
 \ i / 
 
 V 
 
 The angle c y (< = 120° (by construction) 
 < c5r/= < <-gd-{- < dgf. 
 
 In the rectangular triangle d gf there is : 
 gd = 0,2887 (radius of locking circle) 
 df= the sum of: 
 
 half the thickness of the pin = 10.0109 
 
 + the difference of outer and prim, radius = 0.03288. 
 
 004379. 
 
 tang, dgf- 
 
 d,f _ 0.04379 
 
 0.2887 
 
 0.1.517 
 
 < d^/=8°40' 
 
 <cgf^egd+ <dgj = 120° + 8° 40' 
 
 = 128° 40' 
 By the construction, the pin of the entrance arm is sup- 
 posed to be on the locking, and consequently it will not be 
 in c, but in h, that is, by the locking angle of H° more 
 towords the wheel center. Thus, the angle from the pallet 
 center h gf in which the two pins stand to each other, is 
 ■ — 128° 40' — 1° 30' = 127" 10' 
 
 ^ w / /•; 180° — 127° 10' 
 >ghf'= < gfh 
 
 2 
 52° ,50' 
 
 26° 25' 
 
 hf- 
 
 gf.sm hgf _ 0.2887 . sin . 127° 10' 
 
 sin g hf sin . 26° 25' 
 
 0.2887 . 0.7969 0.230065 
 
 0.4449 
 
 0.4449 
 
 = 0.5171 
 
 COLUMN EIGHT. 
 
 The distance, measured from the outside of one pin to 
 that of the other, may be useful when it is required to 
 make an escape wheel to a ready made pin anchor. In this 
 case the sizes of columns eight, nine and ten must serve to 
 ascertain the diameter of wheel, proportionate to the an- 
 chor. 
 
 84 
 
This distance is the sum of: 
 
 the line /(/, just calculated = (1.5171. 
 4- the thickness of one pin = 0.0318. 
 
 COLtTtfN NINE. 
 
 The diameter of the circle from the pallet centre, in 
 which the centres of the pin are embraced, is equal to 
 the diameter of locking circle in Tables II and IV,=:<).5774. 
 
 COLfMN TEN. 
 
 The height of triangle is the distance from the centre 
 of the anchor to the line, touching the two pins on the side 
 turned towards the centre of the wheel. 
 
 The line g k, in the diagram belonging to column seven, 
 is = 7/ . sin. f/fl- = 0.2887 . sin. 26° 2.V 
 
 = 0.2887 . 0.4440 = <l. 1 284 . 
 To this length, half the thickne.«s of 
 the pin must be added = 0.01 09 . 
 
 g 0.1393 
 
 When the height of triangle is measured on a ready- 
 made anchor, which will be done in most "cases, including 
 the anchor staff, half the thickne.w of this staff must be sub- 
 tracted from the measured size. 
 
 COI.OIN ELEVEN. 
 
 The distance of centres is the same as in all the other 
 tables = 0.5774. 
 
 Explanation of Table VII. 
 
 This table is intended to give the proportions of the 
 acting lengths of lever and impulse pin, and the centre dis- 
 tances for different angles of pallet movement, combined 
 with different angles of lifting at the balance roller. 
 
 The calculation of the radius of impulse for a given 
 length of lever is very simple, as these two lengths are in 
 inverse ratio to the angles to be performed by them. For 
 instance, the length of a lever making 1 0° of movement is 
 to the radius of impulse of a roller which is to make an 
 angleof40°, as4to 1. 
 
 The calculation of the centre distance may be illus- 
 trated by the following diagram : 
 
 « is the length of lever. 
 
 b is the radius of impulse circle. 
 
 e is the line of centres. 
 
 B is half the angle of movement of the pallet, and 
 
 A is half the lifting angle on the roller. 
 
 a . sin (A+B) 
 
 sin A . 
 
 85 
 

 a. 
 
 
 
 TABLE 
 
 VII. 
 
 Proportions op 
 
 Fork 
 
 AND EOLLER ACTION. 
 
 
 
 
 
 1 
 
 2 
 
 3- 
 
 4 1 .. 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 1 
 
 15 1 
 
 16 1 
 
 17 
 
 B 
 
 8S of pallet movemeut. 
 25° 1 3ij» 
 
 30 
 
 10 
 
 Q 
 
 ° of pallet movement 
 
 
 
 
 
 12S of pallet movement. 
 
 O 
 
 a> 
 
 Diam. 
 
 of 
 impulse. 
 
 Distance 
 
 Diana. 
 
 Dist 
 
 Diam. 
 
 Dist. 
 
 Diam. 
 
 Dist. 
 
 Diam. 
 
 Dist. 
 
 Diam. Dist. 
 
 Diam. Dist. 
 
 Diam. Dist. 
 
 s 
 
 centres. 
 
 impulse. 
 
 centi'Bs. 
 
 o' 
 impulse. 
 
 of 
 
 centres. 
 
 of 
 impulse. 
 
 of 
 centres. 
 
 of 
 impulse. 
 
 of 
 centi-es. 
 
 of 
 
 impulse. 
 
 of 
 
 centrss. 
 
 of 
 
 impulse. 
 
 of 
 centres. 
 
 of 
 impulse. 
 
 of 
 
 centres. 
 
 
 0.64 
 
 1.3124 
 
 0.533.. 
 
 1.2581 
 
 0.666.. 
 
 1.3215 
 
 0.5714 
 
 , 1.9727 
 
 0.5 
 
 1.234 
 
 0.666.. 
 2.00 
 
 1.3097 
 
 0,5714 
 
 1.2G67 
 
 0.5 
 
 1.2294 
 
 3.0 
 
 1.92 
 
 3.94 
 
 1.60 
 
 3.77 
 
 2.00 
 
 3.96 
 
 1.71 
 
 3.82 
 
 1.5 
 
 3.70 
 
 3.93 
 
 1.71 
 
 3.80 
 
 1.5 
 
 3.09 
 
 0.2 
 
 2.05 
 
 4.20 
 
 1.71 
 
 4.03 
 
 2.13 
 
 4.23 
 
 1.83 
 
 4.07 
 
 1.6 
 
 3.95 
 
 2.13 
 
 4.19 
 
 1.83 
 
 4.05 
 
 1.6 
 
 3.93 
 
 8.4 
 
 2.18 
 
 4.46 
 
 1.81 
 
 4.2S 
 
 2.26 
 
 4.49 
 
 1.94 
 
 4.33 
 
 1.7 
 
 4.20 
 
 2.26 
 
 4.45 
 
 1.94 
 
 4.31 
 
 1.7 
 
 4.18 
 
 8.(i 
 
 2.30 
 
 4.72 
 
 1.92 
 
 4.53 
 
 2.40 
 
 4.76 
 
 2.06 
 
 4.58 
 
 1.8 
 
 4.44 
 
 2.40 
 
 4.71 
 
 2.06 
 
 4.56 
 
 1.8 
 
 4.43 
 
 8.8 
 
 2.43 
 
 4.99 
 
 2.03 
 
 4.78 
 
 2.53 
 
 5.02 
 
 2.17 
 
 4.84 
 
 1.9 
 
 4.69 
 
 2..53 
 
 4.98 
 
 2.17 
 
 4.81 
 
 1.9 
 
 4.67 
 
 4.0 
 
 2..-)G 
 
 5.25 
 
 2.13 
 
 5.03 
 
 2.66 
 
 5.29 
 
 2.29 
 
 5.09 
 
 2.0 
 
 4.94 
 
 2.66 
 
 5.24 
 
 2 29 
 
 5.07 
 
 2.0 
 
 4.92 
 
 4.2 
 
 2.69 
 
 5.51 
 
 2.24 
 
 5.28 
 
 2.80 
 
 5.55 
 
 2.40 
 
 5.35 
 
 2.1 
 
 5.18 
 
 2.80 
 
 5.50 
 
 2.40 
 
 5.32 
 
 2.1 
 
 5.16 
 
 4.4 
 
 
 5.77 
 
 2.35 
 
 5.54 
 
 2.93 
 
 5.82 
 
 2.51 
 
 5.60 
 
 2.2 
 
 5.43 
 
 2.93 
 
 5.76 
 
 2.51 
 
 5.57 
 
 2 2 
 
 5.41 
 
 4.6 
 
 2.94 
 
 6.04 
 
 2.45 
 
 5.79 
 
 3.06 
 
 6.08 
 
 2.63 
 
 5.85 
 
 2.3 
 
 5.68 
 
 3.06 
 
 6.02 
 
 2,63 
 
 5.83 
 
 2.3 
 
 5.66 
 
 4.8 
 
 3.07 
 
 6.30 
 
 2.56 
 
 6.04 
 
 3.20 
 
 6.34 
 
 2.74 
 
 6.11 
 
 2.4 
 
 5.92 
 
 3.20 
 
 6.29 
 
 2.74 
 
 6.08 
 
 2.4 
 
 5.90 
 
 5.0 
 
 3.20 
 
 6.56 
 
 2.67 
 
 6.29 
 
 3.33 
 
 6.61 
 
 2.86 
 
 6.36 
 
 2.5 
 
 6.17 
 
 3.33 
 
 6.55 
 
 2.86 
 
 6.33 
 
 2.5 
 
 6.15 
 
 b:A 
 
 3.33 
 
 6.82 
 
 2.77 
 
 6.54 
 
 3.46 
 
 6.87 
 
 2.97 
 
 6.62 
 
 2.6 
 
 6.42 
 
 3.46 
 
 6.81 
 
 2.97 
 
 6.59 
 
 2.6 
 
 6.39 
 
 K-'* 
 
 3,46 
 
 7.09 
 
 2.88 
 
 6.79 
 
 3.60 
 
 7.14 
 
 3.09 
 
 6.87 
 
 2.7 
 
 6.66 
 
 3.60 
 
 7.07 
 
 3.09 
 
 6.84 
 
 2.7 
 
 6.64 
 
 b.G 
 
 3.58 
 
 7.35 
 
 2.99 
 
 7.05 
 
 3.73 
 
 7.40 
 
 3.20 
 
 7.13 
 
 2.8 
 
 6.91 
 
 3.73 
 
 7.33 
 
 3,20 
 
 7.09 
 
 2.8 
 
 6.88 
 
 b.S 
 
 3.71 
 
 7.61 
 
 3.09 
 
 7.30 
 
 3.86 
 
 7.66 
 
 3.31 
 
 7.38 
 
 2.9 
 
 7.16 
 
 3.86 
 
 7.60 
 
 3.31 
 
 7.35 
 
 2.9 
 
 7,13 
 
 fi.O 
 
 3.84 
 
 7.87 
 
 3.20 
 
 7.55 
 
 4.00 
 
 7.93 
 
 3.43 
 
 7.64 
 
 3.0 
 
 7.40 
 
 4.00 
 
 7.86 
 
 3.43 
 
 7.60 
 
 3.0 
 
 7. .38 
 
 0.2 
 
 3.97 
 
 8.14 
 
 3.31 
 
 7.80 
 
 4.13 
 
 8.19 
 
 3.54 
 
 7.89 
 
 3.1 
 
 7.65 
 
 4.13 
 
 8.12 
 
 3.54 
 
 7.85 
 
 3.1 
 
 7.62 
 
 0.4 
 
 4.10 
 
 8.40 
 
 3.41 
 
 8.05 
 
 4.26 
 
 8.46 
 
 3.66 
 
 8.15 
 
 3.2 
 
 7.90 
 
 4.26 
 
 8.38 
 
 3.66 
 
 S.ll 
 
 3.2 
 
 7.87 
 
 0.0 
 
 4.22 
 
 8.66 
 
 3.52 
 
 8.30 
 
 4.40 
 
 8.72 
 
 3.77 
 
 8.40 
 
 3.3 
 
 8.14 
 
 4.40 
 
 8.64 
 
 3.77 
 
 8.36 
 
 3.3 
 
 8.11 
 
 0.8 
 
 4.35 
 
 8.92 
 
 3.63 
 
 8.50 
 
 4.53 
 
 8.99 
 
 3.89 
 
 8.65 
 
 3.4 
 
 8.39 
 
 4.53 
 
 8.91 
 
 3.89 
 
 8.01 
 
 3.4 
 
 8.36 
 
 7.0 
 
 4.48 
 
 9.19 
 
 3.73 
 
 8.81 
 
 4.66 
 
 9.25 
 
 4.00 
 
 8.91 
 
 3.5 
 
 8.64 
 
 4.GG 
 
 9.17 
 
 4.00 
 
 8.87 
 
 3.5 
 
 8.61 
 
 'i.2 
 
 4.61 
 
 9.45 
 
 3.84 
 
 9.00 
 
 4.80 
 
 9.51 
 
 4.11 
 
 9.16 
 
 3.6 
 
 8.88 
 
 4.80 
 
 9.43 
 
 4.11 
 
 9.12 
 
 3.6 
 
 8.85 
 
 'lA 
 
 4.74 
 
 9.71 
 
 3.95 
 
 9.31 
 
 4.93 
 
 9.78 
 
 4.23 
 
 9.42 
 
 3.7 
 
 9.13 
 
 4.93 
 
 9.69 
 
 4,23 
 
 9 37 
 
 3.7 
 
 9 10 
 
 V.O 
 
 4.86 
 
 9.97 
 
 4.05 
 
 9.56 
 
 5.06 
 
 10.04 
 
 4.34 
 
 9.67 
 
 3.8 
 
 9.38 
 
 5.06 
 
 9.95 
 
 4,34 
 
 9.63 
 
 3.8 
 
 9.34 
 
 V.8 
 
 4.99 
 
 10.24 
 
 4.16 
 
 9.81 
 
 5.20 
 
 10.31 
 
 4.46 
 
 9.93 
 
 3.9 
 
 9.G3 
 
 5.20 
 
 10.22 
 
 4.46 
 
 9.88 
 
 3.9 
 
 9.59 
 
 8.0 
 
 5.12 
 
 10.499, 
 
 4.2G6 
 
 10.0648 
 
 5.3334- 
 
 10.572 
 
 4.5712 
 
 10.1816 
 
 4.00 
 
 9.872 
 
 5.333+ 
 
 10.4776 
 
 4.5712 
 
 10.1336 
 
 4.00 
 
 9.835 
 
Or, supposing a to be = 1, 
 sin (A+B) 
 sin A . 
 
 Example : 
 
 A = 15° 
 £ = 5° 
 
 _ sin (15+5'^ __ sin 20 ° 
 sin 15° sin 15° " 
 
 0.342 
 
 0.1322. 
 
 0.2588 
 
 The table gives, for greater convenience in practical 
 application, the diameters of the impulse circles instead of 
 the radii, though these latter are, properly speaking, the 
 acting lengths. By this arrangement the practical work- 
 man need only make a disc of the exact size of the diame- 
 ter contained in the table for the special given case, and 
 mark the point for the impulse pin by the edge of this disc. 
 
 Calculations to Tabljs VII. 
 
 The (acting) length of lever supposed to be = 1. 
 Column Two. — Angle of pallet = 8°. Angle of roller 
 
 8 
 = 25°. Radius of impulse =-.= 0.32. 
 
 pulse= 2.032 = 0.64. 
 
 Column Four.— Angle of pallet 8°. 
 g 
 30°. Radius of impulse = — = 0.266. 
 
 ^ 30 
 
 pulse = 2.0266... = 0.533... 
 
 Column Six. — Angle of pallet = 10° 
 30-. Radius of impulse = — 
 
 30 
 
 0.3.33. 
 
 impulse = 2.0.333... = O.dCC, 
 
 Column Eight. Angle uf jjallet = 
 
 roller = 35°. Radius of impulse = .^- 
 
 3o 
 
 eter of impulse = 2.02.S')7 = 0.5714. 
 
 Diameter of im- 
 
 Augle of roller 
 Diameter of im- 
 
 Angle of roller 
 Diameter (jf 
 
 10°. Angle of 
 = 0.2857. Diam- 
 
 CoLUMN Ten. — Angle of pallet —10". Angle of roller 
 
 =n 40°. Radius of impulse = = 0.2.5. Diameter of 
 
 impulse — 2.025 = 0.500. 
 
 Column Twelve. — Angle of pallet 12°. Angle of 
 
 12 
 roller 36°. Radius of impulse ==.,. = 0.333 Diame- 
 
 .3(j 
 
 ter of impulse = 2.0333. . . = 0.666. . . 
 
 Column Fourteen. — Angle of pallet 12°. Angle of 
 roller 42°. Radius of impulse= -^^=0.2857. Diameter of 
 impulse = 2.02H57 =^ 0.5714. 
 
 Column Sixteen. — Angle of pallet = 12°. Angle of 
 
 12 
 roller = 48°. Radius of impulse =r _ ^= 0.25. Diam- 
 eter of impulse = 2.0.25 = 0.5. 
 
 Distances of Centres. 
 
 _, , a .sin (A+B) 
 
 Formula : c = ^ ' 
 
 a ^ 1. 
 
 sin A . 
 
 B = 
 
 12A° 
 4° 
 
 A = 
 B = 
 
 1.5° 
 4" 
 
 A = 
 
 15° 
 5° 
 
 ^ = 
 
 17^ 
 5° 
 
 COLUMN THREE. 
 
 sin . 16i° 0.2840 
 
 sin 12i° 0.2164 
 
 1.3124. 
 
 COLUMN FIVE. 
 
 sin 19° = 0.3256 
 
 sin. 15° 0.2588 
 
 COLUMN SEVEN. 
 
 sin 20° ^ 0.3420 
 '' sin 15° 0.2588 
 
 = 1.2581. 
 
 = 1.3215. 
 
 COLUMN NINE. 
 
 sin^22!° _ 0.3827 
 " sin 17.;° 0.3007 
 
 1.27l"i 
 
 87 
 

 COLUMN ELEVEN. 
 
 A = 20° 
 B= 5° 
 
 sin 25° 0.4226 ^ ^34 
 ' sin. 20° 0.3420 
 
 
 COLOMN THIBTEEN 
 
 ^ = 18° 
 5= 0° 
 
 = sin 24S _ 0.4067 _ ^ 3„,^ 
 siu.l8° 0.3090 
 
 
 COLUMN PIPTEEN. 
 
 ^ = 21° 
 
 . _ Sin 27° _ 0.4540 _ , ^^^, 
 
 5= 6° 
 
 sin 21° 0.3584 
 
 
 COLUMN SEVENTEEN. 
 
 ^ = 24° 
 £=6° 
 
 ^ _ sin . 30° _ 0.5000 _ ^ .^.,^^^ 
 sin. 24^ 0.4067 
 
 The following general rules are deductions from the 
 contents of this chapter, and, resuming the constructive 
 necessities tor the two actions of the escapement, may be 
 found useful for the replacement of parts in ready-made 
 watches as well as for constructing new escapements. 
 
 1. If the diameter of a ratchet wheel, or the primitive 
 diameter of a club or pin anchor wheel is given, the dis- 
 tance of centres is determined, and vice versa. (Always 
 supposing a wheel of fifteen teeth and a pallet 'scaping over 
 thi'ee teeth). 
 
 2. To a given wheel, ratchet or club-toothed, a circular 
 pallet may be made as well as one with equidistant lock- 
 ings, and the centre distance will be the same in both cases. 
 
 3. To a given wheel, the pallet may be made with a 
 large or small angle of lifting; the centre distance will not 
 be altered by this difference. 
 
 4. A given pallet will admit but one diameter (primitive 
 diameter) of wheel ; auy larger or smaller wheel is incor- 
 rect. (See Chapter XVI.) 
 
 5. To a given pallet the wheel cannot be made at dis- 
 cretion with club or ratchet teeth ; for, if the pallet be made 
 
 for a club wheel, the ratchet wheel would have too much 
 drop, and if it be made for a ratchet wheel, the club wheel 
 Tould have no drop at all. 
 
 6. If the wheel of a pin anchor escapement is given, the 
 lifting of the anchor is determined. 
 
 7. If the centre distance of fork and roller and the act- 
 ing lengths of the two levers of fork and roller are given, 
 both the angles of movement of the fork and roller are de- 
 termined. 
 
 8. If the centre distance, the acting length of the fork, 
 and its angle of movement are given, the acting length of 
 the roller and its angle of movement are determined. 
 
 9. If the centre distance, the acting length of fork, and 
 the angle of movement of the roller are given, the acting 
 length of roller and the angle of movement of the lever are 
 determined. 
 
 10. If the center distance and both the angles are given, 
 the acting lengths of fork and roller are determined. 
 
 11 . If the centre distance, the acting length of the roller, 
 and one of the two angles are given, the acting length of the 
 fork and the other angle are determined. 
 
 12. If the acting length of the fork and both the angles 
 are given, the acting length of the roller and the centre 
 distance are determined. 
 
 13. If the acting length of the roller and both the angles 
 are given, the acting length of the fork and the center dis- 
 tance are determined. 
 
 14. If the acting lengths of the fork and roller are given, 
 the respective proportions of the two angles are determined, 
 and vice versa. 
 
 15. If the acting lengths of the fork and roller and one 
 of the two angles are given, the other angle and the centre 
 distance are determined. 
 
 88 
 
CHAPTEII XIII. 
 
 PROCEDURE OF MAKING A GOOD AND CORRECT LEVER ES- 
 CAPEMENT. 
 
 After what has been said in the two last chapters on 
 the proper respective proportions of the acting parts of the 
 lever escapement, it remains but to explain how these pro- 
 portions may be accurately observed in the process of con- 
 struction. I deem it unnecessary to explain here the me- 
 chanical processes of tiling, cutting, polishing, etc., for these 
 are things which can never be learned from books. I treat 
 the subject wholly from a mathematical point of view, firmly 
 convinced that this treatise will be found useful for prac- 
 tical escapement makers, not by teaching them how to file 
 and polish, which they already know as well as any body 
 could teach them, but by explaining to them how to avail 
 themselves of the teachings of science, which exists as well 
 for the watchmaker m for the engineer, and should guide 
 the work of the one at; veil as that of the other. 
 
 For the reader w lo has thoroughly mastered the con- 
 tents of the two last chapters itic process of making a cor- 
 rect lever escapemou' , or any part of it, will require little 
 explanati<m, and as this chapter will probably interest the 
 practical workman more than any other, brevity and sim- 
 plicity are of the utmost importance. 
 
 Except the measuring instruments mentioned in Chap- 
 ter II, which will be more amply described in Chapter 
 
 XVI, there are no tools required for sizing the parts and 
 measuring the angles of action, aud all the requisites for 
 constructing an escapement of given proportions can 
 be readily made Ijy any workman. 
 
 To begin with the ordinary course of making a pallet to 
 a ready-made wheel, we will speak at first of a circular pal- 
 let which is to have a total movement of 10*, and to fit to 
 a ratchet escape wheel measuring fi.53 m. 
 
 Look in the second column of Table I for the given 
 diameter (the wheel is supposed with cut teeth, and there- 
 fore the second column must be used here). From this num- 
 ber proceed in the horizontal range of numbers and note 
 the numbers corresponding to this diameter : 
 
 Outer circle of pallet = 4.38 m. 
 
 Inner circle of pallet = 3. 24 m. 
 
 Lifting circle for 10° = 1.64 m. 
 
 Height of segment ^ 3.31 m. 
 Prepare a slip of good, thin cast steel of suitable breadth 
 and thickness, heat it to a low red heat and leave it on a 
 piece of charcoal, covered with another piece, to cool slowly. 
 Finish the surfaces plane and smooth, and drill a hole in it 
 for the pallet axis. Make the piece blue, for better distin- 
 guishing the lines traced ujion it. 
 
 Make three discs of thin steel plate, whose diameters 
 must be made, by the aid of the micrometer, to correspond 
 exactly to the first three of the above mentioned numbers : 
 4.38 m., 3.24 m., and 1.64 m. The holes in the centres of 
 of these discs must be exactly the size of the hole drilled for 
 the pallet axis. Then take the largest of these discs and file 
 away as much on one side of it as to make it a segment the 
 size of which when measured from the straight line to the 
 circumference of the circle opposite to it is exactly 3.31 m. 
 as has been found in Table I. Diagram VIII shows these 
 discs. 
 
 89 
 
With a good rouud pin fitting exactly into both the 
 holes, fit the flattened disc upon the slip of steel prepared to 
 make pallets of, with the flattened side towards the end of 
 the slip, and trace with a very thin and sharp pointed 
 broach the outer circle of the pallet on the slip of steel, 
 quite near to the edge of the disc, and the straight line be- 
 tween the two outermost corners of the pallet. Fix in the 
 same way the second disc and trace the inner circle of pal 
 let round its edge. File away as much of the end ot the 
 steel slip as just to touch the straight line traced by the first 
 disc. 
 
 The next thing is, to shape the outermost faces of the 
 pallet, which may be done by applying two steel angles, 
 one of 112° to the entrance side, and the other of 124" to 
 the delivery point. Both the sides must be filed away in 
 the direction indicated by these two angles, until they 
 touch the outer corners of the pallet. File out ihe space 
 between the pallet arms, making the inner faces parallel 
 to the outer planes and the breadth of pallet arms to cor- 
 respond exactly to the size indicated by Table I, in this 
 case 0.58 m. Fix the third disc, of the diameter 1.U4 m., 
 to the pallet, and draw lines from the outer corners of the 
 pallet, to be tangents to this disc. When the ends of the 
 pallet arms are filed away j ust according to those tangents, 
 the acting parts of the pallet are made, and there remains 
 but to give the pallet a suitable shape. 
 
 This is the entii-e process of making a pallet to a given 
 wheel, and for those especially who make many pallets of 
 the same size, the trouble of making three little steel discs 
 cannot be called a great objection. The two angles re- 
 quired for the outside are the same for all circular i>allets 
 of any size whatever. 
 
 For making a pallet with equidistant lockings, five steel 
 discs are required, whose sizes must be sought for in Table 
 
 II. We suppose the measured diameter of the wheel to be 
 7.72 m., and the angle to be performed, 12°. The corre- 
 sponding sizes would be : 
 
 Outer circle = 5.86 m. 
 
 Locking circle = 4,50 m. 
 
 Inner circle = 3.14 m. 
 
 Fii-st lifting circle = 1.09 m. 
 
 Second lifting circle = 2.91 m. 
 
 Height of segment = 4.23 m. 
 Five discs must be made ot the size indicated by the 
 above mentioned first five numbers, and the largest of them, 
 that of the outer circle, must be flattened away as much as 
 to measure in the right angle to its flattened part, 4.23 m. 
 Then take a slip of steel, prepared as already explaiued, 
 trace the outlines of the pallet according to the three discs, 
 file the open side of the pallet away until touching the line 
 indicated by the segment, file the locking face of the first 
 pallet arm to an angle of 112° and the outer side of the 
 other pallet arm to an angle of 120°, file out the space be- 
 tween the arms and make their inner faces parallel to the 
 outer ones, giving the arms the breadth indicated by the 
 table to be 0.68 m. Fix the fourth disc on the pallet and 
 trace a tangent to it from the entrance corner of the first 
 arm, fix then the fifth disc and draw a tangent to it from 
 the delivery corner of the second arm. File the driving 
 planes on both the pallet arras to agree with these tangents 
 and then the acting [jarts of the pallet are of the righi size 
 and shape. 
 
 In case it is required to make a wheel to a given pallet 
 and centre distance, which occurs often when repairing lever 
 watches, the distance of centres must be measured and the 
 proper size sought in Table I, column 10, if the pallet is a 
 circular one, and in Table II, column 11, if the lockings 
 should be equidistant. Suppose the centre distance to be 
 
 90 
 
5.2 m., we find in the first coliimu of botli tables tliat a 
 disc for a wlieel must be turned of a diameter of 9.0 iii. 
 This .size must lie taken in the first cohimu, because there 
 is a full round disc in question liere — tliat is, the wheel be- 
 fore its teeth are cut. 
 
 If in any case the given sizes and circumstances should 
 not be found to agree perfectly with the numbers contained 
 in the tables — for instance, if a circular pallet with a move- 
 meot of 8'^ is to be made to fit to a wheel of the measured 
 diameter of 6.83 m., the next two diameters in the table 
 must serve to determine the right sizes by a simple system 
 of interpolation The required size (6.83 ra.) is just between 
 the next numbers (in column 2) of which it is the middle- 
 rate, and therefore iu all the columns wauted the middle of 
 the numbers contained in these two horizontal ranges 
 must be taken : 
 
 Outer circle 
 
 Inner circle 
 
 Lifting circle 
 
 4.52 + 4.65 0.17 
 
 2 
 
 = — — = 4.58 m. 
 
 3.34 + 3.43 _ 6.77 
 
 = 3.3S m. 
 
 1.44+1.48 2.92 
 
 Height of segment = - 
 
 3.41 +3.51 _6.92 
 
 = 1.46 m. 
 
 = 3.46 1 
 
 If the diameter of wheel had been 6.78 m., the difference of 
 this size to the next one iu the table, 6.73, would be (1.05 m., 
 or one-fourth of the difference between the two next sizes 
 in the table, 6.73 and 6.93. Therefore in all the columns 
 the number in the horizontal range of 6.73 must be taken 
 and augmented by one-fourth of the difference between this 
 and the next number in the same column : 
 
 Outer circle = 4.52 + Hi-' = 4.52 + 0.033 = 4.55 
 
 4 
 
 Inner 
 
 Liftina: circle 
 
 3..34 +2:!I^ = 3.31 + 0.02 = 3.36 
 4 ^ 
 
 = 1.44 4 
 
 0.04 
 
 1.44 + 0.01 = 1.45 
 
 Height of segment =3.41 +—'!=- .3.41 + 0.03 = 3.44 
 
 4 
 
 The use of Table VII for finding the proportionate lever 
 length and radius of impulse for certain given or intended 
 angles of lifting, is very easy. Supposing the acting length 
 of a lever given to be 4.2 m., having a total movement of 
 8'^, and the lifting angle of the roller intended to be SO'', 
 we must look for the diameter of impulse in the fourth col- 
 umn, where the corresponding size is 2.24 m. Make a disc 
 of steel of that size, fi.x it on the table roller so that it is 
 concentric with it, and trace the circle in which the acting 
 edges of the ruby pin are embraced, close to the edge of 
 this disc. 
 
 If it is required to make a lever and roller to a given 
 centre distance, as 4.45 m., the pallet making an angle of 
 10° and the lifting angle on the roller intended to be 40°, 
 find in column 11 the number 4.45, and in the same hori- 
 zontal range the corresponding diameter of impulse will be 
 found iu column 10, = 180 m., and the acting length of 
 lever in column 1, = 3.60 m. 
 
 If a roller has been lost and is to be replaced so as to 
 give with a lever length of 4.8 m. and a pallet movement 
 of 12°, a lifting angle of 42^ on the roller, look in column 
 1 for the lever length of 4.S tn., and proceed in the horizon- 
 tal range of that nund)er to column 14, where the diameter 
 of impulse will be found to be 2 74 m. 
 
 If in the same case a certain centre distance . must be 
 kept, as in most cases of replacing a roller, there is no lib- 
 erty allowed as to the angle of lifting on the roller. If, for 
 instance, the centre distance is given = 5.9 m., the angle of 
 
 91 
 
lifting on tiic roller must be 18'^, and the inipulso radius 
 2.4 m. 
 
 When in such case this latter would be made 2.74 ni., 
 it would require an alteration of ihe lever length or centre 
 distance, which cannot be granted in a ready-made watch, 
 and without those alterations it would not perform the in- 
 tended angle, and would require a wider banking, because 
 it would force the pallet to travel a much greater angle 
 than it requires for escaping. 
 
 It might be asked, what is the use of making steel discs 
 for every size, and is it not better to measure directly and 
 trace the circles with a compass or depthing tool? Tliis 
 must be answered in the negative, for no compass or depth- 
 ing tool can be adjusted so nicely as to distinguish hun- 
 dredths of a millimeter, but a disc can be directly measured 
 with the micrometer, and consequently be made with all the 
 accuracy required. 
 
 CHAPTER XIV. 
 
 ON THE MATERIAL EMPL(1YED IN MAKING LEVER ES- 
 CAPEMENTS. 
 
 This is a very important question in the construction of 
 the lever escapement, and every escapement maker should 
 make it the subject of his most earnest study, the more 
 especially as we encounter very diverging opinions among 
 the various manufacturers. 
 
 The English lever escapements have almost uniformly 
 a brass escape wheel and the pallet and lever of tempered 
 steel. The Swiss show a greater variety ; still, most of their 
 escapement wheels are of tempered steel, and almost all 
 their pallets and a considerable proportion of their levers 
 are of the same material. Sometimes we see levers of brass 
 or German silver, and wheels of brass and gilt; but it seems 
 that in most cases the choice is decided by taste and fancy, 
 without any regard to the practical service of the parts. 
 Supposing the question, which of these materials is the best 
 suited to the acting parts, we will try to elucidate the mat- 
 ter by discussing the reasons for and against each of them. 
 
 To begin with steel, it cannot be denied that it is in 
 many essential points a very good material for the parts of 
 escapements. It is tolerably hard and elastic, and suscep- 
 tible of a beautiful polish. Besides, its specific weight is the 
 lowest of all materials that are applicable. Still, there are 
 very bad qualities in steel, which are greatly to its disad- 
 vantage. The first is its liability to oxidize or rust. 
 
 92 
 
When we consider huw caieftiUy llie escapenieul maker 
 strives tu reduce the friction of tlie acting parts by giving 
 them the highest polish, it is a discouraging reflection that 
 these beautifully polished surfaces may, by being carelessly 
 touched by a moist hand when the watch is under repair, 
 or even by atmospheric influences, or by the action of gas 
 or vapor of acids, be deprived not only of their nice look- 
 ing appearance, but also of that smoothness of surface 
 which has been produced with so much care. Many ex- 
 cellent specimens of workmanship are destroyed by this 
 natural defect of the steel. 
 
 Another great danger resulting from the employment 
 of steel is its susceptibility of magnetism, especially in 
 watches with compensated balances, which necessarily are 
 made of steel. It has the most detrimental influence on the 
 rate of the watch if, by causes which are not yet fully un- 
 derstood, and which very often cannot be avoided even by 
 the greatest precaution, any part of the escapement has be- 
 come magnetized. The lever, being the longest part of it, 
 is most of all exposed to magnetic polarity, and the influ- 
 ence is the more pernicious because it is acting on its end. 
 It will there produce quite unaccountable deviations of 
 rate, even in watches in which all the requirements for a 
 good performance are united. 
 
 A third and very great drawback in steel as a material, 
 is the necessity of hardening it for such purposes. If not 
 hardened, the steel would hardly offer any essential advan- 
 tage over other good materials, and the process of harden- 
 ing involves unavoidable danger to the soundness of the 
 parts. Nobody can guarantee that a hardened ])iece of the 
 best steel may not have some trifling defect which will ren- 
 der it worthless when ready and finished. True, the skill 
 and care of the workman may reduce the liability of such 
 occurrence, but even then it is bad enough to be aware that 
 
 there may hi' liidden some tendency to break in any ])art 
 of the escapement. 
 
 Besides, the necessity of polishing the steel parts all 
 over after having hardened theui causes much trouble, es- 
 pecially when the wlieel is also made of steel, and necessar- 
 ily augments the manufacturing expense. 
 
 These natural defects would compel the absolute disuse 
 of steel in watchwork if there w-ere another metal known to 
 replace it. So long as this is not the case, we are obliged 
 to make our pinions, arbors, pivots, screws, etc., of steel, but 
 there is no necessity for making the wheel, pallet and lever 
 of our escapements of this material. Therefore we must 
 try to ascertain whether there is any other metal as appro- 
 priate, or more so. 
 
 Another metal very frequently employed, especially for 
 wheels, is brass. Its qualities render it a very proper ma- 
 terial, because when carefully hammered it has considera- 
 ble density and elasticity. Its specific weight, though 
 about one-seventh more than that of steel, is no objection to 
 its employment, and it is free from the above mentioned nat- 
 ural defects of steel. Therefore we have strong reasons to 
 prefer it to the latter for the material of wheel, pallet and 
 lever. Still, it might be objected that it is impossible to 
 give to the brass, however it might be prepared, the degree 
 of hardness and elasticity which is shown by tempered steel. 
 An escape wheel of brass, as has already been mentioned, 
 should always be polished on its surfaces, and not gilt, for 
 reasons which have been explained in Chapter VIII. 
 
 German silver is, in its physical qualities, very much 
 like brass, but experience has shown that the iriction in the 
 German silver fork is greater than in forks of brass and 
 steel. 
 
 Four or five years ago a new alloy was invented at 
 Vienna, and called sterro-metal. It was said to be of very 
 
 93 
 
greal malleability, tenacity and elasticity It occurred to 
 me that it might be very useful for this and similar pur- 
 poses. I procured a quantity of it, in several different 
 thicknesses, and found its exterior very much like brass, of 
 a rather reddish color. I was told that it was composed of 
 copper, zinc, tin and iron, and its tensile strength was stated 
 by a commission in the imperial arsenal at Vienna to be 
 4, .500 kilogr. on the square-centimeter, and consequently 
 approaching that of east steel, which is commonly accepted 
 at between 4,900 to 8,300, while that of brass is about half 
 as much. This encouraged me to try the qualities of the 
 sterro-metal for watchmaking purposes I took five slips 
 of itf each 2.5 m. thick and 18 m. broad, which I worked 
 out in several ways. I took the first between a pair of good 
 flattening rollers and rolled it by degrees down to the thick- 
 ness of 1.1 m., at which point I was obliged to stop because 
 the metal showed many fissures on its edge. The second 
 specimen was heated red hot and cooled in water. This 
 diminished the hardness a little, but not so much as is the 
 case with brass by heating. Then we worked it out between 
 the rollers to the thickness of 1.1 m., after which I found it 
 quite sound. After once more heating and cooling, we re- 
 duced it to O.G m. The specimen, though stretched out to 
 more than three times its length, jiroved to be entirely with- 
 out defects. I cut a part off, heated and cooled it, and 
 rolled it down to 0.2 m. This was a reduction in thickness 
 to 8 ])er cent, of its original size, and the soundness of the 
 metal was perfect. The hardness and elasticity were very 
 satisfactory, and it could only be broken by bending it at a 
 very sharp angle. I took then the third specimen, heated 
 and cooled it, and rolled it down to 0.75 m.. when it was 
 cracked all over. The fourth specimen I rolled four times 
 with red heat, and then forged the fifth specimen four 
 ^mes, lieating it red each time. These two last slips were 
 
 very good, and of excellent elasticity. These experiments 
 were sufficient to convince me of the advantages to be ob- 
 tained by the employment of the sterro-metal for lever es- 
 capements. I have had many escapements made of it, and 
 never experienced any disadvantage from its use. The high 
 degree of tenacity and ductility shown by it is more than 
 the best English or Bavarian brass could be expected to 
 possess. The specific weight is 8.9, about equal to that of 
 brass, and its expansive ratio is a trifle higher than that of 
 brass 
 
 I also tried the sterro-metai lor train wtieels, but found 
 it would not answer, because in cutting the teeth it spoils 
 the cutters very soon. The polished surfaces of the sterro- 
 metal do not look so good as those of good, hard brass. 
 
 When well hammered, gold is a very good material for 
 lever escapements. It may be said to nearly equal in hardness 
 and ductility the sterro metal, but it breaks more easily. It is 
 not necessary for this purpose to employ gold of 18 carat; 
 the alloy of 12 carat will do quite as well, and is capable of 
 a beautiful polish. Still, its specific weight is an objection 
 against its use. Gold of 12 carat is about 14.0. This is 
 too heavy for parts of an escapement, and increases the 
 inertia considerably, a circumstance not to be underrated 
 in the lever escapement, which has so many intermissions 
 in Its action. Besides, the price of the gold would be an 
 objection to its general employment. 
 
 Cousidering its very low specific gravity, aiuminium at 
 one time seemed to me a desirable metal for escapements; 
 but it very soon proved quite unfit, because it was found 
 impossible to give it the hardness and elasticity indispensa- 
 ble for this work. One of the alloys of this metal, however, 
 has claimed the attention of mechanicians by its unrivaled 
 strength, and great hardness, and resistance to wear by 
 friction: It is the alloy of copper and aluminium, known 
 
 94 
 
under the name of aluminium-bronze. Tiie honor of its in- 
 vention is a matter of dispute between France and England, 
 the former claiming it for St. Clauc Deville and Debray, 
 while the English attribute it to Dr. Percy As the most 
 earnest eflbrts were at this time universally dii-ected to the 
 complete e.Karaination of aluminium and its alloys, it is not 
 unlikely that both invented it independently of one another. 
 The only aluminium-bronze 1 have tested in my experi- 
 ments was that of 10 per cent, aluminium to 90 per 
 cent, of copper. The alloys in which a smaller quantity of 
 aluminium is contained wore described in the reports as 
 not promising satisfactory results; besides, the desire for a 
 material of the least specific gravity would naturally lead 
 to the choice of an alloy with the largest proportion of alum 
 inium. But such alloys have been proven brittle, and de- 
 void of the necessary elasticity. The aluminium bronze of 
 10 per cent, has been found by the experiments of Mr. An- 
 derson, at the Royal Gun Factory, Woolwich, Mes.sis. 
 Simms, London, and Mr. Morin, Nanterre, to have a ten- 
 sile strength of 5328 kilogr. on the ['] C" as the mean rate 
 of several trials, thus approaching to tlie average strength 
 of cast steel. Its resistance to compression and its mallea- 
 bility are very satisfactory, though not of much importance 
 for escapement makincr. But a very important point, the 
 transverse strength, or resistance to being bent, was found 
 on a comparative trial with brass and gun metal to be: 
 
 Brass, - - 2.22 
 
 Gun metal, - - 0.15 
 
 Aluminium bronze, 0.05 
 That is to say, three bars of the above mentioned met- 
 ais, of the same dimensions, were fastened at one end so as 
 to be in a horizontal position, and a certain weight applied 
 to the free end of each bar made that of brass bend 2.22 
 degrees of the instrument, etc. This experiment proves 
 
 that the aluminium bronze opposes three times greater re- 
 sistance to flexion than gun metal, and that its resistance is 
 4-1 times as great as that of brass. The exj)ansive ratio is 
 considerably less than that of brass. Its resistance to 
 oxydation by atmospheric inlluences is not determined, but 
 is certainly greater than that of brass, though inferior to gold 
 of 18 k. Resistance to friction is a quality in which, to 
 judge from the reports, the aluminium bronze is unsur- 
 passed. 
 
 This combination of desirable qualities induced me to 
 try the aluminium bronze 'vith special reference to its em- 
 ployment for horological purposes. I took some slips of 10° 
 aluminium bronze plate of 2.4 ni thickness, and tried at 
 first how much they could be treated between the rollers 
 without heating. I soon found ihat this material would 
 not bear .i i';ductioi2 of more thru one-fourth to one-third 
 of its thiclmes:: \.'ithout 'getting many fissures. When heated 
 to red hea'b and cooled in w'atci', however, after having been 
 rolled down about ono-fourth its thickness, it will bear a 
 further operation of tlie same kind and extent. Thus, by 
 alternate heatiu;^' and rolling I brought it to a thickness of 
 0.2 m. The specimen did not show the slightest fissures on 
 its edges, but proved to be of remarkable hardness and 
 elasticity. It occurred to me that it might be useful to 
 make a comparative trial of the resistance to breaking by 
 flexion. I took specimens -f sterro-metal, gold and alum- 
 inium bronze, each reduced in the most careful w;iy t(j the 
 thickness of 0.2 m. I found that the specimen of gold 
 when merely bent with the fingers to a right angle, broke 
 short ofi'. The specimen of sterro-metal did not break by 
 this flexion, but in most cases it broke when it was bent 
 into the straight line, or very little beyond it, to the other 
 side. The specimen of aluminium bronze withstood being 
 bent three or four times at right angles altei'nately to the 
 
 95 
 
one and to the other side before it broke, and even then it 
 did not break at once, but only on a part of its breadth, 
 ■while otlier parts resisted further flexion. This tenacity is 
 very astonishing, and can hardly be equalled by any other 
 material. 
 
 Other experiments in treating the aluminium bronze in 
 a hot state- gave very satisfactory results. It opposes a 
 greater resistance to files and cutters than brass or gold do, 
 but the cut of it is very smooth and regular. 
 
 cannot be denied that a metal possessing so many 
 valuable qualities is an excellent material for lever escape- 
 ments. I have made all my escapements of aluminium 
 bronze since that time, and am very well satisfied with it. 
 The polish is beautiful, and it looks very much like gold. 
 
 I found this alloy also very useful for other purposes 
 where hardened steel was formerly employed, as for click 
 springs, wheels for keyless winding mechanisms, etc., etc. 
 
 I am perfectly aware that I place my opinion in oppo- 
 sition to that of a great majority of horologists, or at least 
 to the usual course adhered to, when I assert that the alum- 
 inium bronze is preferable to all materials hitherto in use 
 for wheels, pallets and levers ; but with such facts as are 
 contained in the following tables 1 think it is easy to sup- 
 port my conclusions. 
 
 PHYSICAI, QUALITIES OF METALS. 
 
 The following are the physical qualities of materials 
 mentioned in this chapter, and of some others of possible 
 adaptation to the same purposes, as they could be found in 
 physical treatises, but for the purpose of estimating the rel- 
 ative value of these diflerent alloys as materials for lever 
 escapements, these notations are very unsatisfactory: 
 
 Gold of 18 k. - 
 Gold of 12 k.- - 
 Gold of 9 k.- - 
 Silver - - . . 
 German Silver - 
 Sterro-metal - - 
 Copper - - - 
 Steel - - . . 
 Steel hardened - 
 Brass .... 
 Aluminium - - 
 Aluminium l)r(iiizi 
 
 Tensile strength. 
 
 5000 
 
 5000 
 6400 
 
 8000—9000 
 
 10000—12000 
 
 2500 
 
 6400 
 
 Specific gravity. 
 
 about 16.8 
 
 about 14.2 
 
 about 12.8 
 
 10.6 
 
 . 8.7 
 
 8.4 
 
 8.9 
 
 7.9 
 
 7.9 
 
 8.7 
 
 2.8 
 
 7.7 
 
 Expansive 
 ratio. 
 
 0.001466 
 0.001520 
 
 0.001910 
 
 0.001700 
 0.001718 
 0.001079 
 0.001240 
 0.001868 
 
 0.001600 
 
 Finding no more definite iniormation in books, I un- 
 dertook myself a series of experiments with a view to sup- 
 plying this deficiency. The qualities necessary in materials 
 for making delicate pieces of mechanism are : transverse 
 strength, resistance against permanent flection, hardness, 
 or resistance against compression, and resistance against 
 breaking by being bent. 
 
 The first step in conducting these experiments was to 
 procure bars of all the materials to be tried, of a certain 
 length, and exactly the same profile. To meet the last 
 requirement the employment of round wire seemed the 
 most convenient, because a carefully drawn wire presents 
 in all its length the same thickness, and consequently for 
 finding its profile it was only required to verify the diameter. 
 
 I took care to prepare of all the materials wires of exactly 
 the same diameter, and drawn as hard as could be without 
 injury to their soundness. Their diameter was 2.50 m. 
 
 For trying the transverse strength, I fixed one end of the 
 wire solidly, and fastened an index upon it at exactly 200 
 m. from the fixed end. I chose three weights, which were 
 hung on the wire close to the index, and noted the flexion 
 produced hy each of them in millimeters. The first of 
 
 96 
 
Diagram XVII. 
 
© 
 
 
 L 
 
 \ 
 
 
 4. 
 
 6. 
 
 o 
 
 19. 
 
 18. 
 
 14. 
 
 15. 
 
 17. 
 
 1 
 
 ( 
 
 
 
 ) 
 
 le. 
 
 K(o: 
 
 
 
 
 / 
 
 ; ! o 
 
 DiAGKAM XVIII. 
 
Diagram XIX 
 
 ^^^ 
 
these weights was 27 grammes, the second 98.5 gr. and the 
 third 140 gr. They were the same for all the experiments. 
 The flexibility of the different materials was found to be: 
 
 
 1st weight. 
 
 2d weight. 
 
 3d weight. 
 
 Cast steel (Sheffield) - 
 
 2.1 
 
 7.4 
 
 11.2 
 
 Cast steel hardened, light blue 
 
 2.3 
 
 8.2 
 
 12.4 
 
 Cast steel hardened and blue 
 
 2.3 
 
 8.2 
 
 12.4 
 
 Cast steel hardened and yellow 
 
 2.3 
 
 8.2 
 
 12.4 
 
 Cast steel hardened 
 
 2.4 
 
 8.4 
 
 12.7 
 
 Cast steel hardened and red - 
 
 2.4 
 
 8.6 
 
 12.S 
 
 Copper . - - - 
 
 3.7 
 
 12.4 
 
 18.6 
 
 German silver 
 
 4.0 
 
 13.2 
 
 19.3 
 
 Toinliac . . - 
 
 4.0 
 
 13.8 
 
 20.7 
 
 Aluminium bronze 
 
 4.4 
 
 15.2 
 
 22.7 
 
 Brass from Berlin - 
 
 4.4 
 
 15.G 
 
 23.4 
 
 Gold of 18 k. 
 
 4.7 
 
 16.3 
 
 24.0 
 
 Gold of 9 k. - 
 
 4.7 
 
 16.4 
 
 24.3 
 
 Gold of 12 k. 
 
 4.8 
 
 16.5 
 
 24.4 
 
 Brass from Augsburg 
 
 5.2 
 
 18.0 
 
 27.0 
 
 Sterro metal . .' . 
 
 5.3 
 
 18.2 
 
 27.1 
 
 Silver, standard 
 
 5.3 
 
 18.7 
 
 28.1 
 
 It will be easily understood that the transverse strength 
 of the specimens must be in the inverse ratio of the num- 
 bers contained in this table. But it is not exactly the flexi- 
 bility or rigidity which must be valued for our purpose ; a 
 much greater importance must be attached to the elasticity, 
 or resistance to permanent flexions. At first sight it might 
 appear that a conclusion may be allowed from the trans- 
 verse strength upon this latter quality, but experiment 
 proved this supposition incorrect. U.sing rods of the 
 same dimensions as before, I bent each specimen, reading 
 by the aid of a graduated arc and the index on the 
 wire, the extent of flexion ; and after leaving the wire free 
 to return to its former position, I verified whether any per- 
 nanent flexion had taken place. This bending was in- 
 creased by five millimetres each time, and continued until 
 
 the permanent flexion amounted to 1 m. or mori'. The re- 
 sults of these experiments are given in the following table : 
 
 ] 5 20 25! 30 35 40 45 50 55| 60 
 
 Cast steel, hard 
 
 Cast steel, hard, yellow 
 
 Cast steel, hard and red 
 
 Cast steel, hard and blue — 
 
 Cast steel, hard,light blue 
 
 Aluminium lironze 
 
 Sterro metal 
 
 Gold of 18 k. - 
 
 Gold of 9 k. 
 
 Brass ii(jm Berlin 
 
 German silver 
 
 Brass from Augsburg 
 
 Gold of 12 k. 
 
 Silver 
 
 Tombac 
 
 Cast steel, soft - 
 
 Copper 
 
 -,0.1 
 - 0.1 
 
 0.1,0.2,0.8 1.0:1.2 
 
 0.1 
 
 .1 
 
 0.2 
 
 0.1 
 
 0.2 
 
 2,0 
 
 1,0 
 
 -0 
 
 1;0 
 •7 
 
 brok'u 
 
 0.1 
 
 0.3 
 0.1 
 0.3 
 
 0.2 
 
 0.4 
 0.2 
 0.3 
 
 0.2 
 
 0.1|0.2;0.4 
 
 0.2 
 
 0.4 
 
 0.2 
 
 0.1 
 
 0.5 
 
 ;o.5,o.6 
 
 tO.50.7 
 : 0.4 0.6 
 ;0.3|0.7 
 i;0.9,1.0 
 
 65 
 
 Cast steel, hard 
 
 Cast steel, hard and yellow 
 
 Cast steel, hard and red 
 
 Cast steel, hard and blue 
 
 Cast steel, hard, light blue 
 
 Aluminium bronze 
 
 Sterro metal - 
 
 Gold of 18 k. 
 
 Gold of 9 k. - 
 
 Brass from Berlin 
 
 German silver 
 
 Brass from Augsburg 
 
 Gold of 12 k. - 
 
 Silver 
 
 Tombac 
 
 Cast steel, soft - ,j 
 
 Copper 
 
 0.1 
 
 70 75 80 85| 90 100 105 110 
 
 0.1 0.1 
 
 0.2 
 0.1: 
 0.5 
 0.2 
 0.4 
 0.5 
 0.8 
 0.9 
 1.0 
 1.7 
 
 0.2 
 0.1 
 0.5 
 0.2 
 0.6 
 ,0.6 
 0.9 
 
 broken. 
 
 0.2 0.3 
 0.2 0.3 
 0.6 0.7 
 0.3 0.5 
 
 0.7 
 0.9 
 
 1.0 
 
 0.3 
 0.4 
 0.8 
 0.9 
 
 0.4 0.4 
 0.5 0.8 
 
 0.5 0.7 
 
 97 
 
Cast steel, hard - 
 
 Cast steel, hard and yellow 
 
 Cast steel, hard and red 
 
 Cast steel, hard and blue 
 
 Cast steel, hard and light l)luc 
 
 Aluminium bronze 
 
 Sterro metal - - - 
 
 Gold of 18 k. 
 
 Gold of 9 k. - 
 
 Brass from Berlin 
 
 German silver - - - 
 
 Brass from Augsburg 
 
 Gold of 12 k. - 
 
 Silver 
 
 Tombac - - - - 
 
 Cast steel, soft 
 
 Copper - - - - 
 
 115-120 
 
 broken. 
 
 O.S 
 
 0.9 
 
 125 
 
 130 
 
 135 
 
 140 
 
 145 
 
 0.1 ; 0.1 
 
 0.2 
 
 A comparison between this and the preceding table 
 shows clearly that there is no great connection between 
 tranverse strength and elasticity. For instance, copper is 
 the least elastic of all the materials in the preceding table, 
 but shows sufficient transverse strength to hold first place 
 among the other materials, except steel. Sterro metal 
 shows great flexibility with a remarkable degree of elas- 
 ticity. 
 
 The superiority of aluminium bronze in this respect is 
 also confirmed by my experiments, though I failed to find 
 it so pronounced as Mr. Anderson states it to be. Perhaps 
 lie has not tried the metals in tlie form of round wire, and, 
 which I think most likely, he may have tried them as they 
 were cast, without being hammered or rolled. For watch 
 making purposes, of course, we have to deal with the ma- 
 terials in their greatest density and hardness. 
 
 Resistance to compression, or hardness, is another jioint 
 which I thought desirable to try. Different methods have 
 
 been employed for this purpose ; the manner of testing the 
 hardness of materials in mineralogy, by scraping the one 
 with the other, is the oldest; but for metals this would 
 hardly answer, and would never admit of any exact grad- 
 uation. Another way was taken by Hugueny. He tried 
 to force a pointed punch into the different specimens by a 
 blow of equal violence, and by the greater or smaller im- 
 pression made he estimated the hardness of the specimens. 
 This method, though giving much more positive results, did 
 not satisfy me, because the degree of hardness was only to 
 be estimated by vision. I tried to find a way to ascertain 
 by direct measurement the compression resulting from a 
 blow, and to this end employed a little stamping press to 
 produce blows of exactly equal force. In the cylinder of 
 this press I inserted a flat punch of one square centimeter, 
 and the wire specimens served at the same time for these ex- 
 periments. Thus, by measuring the compression of the part 
 on which the blow had fallen, I obtained the numbers of 
 hardness contained in the follow'iug table, and I may re- 
 mark here that they are the mean rates of three different 
 experiments. It might be said against this method thf t 
 the employment of wire is not correct, because the impres- 
 sions cannot be in a reirular arithmetic progression with the 
 force of the blow, as might be expected when employing 
 specimens of a rectangular profile. I know that well enough; 
 still, the diameter of the wires and the blow being always 
 exactly the same, I think the results obtained may not be 
 very far from correct. 
 
 Finally, I made the resistance to breaking the object of 
 iiome experiments. I used the same specimens, fastened 
 them in a vise at one end, and bent them to a right angle. 
 After that I bent those which stood against this flexion, 
 straight again to the other side in right angle, and con- 
 tinued so until they broke. By addition of all these angles 
 
of flexion which they had resisted, I obtained the numbers 
 contained in the second column of the table, wh'ch are also 
 the mean rates of three or more experiments, while the 
 third column shows the remarks made upon the manner in 
 which the fracture took place. 
 
 
 Compression 
 
 Resistance 
 
 Bemarks about 
 
 
 iu 
 
 to breaking 
 
 the manner in 
 
 
 MiUimeters. 
 
 (in angles). 
 
 which it broke. 
 
 Cast steel, hard 
 
 Burst 
 
 5-10° 
 
 Very quick. 
 
 Ca?t steel, hard, yell'-w 
 
 Imperceiitiljlf 
 
 10° 
 
 V^ery quick. 
 
 t^ast steel, hard and r d 
 
 0.1)20 111. 
 
 22° 
 
 Very quick. 
 
 Cast steel, hard and blue 
 
 0.027 m. 
 
 25° 
 
 Very quick. 
 
 Cast steel, hard, light blue 
 
 O.OSl m. 
 
 
 Very quick. 
 
 Aluminium bronze 
 
 O.MtiT 111. 
 
 207° 
 
 (^uick. 
 
 Cast steel, soft 
 
 0.3;t8 111. 
 
 45-1 ;io°* 
 
 Very quick. 
 
 Gold of 12 k. - 
 
 0.4-10 111. 
 
 100° 
 
 Quick. 
 
 German silver 
 
 O.-ISS 111. 
 
 17.5° 
 
 Middling. 
 
 Gold of 18 k. - 
 
 0.,")08 111. 
 
 110° 
 
 Quick. 
 
 Gold of 9 k. - 
 
 0.520 ni. 
 
 95° 
 
 Quick. 
 
 Sterro metal 
 
 0.540 111. 
 
 150° 
 
 Very quick. 
 
 Brass, Berlin - 
 
 0.500 111. 
 
 3oa° 
 
 Slow. 
 
 Brass, Augsburg - 
 
 0.570 III. 
 
 103° 
 
 Quick. 
 
 Tombac 
 
 0.043 111. 
 
 210° 
 
 Slow. 
 
 Silver 
 
 0.005 III. 
 
 30S° 
 
 Very slow , 
 
 Copper 
 
 O.SIiG III. 
 
 170° 
 
 81ow. 
 
 I am aware these resear:;hes were of a rather rudimen- 
 tary character and might be imjjroved upon iu many re- 
 spects, and for this reason I would have refrained from pub- 
 lishing them but for the en I ire absence of such tables iu 
 general, and especially for honjlogical purposes. Iu fact, 
 I would feel very much gratified should the incompleteness 
 of the results obtained by me occasion some scientific or 
 practical mau to complete or correct them. 
 
 One of the most important points, however, could not 
 
 *One and the same foot of steel wire, broken at different jilaces, qa\n 
 the numbers: 4r,°, 80°, QU", ll.j', liiJ''. .-ill Ihu other material-; showni a 
 much yreater re.jularity of structure. 
 
 be tested, which is the resistance to wearing by friction, and 
 I fear it would be very difficult to get comparative num- 
 bers of any value for this purpose. It would require a 
 great amount of time, many experiments, and some appar- 
 atus. Perhaps another may be more fortunate thau I in 
 finding a simple way of testing this important quality of 
 materials. 
 
 99 
 
CHAPTER XV. 
 
 OF THE POINTS TO WHICH THE EXAMINER SHOULD 
 DIRECT HIS ATTENTION. 
 
 It is au inseparable consequeiice of the compound 
 action of the lever escapement that for good performance it 
 is not sufficient oufy to have its separate actions correct, 
 each in itself, but a j^ei'fect harmony between these sepa- 
 rate actions is also necessary. Therefore the careftil exam- 
 ining of a detaclied lever escapement is by no means an easy 
 task, for there are many points to be tested on which good 
 performance and time-keeping depend entirely <ir partly. 
 
 To begin with the wheel and pallet action, the exam- 
 iner must ascertain whether the wheel is perfectly conceu ■ 
 trie and true in its division, for any want of accuracy iu 
 these points diminishes the soundness ot action and shortens 
 the mechanical effect, because the amount of drop and lock ■ 
 iug sufficient for a true and correct wheel would not offer 
 the necessary safety of action. 
 
 The cut of the wheel teeth is a matter of some conse- 
 quence, because the accuracy of division would be preju- 
 diced if the surfaces of the teeth, and especially the acting 
 sides of them, were not cut evenly and smoothly, present- 
 ing fiirrows which might, when coinciding with the point 
 of one tooth and not with that of the other, affect the ao 
 curacy of division. 
 
 The form of the teeth must be suited to the work to be 
 done, the foreface being sufficiently inclined (undercut) to 
 produce the draw without great friction or adhesion, and 
 the back not more divergent than required for the solidity 
 of the teeth. 
 
 The examiner must ascertain whether the wheel and 
 pallet are at the jn-oper height to suit each other, and that 
 the end shake of the escape pinion and pallet arbor are 
 equal, or nearly so, to avoid the risk of alteration in the 
 soundness of action arising from the acting of the escape 
 wheel at another part of the driving planes than the highest 
 point of their convexity. To this end it is also essential 
 that the wheel be pertectiy true on the flat. The locking 
 and driving planes of the pallet must be examined to see 
 that the surfaces are well polished and the edges carefully 
 rounded, and the drawing inclination in the right propor- 
 tion so as just to draw the pallet ia, without unnecessary 
 unlocking resistance. The pallet and its shape must also 
 have some attention, as it is desirable that it be as light as 
 possible consistent with solidity. Besides, it is necessary 
 that the part between the arms should allow free passage 
 to the wheel teeth without being filed out so much as to en- 
 danger breaking near the hole iu the center. 
 
 The examiner should then try the action of wheel and 
 pallet, to ascertain whether the pallet has been properly 
 [)itched. This is very often not the case, and if the pallet 
 be pitched too deep the effect will be an increase of the lock- 
 ing arc, and consequently an addition to the unlocking re- 
 sistance and to the arc of vibration required for the unlock- 
 ing. Besides, the drop will be unequally divided, too little 
 of it outside and too much inside the pallet, thereby mak- 
 ing the action unsafe. This is why a defect of this kind 
 cannot be removed by exchanging the escape wheel for a 
 smaller one, which would only amend the first deficiency 
 
 100 
 
without correctiug the inequality of drop. If, on the con- 
 trary, the pallet be pitched too shallow, the hicking will not 
 be safe, and there will be more drop outside and less inside 
 the pallet. Neither would it answer to exchange the wheel 
 for a larger one, for the reasons just mentioned. An altera- 
 tion of the diameter of the wheel and dressing down that 
 part of the pallet where the drop is not sufficient would re- 
 store the necessary extent of the locking arc and make the 
 drop on both sides the same, but as the drop on one side 
 was too much, of course there will afterwards be on both 
 sides an excess of drop, and consequently a loss of power. 
 Therefore, in all cases where the pallet is improperly pitched, 
 the best way will be to alter the pitch in the direction re- 
 quired. 
 
 In all cases where the locking is as it should be, but the 
 drop is not equal, the pallet must be considered defective, 
 and should be replaced, as should also a pallet with too 
 much drop. 
 
 The examiner must also see that the pallet arms are of 
 equal breadth, because if they are not, there will be un- 
 equal distribution of action between the two driving planes, 
 the one liftmg more and the other le.ss than it should. 
 
 With regard to the fork and roller action there are also 
 many essential points to be tested. In first place, the lever 
 must be solidly joined to the pallet in all escapements in 
 which lever and pallet are two separate pieces. Any shake 
 between these parts arising from the pallet arbor or the 
 steady pin not fitting tightly into the holes of either would 
 occasion a great insecurity of action and loss of power. A 
 defect of this kind in a completed watch is not easy to dis- 
 cover, though very easy to remove. 
 
 One of the most essential points is, to examine whether 
 the angles of movement produced by the wheel and pallet 
 action and the fork and roller action exactly correspond to 
 
 each other. It has Ijeeu siiown in a preceding cha2)ter that 
 these angles are quite independent of each other, and that 
 it would be even po.ssible, from a mechanical point of view, 
 to have an extremely large angle at the pailet and a very 
 small one at the roller, and vice versa. The lifting at the 
 roller is merely dependent on the respective lengths of the 
 two levers, or the radii, if the angle of pallet motion is 
 given. But when the lever and roller are ready made, the 
 angle of their lifting is in a certain proportion to the angle 
 of pallet movement, and the balance must be pitched ex- 
 actly so as to produce the angle of lifting for which the 
 proportions of the lever and roller are calculated. If, for 
 instance, the pallet be pitched at a greater distance from 
 the pallet than it should be, a part of the impulse given by 
 the lever is lost in useless drop. 
 
 .Another inconvenience arising from incorrect pitching 
 is that the ruljy pin, in both the unlocking and impelling 
 functions, fails to properly meet the acting fiices of the notch 
 in the fork. In such cases the unlocking and impulse 
 would take place at the edge of notch and horn, or at the 
 beginning of the horn, with decided mechanical disadvan- 
 tage. If, on the contrary, the balance be pitched too close, 
 it will necessitate setting the banking pins farther apart, to 
 allow the ruby pin to perform freely the increased angle of 
 lifting, and by this wider banking the pallet will be drawn 
 farther int(j the wheel than it should be, thus increasing the 
 unlocking resistance. At the same time, the unlocking 
 function of the ruby pin will be rendered more difficult by 
 its taking place at a greater distance from the line of cen- 
 ters, not to speak of the liability of the ruby pin touching 
 the bottom of the fork, which is not intended for this deeper 
 intersection. 
 
 The efl^ects of incorrect pitching of the balance, though 
 very injurious to the performance of the escapement, may 
 
 101 
 
easily be i-emoved by an alteration in the length of the two 
 parts; but as the lever is generally finished when the es- 
 capement passes examination, we will suppose that it must 
 not be touched, and that the above mentioned defects must 
 be removed by altering the place of the impulse pin. 
 
 In the first mentioned case, the impulse pin must be 
 brought a little nearer to the roller edge, to establish a 
 sound intersection and utilize the whole angle of pallet 
 motion. But it must be understood that this alteration,' 
 while it restores the correspondence of the lifting angles in 
 the two actions for the given center distance, produces a 
 diminution of the angle of lifting intended for the balance. 
 If, for instance, the 10° of pallet movement were intended 
 to produce a lifting of 40° at the roller, and the lever and 
 roller were made accordingly, but the balance had been 
 pitched at too great distance, the angle of lifting would by 
 the above alteration of the impulse pin be reduced to 36° 
 or 33° ; but the angles of the two actions would correspond 
 to each other, and the escapement, though not having the 
 lifting angle formerly intended, would still be correct in 
 itself. 
 
 In case the balance is pitched too close, the opposite pro- 
 ceeding will be advisable. The pin must be approached to 
 the center of the roller, by doing which the angle of lifting 
 at the latter is increased. If the circumstances admit, the 
 fork may also be shortened by taking away slightly all 
 along the inner faces of the horn, thereby reducing the act- 
 ing lever length a little, in order not to alter too much the 
 intended lifting angle. The acting parts of fork and roller 
 must be finished as smoothly as can be, as well as the outer 
 edge of the table roller and the inner side of the horns, and 
 the ruby pin must be fixed upright in the roller; any devi- 
 ation in whatever direction is defective. 
 
 Care must be taken that the pin is tightly fixed in its 
 
 hole, and that the notch of the fork be of the right size to 
 afford just the necessary freedom of action. 
 
 The horns should be examined to see that their length 
 is sufficient to complete the safety action during the period 
 of the guard pin passing the hollow of the roller. This is 
 tested by bringing the balance into the position in which 
 the guard pin begins to enter the passing hollow. In tiiis 
 position the end of the horn should [reach at least to the 
 middle of tiie breadth of the impulse pin. The horns of 
 the forks in escapements with the double roller must be 
 longer than those in the table roller escapement, because 
 the safety action performs a m ich larger arc of intersection. 
 The eccentricity of the horns may be supposed suflicient if 
 the balance stands with the guard pin just out of the hol- 
 low, and the end of the horn is at a very little di.stance 
 from the impulse pin when the guard pin is pressed lightly 
 against the roller edge. 
 
 A defect of very pernicious result to the rate of a lever 
 watch with the double roller in different positions is an ex- 
 cess of length of the impulse pin, when the en d of it comes 
 too near the index, and touches it in any position of the 
 watch. This is often caused by a difference of end shake 
 between the balance and pallet staff. These parts and the 
 escape wheel pinion should have nearly the same end shake. 
 
 The examiner must also provide carefully for the neces- 
 sary freedom of the guard pin at the edge of the detaining 
 roller and in the passing hollow. Defects in this particular 
 are very often caused by too much side shake of the bal- 
 ance pivots in their holes, and therefore the holes must also 
 be carefully examined to see that they are not too wide. 
 The guard pin or index must frequently be shortened a lit- 
 tle to obtain the necessary freedom of action. If, on the - 
 contrary, there is too much space between the guard pin 
 end and the roller edge so that the wheel tooth is not on 
 
 102 
 
the locking wheu the guard piu is lightly pressed towards 
 the roller ed^e, aud the impulse piu abuts against the end 
 of the horn, the safety action is defective, and must be cor- 
 rected by the insertion of a larger roller or a longer guard 
 piu. 
 
 It must be observed if the notch in the fork be deep 
 enough to let the impulse piu pass freely without getting too 
 near the bottom of the notch. 
 
 Care must be taken that the horns of the fork are uot 
 too long, so as to rest with their ends against the bahiuee 
 axis. 
 
 The pallet and lever must be examined as to their e(pii- 
 poise, aud if required, they must be carefully poised. A 
 defect in the equipoise of pallet and lever occasions serious 
 differences of rate in positions, especially in those watches 
 in which the lever is iu oblique or right augle to the verti- 
 cal line from the pendant through the middle of the watch. 
 
 Finally, the banking must be looked into. This should 
 not be wider thau just to allow sufficient freedom for the 
 movement of the acting parts. It is also very essential that 
 the banking pins be straight and vertical to the pliitc, for 
 if they are uot, and the pallet staff has a little too much 
 end shake, the width of the banking will be considerably 
 altered, whether the watch is lying on the back or on the 
 glass, especially when the banking pms are not standing 
 near the fork end of the lever. 
 
 Lever watches in which no faults can be found in the 
 escapement in the above mentioned points offer good prom- 
 ise of satisfactory performance. 
 
 CHAPTER XVI. 
 
 ON THE SYSTEM OF MEASUREMENT AND THE MEASURING 
 INSTRUMENTS. 
 
 It has already been mentioned, in Chapter II, that one 
 of the greatest difficulties for the practical horologist is, that 
 he is constantly uuder the necessity of executing the details 
 of his work on a very small scale. This difficulty is much 
 increased by the fact that the nature of the work andj the 
 purpose of the parts constructed demand the utmost precis- 
 ion in sizes and proportions. This technical impediment is 
 generally acknowledged, and has perhaps iu no small de- 
 gree contributed to raise the horological profi^ssion to the 
 particular esteem it enjoys in the eyes of the public. But 
 the difficulty of his occupation alone, in itself, does not en- 
 title the horologist to this esteem; for no man will be es- 
 timated simply for having undertaken a difficult task. The 
 great point consists in the skill aud energy he employs iu 
 overcoming the difficulties he encounters. If we apply this 
 truth to the before-mentioned practical difficulty of horo- 
 logical construction, we shall be compelled to )}Ut the ques- 
 tion to ourselves : " What have ive done to oven-ume in a sac- 
 cei<nful manner the difficulties arising from the very small 
 dimensions of our toorkf" 
 
 The answer to this question, if we are honest and can- 
 did, is hardly gratifying to the community of watchmakers 
 as a body, because it must be admitted that nothing has here- 
 
 103 
 
tofore been done to prepare a safe and rational footing for 
 every one in the trade. The surmounting of the difficulty 
 has been left to the personal efforts of individual workmen, 
 and. they have done as well as they could. It cannot be 
 denied that the skill and sagacity with which many prac- 
 tical men have succeeded in the solution of the problems in 
 their peculiar branch are extremely creditable and praise- 
 worthy. But such successful endeavors, creditable as they 
 may be to the genius of those practical men, are by no 
 means an argument for the sufficiency of the system of 
 working actually in use; on the contrary, they must be 
 looked upon as proof of what a considerable amount of in- 
 genuity and patience must have been required to obtain sat- 
 isfactory results with such very insufficient means. 
 
 The next consequence of this answer to the first question 
 must be the second question: What must be done in order 
 to introduce a better state of thinf/s^ 
 
 There is but one answer to this question : Introduce a 
 universal measuring standard into English watch and clock 
 manufacturing, fit for intercomparison, which is the first 
 condition of mutual understanding on questions of size. 
 The complete want of such a standard will never be satis- 
 fied by the multitude of arbitrary gauges and calipers pro- 
 duced by the immediate want of individuals, and applying 
 only to special purposes. It is certainly one of the most 
 important and creditable steps of the British Horological 
 Institute to have interposed its influence in this matter, and 
 raised its appeal for the promotion of this aim. When the 
 question is to decide which standard is to be chosen for uni- 
 versal introduction in the watch and clock manufacture, 
 there are many essential points to be taken into considera- 
 tion: 
 
 1. The system to be introduced must be applicable to cal- 
 culation. Calculation is the basis upon which eve"-y me- 
 
 chanician should work, and for the watchmaker its neces- 
 sity is of a double nature. It has before been obser > ed that 
 two courses may be taken. The one is the way of calcula- 
 ting the proportions, as indicated in Chapter XII ; but as 
 there are not many practical men able or willing to under- 
 take those calculating operations, the graphic system, con- 
 sisting in drawing the objects to be constructed on a large 
 scale, and in strict accordance with the proportions dictated 
 by mechanical rules, may be considered as an admissible 
 expedient. This- method of proceeding, however, requires 
 the subsequent reduction of the sizes in the drawing to the 
 working size, which is made by such simple calculations as 
 are familiar to a man of but little education or attainments. 
 Therefore, even the employment of the graphic method does 
 not exclude calculation. Any system of measurement inll 
 be unfit for calculation, unless its division is strictly decimal. 
 2. The unit of a standard for watcMvork should be of a 
 dimension corresponding to the dimensions of watchwork. 
 The inch, for example, even if divided decimally, is not an 
 appropriate unit for our purpose, because it is much too 
 large. Watchwork is not a kind of work to be measured 
 by inches. The diflerence between the largest and smallest 
 sizes of movements does not amount to an inch. Now, when 
 such extreme differences can only be expressed by fractions 
 of the unit, we must conclude that this unit is too large. 
 This deficiency of the inch system has been much felt in 
 the trade, and this impression manifests itself by a sizing of 
 the movements and other objects, which has no connection 
 with the inch, and is expressed in merely conventional num- 
 bers. When speaking of a movement of 14-size, nobody 
 can form by this number the slightest conception of the 
 diameter meant by it, and it may be considered rather 
 doubtiol whether watchmakers . agree perfectly between 
 tbeip;ri'7cs as to the ^z^^ct dimensions represented by those 
 
 104 
 
sizes. The Swiss manufacturers have taken a more positive 
 steji by indicating the sizes of their movements by French 
 lines, which are nearly equal to the intervals of the English 
 sizes. Every man, whether he be a watchmaker or not, is 
 enabled to verify the diameter of a watch movement which 
 is said to be one of 19 lignes. 
 
 After it has been proven by the above example that the 
 inch is too large a unit to measure movements with, it must 
 be much more improper for the very small interior parts of 
 the watch. The inch is sufficiently small for mill work and 
 steam engines, but it will never answer as a unit for watch- 
 work sizes. 
 
 3. The system chosen should offer the prospect of as uni- 
 versal adoption as possible. 
 
 It will require no proof that in our time, .when dis- 
 tances are reduced by steam and electricity and bars to 
 international communication are removed by treaties, when 
 the loj'al and liberal interchange of ideas and exjieriences 
 between cultivated nations become stronger every day, that 
 amidst these anxious exertions of the civilized world to pro- 
 mote association it would ill become a body of scientific 
 Englishmen to create a standard in the use of which they 
 would only have the Russians to keep them company, and 
 even those probably but for a short time. This'would in- 
 deed bo electing a kind of a Chinese wall around English 
 watch and cLck manufacture. 
 
 4. The system to he introdvced must not only be perfect 
 in theory, but it should be accompanied by the means of turn- 
 ing it into profit for any purpose in practical work. These 
 means are the measuring instruments. 
 
 5. The measuring instruments must be of such a nature 
 us not to depend upon the sight, which will not answer when 
 grsat accuracy is required, The object to be measured 
 
 must be seized between two parts of the instrument, and 
 the index must register the size. 
 
 It would, for example, be impossible to verify the outer 
 diameter of a pinion to the one-hundredth of an inch with 
 an instrument recommended not long ago in the Horolog- 
 ical Journal, under the head : "The Inch Decimally Di- 
 vided." It is a small rule, on the edges of which a length of 
 two inches is divided into 50 and 100 parts. Besides, a dif- 
 ference of one-hundredth of an English inch is a very essen- 
 tial amount for watchwurk. Let us, then, examine from 
 these points of view whether the metrical system, which is 
 the basis of all the tables and calculations in this treatise, 
 would be suitable for the purpose. 
 
 1. Its applicability for calculation cannot be doubted, 
 because its division is purely decimal, and, by being so, su- 
 perior to any other system. It would be a very tiresome 
 task to prepare or to use tables of proportions founded upon 
 a system of measurement not decimally divided. 
 
 2. Its proportions to the dimensions of watchwork re- 
 quires no demonstration. The millimeter is about one 
 twenty-fifth of the English inch and about two-fifths of the 
 French line, thus admitting of operation with integer num- 
 bers, while with a larger unit the same sizes must be ex- 
 pressed by fractions. 
 
 3. Regarding the prospect of its spreading over the civ- 
 ilized world, the metric system stands decidedly the best 
 chance, and the arguments which have been adduced in be- 
 half of the English inch from this point of view are, on close 
 investigation, of very little value. It has been said by Mr. 
 Rankine that as the English inch is used in Great Britain, 
 Russia and the United States, it is consequently used by 
 one-fourth the population of our planet, which could not be 
 said of any other standard measure. I think there never 
 was a more unlair statement than that. Mr. Rankin^ cal- 
 
 105 
 
culates the population of Great Britam at 174,000,000, of 
 course including India, Australia, etc. At least three-fourths 
 of this number of British subjects are quite ignorant of the 
 fact that there is such a thing as the English inch existing 
 in the world. The population of the Russian empire, too, 
 stated to be 64,000,000, must contain all the different tribes 
 of Eastern Europe and Asia, the Bashkirs, Tartars, Cal- 
 mucks, Kirgheese, etc., who according to all probability 
 measure merely by the spanning of their fingers or by the 
 lengtk of their own feet, instead of by the Englisli foot and 
 inch. Very likely the estimate of population in the United 
 States at 32,000,000 is also swollen to that amount by in- 
 cluding the backwoodsman and the red skin, as well as the 
 negroes. A reduction of the alleged total number of 270,- 
 000,000 to one-fourth of that amount will certainly not be 
 unfair when the question is to be decided how many people 
 are measuring by English inches. When we compare this 
 reduced number with the population of France, consisting 
 of about 40,000,000 of civilized people, to whom the measur- 
 ing standard is a fomiliar thing, augmented by the Spanish 
 and Italian nations, who very soon, we hope, will be joined 
 by the German nation in its totality, not to speak of Bel- 
 gium and other small states, it may be assumed that the ad- 
 herents of the English standard are considerably outnum- 
 bered. 
 
 4. The requirement of the new system being accompan- 
 ied by the necessary instruments for practically using it 
 may be answered in favor of the metrical system by the fol- 
 lowing description of the measuring instruments as they 
 have been used in the watch manufactories of Glashutte for 
 more than twenty years by a considerable number of work- 
 men and employers. 
 
 5. It will be seen by the subsequent description of the 
 measuring instruments that they are so constructed thr.t 
 
 the measuring is not intrusted to the touch or sight, but 
 that on the contrary it is effected by mechanical means, and 
 the result brought to view by an index. 
 
 The metric measuring system has been introduced in 
 Glashutte since the commencement of watch manufactur- 
 ing, in 1845, by the founder, Mr, A. Lange, who even at 
 this eaily period adopted this system in consideration of its 
 general superiority and special applicability to watch work. 
 The construction of the round micrometer is due to Mr. 
 Lange. 
 
 DiSCRIPTION OF THE MEASURING INSTRUMENTS USED AND 
 MANUFACTURED IN GLASHUTTE. 
 
 1. The meter measure is a kind of sliding rule with rec- 
 tangular arms, between which the objects to be measured 
 are inserted. The edge of the rule is divided by millime- 
 ters, and with the aid of a vernier the tenths of millimeters 
 can be read. 
 
 This instrument is very convenient for use as a rule and 
 angle, and to verify the parallelism of two planes by apply- 
 ing the measuring arms. The diameters of wheels, barrels, 
 jjlates, glasses, etc., may be measured with it in the readiest 
 and most accurate manner to one-tenth of the millimeter. 
 (See Diagram XIX, Figs. 1, 2 and 3.) 
 
 For the jsurpose of drawing or tracing calculated lengths 
 upon metal it is very convenient to have two points on it, 
 and the accurate adjustment is facilitated by an adjusting- 
 screw. (Figs. 4, 5 and 6, same Diagram.) 
 
 2. The tenth measure is illustrated by Figs. 7, 8 and 9, 
 and its construction being very simple, it will not require 
 explanation. It will be found very useful for measuring 
 the bottoms of barrels or sinks, for measuring objects on the 
 lathe, for testing the thickness of wire and plate, etc. The 
 
 106 
 
index shows the measured size in tenths of a millimeter. 
 A total opening of 10 m. is provided, and therefore the arc 
 is divided into 100 parts. 
 
 3. The micrometer is illustrated by Diagram XIX, 
 Figs. 10, 11, 12 and l.S. It shows a pair of small steel 
 tongs, b b, cue-half of which is fixed solidly upon the plate, 
 while the other half is fastened to the end of lever a, mov- 
 able cu two pivots around the point h. For multiplying 
 the movement of this lever, in order to make it more per- 
 ceptible to the eye, the lever a carries a rack c, fixed on it 
 concentric to the point h. This rack gears into a pinion (/, 
 on the arbor of which is mounted the small rack e; this lat- 
 ter drives the center pinion, which carries the hand on its 
 projecting pivot. These two elements give a total multipli- 
 cation of 180. The dial is divided into 200 parts, so that 
 half a revolution of the hand indicates the size of 1 milli- 
 meter. But there would be no reliability on the registra- 
 tions of the hand on the dial if the shake wiiich the centre 
 pinion must necessarily have for tree action were not re- 
 moved, because the hand would shake more than one de- 
 gree, and thus destroy all accuracy of measuring. There- 
 fore, the second small rack /, pitching also into the center 
 pinion, has a pendulum spring mounted upon it, with a 
 tendency to move the center pinion back. An angular lever, 
 g, projecting »t the outside of the case, serves to open the 
 tongs. The object to be measured must be inserted between 
 the opened tongs, and when' the lever g is let loose the tongs 
 will hold it, if it is not too heavy, by the tension of the pen- 
 dulum spring constantly acting in a direction so as to shut the 
 tongs The hand on the dial shows the distance at which 
 the two parts of the tongs are kept apart by the object be- 
 tween them, or, which is the same, the thickness of this ob- 
 ject. The total opening of the instrument is 6 to 8 m. The 
 hundredths of a millimeter indicated by this micrometer 
 
 are commonly called degress by our workmen, and this de- 
 gree is the unit for pivots and other small objects. 
 
 A measurement by hundredths of millimeters is a very 
 jQinute one, for the thinnest measurable object, the human 
 hair, for instance, measures 4 to (! degrees. The thinnest 
 paper shows a thickness of 3 degrees. 
 
 This instrument, as well as the tenth measure, has a 
 mathematical defect, because it measures the arc described 
 by the tongs, and not the chord of this arc, which latter is 
 the true thickness of the measured objects. This error in- 
 creases with the angle of opening. Of course it will be of 
 much more consequence in the tenth measure, but in this 
 instrument the error is compensated as much as possible by 
 dividing a straight line into 100 parts, and transferring this 
 division to the arc of the instrument. For the micrometer 
 this elimination of the error is impossil)le, but happily it is 
 not of so great consequence, because its angle of opening, 
 a c supposed to be = m., amounts only to (^°. The error 
 arising out of the dillerence between the arc and chord of 
 an angle of not more than 0°, is very trifling, and may 
 be ignored altogether, even where great accuracy is required. 
 
 The micrometer is commonly made with a base of wood, 
 to have it at convenient height from the surface of the 
 table. The nicety of measuring with the micrometer may 
 be tested by an experiment : Take a piece of brass wire 
 about 1 ui. thick, put one of its ends between the tongs of 
 the micrometer, support the other end, put a lamp under 
 the wire at about 1 to 1 J inches distant from the tongs, and 
 heat the wire to a low red heat. The expansion of the wire 
 will be indicated by an evident movement of the hand, and 
 the subsequent contraction through the cooling of the wire 
 will cause the reverse of this movement. 
 
 These three instruments, the meter measure, the tenth 
 •iieasure and the micrometer, are quite sufficient for all prac- 
 
 107 
 
tical wants of watch and clock making. Their application 
 for the graphic method of working is the following: Sap- 
 pose that a circular pallet is to be made to a ratchet wheel, 
 the real diameter of which is = 8 m. 
 
 The diameter of the wheel, as drawn in Diagram 2, is 
 200 ni., or 25 times the size of the wheel to which the pallet 
 is to be made. Therefore all the sizes of the pallet in the 
 drawing must be measured with the meter measure and 
 divided by 25 or multiplied by 0.04, to give the working 
 sizes. The inner circle of pallet, for example, has on the 
 
 drawing a diameter of 98 ni. The disc of this circle (Chap- 
 no 
 ter XIII; must therefore be made i? =: ".92 m. or 392 
 
 degrees of the micrometer, etc. This is also the size indi- 
 cated by Table I for the diameter of inner pallet circle 
 when the real diameter of the wheel is = 8 ni. 
 
 It is frequently the case that micrometers are ordered 
 for special purposes, such as for iron works, to verify the 
 thickness of wires, for pianoforte makers fur the same pur- 
 pose, for paper mills to guage the quantity of material re- 
 quired for a certain sheet of paper, for spinning establish- 
 ments to ascertain the thickness of the yarns, etc. I have 
 often found that micrometers employed for these technical 
 purposes do not always meet with the careful treatment 
 wa'i,chmakers are accustomed to accord their tools, and some- 
 times I receive the instruments back for repair in very bad 
 condition. This prompted me to devise a measuring instru- 
 ment which would stand rough treatment without getting 
 out of order, yet possessing the same accuracy as the mi- 
 crometer. It occurred to me that the multiplication effected 
 in the micrometer by two depths might be attained with 
 one depth only by employing longer levers. Diagram XX, 
 Figs. 1, 2 and 3, show the simplified micrometer. One of 
 the two arms, a a, is fastened to the plate and carries the 
 
 foot c, serving as the center of motion, and on its other ex- 
 tremity the fixed half of the tongs. The other arm, b b, 
 turns round its axis in r. The foot is hollowed out to re- 
 ceive the arbor, and the lower pivot moves in a hole near 
 the lower end of the foot, while the upper pivot is fitted into 
 a cock screwed upon the upper surfiice of the fixed arm, a a. 
 This arrangement allows a greater length of the axis, and 
 consequently a greater soundness of movement. The mov- 
 able arm h h carries on the extremity of its long lever a 
 rack, d, concentric to the point c, and pitching into a pin- 
 ion,/, of fifteen leaves in the center, the projecting pivot of 
 which carries the hand. The shake of the pinion and hand 
 is eliminated by a secondary rack, identical to the other, 
 and fixed upon it with two screws, leaving it a small shake 
 in the direction in which the rack is moving. A small 
 spring is constantly pressing against the secondary rack, so 
 that its teeth always stand a trifle beside those of the fixed 
 rack, thus exerting an elastic pressure on the pinion leaves, 
 and removing the shake without prejudice to the freedom 
 of movement. The extremity of the short lever of the mov- 
 able arm 6 h carries the other half of the tongs, correspond- 
 ing to that on the arm a a. A long flat spring, g, with a 
 tendency to shut the tongs, completes the arrangement. 
 
 This simplified micrometer has given very satisfactory 
 results. The dial and its division is entirely the same. Its 
 parts are strong enough, and so very simjjle that it does not 
 require the care of a watchmaker to keej) it in acting order. 
 The greater simplicity of construction admits also its sell- 
 ing at a cheaper price than the round micrometer. 
 
 There may be some objection to a micrometer of this 
 kind, in that the unavoidable error formerly alluded to 
 arising from the diflTerence between arc and chord is much 
 more marked, because the shortness of the lever arms car- 
 rying the tongs requires a larger angle of opening. In 
 
 108 
 
fact, this angle Is =; 15° for an opeuing of 6 m. Never- 
 theless, this instrument will be found to answer very well, 
 as many comparative experiments have convinced me that 
 in point of accurate measuring they are in no way inferior 
 to the round micrometer. I attribute this favorable result 
 to the omission of one depth, for pinions and wheels, if even 
 made with the greatest care, will always bear some trifling 
 uuequalities which, by a multiplication of more than 100, 
 become considerable quantities. 
 
 After having tested this principle I received orders for 
 instruments for special purposes, one from a manufacturer 
 of gold and silver lace, fur measuring the finest threads, 
 and the other fur a scientific amateur, both requiring a 
 direct measurement of 1-500 m. I did not think it advis- 
 able to entrust a measurement of such subtlety to the enor- 
 mous multiplication by two depths, but constructed the in- 
 strument in the same way as the preceding. The arms are 
 luuger and the dial is larger, and divided into 500 degrees. 
 'One revolution of the hand is =r 1 m. (Diagram XX, 
 Figs. 4, 5 and tl.) Since that time I have manufactured 
 many such instruments for special purposes, and, as far as 
 I know, they give satisfaction. 
 
 This measuring system may prove very useful for the 
 English watch and clock manufacture if universally intro- 
 duced. 
 
 Finally, I thought it would be convenient to the read- 
 ers of this treatise to have joined to it tables of reduction, 
 in order to compare easily the sizes in millimeters with those 
 expressed in English inches and French lines. 
 
 109 
 
 
 
 Table X. 
 
 
 
 Milli- 
 
 
 
 Milli- 
 
 
 
 meter 
 
 EDgliah inch. 
 
 French line. 
 
 meter 
 
 Engliah inch. 
 
 French line. 
 
 (I.Ol 
 
 0.0003937 
 
 0.004433 
 
 18 
 
 0.70866 
 
 7.9794 
 
 0.02 
 
 0.0007874 
 
 0.008866 
 
 19 
 
 0.74803 
 
 8.4227 
 
 0.03 
 
 0.0011811 
 
 0.013299 
 
 
 
 
 0.04 
 0.05 
 
 0.0015748 
 0.0019685 
 
 0.017732 
 0.022165 
 
 20 
 21 
 
 0.78740 
 0.82677 
 
 8.8660 
 9.3093 
 
 0.06 
 
 0.0023622 
 
 0.026598 
 
 22 
 
 0.86614 
 
 9.7526 
 
 0.07 
 
 0.0026559 
 
 0.031031 
 
 23 
 
 0.90551 
 
 10.1959 
 
 O.OS 
 
 0.0031496 
 
 0.035464 
 
 24 
 
 0.94488 
 
 10.6392 
 
 o.oa 
 
 0.0035433 
 
 0.039897 
 
 25 
 
 0.98425 
 
 11.0825 
 
 
 
 
 26 
 
 1.02362 
 
 11.5258 
 
 0.1 
 
 0.003937 
 
 0.04433 
 
 27 
 
 1.06299 
 
 11.9691 
 
 0.2 
 
 0.007874 
 
 0.08866 
 
 28 
 
 1.10236 
 
 12.4124 
 
 0.3 
 
 0.011811 
 
 0.13299 
 
 29 
 
 1.14173 
 
 12.8557 
 
 0.4 
 
 0.015748 
 
 0.17732 
 
 
 
 
 0.5 
 
 0.019685 
 
 0.22165 
 
 
 
 
 O.G 
 
 0.023622 
 
 0.26598 
 
 30 
 
 1.18110 
 
 13.2990 
 
 0.7 
 
 0.026559 
 
 0.31031 
 
 31 
 
 1.22047 
 
 13.7423 
 
 0.8 
 0.9 
 
 0.031496 
 0.035433 
 
 0.35464 
 
 0.39897 
 
 32 
 33 
 
 1.25984 
 1.29921 
 
 14.1856 
 14.6289 
 
 
 
 
 34 
 
 1.33858 
 
 15.0722 
 
 1 
 
 2 
 
 0.03937 
 0.07874 
 
 0.4433 
 
 0.8866 
 
 35 
 36 
 
 1.37795 
 1.41732 
 
 15.5155 
 
 15.9588 
 
 3 
 
 0.11811 
 
 1.3299 
 
 37 
 
 1.45669 
 
 16.4021 
 
 4 
 
 0.15748 
 
 1.7732 
 
 38 
 
 1.49606 
 
 16.8454 
 
 5 
 
 0.19685 
 
 2.2165 
 
 39 
 
 1.53543 
 
 17.2887 
 
 C 
 
 0.23022 
 
 2.6598 
 
 
 
 
 7 
 
 0.26559 
 
 3.1031 
 
 40 
 
 1.57480 
 
 17.7320 
 
 8 
 
 0.31496 
 
 3.5464 
 
 41 
 
 1.61417 
 
 18.1753 
 
 9 
 
 0.35433 
 
 3.9897 
 
 42 
 
 1.65354 
 
 18.6186 
 
 
 
 
 43 
 
 1.69291 
 
 19.0619 
 
 10 
 
 0.39370 
 
 4.4330 
 
 44 
 
 1.73228 
 
 19.5052 
 
 n 
 
 0.43307 
 
 4.8763 
 
 45 
 
 1.77165 
 
 19.9485 
 
 12 
 
 0.47244 
 
 5.3196 
 
 46 
 
 1.81102 
 
 20.3918 
 
 13 
 
 0.51181 
 
 5.7629 
 
 47 
 
 1.85039 
 
 20.8351 
 
 14 
 
 0.55118 
 
 6.2062 
 
 48 
 
 1.88976 
 
 21.2784 
 
 15 
 
 0.59055 
 
 6.6495 
 
 49 
 
 1.92913 
 
 21.7217 
 
 16 
 
 0.62992 
 
 7.0928 
 
 
 
 
 17 
 
 0.66929 
 
 7.5361 
 
 50 
 
 1.96850 
 
 22.1650 
 

 
 Table XI. 
 
 
 
 English 
 Inch. 
 
 MiUtmeter. 
 
 Fienob line. 
 
 English 
 Inch. 
 
 Millimeter. 
 
 French line. 
 
 0.001 
 
 0.025399 
 
 0.011260 
 
 0.1 
 
 2.5399 
 
 1.12595 
 
 0.002 
 
 0.050798 
 
 0.022519 
 
 0.2 
 
 5.0798 
 
 2.25190 
 
 0.003 
 
 0.076197 
 
 0.033779 
 
 0.3 
 
 7.6197 
 
 3.37785 
 
 0.004 
 
 0.101596 
 
 0.045038 
 
 0.4 
 
 10.1596 
 
 4.50380 
 
 0.005 
 
 0.126995 
 
 0.056298 
 
 0.5 
 
 12.6995 
 
 5.62975 
 
 0.006 
 
 0.152394 
 
 0.067557 
 
 0.6 
 
 15.2394 
 
 6.75570 
 
 0.007 
 
 0.177793 
 
 0.078817 
 
 0.7 
 
 17.7793 
 
 7.88165 
 
 0.008 
 
 0.203192 
 
 0.090076 
 
 0.8 
 
 20.3192 
 
 9.00760 
 
 0,009 
 
 0.228591 
 
 0.101336 
 
 0.9 
 
 22.8591 
 
 10.13355 
 
 0.01 
 
 0.25399 
 
 0.112595 
 
 1.0 
 
 25.3990 
 
 11.25945 
 
 0.02 
 
 0.50798 
 
 0.225190 
 
 1.1 
 
 27.9389 
 
 12.38545 
 
 0.03 
 
 0.76197 
 
 0.337785 
 
 1.2 
 
 30.4788 
 
 13.51140 
 
 0.04 
 
 1.01596 
 
 0.450380 
 
 1.3 
 
 33.0187 
 
 14.63735 
 
 0.05 
 
 1.26995 
 
 0.562975 
 
 1.4 
 
 35.5586 
 
 15.70330 
 
 0.06 
 
 1.52394 
 
 0.675570 
 
 1.5 
 
 38.0985 
 
 16.88925 
 
 0.07 
 
 1.77793 
 
 0.788165 
 
 1.6 
 
 40.6384 
 
 18.01510 
 
 0.08 
 
 2.03192 
 
 0.900760 
 
 1.7 
 
 43.1783 
 
 19.14105 
 
 0.09 
 
 2.28591 
 
 1.013355 
 
 1.8 
 
 45.7182 
 
 20.26700 
 
 
 
 
 1.9 
 
 48.2581 
 
 21.29295 
 
 
 
 
 2.0 
 
 50.7980 
 
 22.51890 
 
 
 
 Table XIL 
 
 
 
 French 
 
 
 
 French 
 
 
 
 line. 
 
 English inch. 
 
 Millimeter. 
 
 line. 
 
 English fnoh. 
 
 Millimeter. 
 
 0.01 
 
 0.000888 
 
 0.0225583 
 
 0.1 
 
 0.008881 
 
 0.225583 
 
 0.02 
 
 0.001776 
 
 0.0451166 
 
 0.2 
 
 0.017763 
 
 0.451166 
 
 0.03 
 
 0.002664 
 
 0.0676749 
 
 0.3 
 
 0.026644 
 
 0,676749 
 
 0.04 
 
 0.003552 
 
 0.0902332 
 
 0.4 
 
 0.035526 
 
 0.902332 
 
 0.05 
 
 0.004440 
 
 0.1127915 
 
 0.5 
 
 0.044407 
 
 1.127915 
 
 0.06 
 
 0.005328 
 
 0.1353498 
 
 0.6 
 
 0.053288 
 
 1.353498 
 
 0.07 
 
 0.006217 
 
 0.1579081 
 
 0.7 
 
 0.062169 
 
 1.579081 
 
 0.08 
 
 0.007105 
 
 0.1804664 
 
 0.8 
 
 0.071051 
 
 1.804664 
 
 0.09 
 
 0.007993 
 
 0.2030247 
 
 0.9 
 
 0.079933 
 
 2.030247 
 
 1.0 
 
 0.088814 
 
 2.25583 
 
 11.0 
 
 0.97696 
 
 24.81413 
 
 2.0 
 
 0.177628 
 
 4.51166 
 
 12.0 
 
 1.06577 
 
 27.06996 
 
 3.0 
 
 0.266442 
 
 6.76749 
 
 13.0 
 
 1.15458 
 
 29.32579 
 
 4.0 
 
 0.355256 
 
 9.02332 
 
 14.0 
 
 1.24340 
 
 31.58162 
 
 5.0 
 
 0.444070 
 
 11.27915 
 
 15.0 
 
 1.33221 
 
 33.83745 
 
 6.0 
 
 0.532884 
 
 13.53498 
 
 16.0 
 
 1.42103 
 
 36.09328 
 
 7.0 
 
 0.621698 
 
 15.79081 
 
 17.0 
 
 1.50984 
 
 38.34911 
 
 8.0 
 
 0.710512 
 
 18.04664 
 
 18.0 
 
 1.59865 
 
 40.60494 
 
 y.o 
 
 0.799326 
 
 20.3024" 
 
 19.0 
 
 1.68747 
 
 42.86077 
 
 10.0 
 
 0.88814 
 
 22.55830 1 
 
 20.0 
 
 1.77628 
 
 45.11660 
 
 110 
 
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