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+The Project Gutenberg eBook, Watch and Clock Escapements, by Anonymous
+
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+
+
+
+Title: Watch and Clock Escapements
+       A Complete Study in Theory and Practice of the Lever, Cylinder and Chronometer Escapements, Together with a Brief Account of the Origin and Evolution of the Escapement in Horology
+
+
+Author: Anonymous
+
+
+
+Release Date: November 6, 2005  [eBook #17021]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+
+***START OF THE PROJECT GUTENBERG EBOOK WATCH AND CLOCK ESCAPEMENTS***
+
+
+E-text prepared by Robert Cicconetti, Janet Blenkinship, and the Project
+Gutenberg Online Distributed Proofreading Team (https://www.pgdp.net/).
+Book provided by the New York University Library.
+
+
+
+Note: Project Gutenberg also has an HTML version of this file which
+      includes the original more than 180 illustrations.
+      See 17021-h.htm or 17021-h.zip:
+      (https://www.gutenberg.org/dirs/1/7/0/2/17021/17021-h/17021-h.htm)
+      or
+      (https://www.gutenberg.org/dirs/1/7/0/2/17021/17021-h.zip)
+
+
+
+
+
+WATCH AND CLOCK ESCAPEMENTS
+
+A Complete Study in Theory and Practice of the Lever, Cylinder and
+Chronometer Escapements, Together with a Brief Account of the Origin
+and Evolution of the Escapement in Horology
+
+Compiled from the well-known Escapement Serials
+published in The Keystone
+
+Nearly Two Hundred Original Illustrations
+
+
+
+
+
+
+
+Published by
+The Keystone
+The Organ of the Jewelry and Optical Trades
+19th & Brown Sts., Philadelphia, U.S.A.
+
+1904
+
+All Rights Reserved
+Copyright, 1904, By B. Thorpe,
+Publisher of the Keystone.
+
+
+
+
+PREFACE
+
+
+Especially notable among the achievements of The Keystone in the field
+of horology were the three serials devoted to the lever, cylinder and
+chronometer escapements. So highly valued were these serials when
+published that on the completion of each we were importuned to republish
+it in book form, but we deemed it advisable to postpone such publication
+until the completion of all three, in order that the volume should be a
+complete treatise on the several escapements in use in horology. The
+recent completion of the third serial gave us the opportunity to
+republish in book form, and the present volume is the result. We present
+it to the trade and students of horology happy in the knowledge that its
+contents have already received their approval. An interesting addition
+to the book is the illustrated story of the escapements, from the first
+crude conceptions to their present perfection.
+
+
+
+
+  CONTENTS
+
+
+  CHAPTER I.
+
+  THE DETACHED LEVER ESCAPEMENT      9
+
+
+  CHAPTER II.
+
+  THE CYLINDER ESCAPEMENT          111
+
+
+  CHAPTER III.
+
+  THE CHRONOMETER ESCAPEMENT       131
+
+
+  CHAPTER IV.
+
+  HISTORY OF ESCAPEMENTS           153
+
+
+  CHAPTER V.
+
+  PUTTING IN A NEW CYLINDER        169
+
+
+  INDEX                            177
+
+
+
+
+
+
+WATCH AND CLOCK ESCAPEMENTS
+
+
+
+
+CHAPTER I.
+
+THE DETACHED LEVER ESCAPEMENT.
+
+
+In this treatise we do not propose to go into the history of this
+escapement and give a long dissertation on its origin and evolution, but
+shall confine ourselves strictly to the designing and construction as
+employed in our best watches. By designing, we mean giving full
+instructions for drawing an escapement of this kind to the best
+proportions. The workman will need but few drawing instruments, and a
+drawing-board about 15" by 18" will be quite large enough. The necessary
+drawing-instruments are a T-square with 15" blade; a scale of inches
+divided into decimal parts; two pairs dividers with pen and pencil
+points--one pair of these dividers to be 5" and the other 6"; one ruling
+pen. Other instruments can be added as the workman finds he needs them.
+Those enumerated above, however, will be all that are absolutely
+necessary.
+
+[Illustration: Fig. 1]
+
+We shall, in addition, need an arc of degrees, which we can best make
+for ourselves. To construct one, we procure a piece of No. 24 brass,
+about 5½" long by 1¼" wide. We show such a piece of brass at _A_,
+Fig. 1. On this piece of brass we sweep two arcs with a pair of dividers
+set at precisely 5", as shown (reduced) at _a a_ and _b b_. On these
+arcs we set off the space held in our dividers--that is 5"--as shown at
+the short radial lines at each end of the two arcs. Now it is a
+well-known fact that the space embraced by our dividers contains exactly
+sixty degrees of the arcs _a a_ and _b b_, or one-sixth of the entire
+circle; consequently, we divide the arcs _a a_ and _b b_ into sixty
+equal parts, to represent degrees, and at one end of these arcs we
+halve five spaces so we can get at half degrees.
+
+[Illustration: Fig. 2]
+
+Before we take up the details of drawing an escapement we will say a few
+words about "degrees," as this seems to be something difficult to
+understand by most pupils in horology when learning to draw parts of
+watches to scale. At Fig. 2 we show several short arcs of fifteen
+degrees, all having the common center _g_. Most learners seem to have an
+idea that a degree must be a specific space, like an inch or a foot. Now
+the first thing in learning to draw an escapement is to fix in our minds
+the fact that the extent of a degree depends entirely on the radius of
+the arc we employ. To aid in this explanation we refer to Fig. 2. Here
+the arcs _c_, _d_, _e_ and _f_ are all fifteen degrees, although the
+linear extent of the degree on the arc _c_ is twice that of the degree
+on the arc _f_. When we speak of a degree in connection with a circle we
+mean the one-three-hundred-and-sixtieth part of the periphery of such a
+circle. In dividing the arcs _a a_ and _b b_ we first divide them into
+six spaces, as shown, and each of these spaces into ten minor spaces, as
+is also shown. We halve five of the degree spaces, as shown at _h_. We
+should be very careful about making the degree arcs shown at Fig. 1, as
+the accuracy of our drawings depends a great deal on the perfection of
+the division on the scale _A_. In connection with such a fixed scale of
+degrees as is shown at Fig. 1, a pair of small dividers, constantly set
+to a degree space, is very convenient.
+
+
+MAKING A PAIR OF DIVIDERS.
+
+[Illustration: Fig. 3]
+
+To make such a pair of small dividers, take a piece of hard sheet brass
+about 1/20" thick, ¼" wide, 1½" long, and shape it as shown at Fig.
+3. It should be explained, the part cut from the sheet brass is shown
+below the dotted line _k_, the portion above (_C_) being a round handle
+turned from hard wood or ivory. The slot _l_ is sawn in, and two holes
+drilled in the end to insert the needle points _i i_. In making the slot
+_l_ we arrange to have the needle points come a little too close
+together to agree with the degree spaces on the arcs _a a_ and _b b_. We
+then put the small screw _j_ through one of the legs _D''_, and by
+turning _j_, set the needle points _i i_ to exactly agree with the
+degree spaces. As soon as the points _i i_ are set correctly, _j_ should
+be soft soldered fast.
+
+The degree spaces on _A_ are set off with these dividers and the spaces
+on _A_ very carefully marked. The upper and outer arc _a a_ should have
+the spaces cut with a graver line, while the lower one, _b b_ is best
+permanently marked with a carefully-made prick punch. After the arc _a a_
+is divided, the brass plate _A_ is cut back to this arc so the
+divisions we have just made are on the edge. The object of having two
+arcs on the plate _A_ is, if we desire to get at the number of degrees
+contained in any arc of a 5" radius we lay the scale _A_ so the edge
+agrees with the arc _a a_, and read off the number of degrees from the
+scale. In setting dividers we employ the dotted spaces on the arc _b b_.
+
+
+DELINEATING AN ESCAPE WHEEL.
+
+[Illustration: Fig. 4]
+
+We will now proceed to delineate an escape wheel for a detached lever.
+We place a piece of good drawing-paper on our drawing-board and provide
+ourselves with a very hard (HHH) drawing-pencil and a bottle of liquid
+India ink. After placing our paper on the board, we draw, with the aid
+of our T-square, a line through the center of the paper, as shown at
+_m m_, Fig. 4. At 5½" from the lower margin of the paper we establish
+the point _p_ and sweep the circle _n n_ with a radius of 5". We have
+said nothing about stretching our paper on the drawing-board; still,
+carefully-stretched paper is an important part of nice and correct
+drawing. We shall subsequently give directions for properly stretching
+paper, but for the present we will suppose the paper we are using is
+nicely tacked to the face of the drawing-board with the smallest tacks
+we can procure. The paper should not come quite to the edge of the
+drawing-board, so as to interfere with the head of the T-square. We are
+now ready to commence delineating our escape wheel and a set of pallets
+to match.
+
+The simplest form of the detached lever escapement in use is the one
+known as the "ratchet-tooth lever escapement," and generally found in
+English lever watches. This form of escapement gives excellent results
+when well made; and we can only account for it not being in more general
+use from the fact that the escape-wheel teeth are not so strong and
+capable of resisting careless usage as the club-tooth escape wheel.
+
+It will be our aim to convey broad ideas and inculcate general
+principles, rather than to give specific instructions for doing "one
+thing one way." The ratchet-tooth lever escapements of later dates
+have almost invariably been constructed on the ten-degree
+lever-and-pallet-action plan; that is, the fork and pallets were
+intended to act through this arc. Some of the other specimens of this
+escapement have larger arcs--some as high as twelve degrees.
+
+
+PALLET-AND-FORK ACTION.
+
+[Illustration: Fig. 5]
+
+We illustrate at Fig. 5 what we mean by ten degrees of pallet-and-fork
+action. If we draw a line through the center of the pallet staff, and
+also through the center of the fork slot, as shown at _a b_, Fig. 5, and
+allow the fork to vibrate five degrees each side of said lines _a b_, to
+the lines _a c_ and _a c'_, the fork has what we term ten-degree pallet
+action. If the fork and pallets vibrate six degrees on each side of the
+line _a b_--that is, to the lines _a d_ and _a d'_--we have twelve
+degrees pallet action. If we cut the arc down so the oscillation is only
+four and one-quarter degrees on each side of _a b_, as indicated by the
+lines _a s_ and _a s'_, we have a pallet-and-fork action of eight and
+one-half degrees; which, by the way, is a very desirable arc for a
+carefully-constructed escapement.
+
+The controlling idea which would seem to rule in constructing a detached
+lever escapement, would be to make it so the balance is free of the
+fork; that is, detached, during as much of the arc of the vibration of
+the balance as possible, and yet have the action thoroughly sound and
+secure. Where a ratchet-tooth escapement is thoroughly well-made of
+eight and one-half degrees of pallet-and-fork action, ten and one-half
+degrees of escape-wheel action can be utilized, as will be explained
+later on.
+
+We will now resume the drawing of our escape wheel, as illustrated at
+Fig. 4. In the drawing at Fig. 6 we show the circle _n n_, which
+represents the periphery of our escape wheel; and in the drawing we are
+supposed to be drawing it ten inches in diameter.
+
+We produce the vertical line _m_ passing through the center _p_ of the
+circle _n_. From the intersection of the circle _n_ with the line _m_
+at _i_ we lay off thirty degrees on each side, and establish the points
+_e f_; and from the center _p_, through these points, draw the radial
+lines _p e'_ and _p f'_. The points _f e_, Fig. 6, are, of course, just
+sixty degrees apart and represent the extent of two and one-half teeth
+of the escape wheel. There are two systems on which pallets for lever
+escapements are made, viz., equidistant lockings and circular pallets.
+The advantages claimed for each system will be discussed subsequently.
+For the first and present illustration we will assume we are to employ
+circular pallets and one of the teeth of the escape wheel resting on the
+pallet at the point _f_; and the escape wheel turning in the direction
+of the arrow _j_. If we imagine a tooth as indicated at the dotted
+outline at _D_, Fig. 6, pressing against a surface which coincides with
+the radial line _p f_, the action would be in the direction of the line
+_f h_ and at right angles to _p f_. If we reason on the action of the
+tooth _D_, as it presses against a pallet placed at _f_, we see the
+action is neutral.
+
+[Illustration: Fig. 6]
+
+
+ESTABLISHING THE CENTER OF PALLET STAFF.
+
+[Illustration: Fig. 7]
+
+With a fifteen-tooth escape wheel each tooth occupies twenty-four
+degrees, and from the point _f_ to _e_ would be two and one-half
+tooth-spaces. We show the dotted points of four teeth at _D D' D''D'''_.
+To establish the center of the pallet staff we draw a line at
+right angles to the line _p e'_ from the point _e_ so it intersects the
+line _f h_ at _k_. For drawing a line at right angles to another line,
+as we have just done, a hard-rubber triangle, shaped as shown at _C_,
+Fig. 7, can be employed. To use such a triangle, we place it so the
+right, or ninety-degrees angle, rests at _e_, as shown at the dotted
+triangle _C_, Fig. 6, and the long side coincides with the radial line
+_p e'_. If the short side of the hard-rubber triangle is too short, as
+indicated, we place a short ruler so it rests against the edge, as shown
+at the dotted line _g e_, Fig. 7, and while holding it securely down on
+the drawing we remove the triangle, and with a fine-pointed pencil draw
+the line _e g_, Fig. 6, by the short rule. Let us imagine a flat surface
+placed at _e_ so its face was at right angles to the line _g e_, which
+would arrest the tooth _D''_ after the tooth _D_ resting on _f_ had been
+released and passed through an arc of twelve degrees. A tooth resting on
+a flat surface, as imagined above, would also rest dead. As stated
+previously, the pallets we are considering have equidistant locking
+faces and correspond to the arc _l l_, Fig. 6.
+
+In order to realize any power from our escape-wheel tooth, we must
+provide an impulse face to the pallets faced at _f e_; and the problem
+before us is to delineate these pallets so that the lever will be
+propelled through an arc of eight and one-half degrees, while the escape
+wheel is moving through an arc of ten and one-half degrees. We make the
+arc of fork action eight and one-half degrees for two reasons--(1)
+because most text-books have selected ten degrees of fork-and-pallet
+action; (2) because most of the finer lever escapements of recent
+construction have a lever action of less than ten degrees.
+
+
+LAYING OUT ESCAPE-WHEEL TEETH.
+
+To "lay out" or delineate our escape-wheel teeth, we continue our
+drawing shown at Fig. 6, and reproduce this cut very nearly at Fig. 8.
+With our dividers set at five inches, we sweep the short arc _a a'_ from
+_f_ as a center. It is to be borne in mind that at the point _f_ is
+located the extreme point of an escape-wheel tooth. On the arc _a a_ we
+lay off from _p_ twenty-four degrees, and establish the point _b_; at
+twelve degrees beyond _b_ we establish the point _c_. From _f_ we draw
+the lines _f b_ and _f c_; these lines establishing the form and
+thickness of the tooth _D_. To get the length of the tooth, we take in
+our dividers one-half a tooth space, and on the radial line _p f_
+establish the point _d_ and draw circle _d' d'_.
+
+To facilitate the drawing of the other teeth, we draw the circles _d' c'_,
+to which the lines _f b_ and _f c_ are tangent, as shown. We divide
+the circle _n n_, representing the periphery of our escape wheel, into
+fifteen spaces, to represent teeth, commencing at _f_ and continued as
+shown at _o o_ until the entire wheel is divided. We only show four
+teeth complete, but the same methods as produced these will produce them
+all. To briefly recapitulate the instructions for drawing the teeth for
+the ratchet-tooth lever escapement: We draw the face of the teeth at an
+angle of twenty-four degrees to a radial line; the back of the tooth at
+an angle of thirty-six degrees to the same radial line; and make teeth
+half a tooth-space deep or long.
+
+[Illustration: Fig. 8]
+
+We now come to the consideration of the pallets and how to delineate
+them. To this we shall add a careful analysis of their action. Let us,
+before proceeding further, "think a little" over some of the factors
+involved. To aid in this thinking or reasoning on the matter, let us
+draw the heavy arc _l_ extending from a little inside of the circle _n_
+at _f_ to the circle _n_ at _e_. If now we imagine our escape wheel to
+be pressed forward in the direction of the arrow _j_, the tooth _D_
+would press on the arc _l_ and be held. If, however, we should revolve
+the arc _l_ on the center _k_ in the direction of the arrow _i_, the
+tooth _D_ would _escape_ from the edge of _l_ and the tooth _D''_ would
+pass through an arc (reckoning from the center _p_) of twelve degrees,
+and be arrested by the inside of the arc _l_ at _e_. If we now should
+reverse the motion and turn the arc _l_ backward, the tooth at _e_
+would, in turn, be released and the tooth following after _D_ (but not
+shown) would engage _l_ at _f_. By supplying motive to revolve the
+escape wheel (_E_) represented by the circle _n_, and causing the arc
+_l_ to oscillate back and forth in exact intervals of time, we should
+have, in effect, a perfect escapement. To accomplish automatically such
+oscillations is the problem we have now on hand.
+
+
+HOW MOTION IS OBTAINED.
+
+In clocks, the back-and-forth movement, or oscillating motion, is
+obtained by employing a pendulum; in a movable timepiece we make use of
+an equally-poised wheel of some weight on a pivoted axle, which device
+we term a balance; the vibrations or oscillations being obtained by
+applying a coiled spring, which was first called a "pendulum spring,"
+then a "balance spring," and finally, from its diminutive size and coil
+form, a "hairspring." We are all aware that for the motive power for
+keeping up the oscillations of the escaping circle _l_ we must contrive
+to employ power derived from the teeth _D_ of the escape wheel. About
+the most available means of conveying power from the escape wheel to the
+oscillating arc _l_ is to provide the lip of said arc with an inclined
+plane, along which the tooth which is disengaged from _l_ at _f_ to
+slide and move said arc _l_ through--in the present instance an arc of
+eight and one-half degrees, during the time the tooth _D_ is passing
+through ten and one-half degrees. This angular motion of the arc _l_ is
+represented by the radial lines _k f'_ and _k r_, Fig. 8. We desire to
+impress on the reader's mind the idea that each of these angular motions
+is not only required to be made, but the motion of one mobile must
+convey power to another mobile.
+
+In this case the power conveyed from the mainspring to the escape wheel
+is to be conveyed to the lever, and by the lever transmitted to the
+balance. We know it is the usual plan adopted by text-books to lay down
+a certain formula for drawing an escapement, leaving the pupil to work
+and reason out the principles involved in the action. In the plan we
+have adopted we propose to induct the reader into the why and how, and
+point out to him the rules and methods of analysis of the problem, so
+that he can, if required, calculate mathematically exactly how many
+grains of force the fork exerts on the jewel pin, and also how much (or,
+rather, what percentage) of the motive power is lost in various "power
+leaks," like "drop" and lost motion. In the present case the mechanical
+result we desire to obtain is to cause our lever pivoted at _k_ to
+vibrate back and forth through an arc of eight and one-half degrees;
+this lever not only to vibrate back and forth, but also to lock and hold
+the escape wheel during a certain period of time; that is, through the
+period of time the balance is performing its excursion and the jewel pin
+free and detached from the fork.
+
+We have spoken of paper being employed for drawings, but for very
+accurate delineations we would recommend the horological student to make
+drawings on a flat metal plate, after perfectly smoothing the surface
+and blackening it by oxidizing.
+
+
+PALLET-AND-FORK ACTION.
+
+By adopting eight and one-half degrees pallet-and-fork action we can
+utilize ten and one-half degrees of escape-wheel action. We show at _A A'_,
+Fig. 9, two teeth of a ratchet-tooth escape wheel reduced one-half;
+that is, the original drawing was made for an escape wheel ten inches in
+diameter. We shall make a radical departure from the usual practice in
+making cuts on an enlarged scale, for only such parts as we are talking
+about. To explain, we show at Fig. 10 about one-half of an escape wheel
+one eighth the size of our large drawing; and when we wish to show some
+portion of such drawing on a larger scale we will designate such
+enlargement by saying one-fourth, one-half or full size.
+
+[Illustration: Fig. 9]
+
+At Fig. 9 we show at half size that portion of our escapement embraced
+by the dotted lines _d_, Fig. 10. This plan enables us to show very
+minutely such parts as we have under consideration, and yet occupy but
+little space. The arc _a_, Fig. 9, represents the periphery of the
+escape wheel. On this line, ten and one-half degrees from the point of
+the tooth _A_, we establish the point _c_ and draw the radial line
+_c c'_. It is to be borne in mind that the arc embraced between the points
+_b_ and _c_ represents the duration of contact between the tooth _A_ and
+the entrance pallet of the lever. The space or short arc _c n_
+represents the "drop" of the tooth.
+
+This arc of one and one-half degrees of escape-wheel movement is a
+complete loss of six and one-fourth per cent. of the entire power of the
+mainspring, as brought down to the escapement; still, up to the present
+time, no remedy has been devised to overcome it. All the other
+escapements, including the chronometer, duplex and cylinder, are quite
+as wasteful of power, if not more so. It is usual to construct
+ratchet-tooth pallets so as to utilize but ten degrees of escape-wheel
+action; but we shall show that half a degree more can be utilized by
+adopting the eight and one-half degree fork action and employing a
+double-roller safety action to prevent over-banking.
+
+[Illustration: Fig. 10]
+
+From the point _e_, which represents the center of the pallet staff, we
+draw through _b_ the line _e f_. At one degree below _e f_ we draw the
+line _e g_, and seven and one-half degrees below the line _e g_ we draw
+the line _e h_. For delineating the lines _e g_, etc., correctly, we
+employ a degree-arc; that is, on the large drawing we are making we
+first draw the line _e b f_, Fig. 10, and then, with our dividers set at
+five inches, sweep the short arc _i_, and on this lay off first one
+degree from the intersection of _f e_ with the arc _i_, and through this
+point draw the line _e g_.
+
+From the intersection of the line _f e_ with the arc _i_ we lay off
+eight and one-half degrees, and through this point draw the line _e h_.
+Bear in mind that we are drawing the pallet at _B_ to represent one with
+eight and one-half degrees fork-and-pallet action, and with equidistant
+lockings. If we reason on the matter under consideration, we will see
+the tooth _A_ and the pallet _B_, against which it acts, part or
+separate when the tooth arrives at the point _c_; that is, after the
+escape wheel has moved through ten and one-half degrees of angular
+motion, the tooth drops from the impulse face of the pallet and falls
+through one and one-half degrees of arc, when the tooth _A''_, Fig. 10,
+is arrested by the exit pallet.
+
+To locate the position of the inner angle of the pallet _B_, sweep the
+short arc _l_ by setting the dividers so one point or leg rests at the
+center _e_ and the other at the point _c_. Somewhere on this arc _l_ is
+to be located the inner angle of our pallet. In delineating this angle,
+Moritz Grossman, in his "Prize Essay on the Detached Lever Escapement,"
+makes an error, in Plate III of large English edition, of more than his
+entire lock, or about two degrees. We make no apologies for calling
+attention to this mistake on the part of an authority holding so high a
+position on such matters as Mr. Grossman, because a mistake is a
+mistake, no matter who makes it.
+
+We will say no more of this error at present, but will farther on show
+drawings of Mr. Grossman's faulty method, and also the correct method of
+drawing such a pallet. To delineate the locking face of our pallet, from
+the point formed by the intersection of the lines _e g b b'_, Fig. 9, as
+a center, we draw the line _j_ at an angle of twelve degrees to _b b''_.
+In doing this we employ the same method of establishing the angle as we
+made use of in drawing the lines _e g_ and _e h_, Fig. 10. The line _j_
+establishes the locking face of the pallet _B_. Setting the locking face
+of the pallet at twelve degrees has been found in practice to give a
+safe "draw" to the pallet and keep the lever secure against the bank. It
+will be remembered the face of the escape-wheel tooth was drawn at
+twenty-four degrees to a radial line of the escape wheel, which, in this
+instance, is the line _b b'_, Fig. 9. It will now be seen that the angle
+of the pallet just halves this angle, and consequently the tooth _A_
+only rests with its point on the locking face of the pallet. We do not
+show the outlines of the pallet _B_, because we have not so far pointed
+out the correct method of delineating it.
+
+
+METHODS OF MAKING GOOD DRAWING INSTRUMENTS.
+
+Perhaps we cannot do our readers a greater favor than to digress from
+the study of the detached lever escapement long enough to say a few
+words about drawing instruments and tablets or surfaces on which to
+delineate, with due precision, mechanical designs or drawings. Ordinary
+drawing instruments, even of the higher grades, and costing a good deal
+of money, are far from being satisfactory to a man who has the proper
+idea of accuracy to be rated as a first-class mechanic. Ordinary
+compasses are obstinate when we try to set them to the hundredth of an
+inch; usually the points are dull and ill-shapen; if they make a
+puncture in the paper it is unsightly.
+
+Watchmakers have one advantage, however, because they can very easily
+work over a cheap set of drawing instruments and make them even superior
+to anything they can buy at the art stores. To illustrate, let us take a
+cheap pair of brass or German-silver five-inch dividers and make them
+over into needle points and "spring set." To do this the points are cut
+off at the line _a a_, Fig 11, and a steel tube is gold-soldered on each
+leg. The steel tube is made by taking a piece of steel wire which will
+fit a No. 16 chuck of a Whitcomb lathe, and drilling a hole in the end
+about one-fourth of an inch deep and about the size of a No. 3 sewing
+needle. We Show at Fig. 12 a view of the point _A'_, Fig. 11, enlarged,
+and the steel tube we have just drilled out attached at _C_. About the
+best way to attach _C_ is to solder. After the tube _C_ is attached a
+hole is drilled through _A'_ at _d_, and the thumb-screw _d_ inserted.
+This thumb-screw should be of steel, and hardened and tempered. The use
+of this screw is to clamp the needle point. With such a device as the
+tube _C_ and set-screw _d_, a No. 3 needle is used for a point; but for
+drawings on paper a turned point, as shown at Fig 13, is to be
+preferred. Such points can be made from a No. 3 needle after softening
+enough to be turned so as to form the point _c_. This point at the
+shoulder _f_ should be about 12/1000 of an inch, or the size of a
+fourth-wheel pivot to an eighteen size movement.
+
+[Illustration: Fig. 11]
+
+[Illustration: Fig. 12]
+
+[Illustration: Fig. 13]
+
+[Illustration: Fig. 14]
+
+The idea is, when drawing on paper the point _c_ enters the paper. For
+drawing on metal the form of the point is changed to a simple cone, as
+shown at _B'_ _c_, Fig. 13. such cones can be turned carefully, then
+hardened and tempered to a straw color; and when they become dull, can
+be ground by placing the points in a wire chuck and dressing them up
+with an emery buff or an Arkansas slip. The opposite leg of the dividers
+is the one to which is attached the spring for close setting of the
+points.
+
+In making this spring, we take a piece of steel about two and
+one-fourth inches long and of the same width as the leg of the divider,
+and attach it to the inside of the leg as shown at Fig. 14, where _D_
+represents the spring and _A_ the leg of the dividers. The spring _D_
+has a short steel tube _C''_ and set-screw _d''_ for a fine point like
+_B_ or _B'_. In the lower end of the leg _A_, Fig. 14, is placed the
+milled-head screw _g_, which serves to adjust the two points of the
+dividers to very close distances. The spring _D_ is, of course, set so
+it would press close to the leg _A_ if the screw _g_ did not force it
+away.
+
+
+SPRING AND ADJUSTING SCREW FOR DRAWING INSTRUMENTS.
+
+[Illustration: Fig. 15]
+
+It will be seen that we can apply a spring _D_ and adjusting screw
+opposite to the leg which carries the pen or pencil point of all our
+dividers if we choose to do so; but it is for metal drawing that such
+points are of the greatest advantage, as we can secure an accuracy very
+gratifying to a workman who believes in precision. For drawing circles
+on metal, "bar compasses" are much the best, as they are almost entirely
+free from spring, which attends the jointed compass. To make (because
+they cannot be bought) such an instrument, take a piece of flat steel,
+one-eighth by three-eighths of an inch and seven inches long, and after
+turning and smoothing it carefully, make a slide half an inch wide, as
+shown at Fig. 15, with a set-screw _h_ on top to secure it at any point
+on the bar _E_. In the lower part of the slide _F_ is placed a steel
+tube like _C_, shown in Figs. 12 and 14, with set-screw for holding
+points like _B B'_, Fig. 13. At the opposite end of the bar _E_ is
+placed a looped spring _G_, which carries a steel tube and point like
+the spring _D_, Fig. 14. Above this tube and point, shown at _j_, Fig.
+15, is placed an adjustment screw _k_ for fine adjustment. The inner end
+of the screw _k_ rests against the end of the bar _E_. The tendency of
+the spring _G_ is to close upon the end of _E_; consequently if we make
+use of the screw _k_ to force away the lower end of _G_, we can set the
+fine point in _j_ to the greatest exactness.
+
+The spring _G_ is made of a piece of steel one-eighth of an inch
+square, and secured to the bar _E_ with a screw and steady pins at _m_.
+A pen and pencil point attachment can be added to the spring _G_; but in
+case this is done it would be better to make another spring like _G_
+without the point _j_, and with the adjusting screw placed at _l_. In
+fitting pen and pencil points to a spring like _G_ it would probably be
+economical to make them outright; that is, make the blades and screw for
+the ruling pen and a spring or clamping tube for the pencil point.
+
+
+CONSIDERATION OF DETACHED LEVER ESCAPEMENT RESUMED.
+
+We will now, with our improved drawing instruments, resume the
+consideration of the ratchet-tooth lever escapement. We reproduce at
+Fig. 16 a portion of diagram III, from Moritz Grossmann's "Prize Essay
+on the Detached Lever Escapement," in order to point out the error in
+delineating the entrance pallet to which we previously called attention.
+The cut, as we give it, is not quite one-half the size of Mr.
+Grossmann's original plate.
+
+In the cut we give the letters of reference employed the same as on the
+original engraving, except where we use others in explanation. The
+angular motion of the lever and pallet action as shown in the cut is ten
+degrees; but in our drawing, where we only use eight and one-half
+degrees, the same mistake would give proportionate error if we did not
+take the means to correct it. The error to which we refer lies in
+drawing the impulse face of the entrance pallet. The impulse face of
+this pallet as drawn by Mr. Grossmann would not, from the action of the
+engaging tooth, carry this pallet through more than eight degrees of
+angular motion; consequently, the tooth which should lock on the exit
+pallet would fail to do so, and strike the impulse face.
+
+We would here beg to add that nothing will so much instruct a person
+desiring to acquire sound ideas on escapements as making a large model.
+The writer calls to mind a wood model of a lever escapement made by one
+of the "boys" in the Elgin factory about a year or two after Mr.
+Grossmann's prize essay was published. It went from hand to hand and did
+much toward establishing sound ideas as regards the correct action of
+the lever escapement in that notable concern.
+
+If a horological student should construct a large model on the lines
+laid down in Mr. Grossmann's work, the entrance pallet would be faulty
+in form and would not properly perform its functions. Why? perhaps says
+our reader. In reply let us analyze the action of the tooth _B_ as it
+rests on the pallet _A_. Now, if we move this pallet through an angular
+motion of one and one-half degrees on the center _g_ (which also
+represents the center of the pallet staff), the tooth _B_ is disengaged
+from the locking face and commences to slide along the impulse face of
+the pallet and "drops," that is, falls from the pallet, when the inner
+angle of the pallet is reached.
+
+[Illustration: Fig. 16]
+
+This inner angle, as located by Mr. Grossmann, is at the intersection of
+the short arc _i_ with the line _g n_, which limits the ten-degree
+angular motion of the pallets. If we carefully study the drawing, we
+will see the pallet has only to move through eight degrees of angular
+motion of the pallet staff for the tooth to escape, _because the tooth
+certainly must be disengaged when the inner angle of the pallet reaches
+the peripheral line a_. The true way to locate the position of the inner
+angle of the pallet, is to measure down on the arc _i_ ten degrees from
+its intersection with the peripheral line _a_ and locate a point to
+which a line is drawn from the intersection of the line _g m_ with the
+radial line _a c_, thus defining the inner angle of the entrance pallet.
+We will name this point the point _x_.
+
+It may not be amiss to say the arc _i_ is swept from the center _g_
+through the point _u_, said point being located ten degrees from the
+intersection of the radial _a c_ with the peripheral line _a_. It will
+be noticed that the inner angle of the entrance pallet _A_ seems to
+extend inward, beyond the radial line _a j_, that is, toward the pallet
+center _g_, and gives the appearance of being much thicker than the exit
+pallet _A'_; but we will see on examination that the extreme angle _x_
+of the entrance pallet must move on the arc _i_ and, consequently, cross
+the peripheral line _a_ at the point _u_. If we measure the impulse
+faces of the two pallets _A A'_, we will find them nearly alike in
+linear extent.
+
+Mr. Grossmann, in delineating his exit pallet, brings the extreme angle
+(shown at _4_) down to the periphery of the escape, as shown in the
+drawing, where it extends beyond the intersection of the line _g f_ with
+the radial line _a 3_. The correct form for the entrance pallet should
+be to the dotted line _z x y_.
+
+[Illustration: Fig. 17]
+
+We have spoken of engaging and disengaging frictions; we do not know how
+we can better explain this term than by illustrating the idea with a
+grindstone. Suppose two men are grinding on the same stone; each has,
+say, a cold chisel to grind, as shown at Fig. 17, where _G_ represents
+the grindstone and _N N'_ the cold chisels. The grindstone is supposed
+to be revolving in the direction of the arrow. The chisels _N_ and _N'_
+are both being ground, but the chisel _N'_ is being cut much the more
+rapidly, as each particle of grit of the stone as it catches on the
+steel causes the chisel to hug the stone and bite in deeper and deeper;
+while the chisel shown at _N_ is thrust away by the action of the grit.
+Now, friction of any kind is only a sort of grinding operation, and the
+same principles hold good.
+
+
+THE NECESSITY FOR GOOD INSTRUMENTS.
+
+It is to be hoped the reader who intends to profit by this treatise has
+fitted up such a pair of dividers as those we have described, because it
+is only with accurate instruments he can hope to produce drawings on
+which any reliance can be placed. The drawing of a ratchet-tooth lever
+escapement of eight and one-half degrees pallet action will now be
+resumed. In the drawing at Fig. 18 is shown a complete delineation of
+such an escapement with eight and one-half degrees of pallet action and
+equidistant locking faces. It is, of course, understood the escape wheel
+is to be drawn ten inches in diameter, and that the degree arcs shown in
+Fig. 1 will be used.
+
+We commence by carefully placing on the drawing-board a sheet of paper
+about fifteen inches square, and then vertically through the center
+draw the line _a' a''_. At some convenient position on this line is
+established the point _a_, which represents the center of the escape
+wheel. In this drawing it is not important that the entire escape wheel
+be shown, inasmuch as we have really to do with but a little over sixty
+degrees of the periphery of the escape wheel. With the dividers
+carefully set at five inches, from _a_, as a center, we sweep the arc
+_n n_, and from the intersection of the perpendicular line _a' a''_ with
+the arc _n_ we lay off on each side thirty degrees from the brass degree
+arc, and through the points thus established are drawn the radial lines
+_a b'_ and _a d'_.
+
+
+[Illustration: Fig. 18]
+
+The point on the arc _n_ where it intersects with the line _b'_ is
+termed the point _b_. At the intersection of the radial line _a d'_ is
+established the point _d_. We take ten and one-half degrees in the
+dividers, and from the point _b_ establish the point _c_, which embraces
+the arc of the escape wheel which is utilized by the pallet action.
+Through the point _b_ the line _h' h_ is drawn at right angles to the
+line _a b'_. The line _j j'_ is also drawn at right angles to the line
+_a d'_ through the point _d_. We now have an intersection of the lines
+just drawn in common with the line _a a'_ at the point _g_, said point
+indicating the center of the pallet action.
+
+The dividers are now set to embrace the space between the points _b_ and
+_g_ on the line _h' h_, and the arc _f f_ is swept; which, in proof of
+the accuracy of the work, intersects the arc _n_ at the point _d_. This
+arc coincides with the locking faces of both pallets. To lay out the
+entrance pallet, the dividers are set to five inches, and from _g_ as a
+center the short arc _o o_ is swept. On this arc one degree is laid off
+below the line _h' h_, and the line _g i_ drawn. The space embraced
+between the lines _h_ and _i_ on the arc _f_ represents the locking face
+of the entrance pallet, and the point formed at the intersection of the
+line _g i_ with the arc _f_ is called the point _p_. To give the proper
+lock to the face of the pallet, from the point _p_ as a center is swept
+the short arc _r r_, and from its intersection with the line _a b'_
+twelve degrees are laid off and the line _b s_ drawn, which defines the
+locking face of the entrance pallet. From _g_ as a center is swept the
+arc _c' c'_, intersecting the arc _n n_ at _c_. On this arc (_c_) is
+located the inner angle of the entrance pallet. The dividers are set to
+embrace the space on the arc _c'_ between the lines _g h'_ and _g k_.
+With this space in the dividers one leg is set at the point _c_,
+measuring down on the arc _c'_ and establishing the point _t_. The
+points _p_ and _t_ are then connected, and thus the impulse face of the
+entrance pallet _B_ is defined. From the point _t_ is drawn the line
+_t t'_, parallel to the line _b s_, thus defining the inner face of the
+entrance pallet.
+
+
+DELINEATING THE EXIT PALLET.
+
+To delineate the exit pallet, sweep the short arc _u u_ (from _g_ as a
+center) with the dividers set at five inches, and from the intersection
+of this arc with the line _g j'_ set off eight and one-half degrees and
+draw the line _g l_. At one degree below this line is drawn the line _g m_.
+The space on the arc _f_ between these lines defines the locking
+face of the exit pallet. The point where the line _g m_ intersects the
+arc _f_ is named the point _x_. From the point _x_ is erected the line
+_x w_, perpendicular to the line _g m_. From _x_ as a center, and with
+the dividers set at five inches, the short arc _y y_ is swept, and on
+this arc are laid off twelve degrees, and the line _x z_ is drawn, which
+line defines the locking face of the exit pallet.
+
+Next is taken ten and one-half degrees from the brass degree-scale, and
+from the point _d_ on the arc _n_ the space named is laid off, and thus
+is established the point _v_; and from _g_ as a center is swept the arc
+_v' v'_ through the point _v_. It will be evident on a little thought,
+that if the tooth _A'_ impelled the exit pallet to the position shown,
+the outer angle of the pallet must extend down to the point _v_, on the
+arc _v' v'_; consequently, we define the impulse face of this pallet by
+drawing a line from point _x_ to _v_. To define the outer face of the
+exit pallet, we draw the line _v e_ parallel to the line _x z_.
+
+There are no set rules for drawing the general form of the pallet arms,
+only to be governed by and conforming to about what we would deem
+appropriate, and to accord with a sense of proportion and mechanical
+elegance. Ratchet-tooth pallets are usually made in what is termed
+"close pallets"; that is, the pallet jewel is set in a slot sawed in the
+steel pallet arm, which is undoubtedly the strongest and most
+serviceable form of pallet made. We shall next consider the
+ratchet-tooth lever escapement with circular pallets and ten degrees of
+pallet action.
+
+
+DELINEATING CIRCULAR PALLETS.
+
+To delineate "circular pallets" for a ratchet-tooth lever escapement, we
+proceed very much as in the former drawing, by locating the point _A_,
+which represents the center of the escape wheel, at some convenient
+point, and with the dividers set at five inches, sweep the arc _m_, to
+represent the periphery of the escape wheel, and then draw the vertical
+line _A B'_, Fig. 19. We (as before) lay off thirty degrees on the arc
+_m_ each side of the intersection of said arc with the line _A B'_, and
+thus establish on the arc _m_ the points _a b_, and from _A_ as a center
+draw through the points so established the radial lines _A a'_ and _A b'_.
+
+We erect from the point _a_ a perpendicular to the line _A a_, and, as
+previously explained, establish the pallet center at _B_. Inasmuch as we
+are to employ circular pallets, we lay off to the left on the arc _m_,
+from the point _a_, five degrees, said five degrees being half of the
+angular motion of the escape wheel utilized in the present drawing, and
+thus establish the point _c_, and from _A_ as a center draw through this
+point the radial line _A c'_. To the right of the point _a_ we lay off
+five degrees and establish the point _d_. To illustrate the underlying
+principle of our circular pallets: with one leg of the dividers set at
+_B_ we sweep through the points _c a d_ the arcs _c'' a'' d''_.
+
+From _B_ as a center, we continue the line _B a_ to _f_, and with the
+dividers set at five inches, sweep the short arc _e e_. From the
+intersection of this arc with the line _B f_ we lay off one and a half
+degrees and draw the line _B g_, which establishes the extent of the
+lock on the entrance pallet. It will be noticed the linear extent of
+the locking face of the entrance pallet is greater than that of the
+exit, although both represent an angle of one and a half degrees.
+Really, in practice, this discrepancy is of little importance, as the
+same side-shake in banking would secure safety in either case.
+
+[Illustration: Fig. 19]
+
+The fault we previously pointed out, of the generally accepted method of
+delineating a detached lever escapement, is not as conspicuous here as
+it is where the pallets are drawn with equidistant locking faces; that
+is, the inner angle of the entrance pallet (shown at _s_) does not have
+to be carried down on the arc _d'_ as far to insure a continuous pallet
+action of ten degrees, as with the pallets with equidistant locking
+faces. Still, even here we have carried the angle _s_ down about half a
+degree on the arc _d'_, to secure a safe lock on the exit pallet.
+
+
+THE AMOUNT OF LOCK.
+
+If we study the large drawing, where we delineate the escape wheel ten
+inches in diameter, it will readily be seen that although we claim one
+and a half degrees lock, we really have only about one degree, inasmuch
+as the curve of the peripheral line _m_ diverges from the line _B f_,
+and, as a consequence, the absolute lock of the tooth _C_ on the locking
+face of the entrance pallet _E_ is but about one degree. Under these
+conditions, if we did not extend the outer angle of the exit pallet at
+_t_ down to the peripheral line _m_, we would scarcely secure one-half a
+degree of lock. This is true of both pallets. We must carry the pallet
+angles at _r s n t_ down on the circles _c'' d'_ if we would secure the
+lock and impulse we claim; that is, one and a half degrees lock and
+eight and a half degrees impulse.
+
+Now, while the writer is willing to admit that a one-degree lock in a
+sound, well-made escapement is ample, still he is not willing to allow
+of a looseness of drawing to incorporate to the extent of one degree in
+any mechanical matter demanding such extreme accuracy as the parts of a
+watch. It has been claimed that such defects can, to a great extent, be
+remedied by setting the escapement closer; that is, by bringing the
+centers of the pallet staff and escape wheel nearer together. We hold
+that such a course is not mechanical and, further, that there is not the
+slightest necessity for such a policy.
+
+
+ADVANTAGE OF MAKING LARGE DRAWINGS.
+
+By making the drawings large, as we have already suggested and insisted
+upon, we can secure an accuracy closely approximating perfection. As,
+for instance, if we wish to get a lock of one and a half degrees on the
+locking face of the entrance pallet _E_, we measure down on the arc
+_c''_ from its intersection with the peripheral line _m_ one and a half
+degrees, and establish the point _r_ and thus locate the outer angle of
+the entrance pallet _E_, so there will really be one and a half degrees
+of lock; and by measuring down on the arc _d'_ ten degrees from its
+intersection with the peripheral line _m_, we locate the point _s_,
+which determines the position of the inner angle of the entrance pallet,
+and we know for a certainty that when this inner angle is freed from the
+tooth it will be after the pallet (and, of course, the lever) has passed
+through exactly ten degrees of angular motion.
+
+For locating the inner angle of the exit pallet, we measure on the arc
+_d'_, from its intersection with the peripheral line _m_, eight and a
+half degrees, and establish the point _n_, which locates the position of
+this inner angle; and, of course, one and a half degrees added on the
+arc _d'_ indicates the extent of the lock on this pallet. Such drawings
+not only enable us to theorize to extreme exactness, but also give us
+proportionate measurements, which can be carried into actual
+construction.
+
+
+THE CLUB-TOOTH LEVER ESCAPEMENT.
+
+We will now take up the club-tooth form of the lever escapement. This
+form of tooth has in the United States and in Switzerland almost
+entirely superceded the ratchet tooth. The principal reason for its
+finding so much favor is, we think, chiefly owing to the fact that this
+form of tooth is better able to stand the manipulations of the
+able-bodied watchmaker, who possesses more strength than skill. We will
+not pause now, however, to consider the comparative merits of the
+ratchet and club-tooth forms of the lever escapement, but leave this
+part of the theme for discussion after we have given full instructions
+for delineating both forms.
+
+With the ratchet-tooth lever escapement all of the impulse must be
+derived from the pallets, but in the club-tooth escapement we can divide
+the impulse planes between the pallets and the teeth to suit our fancy;
+or perhaps it would be better to say carry out theories, because we have
+it in our power, in this form of the lever escapement, to indulge
+ourselves in many changes of the relations of the several parts. With
+the ratchet tooth the principal changes we could make would be from
+pallets with equidistant lockings to circular pallets. The club-tooth
+escape wheel not only allows of circular pallets and equidistant
+lockings, but we can divide the impulse between the pallets and the
+teeth in such a way as will carry out many theoretical advantages which,
+after a full knowledge of the escapement action is acquired, will
+naturally suggest themselves. In the escapement shown at Fig. 20 we have
+selected, as a very excellent example of this form of tooth, circular
+pallets of ten degrees fork action and ten and a half degrees of
+escape-wheel action.
+
+It will be noticed that the pallets here are comparatively thin to those
+in general use; this condition is accomplished by deriving the principal
+part of the impulse from driving planes placed on the teeth. As relates
+to the escape-wheel action of the ten and one-half degrees, which gives
+impulse to the escapement, five and one-half degrees are utilized by the
+driving planes on the teeth and five by the impulse face of the pallet.
+Of the ten degrees of fork action, four and a half degrees relate to the
+impulse face of the teeth, one and a half degrees to lock, and four
+degrees to the driving plane of the pallets.
+
+In delineating such a club-tooth escapement, we commence, as in former
+examples, by first assuming the center of the escape wheel at _A_, and
+with the dividers set at five inches sweeping the arc _a a_. Through _A_
+we draw the vertical line _A B'_. On the arc _a a_, and each side of its
+intersection with the line _A B'_, we lay off thirty degrees, as in
+former drawings, and through the points so established on the arc _a a_
+we draw the radial lines _A b_ and _A c_. From the intersection of the
+radial line _A b_ with the arc _a_ we draw the line _h h_ at right
+angles to _A b_. Where the line _h_ intersects the radial lines _A B'_
+is located the center of the pallet staff, as shown at _B_. Inasmuch as
+we decided to let the pallet utilize five degrees of escape-wheel
+action, we take a space of two and a half degrees in the dividers, and
+on the arc _a a_ lay off the said two and a half degrees to the left of
+this intersection, and through the point so established draw the radial
+line _A g_. From _B_ as a center we sweep the arc _d d_ so it passes
+through the point of intersection of the arc _a_ with the line _A g_.
+
+[Illustration: Fig. 20]
+
+We again lay off two and a half degrees from the intersection of the
+line _A b_ with the arc _a_, but this time to the right of said
+intersection, and through the point so established, and from _B_ as a
+center, we sweep the arc _e_. From the intersection of the radial line
+_A g_ with the arc _a_ we lay off to the left five and a half degrees on
+said arc, and through the point so established draw the radial line _A f_.
+With the dividers set at five inches we sweep the short arc _m_ from
+_B_ as a center. From the intersection of the line _h B h'_ with the
+arc _m_ we lay off on said arc and above the line _h'_ four and a half
+degrees, and through the point so established draw the line _B j_.
+
+We next set the dividers so they embrace the space on the radial line _A b_
+between its intersection with the line _B j_ and the center _A_, and
+from _A_ as a center sweep the arc _i_, said arc defining the _addendum_
+of the escape-wheel teeth. We draw a line from the intersection of the
+radial line _A f_ with the arc _i_ to the intersection of the radial
+line _A g_ with the arc _a_, and thus define the impulse face of the
+escape-wheel tooth _D_. For defining the locking face of the tooth we
+draw a line at an angle of twenty-four degrees to the line _A g_, as
+previously described. The back of the tooth is defined with a curve
+swept from some point on the addendum circle _i_, such as our judgment
+will dictate.
+
+In the drawing shown at Fig. 20 the radius of this curve was obtained by
+taking eleven and a half degrees from the degree arc of 5" radius in the
+dividers, and setting one leg at the intersection of the radial line _A f_
+with the arc _i_, and placing the other on the line _i_, and allowing
+the point so established to serve as a center, the arc was swept for the
+back of the tooth, the small circle at _n_ denoting one of the centers
+just described. The length for the face of the tooth was obtained by
+taking eleven degrees from the degree arc just referred to and laying
+that space off on the line _p_, which defined the face of the tooth. The
+line _B k_ is laid off one and a half degrees below _B h_ on the arc
+_m_. The extent of this arc on the arc _d_ defines the locking face of
+the entrance pallet. We set off four degrees on the arc _m_ below the
+line _B k_, and through the point so established draw the line _B l_. We
+draw a line from the intersection of the line _A g_ with the line _c h_
+to the intersection of the arc _e_ with the line _c l_, and define the
+impulse face of the entrance pallet.
+
+
+RELATIONS OF THE SEVERAL PARTS.
+
+Before we proceed to delineate the exit pallet of our escapement, let us
+reason on the relations of the several parts.
+
+The club-tooth lever escapement is really the most complicated
+escapement made. We mean by this that there are more factors involved in
+the problem of designing it correctly than in any other known
+escapement. Most--we had better say all, for there are no exceptions
+which occur to us--writers on the lever escapement lay down certain
+empirical rules for delineating the several parts, without giving
+reasons for this or that course. For illustration, it is an established
+practice among escapement makers to employ tangential lockings, as we
+explained and illustrated in Fig. 16.
+
+Now, when we adopt circular pallets and carry the locking face of the
+entrance pallet around to the left two and a half degrees, the true
+center for the pallet staff, if we employ tangent lockings, would be
+located on a line drawn tangent to the circle _a a_ from its
+intersection with the radial line _A k_, Fig. 21. Such a tangent is
+depicted at the line _s l'_. If we reason on the situation, we will see
+that the line _A k_ is not at right angles to the line _s l_; and,
+consequently, the locking face of the entrance pallet _E_ has not really
+the twelve-degree lock we are taught to believe it has.
+
+[Illustration: Fig. 21]
+
+We will not discuss these minor points further at present, but leave
+them for subsequent consideration. We will say, however, that we could
+locate the center of the pallet action at the small circle _B'_ above
+the center _B_, which we have selected as our fork-and-pallet action,
+and secure a perfectly sound escapement, with several claimed
+advantages.
+
+Let us now take up the delineation of the exit pallet. It is very easy
+to locate the outer angle of this pallet, as this must be situated at
+the intersection of the addendum circle _i_ and the arc _g_, and located
+at _o_. It is also self-evident that the inner or locking angle must be
+situated at some point on the arc _h_. To determine this location we
+draw the line _B c_ from _B_ (the pallet center) through the
+intersection of the arc _h_ with the pitch circle _a_.
+
+Again, it follows as a self-evident fact, if the pallet we are dealing
+with was locked, that is, engaged with the tooth _D''_, the inner angle
+_n_ of the exit pallet would be one and a half degrees inside the pitch
+circle _a_. With the dividers set at 5", we sweep the short arc _b b_,
+and from the intersection of this arc with the line _B c_ we lay off ten
+degrees, and through the point so established, from _B_, we draw the
+line _B d_. Below the point of intersection of the line _B d_ with the
+short arc _b b_ we lay off one and a half degrees, and through the point
+thus established we draw the line _B e_.
+
+
+LOCATING THE INNER ANGLE OF THE EXIT PALLET.
+
+The intersection of the line _B e_ with the arc _h_, which we will term
+the point _n_, represents the location of the inner angle of the exit
+pallet. We have already explained how we located the position of the
+outer angle at _o_. We draw the line _n o_ and define the impulse face
+of the exit pallet. If we mentally analyze the problem in hand, we will
+see that as the exit pallet vibrates through its ten degrees of arc the
+line _B d_ and _B c_ change places, and the tooth _D''_ locks one and a
+half degrees. To delineate the locking face of the exit pallet, we erect
+a perpendicular to the line _B e_ from the point _n_, as shown by the
+line _n p_.
+
+From _n_ as a center we sweep the short arc _t t_, and from its
+intersection with the line _n p_ we lay off twelve degrees, and through
+the point so established we draw the line _n u_, which defines the
+locking face of the exit pallet. We draw the line _o o'_ parallel with
+_n u_ and define the outer face of said pallet. In Fig. 21 we have not
+made any attempt to show the full outline of the pallets, as they are
+delineated in precisely the same manner as those previously shown.
+
+We shall next describe the delineation of a club-tooth escapement with
+pallets having equidistant locking faces; and in Fig. 22 we shall show
+pallets with much wider arms, because, in this instance, we shall derive
+more of the impulse from the pallets than from the teeth. We do this to
+show the horological student the facility with which the club-tooth
+lever escapement can be manipulated. We wish also to impress on his mind
+the facts that the employment of thick pallet arms and thin pallet arms
+depends on the teeth of the escape wheel for its efficiency, and that
+he must have knowledge enough of the principles of action to tell at a
+glance on what lines the escapement was constructed.
+
+Suppose, for illustration, we get hold of a watch which has thin pallet
+arms, or stones, if they are exposed pallets, and the escape was
+designed for pallets with thick arms. There is no sort of tinkering we
+can do to give such a watch a good motion, except to change either the
+escape wheel or the pallets. If we know enough of the lever escapement
+to set about it with skill and judgment, the matter is soon put to
+rights; but otherwise we can look and squint, open and close the
+bankings, and tinker about till doomsday, and the watch be none the
+better.
+
+
+CLUB-TOOTH LEVER WITH EQUIDISTANT LOCKING FACES.
+
+In drawing a club-tooth lever escapement with equidistant locking, we
+commence, as on former occasions, by producing the vertical line _A k_,
+Fig. 22, and establishing the center of the escape wheel at _A_, and
+with the dividers set at 5" sweep the pitch circle _a_. On each side of
+the intersection of the vertical line _A k_ with the arc _a_ we set off
+thirty degrees on said arc, and through the points so established draw
+the radial lines _A b_ and _A c_.
+
+From the intersection of the radial line _A b_ with the arc _a_ lay off
+three and a half degrees to the left of said intersection on the arc
+_a_, and through the point so established draw the radial line _A e_.
+From the intersection of the radial line _A b_ with the arc _a_ erect
+the perpendicular line _f_, and at the crossing or intersection of said
+line with the vertical line _A k_ establish the center of the pallet
+staff, as indicated by the small circle _B_. From _B_ as a center sweep
+the short arc _l_ with a 5" radius; and from the intersection of the
+radial line _A b_ with the arc _a_ continue the line _f_ until it
+crosses the short arc _l_, as shown at _f'_. Lay off one and a half
+degrees on the arc _l_ below its intersection with the line _f'_, and
+from _B_ as a center draw the line _B_ _i_ through said intersection.
+From _B_ as a center, through the intersection of the radial line _A b_
+and the arc _a_, sweep the arc _g_.
+
+The space between the lines _B f'_ and _B i_ on the arc _g_ defines the
+extent of the locking face of the entrance pallet _C_. The intersection
+of the line _B f'_ with the arc _g_ we denominate the point _o_, and
+from this point as a center sweep the short arc _p_ with a 5" radius;
+and on this arc, from its intersection with the radial line _A b_, lay
+off twelve degrees, and through the point so established, from _o_ as a
+center, draw the radial line _o m_, said line defining the locking face
+of the entrance pallet _C_.
+
+[Illustration: Fig. 22]
+
+It will be seen that this gives a positive "draw" of twelve degrees to
+the entrance pallet; that is, counting to the line _B f'_. In this
+escapement as delineated there is perfect tangential locking. If the
+locking face of the entrance-pallet stone at _C_ was made to conform to
+the radial line _A b_, the lock of the tooth _D_ at _o_ would be "dead";
+that is, absolutely neutral. The tooth _D_ would press the pallet _C_ in
+the direction of the arrow _x_, toward the center of the pallet staff
+_B_, with no tendency on the part of the pallet to turn on its axis _B_.
+Theoretically, the pallet with the locking face cut to coincide with the
+line _A b_ would resist movement on the center _B_ in either direction
+indicated by the double-headed arrow _y_.
+
+A pallet at _C_ with a circular locking face made to conform to the arc
+_g_, would permit movement in the direction of the double-headed arrow
+_y_ with only mechanical effort enough to overcome friction. But it is
+evident on inspection that a locking face on the line _A b_ would cause
+a retrograde motion of the escape wheel, and consequent resistance, if
+said pallet was moved in either direction indicated by the double-headed
+arrow _y_. Precisely the same conditions obtain at the point _u_, which
+holds the same relations to the exit pallet as the point _o_ does to the
+entrance pallet _C_.
+
+
+ANGULAR MOTION OF ESCAPE WHEEL DETERMINED.
+
+The arc (three and a half degrees) of the circle _a_ embraced between
+the radial lines _A b_ and _A e_ determines the angular motion of the
+escape wheel utilized by the escape-wheel tooth. To establish and define
+the extent of angular motion of the escape wheel utilized by the pallet,
+we lay off seven degrees on the arc _a_ from the point _o_ and establish
+the point _n_, and through the point _n_, from _B_ as a center, we sweep
+the short arc _n'_. Now somewhere on this arc _n'_ will be located the
+inner angle of the entrance pallet. With a carefully-made drawing,
+having the escape wheel 10" in diameter, it will be seen that the arc
+_a_ separates considerably from the line, _B f'_ where it crosses the
+arc _n'_.
+
+It will be remembered that when drawing the ratchet-tooth lever
+escapement a measurement of eight and a half degrees was made on the arc
+_n'_ down from its intersection with the pitch circle, and thus the
+inner angle of the pallet was located. In the present instance the
+addendum line _w_ becomes the controlling arc, and it will be further
+noticed on the large drawing that the line _B h_ at its intersection
+with the arc _n'_ approaches nearer to the arc _w_ than does the line
+_B f'_ to the pitch circle _a_; consequently, the inner angle of the pallet
+should not in this instance be carried down on the arc _n'_ so far to
+correct the error as in the ratchet tooth.
+
+Reason tells us that if we measure ten degrees down on the arc _n'_ from
+its intersection with the addendum circle _w_ we must define the
+position of the inner angle of the entrance pallet. We name the point so
+established the point _r_. The outer angle of this pallet is located at
+the intersection of the radial line _A b_ with the line _B i_; said
+intersection we name the point _v_. Draw a line from the point _v_ to
+the point _r_, and we define the impulse face of the entrance pallet;
+and the angular motion obtained from it as relates to the pallet staff
+embraces six degrees.
+
+Measured on the arc _l_, the entire ten degrees of angular motion is as
+follows: Two and a half degrees from the impulse face of the tooth, and
+indicated between the lines _B h_ and _B f_; one and a half degrees lock
+between the lines _B f'_ and _B i_; six degrees impulse from pallet
+face, entrance between the lines _B i_ and _B j_.
+
+
+A DEPARTURE FROM FORMER PRACTICES.
+
+Grossmann and Britten, in all their delineations of the club-tooth
+escapement, show the exit pallet as disengaged. To vary from this
+beaten track we will draw our exit pallet as locked. There are other
+reasons which prompt us to do this, one of which is, pupils are apt to
+fall into a rut and only learn to do things a certain way, and that way
+just as they are instructed.
+
+To illustrate, the writer has met several students of the lever
+escapement who could make drawings of either club or ratchet-tooth
+escapement with the lock on the entrance pallet; but when required to
+draw a pallet as illustrated at Fig. 23, could not do it correctly.
+Occasionally one could do it, but the instances were rare. A still
+greater poser was to request them to delineate a pallet and tooth when
+the action of escaping was one-half or one-third performed; and it is
+easy to understand that only by such studies the master workman can
+thoroughly comprehend the complications involved in the club-tooth lever
+escapement.
+
+
+AN APT ILLUSTRATION.
+
+As an illustration: Two draughtsmen, employed by two competing watch
+factories, each designs a club-tooth escapement. We will further suppose
+the trains and mainspring power used by each concern to be precisely
+alike. But in practice the escapement of the watches made by one factory
+would "set," that is, if you stopped the balance dead still, with the
+pin in the fork, the watch would not start of itself; while the
+escapement designed by the other draughtsman would not "set"--stop the
+balance dead as often as you choose, the watch would start of itself.
+Yet even to experienced workmen the escape wheels and pallets _looked_
+exactly alike. Of course, there was a difference, and still none of the
+text-books make mention of it.
+
+For the present we will go on with delineating our exit pallet. The
+preliminaries are the same as with former drawings, the instructions for
+which we need not repeat. Previous to drawing the exit pallet, let us
+reason on the matter. The point _r_ in Fig. 23 is located at the
+intersection of pitch circle _a_ and the radial line _A c_; and this
+will also be the point at which the tooth _C_ will engage the locking
+face of the exit pallet.
+
+This point likewise represents the advance angle of the engaging tooth.
+Now if we measure on the arc _k_ (which represents the locking faces of
+both pallets) downward one and a half degrees, we establish the lock of
+the pallet _E_. To get this one and a half degrees defined on the arc
+_k_, we set the dividers at 5", and from _B_ as a center sweep the
+short arc _i_, and from the intersection of the arc _i_ with the line
+_B e_ we lay off on said arc _i_ one and a half degrees, and through the
+point so established draw the line _B f_.
+
+Now the space on the arc _k_ between the lines _B e_ and _B f_ defines
+the angular extent of the locking face. With the dividers set at 5" and
+one leg resting at the point _r_, we sweep the short arc _t_, and from
+the intersection of said arc with the line _A c_ we draw the line _n p_;
+but in doing so we extend it (the line) so that it intersects the line
+_B f_, and at said intersection is located the inner angle of the exit
+pallet. This intersection we will name the point _n_.
+
+[Illustration: Fig. 23]
+
+From the intersection of the line _B e_ with the arc _i_ we lay off two
+and a half degrees on said arc, and through the point so established we
+draw the line _B g_. The intersection of this line with the arc _k_ we
+name the point _z_. With one leg of our dividers set at _A_ we sweep the
+arc _l_ so it passes through the point _z_. This last arc defines the
+addendum of the escape-wheel teeth. From the point _r_ on the arc _a_ we
+lay off three and a half degrees, and through the point so established
+draw the line _A j_.
+
+
+LOCATING THE OUTER ANGLE OF THE IMPULSE PLANES.
+
+The intersection of this line with the addendum arc _l_ locates the
+outer angle of the impulse planes of the teeth, and we name it the point
+_x_. From the point _r_ we lay off on the arc _a_ seven degrees and
+establish the point _v_, which defines the extent of the angular motion
+of the escape wheel utilized by pallet. Through the point _v_, from _B_
+as a center, we sweep the short arc _m_. It will be evident on a
+moment's reflection that this arc _m_ must represent the path of
+movement of the outer angle of the exit pallet, and if we measure down
+ten degrees from the intersection of the arc _l_ with the arc _m_, the
+point so established (which we name the point _s_) must be the exact
+position of the outer angle of the pallet during locking. We have a
+measure of ten degrees on the arc _m_, between the lines _B g_ and _B
+h_, and by taking this space in the dividers and setting one leg at the
+intersection of the arc _l_ with the arc _m_, and measuring down on _m_,
+we establish the point _s_. Drawing a line from point _n_ to point _s_
+we define the impulse face of the pallet.
+
+
+MAKING AN ESCAPEMENT MODEL.
+
+[Illustration: Fig. 24]
+
+It is next proposed we apply the theories we have been considering and
+make an enlarged model of an escapement, as shown at Figs. 24 and 25.
+This model is supposed to have an escape wheel one-fifth the size of the
+10" one we have been drawing. In the accompanying cuts are shown only
+the main plate and bridges in full lines, while the positions of the
+escape wheel and balance are indicated by the dotted circles _I B_. The
+cuts are to no precise scale, but were reduced from a full-size drawing
+for convenience in printing. We shall give exact dimensions, however, so
+there will be no difficulty in carrying out our instructions in
+construction.
+
+[Illustration: Fig. 25]
+
+Perhaps it would be as well to give a general description of the model
+before taking up the details. A reduced side view of the complete model
+is given at Fig. 26. In this cut the escapement model shown at Figs. 24
+and 25 is sketched in a rough way at _R_, while _N_ shows a glass cover,
+and _M_ a wooden base of polished oak or walnut. This base is recessed
+on the lower side to receive an eight-day spring clock movement, which
+supplies the motive power for the model. This base is recessed on top to
+receive the main plate _A_, Fig. 24, and also to hold the glass shade
+_N_ in position. The base _M_ is 2½" high and 8" diameter. The glass
+cover _N_ can have either a high and spherical top, as shown, or, as
+most people prefer, a flattened oval.
+
+[Illustration: Fig. 26]
+
+The main plate _A_ is of hard spring brass, 1/10" thick and 6" in
+diameter; in fact, a simple disk of the size named, with slightly
+rounded edges. The top plate, shown at _C_, Figs. 24 and 25, is 1/8"
+thick and shaped as shown. This plate (_C_) is supported on two pillars
+½" in diameter and 1¼" high. Fig. 25 is a side view of Fig. 24 seen
+in the direction of the arrow _p_. The cock _D_ is also of 1/8" spring
+brass shaped as shown, and attached by the screw _f_ and steady pins _s s_
+to the top plate _C_. The bridge _F G_ carries the top pivots of
+escape wheel and pallet staff, and is shaped as shown at the full
+outline. This bridge is supported on two pillars ½" high and ½" in
+diameter, one of which is shown at _E_, Fig. 25, and both at the dotted
+circles _E E'_, Fig. 24.
+
+To lay out the lower plate we draw the line _a a_ so it passes through
+the center of _A_ at _m_. At 1.3" from one edge of _A_ we establish on
+the line _a_ the point _d_, which locates the center of the escape
+wheel. On the same line _a_ at 1.15" from _d_ we establish the point
+_b_, which represents the center of the pallet staff. At the distance of
+1.16" from _b_ we establish the point _c_, which represents the center
+of the balance staff. To locate the pillars _H_, which support the top
+plate _C_, we set the dividers at 2.58", and from the center _m_ sweep
+the arc _n_.
+
+From the intersection of this arc with the line _a_ (at _r_) we lay off
+on said arc _n_ 2.1" and establish the points _g g'_, which locate the
+center of the pillars _H H_. With the dividers set so one leg rests at
+the center _m_ and the other leg at the point _d_, we sweep the arc _t_.
+With the dividers set at 1.33" we establish on the arc _t_, from the
+point _d_, the points _e e'_, which locate the position of the pillars
+_E E'_. The outside diameter of the balance _B_ is 3-5/8" with the rim
+3/16" wide and 5/16" deep, with screws in the rim in imitation of the
+ordinary compensation balance.
+
+Speaking of a balance of this kind suggests to the writer the trouble he
+experienced in procuring material for a model of this kind--for the
+balance, a pattern had to be made, then a casting made, then a machinist
+turned the casting up, as it was too large for an American lathe. A
+hairspring had to be specially made, inasmuch as a mainspring was too
+short, the coils too open and, more particularly, did not look well.
+Pallet jewels had to be made, and lapidists have usually poor ideas of
+close measurements. Present-day conditions, however, will, no doubt,
+enable the workman to follow our instructions much more readily.
+
+
+MAKING THE BRIDGES.
+
+In case the reader makes the bridges _C_ and _F_, as shown in Fig. 27,
+he should locate small circles on them to indicate the position of the
+screws for securing these bridges to the pillars which support them, and
+also other small circles to indicate the position of the pivot holes _d b_
+for the escape wheel and pallet staff. In practice it will be well to
+draw the line _a a_ through the center of the main plate _A_, as
+previously directed, and also establish the point _d_ as therein
+directed.
+
+The pivot hole _d'_ for the escape wheel, and also the holes at _e e_
+and _b_, are now drilled in the bridge _F_. These holes should be about
+1/16" in diameter. The same sized hole is also drilled in the main plate
+_A_ at _d_. We now place a nicely-fitting steel pin in the hole _d'_ in
+the bridge _F_ and let it extend into the hole _d_ in the main plate. We
+clamp the bridge _F_ to _A_ so the hole _b_ comes central on the line
+_a_, and using the holes _e e_ in _F_ as guides, drill or mark the
+corresponding holes _e' e'_ and _b_ in the main plate for the pillars
+_E E'_ and the pallet staff.
+
+[Illustration: Fig. 27]
+
+This plan will insure the escape wheel and pallet staff being perfectly
+upright. The same course pursued with the plate _C_ will insure the
+balance being upright. The pillars which support the bridges are shaped
+as shown at Fig. 28, which shows a side view of one of the pillars which
+support the top plate or bridge _C_. The ends are turned to ¼" in
+diameter and extend half through the plate, where they are held by
+screws, the same as in American movements.
+
+[Illustration: Fig. 28]
+
+The pillars (like _H_) can be riveted in the lower plate _A_, but we
+think most workmen will find it more satisfactory to employ screws, as
+shown at Fig. 29. The heads of such screws should be about 3/8" in
+diameter and nicely rounded, polished and blued. We would not advise
+jeweling the pivot holes, because there is but slight friction, except
+to the foot of the balance pivot, which should be jeweled with a
+plano-convex garnet.
+
+[Illustration: Fig. 29]
+
+IMITATION RUBIES FOR CAPPING THE TOP PIVOTS.
+
+The top pivots to the escape wheel should be capped with imitation
+rubies for appearance sake only, letting the cap settings be red gold,
+or brass red gilded. If real twelve-karat gold is employed the cost will
+not be much, as the settings are only about 3/8" across and can be
+turned very thin, so they will really contain but very little gold. The
+reason why we recommend imitation ruby cap jewels for the upper holes,
+is that such jewels are much more brilliant than any real stone we can
+get for a moderate cost. Besides, there is no wear on them.
+
+The pallet jewels are also best made of glass, as garnet or any red
+stone will look almost black in such large pieces. Red carnelian has a
+sort of brick-red color, which has a cheap appearance. There is a new
+phosphorus glass used by optical instrument makers which is intensely
+hard, and if colored ruby-red makes a beautiful pallet jewel, which will
+afford as much service as if real stones were used; they are no cheaper
+than carnelian pallets, but much richer looking. The prettiest cap for
+the balance is one of those foilback stones in imitation of a rose-cut
+diamond.
+
+[Illustration: Fig. 30]
+
+[Illustration: Fig. 31]
+
+In turning the staffs it is the best plan to use double centers, but a
+piece of Stubs steel wire that will go into a No. 40 wire chuck, will
+answer; in case such wire is used, a brass collet must be provided. This
+will be understood by inspecting Fig. 30, where _L_ represents the Stubs
+wire and _B N_ the brass collet, with the balance seat shown at _k_. The
+escape-wheel arbor and pallet staff can be made in the same way. The
+lower end of the escape wheel pivot is made about ¼" long, so that a
+short piece of brass wire can be screwed upon it, as shown in Fig. 31,
+where _h_ represents the pivot, _A_ the lower plate, and the dotted line
+at _p_ the brass piece screwed on the end of the pivot. This piece _p_
+is simply a short bit of brass wire with a female screw tapped into the
+end, which screws on to the pivot. An arm is attached to _p_, as shown
+at _T_. The idea is, the pieces _T p_ act like a lathe dog to convey the
+power from one of the pivots of an old eight-day spring clock movement,
+which is secured by screws to the lower side of the main plate _A_. The
+plan is illustrated at Fig. 32, where _l_ represents pivot of the
+eight-day clock employed to run the model. Counting the escape-wheel
+pivot of the clock as one, we take the third pivot from this in the
+clock train, placing the movement so this point comes opposite the
+escape-wheel pivot of the model, and screw the clock movement fast to
+the lower side of the plate _A_. The parts _T_, Fig. 33, are alike on
+both pivots.
+
+[Illustration: Fig. 32]
+
+[Illustration: Fig. 33]
+
+
+PROFITABLE FOR EXPLAINING TO A CUSTOMER.
+
+To fully appreciate such a large escapement model as we have been
+describing, a person must see it with its great balance, nearly 4"
+across, flashing and sparkling in the show window in the evening, and
+the brilliant imitation ruby pallets dipping in and out of the escape
+wheel. A model of this kind is far more attractive than if the entire
+train were shown, the mystery of "What makes it go?" being one of the
+attractions. Such a model is, further, of great value in explaining to a
+customer what you mean when you say the escapement of his watch is out
+of order. Any practical workman can easily make an even $100 extra in a
+year by making use of such a model.
+
+For explaining to customers an extra balance cock can be used to show
+how the jewels (hole and cap) are arranged. Where the parts are as large
+as they are in the model, the customer can see and understand for
+himself what is necessary to be done.
+
+It is not to be understood that our advice to purchase the jewels for an
+extra balance cock conflicts with our recommending the reader not to
+jewel the holes of his model. The extra cock is to be shown, not for
+use, and is employed solely for explaining to a customer what is
+required when a pivot or jewel is found to be broken.
+
+
+HOW LARGE SCREWS ARE MADE.
+
+The screws which hold the plates in place should have heads about 3/8"
+in diameter, to be in proportion to the scale on which the balance and
+escape wheel are gotten up. There is much in the manner in which the
+screw heads are finished as regards the elegance of such a model. A
+perfectly flat head, no matter how highly polished, does not look well,
+neither does a flattened conehead, like Fig. 35. The best head for this
+purpose is a cupped head with chamfered edges, as shown at Fig. 34 in
+vertical section. The center _b_ is ground and polished into a perfect
+concave by means of a metal ball. The face, between the lines _a a_, is
+polished dead flat, and the chamfered edge _a c_ finished a trifle
+convex. The flat surface at _a_ is bright, but the concave _b_ and
+chamfer at _c_ are beautifully blued. For a gilt-edged, double extra
+head, the chamfer at _c_ can be "snailed," that is, ground with a
+suitable lap before bluing, like the stem-wind wheels on some watches.
+
+[Illustration: Fig. 34]
+
+[Illustration: Fig. 35]
+
+
+FANCY SCREWHEADS.
+
+There are two easy methods of removing the blue from the flat part of
+the screwhead at _a_. (1) Make a special holder for the screw in the end
+of a cement brass, as shown at _E_, Fig. 36, and while it is slowly
+revolving in the lathe touch the flat surface _a_ with a sharpened
+pegwood wet with muriatic acid, which dissolves the blue coating of
+oxide of iron. (2) The surface of the screwhead is coated with a very
+thin coating of shellac dissolved in alcohol and thoroughly dried, or a
+thin coating of collodion, which is also dried. The screw is placed in
+the ordinary polishing triangle and the flat face at _a_ polished on a
+tin lap with diamantine and oil. In polishing such surfaces the thinnest
+possible coating of diamantine and oil is smeared on the lap--in fact,
+only enough to dim the surface of the tin. It is, of course, understood
+that it is necessary to move only next to nothing of the material to
+restore the polish of the steel. The polishing of the other steel parts
+is done precisely like any other steel work.
+
+[Illustration: Fig. 36]
+
+The regulator is of the Howard pattern. The hairspring stud is set in
+the cock like the Elgin three-quarter-plate movement. The richest finish
+for such a model is frosted plates and bridges. The frosting should not
+be a fine mat, like a watch movement, but coarse-grained--in fact, the
+grain of the frosting should be proportionate to the size of the
+movement. The edges of the bridges and balance cock can be left smooth.
+The best process for frosting is by acid. Details for doing the work
+will now be given.
+
+[Illustration: Fig. 37]
+
+[Illustration: Fig. 38]
+
+To do this frosting by acid nicely, make a sieve by tacking and gluing
+four pieces of thin wood together, to make a rectangular box without a
+bottom. Four pieces of cigar-box wood, 8" long by 1½" wide, answer
+first rate. We show at _A A A A_, Fig. 37, such a box as if seen from
+above; with a side view, as if seen in the direction of the arrow _a_,
+at Fig. 38. A piece of India muslin is glued across the bottom, as shown
+at the dotted lines _b b_. By turning up the edges on the outside of the
+box, the muslin bottom can be drawn as tight as a drum head.
+
+
+HOW TO DO ACID FROSTING.
+
+To do acid frosting, we procure two ounces of gum mastic and place in
+the square sieve, shown at Fig. 37. Usually more than half the weight of
+gum mastic is in fine dust, and if not, that is, if the gum is in the
+shape of small round pellets called "mastic tears," crush these into
+dust and place the dust in _A_. Let us next suppose we wish to frost
+the cock on the balance, shown at Fig. 39. Before we commence to frost,
+the cock should be perfectly finished, with all the holes made, the
+regulator cap in position, the screw hole made for the Howard regulator
+and the index arc engraved with the letters S and F.
+
+[Illustration: Fig. 39]
+
+It is not necessary the brass should be polished, but every file mark
+and scratch should be stoned out with a Scotch stone; in fact, be in the
+condition known as "in the gray." It is not necessary to frost any
+portion of the cock _C_, except the upper surface. To protect the
+portion of the cock not to be frosted, like the edges and the back, we
+"stop out" by painting over with shellac dissolved in alcohol, to which
+a little lampblack is added. It is not necessary the coating of shellac
+should be very thick, but it is important it should be well dried.
+
+
+HOW TO PREPARE THE SURFACE.
+
+For illustration, let us suppose the back and edges of the cock at Fig.
+39 are coated with shellac and it is laid flat on a piece of paper about
+a foot square to catch the excess of mastic. Holes should be made in
+this paper and also in the board on which the paper rests to receive the
+steady pins of the cock. We hold the sieve containing the mastic over
+the cock and, gently tapping the box _A_ with a piece of wood like a
+medium-sized file handle, shake down a little snowstorm of mastic dust
+over the face of the cock _C_.
+
+Exactly how much mastic dust is required to produce a nice frosting is
+only to be determined by practice. The way to obtain the knack is to
+frost a few scraps to "get your hand in." Nitric acid of full strength
+is used, dipping the piece into a shallow dish for a few seconds. A
+good-sized soup plate would answer very nicely for frosting the bottom
+plate, which, it will be remembered, is 6" in diameter.
+
+
+HOW TO ETCH THE SURFACE.
+
+After the mastic is sifted on, the cock should be heated up to about
+250° F., to cause the particles of mastic to adhere to the surface. The
+philosophy of the process is, the nitric acid eats or dissolves the
+brass, leaving a little brass island the size of the particle of mastic
+which was attached to the surface. After heating to attach the particles
+of mastic, the dipping in nitric acid is done as just described. Common
+commercial nitric acid is used, it not being necessary to employ
+chemically pure acid. For that matter, for such purposes the commercial
+acid is the best.
+
+After the acid has acted for fifteen or twenty seconds the brass is
+rinsed in pure water to remove the acid, and dried by patting with an
+old soft towel, and further dried by waving through the air. A little
+turpentine on a rag will remove the mastic, but turpentine will not
+touch the shellac coating. The surface of the brass will be found
+irregularly acted upon, producing a sort of mottled look. To obtain a
+nice frosting the process of applying the mastic and etching must be
+repeated three or four times, when a beautiful coarse-grain mat or
+frosting will be produced.
+
+The shellac protection will not need much patching up during the three
+or four bitings of acid, as the turpentine used to wash off the mastic
+does not much affect the shellac coating. All the screw holes like _s s_
+and _d_, also the steady pins on the back, are protected by varnishing
+with shellac. The edges of the cocks and bridges should be polished by
+rubbing lengthwise with willow charcoal or a bit of chamois skin
+saturated with oil and a little hard rouge scattered upon it. The
+frosting needs thorough scratch-brushing.
+
+[Illustration: Fig. 40]
+
+At Fig. 40 we show the balance cock of our model with modified form of
+Howard regulator. The regulator bar _A_ and spring _B_ should be ground
+smooth on one side and deeply outlined to perfect form. The regulator
+cap _C_ is cut out to the correct size. These parts are of decarbonized
+cast steel, annealed until almost as soft as sheet brass. It is not so
+much work to finish these parts as one might imagine. Let us take the
+regulator bar for an example and carry it through the process of making.
+The strip of soft sheet steel on which the regulator bar is outlined is
+represented by the dotted outline _b_, Fig. 41.
+
+[Illustration: Fig. 41]
+
+To cut out sheet steel rapidly we take a piece of smooth clock
+mainspring about ¾" and 10" long and double it together, softening the
+bending point with the lamp until the piece of mainspring assumes the
+form shown at Fig. 42, where _c_ represents the piece of spring and
+_H H_ the bench-vise jaws. The piece of soft steel is placed between the
+limbs of _c c'_ of the old mainspring up to the line _a_, Fig. 41, and
+clamped in the vise jaws. The superfluous steel is cut away with a sharp
+and rather thin cold chisel.
+
+[Illustration: Fig. 42]
+
+The chisel is presented as shown at _G_, Fig. 43 (which is an end view
+of the vise jaws _H H_ and regulator bar), and held to cut obliquely and
+with a sort of shearing action, as illustrated in Fig. 42, where _A''_
+represents the soft steel and _G_ the cold chisel. We might add that
+Fig. 42 is a view of Fig. 43 seen in the direction of the arrow _f_. It
+is well to cut in from the edge _b_ on the line _d_, Fig. 41, with a
+saw, in order to readily break out the surplus steel and not bend the
+regulator bar. By setting the pieces of steel obliquely in the vise, or
+so the line _e_ comes even with the vise jaws, we can cut to more nearly
+conform to the circular loop _A''_ of the regulator _A_.
+
+[Illustration: Fig. 43]
+
+The smooth steel surface of the bent mainspring _c_ prevents the vise
+jaws from marking the soft steel of the regulator bar. A person who has
+not tried this method of cutting out soft steel would not believe with
+what facility pieces can be shaped. Any workman who has a universal face
+plate to his lathe can turn out the center of the regulator bar to
+receive the disk _C_, and also turn out the center of the regulator
+spring _B_. What we have said about the regulator bar applies also to
+the regulator spring _B_. This spring is attached to the cock _D_ by
+means of two small screws at _n_.
+
+The micrometer screw _F_ is tapped through _B''_ as in the ordinary
+Howard regulator, and the screw should be about No. 6 of a Swiss
+screw-plate. The wire from which such screw is made should be 1/10" in
+diameter. The steel cap _C_ is fitted like the finer forms of Swiss
+watches. The hairspring stud _E_ is of steel, shaped as shown, and comes
+outlined with the other parts.
+
+
+TO TEMPER AND POLISH STEEL.
+
+The regulator bar should be hardened by being placed in a folded piece
+of sheet iron and heated red hot, and thrown into cold water. The
+regulator bar _A A'_ is about 3" long; and for holding it for
+hardening, cut a piece of thin sheet iron 2½" by 3¼" and fold it
+through the middle lengthwise, as indicated by the dotted line _g_, Fig.
+44. The sheet iron when folded will appear as shown at Fig. 45. A piece
+of flat sheet metal of the same thickness as the regulator bar should be
+placed between the iron leaves _I I_, and the leaves beaten down with a
+hammer, that the iron may serve as a support for the regulator during
+heating and hardening. A paste made of castile soap and water applied to
+the regulator bar in the iron envelope will protect it from oxidizing
+much during the heating. The portions of the regulator bar marked _h_
+are intended to be rounded, while the parts marked _m_ are intended to
+be dead flat. The rounding is carefully done, first with a file and
+finished with emery paper. The outer edge of the loop _A''_ is a little
+rounded, also the inner edge next the cap _C_. This will be understood
+by inspecting Fig. 46, where we show a magnified vertical section of the
+regulator on line _l_, Fig. 40. The curvature should embrace that
+portion of _A''_ between the radial lines _o o'_, and should, on the
+model, not measure more than 1/40". It will be seen that the curved
+surface of the regulator is sunk so it meets only the vertical edge of
+the loop _A''_. For the average workman, polishing the flat parts _m_ is
+the most difficult to do, and for this reason we will give entire
+details. It is to be expected that the regulator bar will spring a
+little in hardening, but if only a little we need pay no attention to
+it.
+
+[Illustration: Fig. 44]
+
+[Illustration: Fig. 45]
+
+[Illustration: Fig. 46]
+
+
+HOW FLAT STEEL POLISHING IS DONE.
+
+Polishing a regulator bar for a large model, such as we are building, is
+only a heavy job of flat steel work, a little larger but no more
+difficult than to polish a regulator for a sixteen-size watch. We would
+ask permission here to say that really nice flat steel work is something
+which only a comparatively few workmen can do, and, still, the process
+is quite simple and the accessories few and inexpensive. First,
+ground-glass slab 6" by 6" by ¼"; second, flat zinc piece 3¼" by
+3¼" by ¼"; third, a piece of thick sheet brass 3" by 2" by 1/8";
+and a bottle of Vienna lime. The glass slab is only a piece of plate
+glass cut to the size given above. The zinc slab is pure zinc planed
+dead flat, and the glass ground to a dead surface with another piece of
+plate glass and some medium fine emery and water, the whole surface
+being gone over with emery and water until completely depolished. The
+regulator bar, after careful filing and dressing up on the edges with an
+oilstone slip or a narrow emery buff, is finished as previously
+described. We would add to the details already given a few words on
+polishing the edges.
+
+[Illustration: Fig. 47]
+
+It is not necessary that the edges of steelwork, like the regulator bar
+_B_, Fig. 47, should be polished to a flat surface; indeed, they look
+better to be nicely rounded. Perhaps we can convey the idea better by
+referring to certain parts: say, spring to the regulator, shown at _D_,
+Fig. 40, and also the hairspring stud _E_. The edges of these parts look
+best beveled in a rounded manner.
+
+[Illustration: Fig. 48]
+
+[Illustration: Fig. 49]
+
+It is a little difficult to convey in words what is meant by "rounded"
+manner. To aid in understanding our meaning, we refer to Figs. 48 and
+49, which are transverse sections of _D_, Fig. 50, on the line _f_. The
+edges of _D_, in Fig. 48, are simply rounded. There are no rules for
+such rounding--only good judgment and an eye for what looks well. The
+edges of _D_ as shown in Fig. 49 are more on the beveled order. In
+smoothing and polishing such edges, an ordinary jeweler's steel burnish
+can be used.
+
+[Illustration: Fig. 50]
+
+
+SMOOTHING AND POLISHING.
+
+The idea in smoothing and polishing such edges is to get a fair gloss
+without much attention to perfect form, inasmuch as it is the flat
+surface _d_ on top which produces the impression of fine finish. If this
+is flat and brilliant, the rounded edges, like _g c_ can really have
+quite an inferior polish and still look well. For producing the flat
+polish on the upper surface of the regulator bar _B_ and spring _D_, the
+flat surface _d_, Figs. 48, 49, 51 and 52, we must attach the regulator
+bar to a plate of heavy brass, as shown at Fig. 47, where _A_ represents
+the brass plate, and _B_ the regulator bar, arranged for grinding and
+polishing flat.
+
+[Illustration: Fig. 51]
+
+[Illustration: Fig. 52]
+
+For attaching the regulator bar _B_ to the brass plate _A_, a good plan
+is to cement it fast with lathe wax; but a better plan is to make the
+plate _A_ of heavy sheet iron, something about 1/8" thick, and secure
+the two together with three or four little catches of soft solder. It is
+to be understood the edges of the regulator bar or the regulator spring
+are polished, and all that remains to be done is to grind and polish the
+flat face.
+
+Two pieces _a a_ of the same thickness as the regulator bar are placed
+as shown and attached to _A_ to prevent rocking. After _B_ is securely
+attached to _A_, the regulator should be coated with shellac dissolved
+in alcohol and well dried. The object of this shellac coating is to keep
+the angles formed at the meeting of the face and side clean in the
+process of grinding with oilstone dust and oil. The face of the
+regulator is now placed on the ground glass after smearing it with oil
+and oilstone dust. It requires but a very slight coating to do the work.
+
+The grinding is continued until the required surface is dead flat, after
+which the work is washed with soap and water and the shellac dissolved
+away with alcohol. The final polish is obtained on the zinc lap with
+Vienna lime and alcohol. Where lathe cement is used for securing the
+regulator to the plate _A_, the alcohol used with the Vienna lime
+dissolves the cement and smears the steel. Diamantine and oil are the
+best materials for polishing when the regulator bar is cemented to the
+plate _A_.
+
+
+KNOWLEDGE THAT IS MOST ESSENTIAL.
+
+_The knowledge most important for a practical working watchmaker to
+possess is how to get the watches he has to repair in a shape to give
+satisfaction to his customers._ No one will dispute the truth of the
+above italicised statement. It is only when we seek to have limits set,
+and define what such knowledge should consist of, that disagreement
+occurs.
+
+One workman who has read Grossmann or Saunier, or both, would insist on
+all watches being made to a certain standard, and, according to their
+ideas, all such lever watches as we are now dealing with should have
+club-tooth escapements with equidistant lockings, ten degrees lever and
+pallet action, with one and one-half degrees lock and one and one-half
+degrees drop. Another workman would insist on circular pallets, his
+judgment being based chiefly on what he had read as stated by some
+author. Now the facts of the situation are that lever escapements vary
+as made by different manufacturers, one concern using circular pallets
+and another using pallets with equidistant lockings.
+
+WHAT A WORKMAN SHOULD KNOW TO REPAIR A WATCH.
+
+One escapement maker will divide the impulse equally between the tooth
+and pallet; another will give an excess to the tooth. Now while these
+matters demand our attention in the highest degree in a theoretical
+sense, still, for such "know hows" as count in a workshop, they are of
+but trivial importance in practice.
+
+We propose to deal in detail with the theoretical consideration of
+"thick" and "thin" pallets, and dwell exhaustively on circular pallets
+and those with equidistant locking faces; but before we do so we wish to
+impress on our readers the importance of being able to free themselves
+of the idea that all lever escapements should conform to the rigid rules
+of any dictum.
+
+
+EDUCATE THE EYE TO JUDGE OF ANGULAR AS WELL AS LINEAR EXTENT.
+
+For illustration: It would be easy to design a lever escapement that
+would have locking faces which were based on the idea of employing
+neither system, but a compromise between the two, and still give a good,
+sound action. All workmen should learn to estimate accurately the extent
+of angular motion, so as to be able to judge correctly of escapement
+actions. It is not only necessary to know that a club-tooth escapement
+should have one and one-half degrees drop, but the eye should be
+educated, so to speak, as to be able to judge of angular as well as
+linear extent.
+
+[Illustration: Fig. 53]
+
+Most mechanics will estimate the size of any object measured in inches
+or parts of inches very closely; but as regards angular extent, except
+in a few instances, we will find mechanics but indifferent judges. To
+illustrate, let us refer to Fig. 53. Here we have the base line _A A'_
+and the perpendicular line _a B_. Now almost any person would be able to
+see if the angle _A a B_ was equal to _B a A'_; but not five in one
+hundred practical mechanics would be able to estimate with even
+tolerable accuracy the measure the angles made to the base by the lines
+_b c d_; and still watchmakers are required in the daily practice of
+their craft to work to angular motions and movements almost as important
+as to results as diameters.
+
+What is the use of our knowing that in theory an escape-wheel tooth
+should have one and one-half degrees drop, when in reality it has three
+degrees? It is only by educating the eye from carefully-made drawings;
+or, what is better, constructing a model on a large scale, that we can
+learn to judge of proper proportion and relation of parts, especially as
+we have no convenient tool for measuring the angular motion of the fork
+or escape wheel. Nor is it important that we should have, if the workman
+is thoroughly "booked up" in the principles involved.
+
+As we explained early in this treatise, there is no imperative necessity
+compelling us to have the pallets and fork move through ten degrees any
+more than nine and one-half degrees, except that experience has proven
+that ten degrees is about the right thing for good results. In this day,
+when such a large percentage of lever escapements have exposed pallets,
+we can very readily manipulate the pallets to match the fork and roller
+action. For that matter, in many instances, with a faulty lever
+escapement, the best way to go about putting it to rights is to first
+set the fork and roller so they act correctly, and then bring the
+pallets to conform to the angular motion of the fork so adjusted.
+
+
+FORK AND ROLLER ACTION.
+
+Although we could say a good deal more about pallets and pallet action,
+still we think it advisable to drop for the present this particular part
+of the lever escapement and take up fork and roller action, because, as
+we have stated, frequently the fork and roller are principally at fault.
+In considering the action and relation of the parts of the fork and
+roller, we will first define what is considered necessary to constitute
+a good, sound construction where the fork vibrates through ten degrees
+of angular motion and is supposed to be engaged with the roller by means
+of the jewel pin for thirty degrees of angular motion of the balance.
+
+There is no special reason why thirty degrees of roller action should be
+employed, except that experience in practical construction has come to
+admit this as about the right arc for watches of ordinary good, sound
+construction. Manufacturers have made departures from this standard, but
+in almost every instance have finally come back to pretty near these
+proportions. In deciding on the length of fork and size of roller, we
+first decide on the distance apart at which to place the center of the
+balance and the center of the pallet staff. These two points
+established, we have the length of the fork and diameter of the roller
+defined at once.
+
+
+HOW TO FIND THE ROLLER DIAMETER FROM THE LENGTH OF THE FORK.
+
+To illustrate, let us imagine the small circles _A B_, Fig. 54, to
+represent the center of a pallet staff and balance staff in the order
+named. We divide this space into four equal parts, as shown, and the
+third space will represent the point at which the pitch circles of the
+fork and roller will intersect, as shown by the arc _a_ and circle _b_.
+Now if the length of the radii of these circles stand to each other as
+three to one, and the fork vibrates through an arc of ten degrees, the
+jewel pin engaging such fork must remain in contact with said fork for
+thirty degrees of angular motion of the balance.
+
+[Illustration: Fig. 54]
+
+Or, in other words, the ratio of angular motion of two _mobiles_ acting
+on each must be in the same ratio as the length of their radii at the
+point of contact. If we desire to give the jewel pin, or, in ordinary
+horological phraseology, have a greater arc of roller action, we would
+extend the length of fork (say) to the point _c_, which would be
+one-fifth of the space between _A_ and _B_, and the ratio of fork to
+roller action would be four to one, and ten degrees of fork action would
+give forty degrees of angular motion to the roller--and such escapements
+have been constructed.
+
+
+WHY THIRTY DEGREES OF ROLLER ACTION IS ABOUT RIGHT.
+
+Now we have two sound reasons why we should not extend the arc of
+vibration of the balance: (_a_) If there is an advantage to be derived
+from a detached escapement, it would surely be policy to have the arc of
+contact, that is, for the jewel pin to engage the fork, as short an arc
+as is compatible with a sound action. (_b_) It will be evident to any
+thinking mechanic that the acting force of a fork which would carry the
+jewel pin against the force exerted by the balance spring through an arc
+of fifteen degrees, or half of an arc of thirty degrees, would fail to
+do so through an arc of twenty degrees, which is the condition imposed
+when we adopt forty degrees of roller action.
+
+For the present we will accept thirty degrees of roller action as the
+standard. Before we proceed to delineate our fork and roller we will
+devote a brief consideration to the size and shape of a jewel pin to
+perform well. In this matter there has been a broad field gone over,
+both theoretically and in practical construction. Wide jewel pins, round
+jewel pins, oval jewel pins have been employed, but practical
+construction has now pretty well settled on a round jewel pin with about
+two-fifths cut away. And as regards size, if we adopt the linear extent
+of four degrees of fork or twelve degrees of roller action, we will find
+it about right.
+
+
+HOW TO SET A FORK AND ROLLER ACTION RIGHT.
+
+As previously stated, frequently the true place to begin to set a lever
+escapement right is with the roller and fork. But to do this properly we
+should know when such fork and roller action is right and safe in all
+respects. We will see on analysis of the actions involved that there are
+three important actions in the fork and roller functions: (_a_) The fork
+imparting perfect impulse through the jewel pin to the balance. (_b_)
+Proper unlocking action. (_c_) Safety action. The last function is in
+most instances sadly neglected and, we regret to add, by a large
+majority of even practical workmen it is very imperfectly understood. In
+most American watches we have ample opportunity afforded to inspect the
+pallet action, but the fork and roller action is placed so that rigid
+inspection is next to impossible.
+
+The Vacheron concern of Swiss manufacturers were acute enough to see the
+importance of such inspection, and proceeded to cut a circular opening
+in the lower plate, which permitted, on the removal of the dial, a
+careful scrutiny of the action of the roller and fork. While writing on
+this topic we would suggest the importance not only of knowing how to
+draw a correct fork and roller action, but letting the workman who
+desires to be _au fait_ in escapements delineate and study the action of
+a faulty fork and roller action--say one in which the fork, although of
+the proper form, is too short, or what at first glance would appear to
+amount to the same thing, a roller too small.
+
+Drawings help wonderfully in reasoning out not only correct actions, but
+also faulty ones, and our readers are earnestly advised to make such
+faulty drawings in several stages of action. By this course they will
+educate the eye to discriminate not only as to correct actions, but also
+to detect those which are imperfect, and we believe most watchmakers
+will admit that in many instances it takes much longer to locate a fault
+than to remedy it after it has been found.
+
+[Illustration: Fig. 55]
+
+Let us now proceed to delineate a fork and roller. It is not imperative
+that we should draw the parts to any scale, but it is a rule among
+English makers to let the distance between the center of the pallet
+staff and the center of the balance staff equal in length the chord of
+ninety-six degrees of the pitch circle of the escape wheel, which, in
+case we employ a pitch circle of 5" radius, would make the distance
+between _A_ and _B_, Fig. 55, approximately 7½", which is a very fair
+scale for study drawings.
+
+
+HOW TO DELINEATE A FORK AND ROLLER.
+
+To arrive at the proper proportions of the several parts, we divide the
+space _A B_ into four equal parts, as previously directed, and draw the
+circle _a_ and short arc _b_. With our dividers set at 5", from _B_ as a
+center we sweep the short arc _c_. From our arc of sixty degrees, with a
+5" radius, we take five degrees, and from the intersection of the right
+line _A B_ with the arc _c_ we lay off on each side five degrees and
+establish the points _d e_; and from _B_ as a center, through these
+points draw the lines _B d'_ and _B e'_. Now the arc embraced between
+these lines represents the angular extent of our fork action.
+
+From _A_ as a center and with our dividers set at 5", we sweep the arc
+_f_. From the scale of degrees we just used we lay off fifteen degrees
+on each side of the line _A B_ on the arc _f_, and establish the points
+_g h_. From _A_ as a center, through the points just established we draw
+the radial lines _A g'_ and _A h'_. The angular extent between these
+lines defines the limit of our roller action.
+
+Now if we lay off on the arc _f_ six degrees each side of its
+intersection with the line _A B_, we define the extent of the jewel pin;
+that is, on the arc _f_ we establish the points _l m_ at six degrees
+from the line _A B_, and through the points _l m_ draw, from _A_ as a
+center, the radial lines _A l'_ and _A m'_. The extent of the space
+between the lines _A l'_ and _A m'_ on the circle _a_ defines the size
+of our jewel pin.
+
+
+TO DETERMINE THE SIZE OF A JEWEL PIN.
+
+[Illustration: Fig. 56]
+
+To make the situation better understood, we make an enlarged drawing of
+the lines defining the jewel pin at Fig. 56. At the intersection of the
+line _A B_ with the arc _a_ we locate the point _k_, and from it as a
+center we sweep the circle _i_ so it passes through the intersection of
+the lines _A l'_ and _A m'_ with the arc _a_. We divide the radius of
+the circle _i_ on the line _A B_ into five equal parts, as shown by the
+vertical lines _j_. Of these five spaces we assume three as the extent
+of the jewel pin, cutting away that portion to the right of the heavy
+vertical line at _k_.
+
+[Illustration: Fig. 57]
+
+We will now proceed to delineate a fork and roller as the parts are
+related on first contact of jewel pin with fork and initial with the
+commencing of the act of unlocking a pallet. The position and relations
+are also the same as at the close of the act of impulse. We commence the
+drawing at Fig. 57, as before, by drawing the line _A B_ and the arcs
+_a_ and _b_ to represent the pitch circles. We also sweep the arc _f_ to
+enable us to delineate the line _A g'_. Next in order we draw our jewel
+pin as shown at _D_. In drawing the jewel pin we proceed as at Fig. 56,
+except we let the line _A g'_, Fig. 57, assume the same relations to the
+jewel pin as _A B_ in Fig. 56; that is, we delineate the jewel pin as if
+extending on the arc _a_ six degrees on each side of the line _A g'_,
+Fig. 57.
+
+
+THE THEORY OF THE FORK ACTION.
+
+To aid us in reasoning, we establish the point _m_, as in Fig. 55, at
+_m_, Fig. 57, and proceed to delineate another and imaginary jewel pin
+at _D'_ (as we show in dotted outline). A brief reasoning will show that
+in allowing thirty degrees of contact of the fork with the jewel pin,
+the center of the jewel pin will pass through an arc of thirty degrees,
+as shown on the arcs _a_ and _f_. Now here is an excellent opportunity
+to impress on our minds the true value of angular motion, inasmuch as
+thirty degrees on the arc _f_ is of more than twice the linear extent as
+on the arc _a_.
+
+Before we commence to draw the horn of the fork engaging the jewel pin
+_D_, shown at full line in Fig. 57, we will come to perfectly understand
+what mechanical relations are required. As previously stated, we assume
+the jewel pin, as shown at _D_, Fig. 57, is in the act of encountering
+the inner face of the horn of the fork for the end or purpose of
+unlocking the engaged pallet. Now if the inner face of the horn of the
+fork was on a radial line, such radial line would be _p B_, Fig. 57. We
+repeat this line at _p_, Fig. 56, where the parts are drawn on a larger
+scale.
+
+To delineate a fork at the instant the last effort of impulse has been
+imparted to the jewel pin, and said jewel pin is in the act of
+separating from the inner face of the prong of the fork--we would also
+call attention to the fact that relations of parts are precisely the
+same as if the jewel pin had just returned from an excursion of
+vibration and was in the act of encountering the inner face of the prong
+of the fork in the act of unlocking the escapement.
+
+We mentioned this matter previously, but venture on the repetition to
+make everything clear and easily understood. We commence by drawing the
+line _A B_ and dividing it in four equal parts, as on previous
+occasions, and from _A_ and _B_ as centers draw the pitch circles _c d_.
+By methods previously described, we draw the lines _A a_ and _A a'_,
+also _B b_ and _B b'_ to represent the angular motion of the two
+mobiles, viz., fork and roller action. As already shown, the roller
+occupies twelve degrees of angular extent. To get at this conveniently,
+we lay off on the arc by which we located the lines _A a_ and _A a'_ six
+degrees above the line _A a_ and draw the line _A h_.
+
+Now the angular extent on the arc _c_ between the lines _A a_ and _A h_
+represents the radius of the circle defining the jewel pin. From the
+intersection of the line _A a_ with the arc _c_ as a center, and with
+the radius just named, we sweep the small circle _D_, Fig. 58, which
+represents our jewel pin; we afterward cut away two-fifths and draw the
+full line _D_, as shown. We show at Fig. 59 a portion of Fig. 58,
+enlarged four times, to show certain portions of our delineations more
+distinctly. If we give the subject a moment's consideration we will see
+that the length of the prong _E_ of the lever fork is limited to such a
+length as will allow the jewel pin _D_ to pass it.
+
+
+HOW TO DELINEATE THE PRONGS OF A LEVER FORK.
+
+[Illustration: Fig. 58]
+
+[Illustration: Fig. 59]
+
+To delineate this length, from _B_ as a center we sweep the short arc
+_f_ so it passes through the outer angle _n_, Fig. 59, of the jewel pin.
+This arc, carried across the jewel pin _D_, limits the length of the
+opposite prong of the fork. The outer face of the prong of the fork can
+be drawn as a line tangent to a circle drawn from _A_ as a center
+through the angle _n_ of the jewel pin. Such a circle or arc is shown at
+_o_, Figs. 58 and 59. There has been a good deal said as to whether the
+outer edge of the prong of a fork should be straight or curved.
+
+To the writer's mind, a straight-faced prong, like from _s_ to _m_, is
+what is required for a fork with a single roller, while a fork with a
+curved prong will be best adapted for a double roller. This subject will
+be taken up again when we consider double-roller action. The extent or
+length of the outer face of the prong is also an open subject, but as
+there is but one factor of the problem of lever escapement construction
+depending on it, when we name this and see this requirement satisfied we
+have made an end of this question. The function performed by the outer
+face of the prong of a fork is to prevent the engaged pallet from
+unlocking while the guard pin is opposite to the passing hollow.
+
+The inner angle _s_ of the horn of the fork must be so shaped and
+located that the jewel pin will just clear it as it passes out of the
+fork, or when it passes into the fork in the act of unlocking the
+escapement. In escapements with solid bankings a trifle is allowed, that
+is, the fork is made enough shorter than the absolute theoretical length
+to allow for safety in this respect.
+
+
+THE PROPER LENGTH OF A LEVER.
+
+We will now see how long a lever must be to perform its functions
+perfectly. Now let us determine at what point on the inner face of the
+prong _E'_ the jewel pin parts from the fork, or engages on its return.
+To do this we draw a line from the center _r_ (Fig. 59) of the jewel
+pin, so as to meet the line _e_ at right angles, and the point _t_ so
+established on the line _e_ is where contact will take place between the
+jewel pin and fork.
+
+It will be seen this point (_t_) of contact is some distance back of the
+angle _u_ which terminates the inner face of the prong _E'_;
+consequently, it will be seen the prongs _E E'_ of the fork can with
+safety be shortened enough to afford a safe ingress or egress to the
+jewel pin to the slot in the fork. As regards the length of the outer
+face of the prong of the fork, a good rule is to make it one and a half
+times the diameter of the jewel pin. The depth of the slot need be no
+more than to free the jewel in its passage across the ten degrees of
+fork action. A convenient rule as to the depth of the slot in a fork is
+to draw the line _k_, which, it will be seen, coincides with the circle
+which defines the jewel pin.
+
+
+HOW TO DELINEATE THE SAFETY ACTION.
+
+[Illustration: Fig. 60]
+
+We will next consider a safety action of the single roller type. The
+active or necessary parts of such safety action consist of a roller or
+disk of metal, usually steel, shaped as shown in plan at _A_, Fig. 60.
+In the edge of this disk is cut in front of the jewel pin a circular
+recess shown at _a_ called the passing hollow. The remaining part of the
+safety action is the guard pin shown at _N_ Figs. 61 and 62, which is
+placed in the lever. Now it is to be understood that the sole function
+performed by the guard pin is to strike the edge of the roller _A_ at
+any time when the fork starts to unlock the engaged pallet, except when
+the jewel pin is in the slot of the fork. To avoid extreme care in
+fitting up the passing hollow, the horns of the fork are arranged to
+strike the jewel pin and prevent unlocking in case the passing hollow is
+made too wide. To delineate the safety action we first draw the fork and
+jewel pin as previously directed and as shown at Fig. 63. The position
+of the guard pin should be as close to the bottom of the slot of the
+fork as possible and be safe. As to the size of the guard pin, it is
+usual to make it about one-third or half the diameter of the jewel pin.
+The size and position of the guard pin decided on and the small circle
+_N_ drawn, to define the size and position of the roller we set our
+dividers so that a circle drawn from the center _A_ will just touch the
+edge of the small circle _N_, and thus define the outer boundary of our
+roller, or roller table, as it is frequently called.
+
+[Illustration: Fig. 61]
+
+[Illustration: Fig. 62]
+
+For deciding the angular extent of the passing hollow we have no fixed
+rule, but if we make it to occupy about half more angular extent on the
+circle _y_ than will coincide with the angular extent of the jewel pin,
+it will be perfectly safe and effectual. We previously stated that the
+jewel pin should occupy about twelve degrees of angular extent on the
+circle _c_, and if we make the passing hollow occupy eighteen degrees
+(which is one and a half the angular extent of the jewel pin) it will do
+nicely. But if we should extend the width of the passing hollow to
+twenty-four degrees it would do no harm, as the jewel pin would be well
+inside the horn of the fork before the guard pin could enter the passing
+hollow.
+
+[Illustration: Fig. 63]
+
+We show in Fig. 61 the fork as separated from the roller, but in Fig.
+62, which is a side view, we show the fork and jewel pin as engaged.
+When drawing a fork and roller action it is safe to show the guard pin
+as if in actual contact with the roller. Then in actual construction, if
+the parts are made to measure and agree with the drawing in the gray,
+that is, before polishing, the process of polishing will reduce the
+convex edge of the roller enough to free it.
+
+It is evident if thought is given to the matter, that if the guard pin
+is entirely free and does not touch the roller in any position, a
+condition and relation of parts exist which is all we can desire. We are
+aware that it is usual to give a considerable latitude in this respect
+even by makers, and allow a good bit of side shake to the lever, but our
+judgment would condemn the practice, especially in high-grade watches.
+
+
+RESTRICT THE FRICTIONAL SURFACES.
+
+Grossmann, in his essay on the detached lever escapement, adopts one and
+a half degrees lock. Now, we think that one degree is ample; and we are
+sure that every workman experienced in the construction of the finer
+watches will agree with us in the assertion that we should in all
+instances seek to reduce the extent of all frictional surfaces, no
+matter how well jeweled. Acting under such advice, if we can reduce the
+surface friction on the lock from one and a half degrees to one degree
+or, better, to three-fourths of a degree, it is surely wise policy to do
+so. And as regards the extent of angular motion of the lever, if we
+reduce this to six degrees, exclusive of the lock, we would undoubtedly
+obtain better results in timing.
+
+We shall next consider the effects of opening the bankings too wide, and
+follow with various conditions which are sure to come in the experience
+of the practical watch repairer. It is to be supposed in this problem
+that the fork and roller action is all right. The reader may say to
+this, why not close the banking? In reply we would offer the supposition
+that some workman had bent the guard pin forward or set a pallet stone
+too far out.
+
+We have now instructed our readers how to draw and construct a lever
+escapement complete, of the correct proportions, and will next take up
+defective construction and consider faults existing to a lesser or
+greater degree in almost every watch. Faults may also be those arising
+from repairs by some workman not fully posted in the correct form and
+relation of the several parts which go to make up a lever escapement. It
+makes no difference to the artisan called upon to put a watch in
+perfect order as to whom he is to attribute the imperfection, maker or
+former repairer; all the workman having the job in hand has to do is to
+know positively that such a fault actually exists, and that it devolves
+upon him to correct it properly.
+
+
+BE FEARLESS IN REPAIRS, IF SURE YOU ARE RIGHT.
+
+Hence the importance of the workman being perfectly posted on such
+matters and, knowing that he is right, can go ahead and make the watch
+as it should be. The writer had an experience of this kind years ago in
+Chicago. A Jules Jurgensen watch had been in the hands of several good
+workmen in that city, but it would stop. It was then brought to him with
+a statement of facts given above. He knew there must be a fault
+somewhere and searched for it, and found it in the exit pallet--a
+certain tooth of the escape wheel under the right conditions would
+sometimes not escape. It might go through a great many thousand times
+and yet it might, and did sometimes, hold enough to stop the watch.
+
+Now probably most of my fellow-workmen in this instance would have been
+afraid to alter a "Jurgensen," or even hint to the owner that such a
+thing could exist as a fault in construction in a watch of this
+justly-celebrated maker. The writer removed the stone, ground a little
+from the base of the offending pallet stone, replaced it, and all
+trouble ended--no stops from that on.
+
+
+STUDY OF AN ESCAPEMENT ERROR.
+
+[Illustration: Fig. 64]
+
+Now let us suppose a case, and imagine a full-plate American movement in
+which the ingress or entrance pallet extends out too far, and in order
+to have it escape, the banking on that side is opened too wide. We show
+at Fig. 64 a drawing of the parts in their proper relations under the
+conditions named. It will be seen by careful inspection that the jewel
+pin _D_ will not enter the fork, which is absolutely necessary. This
+condition very frequently exists in watches where a new pallet stone has
+been put in by an inexperienced workman. Now this is one of the
+instances in which workmen complain of hearing a "scraping" sound when
+the watch is placed to the ear. The remedy, of course, lies in warming
+up the pallet arms and pushing the stone in a trifle, "But how much?"
+say some of our readers. There is no definite rule, but we will tell
+such querists how they can test the matter.
+
+Remove the hairspring, and after putting the train in place and securing
+the plates together, give the winding arbor a turn or two to put power
+on the train; close the bankings well in so the watch cannot escape on
+either pallet. Put the balance in place and screw down the cock.
+Carefully turn back the banking on one side so the jewel pin will just
+pass out of the slot in the fork. Repeat this process with the opposite
+banking; the jewel pin will now pass out on each side. Be sure the guard
+pin does not interfere with the fork action in any way. The fork is now
+in position to conform to the conditions required.
+
+
+HOW TO ADJUST THE PALLETS TO MATCH THE FORK.
+
+If the escapement is all right, the teeth will have one and a half
+degrees lock and escape correctly; but in the instance we are
+considering, the stone will not permit the teeth to pass, and must be
+pushed in until they will. It is not a very difficult matter after we
+have placed the parts together so we can see exactly how much the pallet
+protrudes beyond what is necessary, to judge how far to push it back
+when we have it out and heated. There is still an "if" in the problem we
+are considering, which lies in the fact that the fork we are
+experimenting with may be too short for the jewel pin to engage it for
+ten degrees of angular motion.
+
+This condition a man of large experience will be able to judge of very
+closely, but the better plan for the workman is to make for himself a
+test gage for the angular movement of the fork. Of course it will be
+understood that with a fork which engages the roller for eight degrees
+of fork action, such fork will not give good results with pallets ground
+for ten degrees of pallet action; still, in many instances, a compromise
+can be effected which will give results that will satisfy the owner of a
+watch of moderate cost, and from a financial point of view it stands the
+repairer in hand to do no more work than is absolutely necessary to keep
+him well pleased.
+
+We have just made mention of a device for testing the angular motion of
+the lever. Before we take up this matter, however, we will devote a
+little time and attention to the subject of jewel pins and how to set
+them. We have heretofore only considered jewel pins of one form, that
+is, a round jewel pin with two-fifths cut away. We assumed this form
+from the fact that experience has demonstrated that it is the most
+practicable and efficient form so far devised or applied. Subsequently
+we shall take up the subject of jewel pins of different shapes.
+
+
+HOW TO SET A JEWEL PIN AS IT SHOULD BE.
+
+Many workmen have a mortal terror of setting a jewel pin and seem to
+fancy that they must have a specially-devised instrument for
+accomplishing this end. Most American watches have the hole for the
+jewel pin "a world too wide" for it, and we have heard repeated
+complaints from this cause. Probably the original object of this
+accommodating sort of hole was to favor or obviate faults of pallet
+action. Let us suppose, for illustration, that we have a roller with the
+usual style of hole for a jewel pin which will take almost anything from
+the size of a No. 12 sewing needle up to a round French clock pallet.
+
+[Illustration: Fig. 65]
+
+We are restricted as regards the proper size of jewel pin by the width
+of the slot in the fork. Selecting a jewel which just fits the fork, we
+can set it as regards its relation to the staff so it will cause the
+pitch circle of the jewel pin to coincide with either of dotted circles
+_a_ or _a'_, Fig. 65. This will perhaps be better understood by
+referring to Fig. 66, which is a view of Fig. 65 seen in the direction
+of the arrow _c_. Here we see the roller jewel at _D_, and if we bring
+it forward as far as the hole in the roller will permit, it will occupy
+the position indicated at the dotted lines; and if we set it in (toward
+the staff) as far as the hole will allow, it will occupy the position
+indicated by the full outline.
+
+[Illustration: Fig. 66]
+
+Now such other condition might very easily exist, that bringing the
+jewel pin forward to the position indicated by the dotted lines at _D_,
+Fig. 66, would remedy the defect described and illustrated at Fig. 64
+without any other change being necessary. We do not assert, understand,
+that a hole too large for the jewel pin is either necessary or
+desirable--what we wish to convey to the reader is the necessary
+knowledge so that he can profit by such a state if necessary. A hole
+which just fits the jewel pin so the merest film of cement will hold it
+in place is the way it should be; but we think it will be some time
+before such rollers are made, inasmuch as economy appears to be a chief
+consideration.
+
+
+ABOUT JEWEL-PIN SETTERS.
+
+To make a jewel-pin setter which will set a jewel pin straight is easy
+enough, but to devise any such instrument which will set a jewel so as
+to perfectly accord with the fork action is probably not practicable.
+What the workman needs is to know from examination when the jewel pin is
+in the proper position to perform its functions correctly, and he can
+only arrive at this knowledge by careful study and thought on the
+matter. If we make up our minds on examining a watch that a jewel pin is
+"set too wide," that is, so it carries the fork over too far and
+increases the lock to an undue degree, take out the balance, remove the
+hairspring, warm the roller with a small alcohol lamp, and then with the
+tweezers move the jewel pin in toward the staff.
+
+[Illustration: Fig. 67]
+
+[Illustration: Fig. 68]
+
+[Illustration: Fig. 69]
+
+[Illustration: Fig. 70]
+
+No attempt should be made to move a jewel pin unless the cement which
+holds the jewel is soft, so that when the parts cool off the jewel is as
+rigid as ever. A very little practice will enable any workman who has
+the necessary delicacy of touch requisite to ever become a good
+watchmaker, to manipulate a jewel pin to his entire satisfaction with no
+other setter than a pair of tweezers and his eye, with a proper
+knowledge of what he wants to accomplish. To properly heat a roller for
+truing up the jewel pin, leave it on the staff, and after removing the
+hairspring hold the balance by the rim in a pair of tweezers, "flashing
+it" back and forth through the flame of a rather small alcohol lamp
+until the rim of the balance is so hot it can just be held between the
+thumb and finger, and while at this temperature the jewel pin can be
+pressed forward or backward, as illustrated in Fig. 66, and then a touch
+or two will set the pin straight or parallel with the staff. Figs. 68
+and 69 are self-explanatory. For cementing in a jewel pin a very
+convenient tool is shown at Figs. 67 and 70. It is made of a piece of
+copper wire about 1/16" in diameter, bent to the form shown at Fig. 67.
+The ends _b b_ of the copper wire are flattened a little and recessed on
+their inner faces, as shown in Fig. 70, to grasp the edges of the roller
+_A_. The heat of an alcohol lamp is applied to the loop of the wire at
+_g_ until the small bit of shellac placed in the hole _h_ melts. The
+necessary small pieces of shellac are made by warming a bit of the gum
+to near the melting point and then drawing the softened gum into a
+filament the size of horse hair. A bit of this broken off and placed in
+the hole _h_ supplies the cement necessary to fasten the jewel pin.
+Figs. 68 and 69 will, no doubt, assist in a clear understanding of the
+matter.
+
+
+HOW TO MAKE AN ANGLE-MEASURING DEVICE.
+
+We will now resume the consideration of the device for measuring the
+extent of the angular motion of the fork and pallets. Now, before we
+take this matter up in detail we wish to say, or rather repeat what we
+have said before, which is to the effect that ten degrees of fork and
+lever action is not imperative, as we can get just as sound an action
+and precisely as good results with nine and a half or even nine degrees
+as with ten, if other acting parts are in unison with such an arc of
+angular motion. The chief use of such an angle-measuring device is to
+aid in comparing the relative action of the several parts with a known
+standard.
+
+[Illustration: Fig. 71]
+
+For use with full-plate movements about the best plan is a spring clip
+or clasp to embrace the pallet staff below the pallets. We show at Fig.
+71 such a device. To make it, take a rather large size of sewing
+needle--the kind known as a milliner's needle is about the best. The
+diameter of the needle should be about No. 2, so that at _b_ we can
+drill and put in a small screw. It is important that the whole affair
+should be very light. The length of the needle should be about 1-5/8",
+in order that from the notch _a_ to the end of the needle _A'_ should be
+1½". The needle should be annealed and flattened a little, to give a
+pretty good grasp to the notch _a_ on the pallet staff.
+
+Good judgment is important in making this clamp, as it is nearly
+impossible to give exact measurements. About 1/40" in width when seen in
+the direction of the arrow _j_ will be found to be about the right
+width. The spring _B_ can be made of a bit of mainspring, annealed and
+filed down to agree in width with the part _A_. In connection with the
+device shown at Fig. 71 we need a movement-holder to hold the movement
+as nearly a constant height as possible above the bench. The idea is,
+when the clamp _A B_ is slipped on the pallet staff the index hand _A'_
+will extend outward, as shown in Fig. 72, where the circle _C_ is
+supposed to represent the top plate of a watch, and _A'_ the index hand.
+
+
+HOW THE ANGULAR MOTION IS MEASURED.
+
+[Illustration: Fig. 72]
+
+Fig. 72 is supposed to be seen from above. It is evident that if we
+remove the balance from the movement shown at _C_, leaving power on the
+train, and with an oiling tool or hair broach move the lever back and
+forth, the index hand _A'_ will show in a magnified manner the angular
+motion of the lever. Now if we provide an index arc, as shown at _D_, we
+can measure the extent of such motion from bank to bank.
+
+[Illustration: Fig. 73]
+
+[Illustration: Fig. 74]
+
+To get up such an index arc we first make a stand as shown at _E F_,
+Fig. 73. The arc _D_ is made to 1½" radius, to agree with the index
+hand _A'_, and is divided into twelve degree spaces, six each side of a
+zero, as shown at Fig. 74, which is an enlarged view of the index _D_ in
+Fig. 72. The index arc is attached to a short bit of wire extending down
+into the support _E_, and made adjustable as to height by the set-screw
+_l_. Let us suppose the index arc is adjusted to the index hand _A'_,
+and we move the fork as suggested; you see the hand would show exactly
+the arc passed through from bank to bank, and by moving the stand _E F_
+we can arrange so the zero mark on the scale stands in the center of
+such arc. This, of course, gives the angular motion from bank to bank.
+As an experiment, let us close the bankings so they arrest the fork at
+the instant the tooth drops from each pallet. If this arc is ten
+degrees, the pallet action is as it should be with the majority of
+modern watches.
+
+
+TESTING LOCK AND DROP WITH OUR NEW DEVICE.
+
+Let us try another experiment: We carefully move the fork away from the
+bank, and if after the index hand has passed through one and a half
+degrees the fork flies over, we know the lock is right. We repeat the
+experiment from the opposite bank, and in the same manner determine if
+the lock is right on the other pallets. You see we have now the means
+of measuring not only the angular motion of the lever, but the angular
+extent of the lock. At first glance one would say that if now we bring
+the roller and fork action to coincide and act in unison with the pallet
+action, we would be all right; and so we would, but frequently this
+bringing of the roller and fork to agree is not so easily accomplished.
+
+It is chiefly toward this end the Waltham fork is made adjustable, so it
+can be moved to or from the roller, and also that we can allow the
+pallet arms to be moved, as we will try and explain. As we set the
+bankings the pallets are all right; but to test matters, let us remove
+the hairspring and put the balance in place. Now, if the jewel pin
+passes in and out of the fork, it is to be supposed the fork and roller
+action is all right. To test the fork and roller action we close the
+banking a little on one side. If the fork and jewel pin are related to
+each other as they should be, the jewel pin will not pass out of the
+fork, nor will the engaged tooth drop from that pallet. This condition
+should obtain on both pallets, that is, if the jewel pin will not pass
+out of the fork on a given bank the tooth engaged on its pallet should
+not drop.
+
+We have now come to the most intricate and important problems which
+relate to the lever escapement. However, we promise our readers that if
+they will take the pains to follow closely our elucidations, to make
+these puzzles plain. But we warn them that they are no easy problems to
+solve, but require good, hard thinking. The readiest way to master this
+matter is by means of such a model escapement as we have described. With
+such a model, and the pallets made to clamp with small set-screws, and
+roller constructed so the jewel pin could be set to or from the staff,
+this matter can be reduced to object lessons. But study of the due
+relation of the parts in good drawings will also master the situation.
+
+
+A FEW EXPERIMENTS WITH OUR ANGLE-MEASURING DEVICE.
+
+In using the little instrument for determining angular motion that we
+have just described, care must be taken that the spring clamp which
+embraces the pallet staff does not slip. In order to thoroughly
+understand the methods of using this angle-measuring device, let us take
+a further lesson or two.
+
+We considered measuring the amount of lock on each pallet, and advised
+the removal of the balance, because if we left the balance in we could
+not readily tell exactly when the tooth passed on to the impulse plane;
+but if we touch the fork lightly with an oiling tool or a hair broach,
+moving it (the fork) carefully away from the bank and watching the arc
+indicated by the hand _A_, Fig. 72, we can determine with great
+exactness the angular extent of lock. The diagram at Fig. 75 illustrates
+how this experiment is conducted. We apply the hair broach to the end of
+the fork _M_, as shown at _L_, and gently move the fork in the direction
+of the arrow _i_, watching the hand _A_ and note the number of degrees,
+or parts of degrees, indicated by the hand as passed over before the
+tooth is unlocked and passes on to the impulse plane and the fork flies
+forward to the opposite bank. Now, the quick movement of the pallet and
+fork may make the hand mark more or less of an arc on the index than one
+of ten degrees, as the grasp may slip on the pallet staff; but the arc
+indicated by the slow movement in unlocking will be correct.
+
+[Illustration: Fig. 75]
+
+By taking a piece of sharpened pegwood and placing the point in the slot
+of the fork, we can test the fork to see if the drop takes place much
+before the lever rests against the opposite bank. As we have previously
+stated, the drop from the pallet should not take place until the lever
+_almost_ rests on the banking pin. What the reader should impress on his
+mind is that the lever should pass through about one and a half degrees
+arc to unlock, and the remainder (eight and a half degrees) of the ten
+degrees are to be devoted to impulse. But, understand, if the impulse
+angle is only seven and a half degrees, and the jewel pin acts in
+accordance with the rules previously given, do not alter the pallet
+until you know for certain you will gain by it. An observant workman
+will, after a little practice, be able to determine this matter.
+
+We will next take up the double roller and fork action, and also
+consider in many ways the effect of less angles of action than ten
+degrees. This matter now seems of more importance, from the fact that we
+are desirous to impress on our readers that _there is no valid reason
+for adopting ten degrees of fork and roller action with the table
+roller, except that about this number of degrees of action are required
+to secure a reliable safety action_. With the double roller, as low as
+six degrees fork and pallet action can be safely employed. In fork and
+pallet actions below six degrees of angular motion, side-shake in pivot
+holes becomes a dangerous factor, as will be explained further on. It is
+perfectly comprehending the action of the lever escapement and then
+being able to remedy defects, that constitute the master workman.
+
+
+HOW TO MEASURE THE ANGULAR MOTION OF AN ESCAPE WHEEL.
+
+[Illustration: Fig. 76]
+
+We can also make use of our angle-testing device for measuring our
+escape-wheel action, by letting the clasp embrace the arbor of the
+escape wheel, instead of the pallet staff. We set the index arc as in
+our former experiments, except we place the movable index _D_, Fig. 76,
+so that when the engaged tooth rests on the locking face of a pallet,
+the index hand stands at the extreme end of our arc of twelve degrees.
+We next, with our pointed pegwood, start to move the fork away from the
+bank, as before, we look sharp and see the index hand move backward a
+little, indicating the "draw" on the locking face. As soon as the pallet
+reaches the impulse face, the hand _A_ moves rapidly forward, and if the
+escapement is of the club-tooth order and closely matched, the hand _A_
+will pass over ten and a half degrees of angular motion before the drop
+takes place.
+
+[Illustration: Fig. 77]
+
+We will warn our readers in advance, that if they make such a testing
+device they will be astonished at the inaccuracy which they will find in
+the escapements of so-called fine watches. The lock, in many instances,
+instead of being one and a half degrees, will oftener be found to be
+from two to four degrees, and the impulse derived from the escape wheel,
+as illustrated at Fig. 76, will often fall below eight degrees. Such
+watches will have a poor motion and tick loud enough to keep a policeman
+awake. Trials with actual watches, with such a device as we have just
+described, in conjunction with a careful study of the acting parts,
+especially if aided by a large model, such as we have described, will
+soon bring the student to a degree of skill unknown to the old-style
+workman, who, if a poor escapement bothered him, would bend back the
+banking pins or widen the slot in the fork.
+
+We hold that educating our repair workmen up to a high knowledge of what
+is required to constitute a high-grade escapement, will have a
+beneficial effect on manufacturers. When we wish to apply our device to
+the measurement of the escapement of three-quarter-plate watches, we
+will require another index hand, with the grasping end bent downward, as
+shown at Fig. 77. The idea with this form of index hand is, the
+bent-down jaws _B'_, Fig. 77, grasp the fork as close to the pallet
+staff as possible, making an allowance for the acting center by so
+placing the index arc that the hand _A_ will read correctly on the index
+_D_. Suppose, for instance, we place the jaws _B'_ inside the pallet
+staff, we then place the index arc so the hand reads to the arc
+indicated by the dotted arc _m_, Fig. 78, and if set outside of the
+pallet staff, read by the arc _o_.
+
+[Illustration: Fig. 78]
+
+
+HOW A BALANCE CONTROLS THE TIMEKEEPING OF A WATCH.
+
+We think a majority of the fine lever escapements made abroad in this
+day have what is termed double-roller safety action. The chief gains to
+be derived from this form of safety action are: (1) Reducing the arc of
+fork and roller action; (2) reducing the friction of the guard point to
+a minimum. While it is entirely practicable to use a table roller for
+holding the jewel pin with a double-roller action, still a departure
+from that form is desirable, both for looks and because as much of the
+aggregate weight of a balance should be kept as far from the axis of
+rotation as possible.
+
+We might as well consider here as elsewhere, the relation the balance
+bears to the train as a controlling power. Strictly speaking, _the
+balance and hairspring are the time measurers_, the train serving only
+two purposes: (_a_) To keep the balance in motion; (_b_) to classify and
+record the number of vibrations of the balance. Hence, it is of
+paramount importance that the vibrations of the balance should be as
+untrammeled as possible; this is why we urge reducing the arc of
+connection between the balance and fork to one as brief as is consistent
+with sound results. With a double-roller safety action we can easily
+reduce the fork action to eight degrees and the roller action to
+twenty-four degrees.
+
+Inasmuch as satisfactory results in adjustment depend very much on the
+perfection of construction, we shall now dwell to some extent on the
+necessity of the several parts being made on correct principles. For
+instance, by reducing the arc of engagement between the fork and roller,
+we lessen the duration of any disturbing influence of escapement action.
+
+To resume the explanation of why it is desirable to make the staff and
+all parts near the axis of the balance as light as possible, we would
+say it is the moving portion of the balance which controls the
+regularity of the intervals of vibration. To illustrate, suppose we have
+a balance only 3/8" in diameter, but of the same weight as one in an
+ordinary eighteen-size movement. We can readily see that such a balance
+would require but a very light hairspring to cause it to give the usual
+18,000 vibrations to the hour. We can also understand, after a little
+thought, that such a balance would exert as much breaking force on its
+pivots as a balance of the same weight, but ¾" in diameter acting
+against a very much stronger hairspring. There is another factor in the
+balance problem which deserves our attention, which factor is
+atmospheric resistance. This increases rapidly in proportion to the
+velocity.
+
+
+HOW BAROMETRIC PRESSURE AFFECTS A WATCH.
+
+The most careful investigators in horological mechanics have decided
+that a balance much above 75/100" in diameter, making 18,000 vibrations
+per hour, is not desirable, because of the varying atmospheric
+disturbances as indicated by barometric pressure. A balance with all of
+its weight as near the periphery as is consistent with strength, is what
+is to be desired for best results. It is the moving matter composing the
+balance, pitted against the elastic force of the hairspring, which we
+have to depend upon for the regularity of the timekeeping of a watch,
+and if we can take two grains' weight of matter from our roller table
+and place them in the rim or screws of the balance, so as to act to
+better advantage against the hairspring, we have disposed of these two
+grains so as to increase the efficiency of the controlling power and not
+increase the stress on the pivots.
+
+[Illustration: Fig. 79]
+
+We have deduced from the facts set forth, two axioms: (_a_) That we
+should keep the weight of our balance as much in the periphery as
+possible, consistent with due strength; (_b_) avoid excessive size from
+the disturbing effect of the air. We show at _A_, Fig. 79, the shape of
+the piece which carries the jewel pin. As shown, it consists of three
+parts: (1) The socket _A_, which receives the jewel pin _a_; (2) the
+part _A''_ and hole _b_, which goes on the balance staff; (3) the
+counterpoise _A'''_, which makes up for the weight of the jewel socket
+_A_, neck _A'_ and jewel pin. This counterpoise also makes up for the
+passing hollow _C_ in the guard roller _B_, Fig. 80. As the piece _A_
+is always in the same relation to the roller _B_, the poise of the
+balance must always remain the same, no matter how the roller action is
+placed on the staff. We once saw a double roller of nearly the shape
+shown at Fig. 79, which had a small gold screw placed at _d_, evidently
+for the purpose of poising the double rollers; but, to our thinking, it
+was a sort of hairsplitting hardly worth the extra trouble. Rollers for
+very fine watches should be poised on the staff before the balance is
+placed upon it.
+
+[Illustration: Fig. 80]
+
+We shall next give detailed instructions for drawing such a double
+roller as will be adapted for the large model previously described,
+which, as the reader will remember, was for ten degrees of roller
+action. We will also point out the necessary changes required to make it
+adapted for eight degrees of fork action. We would beg to urge again the
+advantages to be derived from constructing such a model, even for
+workmen who have had a long experience in escapements, our word for it
+they will discover a great many new wrinkles they never dreamed of
+previously.
+
+It is important that every practical watchmaker should thoroughly master
+the theory of the lever escapement and be able to comprehend and
+understand at sight the faults and errors in such escapements, which, in
+the every-day practice of his profession, come to his notice. In no
+place is such knowledge more required than in fork and roller action. We
+are led to say the above chiefly for the benefit of a class of workmen
+who think there is a certain set of rules which, if they could be
+obtained, would enable them to set to rights any and all escapements. It
+is well to understand that no such system exists and that, practically,
+we must make one error balance another; and it is the "know how" to make
+such faults and errors counteract each other that enables one workman to
+earn more for himself or his employer in two days than another workman,
+who can file and drill as well as he can, will earn in a week.
+
+
+PROPORTIONS OF THE DOUBLE-ROLLER ESCAPEMENT.
+
+The proportion in size between the two rollers in a double-roller
+escapement is an open question, or, at least, makers seldom agree on it.
+Grossmann shows, in his work on the lever escapement, two sizes: (1)
+Half the diameter of the acting roller; (2) two-thirds of the size of
+the acting roller. The chief fault urged against a smaller safety roller
+is, that it necessitates longer horns to the fork to carry out the
+safety action. Longer horns mean more metal in the lever, and it is the
+conceded policy of all recent makers to have the fork and pallets as
+light as possible. Another fault pertaining to long horns is, when the
+horn does have to act as safety action, a greater friction ensues.
+
+In all soundly-constructed lever escapements the safety action is only
+called into use in exceptional cases, and if the watch was lying still
+would theoretically never be required. Where fork and pallets are poised
+on their arbor, pocket motion (except torsional) should but very little
+affect the fork and pallet action of a watch, and torsional motion is
+something seldom brought to act on a watch to an extent to make it
+worthy of much consideration. In the double-roller action which we shall
+consider, we shall adopt three-fifths of the pitch diameter of the
+jewel-pin action as the proper size. Not but what the proportions given
+by Grossmann will do good service; but we adopt the proportions named
+because it enables us to use a light fork, and still the friction of the
+guard point on the roller is but little more than where a guard roller
+of half the diameter of the acting roller is employed.
+
+The fork action we shall consider at present is ten degrees, but
+subsequently we shall consider a double-roller action in which the fork
+and pallet action is reduced to eight degrees. We shall conceive the
+play between the guard point and the safety roller as one degree, which
+will leave half a degree of lock remaining in action on the engaged
+pallet.
+
+
+THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED.
+
+In the drawing at Fig. 81 we show a diagram of the action of the
+double-roller escapement. The small circle at _A_ represents the center
+of the pallet staff, and the one at _B_ the center of the balance staff.
+The radial lines _A d_ and _A d'_ represent the arc of angular motion of
+fork action. The circle _b b_ represents the pitch circle of the jewel
+pin, and the circle at _c c_ the periphery of the guard or safety
+roller. The points established on the circle _c c_ by intersection of
+the radial lines _A d_ and _A d'_ we will denominate the points _h_ and
+_h'_. It is at these points the end of the guard point of the fork will
+terminate. In construction, or in delineating for construction, we show
+the guard enough short of the points _h h'_ to allow the fork an angular
+motion of one degree, from _A_ as a center, before said point would come
+in contact with the safety roller.
+
+[Illustration: Fig. 81]
+
+We draw through the points _h h'_, from _B_ as a center, the radial
+lines _B g_ and _B g'_. We measure this angle by sweeping the short arc
+_i_ with any of the radii we have used for arc measurement in former
+delineations, and find it to be a trifle over sixty degrees. To give
+ourselves a practical object lesson, let us imagine that a real guard
+point rests on the circle _c_ at _h_. Suppose we make a notch in the
+guard roller represented by the circle _c_, to admit such imaginary
+guard point, and then commence to revolve the circle _c_ in the
+direction of the arrow _j_, letting the guard point rest constantly in
+such notch. When the notch _n_ in _c_ has been carried through thirty
+degrees of arc, counting from _B_ as a center, the guard point, as
+relates to _A_ as a center, would only have passed through an arc of
+five degrees. We show such a guard point and notch at _o n_. In fact, if
+a jewel pin was set to engage the fork on the pitch circle _b a_, the
+escapement would lock. To obviate such lock we widen the notch _n_ to
+the extent indicated by the dotted lines _n'_, allowing the guard point
+to fall back, so to speak, into the notch _n_, which really represents
+the passing hollow. It is not to be understood that the extended notch
+at _n_ is correctly drawn as regards position, because when the guard
+point was on the line _A f_ the point _o_ would be in the center of the
+extended notch, or passing hollow. We shall next give the details of
+drawing the double roller, but before doing so we deemed it important to
+explain the action of such guard points more fully than has been done
+heretofore.
+
+
+HOW TO DESIGN A DOUBLE-ROLLER ESCAPEMENT.
+
+We have already given very desirable forms for the parts of a
+double-roller escapement, consequently we shall now deal chiefly with
+acting principles as regards the rollers, but will give, at Fig. 82, a
+very well proportioned and practical form of fork. The pitch circle of
+the jewel pin is indicated by the dotted circle _a_, and the jewel pin
+of the usual cylindrical form, with two-fifths cut away. The safety
+roller is three-fifths of the diameter of the pitch diameter of the
+jewel-pin action, as indicated by the dotted circle _a_.
+
+The safety roller is shown in full outline at _B'_, and the passing
+hollow at _E_. It will be seen that the arc of intersection embraced
+between the radial lines _B c_ and _B d_ is about sixty-one and a half
+degrees for the roller, but the angular extent of the passing hollow is
+only a little over thirty-two degrees. The passing hollow _E_ is located
+and defined by drawing the radial line _B c_ from the center _B_ through
+the intersection of radial line _A i_ with the dotted arc _b_, which
+represents the pitch circle of the safety roller. We will name this
+intersection the point _l_. Now the end of the guard point _C_
+terminates at the point _l_, and the passing hollow _E_ extends on _b_
+sixteen degrees on each side of the radial line _B c_.
+
+[Illustration: Fig. 82]
+
+The roller action is supposed to continue through thirty degrees of
+angular motion of the balance staff, and is embraced on the circle _a_
+between the radial line _B k_ and _B o_. To delineate the inner face of
+the horn _p_ of the fork _F_ we draw the short arc _g_, from _A_ as a
+center, and on said arc locate at two degrees from the center at _B_ the
+point _f_. We will designate the upper angle of the outer face of the
+jewel pin _D_ as the point _s_ and, from _A_ as a center, sweep through
+this point _s_ the short arc _n n_. Parallel with the line _A i_ and at
+the distance of half the diameter of the jewel pin _D_, we draw the
+short lines _t t'_, which define the inner faces of the fork.
+
+The intersection of the short line _t_ with the arc _n_ we will
+designate the point _r_. With our dividers set to embrace the space
+between the point _r_ and the point _f_, we sweep the arc which defines
+the inner face of the prong of the fork. The space we just made use of
+is practically the same as the radius of the circle _a_, and
+consequently of the same curvature. Practically, the length of the guard
+point _C'_ is made as long as will, with certainty, clear the safety
+roller _B_ in all positions. While we set the point _f_ at two degrees
+from the center _B_, still, in a well-constructed escapement, one and a
+half degrees should be sufficient, but the extra half degree will do no
+harm. If the roller _B'_ is accurately made and the guard point _C'_
+properly fitted, the fork will not have half a degree of play.
+
+The reader will remember that in the escapement model we described we
+cut down the drop to one degree, being less by half a degree than
+advised by Grossmann and Saunier. We also advised only one degree of
+lock. In the perfected lever escapement, which we shall describe and
+give working drawings for the construction of, we shall describe a
+detached lever escapement with only eight degrees fork and pallet
+action, with only three-fourths of a degree drop and three-fourths of a
+degree lock, which we can assure our readers is easily within the limits
+of practical construction by modern machinery.
+
+
+HOW THE GUARD POINT IS MADE.
+
+[Illustration: Fig. 83]
+
+The guard point _C'_, as shown at Fig. 82, is of extremely simple
+construction. Back of the slot of the fork, which is three-fifths of the
+diameter of the jewel pin in depth, is made a square hole, as shown at
+_u_, and the back end of the guard point _C_ is fitted to this hole so
+that it is rigid in position. This manner of fastening the guard point
+is equally efficient as that of attaching it with a screw, and much
+lighter--a matter of the highest importance in escapement construction,
+as we have already urged. About the best material for such guard points
+is either aluminum or phosphor bronze, as such material is lighter than
+gold and very rigid and strong. At Fig. 83 we show a side view of the
+essential parts depicted in Fig. 82, as if seen in the direction of the
+arrow _v_, but we have added the piece which holds the jewel pin _D_. A
+careful study of the cut shown at Fig. 82 will soon give the horological
+student an excellent idea of the double-roller action.
+
+We will now take up and consider at length why Saunier draws his
+entrance pallet with fifteen degrees draw and his exit pallet with only
+twelve degrees draw. To make ourselves more conversant with Saunier's
+method of delineating the lever escapement, we reproduce the essential
+features of his drawing, Fig. 1, plate VIII, of his "Modern Horology,"
+in which he makes the draw of the locking face of the entrance pallet
+fifteen degrees and his exit pallet twelve degrees. In the cut shown at
+Fig. 84 we use the same letters of reference as he employs. We do not
+quote his description or directions for delineation because he refers to
+so much matter which he has previously given in the book just referred
+to. Besides we cannot entirely endorse his methods of delineations for
+many reasons, one of which appears in the drawing at Fig. 84.
+
+[Illustration: Fig. 84]
+
+
+MORE ABOUT TANGENTIAL LOCKINGS.
+
+Most writers endorse the idea of tangential lockings, and Saunier speaks
+of the escapement as shown at Fig. 84 as having such tangential
+lockings, which is not the case. He defines the position of the pallet
+staff from the circle _t_, which represents the extreme length of the
+teeth; drawing the radial lines _A D_ and _A E_ to embrace an arc of
+sixty degrees, and establishing the center of his pallet staff _C_ at
+the intersection of the lines _D C_ and _E C_, which are drawn at right
+angles to the radial lines _A D_ and _A E_, and tangential to the circle
+_t_.
+
+Here is an error; the lines defining the center of the pallet staff
+should have been drawn tangent to the circle _s_, which represents the
+locking angle of the teeth. This would have placed the center of the
+pallet staff farther in, or closer to the wheel. Any person can see at a
+glance that the pallets as delineated are not tangential in a true
+sense.
+
+[Illustration: Fig. 85]
+
+We have previously considered engaging friction and also repeatedly have
+spoken of tangential lockings, but will repeat the idea of tangential
+lockings at Fig. 85. A tangential locking is neutral, or nearly so, as
+regards engaging friction. For illustration we refer to Fig. 85, where
+_A_ represents the center of an escape wheel. We draw the radial lines
+_A y_ and _A z_ so that they embrace sixty degrees of the arcs _s_ or
+_t_, which correspond to similar circles in Fig. 84, and represent the
+extreme extent of the teeth and likewise the locking angle of such
+teeth. In fact, with the club-tooth escapement all that part of a tooth
+which extends beyond the line _s_ should be considered the same as the
+addendum in gear wheels. Consequently, a tangential locking made to
+coincide with the center of the impulse plane, as recommended by
+Saunier, would require the pallet staff to be located at _C'_ instead of
+_C_, as he draws it. If the angle _k'_ of the tooth _k_ in Fig. 84 was
+extended outward from the center _A_ so it would engage or rest on the
+locking face of the entrance pallet as shown at Fig. 84, then the draw
+of the locking angle would not be quite fifteen degrees; but it is
+evident no lock can take place until the angle _a_ of the entrance
+pallet has passed inside the circle _s_. We would say here that we have
+added the letters _s_ and _t_ to the original drawings, as we have
+frequently to refer to these circles, and without letters had no means
+of designation. Before the locking angle _k'_ of the tooth can engage
+the pallet, as shown in Fig. 84, the pallet must turn on the center _C_
+through an angular movement of at least four degrees. We show the
+situation in the diagram at Fig. 86, using the same letters of reference
+for similar parts as in Fig. 84.
+
+[Illustration: Fig. 86]
+
+As drawn in Fig. 84 the angle of draft _G a I_ is equal to fifteen
+degrees, but when brought in a position to act as shown at _G a' I'_,
+Fig. 86, the draw is less even than twelve degrees. The angle _C a I_
+remains constant, as shown at _C a' I'_, but the relation to the radial
+_A G_ changes when the pallet moves through the angle _w C w'_, as it
+must when locked. A tangential locking in the true sense of the meaning
+of the phrase is a locking set so that a pallet with its face coinciding
+with a radial line like _A G_ would be neutral, and the thrust of the
+tooth would be tangent to the circle described by the locking angle of
+the tooth. Thus the center _C_, Fig. 86, is placed on the line _w'_
+which is tangent to the circle _s_; said line _w'_ also being at right
+angles to the radial line _A G_.
+
+The facts are, the problems relating to the club-tooth lever escapement
+are very intricate and require very careful analysis, and without such
+care the horological student can very readily be misled. Faulty
+drawings, when studying such problems, lead to no end of errors, and
+practical men who make imperfect drawings lead to the popular phrase,
+"Oh, such a matter may be all right in theory, but will not work in
+practice." We should always bear in mind that _theory, if right, must
+lead practice_.
+
+
+CORRECT DRAWING REQUIRED.
+
+If we delineate our entrance pallet to have a draw of twelve degrees
+when in actual contact with the tooth, and then construct in exact
+conformity with such drawings, we will find our lever to "hug the banks"
+in every instance. It is inattention to such details which produces the
+errors of makers complained of by Saunier in section 696 of his "Modern
+Horology," and which he attempts to correct by drawing the locking face
+at fifteen degrees draw.
+
+We shall show that neither _C_ nor _C'_, Fig. 85, is the theoretically
+correct position for the pallet center for a tangential locking.
+
+We will now take up the consideration of a club-tooth lever escapement
+with circular pallets and tangential lockings; but previous to making
+the drawings we must decide several points, among which are the
+thickness of the pallet arms, which establishes the angular motion of
+the escape wheel utilized by such pallet arms, and also the angular
+motion imparted to the pallets by the impulse faces of the teeth. We
+will, for the present, accept the thickness of the arms as being
+equivalent to five degrees of angular extent of the pitch circle of the
+escape wheel.
+
+[Illustration: Fig. 87]
+
+[Illustration: Fig. 88]
+
+In making our drawings we commence, as on former occasions, by
+establishing the center of our escape wheel at _A_, Fig. 87, and
+sweeping the arc _a a_ to represent the pitch circle of such wheel.
+Through the center _A_ we draw the vertical line _A B_, which is
+supposed to also pass through the center of the pallet staff. The
+intersection of the line _A B_ with the arc _a_ we term the point _d_,
+and from this point we lay off on said arc _a_ thirty degrees each side
+of said intersection, and thus establish the points _c b_. From _A_,
+through the point _c_, we draw the line _A c c'_. On the arc _a a_ and
+two and a half degrees to the left of the point _c_ we establish the
+point _f_, which space represents half of the thickness of the entrance
+pallet. From _A_ we draw through the point _f_ the line _A f f'_. From
+_f_, and at right angles to said line _A f_, we draw the line _f e_
+until it crosses the line _A B_.
+
+Now this line _f e_ is tangent to the arc _a_ from the point _f_, and
+consequently a locking placed at the point _f_ is a true tangential
+locking; and if the resting or locking face of a pallet was made to
+coincide with the line _A f'_, such locking face would be strictly
+"dead" or neutral. The intersection of the line _f e_ with the line _A
+B_ we call the point _C_, and locate at this point the center of our
+pallet staff. According to the method of delineating the lever
+escapement by Moritz Grossmann the tangent line for locating the center
+of the pallet staff is drawn from the point _c_, which would locate the
+center of the pallet staff at the point _h_ on the line _A B_.
+
+Grossmann, in delineating his locking face for the draw, shows such face
+at an angle of twelve degrees to the radial line _A f'_, when he should
+have drawn it twelve degrees to an imaginary line shown at _f i_, which
+is at right angles to the line _f h_. To the writer's mind this is not
+just as it should be, and may lead to misunderstanding and bad
+construction. We should always bear in mind the fact that the basis of a
+locking face is a neutral plane placed at right angles to the line of
+thrust, and the "draw" comes from a locking face placed at an angle to
+such neutral plane. A careful study of the diagram at Fig. 88 will give
+the reader correct ideas. If a tooth locks at the point _c_, the
+tangential thrust would be on the line _c h'_, and a neutral locking
+face would be on the line _A c_.
+
+
+NEUTRAL LOCKINGS.
+
+To aid in explanation, let us remove the pallet center to _D_; then the
+line of thrust would be _c D_ and a neutral locking face would coincide
+with the line _m m_, which is at right angles to the line _c D_. If we
+should now make a locking face with a "draw" and at an angle to the line
+_c D_, say, for illustration, to correspond to the line _c c'_ (leaving
+the pallet center at _D_), we would have a strong draw and also a cruel
+engaging friction.
+
+If, however, we removed the engaging tooth, which we have just conceived
+to be at _c_, to the point _k_ on the arc _a' a'_, Fig. 88, the pallet
+center _D_ would then represent a tangential locking, and a neutral
+pallet face would coincide with the radial line _A k'_; and a locking
+face with twelve degrees draw would coincide nearly with the line _l_.
+Let us next analyze what the effect would be if we changed the pallet
+center to _h'_, Fig. 88, leaving the engaging tooth still at _k_. In
+this instance the line _l l_ would then coincide with a neutral locking
+face, and to obtain the proper draw we should delineate the locking face
+to correspond to the line _k n_, which we assume to be twelve degrees
+from _k l_.
+
+It is not to be understood that we insist on precisely twelve degrees
+draw from a neutral plane for locking faces for lever pallets. What we
+do insist upon, however, is a "safe and sure draw" for a lever pallet
+which will hold a fork to the banks and will also return it to such
+banks if by accident the fork is moved away. We are well aware that it
+takes lots of patient, hard study to master the complications of the
+club-tooth lever escapement, but it is every watchmaker's duty to
+conquer the problem. The definition of "lock," in the detached lever
+escapement, is the stoppage or arrest of the escape wheel of a watch
+while the balance is left free or detached to perform the greater
+portion of its arc of vibration. "Draw" is a function of the locking
+parts to preserve the fork in the proper position to receive and act on
+the jewel pin of the balance.
+
+It should be borne in mind in connection with "lock" and "draw," that
+the line of thrust as projected from the locked tooth of the escape
+wheel should be as near tangential as practicable. This maxim applies
+particularly to the entrance pallet. We would beg to add that
+practically it will make but little odds whether we plant the center of
+our pallet staff at _C_ or _h_, Fig. 87, provided we modify the locking
+and impulse angles of our pallets to conform to such pallet center. But
+it will not do to arrange the parts for one center and then change to
+another.
+
+
+PRACTICAL HINTS FOR LEVER ESCAPEMENTS.
+
+Apparently there seems to be a belief with very many watchmakers that
+there is a set of shorthand rules for setting an escapement, especially
+in American watches, which, if once acquired, conquers all
+imperfections. Now we wish to disabuse the minds of our readers of any
+such notions. Although the lever escapement, as adopted by our American
+factories, is constructed on certain "lines," still these lines are
+subject to modifications, such as may be demanded for certain defects of
+construction. If we could duplicate every part of a watch movement
+perfectly, then we could have certain rules to go by, and fixed
+templets could be used for setting pallet stones and correcting other
+escapement faults.
+
+Let us now make an analysis of the action of a lever escapement. We show
+at Fig. 89 an ordinary eighteen-size full-plate lever with fork and
+pallets. The dotted lines _a b_ are supposed to represent an angular
+movement of ten degrees. Now, it is the function of the fork to carry
+the power of the train to the balance. How well the fork performs its
+office we will consider subsequently; for the present we are dealing
+with the power as conveyed to the fork by the pallets as shown at Fig.
+89.
+
+[Illustration: Fig. 89]
+
+The angular motion between the lines _a c_ (which represents the lock)
+is not only absolutely lost--wasted--but during this movement the train
+has to retrograde; that is, the dynamic force stored in the momentum of
+the balance has to actually turn the train backward and against the
+force of the mainspring. True, it is only through a very short arc, but
+the necessary force to effect this has to be discounted from the power
+stored in the balance from a former impulse. For this reason we should
+make the angular motion of unlocking as brief as possible. Grossmann, in
+his essay, endorses one and a half degrees as the proper lock.
+
+In the description which we employed in describing the large model for
+illustrating the action of the detached lever escapement, we cut the
+lock to one degree, and in the description of the up-to-date lever
+escapement, which we shall hereafter give, we shall cut the lock down to
+three-quarters of a degree, a perfection easily to be attained by modern
+tools and appliances. We shall also cut the drop down to three-quarters
+of a degree. By these two economies we more than make up for the power
+lost in unlocking. With highly polished ruby or sapphire pallets ten
+degrees of draw is ample. But such draw must positively be ten degrees
+from a neutral locking face, not an escapement drawn on paper and
+called ten degrees, but when actually measured would only show eight and
+a half or nine degrees.
+
+
+THE PERFECTED LEVER ESCAPEMENT.
+
+With ten degrees angular motion of the lever and one and a half degrees
+lock, we should have eight and a half degrees impulse. The pith of the
+problem, as regards pallet action, for the practical workman can be
+embodied in the following question: What proportion of the power derived
+from the twelve degrees of angular motion of the escape wheel is really
+conveyed to the fork? The great leak of power as transmitted by the
+lever escapement to the balance is to be found in the pallet action, and
+we shall devote special attention to finding and stopping such leaks.
+
+
+WHEN POWER IS LOST IN THE LEVER ESCAPEMENT.
+
+If we use a ratchet-tooth escape wheel we must allow at least one and a
+half degrees drop to free the back of the tooth; but with a club-tooth
+escape wheel made as can be constructed by proper skill and care, the
+drop can be cut down to three-quarters of a degree, or one-half of the
+loss with the ratchet tooth. We do not wish our readers to imagine that
+such a condition exists in most of the so-called fine watches, because
+if we take the trouble to measure the actual drop with one of the little
+instruments we have described, it will be found that the drop is seldom
+less than two, or even three degrees.
+
+If we measure the angular movement of the fork while locked, it will
+seldom be found less than two or three degrees. Now, we can all
+understand that the friction of the locking surface has to be counted as
+well as the recoil of the draw. Locking friction is seldom looked after
+as carefully as the situation demands. Our factories make the impulse
+face of the pallets rounded, but leave the locking face flat. We are
+aware this condition is, in a degree, necessary from the use of exposed
+pallets. In many of the English lever watches with ratchet teeth, the
+locking faces are made cylindrical, but with such watches the pallet
+stones, as far as the writer has seen, are set "close"; that is, with
+steel pallet arms extending above and below the stone.
+
+There is another feature of the club-tooth lever escapement that next
+demands our attention which we have never seen discussed. We refer to
+arranging and disposing of the impulse of the escape wheel to meet the
+resistance of the hairspring. Let us imagine the dotted line _A d_, Fig.
+89, to represent the center of action of the fork. We can readily see
+that the fork in a state of rest would stand half way between the two
+banks from the action of the hairspring, and in the pallet action the
+force of the escape wheel, one tooth of which rests on the impulse face
+of a pallet, would be exerted against the elastic force of the
+hairspring. If the force of the mainspring, as represented by the
+escape-wheel tooth, is superior to the power of the hairspring, the
+watch starts itself. The phases of this important part of the detached
+lever escapement will be fully discussed.
+
+
+ABOUT THE CLUB-TOOTH ESCAPEMENT.
+
+We will now take up a study of the detached lever escapement as relates
+to pallet action, with the point specially in view of constructing an
+escapement which cannot "set" in the pocket, or, in other words, an
+escapement which will start after winding (if run down) without shaking
+or any force other than that supplied by the train as impelled by the
+mainspring. In the drawing at Fig. 90 we propose to utilize eleven
+degrees of escape-wheel action, against ten and a half, as laid down by
+Grossmann. Of this eleven degrees we propose to divide the impulse arc
+of the escape wheel in six and five degrees, six to be derived from the
+impulse face of the club tooth and five from the impulse plane of the
+pallet.
+
+The pallet action we divide into five and four, with one degree of lock.
+Five degrees of pallet action is derived from the impulse face of the
+tooth and four from the impulse face of the pallet. The reader will
+please bear in mind that we do not give these proportions as imperative,
+because we propose to give the fullest evidence into the reader's hands
+and enable him to judge for himself, as we do not believe in laying down
+imperious laws that the reader must accept on our assertion as being
+correct. Our idea is rather to furnish the proper facts and put him in a
+situation to know for himself.
+
+The reader is urged to make the drawings for himself on a large scale,
+say, an escape wheel 10" pitch diameter. Such drawings will enable him
+to realize small errors which have been tolerated too much in drawings
+of this kind. The drawings, as they appear in the cut, are one-fourth
+the size recommended, and many of the lines fail to show points we
+desire to call attention to. As for instance, the pallet center at _B_
+is tangential to the pitch circle _a_ from the point of tooth contact at
+_f_. To establish this point we draw the radial lines _A c_ and _A d_
+from the escape-wheel center _A_, as shown, by laying off thirty degrees
+on each side of the intersection of the vertical line _i_ (passing
+through the centers _A B_) with the arc _a_, and then laying off two and
+a half degrees on _a_ and establishing the point _f_, and through _f_
+from the center _A_ draw the radial line _A f'_. Through the point _f_
+we draw the tangent line _b' b b''_, and at the intersection of the line
+_b_ with _i_ we establish the center of our pallet staff at _B_. At two
+and a half degrees from the point _c_ we lay off two and a half degrees
+to the right of said point and establish the point _n_, and draw the
+radial line _A n n'_, which establishes the extent of the arc of angular
+motion of the escape wheel utilized by the pallet arm.
+
+[Illustration: Fig. 90]
+
+We have now come to the point where we must exercise our reasoning
+powers a little. We know the locking angle of the escape-wheel tooth
+passes on the arc _a_, and if we utilize the impulse face of the tooth
+for five degrees of pallet or lever motion we must shape it to this end.
+We draw the short arc _k_ through the point _n_, knowing that the inner
+angle of the pallet stone must rest on this arc wherever it is situated.
+As, for instance, when the locking face of the pallet is engaged, the
+inner angle of the pallet stone must rest somewhere on this arc (_k_)
+inside of _a_, and the extreme outer angle of the impulse face of the
+tooth must part with the pallet on this arc _k_.
+
+
+HOW TO LOCATE THE PALLET ACTION.
+
+With the parts related to each other as shown in the cut, to establish
+where the inner angle of the pallet stone is located in the drawing, we
+measure down on the arc _k_ five degrees from its intersection with _a_,
+and establish the point _s_. The line _B b_, Fig. 90, as the reader will
+see, does not coincide with the intersection of the arcs _a_ and _k_,
+and to conveniently get at the proper location for the inner angle of
+our pallet stone, we draw the line _B b'_, which passes through the
+point _n_ located at the intersection of the arc _a_ with the arc _k_.
+From _B_ as a center we sweep the short arc _j_ with any convenient
+radius of which we have a sixty-degree scale, and from the intersection
+of _B b'_ with _j_ we lay off five degrees and draw the line _B s'_,
+which establishes the point _s_ on the arc _k_. As stated above, we
+allow one degree for lock, which we establish on the arc _o_ by laying
+off one degree on the arc _j_ below its intersection with the line _B
+b_. We do not show this line in the drawing, from the fact that it comes
+so near to _B b'_ that it would confuse the reader. Above the arc _a_ on
+the arc _k_ at five degrees from the point _n_ we establish the point
+_l_, by laying off five degrees on the arc _j_ above the intersection of
+the line _B b_ with _j_.
+
+The point _l_, Fig. 90, establishes where the outer angle of the tooth
+will pass the arc _k_ to give five degrees of angular motion to the
+lever. From _A_ as a center we sweep the arc _m_, passing through the
+point _l_. The intersection of the arc _m_ with the line _A h_ we call
+the point _r_, and by drawing the right line _r f_ we delineate the
+impulse face of the tooth. On the arc _o_ and one degree below its
+intersection with the line _B b_ we establish the point _t_, and by
+drawing a right line from _t_ to _s_ we delineate the impulse face of
+our entrance pallet.
+
+
+"ACTION" DRAWINGS.
+
+One great fault with most of our text books on horology lies in the fact
+that when dealing with the detached lever escapement the drawings show
+only the position of the pallets when locked, and many of the conditions
+assumed are arrived at by mental processes, without making the proper
+drawings to show the actual relation of the parts at the time such
+conditions exist. For illustration, it is often urged that there is a
+time in the action of the club-tooth lever escapement action when the
+incline on the tooth and the incline on the pallet present parallel
+surfaces, and consequently endure excessive friction, especially if the
+oil is a little thickened.
+
+We propose to make drawings to show the exact position and relation of
+the entrance pallet and tooth at three intervals viz: (1) Locked; (2)
+the position of the parts when the lever has performed one-half of its
+angular motion; (3) when half of the impulse face of the tooth has
+passed the pallet. The position of the entrance pallet when locked is
+sufficiently well shown in Fig. 90 to give a correct idea of the
+relations with the entrance pallet; and to conform to statement (2), as
+above. We will now delineate the entrance pallet, not in actual contact,
+however, with the pallet, because if we did so the lines we employed
+would become confused. The methods we use are such that _we can
+delineate with absolute correctness either a pallet or tooth at any
+point in its angular motion_.
+
+We have previously given instructions for drawing the pallet locked; and
+to delineate the pallet after five degrees of angular motion, we have
+only to conceive that we substitute the line _s'_ for the line _b'_. All
+angular motions and measurements for pallet actions are from the center
+of the pallet staff at _B_. As we desire to now delineate the entrance
+pallet, it has passed through five degrees of angular motion and the
+inner angle _s_ now lies on the pitch circle of the escape wheel, the
+angular space between the lines _b' s'_ being five degrees, the line
+_b''_ reducing the impulse face to four degrees.
+
+
+DRAWING AN ESCAPEMENT TO SHOW ANGULAR MOTION.
+
+To delineate our locking face we draw a line at right angles to the line
+_B b''_ from the point _t_, said point being located at the intersection
+of the arc _o_ with the line _B b''_. To draw a line perpendicular to
+_B b''_ from the point _t_, we take a convenient space in our dividers and
+establish on the line _B b''_ the points _x x'_ at equal distances from
+the point _t_. We open the dividers a little (no special distance) and
+sweep the short arcs _x'' x'''_, as shown at Fig. 91. Through the
+intersection of the short arcs _x'' x'''_ and to the point _t_ we draw
+the line _t y_. The reader will see from our former explanations that
+the line _t y_ represents the neutral plane of the locking face, and
+that to have the proper draw we must delineate the locking face of our
+pallet at twelve degrees. To do this we draw the line _t x'_ at twelve
+degrees to the line _t y_, and proceed to outline our pallet faces as
+shown. We can now understand, after a moment's thought, that we can
+delineate the impulse face of a tooth at any point or place we choose by
+laying off six degrees on the arc _m_, and drawing radial lines from _A_
+to embrace such arc. To illustrate, suppose we draw the radial lines
+_w' w''_ to embrace six degrees on the arc _a_. We make these lines
+contiguous to the entrance pallet _C_ for convenience only. To delineate
+the impulse face of the tooth, we draw a line extending from the
+intersection of the radial line _A' w'_ with the arc _m_ to the
+intersection of the arc _a_ with the radial line _A w''_.
+
+[Illustration: Fig. 91]
+
+We next desire to know where contact will take place between the
+wheel-tooth _D_ and pallet _C_. To determine this we sweep, with our
+dividers set so one leg rests at the escape-wheel center _A_ and the
+other at the outer angle _t_ of the entrance pallet, the short arc _t' w_.
+Where this arc intersects the line _w_ (which represents the impulse
+face of the tooth) is where the outer angle _t_ of the entrance pallet
+_C_ will touch the impulse face of the tooth. To prove this we draw the
+radial line _A v_ through the point where the short arc _t t'_ passes
+through the impulse face _w_ of the tooth _D_. Then we continue the line
+_w_ to _n_, to represent the impulse face of the tooth, and then measure
+the angle _A w n_ between the lines _w n_ and _v A_, and find it to be
+approximately sixty-four degrees. We then, by a similar process, measure
+the angle _A t s'_ and find it to be approximately sixty-six degrees.
+When contact ensues between the tooth _D_ and pallet _C_ the tooth _D_
+will attack the pallet at the point where the radial line _A v_ crosses
+the tooth face. We have now explained how we can delineate a tooth or
+pallet at any point of its angular motion, and will next explain how to
+apply this knowledge in actual practice.
+
+
+PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT.
+
+To delineate our entrance pallet after one-half of the engaged tooth has
+passed the inner angle of the entrance pallet, we proceed, as in former
+illustrations, to establish the escape-wheel center at _A_, and from it
+sweep the arc _b_, to represent the pitch circle. We next sweep the
+short arcs _p s_, to represent the arcs through which the inner and
+outer angles of the entrance pallet move. Now, to comply with our
+statement as above, we must draw the tooth as if half of it has passed
+the arc _s_.
+
+To do this we draw from _A_ as a center the radial line _A j_, passing
+through the point _s_, said point _s_ being located at the intersection
+of the arcs _s_ and _b_. The tooth _D_ is to be shown as if one half of
+it has passed the point _s_; and, consequently, if we lay off three
+degrees on each side of the point _s_ and establish the points _d m_, we
+have located on the arc _b_ the angular extent of the tooth to be drawn.
+To aid in our delineations we draw from the center _A_ the radial lines
+_A d'_ and _A m'_, passing through the points _d m_. The arc _a_ is next
+drawn as in former instructions and establishes the length of the
+addendum of the escape-wheel teeth, the outer angle of our escape-wheel
+tooth being located at the intersection of the arc _a_ with the radial
+line _A d'_.
+
+As shown in Fig. 92, the impulse planes of the tooth _D_ and pallet _C_
+are in contact and, consequently, in parallel planes, as mentioned on
+page 91. It is not an easy matter to determine at exactly what degree of
+angular motion of the escape wheel such condition takes place; because
+to determine such relation mathematically requires a knowledge of higher
+mathematics, which would require more study than most practical men
+would care to bestow, especially as they would have but very little use
+for such knowledge except for this problem and a few others in dealing
+with epicycloidal curves for the teeth of wheels.
+
+For all practical purposes it will make no difference whether such
+parallelism takes place after eight or nine degrees of angular motion of
+the escape wheel subsequent to the locking action. The great point, as
+far as practical results go, is to determine if it takes place at or
+near the time the escape wheel meets the greatest resistance from the
+hairspring. We find by analysis of our drawing that parallelism takes
+place about the time when the tooth has three degrees of angular motion
+to make, and the pallet lacks about two degrees of angular movement for
+the tooth to escape. It is thus evident that the relations, as shown in
+our drawing, are in favor of the train or mainspring power over
+hairspring resistance as three is to two, while the average is only as
+eleven to ten; that is, the escape wheel in its entire effort passes
+through eleven degrees of angular motion, while the pallets and fork
+move through ten degrees. The student will thus see we have arranged to
+give the train-power an advantage where it is most needed to overcome
+the opposing influence of the hairspring.
+
+[Illustration: Fig. 92]
+
+As regards the exalted adhesion of the parallel surfaces, we fancy there
+is more harm feared than really exists, because, to take the worst view
+of the situation, such parallelism only exists for the briefest
+duration, in a practical sense, because theoretically these surfaces
+never slide on each other as parallel planes. Mathematically
+considered, the theoretical plane represented by the impulse face of
+the tooth approaches parallelism with the plane represented by the
+impulse face of the pallet, arrives at parallelism and instantly passes
+away from such parallelism.
+
+
+TO DRAW A PALLET IN ANY POSITION.
+
+As delineated in Fig. 92, the impulse planes of the tooth and pallet are
+in contact; but we have it in our power to delineate the pallet at any
+point we choose between the arcs _p s_. To describe and illustrate the
+above remark, we say the lines _B e_ and _B f_ embrace five degrees of
+angular motion of the pallet. Now, the impulse plane of the pallet
+occupies four of these five degrees. We do not draw a radial line from
+_B_ inside of the line _B e_ to show where the outer angle of the
+impulse plane commences, but the reader will see that the impulse plane
+is drawn one degree on the arc _p_ below the line _B e_. We continue the
+line _h h_ to represent the impulse face of the tooth, and measure the
+angle _B n h_ and find it to be twenty-seven degrees. Now suppose we
+wish to delineate the entrance pallet as if not in contact with the
+escape-wheel tooth--for illustration, say, we wish the inner angle of
+the pallet to be at the point _v_ on the arc _s_. We draw the radial
+line _B l_ through _v_; and if we draw another line so it passes through
+the point _v_ at an angle of twenty-seven degrees to _B l_, and continue
+said line so it crosses the arc _p_, we delineate the impulse face of
+our pallet.
+
+We measure the angle _i n B_, Fig. 92, and find it to be seventy-four
+degrees; we draw the line _v t_ to the same angle with _v B_, and we
+define the inner face of our pallet in the new position. We draw a line
+parallel with _v t_ from the intersection of the line _v y_ with the arc
+_p_, and we define our locking face. If now we revolve the lines we have
+just drawn on the center _B_ until the line _l B_ coincides with the
+line _f B_, we will find the line _y y_ to coincide with _h h_, and the
+line _v v'_ with _n i_.
+
+
+HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT.
+
+We have now instructed the reader how to delineate either tooth or
+pallet in any conceivable position in which they can be related to each
+other. Probably nothing has afforded more efficient aid to practical
+mechanics than has been afforded by the graphic solution of abstruce
+mathematical problems; and if we add to this the means of correction by
+mathematical calculations which do not involve the highest mathematical
+acquirements, we have approached pretty close to the actual requirements
+of the practical watchmaker.
+
+[Illustration: Fig. 93]
+
+To better explain what we mean, we refer the reader to Fig. 93, where we
+show preliminary drawings for delineating a lever escapement. We wish to
+ascertain by the graphic method the distance between the centers of
+action of the escape wheel and the pallet staff. We make our drawing
+very carefully to a given scale, as, for instance, the radius of the arc
+_a_ is 5". After the drawing is in the condition shown at Fig. 93 we
+measure the distance on the line _b_ between the points (centers) _A B_,
+and we thus by graphic means obtain a measure of the distance between _A
+B_. Now, by the use of trigonometry, we have the length of the line _A
+f_ (radius of the arc _a_) and all the angles given, to find the length
+of _f B_, or _A B_, or both _f B_ and _A B_. By adopting this policy we
+can verify the measurements taken from our drawings. Suppose we find by
+the graphic method that the distance between the points _A B_ is 5.78",
+and by trigonometrical computation find the distance to be 5.7762". We
+know from this that there is .0038" to be accounted for somewhere; but
+for all practical purposes either measurement should be satisfactory,
+because our drawing is about thirty-eight times the actual size of the
+escape wheel of an eighteen-size movement.
+
+
+HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED.
+
+Let us further suppose the diameter of our actual escape wheel to be
+.26", and we were constructing a watch after the lines of our drawing.
+By "lines," in this case, we mean in the same general form and ratio of
+parts; as, for illustration, if the distance from the intersection of
+the arc _a_ with the line _b_ to the point _B_ was one-fifteenth of the
+diameter of the escape wheel, this ratio would hold good in the actual
+watch, that is, it would be the one-fifteenth part of .26". Again,
+suppose the diameter of the escape wheel in the large drawing is 10" and
+the distance between the centers _A B_ is 5.78"; to obtain the actual
+distance for the watch with the escape wheel .26" diameter, we make a
+statement in proportion, thus: 10 : 5.78 :: .26 to the actual distance
+between the pivot holes of the watch. By computation we find the
+distance to be .15". These proportions will hold good in every part of
+actual construction.
+
+All parts--thickness of the pallet stones, length of pallet arms,
+etc.--bear the same ratio of proportion. We measure the thickness of the
+entrance pallet stone on the large drawing and find it to be .47"; we
+make a similar statement to the one above, thus: 10 : .47 :: .26 to the
+actual thickness of the real pallet stone. By computation we find it to
+be .0122". All angular relations are alike, whether in the large drawing
+or the small pallets to match the actual escape wheel .26" in diameter.
+Thus, in the pallet _D_, Fig. 93, the impulse face, as reckoned from _B_
+as a center, would occupy four degrees.
+
+
+MAKE A LARGE ESCAPEMENT MODEL.
+
+Reason would suggest the idea of having the theoretical keep pace and
+touch with the practical. It has been a grave fault with many writers on
+horological matters that they did not make and measure the abstractions
+which they delineated on paper. We do not mean by this to endorse the
+cavil we so often hear--"Oh, that is all right in theory, but it will
+not work in practice." If theory is right, practice must conform to it.
+The trouble with many theories is, they do not contain all the elements
+or factors of the problem.
+
+[Illustration: Fig. 94]
+
+Near the beginning of this treatise we advised our readers to make a
+large model, and described in detail the complete parts for such a
+model. What we propose now is to make adjustable the pallets and fork to
+such a model, in order that we can set them both right and wrong, and
+thus practically demonstrate a perfect action and also the various
+faults to which the lever escapement is subject. The pallet arms are
+shaped as shown at _A_, Fig. 94. The pallets _B B'_ can be made of steel
+or stone, and for all practical purposes those made of steel answer
+quite as well, and have the advantage of being cheaper. A plate of sheet
+brass should be obtained, shaped as shown at _C_, Fig. 95. This plate is
+of thin brass, about No. 18, and on it are outlined the pallet arms
+shown at Fig. 94.
+
+[Illustration: Fig. 95]
+
+[Illustration: Fig. 96]
+
+[Illustration: Fig. 97]
+
+[Illustration: Fig. 98]
+
+To make the pallets adjustable, they are set in thick disks of sheet
+brass, as shown at _D_, Figs. 95, 96 and 97. At the center of the plate
+_C_ is placed a brass disk _E_, Fig. 98, which serves to support the
+lever shown at Fig. 99. This disk _E_ is permanently attached to the
+plate _C_. The lever shown at Fig. 99 is attached to the disk _E_ by two
+screws, which pass through the holes _h h_. If we now place the brass
+pieces _D D'_ on the plate _C_ in such a way that the pallets set in
+them correspond exactly to the pallets as outlined on the plate _C_, we
+will find the action of the pallets to be precisely the same as if the
+pallet arms _A A'_, Fig. 94, were employed.
+
+[Illustration: Fig. 99]
+
+To enable us to practically experiment with and to fully demonstrate all
+the problems of lock, draw, drop, etc., we make quite a large hole in
+_C_ where the screws _b_ come. To explain, if the screws _b b_ were
+tapped directly into _C_, as they are shown at Fig. 95, we could only
+turn the disk _D_ on the screw _b_; but if we enlarge the screw hole in
+_C_ to three or four times the natural diameter, and then place the nut
+_e_ under _C_ to receive the screw _b_, we can then set the disks _D D'_
+and pallets _B B'_ in almost any relation we choose to the escape wheel,
+and clamp the pallets fast and try the action. We show at Fig. 97 a view
+of the pallet _B'_, disk _D'_ and plate _C_ (seen in the direction of
+the arrow _c_) as shown in Fig. 95.
+
+
+PRACTICAL LESSONS WITH FORK AND PALLET ACTION.
+
+It will be noticed in Fig. 99 that the hole _g_ for the pallet staff in
+the lever is oblong; this is to allow the lever to be shifted back and
+forth as relates to roller and fork action. We will not bother about
+this now, and only call attention to the capabilities of such
+adjustments when required. At the outset we will conceive the fork _F_
+attached to the piece _E_ by two screws passing through the holes _h h_,
+Fig. 99. Such an arrangement will insure the fork and roller action
+keeping right if they are put right at first. Fig. 100 will do much to
+aid in conveying a clear impression to the reader.
+
+The idea of the adjustable features of our escapement model is to show
+the effects of setting the pallets wrong or having them of bad form. For
+illustration, we make use of a pallet with the angle too acute, as shown
+at _B'''_, Fig. 101. The problem in hand is to find out by mechanical
+experiments and tests the consequences of such a change. It is evident
+that the angular motion of the pallet staff will be increased, and that
+we shall have to open one of the banking pins to allow the engaging
+tooth to escape. To trace out _all_ the consequences of this one little
+change would require a considerable amount of study, and many drawings
+would have to be made to illustrate the effects which would naturally
+follow only one such slight change.
+
+[Illustration: Fig. 100]
+
+[Illustration: Fig. 101]
+
+Suppose, for illustration, we should make such a change in the pallet
+stone of the entrance pallet; we have increased the angle between the
+lines _k l_ by (say) one and a half degrees; by so doing we would
+increase the lock on the exit pallet to three degrees, provided we were
+working on a basis of one and a half degrees lock; and if we pushed back
+the exit pallet so as to have the proper degree of lock (one and a half)
+on it, the tooth which would next engage the entrance pallet would not
+lock at all, but would strike the pallet on the impulse instead of on
+the locking face. Again, such a change might cause the jewel pin to
+strike the horn of the fork, as indicated at the dotted line _m_, Fig.
+99.
+
+Dealing with such and similar abstractions by mental process requires
+the closest kind of reasoning; and if we attempt to delineate all the
+complications which follow even such a small change, we will find the
+job a lengthy one. But with a large model having adjustable parts we
+provide ourselves with the means for the very best practical solution,
+and the workman who makes and manipulates such a model will soon master
+the lever escapement.
+
+
+QUIZ PROBLEMS IN THE DETACHED LEVER ESCAPEMENT.
+
+Some years ago a young watchmaker friend of the writer made, at his
+suggestion, a model of the lever escapement similar to the one
+described, which he used to "play with," as he termed it--that is, he
+would set the fork and pallets (which were adjustable) in all sorts of
+ways, right ways and wrong ways, so he could watch the results. A
+favorite pastime was to set every part for the best results, which was
+determined by the arc of vibration of the balance. By this sort of
+training he soon reached that degree of proficiency where one could no
+more puzzle him with a bad lever escapement than you could spoil a meal
+for him by disarranging his knife, fork and spoon.
+
+Let us, as a practical example, take up the consideration of a short
+fork. To represent this in our model we take a lever as shown at Fig.
+99, with the elongated slot for the pallet staff at _g_. To facilitate
+the description we reproduce at Fig. 102 the figure just mentioned, and
+also employ the same letters of reference. We fancy everybody who has
+any knowledge of the lever escapement has an idea of exactly what a
+"short fork" is, and at the same time it would perhaps puzzle them a
+good deal to explain the difference between a short fork and a roller
+too small.
+
+[Illustration: Fig. 102]
+
+[Illustration: Fig. 103]
+
+In our practical problems, as solved on a large escapement model, say we
+first fit our fork of the proper length, and then by the slot _g_ move
+the lever back a little, leaving the bankings precisely as they were.
+What are the consequences of this slight change? One of the first
+results which would display itself would be discovered by the guard pin
+failing to perform its proper functions. For instance, the guard pin
+pushed inward against the roller would cause the engaged tooth to pass
+off the locking face of the pallet, and the fork, instead of returning
+against the banking, would cause the guard pin to "ride the roller"
+during the entire excursion of the jewel pin. This fault produces a
+scraping sound in a watch. Suppose we attempt to remedy the fault by
+bending forward the guard pin _b_, as indicated by the dotted outline
+_b'_ in Fig. 103, said figure being a side view of Fig. 102 seen in the
+direction of the arrow _a_. This policy would prevent the engaged pallet
+from passing off of the locking face of the pallet, but would be
+followed by the jewel pin not passing fully into the fork, but striking
+the inside face of the prong of the fork at about the point indicated by
+the dotted line _m_. We can see that if the prong of the fork was
+extended to about the length indicated by the outline at _c_, the action
+would be as it should be.
+
+To practically investigate this matter to the best advantage, we need
+some arrangement by which we can determine the angular motion of the
+lever and also of the roller and escape wheel. To do this, we provide
+ourselves with a device which has already been described, but of smaller
+size, for measuring fork and pallet action. The device to which we
+allude is shown at Figs. 104, 105 and 106. Fig. 104 shows only the index
+hand, which is made of steel about 1/20" thick and shaped as shown. The
+jaws _B''_ are intended to grasp the pallet staff by the notches _e_,
+and hold by friction. The prongs _l l_ are only to guard the staff so it
+will readily enter the notch _e_. The circle _d_ is only to enable us to
+better hold the hand _B_ flat.
+
+[Illustration: Fig. 104]
+
+
+HOW TO MEASURE ESCAPEMENT ANGLES.
+
+From the center of the notches _e_ to the tip of the index hand _B'_ the
+length is 2". This distance is also the radius of the index arc _C_.
+This index arc is divided into thirty degrees, with three or four
+supplementary degrees on each side, as shown. For measuring pallet
+action we only require ten degrees, and for roller action thirty
+degrees. The arc _C_, Fig. 105, can be made of brass and is about 1½"
+long by ¼" wide; said arc is mounted on a brass wire about 1/8"
+diameter, as shown at _k_, Fig. 106, which is a view of Fig. 105 seen in
+the direction of the arrow _i_. This wire _k_ enters a base shown at
+_D E_, Fig. 106, which is provided with a set-screw at _j_ for holding
+the index arc at the proper height to coincide with the hand _B_.
+
+[Illustration: Fig. 105]
+
+[Illustration: Fig. 106]
+
+A good way to get up the parts shown in Fig. 106 is to take a disk of
+thick sheet brass about 1" in diameter and insert in it a piece of brass
+wire about ¼" diameter and 3/8" long, through which drill axially a
+hole to receive the wire _k_. After the jaws _B''_ are clamped on the
+pallet staff, we set the index arc _C_ so the hand _B'_ will indicate
+the angular motion of the pallet staff. By placing the index hand _B_
+on the balance staff we can get at the exact angular duration of the
+engagement of the jewel pin in the fork.
+
+Of course, it is understood that this instrument will also measure the
+angles of impulse and lock. Thus, suppose the entire angular motion of
+the lever from bank to bank is ten degrees; to determine how much of
+this is lock and how much impulse, we set the index arc _C_ so that the
+hand _B'_ marks ten degrees for the entire motion of the fork, and when
+the escapement is locked we move the fork from its bank and notice by
+the arc _C_ how many degrees the hand indicated before it passed of its
+own accord to the opposite bank. If we have more than one and a half
+degrees of lock we have too much and should seek to remedy it. How? It
+is just the answers to such questions we propose to give by the aid of
+our big model.
+
+
+DETERMINATION OF "RIGHT" METHODS.
+
+"Be sure you are right, then go ahead," was the advice of the celebrated
+Davie Crockett. The only trouble in applying this motto to watchmaking
+is to know when you are right. We have also often heard the remark that
+there was only one right way, but any number of wrong ways. Now we are
+inclined to think that most of the people who hold to but one right way
+are chiefly those who believe all ways but their own ways are wrong.
+Iron-bound rules are seldom sound even in ethics, and are utterly
+impracticable in mechanics.
+
+We have seen many workmen who had learned to draw a lever escapement of
+a given type, and lived firm in the belief that all lever escapements
+were wrong which were not made so as to conform to this certain method.
+One workman believes in equidistant lockings, another in circular
+pallets; each strong in the idea that their particular and peculiar
+method of designing a lever escapement was the only one to be tolerated.
+The writer is free to confess that he has seen lever escapements of both
+types, that is, circular pallets and equidistant lockings, which gave
+excellent results.
+
+Another mooted point in the lever escapement is, to decide between the
+merits of the ratchet and the club-tooth escape wheel. English makers,
+as a rule, hold to the ratchet tooth, while Continental and American
+manufacturers favor the club tooth. The chief arguments in favor of the
+ratchet tooth are: (_a_) It will run without oiling the pallets; (_b_)
+in case the escape wheel is lost or broken it is more readily replaced,
+as all ratchet-tooth escape wheels are alike, either for circular
+pallets or equidistant lockings. The objections urged against it are:
+(_a_) Excessive drop; (_b_) the escape wheel, being frail, is liable to
+be injured by incompetent persons handling it; (_c_) this escapement in
+many instances does require to have the pallets oiled.
+
+
+ESCAPEMENTS COMPARED.
+
+(_a_) That a ratchet-tooth escape wheel requires more drop than a club
+tooth must be admitted without argument, as this form of tooth requires
+from one-half to three-fourths of a degree more drop than a club tooth;
+(_b_) as regards the frailty of the teeth we hold this as of small
+import, as any workman who is competent to repair watches would never
+injure the delicate teeth of an escape wheel; (_c_) ratchet-tooth lever
+escapements will occasionally need to have the pallets oiled. The writer
+is inclined to think that this defect could be remedied by proper care
+in selecting the stone (ruby or sapphire) and grinding the pallets in
+such a way that the escape-wheel teeth will not act against the
+foliations with which all crystalline stones are built up.
+
+All workmen who have had an extended experience in repair work are well
+aware that there are some lever escapements in which the pallets
+absolutely require oil; others will seem to get along very nicely
+without. This applies also to American brass club-tooth escapements;
+hence, we have so much contention about oiling pallets. The writer does
+not claim to know positively that the pallet stones are at fault because
+some escapements need oiling, but the fact must admit of explanation
+some way, and is this not at least a rational solution? All persons who
+have paid attention to crystallography are aware that crystals are built
+up, and have lines of cleavage. In the manufacture of hole jewels, care
+must be taken to work with the axis of crystallization, or a smooth hole
+cannot be obtained.
+
+The advantages claimed for the club-tooth escapement are many; among
+them may be cited (_a_) the fact that it utilizes a greater arc of
+impulse of the escape wheel; (_b_) the impulse being divided between the
+tooth and the pallet, permits greater power to be utilized at the close
+of the impulse. This feature we have already explained. It is no doubt
+true that it is more difficult to match a set of pallets with an escape
+wheel of the club-tooth order than with a ratchet tooth; still the
+writer thinks that this objection is of but little consequence where a
+workman knows exactly what to do and how to do it; in other words, is
+sure he is right, and can then go ahead intelligently.
+
+It is claimed by some that all American escape wheels of a given grade
+are exact duplicates; but, as we have previously stated, this is not
+exactly the case, as they vary a trifle. So do the pallet jewels vary a
+little in thickness and in the angles. Suppose we put in a new escape
+wheel and find we have on the entrance pallet too much drop, that is,
+the tooth which engaged this pallet made a decided movement forward
+before the tooth which engaged the exit pallet encountered the locking
+face of said pallet. If we thoroughly understand the lever escapement we
+can see in an instant if putting in a thicker pallet stone for entrance
+pallet will remedy the defect. Here again we can study the effects of a
+change in our large model better than in an escapement no larger than is
+in an ordinary watch.
+
+
+HOW TO SET PALLET STONES.
+
+There have been many devices brought forward to aid the workman in
+adjusting the pallet stones to lever watches. Before going into the
+details of any such device we should thoroughly understand exactly what
+we desire to accomplish. In setting pallet stones we must take into
+consideration the relation of the roller and fork action. As has already
+been explained, the first thing to do is to set the roller and fork
+action as it should be, without regard in a great degree to pallet
+action.
+
+[Illustration: Fig. 107]
+
+To explain, suppose we have a pallet stone to set in a full-plate
+movement. The first thing to do is to close the bankings so that the
+jewel pin will not pass out of the slot in the fork on either side; then
+gradually open the bankings until the jewel pin will pass out. This will
+be understood by inspecting Fig. 107, where _A A'_ shows a lever fork as
+if in contact with both banks, and the jewel pin, represented at _B
+B''_, just passes the angle _a c'_ of the fork. The circle described by
+the jewel pin _B_ is indicated by the arc _e_. It is well to put a
+slight friction under the balance rim, in order that we can try the
+freedom of the guard pin. As a rule, all the guard pin needs is to be
+free and not touch the roller. The entire point, as far as setting the
+fork and bankings is concerned, is to have the fork and roller action
+sound. For all ordinary lever escapements the angular motion of the
+lever banked in as just described should be _about_ ten degrees. As
+explained in former examples, if the fork action is entirely sound and
+the lever only vibrates through an arc of nine degrees, it is quite as
+well to make the pallets conform to this arc as to make the jewel pin
+carry the fork through full ten degrees. Again, if the lever vibrates
+through eleven degrees, it is as well to make the pallets conform to
+this arc.
+
+The writer is well aware that many readers will cavil at this idea and
+insist that the workman should bring all the parts right on the basis of
+ten degrees fork and lever action. In reply we would say that no
+escapement is perfect, and it is the duty of the workman to get the best
+results he can for the money he gets for the job. In the instance given
+above, of the escapement with nine degrees of lever action, when the
+fork worked all right, if we undertook to give the fork the ten degrees
+demanded by the stickler for accuracy we would have to set out the jewel
+pin or lengthen the fork, and to do either would require more time than
+it would to bring the pallets to conform to the fork and roller action.
+It is just this knowing how and the decision to act that makes the
+difference in the workman who is worth to his employer twelve or
+twenty-five dollars per week.
+
+We have described instruments for measuring the angle of fork and pallet
+action, but after one has had experience he can judge pretty nearly and
+then it is seldom necessary to measure the angle of fork action as long
+as it is near the proper thing, and then bring the pallets to match the
+escape wheel after the fork and roller action is as it should be--that
+is, the jewel pin and fork work free, the guard pin has proper freedom,
+and the fork vibrates through an arc of about ten degrees.
+
+Usually the workman can manipulate the pallets to match the escape wheel
+so that the teeth will have the proper lock and drop at the right
+instant, and again have the correct lock on the next succeeding pallet.
+The tooth should fall but a slight distance before the tooth next in
+action locks it, because all the angular motion the escape wheel makes
+except when in contact with the pallets is just so much lost power,
+which should go toward giving motion to the balance.
+
+There seems to be a little confusion in the use of the word "drop" in
+horological phrase, as it is used to express the act of parting of the
+tooth with the pallet. The idea will be seen by inspecting Fig. 108,
+where we show the tooth _D_ and pallet _C_ as about parting or dropping.
+When we speak of "banking up to the drop" we mean we set the banking
+screws so that the teeth will just escape from each pallet. By the term
+"fall" we mean the arc the tooth passes through before the next pallet
+is engaged. This action is also illustrated at Fig. 108, where the tooth
+_D_, after dropping from the pallet _C_, is arrested at the position
+shown by the dotted outline. We designate this arc by the term "fall,"
+and we measure this motion by its angular extent, as shown by the dotted
+radial lines _i f_ and _i g_. As we have explained, this fall should
+only extend through an arc of one and a half degrees, but by close
+escapement matching this arc can be reduced to one degree, or even a
+trifle less.
+
+[Illustration: Fig. 108]
+
+We shall next describe an instrument for holding the escape wheel and
+pallets while adjusting them. As shown at Fig. 107, the fork _A'_ is
+banked a little close and the jewel pin as shown would, in some
+portions, rub on _C'_, making a scraping sound.
+
+
+HOW TO MAKE AN ESCAPEMENT MATCHING TOOL.
+
+[Illustration: Fig. 109]
+
+A point has now been reached where we can use an escapement matcher to
+advantage. There are several good ones on the market, but we can make
+one very cheaply and also add our own improvements. In making one, the
+first thing to be provided is a movement holder. Any of the three-jaw
+types of such holders will answer, provided the jaws hold a movement
+plate perfectly parallel with the bed of the holder. This will be better
+understood by inspecting Fig. 109, which is a side view of a device of
+this kind seen edgewise in elevation. In this _B_ represents the bed
+plate, which supports three swing jaws, shown at _C_, Figs. 109 and 110.
+The watch plate is indicated by the parallel dotted lines _A_, Fig. 109.
+The seat _a_ of the swing jaws _C_ must hold the watch plate _A_ exactly
+parallel with the bed plate _B_. In the cheap movement holders these
+seats (_a_) are apt to be of irregular heights, and must be corrected
+for our purpose. We will take it for granted that all the seats _a_ are
+of precisely the same height, measured from _B_, and that a watch plate
+placed in the jaws _C_ will be held exactly parallel with the said bed
+_B_. We must next provide two pillars, shown at _D E_, Figs. 109 and
+111. These pillars furnish support for sliding centers which hold the
+top pivots of the escape wheel and pallet staff while we are testing the
+depths and adjusting the pallet stones. It will be understood that these
+pillars _D E_ are at right angles to the plane of the bed _B_, in order
+that the slides like _G N_ on the pillars _D E_ move exactly vertical.
+In fact, all the parts moving up and down should be accurately made, so
+as not to destroy the depths taken from the watch plate _A_. Suppose, to
+illustrate, that we place the plate _A_ in position as shown, and insert
+the cone point _n_, Figs. 109 and 112, in the pivot hole for the pallet
+staff, adjusting the slide _G N_ so that the cone point rests accurately
+in said pivot hole. It is further demanded that the parts _I H F G N D_
+be so constructed and adjusted that the sliding center _I_ moves truly
+vertical, and that we can change ends with said center _I_ and place the
+hollow cone end _m_, Fig. 112, so it will receive the top pivot of the
+pallet staff and hold it exactly upright.
+
+[Illustration: Fig. 110]
+
+[Illustration: Fig. 111]
+
+[Illustration: Fig. 112]
+
+The idea of the sliding center _I_ is to perfectly supply the place of
+the opposite plate of the watch and give us exactly the same practical
+depths as if the parts were in their place between the plates of the
+movement. The foot of the pillar _D_ has a flange attached, as shown at
+_f_, which aids in holding it perfectly upright. It is well to cut a
+screw on _D_ at _D'_, and screw the flange _f_ on such screw and then
+turn the lower face of _f_ flat to aid in having the pillar _D_
+perfectly upright.
+
+
+DETAILS OF FITTING UP ESCAPEMENT MATCHER.
+
+It is well to fit the screw _D'_ loosely, so that the flange _f_ will
+come perfectly flat with the upper surface of the base plate _B_. The
+slide _G N_ on the pillar _D_ can be made of two pieces of small brass
+tube, one fitting the pillar _D_ and the other the bar _F_. The slide _G
+N_ is held in position by the set screw _g_, and the rod _F_ by the set
+screw _h_.
+
+[Illustration: Fig. 113]
+
+[Illustration: Fig. 114]
+
+The piece _H_ can be permanently attached to the rod _F_. We show
+separate at Figs. 113 and 114 the slide _G N_ on an enlarged scale from
+Fig. 109. Fig. 114 is a view of Fig. 113 seen in the direction of the
+arrow _e_. All joints and movable parts should work free, in order that
+the center _I_ may be readily and accurately set. The parts _H F_ are
+shown separate and enlarged at Figs. 115 and 116. The piece _H_ can be
+made of thick sheet brass securely attached to _F_ in such a way as to
+bring the V-shaped groove at right angles to the axis of the rod _F_. It
+is well to make the rod _F_ about 1/8" in diameter, while the sliding
+center _I_ need not be more than 1/16" in diameter. The cone point _n_
+should be hardened to a spring temper and turned to a true cone in an
+accurately running wire chuck.
+
+[Illustration: Fig. 115]
+
+[Illustration: Fig. 116]
+
+The hollow cone end _m_ of _I_ should also be hardened, but this is best
+done after the hollow cone is turned in. The hardening of both ends
+should only be at the tips. The sliding center _I_ can be held in the
+V-shaped groove by two light friction springs, as indicated at the
+dotted lines _s s_, Fig. 115, or a flat plate of No. 24 or 25 sheet
+brass of the size of _H_ can be employed, as shown at Figs. 116 and 117,
+where _o_ represents the plate of No. 24 brass, _p p_ the small screws
+attaching the plate _o_ to _H_, and _k_ a clamping screw to fasten _I_
+in position. It will be found that the two light springs _s s_, Fig. 115
+will be the most satisfactory. The wire legs, shown at _L_, will aid in
+making the device set steady. The pillar _E_ is provided with the same
+slides and other parts as described and illustrated as attached to _D_.
+The position of the pillars _D_ and _E_ are indicated at Fig. 110.
+
+[Illustration: Fig. 117]
+
+[Illustration: Fig. 118]
+
+We will next tell how to flatten _F_ to keep _H_ exactly vertical. To
+aid in explanation, we will show (enlarged) at Fig. 118 the bar _F_
+shown in Fig. 109. In flattening such pieces to prevent turning, we
+should cut away about two-fifths, as shown at Fig. 119, which is an end
+view of Fig. 118 seen in the direction of the arrow _c_. In such
+flattening we should not only cut away two-fifths at one end, but we
+must preserve this proportion from end to end. To aid in this operation
+we make a fixed gage of sheet metal, shaped as shown at _I_, Fig. 120.
+
+[Illustration: Fig. 119]
+
+
+ESCAPEMENT MATCHING DEVICE DESCRIBED.
+
+[Illustration: Fig. 120]
+
+In practical construction we first file away about two-fifths of _F_ and
+then grind the flat side on a glass slab to a flat, even surface and, of
+course, equal thickness from end to end. We reproduce the sleeve _G_ as
+shown at Fig. 113 as if seen from the left and in the direction of the
+axis of the bar _F_. To prevent the bar _F_ turning on its axis, we
+insert in the sleeve _G_ a piece of wire of the same size as _F_ but
+with three-fifths cut away, as shown at _y_, Fig. 121. This piece _y_ is
+soldered in the sleeve _G_ so its flat face stands vertical. To give
+service and efficiency to the screw _h_, we thicken the side of the
+sleeve _F_ by adding the stud _w_, through which the screw _h_ works. A
+soft metal plug goes between the screw _h_ and the bar _F_, to prevent
+_F_ being cut up and marred. It will be seen that we can place the top
+plate of a full-plate movement in the device shown at Fig. 109 and set
+the vertical centers _I_ so the cone points _n_ will rest in the pivot
+holes of the escape wheel and pallets. It is to be understood that the
+lower side of the top plate is placed uppermost in the movement holder.
+
+[Illustration: Fig. 121]
+
+If we now reverse the ends of the centers _I_ and let the pivots of the
+escape wheel and pallet staff rest in the hollow cones of these centers
+_I_, we have the escape wheel and pallets in precisely the same position
+and relation to each other as if the lower plate was in position. It is
+further to be supposed that the balance is in place and the cock screwed
+down, although the presence of the balance is not absolutely necessary
+if the banking screws are set as directed, that is, so the jewel pin
+will just freely pass in and out of the fork.
+
+
+HOW TO SET PALLET STONES.
+
+We have now come to setting or manipulating the pallet stones so they
+will act in exact conjunction with the fork and roller. To do this we
+need to have the shellac which holds the pallet stones heated enough to
+make it plastic. The usual way is to heat a piece of metal and place it
+in close proximity to the pallets, or to heat a pair of pliers and clamp
+the pallet arms to soften the cement.
+
+Of course, it is understood that the movement holder cannot be moved
+about while the stones are being manipulated. The better way is to set
+the movement holder on a rather heavy plate of glass or metal, so that
+the holder will not jostle about; then set the lamp so it will do its
+duty, and after a little practice the setting of a pair of pallet stones
+to perfectly perform their functions will take but a few minutes. In
+fact, if the stones will answer at all, three to five minutes is as much
+time as one could well devote to the adjustment. The reader will see
+that if the lever is properly banked all he has to do is to set the
+stones so the lock, draw and drop are right, when the entire escapement
+is as it should be, and will need no further trial or manipulating.
+
+
+
+
+CHAPTER II.
+
+THE CYLINDER ESCAPEMENT.
+
+
+There is always in mechanical matters an underlying combination of
+principles and relations of parts known as "theory." We often hear the
+remark made that such a thing may be all right in theory, but will not
+work in practice. This statement has no foundation in fact. If a given
+mechanical device accords strictly with theory, it will come out all
+right practically. _Mental conceptions_ of a machine are what we may
+term their theoretical existence.
+
+When we make drawings of a machine mentally conceived, we commence its
+mechanical construction, and if we make such drawings to scale, and add
+a specification stating the materials to be employed, we leave only the
+merest mechanical details to be carried out; the brain work is done and
+only finger work remains to be executed.
+
+With these preliminary remarks we will take up the consideration of the
+cylinder escapement invented by Robert Graham about the year 1720. It is
+one of the two so-called frictional rest dead-beat escapements which
+have come into popular use, the other being the duplex. Usage, or, to
+put it in other words, experience derived from the actual manufacture of
+the cylinder escapement, settled the best forms and proportions of the
+several parts years ago. Still, makers vary slightly on certain lines,
+which are important for a man who repairs such watches to know and be
+able to carry out, in order to put them in a condition to perform as
+intended by the manufacturers. It is not knowing these lines which
+leaves the average watchmaker so much at sea. He cuts and moves and
+shifts parts about to see if dumb luck will not supply the correction he
+does not know how to make. This requisite knowledge does not consist so
+much in knowing how to file or grind as it does in discriminating where
+such application of manual dexterity is to be applied. And right here
+let us make a remark to which we will call attention again later on. The
+point of this remark lies in the question--How many of the so-called
+practical watchmakers could tell you what proportion of a cylinder
+should be cut away from the half shell? How many could explain the
+difference between the "real" and "apparent" lift? Comparatively few,
+and yet a knowledge of these things is as important for a watchmaker as
+it is for a surgeon to understand the action of a man's heart or the
+relations of the muscles to the bones.
+
+
+ESSENTIAL PARTS OF THE CYLINDER ESCAPEMENT.
+
+The cylinder escapement is made up of two essential parts, viz.: the
+escape wheel and the cylinder. The cylinder escape wheel in all modern
+watches has fifteen teeth, although Saunier, in his "Modern Horology,"
+delineates a twelve-tooth wheel for apparently no better reason than
+because it was more easily drawn. We, in this treatise, will consider
+both the theoretical action and the practical construction, but more
+particularly the repair of this escapement in a thorough and complete
+manner.
+
+At starting out, we will first agree on the names of the several parts
+of this escapement, and to aid us in this we will refer to the
+accompanying drawings, in which Fig. 122 is a side elevation of a
+cylinder complete and ready to have a balance staked on to it. Fig. 123
+shows the cylinder removed from the balance collet. Figs. 124 and 125
+show the upper and lower plugs removed from the cylinder. Fig. 126 is a
+horizontal section of Fig. 122 on the line _i_. Fig. 127 is a side view
+of one tooth of a cylinder escape wheel as if seen in the direction of
+the arrow _f_ in Fig. 126. Fig. 128 is a top view of two teeth of a
+cylinder escape wheel. The names of the several parts usually employed
+are as follows:
+
+         _A._--Upper or Main Shell.
+        _A'._--Half Shell.
+       _A''._--Column.
+      _A'''._--Small Shell.
+  _B B' B''._--Balance Collet.
+         _G._--Upper Plug.
+         _H._--Lower Plug.
+         _g._--Entrance Lip of Cylinder.
+         _h._--Exit Lip of Cylinder.
+         _c._--Banking Slot.
+         _C._--Tooth.
+         _D._--U arm.
+         _E._--Stalk of Pillar.
+         _I._--U space.
+         _l._--Point of Tooth.
+         _k._--Heel of Tooth.
+
+The cylinder escapement has two engagements or actions, during the
+passage of each tooth; that is, one on the outside of the cylinder and
+one on the inside of the shell. As we shall show later on, the cylinder
+escapement is the only positively dead-beat escapement in use, all
+others, even the duplex, having a slight recoil during the process of
+escaping.
+
+When the tooth of a cylinder escape wheel while performing its
+functions, strikes the cylinder shell, it rests dead on the outer or
+inner surface of the half shell until the action of the balance spring
+has brought the lip of the cylinder so that the impulse face of the
+tooth commences to impart motion or power to the balance.
+
+[Illustration: Fig. 122]
+
+[Illustration: Fig. 123]
+
+[Illustration: Fig. 124]
+
+[Illustration: Fig. 125]
+
+[Illustration: Fig. 126]
+
+[Illustration: Fig. 127]
+
+[Illustration: Fig. 128]
+
+Most writers on horological matters term this act the "lift," which name
+was no doubt acquired when escapements were chiefly confined to pendulum
+clocks. Very little thought on the matter will show any person who
+inspects Fig. 126 that if the tooth _C_ is released or escapes from the
+inside of the half shell of the cylinder _A_, said cylinder must turn or
+revolve a little in the direction of the arrow _j_, and also that the
+next succeeding tooth of the escape wheel will engage the cylinder on
+the outside of the half shell, falling on the dead or neutral portion of
+said cylinder, to rest until the hairspring causes the cylinder to turn
+in the opposite direction and permitting the tooth now resting on the
+outside of the cylinder to assume the position shown on the drawing.
+
+The first problem in our consideration of the theoretical action of the
+cylinder escapement, is to arrange the parts we have described so as to
+have these two movements of the escape wheel of like angular values. To
+explain what we mean by this, we must premise by saying, that as our
+escape wheel has fifteen teeth and we make each tooth give two impulses
+in alternate directions we must arrange to have these half-tooth
+movements exactly alike, or, as stated above, of equal angular values;
+and also each impulse must convey the same power or force to the
+balance. All escape wheels of fifteen teeth acting by half impulses must
+impel the balance during twelve degrees (minus the drop) of escape-wheel
+action; or, in other words, when a tooth passes out of the cylinder from
+the position shown at Fig. 126, the form of the impulse face of the
+tooth and the shape of the exit lip of the cylinder must be such during
+twelve degrees (less the drop) of the angular motion of the escape
+wheel. The entire power of such an escape wheel is devoted to giving
+impulse to the balance.
+
+The extent of angular motion of the balance during such impulse is, as
+previously stated, termed the "lifting angle." This "lifting angle" is
+by horological writers again divided into real and apparent lifts. This
+last division is only an imaginary one, as the real lift is the one to
+be studied and expresses the arc through which the impulse face of the
+tooth impels the balance during the act of escaping, and so, as we shall
+subsequently show, should no more be counted than in the detached lever
+escapement, where a precisely similar condition exists, but is never
+considered or discussed.
+
+We shall for the present take no note of this lifting angle, but confine
+ourselves to the problem just named, of so arranging and designing our
+escape-wheel teeth and cylinder that each half of the tooth space shall
+give equal impulses to the balance with the minimum of drop. To do this
+we will make a careful drawing of an escape-wheel tooth and cylinder on
+an enlarged scale; our method of making such drawings will be on a new
+and original system, which is very simple yet complete.
+
+
+DRAWING THE CYLINDER ESCAPEMENT.
+
+All horological--and for that matter all mechanical--drawings are based
+on two systems of measurements: (1) Linear extent; (2) angular movement.
+For the first measurement we adopt the inch and its decimals; for the
+second we adopt degrees, minutes and seconds. For measuring the latter
+the usual plan is to employ a protractor, which serves the double
+purpose of enabling us to lay off and delineate any angle and also to
+measure any angle obtained by the graphic method, and it is thus by this
+graphic method we propose to solve very simply some of the most
+abstruce problems in horological delineations. As an instance, we
+propose to draw our cylinder escapement with no other instruments than a
+steel straight-edge, showing one-hundredths of an inch, and a pair of
+dividers; the degree measurement being obtained from arcs of sixty
+degrees of radii, as will be explained further on.
+
+In describing the method for drawing the cylinder escapement we shall
+make a radical departure from the systems usually laid down in
+text-books, and seek to simplify the formulas which have heretofore been
+given for such delineations. In considering the cylinder escapement we
+shall pursue an analytical course and strive to build up from the
+underlying principles. In the drawings for this purpose we shall
+commence with one having an escape wheel of 10" radius, and our first
+effort will be the primary drawing shown at Fig. 129. Here we establish
+the point _A_ for the center of our escape wheel, and from this center
+sweep the short arc _a a_ with a 10" radius, to represent the
+circumference of our escape wheel. From _A_ we draw the vertical line
+_A B_, and from the intersection of said line with the arc _a a_ we lay
+off twelve degree spaces on each side of the line _A B_ on said arc _a_
+and establish the points _b c_. From _A_ as a center we draw through
+the points _b c_ the radial lines _b' c'_.
+
+To define the face of the incline to the teeth we set our dividers to
+the radius of any of the convenient arcs of sixty degrees which we have
+provided, and sweep the arc _t t_. From the intersection of said arc
+with the line _A b'_ we lay off on said arc sixty-four degrees and
+establish the point _g_ and draw the line _b g_. Why we take sixty-four
+degrees for the angle _A b g_ will be explained later on, when we are
+discussing the angular motion of the cylinder. By dividing the eleventh
+degree from the point _b_ on the arc _a a_ into thirds and taking two of
+them, we establish the point _y_ and draw the radial line _A y'_. Where
+this line _A y'_ intersects the line _b g_ we name the point _n_, and in
+it is located the point of the escape-wheel tooth. That portion of the
+line _b g_ which lies between the points _b_ and _n_ represents the
+measure of the inner diameter of the cylinder, and also the length of
+the chord of the arc which rounds the impulse face of the tooth. We
+divide the space _b n_ into two equal portions and establish the point
+_e_, which locates the position of the center of the cylinder. From _A_
+as a center and through the point _e_ we sweep the arc _e' e'_, and it
+is on this line that the points establishing the center of the cylinder
+will in every instance be located. From _A_ as a center, through the
+point _n_ we sweep the arc _k_, and on this line we locate the points of
+the escape-wheel teeth. For delineating the curved impulse faces of the
+escape-wheel teeth we draw from the point _e_ and at right angles to the
+line _b g_ the line _e o_. We next take in our dividers the radius of
+the arc _k_, and setting one leg at either of the points _b_ or _n_,
+establish with the other leg the point _p'_ on the line _e o_, and from
+the point _p'_ as a center we sweep the arc _b v n_, which defines the
+curve of the impulse faces of the teeth. From _A_ as a center through
+the point _p'_ we sweep the arc _p_, and in all instances where we
+desire to delineate the curved face of a tooth we locate either the
+position of the point or the heel of such tooth, and setting one leg of
+our dividers at such point, the other leg resting on the arc _p_, we
+establish the center from which to sweep the arc defining the face of
+said tooth.
+
+
+ADVANTAGES GAINED IN SHAPING.
+
+The reason for giving a curved form to the impulse face of the teeth of
+cylinder escape wheels are somewhat intricate, and the problem involves
+several factors. That there are advantages in so shaping the incline or
+impulse face is conceded, we believe, by all recent manufacturers. The
+chief benefit derived from such curved impulse faces will be evident
+after a little thought and study of the situation and relation of parts
+as shown in Fig. 129. It will be seen on inspection that the angular
+motion imparted to the cylinder by the impulse face of the tooth when
+curved as shown, is greater during the first half of the twelve degrees
+of escape-wheel action than during the last half, thus giving the escape
+wheel the advantage at the time the balance spring increases its
+resistance to the passage of the escape-wheel tooth across the lip of
+the cylinder. Or, in other words, as the ratio of resistance of the
+balance spring increases, in a like ratio the curved form of the impulse
+face of the tooth gives greater power to the escape-wheel action in
+proportion to the angular motion of the escape wheel. Hence, in actual
+service it is found that cylinder watches with curved impulse planes to
+the escape-wheel teeth are less liable to set in the pocket than the
+teeth having straight impulse faces.
+
+
+THE OUTER DIAMETER OF THE CYLINDER.
+
+[Illustration: Fig. 129]
+
+To define the remainder of the form of our escape-wheel tooth we will
+next delineate the heel. To do this we first define the outer diameter
+of our cylinder, which is the extent from the point _n_ to _c_, and
+after drawing the line _n c_ we halve the space and establish the point
+_x_, from which point as a center we sweep the circle _w w_, which
+defines the outer circumference of our cylinder. With our dividers set
+to embrace the extent from the point _n_ to the point _c_ we set one leg
+at the point _b_, and with the other leg establish on the arc _k_ the
+point _h_. We next draw the line _b h_, and from the point _b_ draw the
+line _b f_ at right angle to the line _b h_. Our object for drawing
+these lines is to define the heel of our escape-wheel tooth by a right
+angle line tangent to the circle _w_, from the point _b_; which circle
+_w_ represents the curve of the outer circumference of the cylinder. We
+shape the point of the tooth as shown to give it the proper stability,
+and draw the full line _j_ to a curve from the center _A_. We have now
+defined the form of the upper face of the tooth. How to delineate the U
+arms will be taken up later on, as, in the present case, the necessary
+lines would confuse our drawing.
+
+We would here take the opportunity to say that there is a great latitude
+taken by makers as regards the extent of angular impulse given to the
+cylinder, or, as it is termed, the "actual lift." This latitude governs
+to a great extent the angle _A b g_, which we gave as sixty-four degrees
+in our drawing. It is well to understand that the use of sixty-four
+degrees is based on no hard-and-fast rules, but varies back and forth,
+according as a greater or lesser angle of impulse or lift is employed.
+
+In practical workshop usage the impulse angle is probably more easily
+estimated by the ratio between the diameter of the cylinder and the
+measured (by lineal measure) height of the impulse plane. Or, to be more
+explicit, we measure the radial extent from the center _A_ between the
+arcs _a k_ on the line _A b_, and use this for comparison with the outer
+diameter of the cylinder.
+
+We can readily see that as we increase the height of the heel of the
+impulse face of our tooth we must also increase the angle of impulse
+imparted to the cylinder. With the advantages of accurate micrometer
+calipers now possessed by the horological student it is an easy matter
+to get at the angular extent of the real lift of any cylinder. The
+advantage of such measuring instruments is also made manifest in
+determining when the proper proportion of the cylinder is cut away for
+the half shell.
+
+[Illustration: Fig. 130]
+
+In the older methods of watchmaking it was a very common rule to say,
+let the height of the incline of the tooth be one-seventh of the outer
+diameter of the cylinder, and at the same time the trade was furnished
+with no tools except a clumsy douzieme gage; but with micrometer
+calipers which read to one-thousandths of an inch such rules can be
+definitely carried into effect and not left to guess work. Let us
+compare the old method with the new: Suppose we have a new cylinder to
+put in; we have the old escape wheel, but the former cylinder is gone.
+The old-style workman would take a round broach and calculate the size
+of the cylinder by finding a place where the broach would just go
+between the teeth, and the size of the broach at this point was supposed
+to be the outer diameter of the cylinder. By our method we measure the
+diameter of the escape wheel in thousandths of an inch, and from this
+size calculate exactly what the diameter of the new cylinder should be
+in thousandths of an inch. Suppose, to further carry out our comparison,
+the escape wheel which is in the watch has teeth which have been stoned
+off to permit the use of a cylinder which was too small inside, or, in
+fact, of a cylinder too small for the watch: in this case the broach
+system would only add to the trouble and give us a cylinder which would
+permit too much inside drop.
+
+
+DRAWING A CYLINDER.
+
+We have already instructed the pupil how to delineate a cylinder escape
+wheel tooth and we will next describe how to draw a cylinder. As already
+stated, the center of the cylinder is placed to coincide with the center
+of the chord of the arc which defines the impulse face of the tooth.
+Consequently, if we design a cylinder escape wheel tooth as previously
+described, and setting one leg of our compasses at the point _e_ which
+is situated at the center of the chord of the arc which defines the
+impulse face of the tooth and through the points _d_ and _b_ we define
+the inside of our cylinder. We next divide the chord _d b_ into eight
+parts and set our dividers to five of these parts, and from _e_ as a
+center sweep the circle _h_ and define the outside of our cylinder. From
+_A_ as a center we draw the radial line _A e'_. At right angles to the
+line _A e'_ and through the point _e_ we draw the line from _e_ as a
+center, and with our dividers set to the radius of any of the convenient
+arcs which we have divided into sixty degrees, we sweep the arc _i_.
+Where this arc intersects the line _f_ we term the point _k_, and from
+this point we lay off on the arc _i_ 220 degrees, and draw the line
+_l e l'_, which we see coincides with the chord of the impulse face of the
+tooth. We set our dividers to the same radius by which we sweep the arc
+_i_ and set one leg at the point _b_ for a center and sweep the arc
+_j'_. If we measure this arc from the point _j'_ to intersection of said
+arc _j'_ with the line _l_ we will find it to be sixty-four degrees,
+which accounts for our taking this number of degrees when we defined the
+face of our escape-wheel tooth, Fig. 129.
+
+There is no reason why we should take twenty-degrees for the angle _k e
+l_ except that the practical construction of the larger sizes of
+cylinder watches has established the fact that this is about the right
+angle to employ, while in smaller watches it frequently runs up as high
+as twenty-five. Although the cylinder is seemingly a very simple
+escapement, it is really a very abstruce one to follow out so as to
+become familiar with all of its actions.
+
+
+THE CYLINDER PROPER CONSIDERED.
+
+[Illustration: Fig. 131]
+
+We will now proceed and consider the cylinder proper, and to aid us in
+understanding the position and relation of the parts we refer to Fig.
+131, where we repeat the circles _d_ and _h_, shown in Fig. 130, which
+represents the inside and outside of the cylinder. We have here also
+repeated the line _f_ of Fig. 130 as it cuts the cylinder in half, that
+is, divides it into two segments of 180 degrees each. If we conceive of
+a cylinder in which just one-half is cut away, that is, the lips are
+bounded by straight radial lines, we can also conceive of the relation
+and position of the parts shown in Fig. 130. The first position of which
+we should take cognizance is, the tooth _D_ is moved back to the left so
+as to rest on the outside of our cylinder. The cylinder is also supposed
+to stand so that the lips correspond to the line _f_. On pressing the
+tooth _D_ forward the incline of the tooth would attack the entrance
+lip of the cylinder at just about the center of the curved impulse face,
+imparting to the cylinder twenty degrees of angular motion, but the
+point of the tooth at _d_ would exactly encounter the inner angle of the
+exit lip, and of course the cylinder would afford no rest for the tooth;
+hence, we see the importance of not cutting away too much of the half
+shell of the cylinder.
+
+But before we further consider the action of the tooth _D_ in its action
+as it passes the exit lip of the cylinder we must finish with the action
+of the tooth on the entrance lip. A very little thought and study of
+Fig. 130 will convince us that the incline of the tooth as it enters the
+cylinder will commence at _t_, Fig. 130, but at the close of the action
+the tooth parts from the lip on the inner angle. Now it is evident that
+it would require greater force to propel the cylinder by its inner angle
+than by the outer one. To compensate for this we round the edge of the
+entrance lip so that the action of the tooth instead of commencing on
+the outer angle commences on the center of the edge of the entrance lip
+and also ends its action on the center of the entrance lip. To give
+angular extent enough to the shell of the cylinder to allow for rounding
+and also to afford a secure rest for the tooth inside the cylinder, we
+add six degrees to the angular extent of the entrance lip of the
+cylinder shell, as indicated on the arc _o'_, Fig. 131, three of these
+degrees being absorbed for rounding and three to insure a dead rest for
+the tooth when it enters the cylinder.
+
+
+WHY THE ANGULAR EXTENT IS INCREASED.
+
+Without rounding the exit lip the action of the tooth on its exit would
+be entirely on the inner angle of the shell. To obviate this it is the
+usual practice to increase the angular extent of the cylinder ten
+degrees, as shown on the arc _o'_ between the lines _f_ and _p_, Fig.
+131. Why we should allow ten degrees on the exit lip and but six degrees
+on the entrance lip will be understood by observing Fig. 130, where the
+radial lines _s_ and _r_ show the extent of angular motion of the
+cylinder, which would be lost if the tooth commenced to act on the inner
+angle and ended on the outer angle of the exit lip. This arc is a little
+over six degrees, and if we add a trifle over three degrees for rounding
+we would account for the ten degrees between the lines _f_ and _p_, Fig.
+131. It will now be seen that the angular extent is 196 degrees. If we
+draw the line _w_ we can see in what proportion the measurement should
+be made between the outer diameter of the cylinder and the measure of
+the half shell. It will be seen on measurement that the distance between
+the center _e_ and the line _w_ is about one-fifteenth part of the outer
+diameter of the cylinder and consequently with a cylinder which measures
+45/1000 of an inch in diameter, now the half shell should measure half
+of the entire diameter of the cylinder plus one-fifteenth part of such
+diameter, or 25½ thousandths of an inch.
+
+After these proportions are understood and the drawing made, the eye
+will get accustomed to judging pretty near what is required; but much
+the safer plan is to measure, where we have the proper tools for doing
+so. Most workmen have an idea that the depth or distance at which the
+cylinder is set from the escape wheel is a matter of adjustment; while
+this is true to a certain extent, still there is really only one
+position for the center of the cylinder, and that is so that the center
+of the pivot hole coincides exactly with the center of the chord to the
+curve of the impulse face of the tooth or the point _e_, Fig. 130. Any
+adjustment or moving back and forth of the chariot to change the depth
+could only be demanded where there was some fault existing in the
+cylinder or where it had been moved out of its proper place by some
+genius as an experiment in cylinder depths. It will be evident on
+observing the drawing at Fig. 131 that when the cylinder is performing
+an arc of vibration, as soon as the entrance lip has passed the point
+indicated by the radial line _e x_ the point of the escape-wheel tooth
+will commence to act on the cylinder lip and continue to do so through
+an arc of forty degrees, or from the lines _x_ to _l_.
+
+
+MAKING A WORKING MODEL.
+
+To practically study the action of the cylinder escapement it is well to
+make a working model. It is not necessary that such a model should
+contain an entire escape wheel; all that is really required is two teeth
+cut out of brass of the proper forms and proportions and attached to the
+end of an arm 4-7/8" long with studs riveted to the U arms to support
+the teeth. This U arm is attached to the long arm we have just
+mentioned. A flat ring of heavy sheet brass is shaped to represent a
+short transverse section of a cylinder. This segment is mounted on a
+yoke which turns on pivots. In making such a model we can employ all the
+proportions and exact forms of the larger drawings made on a ten-inch
+radius. Such a model becomes of great service in learning the
+importance of properly shaping the lips of the cylinder. And right here
+we beg to call attention to the fact that in the ordinary repair shop
+the proper shape of cylinder lips is entirely neglected.
+
+
+PROPER SHAPE OF CYLINDER LIPS.
+
+The workman buys a cylinder and whether the proper amount is cut away
+from the half shell, or the lips, the correct form is entirely ignored,
+and still careful attention to the form of the cylinder lips adds full
+ten per cent. to the efficiency of the motive force as applied to the
+cylinder. In making study drawings of the cylinder escapement it is not
+necessary to employ paper so large that we can establish upon it the
+center of the arc which represents the periphery of our escape wheel, as
+we have at our disposal two plans by which this can be obviated. First,
+placing a bit of bristol board on our drawing-board in which we can set
+one leg of our dividers or compasses when we sweep the peripheral arc
+which we use in our delineations; second, making three arcs in brass or
+other sheet metal, viz.: the periphery of the escape wheel, the arc
+passing through the center of the chord of the arc of the impulse face
+of the tooth, and the arc passing through the point of the escape-wheel
+tooth. Of these plans we favor the one of sticking a bit of cardboard on
+the drawing board outside of the paper on which we are making our
+drawing.
+
+[Illustration: Fig. 132]
+
+At Fig. 132 we show the position and relation of the several parts just
+as the tooth passes into the shell of the cylinder, leaving the lip of
+the cylinder just as the tooth parted with it. The half shell of the
+cylinder as shown occupies 196 degrees or the larger arc embraced
+between the radial lines _k_ and _l_. In drawing the entrance lip the
+acting face is made almost identical with a radial line except to round
+the corners for about one-third the thickness of the cylinder shell. No
+portion, however, of the lip can be considered as a straight line, but
+might be described as a flattened curve.
+
+[Illustration: Fig. 133]
+
+A little study of what would be required to get the best results after
+making such a drawing will aid the pupil in arriving at the proper
+shape, especially when he remembers that the thickness of the cylinder
+shell of a twelve-line watch is only about five one-thousandths of an
+inch. But because the parts are small we should not shirk the problem of
+getting the most we possibly can out of a cylinder watch.
+
+The extent of arc between the radial lines _k f_, as shown in Fig. 132,
+is four degrees. Although in former drawings we showed the angular
+extent added as six degrees, as we show the lip _m_ in Fig. 132, two
+degrees are lost in rounding. The space _k f_ on the egress or exit side
+is intended to be about four degrees, which shows the extent of lock. We
+show at Fig. 133 the tooth _D_ just having passed out of the cylinder,
+having parted with the exit lip _p_.
+
+In making this drawing we proceed as with Fig. 132 by establishing a
+center for our radius of 10" outside of our drawing paper and drawing
+the line _A A_ to such center and sweeping the arcs _a b c_. We
+establish the point _e_, which represents the center of our cylinder, as
+before. We take the space to represent the radial extent of the outside
+of our cylinder in our dividers and from _e_ as a center sweep a fine
+pencil line, represented by the dotted line _t_ in our drawing; and
+where this circle intersects the arc _a_ we name it the point _s_; and
+it is at this point the heel of our escape-wheel tooth must part with
+the exit lip of the cylinder. From _e_ as a center and through the point
+_s_ we draw the line _e l''_. With our dividers set to the radius of any
+convenient arc which we have divided into degrees, we sweep the short
+arc _d'_. The intersection of this arc with the line _e l''_ we name the
+point _u_; and from _e_ as a center we draw the radial line _e u f'_. We
+place the letter _f''_ in connection with this line because it (the
+line) bears the same relations to the half shell of the cylinder shown
+in Fig. 133 that the line _f_ does to the half shell (_D_) shown in Fig.
+132. We draw the line _f'' f'''_, Fig. 133, which divides the cylinder
+into two segments of 180 degrees each. We take the same space in our
+dividers with which we swept the interior of the cylinder in Fig. 132
+and sweep the circle _v_, Fig. 133. From _e_ as a center we sweep the
+short arc _d''_, Fig. 133, and from its intersection of the line _f''_
+we lay off six degrees on said arc _d''_ and draw the line _e' k''_,
+which defines the angular extent of our entrance lip to the half shell
+of the cylinder in Fig. 133. We draw the full lines of the cylinder as
+shown.
+
+We next delineate the heel of the tooth which has just passed out of the
+cylinder, as shown at _D'_, Fig. 133. We now have a drawing showing the
+position of the half shell of the cylinder just as the tooth has passed
+the exit lip. This drawing also represents the position of the half
+shell of the cylinder when the tooth rests against it on the outside. If
+we should make a drawing of an escape-wheel tooth shaped exactly as the
+one shown at Fig. 132 and the point of the tooth resting at _x_, we
+would show the position of a tooth encountering the cylinder after a
+tooth which has been engaged in the inside of the shell has passed out.
+By following the instructions now given, we can delineate a tooth in any
+of its relations with the cylinder shell.
+
+
+DELINEATING AN ESCAPE-WHEEL TOOTH WHILE IN ACTION.
+
+We will now go through the operation of delineating an escape-wheel
+tooth while in action. The position we shall assume is the one in which
+the cylinder and escape-wheel tooth are in the relation of the passage
+of half the impulse face of the tooth into the cylinder. To do this is
+simple enough: We first produce the arcs _a b c_, Fig. 133, as directed,
+and then proceed to delineate a tooth as in previous instances. To
+delineate our cylinder in the position we have assumed above, we take
+the space between the points _e d_ in our dividers and setting one leg
+at _d_ establish the point _g_, to represent the center of our cylinder.
+If we then sweep the circle _h_ from the center of _g_ we define the
+inner surface of the shell of our cylinder.
+
+Strictly speaking, we have not assumed the position we stated, that is,
+the impulse face of the tooth as passing half way into the cylinder. To
+comply strictly with our statement, we divide the chord of the impulse
+face of the tooth _A_ into eight equal spaces, as shown. Now as each of
+these spaces represent the thickness of the cylinder, if we take in our
+dividers four of these spaces and half of another, we have the radius of
+a circle passing the center of the cylinder shell. Consequently, if with
+this space in our dividers we set the leg at _d_, we establish on the
+arc _b_ the point _i_. We locate the center of our cylinder when
+one-half of an entering tooth has passed into the cylinder. If now from
+the new center with our dividers set at four of the spaces into which we
+have divided the line _e f_ we can sweep a circle representing the inner
+surface of the cylinder shell, and by setting our dividers to five of
+these spaces we can, from _i_ as a center, sweep an arc representing the
+outside of the cylinder shell. For all purposes of practical study the
+delineation we show at Fig. 133 is to be preferred, because, if we carry
+out all the details we have described, the lines would become confused.
+We set our dividers at five of the spaces on the line _e f_ and from _g_
+as a center sweep the circle _j_, which delineates the outer surface of
+our cylinder shell.
+
+Let us now, as we directed in our former instructions, draw a flattened
+curve to represent the acting surface of the entrance lip of our
+cylinder as if it were in direct contact with the impulse face of the
+tooth. To delineate the exit lip we draw from the center _g_, Fig. 134,
+to the radial line _g k_, said line passing through the point of contact
+between the tooth and entrance lip of the cylinder. Let us next continue
+this line on the opposite side of the point _g_, as shown at _g k'_, and
+we thus bisect the cylinder shell into two equal parts of 180 degrees
+each. As we previously explained, the entire extent of the cylinder half
+shell is 196 degrees. We now set our dividers to the radius of any
+convenient arc which we have divided into degrees, and from _g_ as a
+center sweep the short arc _l l_, and from the intersection of this arc
+with the line _g k'_ we lay off sixteen degrees on the said arc _l_ and
+establish the point _n_, from _g_ as a center draw the radial line _g
+n'_. Take ten degrees from the same parent arc and establish the point
+_m_, then draw the line _g m'_. Now the arc on the circles _h j_ between
+the lines _g n'_ and _g m_ limits the extent of the exit lip of the
+cylinder and the arc between the lines _g k'_ and _g m'_ represents the
+locking surface of the cylinder shell.
+
+[Illustration: Fig. 134]
+
+To delineate the U arms we refer to Fig. 135. Here, again, we draw the
+arc _a b c_ and delineate a tooth as before. From the point _e_ located
+at the heel of the tooth we draw the radial line _e e'_. From the point
+_e_ we lay off on the arc _a_ five degrees and establish the point _p_;
+we halve this space and draw the short radial line _p' s'_ and _p s_.
+From the point _e_ on the arc _A_ we lay off twenty-four degrees and
+establish the point _t_, which locates the heel of the next tooth in
+advance of _A_. At two and a half degrees to the right of the point _t_
+we locate the point _r_ and draw the short radial line _r s_. On the arc
+_b_ and half way between the lines _p s_ and _r s_, we establish the
+point _u_, and from it as a center we sweep the arc _v_ defining the
+curve of the U arms.
+
+We have now given minute instructions for drawing a cylinder escapement
+in all its details except the extent of the banking slot of the
+cylinder, which is usually made to embrace an angular extent of 270
+degrees; consequently, the pillar of the cylinder will not measure more
+than ninety degrees of angular extent.
+
+There is no escapement constructed where carefully-made drawings tend
+more to perfect knowledge of the action than the cylinder. But it is
+necessary with the pupil to institute a careful analysis of the actions
+involved. In writing on a subject of this kind it is extremely
+perplexing to know when to stop; not that there is so much danger of
+saying too much as there is not having the words read with attention.
+
+As an illustration, let us consider the subject of depth between the
+cylinder and the escape wheel. As previously stated, 196 degrees of
+cylinder shell should be employed; but suppose we find a watch in which
+the half shell has had too much cut away, so the tooth on entering the
+half shell after parting with the entrance lip does not strike dead on
+the inside of the shell, but encounters the edge of the exit lip. In
+this case the impulse of the balance would cause the tooth to slightly
+retrograde and the watch would go but would lack a good motion. In such
+an instance a very slight advance of the chariot would remedy the
+fault--not perfectly remedy it, but patch up, so to speak--and the watch
+would run.
+
+[Illustration: Fig. 135]
+
+In this day, fine cylinder watches are not made, and only the common
+kind are met with, and for this reason the student should familiarize
+himself with all the imaginary faults which could occur from bad
+construction. The best way to do this is to delineate what he (the
+student) knows to be a faulty escapement, as, for instance, a cylinder
+in which too much of the half shell is cut away; but in every instance
+let the tooth be of the correct form. Then delineate an escapement in
+which the cylinder is correct but the teeth faulty; also change the
+thickness of the cylinder shell, so as to make the teeth too short. This
+sort of practice makes the pupil think and study and he will acquire a
+knowledge which will never be forgotten, but always be present to aid
+him in the puzzles to which the practical watchmaker is every day
+subject.
+
+The ability to solve these perplexing problems determines in a great
+degree the worth of a man to his employer, in addition to establishing
+his reputation as a skilled workman. The question is frequently asked,
+"How can I profitably employ myself in spare time?" It would seem that a
+watchmaker could do no better than to carefully study matters
+horological, striving constantly to attain a greater degree of
+perfection, for by so doing his earning capacity will undoubtedly be
+increased.
+
+
+
+
+CHAPTER III.
+
+THE CHRONOMETER ESCAPEMENT.
+
+
+Undoubtedly "the detent," or, as it is usually termed, "the chronometer
+escapement," is the most perfect of any of our portable time measurers.
+Although the marine chronometer is in a sense a portable timepiece,
+still it is not, like a pocket watch, capable of being adjusted to
+positions. As we are all aware, the detent escapement is used in fine
+pocket watches, still the general feeling of manufacturers is not
+favorable to it. Much of this feeling no doubt is owing to the
+mechanical difficulties presented in repairing the chronometer
+escapements when the detent is broken, and the fact that the spring
+detent could not be adjusted to position. We shall have occasion to
+speak of position adjustments as relate to the chronometer escapement
+later on.
+
+
+ADVANTAGES OF THE CHRONOMETER.
+
+We will proceed now to consider briefly the advantages the detent
+escapement has over all others. It was soon discovered in constructing
+portable timepieces, that to obtain the best results the vibrations of
+the balance should be as free as possible from any control or influence
+except at such times as it received the necessary impulse to maintain
+the vibrations at a constant arc. This want undoubtedly led to the
+invention of the detent escapement. The early escapements were all
+frictional escapements, i.e., the balance staff was never free from
+the influence of the train. The verge escapement, which was undoubtedly
+the first employed, was constantly in contact with the escape wheel, and
+was what is known as a "recoiling beat," that is, the contact of the
+pallets actually caused the escape wheel to recoil or turn back. Such
+escapements were too much influenced by the train, and any increase in
+power caused the timepiece to gain. The first attempt to correct this
+imperfection led to the invention and introduction of the fusee, which
+enabled the watchmaker to obtain from a coiled spring nearly equal power
+during the entire period of action. The next step in advance was the
+"dead-beat escapement," which included the cylinder and duplex. In these
+frictional escapements the balance staff locked the train while the
+balance performed its arc of vibration.
+
+FRICTIONAL ESCAPEMENTS IN HIGH FAVOR.
+
+These frictional escapements held favor with many eminent watchmakers
+even after the introduction of the detached escapements. It is no more
+than natural we should inquire, why? The idea with the advocates of the
+frictional rest escapements was, the friction of the tooth acted as a
+_corrective_, and led no doubt to the introduction of going-barrel
+watches. To illustrate, suppose in a cylinder watch we increase the
+motive power, such increase of power would not, as in the verge
+escapement, increase the rapidity of the vibrations; it might, in fact,
+cause the timepiece to run slower from the increased friction of the
+escape-wheel tooth on the cylinder; also, in the duplex escapement the
+friction of the locking tooth on the staff retards the vibrations.
+
+Dr. Hooke, the inventor of the balance spring, soon discovered it could
+be manipulated to isochronism, i.e., so arcs of different extent would
+be formed in equal time. Of course, the friction-rest escapement
+requiring a spring to possess different properties from one which would
+be isochronal with a perfectly detached escapement, these two frictional
+escapements also differing, the duplex requiring other properties from
+what would isochronize a spring for a cylinder escapement. Although
+pocket watches with duplex and cylinder escapements having balances
+compensated for heat and cold and balance springs adjusted to
+isochronism gave very good results, careful makers were satisfied that
+an escapement in which the balance was detached and free to act during
+the greater proportion of the arc of vibration and uncontrolled by any
+cause, would do still better, and this led to the detent escapement.
+
+
+FAULTS IN THE DETENT ESCAPEMENT.
+
+As stated previously, the detent escapement having pronounced faults in
+positions which held it back, it is probable it would never have been
+employed in pocket watches to any extent if it had not acquired such a
+high reputation in marine chronometers. Let us now analyze the
+influences which surround the detent escapement in a marine chronometer
+and take account of the causes which are combined to make it an accurate
+time measurer, and also take cognizance of other interfering causes
+which have a tendency to prevent desired results. First, we will imagine
+a balance with its spring such as we find in fine marine chronometers.
+It has small pivots running in highly-polished jewels; such pivots are
+perfectly cylindrical, and no larger than are absolutely necessary to
+endure the task imposed upon them--of carrying the weight of the balance
+and endure careful handling.
+
+To afford the necessary vibrations a spring is fitted, usually of a
+helical form, so disposed as to cause the balance to vibrate in arcs
+back and forth in equal time, _provided these arcs are of equal extent_.
+It is now to be taken note of that we have it at our disposal and option
+to make these arcs equal in time duration, i.e., to make the long or
+short arcs the quickest or to synchronize them. We can readily
+comprehend we have now established a very perfect measure of short
+intervals of time. We can also see if we provide the means of
+maintaining these vibrations and counting them we should possess the
+means of counting the flights of time with great accuracy. The
+conditions which surround our balance are very constant, the small
+pivots turning in fine hard jewels lubricated with an oil on which
+exposure to the action of the air has little effect, leaves but few
+influences which can interfere with the regular action of our balance.
+We add to the influences an adjustable correction for the disturbances
+of heat and cold, and we are convinced that but little could be added.
+
+
+ANTAGONISTIC INFLUENCES.
+
+In this combination we have pitted two antagonistic forces against each
+other, viz., the elasticity of the spring and the weight and inertia of
+the balance; both forces are theoretically constant and should produce
+constant results. The mechanical part of the problem is simply to afford
+these two forces perfect facilities to act on each other and compel each
+to realize its full effect. We must also devise mechanical means to
+record the duration of each conflict, that is, the time length of each
+vibration. Many years have been spent in experimenting to arrive at the
+best propositions to employ for the several parts to obtain the best
+practical results. Consequently, in designing a chronometer escapement
+we must not only draw the parts to a certain form, but consider the
+quality and weight of material to employ.
+
+To illustrate what we have just said, suppose, in drawing an escape
+wheel, we must not only delineate the proper angle for the acting face
+of the tooth, but must also take cognizance of the thickness of the
+tooth. By thickness we mean the measurement of extent of the tooth in
+the direction of the axis of the escape wheel. An escape-wheel tooth
+might be of the best form to act in conveying power to the balance and
+yet by being too thin soon wear or produce excessive friction. How thick
+an escape wheel should be to produce best results, is one of the many
+matters settled only by actual workshop experience.
+
+
+FACTORS THAT MUST BE CONSIDERED.
+
+Even this experience is in every instance modified by other influences.
+To illustrate: Let us suppose in the ordinary to-day marine chronometer
+the escape-wheel teeth exerted a given average force, which we set down
+as so many grains. Now, if we should employ other material than
+hammer-hardened brass for an escape wheel it would modify the thickness;
+also, if we should decrease the motive power and increase the arc of
+impulse. Or, if we should diminish the extent of the impulse arc and add
+to the motive force, every change would have a controlling influence. In
+the designs we shall employ, it is our purpose to follow such
+proportions as have been adopted by our best makers, in all respects,
+including form, size and material. We would say, however, there has been
+but little deviation with our principal manufacturers of marine
+chronometers for the last twenty years as regards the general principle
+on which they were constructed, the chief aim being to excel in the
+perfection of the several parts and the care taken in the several
+adjustments.
+
+Before we proceed to take up the details of constructing a chronometer
+escapement we had better master the names for the several parts. We show
+at Fig. 136 a complete plan of a chronometer escapement as if seen from
+the back, which is in reality the front or dial side of the "top plate."
+The chronometer escapement consists of four chief or principal parts,
+viz.: The escape wheel, a portion of which is shown at _A_; the impulse
+roller _B_; unlocking or discharging roller _C_, and the detent _D_.
+These principal parts are made up of sub-parts: thus, the escape wheel
+is composed of arms, teeth, recess and collet, the recess being the
+portion of the escape wheel sunk, to enable us to get wide teeth actions
+on the impulse pallet. The collet is a brass bush on which the wheel is
+set to afford better support to the escape wheel than could be obtained
+by the thinned wheel if driven directly on the pinion arbor. The impulse
+roller is composed of a cylindrical steel collet _B_, the impulse pallet
+_d_ (some call it the impulse stone), the safety recess _b b_. The
+diameter of the impulse collet is usually one-half that of the escape
+wheel. This impulse roller is staked directly on the balance staff, and
+its perfection of position assured by resting against the foot of the
+shoulder to which the balance is secured. This will be understood by
+inspecting Fig. 137, which is a vertical longitudinal section of a
+chronometer balance staff, the lower side of the impulse roller being
+cupped out at _c_ with a ball grinder and finished a ball polish.
+
+[Illustration: Fig. 136]
+
+[Illustration: Fig. 137]
+
+It will be seen the impulse roller is staked flat against the hub _E_ of
+the balance staff. The unlocking roller, or, as it is also called, the
+discharging roller, _C_, is usually thinner than the impulse roller and
+has a jewel similar to the impulse jewel _a_ shown at _f_. This roller
+is fitted by friction to the lower part of the balance staff and for
+additional security has a pipe or short socket _e_ which embraces the
+balance staff at _g_. The pipe _e_ is usually flattened on opposite
+sides to admit of employing a special wrench for turning the discharging
+roller in adjusting the jewel for opening the escapement at the proper
+instant to permit the escape wheel to act on the impulse jewel _a_. The
+parts which go to make up the detent _D_ consist of the "detent foot"
+_F_, the detent spring _h_, the detent blade _i_, the jewel pipe _j_,
+the locking jewel (or stone) _s_, the "horn" of the detent _k_, the
+"gold spring" (also called the auxiliary and lifting spring) _m_. This
+lifting or gold spring _m_ should be made as light and thin as possible
+and stand careful handling.
+
+We cannot impress on our readers too much the importance of making a
+chronometer detent light. Very few detents, even from the hands of our
+best makers, are as light as they might be. We should in such
+construction have very little care for clumsy workmen who may have to
+repair such mechanism. This feature should not enter into consideration.
+
+We should only be influenced by the feeling that we are working for best
+results, and it is acting under this influence that we devote so much
+time to establishing a correct idea of the underlying principles
+involved in a marine chronometer, instead of proceeding directly to the
+drawing of such an escapement and give empirical rules for the length of
+this or the diameter of that. As, for instance, in finishing the detent
+spring _h_, suppose we read in text books the spring should be reduced
+in thickness, so that a weight of one pennyweight suspended from the
+pipe _j_ will deflect the detent ¼". This is a rule well enough for
+people employed in a chronometer factory, but for the horological
+student such fixed rules (even if remembered) would be of small use.
+What the student requires is sound knowledge of the "whys," in order
+that he may be able to thoroughly master this escapement.
+
+
+FUNCTIONS OF THE DETENT.
+
+We can see, after a brief analysis of the principles involved, that the
+functions required of the detent _D_ are to lock the escape wheel _A_
+and hold it while the balance performs its excursion, and that the
+detent or recovering spring _h_ must have sufficient strength and power
+to perform two functions: (1) Return the locking stone _s_ back to the
+proper position to arrest and hold the escape wheel; (2) the spring _h_
+must also be able to resist, without buckling or cockling, the thrust of
+the escape wheel, represented by the arrows _p o_. Now we can readily
+understand that the lighter we make the parts _i j k m_, the weaker the
+spring _h_ can be. You say, perhaps, if we make it too weak it will be
+liable to buckle under the pressure of the escape wheel; this, in turn,
+will depend in a great measure on the condition of the spring _h_.
+Suppose we have it straight when we put it in position, it will then
+have no stress to keep it pressed to the holding, stop or banking screw,
+which regulates the lock of the tooth. To obtain this stress we set the
+foot _F_ of the detent around to the position indicated by the dotted
+lines _r_ and _n_, and we get the proper tension on the detent spring to
+effect the lock, or rather of the detent in time to lock the escape
+wheel; but the spring _h_, instead of being perfectly straight, is bent
+and consequently not in a condition to stand the thrust of the escape
+wheel, indicated by the arrows _o p_.
+
+
+OBTAINING THE BEST CONDITIONS.
+
+Now the true way to obtain the best conditions is to give the spring _h_
+a set curvature before we put it in place, and then when the detent is
+in the proper position the spring _h_ will have tension enough on it to
+bring the jewel _s_ against the stop screw, which regulates the lock,
+and still be perfectly straight. This matter is of so much importance
+that we will give further explanation. Suppose we bend the detent spring
+_h_ so it is curved to the dotted line _t_, Fig. 136, and then the foot
+_F_ would assume the position indicated at the dotted line _r_. We next
+imagine the foot _F_ to be put in the position shown by the full lines,
+the spring _h_ will become straight again and in perfect shape to resist
+the thrust of the escape wheel.
+
+Little "ways and methods" like the above have long been known to the
+trade, but for some reason are never mentioned in our text books. A
+detent spring 2/1000" thick and 80/1000" wide will stand the thrust for
+any well-constructed marine chronometer in existence, and yet it will
+not require half a pennyweight to deflect it one-fourth of an inch. It
+is a good rule to make the length of the detent from the foot _F_ to the
+center of the locking jewel pipe _j_ equal to the diameter of the escape
+wheel, and the length of the detent spring _h_ two-sevenths of this
+distance. The length of the horn _k_ is determined by the graphic plan
+and can be taken from the plotted plan. The end, however, should
+approach as near to the discharging jewel as possible and not absolutely
+touch. The discharging (gold) spring _m_ is attached to the blade _i_ of
+the detent with a small screw _l_ cut in a No. 18 hole of a Swiss plate.
+While there should be a slight increase in thickness in the detent blade
+at _w_, where the gold spring is attached, still it should be no more
+than to separate the gold spring _m_ from the detent blade _i_.
+
+
+IMPORTANT CONSIDERATIONS.
+
+It is important the spring should be absolutely free and not touch the
+detent except at its point of attachment at _w_ and to rest against the
+end of the horn _k_, and the extreme end of _k_, where the gold spring
+rests, should only be what we may term a dull or thick edge. The end of
+the horn _k_ (shown at _y_) is best made, for convenience of elegant
+construction, square--that is, the part _y_ turns at right angles to
+_k_ and is made thicker than _k_ and at the same time deeper; or, to
+make a comparison to a clumsy article, _y_ is like the head of a nail,
+which is all on one side. Some makers bend the horn _k_ to a curve and
+allow the end of the horn to arrest or stop the gold spring; but as it
+is important the entire detent should be as light as possible, the
+square end best answers this purpose. The banking placed at _j_ should
+arrest the detent as thrown back by the spring _h_ at the "point of
+percussion." This point of percussion is a certain point in a moving
+mass where the greatest effort is produced and would be somewhere near
+the point _x_, in a bar _G_ turning on a pivot at _z_, Fig. 138. It will
+be evident, on inspection of this figure, if the bar _G_ was turning on
+the center _z_ it would not give the hardest impact at the end _v_, as
+parts of its force would be expended at the center _z_.
+
+[Illustration: Fig. 138]
+
+
+DECISIONS ARRIVED AT BY EXPERIENCE.
+
+Experience has decided that the impulse roller should be about half the
+diameter of the escape wheel, and experience has also decided that an
+escape wheel of fifteen teeth has the greatest number of advantages;
+also, that the balance should make 14,400 vibrations in one hour. We
+will accept these proportions and conditions as best, from the fact that
+they are now almost universally adopted by our best chronometer makers.
+Although it would seem as if these proportions should have established
+themselves earlier among practical men, we shall in these drawings
+confine ourselves to the graphic plan, considering it preferable. In the
+practical detail drawing we advise the employment of the scale given,
+i.e., delineating an escape wheel 10" in diameter. The drawings which
+accompany the description are one-fourth of this size, for the sake of
+convenience in copying.
+
+With an escape wheel of fifteen teeth the impulse arc is exactly
+twenty-four degrees, and of course the periphery of the impulse roller
+must intersect the periphery of the escape wheel for this arc (24°).
+The circles _A B_, Fig. 139, represent the peripheries of these two
+mobiles, and the problem in hand is to locate and define the position of
+the two centers _a c_. These, of course, are not separated, the sum of
+the two radii, i.e., 5" + 2½" (in the large drawing), as these
+circles intersect, as shown at _d_. Arithmetically considered, the
+problem is quite difficult, but graphically, simple enough. After we
+have swept the circle _A_ with a radius of 5", we draw the radial line
+_a f_, said line extending beyond the circle _A_.
+
+
+LOCATING THE CENTER OF THE BALANCE STAFF.
+
+Somewhere on this line is located the center of the balance staff, and
+it is the problem in hand to locate or establish this center. Now, it is
+known the circles which define the peripheries of the escape wheel and
+the impulse roller intersect at _e e^2_. We can establish on our
+circle _A_ where these intersections take place by laying off twelve
+degrees, one-half of the impulse arc on each side of the line of centers
+_a f_ on this circle and establishing the points _e e^2_. These points
+_e e^2_ being located at the intersection of the circles _A_ and _B_,
+must be at the respective distances of 5" and 2½" distance from the
+center of the circles _A B_; consequently, if we set our dividers at
+2½" and place one leg at _e_ and sweep the short arc _g^2_, and
+repeat this process when one leg of the dividers is set at _e^2_, the
+intersection of the short arcs _g_ and _g^2_ will locate the center of
+our balance staff. We have now our two centers established, whose
+peripheries are in the relation of 2 to 1.
+
+To know, in the chronometer which we are supposed to be constructing,
+the exact distance apart at which to plant the hole jewels for our two
+mobiles, i.e., escape wheel and balance staff, we measure carefully on
+our drawing the distance from _a_ to _c_ (the latter we having just
+established) and make our statement in the rule of three, as follows: As
+(10) the diameter of drawn escape wheel is to our real escape wheel so
+is the measured distance on our drawing to the real distance in the
+chronometer we are constructing.
+
+It is well to use great care in the large drawing to obtain great
+accuracy, and make said large drawing on a sheet of metal. This course
+is justified by the degree of perfection to which measuring tools have
+arrived in this day. It will be found on measurement of the arc of the
+circle _B_, embraced between the intersections _e e^2_, that it is
+about forty-eight degrees. How much of this we can utilize in our
+escapement will depend very much on the perfection and accuracy of
+construction.
+
+[Illustration: Fig. 139]
+
+We show at Fig. 140 three teeth of an escape wheel, together with the
+locking jewel _E_ and impulse jewel _D_. Now, while theoretically we
+could commence the impulse as soon as the impulse jewel _D_ was inside
+of the circle representing the periphery of the escape wheel, still, in
+practical construction, we must allow for contingencies. Before it is
+safe for the escape wheel to attack the impulse jewel, said jewel must
+be safely inside of said escape wheel periphery, in order that the
+attacking tooth shall act with certainty and its full effect. A good
+deal of thought and study can be bestowed to great advantage on the
+"action" of a chronometer escapement. Let us examine the conditions
+involved. We show in Fig. 140 the impulse jewel _D_ just passing inside
+the circle of the periphery of the escape wheel. Now the attendant
+conditions are these: The escape wheel is locked fast and perfectly
+dead, and in the effort of unlocking it has to first turn backward
+against the effort of the mainspring; the power of force required for
+this effort is derived from the balance in which is stored up, so to
+speak, power from impulses imparted to the balance by former efforts of
+the escape wheel. In actual fact, the balance at the time the unlocking
+takes place is moving with nearly its greatest peripheral velocity and,
+as stated above, the escape wheel is at rest.
+
+Here comes a very delicate problem as regards setting the unlocking or
+discharging jewel. Let us first suppose we set the discharging jewel so
+the locking jewel frees its tooth at the exact instant the impulse jewel
+is inside the periphery of the escape wheel. As just stated, the escape
+wheel is not only dead but actually moving back at the time the release
+takes place. Now, it is evident that the escape wheel requires an
+appreciable time to move forward and attack the impulse jewel, and
+during this appreciable time the impulse jewel has been moving forward
+inside of the arc _A A_, which represents the periphery of the escape
+wheel. The proper consideration of this problem is of more importance in
+chronometer making than we might at first thought have imagined,
+consequently, we shall dwell upon it at some length.
+
+
+HOW TO SET THE DISCHARGING JEWEL.
+
+[Illustration: Fig. 140]
+
+Theoretically, the escape-wheel tooth should encounter the impulse jewel
+at the time--instant--both are moving with the same velocity. It is
+evident then that there can be no special rule given for this, i.e.,
+how to set the discharging jewel so it will free the tooth at exactly
+the proper instant, from the fact that one chronometer train may be much
+slower in getting to move forward from said train being heavy and clumsy
+in construction. Let us make an experiment with a real chronometer in
+illustration of our problem. To do so we remove our balance spring and
+place the balance in position. If we start the balance revolving in the
+direction of the arrow _y_, Fig. 140, it will cause the escapement to be
+unlocked and the balance to turn rapidly in one direction and with
+increasing velocity until, in fact, the escape wheel has but very little
+effect on the impulse jewel; in fact, we could, by applying some outside
+source of power--like blowing with a blow pipe on the balance--cause the
+impulse jewel to pass in advance of the escape wheel; that is, the
+escape-wheel tooth would not be able to catch the impulse jewel during
+the entire impulse arc. Let us suppose, now, we set our unlocking or
+discharging jewel in advance, that is, so the escapement is really
+unlocked a little before the setting parts are in the positions and
+relations shown in Fig. 141. Under the new conditions the escape wheel
+would commence to move and get sufficient velocity on it to act on the
+impulse jewel as soon as it was inside of the periphery of the escape
+wheel. If the balance was turned slowly now the tooth of the escape
+wheel would not encounter the impulse jewel at all, but fall into the
+passing hollow _n_; but if we give the balance a high velocity, the
+tooth would again encounter and act upon the jewel in the proper manner.
+Experienced adjusters of chronometers can tell by listening if the
+escape-wheel tooth attacks the impulse jewel properly, i.e., when both
+are moving with similar velocities. The true sound indicating correct
+action is only given when the balance has its maximum arc of vibration,
+which should be about 1¼ revolutions, or perform an arc of 225
+degrees on each excursion.
+
+
+Fig. 142 is a side view of Fig. 141 seen in the direction of the arrow
+_y_. We have mentioned a chariot to which the detent is attached, but we
+shall make no attempt to show it in the accompanying drawings, as it
+really has no relation to the problem in hand; i.e., explaining the
+action of the chronometer escapement, as the chariot relates entirely to
+the convenience of setting and adjusting the relation of the second
+parts. The size, or better, say, the inside diameter of the pipe at _C_,
+Fig. 143, which holds the locking jewel, should be about one-third of a
+tooth space, and the jewel made to fit perfectly. Usually, jewelmakers
+have a tendency to make this jewel too frail, cutting away the jewel
+back of the releasing angle (_n_, Fig. 143) too much.
+
+
+A GOOD FORM OF LOCKING STONE.
+
+A very practical form for a locking stone is shown in transverse section
+at Fig. 143. In construction it is a piece of ruby, or, better, sapphire
+cut to coincide to its axis of crystallization, into first a solid
+cylinder nicely fitting the pipe _C_ and finished with an
+after-grinding, cutting away four-tenths of the cylinder, as shown at
+_I_, Fig. 143. Here the line _m_ represents the locking face of the
+jewel and the line _o_ the clearance to free the escaping tooth, the
+angle at _n_ being about fifty-four degrees. This angle (_n_) should
+leave the rounding of the stone intact, that is, the rounding of the
+angle should be left and not made after the flat faces _m o_ are ground
+and polished. The circular space at _I_ is filled with an aluminum
+pin. The sizes shown are of about the right relative proportions; but
+we feel it well to repeat the statement made previously, to the effect
+that the detent to a chronometer cannot well be made too light.
+
+[Illustration: Fig. 141]
+
+[Illustration: Fig. 142]
+
+[Illustration: Fig. 143]
+
+The so-called gold spring shown at _H_, Figs. 141 and 142, should also
+be as light as is consistent with due strength and can be made of the
+composite metal used for gold filled goods, as the only real benefit to
+be derived from employing gold is to avoid the necessity of applying oil
+to any part of the escapement. If such gold metal is employed, after
+hammering to obtain the greatest possible elasticity to the spring, the
+gold is filed away, except where the spring is acted upon by the
+discharging jewel _h_. We have previously mentioned the importance of
+avoiding wide, flat contacts between all acting surfaces, like where the
+gold spring rests on the horn of the detent at _p_; also where the
+detent banks on the banking screw, shown at _G_, Fig. 142. Under this
+principle the impact of the face of the discharging jewel with the end
+of the gold spring should be confined to as small a surface as is
+consistent with what will not produce abrasive action. The gold spring
+is shaped as shown at Fig. 142 and loses, in a measure, under the pipe
+of the locking jewel, a little more than one-half of the pipe below the
+blade of the detent being cut away, as shown in Fig. 143, where the
+lines _r r_ show the extent of the part of the pipe which banks against
+the banking screw _G_. In this place even, only the curved surface of
+the outside of the pipe touches the screw _G_, again avoiding contact of
+broad surfaces.
+
+We show the gold spring separate at Fig. 144. A slight torsion or twist
+is given to the gold spring to cause it to bend with a true curvature in
+the act of allowing the discharging pallet to pass back after unlocking.
+If the gold spring is filed and stoned to the right flexure, that is,
+the thinnest point properly placed or, say, located, the gold spring
+will not continue in contact with the discharging pallet any longer time
+or through a greater arc than during the process of unlocking. To make
+this statement better understood, let us suppose the weakest part of the
+gold spring _H_ is opposite the arrow _y_, Fig. 141, it will readily be
+understood the contact of the discharging stone _h_ would continue
+longer than if the point of greatest (or easiest) flexure was nearer to
+the pipe _C_. If the end _D^2_ of the horn of the detent is as near as
+it should be to the discharging stone there need be no fear but the
+escapement will be unlocked. The horn _D^2_ of the detent should be
+bent until five degrees of angular motion of the balance will unlock the
+escape, and the contact of discharging jewel _h_ should be made without
+engaging friction. This condition can be determined by observing if the
+jewel seems to slide up (toward the pipe _C_) on the gold spring after
+contact. Some adjusters set the jewel _J_, Figs. 143 and 141, in such a
+way that the tooth rests close to the base; such adjusters claiming this
+course has a tendency to avoid cockling or buckling of the detent spring
+_E_. Such adjusters also set the impulse jewel slightly oblique, so as
+to lean on the opposite angle of the tooth. Our advice is to set both
+stones in places corresponding to the axis of the balance staff, and the
+escape-wheel mobiles.
+
+
+THE DETENT SPRING.
+
+[Illustration: Fig. 144]
+
+It will be noticed we have made the detent spring _E_ pretty wide and
+extended it well above the blade of the detent. By shaping the detent in
+this way nearly all the tendency of the spring _E_ to cockle is
+annulled. We would beg to add to what we said in regard to setting
+jewels obliquely. We are unable to understand the advantage of
+wide-faced stones and deep teeth when we do not take advantage of the
+wide surfaces which we assert are important. We guarantee that with a
+detent and spring made as we show, there will be no tendency to cockle,
+or if there is, it will be too feeble to even display itself. Those who
+have had extended experience with chronometers cannot fail to have
+noticed a gummy secretion which accumulates on the impulse and
+discharging stones of a chronometer, although no oil is ever applied to
+them. We imagine this coating is derived from the oil applied to the
+pivots, which certainly evaporates, passes into vapor, or the remaining
+oil could not become gummy. We would advise, when setting jewels (we
+mean the locking, impulse and discharging jewels), to employ no more
+shellac than is absolutely necessary, depending chiefly on metallic
+contact for security.
+
+
+DETAILS OF CONSTRUCTION.
+
+We will now say a few words about the number of beats to the hour for a
+box or marine chronometer to make to give the best results. Experience
+shows that slow but most perfect construction has settled that 14,400,
+or four vibrations of the balance to a second, as the proper number, the
+weight of balance, including balance proper and movable weights, to be
+about 5½ pennyweights, and the compensating curb about 1-2/10" in
+diameter. The escape wheel, 55/100" in diameter and recessed so as to be
+as light as possible, should have sufficient strength to perform its
+functions properly. The thickness or, more properly, the face extent of
+the tooth, measured in the direction of the axis of the escape wheel,
+should be about 1/20". The recessing should extend half way up the
+radial back of the tooth at _t_. The curvature of the back of the teeth
+is produced with the same radii as the impulse roller. To locate the
+center from which the arc which defines the back of the teeth is swept,
+we halve the space between the teeth _A^2_ and _a^4_ and establish
+the point _n_, Fig. 141, and with our dividers set to sweep the circle
+representing the impulse roller, we sweep an arc passing the point of
+the tooth _A^3_ and _u_, thus locating the center _w_. From the center
+_k_ of the escape wheel we sweep a complete circle, a portion of which
+is represented by the arc _w v_. For delineating other teeth we set one
+leg of our dividers to agree with the point of the tooth and the other
+leg on the circle _w v_ and produce an arc like _z u_.
+
+
+ORIGINAL DESIGNING OF THE ESCAPEMENT.
+
+On delineating our chronometer escapement shown at Fig. 141 we have
+followed no text-book authority, but have drawn it according to such
+requirements as are essential to obtain the best results. An escapement
+of any kind is only a machine, and merely requires in its construction a
+combination of sound mechanical principles. Neither Saunier nor Britten,
+in their works, give instructions for drawing this escapement which will
+bear close analysis. It is not our intention, however, to criticise
+these authors, except we can present better methods and give correct
+systems.
+
+
+TANGENTIAL LOCKINGS.
+
+It has been a matter of great contention with makers of chronometer and
+also lever escapements as to the advantages of "tangential lockings." By
+this term is meant a locking the same as is shown at _C_, Fig. 141, and
+means a detent planted at right angles to a line radial to the
+escape-wheel axis, said radial line passing through the point of the
+escape-wheel tooth resting on the locking jewel. In escapements not set
+tangential, the detent is pushed forward in the direction of the arrow
+_x_ about half a tooth space. Britten, in his "Hand-Book," gives a
+drawing of such an escapement. We claim the chief advantage of
+tangential locking to lie in the action of the escape-wheel teeth, both
+on the impulse stone and also on the locking stone of the detent.
+Saunier, in his "Modern Horology," gives the inclination of the front
+fan of the escape-wheel teeth as being at an angle of twenty-seven
+degrees to a radial line. Britten says twenty degrees, and also employs
+a non-tangential locking.
+
+Our drawing is on an angle of twenty-eight degrees, which is as low as
+is safe, as we shall proceed to demonstrate. For establishing the angle
+of an escape-wheel tooth we draw the line _C d_, from the point of the
+escape-wheel tooth resting on the locking stone shown at _C_ at an angle
+of twenty-eight degrees to radial line _C k_. We have already discussed
+how to locate and plant the center of the balance staff.
+
+We shall not show in this drawing the angular motion of the escape
+wheel, but delineate at the radial lines _c e_ and _c f_ of the arc of
+the balance during the extent of its implication with the periphery of
+the escape wheel, which arc is one of about forty-eight degrees. Of this
+angle but forty-three degrees is attempted to be utilized for the
+purpose of impulse, five degrees being allowed for the impulse jewel to
+pass inside of the arc of periphery of the escape wheel before the
+locking jewel releases the tooth of the escape wheel resting upon it. At
+this point it is supposed the escape wheel attacks the impulse jewel,
+because, as we just explained, the locking jewel has released the tooth
+engaging it. Now, if the train had no weight, no inertia to overcome,
+the escape wheel tooth _A^2_ would move forward and attack the impulse
+pallet instantly; but, in fact, as we have already explained, there will
+be an appreciable time elapse before the tooth overtakes the
+rapidly-moving impulse jewel. It will, of course, be understood that the
+reference letters used herein refer to the illustrations that have
+appeared on preceding pages.
+
+If we reason carefully on the matter, we will readily comprehend that we
+can move the locking jewel, i.e., set it so the unlocking will take
+place in reality before the impulse jewel has passed through the entire
+five degrees of arc embraced between the radial lines _c e_ and _c g_,
+Fig. 141, and yet have the tooth attack the jewel after the five degrees
+of arc. In practice it is safe to set the discharging jewel _h_ so the
+release of the held tooth _A^1_ will take place as soon as the tooth
+_A^2_ is inside the principal line of the escape wheel. As we
+previously explained, the contact between _A^2_ and the impulse jewel
+_i_ would not in reality occur until the said jewel _i_ had fully passed
+through the arc (five degrees) embraced between the radial lines _c e_
+and _c g_.
+
+At this point we will explain why we drew the front fan of the
+escape-wheel teeth at the angle of twenty-eight degrees. If the fan of
+impulse jewel _i_ is set radial to the axis of the balance, the
+engagement of the tooth _A^2_ would be at a disadvantage if it took
+place prior to this jewel passing through an arc of five degrees inside
+the periphery of the escape wheel. It will be evident on thought that if
+an escape-wheel tooth engaged the impulse stone before the five-degrees
+angle had passed, the contact would not be on its flat face, but the
+tooth would strike the impulse jewel on its outer angle. A continued
+inspection will also reveal the fact that in order to have the point of
+the tooth engage the flat surface of the impulse pallet the impulse
+jewel must coincide with the radial line _c g_. If we seek to remedy
+this condition by setting the impulse jewel so the face is not radial,
+but inclined backward, we encounter a bad engaging friction, because,
+during the first part of the impulse action, the tooth has to slide up
+the face of the impulse jewel. All things considered, the best action is
+obtained with the impulse jewel set so the acting face is radial to the
+balance staff and the engagement takes place between the tooth and the
+impulse jewel when both are moving with equal velocities, i.e., when
+the balance is performing with an arc (or motion) of 1¼ revolutions
+or 225 degrees each way from a point of rest. Under such conditions the
+actual contact will not take place before some little time after the
+impulse jewel has passed the five-degree arc between the lines _c e_ and
+_c g_.
+
+
+THE DROP AND DRAW CONSIDERED.
+
+Exactly how much drop must be allowed from the time the tooth leaves the
+impulse jewel before the locking tooth engages the locking jewel will
+depend in a great measure on the perfection of workmanship, but should
+in no instance be more than what is absolutely required to make the
+escapement safe. The amount of draw given to the locking stone _c_ is
+usually about twelve degrees to the radial line _k a_. Much of the
+perfection of the chronometer escapement will always depend on the skill
+of the escapement adjuster and not on the mechanical perfection of the
+parts.
+
+The jewels all have to be set by hand after they are made, and the
+distance to which the impulse jewel protrudes beyond the periphery of
+the impulse roller is entirely a matter for hand and eye, but should
+never exceed 2/1000". After the locking jewel _c_ is set, we can set the
+foot _F_ of the detent _D_ forward or back, to perfect and correct the
+engagement of the escape-wheel teeth with the impulse roller _B_. If we
+set this too far forward, the tooth _A^3_ will encounter the roller
+while the tooth _A^2_ will be free.
+
+We would beg to say here there is no escape wheel made which requires
+the same extreme accuracy as the chronometer, as the tooth spaces and
+the equal radial extent of each tooth should be only limited by our
+powers toward perfection. It is usual to give the detent a locking of
+about two degrees; that is, it requires about two degrees to open it,
+counting the center of fluxion of the detent spring _E_ and five degrees
+of balance arc.
+
+
+FITTING UP OF THE FOOT.
+
+Several attempts have been made by chronometer makers to have the foot
+_F_ adjustable; that is, so it could be moved back and forth with a
+screw, but we have never known of anything satisfactory being
+accomplished in this direction. About the best way of fitting up the
+foot _F_ seems to be to provide it with two soft iron steady pins (shown
+at _j_) with corresponding holes in the chariot, said holes being
+conically enlarged so they (the pins) can be bent and manipulated so the
+detent not only stands in the proper position as regards the escape
+wheel, but also to give the detent spring _E_ the proper elastic force
+to return in time to afford a secure locking to the arresting tooth of
+the escape wheel after an impulse has been given.
+
+If these pins _j_ are bent properly by the adjuster, whoever afterwards
+cleans the chronometer needs only to gently push the foot _F_ forward so
+as to cause the pins _j_ to take the correct positions as determined by
+the adjuster and set the screw _l_ up to hold the foot _F_ when all the
+other relations are as they should be, except such as we can control by
+the screw _G_, which prevents the locking jewel from entering too deeply
+into the escape wheel.
+
+In addition to being a complete master of the technical part of his
+business, it is also desirable that the up-to-date workman should be
+familiar with the subject from a historical point of view. To aid in
+such an understanding of the matter we have translated from "L'Almanach
+de l'Horologerie et de la Bijouterie" the matter contained in the
+following chapter.
+
+
+
+
+CHAPTER IV.
+
+HISTORY OF ESCAPEMENTS.
+
+
+It could not have been long after man first became cognizant of his
+reasoning faculties that he began to take more or less notice of the
+flight of time. The motion of the sun by day and of the moon and stars
+by night served to warn him of the recurring periods of light and
+darkness. By noting the position of these stellar bodies during his
+lonely vigils, he soon became proficient in roughly dividing up the
+cycle into sections, which he denominated the hours of the day and of
+the night. Primitive at first, his methods were simple, his needs few
+and his time abundant. Increase in numbers, multiplicity of duties, and
+division of occupation began to make it imperative that a more
+systematic following of these occupations should be instituted, and with
+this end in view he contrived, by means of burning lights or by
+restricting the flowing of water or the falling of weights, to subdivide
+into convenient intervals and in a tolerably satisfactory manner the
+periods of light.
+
+These modest means then were the first steps toward the exact
+subdivisions of time which we now enjoy. Unrest, progress, discontent
+with things that be, we must acknowledge, have, from the appearance of
+the first clock to the present hour, been the powers which have driven
+on the inventive genius of watch and clockmakers to designate some new
+and more acceptable system for regulating the course of the movement. In
+consequence of this restless search after the best, a very considerable
+number of escapements have been invented and made up, both for clocks
+and watches; only a few, however, of the almost numberless systems have
+survived the test of time and been adopted in the manufacture of the
+timepiece as we know it now. Indeed, many such inventions never passed
+the experimental stage, and yet it would be very interesting to the
+professional horologist, the apprentice and even the layman to become
+more intimately acquainted with the vast variety of inventions made upon
+this domain since the inception of horological science. Undoubtedly, a
+complete collection of all the escapements invented would constitute a
+most instructive work for the progressive watchmaker, and while we are
+waiting for a competent author to take such an exhaustive work upon his
+hands, we shall endeavor to open the way and trust that a number of
+voluntary collaborators will come forward and assist us to the extent of
+their ability in filling up the chinks.
+
+
+PROBLEMS TO BE SOLVED.
+
+The problem to be solved by means of the escapement has always been to
+govern, within limits precise and perfectly regular, if it be possible,
+the flow of the motive force; that means the procession of the
+wheel-work and, as a consequence, of the hands thereto attached. At
+first blush it seems as if a continually-moving governor, such as is in
+use on steam engines, for example, ought to fulfil the conditions, and
+attempts have accordingly been made upon this line with results which
+have proven entirely unsatisfactory.
+
+Having thoroughly sifted the many varieties at hand, it has been finally
+determined that the only means known to provide the most regular flow of
+power consists in intermittently interrupting the procession of the
+wheel-work, and thereby gaining a periodically uniform movement.
+Whatever may be the system or kind of escapement employed, the
+functioning of the mechanism is characterized by the suspension, at
+regular intervals, of the rotation of the last wheel of the train and in
+transmitting to a regulator, be it a balance or a pendulum, the power
+sent into that wheel.
+
+
+ESCAPEMENT THE MOST ESSENTIAL PART.
+
+Of all the parts of the timepiece the escapement is then the most
+essential; it is the part which assures regularity in the running of the
+watch or clock, and that part of parts that endows the piece with real
+value. The most perfect escapement would be that one which should
+perform its duty with the least influence upon the time of oscillation
+or vibration of the regulating organ. The stoppage of the train by the
+escapement is brought about in different ways, which may be gathered
+under three heads or categories. In the two which we shall mention
+first, the stop is effected directly upon the axis of the regulator, or
+against a piece which forms a part of that axis; the tooth of the escape
+wheel at the moment of its disengagement remains supported upon or
+against that stop.
+
+In the first escapement invented and, indeed, in some actually employed
+to-day for certain kinds of timekeepers, we notice during the locking a
+retrograde movement of the escape wheel; to this kind of movement has
+been given the name of _recoil escapement_. It was recognized by the
+fraternity that this recoil was prejudicial to the regularity of the
+running of the mechanism and, after the invention of the pendulum and
+the spiral, inventive makers succeeded in replacing this sort of
+escapement with one which we now call the _dead-beat escapement_. In
+this latter the wheel, stopped by the axis of the regulator, remains
+immovable up to the instant of its disengagement or unlocking.
+
+In the third category have been collected all those forms of escapement
+wherein the escape wheel is locked by an intermediate piece, independent
+of the regulating organ. This latter performs its vibrations of
+oscillation quite without interference, and it is only in contact with
+the train during the very brief moment of impulse which is needful to
+keep the regulating organ in motion. This category constitutes what is
+known as the _detached escapement_ class.
+
+Of the _recoil escapement_ the principal types are: the _verge
+escapement_ or _crown-wheel escapement_ for both watches and clocks, and
+the _recoil anchor escapement_ for clocks. The _cylinder_ and _duplex
+escapements_ for watches and the _Graham anchor escapement_ for clocks
+are styles of the _dead-beat escapement_ most often employed. Among the
+_detached escapements_ we have the _lever_ and _detent_ or _chronometer
+escapements_ for watches; for clocks there is no fixed type of detached
+lever and it finds no application to-day.
+
+
+THE VERGE ESCAPEMENT.
+
+The _verge escapement_, called also the _crown-wheel escapement_, is by
+far the simplest and presents the least difficulty in construction. We
+regret that the world does not know either the name of its originator
+nor the date at which the invention made its first appearance, but it
+seems to have followed very closely upon the birth of mechanical
+horology.
+
+Up to 1750 it was employed to the exclusion of almost all the others. In
+1850 a very large part of the ordinary commercial watches were still
+fitted with the verge escapement, and it is still used under the form of
+_recoil anchor_ in clocks, eighty years after the invention of the
+cylinder escapement, or in 1802. Ferdinand Berthoud, in his "History of
+the Measurement of Time," says of the balance-wheel escapement: "Since
+the epoch of its invention an infinite variety of escapements have been
+constructed, but the one which is employed in ordinary watches for
+every-day use is still the best." In referring to our illustrations, we
+beg first to call attention to the plates marked Figs. 145 and 146.
+This plate gives us two views of a verge escapement; that is, a balance
+wheel and a verge formed by its two opposite pallets. The views are
+intentionally presented in this manner to show that the verge _V_ may be
+disposed either horizontally, as in Fig. 146, or vertically, as in Fig.
+145.
+
+[Illustration: Figs. 145 and 146]
+
+[Illustration: Fig. 147]
+
+Let us imagine that our drawing is in motion, then will the tooth _d_,
+of the crown wheel _R_, be pushing against the pallet _P_, and just upon
+the point of slipping by or escaping, while the opposite tooth _e_ is
+just about to impinge upon the advancing pallet _P'_. This it does, and
+will at first, through the impulse received from the tooth _d_ be forced
+back by the momentum of the pallet, that is, suffer a recoil; but on the
+return journey of the pallet _P'_, the tooth _e_ will then add its
+impulse to the receding pallet. The tooth _e_ having thus accomplished
+its mission, will now slip by and the tooth _c_ will come in lock with
+the pallet _P_ and, after the manner just described for _e_, continue
+the escapement. Usually these escape wheels are provided with teeth to
+the number of 11, 13 or 15, and always uneven. A great advantage
+possessed by this form of escapement is that it does not require any
+oil, and it may be made to work even under very inferior construction.
+
+
+OLDEST ARRANGEMENT OF A CROWN-WHEEL ESCAPEMENT.
+
+[Illustration: Fig. 148]
+
+Plate 147 shows us the oldest known arrangement of a crown-wheel
+escapement in a clock. _R_ is the crown wheel or balance wheel acting
+upon the pallets _P_ and _P'_, which form part of the verge _V_. This
+verge is suspended as lightly as possible upon a pliable cord _C_ and
+carries at its upper end two arms, _B_ and _B_, called adjusters,
+forming the balance. Two small weights _D D_, adapted to movement along
+the rules or adjusters serve to regulate the duration of a vibration. In
+Fig. 148 we have the arrangement adopted in small timepieces and
+watches: _B_ represents the regulator in the form of a circular balance,
+but not yet furnished with a spiral regulating spring; _c_ is the last
+wheel of the train and called the _fourth wheel_, it being that number
+distant from the great wheel. As will be seen, the verge provided with
+its pallets is vertically placed, as in the preceding plate.
+
+[Illustration: Fig. 149]
+
+Here it will quickly be seen that regarded from the standpoint of
+regularity of motion, this arrangement can be productive of but meager
+results. Subjected as it is to the influence of the slightest variation
+in the motive power and of the least jar or shaking, a balance wheel
+escapement improvided with a regulator containing within itself a
+regulating force, could not possibly give forth anything else than an
+unsteady movement. However, mechanical clocks fitted with this
+escapement offer indisputable advantages over the ancient clepsydra; in
+spite of their imperfections they rendered important services,
+especially after the striking movement had been added. For more than
+three centuries both this crude escapement and the cruder regulator were
+suffered to continue in this state without a thought of improvement;
+even in 1600, when Galileo discovered the law governing the oscillation
+of the pendulum, they did not suspect how important this discovery was
+for the science of time measurement.
+
+
+GALILEO'S EXPERIMENTS.
+
+[Illustration: Fig. 150]
+
+Galileo, himself, in spite of his genius for investigation, was so
+engrossed in his researches that he could not seem to disengage the
+simple pendulum from the compound pendulums to which he devoted his
+attention; besides, he attributed to the oscillation an absolute
+generality of isochronism, which they did not possess; nor did he know
+how to apply his famous discovery to the measurement of time. In fact,
+it was not till after more than half a century had elapsed, in 1657, to
+be exact, that the celebrated Dutch mathematician and astronomer,
+Huygens, published his memoirs in which he made known to the world the
+degree of perfection which would accrue to clocks if the pendulum were
+adopted to regulate their movement.
+
+[Illustration: Fig. 151]
+
+An attempt was indeed made to snatch from Huygens and confer upon
+Galileo the glory of having first applied the pendulum to a clock, but
+this attempt not having been made until some time after the publication
+of "Huygens' Memoirs," it was impossible to place any faith in the
+contention. If Galileo had indeed solved the beautiful problem, both in
+the conception and the fact, the honor of the discovery was lost to him
+by the laziness and negligence of his pupil, Viviani, upon whom he had
+placed such high hopes. One thing is certain, that the right of priority
+of the discovery and the recognition of the entire world has been
+incontestably bestowed upon Huygens. The escapement which Galileo is
+supposed to have conceived and to which he applied the pendulum, is
+shown in Fig. 149. The wheel _R_ is supplied with teeth, which lock
+against the piece _D_ attached to a lever pivoted at _a_, and also with
+pins calculated to impart impulses to the pendulum through the pallet
+_P_. The arm _L_ serves to disengage or unlock the wheel by lifting the
+lever _D_ upon the return oscillation of the pendulum.
+
+[Illustration: Fig. 152]
+
+[Illustration: Fig. 153]
+
+A careful study of Fig. 150 will discover a simple transposition which
+it became necessary to make in the clocks, for the effectual adaptation
+of the pendulum to their regulation. The verge _V_ was set up
+horizontally and the pendulum _B_, suspended freely from a flexible
+cord, received the impulses through the intermediation of the forked arm
+_F_, which formed a part of the verge. At first this forked arm was not
+thought of, for the pendulum itself formed a part of the verge. A
+far-reaching step had been taken, but it soon became apparent that
+perfection was still a long way off. The crown-wheel escapement forcibly
+incited the pendulum to wider oscillations; these oscillations not being
+as Galileo had believed, of unvaried durations, but they varied sensibly
+with the intensity of the motive power.
+
+
+THE ATTAINMENT OF ISOCHRONISM BY HUYGENS.
+
+Huygens rendered his pendulum _isochronous_; that is, compelled it to
+make its oscillations of equal duration, whatever might be the arc
+described, by suspending the pendulum between two metallic curves _c
+c'_, each one formed by an arc of a cycloid and against which the
+suspending cord must lie upon each forward or backward oscillation. We
+show this device in Fig. 151. In great oscillations, and by that we mean
+oscillations under a greater impulse, the pendulum would thus be
+shortened and the shortening would correct the time of the oscillation.
+However, the application of an exact cycloidal arc was a matter of no
+little difficulty, if not an impossibility in practice, and practical
+men began to grope about in search of an escapement which would permit
+the use of shorter arcs of oscillation. At London the horologist, G.
+Clement, solved the problem in 1675 with his rack escapement and recoil
+anchor. In the interval other means were invented, especially the
+addition of a second pendulum to correct the irregularities of the
+first. Such an escapement is pictured in Fig. 152. The verge is again
+vertical and carries near its upper end two arms _D D_, which are each
+connected by a cord with a pendulum. The two pendulums oscillate
+constantly in the inverse sense the one to the other.
+
+[Illustration: Fig. 154]
+
+[Illustration: Fig. 155]
+
+
+ANOTHER TWO-PENDULUM ESCAPEMENT.
+
+We show another escapement with two pendulums in Fig. 153. These are
+fixed directly upon two axes, each one carrying a pallet _P P'_ and a
+segment of a toothed wheel _D D_, which produces the effect of
+solidarity between them. The two pendulums oscillate inversely one to
+the other, and one after the other receives an impulse. This escapement
+was constructed by Jean Baptiste Dutertre, of Paris.
+
+Fig. 154 shows another disposition of a double pendulum. While the
+pendulum here is double, it has but one bob; it receives the impulse by
+means of a double fork _F_. _C C_ represents the cycloidal curves and
+are placed with a view of correcting the inequality in the duration of
+the oscillations. In watches the circular balances did not afford any
+better results than the regulating rods or rules of the clocks, and the
+pendulum, of course, was out of the question altogether; it therefore
+became imperative to invent some other regulating system.
+
+[Illustration: Fig. 156]
+
+[Illustration: Fig. 157]
+
+It occured to the Abbé d'Hautefeuille to form a sort of resilient
+mechanism by attaching one end of a hog's bristle to the plate and the
+other to the balance near the axis. Though imperfect in results, this
+was nevertheless a brilliant idea, and it was but a short step to
+replace the bristle with a straight and very flexible spring, which
+later was supplanted by one coiled up like a serpent; but in spite of
+this advancement, the watches did not keep much better time. Harrison,
+the celebrated English horologist, had recourse to two artifices, of
+which the one consisted in giving to the pallets of the escapement such
+a curvature that the balance could be led back with a velocity
+corresponding to the extension of the oscillation; the second consisted
+of an accessory piece, the resultant action of which was analogous to
+that of the cycloidal curves in connection with the pendulum.
+
+
+CORRECTING IRREGULARITIES IN THE VERGE ESCAPEMENT.
+
+Huygens attempted to correct these irregularities in the verge
+escapement in watches by amplifying the arc of oscillation of the
+balance itself. He constructed for that purpose a pirouette escapement
+shown in Fig. 155, in which a toothed wheel _A_ adjusted upon the verge
+_V_ serves as an intermediary between that and the balance _B_, upon the
+axis of which was fixed a pinion _D_. By this method he obtained
+extended arcs of vibration, but the vibrations were, as a consequence,
+very slow, and they still remained subject to all the irregularities
+arising from the variation in the motive power as well as from shocks. A
+little later, but about the same epoch, a certain Dr. Hook, of the Royal
+Society of London, contrived another arrangement by means of which he
+succeeded, so it appeared to him at least, in greatly diminishing the
+influence of shock upon the escapement; but many other, perhaps greater,
+inconveniences caused his invention to be speedily rejected. We shall
+give our readers an idea of what Dr. Hook's escapement was like.
+
+[Illustration: Fig. 158]
+
+[Illustration: Fig. 159]
+
+On looking at Fig. 156 we see the escape wheel _R_, which was flat and
+in the form of a ratchet; it was provided with two balances. _B B_
+engaging each other in teeth, each one carrying a pallet _P P'_ upon its
+axis; the axes of the three wheels being parallel. Now, in our drawing,
+the tooth _a_ of the escape wheel exerts its lift upon the pallet _P'_;
+when this tooth escapes the tooth _b_ will fall upon the pallet _P'_ on
+the opposite side, a recoil will be produced upon the action of the two
+united balances, then the tooth _b_ will give its impulse in the
+contrary direction. Considerable analogy exists between this form of
+escapement and that shown in Fig. 153 and intended for clocks. This was
+the busy era in the watchmaker's line. All the great heads were
+pondering upon the subject and everyone was on the _qui vive_ for the
+newest thing in the art.
+
+In 1674 Huygens brought out the first watch having a regulating spring
+in the form of a spiral; the merit of this invention was disputed by the
+English savant, Dr. Hook, who pretended, as did Galileo, in the
+application of the pendulum, to have priority in the idea. Huygens, who
+had discovered and corrected the irregularities in the oscillations of
+the pendulum, did not think of those of the balance with the spiral
+spring. And it was not until the close of the year 1750 that Pierre Le
+Roy and Ferdinand Berthoud studied the conditions of isochronism
+pertaining to the spiral.
+
+
+AN INVENTION THAT CREATED MUCH ENTHUSIASM.
+
+However that may be, this magnificent invention, like the adaptation of
+the pendulum, was welcomed with general enthusiasm throughout the
+scientific world: without spiral and without pendulum, no other
+escapement but the recoil escapement was possible; a new highway was
+thus opened to the searchers. The water clocks (clepsydræ) and the hour
+glasses disappeared completely, and the timepieces which had till then
+only marked the hours, having been perfected up to the point of keeping
+more exact time, were graced with the addition of another hand to tell
+off the minutes.
+
+[Illustration: Fig. 160]
+
+[Illustration: Fig. 161]
+
+It was not until 1695 that the first _dead-beat escapement_ appeared
+upon the scene; during the interval of over twenty years all thought had
+been directed toward the one goal, viz.: the perfecting of the _verge
+escapement_; but practice demonstrated that no other arrangement of the
+parts was superior to the original idea. For the benefit of our readers
+we shall give a few of these attempts at betterment, and you may see for
+yourselves wherein the trials failed.
+
+Fig. 157 represents a _verge escapement_ with a ratchet wheel, the
+pallets _P P'_ being carried upon separate axes. The two axes are
+rigidly connected, the one to the other, by means of the arms _o o'_.
+One of the axes carries besides the fork _F_, which transmits the
+impulse to the pendulum _B_. In the front view, at the right of the
+plate, for the sake of clearness the fork and the pendulum are not
+shown, but one may easily see the jointure of the arms _o o'_ and their
+mode of operation.
+
+Another very peculiar arrangement of the _verge escapement_ we show at
+Fig. 158. In this there are two wheels, one, _R'_, a small one in the
+form of a ratchet; the other, _R_, somewhat larger, called the balance
+wheel, but being supplied with straight and slender teeth. The verge _V_
+carrying the two pallets is pivoted in the vertical diameter of the
+larger wheel. The front view shows the _modus operandi_ of this
+combination, which is practically the same as the others. The tooth _a_
+of the large wheel exerts its force upon the pallet _P_, and the tooth
+_b_ of the ratchet will encounter the pallet _P'_. This pallet, after
+suffering its recoil, will receive the impulse communicated by the tooth
+_b_. This escapement surely could not have given much satisfaction, for
+it offers no advantage over the others, besides it is of very difficult
+construction.
+
+[Illustration: Fig. 162]
+
+[Illustration: Fig. 163]
+
+
+INGENIOUS ATTEMPTS AT SOLUTION OF A DIFFICULT PROBLEM.
+
+Much ingenuity to a worthy end, but of little practical value, is
+displayed in these various attempts at the solution of a very difficult
+problem. In Fig. 159 we have a mechanism combining two escape wheels
+engaging each other in gear; of the two wheels, _R R'_, one alone is
+driven directly by the train, the other being turned in the opposite
+direction by its comrade. Both are furnished with pins _c c'_, which act
+alternately upon the pallets _P P'_ disposed in the same plane upon the
+verge _V_ and pivoted between the wheels. Our drawing represents the
+escapement at the moment when the pin _C'_ delivers its impulse, and
+this having been accomplished, the locking takes place upon the pin _C_
+of the other wheel upon the pallet _P'_. Another system of two escape
+wheels is shown in Fig. 160, but in this case the two wheels _R R_ are
+driven in a like direction by the last wheel _A_ of the train. The
+operation of the escapement is the same as in Fig. 159.
+
+[Illustration: Fig. 164]
+
+[Illustration: Fig. 165]
+
+In Fig. 161 we have a departure from the road ordinarily pursued. Here
+we see an escapement combining two levers, invented by the Chevalier de
+Béthune and applied by M. Thiout, master-horologist, at Paris in 1727.
+_P P'_ are the two levers or pallets separately pivoted. Upon the axis
+_V_, of the lever _P_, is fixed a fork which communicates the motion to
+the pendulum. The two levers are intimately connected by the two arms _B
+B'_, of which the former carries an adjusting screw, a well-conceived
+addition for regulating the opening between the pallets. The
+counter-weight _C_ compels constant contact between the arms _B B'_. The
+function is always the same, the recoil and the impulsion operate upon
+the two pallets simultaneously. This escapement enjoyed a certain degree
+of success, having been employed by a number of horologists who modified
+it in various ways.
+
+
+VARIOUS MODIFICATIONS
+
+Some of these modifications we shall show. For the first example, then,
+let Fig. 162 illustrate. In this arrangement the fork is carried upon
+the axis of the pallet _P'_, which effectually does away with the
+counter-weight _C_, as shown. Somewhat more complicated, but of the same
+intrinsic nature, is the arrangement displayed in Fig. 163. We should
+not imagine that it enjoyed a very extensive application. Here the two
+levers are completely independent of each other; they act upon the piece
+_B B_ upon the axis _V_ of the fork. The counter-weights _C C'_ maintain
+the arms carrying the rollers _D D'_ in contact with the piece _B B'_
+which thus receives the impulse from the wheel _R_. Two adjusting screws
+serve to place the escapement upon the center. By degrees these
+fantastic constructions were abandoned to make way for the anchor recoil
+escapement, which was invented, as we have said, in 1675, by G. Clement,
+a horologist, of London. In Fig. 164 we have the disposition of the
+parts as first arranged by this artist. Here the pallets are replaced by
+the inclines _A_ and _B_ of the anchor, which is pivoted at _V_ upon an
+axis to which is fixed also the fork. The tooth _a_ escapes from the
+incline or lever _A_, and the tooth _b_ immediately rests upon the lever
+_B_; by the action of the pendulum the escape wheel suffers a recoil as
+in the pallet escapement, and on the return of the pendulum the tooth
+_c_ gives out its impulse in the contrary direction. With this new
+system it became possible to increase the weight of the bob and at the
+same time lessen the effective motor power. The travel of the pendulum,
+or arc of oscillation, being reduced in a marked degree, an accuracy of
+rate was obtained far superior to that of the crown-wheel escapement.
+However, this new application of the recoil escapement was not adopted
+in France until 1695.
+
+[Illustration: Fig. 166]
+
+[Illustration: Fig. 167]
+
+The travel of the pendulum, though greatly reduced, still surpassed in
+breadth the arc in which it is isochronous, and repeated efforts were
+made to give such shape to the levers as would compel its oscillation
+within the arc of equal time; a motion which is, as was recognized even
+at that epoch, the prime requisite to a precise rating. Thus, in 1720,
+Julien Leroy occupied himself working out the proper shapes for the
+inclines to produce this desired isochronism. Searching along the same
+path, Ferd. Berthoud constructed an escapement represented by the Fig.
+165. In it we see the same inclines _A B_ of the former construction,
+but the locking is effected against the slides _C_ and _D_, the curved
+faces of which produce isochronous oscillations of the pendulum. The
+tooth _b_ imparts its lift and the tooth _c_ will lock against the face
+_C_; after having passed through its recoil motion this tooth _c_ will
+butt against the incline _A_ and work out its lift or impulse upon it.
+
+
+THE GABLE ESCAPEMENT.
+
+[Illustration: Fig. 168]
+
+[Illustration: Fig. 169]
+
+The _gable escapement_, shown in Fig. 166, allows the use of a heavier
+pendulum, at the same time the anchor embraces within its jaws a greater
+number of the escape-wheel teeth; an arrangement after this manner leads
+to the conclusion that with these long levers of the anchor the friction
+will be considerably increased and the recoil faces will, as a
+consequence, be quickly worn away. Without doubt, this was invented to
+permit of opening and closing the contact points of the anchor more
+easily. Under the name of the _English recoil anchor_ there came into
+use an escapement with a _reduced gable_, which embraced fewer teeth
+between the pallets or inclines; we give a representation of this in
+Fig. 167. This system seems to have been moderately successful. The
+anchor recoil escapement in use in Germany to-day is demonstrated in
+Fig. 168; this arrangement is also found in the American clocks. As we
+see, the anchor is composed of a single piece of curved steel bent to
+the desired curves. Clocks provided with this escapement keep reasonably
+good time; the resistance of the recoils compensate in a measure for the
+want of isochronism in the oscillations of the pendulum. Ordinary clocks
+require considerably more power to drive them than finer clocks and, as
+a consequence, their ticking is very noisy. Several means have been
+employed to dampen this noise, one of which we show in Fig. 169.
+
+[Illustration: Fig. 170]
+
+Here the anchor is composed of two pieces, _A B_, screwed upon a plate
+_H_ pivoting at _V_. In their arrangement the two pieces represent, as
+to distance and curvature, the counterpart of Fig. 168. At the moment of
+impact their extreme ends recoil or spring back from the shock of the
+escape teeth, but the resiliency of the metal is calculated to be strong
+enough to return them immediately to the contact studs _e e_.
+
+As a termination to this chapter, we shall mention the use made at the
+present day of the recoil lever escapement in repeating watches. We give
+a diagram of this construction in Fig. 170. The lever here is intended
+to restrain and regulate the motion of the small striking work. It is
+pivoted at _V_ and is capable of a very rapid oscillatory motion, the
+arc of which may, however, be fixed by the stud or stop _D_, which
+limits the swing of the fly _C_. This fly is of one piece with the lever
+and, together with the stud _D_, determines the angular motion of the
+lever. If the angle be large that means the path of the fly be long,
+then the striking train will move slowly; but if the teeth of the escape
+wheel _R_ can just pass by without causing the lever to describe a
+supplementary or extended arc, the striking work will run off rapidly.
+
+
+
+
+CHAPTER V.
+
+PUTTING IN A NEW CYLINDER.
+
+
+Putting in a new cylinder is something most watchmakers fancy they can
+do, and do well; but still it is a job very few workmen can do and
+fulfill all the requirements a job of this kind demands under the
+ever-varying conditions and circumstances presented in repairs of this
+kind. It is well to explain somewhat at this point: Suppose we have five
+watches taken in with broken cylinders. Out of this number probably two
+could be pivoted to advantage and make the watches as good as ever. As
+to the pivoting of a cylinder, we will deal with this later on. The
+first thing to do is to make an examination of the cylinder, not only to
+see if it is broken, but also to determine if pivoting is going to bring
+it out all right. Let us imagine that some workman has, at some previous
+time, put in a new cylinder, and instead of putting in one of the proper
+size he has put one in too large or too small. Now, in either case he
+would have to remove a portion of the escape-wheel tooth, that is,
+shorten the tooth: because, if the cylinder was too large it would not
+go in between the teeth, and consequently the teeth would have to be cut
+or stoned away. If the cylinder was too small, again the teeth would
+have to be cut away to allow them to enter the cylinder. All workmen
+have traditions, rules some call them, that they go by in relation to
+the right way to dress a cylinder tooth; some insisting that the toe or
+point of the tooth is the only place which should be tampered with.
+Other workmen insist that the heel of the tooth is the proper place.
+Now, with all due consideration, we would say that in ninety-nine cases
+out of a hundred the proper thing to do is to let the escape-wheel teeth
+entirely alone. As we can understand, after a moment's thought, that it
+is impossible to have the teeth of the escape wheel too long and have
+the watch run at all; hence, the idea of stoning a cylinder escape-wheel
+tooth should not be tolerated.
+
+
+ESCAPE-WHEEL TEETH _vs._ CYLINDER.
+
+It will not do, however, to accept, and take it for granted that the
+escape-wheel teeth are all right, because in many instances they have
+been stoned away and made too short; but if we accept this condition as
+being the case, that is, that the escape-wheel teeth are too short, what
+is the workman going to do about it? The owner of the watch will not pay
+for a new escape wheel as well as a new cylinder. The situation can be
+summed up about in this way, that we will have to make the best we can
+out of a bad job, and pick out and fit a cylinder on a compromise idea.
+
+In regard to picking out a new cylinder, it may not do to select one of
+the same size as the old one, from the fact that the old one may not
+have been of the proper size for the escape wheel, because, even in new,
+cheap watches, the workmen who "run in" the escapement knew very well
+the cylinder and escape wheel were not adapted for each other, but they
+were the best he had. Chapter II, on the cylinder escapement, will
+enable our readers to master the subject and hence be better able to
+judge of allowances to be made in order to permit imperfect material to
+be used.
+
+In illustration, let us imagine that we have to put in a new cylinder,
+and we have none of precisely the proper size, but we have them both a
+mere trifle too large and too small, and the question is which to use.
+Our advice is to use the smaller one if it does not require the
+escape-wheel teeth to be "dressed," that is, made smaller. Why we make
+this choice is based on the fact that the smaller cylinder shell gives
+less friction, and the loss from "drop"--that is, side play between the
+escape-wheel teeth and the cylinder--will be the same in both instances
+except to change the lost motion from inside to outside drop.
+
+In devising a system to be applied to selecting a new cylinder, we meet
+the same troubles encountered throughout all watchmakers' repair work,
+and chief among these are good and convenient measuring tools. But even
+with perfect measuring tools we would have to exercise good judgment, as
+just explained. In Chapter II we gave a rule for determining the outside
+diameter of a cylinder from the diameter of the escape wheel; but such
+rules and tables will, in nine instances out of ten, have to be modified
+by attendant circumstances--as, for instance, the thickness of the shell
+of the cylinder, which should be one-tenth of the outer diameter of the
+shell, but the shell is usually thicker. A tolerably safe practical rule
+and one also depending very much on the workman's good judgment is, when
+the escape-wheel teeth have been shortened, to select a cylinder giving
+ample clearance inside the shell to the tooth, but by no means large
+enough to fill the space between the teeth. After studying carefully
+the instructions just given we think the workman will have no difficulty
+in selecting a cylinder of the right diameter.
+
+
+MEASURING THE HEIGHTS.
+
+The next thing is to get the proper heights. This is much more easily
+arrived at: the main measurement being to have the teeth of the escape
+wheel clear the upper face of the lower plug. In order to talk
+intelligently we will make a drawing of a cylinder and agree on the
+proper names for the several parts to be used in this chapter. Such
+drawing is shown at Fig. 171. The names are: The hollow cylinder, made
+up of the parts _A A' A'' A'''_, called the shell--_A_ is the great
+shell, _A'_ the half shell, _A''_ the banking slot, and _A'''_ the small
+shell. The brass part _D_ is called the collet and consists of three
+parts--the hairspring seat _D_, the balance seat _D'_ and the shoulder
+_D''_, against which the balance is riveted.
+
+[Illustration: Fig. 171]
+
+The first measurement for fitting a new cylinder is to determine the
+height of the lower plug face, which corresponds to the line _x x_,
+Fig. 171. The height of this face is such as to permit the escape wheel
+to pass freely over it. In selecting a new cylinder it is well to choose
+one which is as wide at the banking slot _A''_ as is consistent with
+safety. The width of the banking slot is represented by the dotted lines
+_x u_. The dotted line _v_ represents the length to which the lower
+pivot _y_ is to be cut.
+
+[Illustration: Fig. 172]
+
+[Illustration: Fig. 173]
+
+There are several little tools on the market used for making the
+necessary measurements, but we will describe a very simple one which can
+readily be made. To do so, take about a No. 5 sewing needle and, after
+annealing, cut a screw thread on it, as shown at Fig, 172, where _E_
+represents the needle and _t t_ the screw cut upon it. After the screw
+is cut, the needle is again hardened and tempered to a spring temper and
+a long, thin pivot turned upon it. The needle is now shaped as shown at
+Fig. 173. The pivot at _s_ should be small enough to go easily through
+the smallest hole jewel to be found in cylinder watches, and should be
+about 1/16" long. The part at _r_ should be about 3/16" long and only
+reduced in size enough to fully remove the screw threads shown at _t_.
+
+[Illustration: Fig. 174]
+
+[Illustration: Fig. 175]
+
+[Illustration: Fig. 176]
+
+[Illustration: Fig. 177]
+
+We next provide a sleeve or guard for our gage. To do this we take a
+piece of hard brass bushing wire about ½" long and, placing it in a
+wire chuck, center and drill it nearly the entire length, leaving, say,
+1/10" at one end to be carried through with a small drill. We show at
+_F_, Fig. 174, a magnified longitudinal section of such a sleeve. The
+piece _F_ is drilled from the end _l_ up to the line _q_ with a drill of
+such a size that a female screw can be cut in it to fit the screw on the
+needle, and _F_ is tapped out to fit such a screw from _l_ up to the
+dotted line _p_. The sleeve _F_ is run on the screw _t_ and now appears
+as shown at Fig. 175, with the addition of a handle shown at _G G'_. It
+is evident that we can allow the pivot _s_ to protrude from the sleeve
+_F_ any portion of its length, and regulate such protrusion by the screw
+_t_. To employ this tool for getting the proper length to which to cut
+the pivot _y_, Fig. 171, we remove the lower cap jewel to the cylinder
+pivot and, holding, the movement in the left hand, pass the pivot _s_,
+Fig. 175, up through the hole jewel, regulate the length by turning the
+sleeve _F_ until the arm of the escape wheel _I_, Fig. 176, will just
+turn free over it. Now the length of the pivot _s_, which protrudes
+beyond the sleeve _F_, coincides with the length to which we must cut
+the pivot _y_, Fig. 171. To hold a cylinder for reducing the length of
+the pivot _y_, we hold said pivot in a pair of thin-edged cutting
+pliers, as shown at Fig. 177, where _N N'_ represent the jaws of a pair
+of cutting pliers and _y_ the pivot to be cut. The measurement is made
+by putting the pivot _s_ between the jaws _N N'_ as they hold the pivot.
+The cutting is done by simply filing back the pivot until of the right
+length.
+
+
+TURNING THE PIVOTS.
+
+We have now the pivot _y_ of the proper length, and what remains to be
+done is to turn it to the right size. We do not think it advisable to
+try to use a split chuck, although we have seen workmen drive the shell
+_A A'''_ out of the collet _D_ and then turn up the pivots _y z_ in said
+wire chuck. To our judgment there is but one chuck for turning pivots,
+and this is the cement chuck provided with all American lathes. Many
+workmen object to a cement chuck, but we think no man should lay claim
+to the name of watchmaker until he masters the mystery of the cement
+chuck. It is not such a very difficult matter, and the skill once
+acquired would not be parted with cheaply. One thing has served to put
+the wax or cement chuck into disfavor, and that is the abominable stuff
+sold by some material houses for lathe cement. The original cement, made
+and patented by James Bottum for his cement chuck, was made up of a
+rather complicated mixture; but all the substances really demanded in
+such cement are ultramarine blue and a good quality of shellac. These
+ingredients are compounded in the proportion of 8 parts of shellac and 1
+part of ultramarine--all by weight.
+
+
+HOW TO USE A CEMENT CHUCK.
+
+The shellac is melted in an iron vessel, and the ultramarine added and
+stirred to incorporate the parts. Care should be observed not to burn
+the shellac. While warm, the melted mass is poured on to a cold slab of
+iron or stone, and while plastic made into sticks about ½" in
+diameter.
+
+[Illustration: Fig. 178]
+
+[Illustration: Fig. 179]
+
+We show at Fig. 178 a side view of the outer end of a cement chuck with
+a cylinder in position. We commence to turn the lower pivot of a
+cylinder, allowing the pivot _z_ to rest at the apex of the hollow cone
+_a_, as shown. There is something of a trick in turning such a hollow
+cone and leaving no "tit" or protuberance in the center, but it is
+important it should be done. A little practice will soon enable one to
+master the job. A graver for this purpose should be cut to rather an
+oblique point, as shown at _L_, Fig. 179. The slope of the sides to the
+recess _a_, Fig. 178, should be to about forty-five degrees, making the
+angle at _a_ about ninety degrees. The only way to insure perfect
+accuracy of centering of a cylinder in a cement chuck is center by the
+shell, which is done by cutting a piece of pegwood to a wedge shape and
+letting it rest on the T-rest; then hold the edge of the pegwood to the
+cylinder as the lathe revolves and the cement soft and plastic. A
+cylinder so centered will be absolutely true. The outline curve at _c_,
+Fig. 178, represents the surface of the cement.
+
+The next operation is turning the pivot to the proper size to fit the
+jewel. This is usually done by trial, that is, trying the pivot into the
+hole in the jewel. A quicker way is to gage the hole jewel and then turn
+the pivot to the right size, as measured by micrometer calipers. In some
+cylinder watches the end stone stands at some distance from the outer
+surface of the hole jewel; consequently, if the measurement for the
+length of the pivot is taken by the tool shown at Fig. 175, the pivot
+will apparently be too short. When the lower end stone is removed we
+should take note if any allowance is to be made for such extra space.
+The trouble which would ensue from not providing for such extra end
+shake would be that the lower edge of the half shell, shown at _e_, Fig.
+171, would strike the projection on which the "stalk" of the tooth is
+planted. After the lower pivot is turned to fit the jewel the cylinder
+is to be removed from the cement chuck and the upper part turned. The
+measurements to be looked to now are, first, the entire length of the
+cylinder, which is understood to be the entire distance between the
+inner faces of the two end stones, and corresponds to the distance
+between the lines _v d_, Fig. 171. This measurement can be got by
+removing both end stones and taking the distance with a Boley gage or a
+douzieme caliper.
+
+
+A CONVENIENT TOOL FOR LENGTH MEASUREMENT.
+
+[Illustration: Fig. 180]
+
+A pair of common pinion calipers slightly modified makes as good a pair
+of calipers for length measurement as one can desire. This instrument is
+made by inserting a small screw in one of the blades--the head on the
+inner side, as shown at _f_, Fig. 180. The idea of the tool is, the
+screw head _f_ rests in the sink of the cap jewel or end stone, while
+the other blade rests on the cock over the balance. After the adjusting
+screw to the caliper is set, the spring of the blades allows of their
+removal. The top pivot _z_ of the cylinder is next cut to the proper
+length, as indicated by the space between the screwhead _f_ and the
+other blade of the pinion caliper. The upper pinion _z_ is held in the
+jaws of the cutting pliers, as shown in Fig. 177, the same as the lower
+one was held, until the proper length between the lines _d v_, Fig. 171,
+is secured, after which the cylinder is put back into the cement chuck,
+as shown at Fig. 178, except this time the top portion of the cylinder
+is allowed to protrude so that we can turn the top pivot and the balance
+collet _D_, Fig. 171.
+
+The sizes we have now to look to is to fit the pivot _z_ to the top
+hole jewel in the cock, also the hairspring seat _D_ and balance seat
+_D'_. These are turned to diameters, and are the most readily secured by
+the use of the micrometer calipers to be had of any large watchmakers'
+tool and supply house. In addition to the diameters named, we must get
+the proper height for the balance, which is represented by the dotted
+line _b_. The measurement for this can usually be obtained from the old
+cylinder by simply comparing it with the new one as it rests in the
+cement chuck. The true tool for such measurements is a height gage. We
+have made no mention of finishing and polishing the pivots, as these
+points are generally well understood by the trade.
+
+
+REMOVING THE LATHE CEMENT.
+
+One point perhaps we might well say a few words on, and this is in
+regard to removing the lathe cement. Such cement is usually removed by
+boiling in a copper dish with alcohol. But there are several objections
+to the practice. In the first place, it wastes a good deal of alcohol,
+and also leaves the work stained. We can accomplish this operation
+quicker, and save alcohol, by putting the cylinder with the wax on it in
+a very small homeopathic bottle and corking it tight. The bottle is then
+boiled in water, and in a few seconds the shellac is dissolved away. The
+balance to most cylinder watches is of red brass, and in some instances
+of low karat gold; in either case the balance should be repolished. To
+do this dip in a strong solution of cyanide of potassium dissolved in
+water; one-fourth ounce of cyanide in half pint of water is about the
+proper strength. Dip and rinse, then polish with a chamois buff and
+rouge.
+
+[Illustration: Fig. 181]
+
+In staking on the balance, care should be observed to set the banking
+pin in the rim so it will come right; this is usually secured by setting
+said pin so it stands opposite to the opening in the half shell. The
+seat of the balance on the collet _D_ should be undercut so that there
+is only an edge to rivet down on the balance. This will be better
+understood by inspecting Fig. 181, where we show a vertical section of
+the collet _D_ and cylinder _A_. At _g g_ is shown the undercut edge of
+the balance seat, which is folded over as the balance is rivetted fast.
+
+About all that remains now to be done is to true up the balance and
+bring it to poise. The practice frequently adopted to poise a plain
+balance is to file it with a half-round file on the inside, in order not
+to show any detraction when looking at the outer edge of the rim. A
+better and quicker plan is to place the balance in a split chuck, and
+with a diamond or round-pointed tool scoop out a little piece of metal
+as the balance revolves. In doing this, the spindle of the lathe is
+turned by the hand grasping the pulley between the finger and thumb. The
+so-called diamond and round-pointed tools are shown at _o o'_, Fig. 182.
+The idea of this plan of reducing the weight of a balance is, one of the
+tools _o_ is rested on the T-rest and pressed forward until a chip is
+started and allowed to enter until sufficient metal is engaged, then, by
+swinging down on the handle of the tool, the chip is taken out.
+
+[Illustration: Fig. 182]
+
+[Illustration: Fig. 183]
+
+In placing a balance in a step chuck, the banking pin is caused to enter
+one of the three slots in the chuck, so as not to be bent down on to the
+rim of the balance. It is seldom the depth between the cylinder and
+escape wheel will need be changed after putting in a new cylinder; if
+such is the case, however, move the chariot--we mean the cock attached
+to the lower plate. Do not attempt to change the depth by manipulating
+the balance cock. Fig. 183 shows, at _h h_, the form of chip taken out
+by the tool _o o'_, Fig. 182.
+
+
+
+
+INDEX
+
+
+  A
+
+  Acid frosting, 46
+
+  "Action" drawings, 90
+
+  Action of a chronometer escapement, 142
+
+  Acting surface of entrance lip, 127
+
+  Actions of cylinder escapement, 112
+
+  Adhesion of parallel surfaces, 94
+
+  Adjustable pallets, 98
+
+  Adjusting screw for drawing instruments, 21
+
+  Analysis of principles involved in detent, 137
+
+  Analysis of the action of a lever escapement, 86
+
+  Angle-measuring device, 68
+
+  Angular extent of shell of cylinder, 122
+
+  Angular motion, drawing an escapement to show, 91
+    How measured, 69
+    Of escape wheel, 37
+
+  Antagonistic influences, 133
+
+  Arc of degrees, 9
+
+  Atmospheric disturbances, 74
+
+  Attainment of isochronism, 159
+
+
+  B
+
+  Balance, how it controls timekeeping, 73
+    Weight and inertia of, 133
+
+  Balance spring, inventor of, 132
+
+  Banking slot of cylinder, 112
+
+  Bankings, effect of opening too wide, 63
+
+  Bar compasses, 21
+
+  Barometric pressure, 74
+
+  Basis for close measurements, 96
+
+
+  C
+
+  Cement chuck, how to use, 173
+
+  Chronometer detent, importance of light construction, 136
+
+  Chronometer escapement, 131, 155
+    Four principal parts of, 134
+
+  Circular pallets, 27
+
+  Club-tooth escapement, 30, 34
+
+  Club-tooth lever escapement with circular pallets and
+    tangential lockings, 83
+
+  Crown-wheel escapement, 155
+
+  Cylinder, drawing a, 120
+    Outer diameter of, 116
+    Putting in a new, 169
+
+  Cylinder escapement, 155
+    Date of invention, etc., 111
+    Forms and proportions of several parts of, 111
+    Names of various parts, 112
+
+  Cylinder lips, proper shape of, 124
+
+
+  D
+
+  Dead-beat escapement, 131, 135
+    Only one true, 112
+
+  Depth, between cylinder and escape wheel, 129
+    Effect of changing, 176
+
+  Designing a double roller, 77
+
+  Detached escapement, 155
+
+  Detent, functions of the, 137
+
+  Detent escapement, 131, 155
+    Faults in, 132
+
+  Detent spring dimensions, 138
+
+  Detent springs, width of, 147
+
+  Discharging jewel, setting the, 142
+
+  Discharging roller, 136
+
+  Dividers, 9
+    Making, 10
+
+  Double pendulum, 160
+
+  Double-roller escapement, 75
+
+  Draw defined, 85
+
+  Drawing-board, 11
+
+  Drawing instruments, 9
+
+  Drawings, advantage of large, 29
+
+  Drop and draw, 150
+
+  Duplex escapement, 131, 155
+
+
+  E
+
+  Elasticity of spring, 133
+
+  Engaging friction, 81
+
+  English recoil anchor, 167
+
+  Entrance lip of cylinder escapement, 125
+
+  Escapement angles, measuring, 101
+
+  Escapement error, study of, 64
+
+  Escapement matching tool, 106
+
+  Escapement model, 40
+    Balance, 42
+    Balance staff, 44
+    Bridges, 41, 42
+    Escape wheel, 43
+    Extra balance cock, 45
+    "Frosting", 46
+    Hairspring, 42
+    Jewel for, 43
+    Lower plate, 41
+    Main plate, 41
+    Movement for, 41
+    Pallet staff, 42
+    Pillars, 43
+    Regulator, 46
+    Uses of, 44
+    Wood base for, 41
+
+  Escapements compared, 103
+
+  Escapement of Dutertre, 160
+
+  Escape-wheel action, 30
+
+  Escape-wheel, delineating an, 11
+
+  Escape-wheel teeth vs. cylinder, 169
+
+  Escape-wheel tooth in action, delineating an, 126
+
+  Exit pallet, 26
+
+  Experiments of Galileo, 158
+
+  Experiments with a chronometer, 142
+
+  Extent of angular impulse, 118
+
+
+  F
+
+  "Fall" defined, 106
+
+  Faults in the detent escapement, 132
+
+  Fixed rules, of little value to student, 137
+
+  Flexure of gold spring, 146
+
+  Foot, fitting up the, 151
+
+  Fork, testing the, 71
+
+  Fork action, 30
+    Theory of, 59
+
+  Fork and roller action, 54
+
+  Formulas for delineating cylinder escapement, 115
+
+  Frictions, 24
+
+  Frictional escapement, 131, 132
+
+  Frictional surfaces, 63
+
+  Fusee, 131
+
+
+  G
+
+  Gable escapement, 167
+
+  Gage, a new, 172
+
+  Graham anchor escapement, 155
+
+  Gold spring, 146
+
+  Guard point, 79
+    Material for, 79
+
+  Gummy secretion on impulse and discharging stones, 147
+
+
+  H
+
+  Heights in cylinders, how obtained, 171
+
+  Hole jewels, distance apart, 140
+
+
+  I
+
+  Imaginary faults in cylinders, 129
+
+  Impulse angle, 118
+
+  Impulse arc, extent of, 134
+
+  Impulse jewel set oblique, 147
+
+  Impulse planes, locating outer angle of, 39
+
+  Impulse roller, 136
+
+  Incline of teeth, 122
+
+  Inertia of balance, 133
+
+  Inventions of
+    Berthoud, 163
+    Béthune, 165
+    Clement, 166
+    Dr. Hook, 162
+    Harrison, 161
+    Hautefeuille, 161
+    Huygens, 158
+    Leroy, 163
+    Thiout, 165
+
+
+  J
+
+  Jewel pin, determining size, 58
+    Cementing in, 67
+    Settings, 66
+
+  Jewel-pin setters, 67
+
+
+  L
+
+  Lathe cement, 173
+    Removing, 175
+
+  Lever, proper length of, 61
+
+  Lever fork, horn of, 61
+    prongs of, 60
+
+  Lift, real and apparent, 112
+
+  Lifting angle, 114
+
+  Lock, amount of, 28
+    Defined, 85
+
+  Lock and drop testing, 69
+
+  Locking jewel, moving the, 149
+
+  Locking stone, good form of, 144
+
+  Lower plate, circular opening in, 56
+
+
+  M
+
+  Marine chronometer, number of beats to hour, 148
+
+  Mathematics, 95
+
+  Measuring tools, 171
+
+  Metal drawings, advantages of, 140
+
+  Motion, how obtained, 16
+
+  Movement holder, 110
+
+
+  N
+
+  Neutral lockings, 84
+
+
+  O
+
+  Original designing, 148
+
+
+  P
+
+  Pallet action, locating the, 90
+
+  Pallet-and-fork action, 12, 13, 17, 18
+
+  Pallet stones, how to set, 104
+
+  Pallets, adjusting to match the fork, 65
+
+  Paper for drawing, 11
+
+  Parts, relations of the, 32
+
+  Passing hollow, 62
+
+  Perfected lever escapement, 87
+
+  Pivots, turning, 172
+
+  Point of percussion, 139
+
+  Points for drawing instruments, 20
+
+  Polishing materials, 52
+
+  Power leaks, 16
+
+  Power lost in lever escapement, 87
+
+  Practical problems in the lever escapement, 98
+
+
+  R
+
+  Radial extent of outside of cylinder, 125
+
+  Ratchet-tooth escape wheel, 12
+
+  Recoil anchor escapement, 155
+
+  Recoil escapement, 154
+
+  Reduced gable escapement, 167
+
+  Retrograde motion, 36
+
+  Roller action, why 30 degrees, 55
+    Of double roller, 78
+
+  Roller diameter, determining the, 55
+
+  Ruling pen, 9
+
+
+  S
+
+  Safety action, 56
+
+  Scale of inches, 9
+
+  Screws, making extra large, 45
+
+  Screwheads, fancy, 45
+
+  Selecting new cylinder, 170
+
+  Shaping, advantages gained in, 116
+
+  Sheet steel, cutting, 48
+
+  Short fork, 100
+
+  Sound as indicator of correct action, 144
+
+  Spring, elasticity of, 133
+
+  Staking on a balance, 175
+
+  Steel, polishing, 49
+    Tempering, 49
+
+  Study drawings, 124
+
+  Systems of measurements, 114
+
+
+  T
+
+  Tangential lockings, 80, 148
+
+  Test gage for angular movement, 65
+
+  Theoretical action of double roller, 76
+
+  Timekeeping, controlled by balance, 73
+
+  Tool for length measurement, 174
+
+  Tools, measuring, 171
+
+  Triangle, 18
+
+  T-square, 9
+
+
+  U
+
+  Unlocking action, 56
+
+  Unlocking roller, 136
+
+
+  V
+
+  Verge escapement, 131, 155
+
+
+  W
+
+  Weight and inertia of balance, 133
+
+  Working model of cylinder escapement, 123
+
+
+
+     *     *     *     *     *     *
+
+
+
+THE WATCH ADJUSTER'S MANUAL
+
+[Illustration]
+
+A Complete and Practical Guide for Watchmakers in Adjusting Watches and
+Chronometers for Isochronism, Position, Heat and Cold.
+
+
+BY CHARLES EDGAR FRITTS (EXCELSIOR),
+
+Author of "Practical Hints on Watch Repairing," "Practical Treatise on
+Balance Spring," "Electricity and Magnetism for Watchmakers," etc., etc.
+
+This well-known work is now recognized as the standard authority on the
+adjustments and kindred subjects, both here and in England. It contains
+an exhaustive consideration of the various theories proposed, the
+mechanical principles on which the adjustments are based, and the
+different methods followed in actual practice, giving all that is
+publicly known in the trade, with a large amount of entirely new
+practical matter not to be found elsewhere, obtained from the best
+manufacturers and workmen, as well as from the author's own studies and
+experiences.
+
+Sent postpaid to any part of the world on receipt of $2.50 (10s. 5d.)
+
+  THE KEYSTONE (SOLE AGENT),
+  19TH AND BROWN STREETS, PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE ART OF ENGRAVING
+
+[Illustration]
+
+A Complete Treatise on the Engraver's Art, with Special Reference to
+Letter and Monogram Engraving. Specially Compiled as a Standard
+Text-Book for Students and a Reliable Reference Book for Engravers.
+
+This work is the only thoroughly reliable and exhaustive treatise
+published on this important subject. It is an ideal text-book, beginning
+with the rudiments and leading the student step by step to a complete
+and practical mastery of the art. Back of the authorship is a long
+experience as a successful engraver, also a successful career as an
+instructor in engraving. These qualifications ensure accuracy and
+reliability of matter, and such a course of instruction as is best for
+the learner and qualified engraver.
+
+The most notable feature of the new treatise is the instructive
+character of the illustrations. There are over 200 original
+illustrations by the author. A very complete index facilitates reference
+to any required topic.
+
+Bound in Silk Cloth--208 Pages and 216 Illustrations.
+
+Sent postpaid to any part of the world on receipt of price, $1.50 (6s.
+3d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE KEYSTONE PORTFOLIO OF MONOGRAMS
+
+[Illustration: C.B.R.]
+
+[Illustration: A.O.U.W]
+
+[Illustration: I.R.C.]
+
+[Illustration: G.H.I.]
+
+This portfolio contains 121 combination designs. These designs were
+selected from the best of those submitted in a prize competition held by
+The Keystone, and will be found of value to every one doing engraving.
+
+The designs are conceded to be the best in the market, excelling in art
+and novelty of combination and skill in execution.
+
+They are printed from steel plates on stiff, durable paper, and contain
+sample monograms in a variety of combinations.
+
+The portfolio is a bench requirement that no jeweler can afford to be
+without. It is a necessary supplement to any text-book on letter
+engraving.
+
+  Price,
+  50 Cents (2s.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE OPTICIAN'S MANUAL
+
+VOL. I.
+
+BY C.H. BROWN, M.D.
+
+Graduate University of Pennsylvania; Professor of Optics and Refraction;
+formerly Physician in Philadelphia Hospital; Member of Philadelphia
+County, Pennsylvania State and American Medical Societies.
+
+[Illustration]
+
+The Optician's Manual, Vol. I., has proved to be the most popular work
+on practical refraction ever published. The knowledge it contains has
+been more effective in building up the optical profession than any other
+educational factor. A study of it is essential to an intelligent
+appreciation of Vol. II., for it lays the foundation structure of all
+optical knowledge, as the titles of its ten chapters show:
+
+  Chapter    I.--Introductory Remarks.
+  Chapter   II.--The Eye Anatomically.
+  Chapter  III.--The Eye Optically; or, The Physiology of Vision.
+  Chapter   IV.--Optics.
+  Chapter    V.--Lenses.
+  Chapter   VI.--Numbering of Lenses.
+  Chapter  VII.--The Use and Value of Glasses.
+  Chapter VIII.--Outfit Required.
+  Chapter   IX.--Method of Examination.
+  Chapter    X.--Presbyopia.
+
+The Optician's Manual, Vol. I., is complete in itself, and has been the
+entire optical education of many successful opticians. For student and
+teacher it is the best treatise of its kind, being simple in style,
+accurate in statement and comprehensive in its treatment of refractive
+procedure and problems. It merits the place of honor beside Vol. II. in
+every optical library.
+
+Bound in Cloth--422 pages--colored plates and Illustrations.
+
+Sent postpaid on receipt of $2.00 (8s. 4d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE OPTICIAN'S MANUAL
+
+VOL. II.
+
+BY C.H. BROWN, M.D.
+
+Graduate University of Pennsylvania; Professor of Optics and Refraction;
+formerly Physician in Philadelphia Hospital; Member of Philadelphia
+County, Pennsylvania State and American Medical Societies.
+
+[Illustration]
+
+The Optician's Manual, Vol. II., is a direct continuation of The
+Optician's Manual, Vol. I., being a much more advanced and comprehensive
+treatise. It covers in minutest detail the four great subdivisions of
+practical eye refraction, viz:
+
+  Myopia.
+  Hypermetropia.
+  Astigmatism.
+  Muscular Anomalies.
+
+It contains the most authoritative and complete researches up to date on
+these subjects, treated by the master hand of an eminent oculist and
+optical teacher. It is thoroughly practical, explicit in statement and
+accurate as to fact. All refractive errors and complications are clearly
+explained, and the methods of correction thoroughly elucidated.
+
+This book fills the last great want in higher refractive optics, and the
+knowledge contained in it marks the standard of professionalism.
+
+Bound in Cloth--408 pages--with illustrations.
+
+Sent postpaid on receipt of $2.00 (8s. 4d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+SKIASCOPY AND THE USE OF THE RETINOSCOPE
+
+[Illustration]
+
+A Treatise on the Shadow Test in its Practical Application to the Work
+of Refraction, with an Explanation in Detail of the Optical Principles
+on which the Science is Based.
+
+This new work, the sale of which has already necessitated a second
+edition, far excels all previous treatises on the subject in
+comprehensiveness and practical value to the refractionist. It not only
+explains the test, but expounds fully and explicitly the principles
+underlying it--not only the phenomena revealed by the test, but the why
+and wherefore of such phenomena.
+
+It contains a full description of skiascopic apparatus, including the
+latest and most approved instruments.
+
+In depth of research, wealth of illustration and scientific completeness
+this work is unique.
+
+Bound in cloth; contains 231 pages and 73 illustrations and colored
+plates.
+
+Sent postpaid to any part of the world on receipt of $1.00 (4s. 2d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH AND BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+PHYSIOLOGIC OPTICS
+
+Ocular Dioptrics--Functions of the Retina--Ocular Movements and
+Binocular Vision
+
+BY DR. M. TSCHERNING
+
+Adjunct-Director of the Laboratory of Ophthalmology at the Sorbonne,
+Paris
+
+AUTHORIZED TRANSLATION
+
+BY CARL WEILAND, M.D.
+
+Former Chief of Clinic in the Eye Department of the Jefferson College
+Hospital, Philadelphia, Pa.
+
+This is the crowning work on physiologic optics, and will mark a new era
+in optical study. Its distinguished author is recognized in the world of
+science as the greatest living authority on this subject, and his book
+embodies not only his own researches, but those of the several hundred
+investigators who, in the past hundred years, made the eye their
+specialty and life study.
+
+Tscherning has sifted the gold of all optical research from the dross,
+and his book, as now published in English with many additions, is the
+most valuable mine of reliable optical knowledge within reach of
+ophthalmologists. It contains 380 pages and 212 illustrations, and its
+reference list comprises the entire galaxy of scientists who have made
+the century famous in the world of optics.
+
+The chapters on Ophthalmometry, Ophthalmoscopy, Accommodation,
+Astigmatism, Aberration and Entoptic Phenomena, etc.--in fact, the
+entire book contains so much that is new, practical and necessary that
+no refractionist can afford to be without it.
+
+Bound in Cloth. 380 Pages, 212 Illustrations.
+
+Price, $3.50 (14s. 7d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+OPHTHALMIC LENSES
+
+Dioptric Formulæ for Combined Cylindrical Lenses, The Prism-Dioptry and
+Other Original Papers
+
+BY CHARLES F. PRENTICE, M.E.
+
+A new and revised edition of all the original papers of this noted
+author, combined in one volume. In this revised form, with the addition
+of recent research, these standard papers are of increased value.
+Combined for the first time in one volume, they are the greatest
+compilation on the subject of lenses extant.
+
+This book of over 200 pages contains the following papers:
+
+  Ophthalmic Lenses.
+  Dioptric Formulæ for Combined Cylindrical Lenses.
+  The Prism-Dioptry.
+  A Metric System of Numbering and Measuring Prisms.
+    The Relation of the Prism-Dioptry to the Meter Angle.
+    The Relation of the Prism-Dioptry to the Lens-Dioptry.
+  The Perfected Prismometer.
+  The Prismometric Scale.
+  On the Practical Execution of Ophthalmic Prescriptions involving Prisms.
+  A Problem in Cemented Bi-Focal Lenses, Solved by the Prism-Dioptry.
+  Why Strong Contra-Generic Lenses of Equal Power Fail to Neutralize
+    Each Other.
+  The Advantages of the Sphero-Toric Lens.
+  The Iris, as Diaphragm and Photostat.
+  The Typoscope.
+  The Correction of Depleted Dynamic Refraction (Presbyopia).
+
+_Press Notices on the Original Edition:_
+
+
+OPHTHALMIC LENSES.
+
+"The work stands alone, in its present form, a compendium of the various
+laws of physics relative to this subject that are so difficult of access
+in scattered treatises."--_New England Medical Gazette._
+
+"It is the most complete and best illustrated book on this special
+subject ever published."--_Horological Review_, New York.
+
+"Of all the simple treatises on the properties of lenses that we have
+seen, this is incomparably the best.... The teacher of the average
+medical student will hail this little work as a great boon."--_Archives
+of Ophthalmology, edited by H. Knapp, M.D._
+
+DIOPTRIC FORMULÆ FOR COMBINED CYLINDRICAL LENSES.
+
+"This little brochure solves the problem of combined cylinders in all
+its aspects, and in a manner simple enough for the comprehension of the
+average student of ophthalmology. The author is to be congratulated upon
+the success that has crowned his labors, for nowhere is there to be
+found so simple and yet so complete an explanation as is contained in
+these pages."--_Archives of Ophthalmology, edited by H. Knapp, M.D._
+
+"This exhaustive work of Mr. Prentice is a solution of one of the most
+difficult problems in ophthalmological optics. Thanks are due to Mr.
+Prentice for the excellent manner in which he has elucidated a subject
+which has not hitherto been satisfactorily explained."--_The Ophthalmic
+Review_, London.
+
+The book contains 110 Original Diagrams. Bound in cloth.
+
+Price, $1.50 (6s. 3d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+OPTOMETRIC RECORD BOOK
+
+
+A record book, wherein to record optometric examinations, is an
+indispensable adjunct of an optician's outfit.
+
+The Keystone Optometric Record Book was specially prepared for this
+purpose. It excels all others in being not only a record book, but an
+invaluable guide in examination.
+
+The book contains two hundred record forms with printed headings,
+suggesting, in the proper order, the course of examination that should
+be pursued to obtain most accurate results.
+
+Each book has an index, which enables the optician to refer instantly to
+the case of any particular patient.
+
+The Keystone Record Book diminishes the time and labor required for
+examinations, obviates possible oversights from carelessness and assures
+a systematic and thorough examination of the eye, as well as furnishes a
+permanent record of all examinations.
+
+Sent postpaid on receipt of $1.00 (4s. 2d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE KEYSTONE BOOK OF MONOGRAMS
+
+This book contains 2400 designs and over 6000 different combinations of
+two and three letters.
+
+Is an essential to every jeweler's outfit. It is not only necessary for
+the jeweler's own use and guidance, but also to enable customers to
+indicate exactly what they want, thus saving time and possible
+dissatisfaction.
+
+The Monograms are purposely left in outline, in order to show clearly
+how the letters are intertwined or woven together. This permits such
+enlargement or reduction of the Monogram as may be desired, and as much
+shading, ornamentation and artistic finish as the jeweler may wish to
+add.
+
+This comprehensive compilation of Monograms is especially available as a
+reference book in busy seasons. Its use saves time, thought and labor,
+and ensures quick and satisfactory work.
+
+Monograms are the fad of the time, and there's money for the jeweler in
+Monogram engraving. The knowledge in this book can be turned into cash.
+All the various styles of letters are illustrated.
+
+Price, $1.00 (4s. 2d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE KEYSTONE RECORD BOOK OF WATCH REPAIRS
+
+This book is 9 × 11 inches, has 120 pages, and space for recording
+sixteen hundred jobs in detail. It is made of linen ledger paper, bound
+in cloth with leather back and corners.
+
+Price, $1.00 (4s. 2d.), prepaid.
+
+No other record book on the market is so complete, and all cost more.
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+  THE KEYSTONE
+  BOOK OF GUARANTEES OF WATCH REPAIRS
+
+  This book contains two hundred printed guarantees, and is
+  handsomely bound. Each guarantee is 3¼ × 7½ inches, and
+  most carefully worded. Jewelers have discovered that the use
+  of these guarantees is a most effective way to secure and cultivate
+  public confidence. We sell a book of two hundred for
+
+  $1.00 (4s. 2d.), prepaid,
+
+  which is one-third less than the price charged by others for a
+  similar book.
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+
+
+***END OF THE PROJECT GUTENBERG EBOOK WATCH AND CLOCK ESCAPEMENTS***
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+<h1>The Project Gutenberg eBook, Watch and Clock Escapements, by Anonymous</h1>
+<pre>
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at <a href = "https://www.gutenberg.org">www.gutenberg.org</a></pre>
+<p>Title: Watch and Clock Escapements</p>
+<p>       A Complete Study in Theory and Practice of the Lever, Cylinder and Chronometer Escapements, Together with a Brief Account of the Origin and Evolution of the Escapement in Horology</p>
+<p>Author: Anonymous</p>
+<p>Release Date: November 6, 2005  [eBook #17021]</p>
+<p>Language: English</p>
+<p>Character set encoding: ISO-8859-1</p>
+<p>***START OF THE PROJECT GUTENBERG EBOOK WATCH AND CLOCK ESCAPEMENTS***</p>
+<p>&nbsp;</p>
+<h3>E-text prepared by Robert Cicconetti, Janet Blenkinship,<br />
+    and the Project Gutenberg Online Distributed Proofreading Team<br />
+    (https://www.pgdp.net/).<br />
+    Book provided by the New York University Library.</h3>
+<p>&nbsp;</p>
+<hr class="full" />
+<p><a name="Page_1" id="Page_1"></a><a name="Page_2" id="Page_2"></a></p>
+
+<h1>WATCH AND CLOCK</h1>
+
+<h1>ESCAPEMENTS</h1>
+
+<p class='center'><span class="smcap">A Complete Study In Theory and Practice
+of the Lever, Cylinder and Chronometer
+Escapements, Together with a Brief
+Account of the Origin and Evolution
+of the Escapement
+in Horology</span></p>
+
+
+<hr style='width: 45%;' />
+
+<p class='center'>Compiled from the well-known Escapement Serials
+published in The Keystone</p>
+
+<hr style='width: 45%;' />
+
+<h4><i>NEARLY TWO HUNDRED ORIGINAL ILLUSTRATIONS</i></h4>
+
+<p class='center'>PUBLISHED BY<br />
+THE KEYSTONE<br />
+THE ORGAN OF THE JEWELRY AND OPTICAL TRADES<br />
+<span class="smcap">19th &amp; Brown Sts., Philadelphia, U.S.A.</span></p>
+
+<p class='center'><i>All Rights Reserved</i>
+</p>
+
+<p class='center'><a name="Page_3" id="Page_3"></a>
+<span class="smcap">Copyright, 1904, BY B. Thorpe,
+Publisher of The Keystone.</span>
+</p>
+
+
+
+<hr style="width: 65%;" /><p><a name="Page_4" id="Page_4"></a></p>
+<h2>PREFACE</h2>
+
+
+<p>Especially notable among the achievements of The Keystone in the field
+of horology were the three serials devoted to the lever, cylinder and
+chronometer escapements. So highly valued were these serials when
+published that on the completion of each we were importuned to republish
+it in book form, but we deemed it advisable to postpone such publication
+until the completion of all three, in order that the volume should be a
+complete treatise on the several escapements in use in horology. The
+recent completion of the third serial gave us the opportunity to
+republish in book form, and the present volume is the result. We present
+it to the trade and students of horology happy in the knowledge that its
+contents have already received their approval. An interesting addition
+to the book is the illustrated story of the escapements, from the first
+crude conceptions to their present perfection.</p>
+
+
+
+<hr style="width: 65%;" /><p><a name="Page_5" id="Page_5"></a></p><p><a name="Page_6" id="Page_6"></a></p>
+<h2>CONTENTS</h2>
+
+
+
+<table border="0" cellpadding="4" width="60%" cellspacing="0" summary="TABLE OF CONTENTS">
+<tr><th>CHAPTER I.</th></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td align='left'><span class="smcap">The Detached Lever Escapement</span></td><td align='right'><a href='#Page_9'><b>9</b></a></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><th>CHAPTER II.</th></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td align='left'><span class="smcap">The Cylinder Escapement</span></td><td align='right'><a href='#Page_111'><b>111</b></a></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><th>CHAPTER III.</th></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td align='left'><span class="smcap">The Chronometer Escapement</span></td><td align='right'><a href='#Page_131'><b>131</b></a></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><th>CHAPTER IV.</th></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td align='left'><span class="smcap">History of Escapements</span></td><td align='right'><a href='#Page_153'><b>153</b></a></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><th>CHAPTER V.</th></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td align='left'><span class="smcap">Putting in a New Cylinder</span></td><td align='right'><a href='#Page_169'><b>169</b></a></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><td colspan='2'></td></tr>
+<tr><th>INDEX</th><td align='right'><a href='#Page_177'><b>177</b></a></td></tr>
+</table>
+
+
+<p><a name="Page_7" id="Page_7"></a></p>
+
+<hr style="width: 65%;" /><p><a name="Page_8" id="Page_8"></a></p><p><a name="Page_9" id="Page_9"></a><br /><br /></p>
+<h2>CHAPTER I.</h2>
+
+<h3>THE DETACHED LEVER ESCAPEMENT.</h3>
+
+
+<p>In this treatise we do not propose to go into the history of this
+escapement and give a long dissertation on its origin and evolution, but
+shall confine ourselves strictly to the designing and construction as
+employed in our best watches. By designing, we mean giving full
+instructions for drawing an escapement of this kind to the best
+proportions. The workman will need but few drawing instruments, and a
+drawing-board about 15" by 18" will be quite large enough. The necessary
+drawing-instruments are a T-square with 15" blade; a scale of inches
+divided into decimal parts; two pairs dividers with pen and pencil
+points&mdash;one pair of these dividers to be 5" and the other 6"; one ruling
+pen. Other instruments can be added as the workman finds he needs them.
+Those enumerated above, however, will be all that are absolutely
+necessary.</p>
+
+<div class="figcenter"><img src="images/pict001.jpg" alt="Fig. 001" title="Fig. 001" /></div>
+
+
+<p>We shall, in addition, need an arc of degrees, which we can best make
+for ourselves. To construct one, we procure a piece of No. 24 brass,
+about 5-1/2" long by 1-1/4" wide. We show such a piece of brass at <i>A</i>,
+Fig. 1. On this piece of brass we sweep two arcs with a pair of dividers
+set at precisely 5", as shown (reduced) at <i>a a</i> and <i>b b</i>. On these
+arcs we set off the space held in our dividers&mdash;that is 5"&mdash;as shown at
+the short radial lines at each end of the two arcs. Now it is a
+well-known fact that the space embraced by our dividers contains exactly
+sixty degrees of the arcs <i>a a</i> and <i>b b</i>, or one-sixth of the entire
+circle; consequently, we divide the arcs <i>a a</i> and <i>b b</i> into sixty
+equal parts, to represent <a name="Page_10" id="Page_10"></a>degrees, and at one end of these arcs we
+halve five spaces so we can get at half degrees.</p>
+
+<div class="figleft"><img src="images/pict002.jpg" alt="Fig. 2" title="Fig. 2" /></div>
+
+<p>Before we take up the details of drawing an escapement we will say a few
+words about "degrees," as this seems to be something difficult to
+understand by most pupils in horology when learning to draw parts of
+watches to scale. At Fig. 2 we show several short arcs of fifteen
+degrees, all having the common center <i>g</i>. Most learners seem to have an
+idea that a degree must be a specific space, like an inch or a foot. Now
+the first thing in learning to draw an escapement is to fix in our minds
+the fact that the extent of a degree depends entirely on the radius of
+the arc we employ. To aid in this explanation we refer to Fig. 2. Here
+the arcs <i>c</i>, <i>d</i>, <i>e</i> and <i>f</i> are all fifteen degrees, although the
+linear extent of the degree on the arc <i>c</i> is twice that of the degree
+on the arc <i>f</i>. When we speak of a degree in connection with a circle we
+mean the one-three-hundred-and-sixtieth part of the periphery of such a
+circle. In dividing the arcs <i>a a</i> and <i>b b</i> we first divide them into
+six spaces, as shown, and each of these spaces into ten minor spaces, as
+is also shown. We halve five of the degree spaces, as shown at <i>h</i>. We
+should be very careful about making the degree arcs shown at Fig. 1, as
+the accuracy of our drawings depends a great deal on the perfection of
+the division on the scale <i>A</i>. In connection with such a fixed scale of
+degrees as is shown at Fig. 1, a pair of small dividers, constantly set
+to a degree space, is very convenient.</p>
+
+
+<h4>MAKING A PAIR OF DIVIDERS.</h4>
+
+<div class="figright"><img src="images/pict003.jpg" alt="Fig. 3" title="Fig. 3" /></div>
+
+<p>To make such a pair of small dividers, take a piece of hard sheet brass
+about 1/20" thick, 1/4" wide, 1-1/2" long, and shape it as shown at Fig.
+3. It should be explained, the part cut from the sheet brass is shown
+below the dotted line <i>k</i>, the portion above (<i>C</i>) being a round handle
+turned from hard wood or ivory. The slot <i>l</i> is sawn in, and two holes
+drilled in the end to insert the needle points <i>i i</i>. In making the slot
+<i>l</i> we arrange to have the needle points come a little too close
+together to agree with the degree spaces on the arcs <i>a a</i> and <i>b b</i>. We
+then put the small screw <i>j</i> through one of the legs <i>D''</i>, <a name="Page_11" id="Page_11"></a>and by
+turning <i>j</i>, set the needle points <i>i i</i> to exactly agree with the
+degree spaces. As soon as the points <i>i i</i> are set correctly, <i>j</i> should
+be soft soldered fast.</p>
+
+<p>The degree spaces on <i>A</i> are set off with these dividers and the spaces
+on <i>A</i> very carefully marked. The upper and outer arc <i>a a</i> should have
+the spaces cut with a graver line, while the lower one, <i>b b</i> is best
+permanently marked with a carefully-made prick punch. After the arc <i>a
+a</i> is divided, the brass plate <i>A</i> is cut back to this arc so the
+divisions we have just made are on the edge. The object of having two
+arcs on the plate <i>A</i> is, if we desire to get at the number of degrees
+contained in any arc of a 5" radius we lay the scale <i>A</i> so the edge
+agrees with the arc <i>a a</i>, and read off the number of degrees from the
+scale. In setting dividers we employ the dotted spaces on the arc <i>b b</i>.</p>
+
+
+<h4>DELINEATING AN ESCAPE WHEEL.</h4>
+
+<div class="figright"><img src="images/pict004.jpg" alt="Fig. 4" title="Fig. 4" /></div>
+
+<p>We will now proceed to delineate an escape wheel for a detached lever.
+We place a piece of good drawing-paper on our drawing-board and provide
+ourselves with a very hard (HHH) drawing-pencil and a bottle of liquid
+India ink. After placing our paper on the board, we draw, with the aid
+of our T-square, a line through the center of the paper, as shown at <i>m
+m</i>, Fig. 4. At 5-1/2" from the lower margin of the paper we establish
+the point <i>p</i> and sweep the circle <i>n n</i> with a radius of 5". We have
+said nothing about stretching our paper on the drawing-board; still,
+carefully-stretched paper is an important part of nice and correct
+drawing. We shall subsequently give directions for properly stretching
+paper, but for the present we will suppose the paper we are using is
+nicely tacked to the face of the drawing-board with the smallest tacks
+we can procure. The paper should not come quite to the edge of the
+drawing-board, so as to interfere with the head of the T-square. We are
+now ready to commence delineating our escape wheel and a set of pallets
+to match.</p>
+
+<p>The simplest form of the detached lever escapement in use is the one
+known as the "ratchet-tooth lever escapement," and generally found in
+English lever watches. This form of escapement gives excellent results
+when well made; and we can only account for it not being in more general
+use from the fact that the <a name="Page_12" id="Page_12"></a>escape-wheel teeth are not so strong and
+capable of resisting careless usage as the club-tooth escape wheel.</p>
+
+<p>It will be our aim to convey broad ideas and inculcate general
+principles, rather than to give specific instructions for doing "one
+thing one way." The ratchet-tooth lever escapements of later dates have
+almost invariably been constructed on the ten-degree
+lever-and-pallet-action plan; that is, the fork and pallets were
+intended to act through this arc. Some of the other specimens of this
+escapement have larger arcs&mdash;some as high as twelve degrees.</p>
+
+
+<h4>PALLET-AND-FORK ACTION.</h4>
+
+<div class="figleft"><img src="images/pict005.jpg" alt="Fig. 5" title="Fig. 5" /></div>
+
+<p>We illustrate at Fig. 5 what we mean by ten degrees of pallet-and-fork
+action. If we draw a line through the center of the pallet staff, and
+also through the center of the fork slot, as shown at <i>a b</i>, Fig. 5, and
+allow the fork to vibrate five degrees each side of said lines <i>a b</i>, to
+the lines <i>a c</i> and <i>a c'</i>, the fork has what we term ten-degree pallet
+action. If the fork and pallets vibrate six degrees on each side of the
+line <i>a b</i>&mdash;that is, to the lines <i>a d</i> and <i>a d'</i>&mdash;we have twelve
+degrees pallet action. If we cut the arc down so the oscillation is only
+four and one-quarter degrees on each side of <i>a b</i>, as indicated by the
+lines <i>a s</i> and <i>a s'</i>, we have a pallet-and-fork action of eight and
+one-half degrees; which, by the way, is a very desirable arc for a
+carefully-constructed escapement.</p>
+
+<p>The controlling idea which would seem to rule in constructing a detached
+lever escapement, would be to make it so the balance is free of the
+fork; that is, detached, during as much of the arc of the vibration of
+the balance as possible, and yet have the action thoroughly sound and
+secure. Where a ratchet-tooth escapement is thoroughly well-made of
+eight and one-half degrees of pallet-and-fork action, ten and one-half
+degrees of escape-wheel action can be utilized, as will be explained
+later on.</p>
+
+<div class="figright"><img src="images/pict006.jpg" alt="Fig. 6" title="Fig. 6" /></div>
+
+<p>We will now resume the drawing of our escape wheel, as illustrated at
+Fig. 4. In the drawing at Fig. 6 we show the circle <i>n n</i>, which
+represents the periphery of our escape wheel; and in the drawing we are
+supposed to be drawing it ten inches in diameter.</p>
+
+<p>We produce the vertical line <i>m</i> passing through the center <i>p</i> of the
+circle <i>n</i>. From the intersection of the circle <i>n</i> with the line <i>m</i><a name="Page_13" id="Page_13"></a>
+at <i>i</i> we lay off thirty degrees on each side, and establish the points
+<i>e f</i>; and from the center <i>p</i>, through these points, draw the radial
+lines <i>p e'</i> and <i>p f'</i>. The points <i>f e</i>, Fig. 6, are, of course, just
+sixty degrees apart and represent the extent of two and one-half teeth
+of the escape wheel. There are two systems on which pallets for lever
+escapements are made, viz., equidistant lockings and circular pallets.
+The advantages claimed for each system will be discussed subsequently.
+For the first and present illustration we will assume we are to employ
+circular pallets and one of the teeth of the escape wheel resting on the
+pallet at the point <i>f</i>; and the escape wheel turning in the direction
+of the arrow <i>j</i>. If we imagine a tooth as indicated at the dotted
+outline at <i>D</i>, Fig. 6, pressing against a surface which coincides with
+the radial line <i>p f</i>, the action would be in the direction of the line
+<i>f h</i> and at right angles to <i>p f</i>. If we reason on the action of the
+tooth <i>D</i>, as it presses against a pallet placed at <i>f</i>, we see the
+action is neutral.</p>
+
+
+<h4>ESTABLISHING THE CENTER OF PALLET STAFF.</h4>
+
+<div class="figleft"><img src="images/pict007.jpg" alt="Fig. 7" title="Fig. 7" /></div>
+
+<p>With a fifteen-tooth escape wheel each tooth occupies twenty-four
+degrees, and from the point <i>f</i> to <i>e</i> would be two and one-half
+tooth-spaces. We show the dotted points of four teeth at <i>D D' D''
+D'''</i>. To establish the center of the pallet staff we draw a line at
+right angles to the line <i>p e'</i> from the point <i>e</i> so it intersects the
+line <i>f h</i> at <i>k</i>. For drawing a line at right angles to another line,
+as we have just done, a hard-rubber triangle, shaped as shown at <i>C</i>,
+Fig. 7, can be employed. To use such a triangle, we place it so the
+right, or ninety-degrees angle, rests at <i>e</i>, as shown at the dotted
+triangle <i>C</i>, Fig. 6, and the long side coincides with the radial line
+<i>p e'</i>. If the short side of the hard-rubber triangle is too short, as
+indicated, we place a short ruler so it rests against the edge, as shown
+at the dotted line <i>g e</i>, Fig. 7, and while holding it securely down on
+the drawing we <a name="Page_14" id="Page_14"></a>remove the triangle, and with a fine-pointed pencil draw
+the line <i>e g</i>, Fig. 6, by the short rule. Let us imagine a flat surface
+placed at <i>e</i> so its face was at right angles to the line <i>g e</i>, which
+would arrest the tooth <i>D''</i> after the tooth <i>D</i> resting on <i>f</i> had been
+released and passed through an arc of twelve degrees. A tooth resting on
+a flat surface, as imagined above, would also rest dead. As stated
+previously, the pallets we are considering have equidistant locking
+faces and correspond to the arc <i>l l</i>, Fig. 6.</p>
+
+<p>In order to realize any power from our escape-wheel tooth, we must
+provide an impulse face to the pallets faced at <i>f e</i>; and the problem
+before us is to delineate these pallets so that the lever will be
+propelled through an arc of eight and one-half degrees, while the escape
+wheel is moving through an arc of ten and one-half degrees. We make the
+arc of fork action eight and one-half degrees for two reasons&mdash;(1)
+because most text-books have selected ten degrees of fork-and-pallet
+action; (2) because most of the finer lever escapements of recent
+construction have a lever action of less than ten degrees.</p>
+
+
+<h4>LAYING OUT ESCAPE-WHEEL TEETH.</h4>
+
+<p>To "lay out" or delineate our escape-wheel teeth, we continue our
+drawing shown at Fig. 6, and reproduce this cut very nearly at Fig. 8.
+With our dividers set at five inches, we sweep the short arc <i>a a'</i> from
+<i>f</i> as a center. It is to be borne in mind that at the point <i>f</i> is
+located the extreme point of an escape-wheel tooth. On the arc <i>a a</i> we
+lay off from <i>p</i> twenty-four degrees, and establish the point <i>b</i>; at
+twelve degrees beyond <i>b</i> we establish the point <i>c</i>. From <i>f</i> we draw
+the lines <i>f b</i> and <i>f c</i>; these lines establishing the form and
+thickness of the tooth <i>D</i>. To get the length of the tooth, we take in
+our dividers one-half a tooth space, and on the radial line <i>p f</i>
+establish the point <i>d</i> and draw circle <i>d' d'</i>.</p>
+
+<p>To facilitate the drawing of the other teeth, we draw the circles <i>d'
+c'</i>, to which the lines <i>f b</i> and <i>f c</i> are tangent, as shown. We divide
+the circle <i>n n</i>, representing the periphery of our escape wheel, into
+fifteen spaces, to represent teeth, commencing at <i>f</i> and continued as
+shown at <i>o o</i> until the entire wheel is divided. We only show four
+teeth complete, but the same methods as produced these will produce them
+all. To briefly recapitulate the instructions for drawing the teeth for
+the ratchet-tooth lever escapement: We draw the face of the teeth at an
+angle of twenty-four degrees to a <a name="Page_15" id="Page_15"></a>radial line; the back of the tooth at
+an angle of thirty-six degrees to the same radial line; and make teeth
+half a tooth-space deep or long.</p>
+
+<div class="figcenter"><a href="images/pict008.jpg"><img src="images/pict008-tb.jpg" alt="Fig. 8" title="Fig. 8" /></a></div>
+
+<p>We now come to the consideration of the pallets and how to delineate
+them. To this we shall add a careful analysis of their action. Let us,
+before proceeding further, "think a little" over some of the factors
+involved. To aid in this thinking or reasoning on the matter, let us
+draw the heavy arc <i>l</i> extending from a little inside of the circle <i>n</i>
+at <i>f</i> to the circle <i>n</i> at <i>e</i>. If now we imagine our escape wheel to
+be pressed forward in the direction of the arrow <i>j</i>, the tooth <i>D</i>
+would press on the arc <i>l</i> and be held. If, however, we should revolve
+the arc <i>l</i> on the center <i>k</i> in the direction of the arrow <i>i</i>, the
+tooth <i>D</i> would <i>escape</i> from the edge of <i>l</i> and the tooth <i>D''</i> would
+pass through an arc (reckoning from the center <i>p</i>) of twelve degrees,
+and be arrested by the inside of the arc <i>l</i> at <i>e</i>. If we now should
+reverse the motion and turn the arc <i>l</i> backward, the tooth at <i>e</i>
+would, in turn, be released and the tooth following after <i>D</i> (but not
+shown) would engage <i>l</i> at <i>f</i>. By supplying motive to revolve the
+escape wheel (<i>E</i>) represented by the circle <i>n</i>, and causing the arc
+<i>l</i> to oscillate back and forth in exact <a name="Page_16" id="Page_16"></a>intervals of time, we should
+have, in effect, a perfect escapement. To accomplish automatically such
+oscillations is the problem we have now on hand.</p>
+
+
+<h4>HOW MOTION IS OBTAINED.</h4>
+
+<p>In clocks, the back-and-forth movement, or oscillating motion, is
+obtained by employing a pendulum; in a movable timepiece we make use of
+an equally-poised wheel of some weight on a pivoted axle, which device
+we term a balance; the vibrations or oscillations being obtained by
+applying a coiled spring, which was first called a "pendulum spring,"
+then a "balance spring," and finally, from its diminutive size and coil
+form, a "hairspring." We are all aware that for the motive power for
+keeping up the oscillations of the escaping circle <i>l</i> we must contrive
+to employ power derived from the teeth <i>D</i> of the escape wheel. About
+the most available means of conveying power from the escape wheel to the
+oscillating arc <i>l</i> is to provide the lip of said arc with an inclined
+plane, along which the tooth which is disengaged from <i>l</i> at <i>f</i> to
+slide and move said arc <i>l</i> through&mdash;in the present instance an arc of
+eight and one-half degrees, during the time the tooth <i>D</i> is passing
+through ten and one-half degrees. This angular motion of the arc <i>l</i> is
+represented by the radial lines <i>k f'</i> and <i>k r</i>, Fig. 8. We desire to
+impress on the reader's mind the idea that each of these angular motions
+is not only required to be made, but the motion of one mobile must
+convey power to another mobile.</p>
+
+<p>In this case the power conveyed from the mainspring to the escape wheel
+is to be conveyed to the lever, and by the lever transmitted to the
+balance. We know it is the usual plan adopted by text-books to lay down
+a certain formula for drawing an escapement, leaving the pupil to work
+and reason out the principles involved in the action. In the plan we
+have adopted we propose to induct the reader into the why and how, and
+point out to him the rules and methods of analysis of the problem, so
+that he can, if required, calculate mathematically exactly how many
+grains of force the fork exerts on the jewel pin, and also how much (or,
+rather, what percentage) of the motive power is lost in various "power
+leaks," like "drop" and lost motion. In the present case the mechanical
+result we desire to obtain is to cause our lever pivoted at <i>k</i> to
+vibrate back and forth through an arc of eight and one-half degrees;
+this lever not only to vibrate back and forth, but also to lock and hold
+the <a name="Page_17" id="Page_17"></a>escape wheel during a certain period of time; that is, through the
+period of time the balance is performing its excursion and the jewel pin
+free and detached from the fork.</p>
+
+<p>We have spoken of paper being employed for drawings, but for very
+accurate delineations we would recommend the horological student to make
+drawings on a flat metal plate, after perfectly smoothing the surface
+and blackening it by oxidizing.</p>
+
+
+<h4>PALLET-AND-FORK ACTION.</h4>
+
+<p>By adopting eight and one-half degrees pallet-and-fork action we can
+utilize ten and one-half degrees of escape-wheel action. We show at <i>A
+A'</i>, Fig. 9, two teeth of a ratchet-tooth escape wheel reduced one-half;
+that is, the original drawing was made for an escape wheel ten inches in
+diameter. We shall make a radical departure from the usual practice in
+making cuts on an enlarged scale, for only such parts as we are talking
+about. To explain, we show at Fig. 10 about one-half of an escape wheel
+one eighth the size of our large drawing; and when we wish to show some
+portion of such drawing on a larger scale we will designate such
+enlargement by saying one-fourth, one-half or full size.</p>
+
+<div class="figcenter"><a href="images/pict009.jpg"><img src="images/pict009-tb.jpg" alt="Fig. 9" title="Fig. 9" /></a></div>
+
+<p>At Fig. 9 we show at half size that portion of our escapement embraced
+by the dotted lines <i>d</i>, Fig. 10. This plan enables us to show very
+minutely such parts as we have under consideration, and yet occupy but
+little space. The arc <i>a</i>, Fig. 9, represents the periphery of the
+escape wheel. On this line, ten and one-half degrees from the point of
+the tooth <i>A</i>, we establish the point <i>c</i> and draw the radial line <i>c
+c'</i>. It is to be borne in mind that the arc <a name="Page_18" id="Page_18"></a>embraced between the points
+<i>b</i> and <i>c</i> represents the duration of contact between the tooth <i>A</i> and
+the entrance pallet of the lever. The space or short arc <i>c n</i>
+represents the "drop" of the tooth.</p>
+
+<p>This arc of one and one-half degrees of escape-wheel movement is a
+complete loss of six and one-fourth per cent. of the entire power of the
+mainspring, as brought down to the escapement; still, up to the present
+time, no remedy has been devised to overcome it. All the other
+escapements, including the chronometer, duplex and cylinder, are quite
+as wasteful of power, if not more so. It is usual to construct
+ratchet-tooth pallets so as to utilize but ten degrees of escape-wheel
+action; but we shall show that half a degree more can be utilized by
+adopting the eight and one-half degree fork action and employing a
+double-roller safety action to prevent over-banking.</p>
+
+<div class="figleft"><img src="images/pict010.jpg" alt="Fig. 10" title="Fig. 10" /></div>
+
+<p>From the point <i>e</i>, which represents the center of the pallet staff, we
+draw through <i>b</i> the line <i>e f</i>. At one degree below <i>e f</i> we draw the
+line <i>e g</i>, and seven and one-half degrees below the line <i>e g</i> we draw
+the line <i>e h</i>. For delineating the lines <i>e g</i>, etc., correctly, we
+employ a degree-arc; that is, on the large drawing we are making we
+first draw the line <i>e b f</i>, Fig. 10, and then, with our dividers set at
+five inches, sweep the short arc <i>i</i>, and on this lay off first one
+degree from the intersection of <i>f e</i> with the arc <i>i</i>, and through this
+point draw the line <i>e g</i>.</p>
+
+<p>From the intersection of the line <i>f e</i> with the arc <i>i</i> we lay off
+eight and one-half degrees, and through this point draw the line <i>e h</i>.
+Bear in mind that we are drawing the pallet at <i>B</i> to represent one with
+eight and one-half degrees fork-and-pallet action, and with equidistant
+lockings. If we reason on the matter under consideration, we will see
+the tooth <i>A</i> and the pallet <i>B</i>, against which it acts, part or
+separate when the tooth arrives at the point <i>c</i>; that is, after the
+escape wheel has moved through ten and one-half degrees of angular
+motion, the tooth drops from the impulse face of the pallet and falls
+through one and one-half degrees of arc, when the tooth <i>A''</i>, Fig. 10,
+is arrested by the exit pallet.</p>
+
+<p>To locate the position of the inner angle of the pallet <i>B</i>, sweep the
+short arc <i>l</i> by setting the dividers so one point or leg rests at the
+center <i>e</i> and the other at the point <i>c</i>. Somewhere on this arc <i>l</i> is
+<a name="Page_19" id="Page_19"></a>to be located the inner angle of our pallet. In delineating this angle,
+Moritz Grossman, in his "Prize Essay on the Detached Lever Escapement,"
+makes an error, in Plate III of large English edition, of more than his
+entire lock, or about two degrees. We make no apologies for calling
+attention to this mistake on the part of an authority holding so high a
+position on such matters as Mr. Grossman, because a mistake is a
+mistake, no matter who makes it.</p>
+
+<p>We will say no more of this error at present, but will farther on show
+drawings of Mr. Grossman's faulty method, and also the correct method of
+drawing such a pallet. To delineate the locking face of our pallet, from
+the point formed by the intersection of the lines <i>e g b b'</i>, Fig. 9, as
+a center, we draw the line <i>j</i> at an angle of twelve degrees to <i>b b''</i>.
+In doing this we employ the same method of establishing the angle as we
+made use of in drawing the lines <i>e g</i> and <i>e h</i>, Fig. 10. The line <i>j</i>
+establishes the locking face of the pallet <i>B</i>. Setting the locking face
+of the pallet at twelve degrees has been found in practice to give a
+safe "draw" to the pallet and keep the lever secure against the bank. It
+will be remembered the face of the escape-wheel tooth was drawn at
+twenty-four degrees to a radial line of the escape wheel, which, in this
+instance, is the line <i>b b'</i>, Fig. 9. It will now be seen that the angle
+of the pallet just halves this angle, and consequently the tooth <i>A</i>
+only rests with its point on the locking face of the pallet. We do not
+show the outlines of the pallet <i>B</i>, because we have not so far pointed
+out the correct method of delineating it.</p>
+
+
+<h4>METHODS OF MAKING GOOD DRAWING INSTRUMENTS.</h4>
+
+
+<div class="figleft"><img src="images/pict011.jpg" alt="Fig. 11" title="Fig. 11" /></div>
+<div class="figright"><img src="images/pict012.jpg" alt="Fig. 12" title="Fig. 12" /></div>
+<p>Perhaps we cannot do our readers a greater favor than to digress from
+the study of the detached lever escapement long enough to say a few
+words about drawing instruments and tablets or surfaces on which to
+delineate, with due precision, mechanical designs or drawings. Ordinary
+drawing instruments, even of the higher grades, and costing a good deal
+of money, are far from being satisfactory to a man who has the proper
+idea of accuracy to be rated as a first-class mechanic. Ordinary
+compasses are obstinate when we try to set them to the hundredth of an
+inch; usually the points are dull and ill-shapen; if they make a
+puncture in the paper it is unsightly.</p>
+
+<div class="figleft"><img src="images/pict013.jpg" alt="Fig. 13" title="Fig. 13" /></div>
+
+<p>Watchmakers have one advantage, however, because they can very easily
+work over a cheap set of drawing instruments and make them even superior
+to anything they can buy at the art stores. To illustrate, let us take a
+cheap pair of brass or German-silver five-inch dividers and make them
+over into needle points and "spring set." To do this the points are cut
+off at the line <i>a a</i>, Fig 11, and a steel tube is gold-soldered on each
+leg. The steel tube is made by taking a piece of steel wire which will
+fit a No. 16 chuck of a Whitcomb lathe, and drilling a hole in the end
+about one-fourth of an inch deep and about the size of a No. 3 sewing
+needle. We Show at Fig. 12 a view of the point <i>A'</i>, Fig. 11, enlarged,
+and the steel tube we have just drilled out attached at <i>C</i>. About the
+best way to attach <i>C</i> is to solder. After the tube <i>C</i> is attached a
+hole is drilled through <i>A'</i> at <i>d</i>, and the thumb-screw <i>d</i> inserted.
+This thumb-screw should be of steel, and hardened and tempered. The use
+of this screw is to clamp the needle point. With such a device as the
+tube <i>C</i> and set-screw <i>d</i>, a No. 3 needle is used for a point; but for
+drawings on paper a turned point, as shown at Fig 13, is to be
+preferred. Such points can be made from a No. 3 needle after softening
+enough to be turned so as to form the point <i>c</i>. This point at the
+shoulder <i>f</i> should be about 12/1000 of an inch, or the size of a
+fourth-wheel pivot to an eighteen size movement.</p>
+
+<p>The idea is, when drawing on paper the point <i>c</i> enters the paper. For
+drawing on metal the form of the point is changed to a simple cone, as
+shown at <i>B'</i> <i>c</i>, Fig. 13. such cones can be turned carefully, then
+hardened and tempered to a straw color; and when they become dull, can
+be ground by placing the points in a wire chuck and dressing them up
+with an emery buff or an Arkansas slip. The opposite leg of the dividers
+is the one to which is attached the spring for close setting of the
+points.</p>
+<div class="figcenter"><img src="images/pict014.jpg" alt="Fig. 14" title="Fig. 14" /></div>
+
+<p><a name="Page_20" id="Page_20"></a><a name="Page_21" id="Page_21"></a>In making this spring, we take a piece of steel about two and
+one-fourth inches long and of the same width as the leg of the divider,
+and attach it to the inside of the leg as shown at Fig. 14, where <i>D</i>
+represents the spring and <i>A</i> the leg of the dividers. The spring <i>D</i>
+has a short steel tube <i>C''</i> and set-screw <i>d''</i> for a fine point like
+<i>B</i> or <i>B'</i>. In the lower end of the leg <i>A</i>, Fig. 14, is placed the
+milled-head screw <i>g</i>, which serves to adjust the two points of the
+dividers to very close distances. The spring <i>D</i> is, of course, set so
+it would press close to the leg <i>A</i> if the screw <i>g</i> did not force it
+away.</p>
+
+
+<h4>SPRING AND ADJUSTING SCREW FOR DRAWING INSTRUMENTS.</h4>
+
+
+<p>It will be seen that we can apply a spring <i>D</i> and adjusting screw
+opposite to the leg which carries the pen or pencil point of all our
+dividers if we choose to do so; but it is for metal drawing that such
+points are of the greatest advantage, as we can secure an accuracy very
+gratifying to a workman who believes in precision. For drawing circles
+on metal, "bar compasses" are much the best, as they are almost entirely
+free from spring, which attends the jointed compass. To make (because
+they cannot be bought) such an instrument, take a piece of flat steel,
+one-eighth by three-eighths of an inch and seven inches long, and after
+turning and smoothing it carefully, make a slide half an inch wide, as
+shown at Fig. 15, with a set-screw <i>h</i> on top to secure it at any point
+on the bar <i>E</i>. In the lower part of the slide <i>F</i> is placed a steel
+tube like <i>C</i>, shown in Figs. 12 and 14, with set-screw for holding
+points like <i>B B'</i>, Fig. 13. At the opposite end of the bar <i>E</i> is
+placed a looped spring <i>G</i>, which carries a steel tube and point like
+the spring <i>D</i>, Fig. 14. Above this tube and point, shown at <i>j</i>, Fig.
+15, is placed an adjustment screw <i>k</i> for fine adjustment. The inner end
+of the screw <i>k</i> rests against the end of the bar <i>E</i>. The tendency of
+the spring <i>G</i> is to close upon the end of <i>E</i>; consequently if we make
+use of the screw <i>k</i> to force away the lower end of <i>G</i>, we can set the
+fine point in <i>j</i> to the greatest exactness.</p>
+
+<div class="figcenter"><img src="images/pict015.jpg" alt="Fig. 15" title="Fig. 15" /></div>
+
+<p><a name="Page_22" id="Page_22"></a>The spring <i>G</i> is made of a piece of steel one-eighth of an inch
+square, and secured to the bar <i>E</i> with a screw and steady pins at <i>m</i>.
+A pen and pencil point attachment can be added to the spring <i>G</i>; but in
+case this is done it would be better to make another spring like <i>G</i>
+without the point <i>j</i>, and with the adjusting screw placed at <i>l</i>. In
+fitting pen and pencil points to a spring like <i>G</i> it would probably be
+economical to make them outright; that is, make the blades and screw for
+the ruling pen and a spring or clamping tube for the pencil point.</p>
+
+
+<h4>CONSIDERATION OF DETACHED LEVER ESCAPEMENT RESUMED.</h4>
+
+<p>We will now, with our improved drawing instruments, resume the
+consideration of the ratchet-tooth lever escapement. We reproduce at
+Fig. 16 a portion of diagram III, from Moritz Grossmann's "Prize Essay
+on the Detached Lever Escapement," in order to point out the error in
+delineating the entrance pallet to which we previously called attention.
+The cut, as we give it, is not quite one-half the size of Mr.
+Grossmann's original plate.</p>
+
+<p>In the cut we give the letters of reference employed the same as on the
+original engraving, except where we use others in explanation. The
+angular motion of the lever and pallet action as shown in the cut is ten
+degrees; but in our drawing, where we only use eight and one-half
+degrees, the same mistake would give proportionate error if we did not
+take the means to correct it. The error to which we refer lies in
+drawing the impulse face of the entrance pallet. The impulse face of
+this pallet as drawn by Mr. Grossmann would not, from the action of the
+engaging tooth, carry this pallet through more than eight degrees of
+angular motion; consequently, the tooth which should lock on the exit
+pallet would fail to do so, and strike the impulse face.</p>
+
+<p>We would here beg to add that nothing will so much instruct a person
+desiring to acquire sound ideas on escapements as making a large model.
+The writer calls to mind a wood model of a lever escapement made by one
+of the "boys" in the Elgin factory about a year or two after Mr.
+Grossmann's prize essay was published. It went from hand to hand and did
+much toward establishing sound ideas as regards the correct action of
+the lever escapement in that notable concern.</p>
+
+<p>If a horological student should construct a large model on the lines
+laid down in Mr. Grossmann's work, the entrance pallet would <a name="Page_23" id="Page_23"></a>be faulty
+in form and would not properly perform its functions. Why? perhaps says
+our reader. In reply let us analyze the action of the tooth <i>B</i> as it
+rests on the pallet <i>A</i>. Now, if we move this pallet through an angular
+motion of one and one-half degrees on the center <i>g</i> (which also
+represents the center of the pallet staff), the tooth <i>B</i> is disengaged
+from the locking face and commences to slide along the impulse face of
+the pallet and "drops," that is, falls from the pallet, when the inner
+angle of the pallet is reached.</p>
+
+<div class="figcenter"><a href="images/pict016.jpg"><img src="images/pict016-tb.jpg" alt="Fig. 16" title="Fig. 16" /></a></div>
+
+<p>This inner angle, as located by Mr. Grossmann, is at the intersection of
+the short arc <i>i</i> with the line <i>g n</i>, which limits the ten-degree
+angular motion of the pallets. If we carefully study the drawing, we
+will see the pallet has only to move through eight degrees of angular
+motion of the pallet staff for the tooth to escape, <i>because the tooth
+certainly must be disengaged when the inner angle of the pallet reaches
+the peripheral line a</i>. The true way to locate the position of the inner
+angle of the pallet, is to measure down on the arc <i>i</i> ten degrees from
+its intersection with the peripheral line <i>a</i> and locate a point to
+which a line is drawn from the intersection of the line <i>g m</i> with the
+radial line <i>a c</i>, thus defining the inner angle of the entrance pallet.
+We will name this point the point <i>x</i>.</p>
+
+<p>It may not be amiss to say the arc <i>i</i> is swept from the center <i>g</i>
+through the point <i>u</i>, said point being located ten degrees from the
+intersection of the radial <i>a c</i> with the peripheral line <i>a</i>. It will
+be noticed that the inner angle of the entrance pallet <i>A</i> seems to
+extend <a name="Page_24" id="Page_24"></a>inward, beyond the radial line <i>a j</i>, that is, toward the pallet
+center <i>g</i>, and gives the appearance of being much thicker than the exit
+pallet <i>A'</i>; but we will see on examination that the extreme angle <i>x</i>
+of the entrance pallet must move on the arc <i>i</i> and, consequently, cross
+the peripheral line <i>a</i> at the point <i>u</i>. If we measure the impulse
+faces of the two pallets <i>A A'</i>, we will find them nearly alike in
+linear extent.</p>
+
+<div class="figleft"><img src="images/pict017.jpg" alt="Fig. 17" title="Fig. 17" /></div>
+
+<p>Mr. Grossmann, in delineating his exit pallet, brings the extreme angle
+(shown at <i>4</i>) down to the periphery of the escape, as shown in the
+drawing, where it extends beyond the intersection of the line <i>g f</i> with
+the radial line <i>a 3</i>. The correct form for the entrance pallet should
+be to the dotted line <i>z x y</i>.</p>
+
+<p>We have spoken of engaging and disengaging frictions; we do not know how
+we can better explain this term than by illustrating the idea with a
+grindstone. Suppose two men are grinding on the same stone; each has,
+say, a cold chisel to grind, as shown at Fig. 17, where <i>G</i> represents
+the grindstone and <i>N N'</i> the cold chisels. The grindstone is supposed
+to be revolving in the direction of the arrow. The chisels <i>N</i> and <i>N'</i>
+are both being ground, but the chisel <i>N'</i> is being cut much the more
+rapidly, as each particle of grit of the stone as it catches on the
+steel causes the chisel to hug the stone and bite in deeper and deeper;
+while the chisel shown at <i>N</i> is thrust away by the action of the grit.
+Now, friction of any kind is only a sort of grinding operation, and the
+same principles hold good.</p>
+
+
+<h4>THE NECESSITY FOR GOOD INSTRUMENTS.</h4>
+
+<p>It is to be hoped the reader who intends to profit by this treatise has
+fitted up such a pair of dividers as those we have described, because it
+is only with accurate instruments he can hope to produce drawings on
+which any reliance can be placed. The drawing of a ratchet-tooth lever
+escapement of eight and one-half degrees pallet action will now be
+resumed. In the drawing at Fig. 18 is shown a complete delineation of
+such an escapement with eight and one-half degrees of pallet action and
+equidistant locking faces. It is, of course, understood the escape wheel
+is to be drawn ten inches in diameter, and that the degree arcs shown in
+Fig. 1 will be used.</p>
+
+<p>We commence by carefully placing on the drawing-board a sheet of paper
+about fifteen inches square, and then vertically <a name="Page_25" id="Page_25"></a>through the center
+draw the line <i>a' a''</i>. At some convenient position on this line is
+established the point <i>a</i>, which represents the center of the escape
+wheel. In this drawing it is not important that the entire escape wheel
+be shown, inasmuch as we have really to do with but a little over sixty
+degrees of the periphery of the escape wheel. With the dividers
+carefully set at five inches, from <i>a</i>, as a center, we sweep the arc <i>n
+n</i>, and from the intersection of the perpendicular line <i>a' a''</i> with
+the arc <i>n</i> we lay off on each side thirty degrees from the brass degree
+arc, and through the points thus established are drawn the radial lines
+<i>a b'</i> and <i>a d'</i>.</p>
+
+<div class="figcenter"><a href="images/pict018.jpg"><img src="images/pict018-tb.jpg" alt="Fig. 18" title="Fig. 18" /></a></div>
+
+<p>The point on the arc <i>n</i> where it intersects with the line <i>b'</i> is
+termed the point <i>b</i>. At the intersection of the radial line <i>a d'</i> is
+established the point <i>d</i>. We take ten and one-half degrees in the
+dividers, and from the point <i>b</i> establish the point <i>c</i>, which embraces
+the arc of the escape wheel which is utilized by the pallet action.
+Through the point <i>b</i> the line <i>h' h</i> is drawn at right angles to the
+line <i>a b'</i>. The line <i>j j'</i> is also drawn at right angles to the line
+<i>a d'</i> through the point <i>d</i>. We now have an intersection of the lines
+just drawn in common with the line <i>a a'</i> at the point <i>g</i>, said point
+indicating the center of the pallet action.</p>
+
+<p>The dividers are now set to embrace the space between the points <i>b</i> and
+<i>g</i> on the line <i>h' h</i>, and the arc <i>f f</i> is swept; which, in <a name="Page_26" id="Page_26"></a>proof of
+the accuracy of the work, intersects the arc <i>n</i> at the point <i>d</i>. This
+arc coincides with the locking faces of both pallets. To lay out the
+entrance pallet, the dividers are set to five inches, and from <i>g</i> as a
+center the short arc <i>o o</i> is swept. On this arc one degree is laid off
+below the line <i>h' h</i>, and the line <i>g i</i> drawn. The space embraced
+between the lines <i>h</i> and <i>i</i> on the arc <i>f</i> represents the locking face
+of the entrance pallet, and the point formed at the intersection of the
+line <i>g i</i> with the arc <i>f</i> is called the point <i>p</i>. To give the proper
+lock to the face of the pallet, from the point <i>p</i> as a center is swept
+the short arc <i>r r</i>, and from its intersection with the line <i>a b'</i>
+twelve degrees are laid off and the line <i>b s</i> drawn, which defines the
+locking face of the entrance pallet. From <i>g</i> as a center is swept the
+arc <i>c' c'</i>, intersecting the arc <i>n n</i> at <i>c</i>. On this arc (<i>c</i>) is
+located the inner angle of the entrance pallet. The dividers are set to
+embrace the space on the arc <i>c'</i> between the lines <i>g h'</i> and <i>g k</i>.
+With this space in the dividers one leg is set at the point <i>c</i>,
+measuring down on the arc <i>c'</i> and establishing the point <i>t</i>. The
+points <i>p</i> and <i>t</i> are then connected, and thus the impulse face of the
+entrance pallet <i>B</i> is defined. From the point <i>t</i> is drawn the line <i>t
+t'</i>, parallel to the line <i>b s</i>, thus defining the inner face of the
+entrance pallet.</p>
+
+
+<h4>DELINEATING THE EXIT PALLET.</h4>
+
+<p>To delineate the exit pallet, sweep the short arc <i>u u</i> (from <i>g</i> as a
+center) with the dividers set at five inches, and from the intersection
+of this arc with the line <i>g j'</i> set off eight and one-half degrees and
+draw the line <i>g l</i>. At one degree below this line is drawn the line <i>g
+m</i>. The space on the arc <i>f</i> between these lines defines the locking
+face of the exit pallet. The point where the line <i>g m</i> intersects the
+arc <i>f</i> is named the point <i>x</i>. From the point <i>x</i> is erected the line
+<i>x w</i>, perpendicular to the line <i>g m</i>. From <i>x</i> as a center, and with
+the dividers set at five inches, the short arc <i>y y</i> is swept, and on
+this arc are laid off twelve degrees, and the line <i>x z</i> is drawn, which
+line defines the locking face of the exit pallet.</p>
+
+<p>Next is taken ten and one-half degrees from the brass degree-scale, and
+from the point <i>d</i> on the arc <i>n</i> the space named is laid off, and thus
+is established the point <i>v</i>; and from <i>g</i> as a center is swept the arc
+<i>v' v'</i> through the point <i>v</i>. It will be evident on a little thought,
+that if the tooth <i>A'</i> impelled the exit pallet to the position shown,
+the outer angle of the pallet must extend down to <a name="Page_27" id="Page_27"></a>the point <i>v</i>, on the
+arc <i>v' v'</i>; consequently, we define the impulse face of this pallet by
+drawing a line from point <i>x</i> to <i>v</i>. To define the outer face of the
+exit pallet, we draw the line <i>v e</i> parallel to the line <i>x z</i>.</p>
+
+<p>There are no set rules for drawing the general form of the pallet arms,
+only to be governed by and conforming to about what we would deem
+appropriate, and to accord with a sense of proportion and mechanical
+elegance. Ratchet-tooth pallets are usually made in what is termed
+"close pallets"; that is, the pallet jewel is set in a slot sawed in the
+steel pallet arm, which is undoubtedly the strongest and most
+serviceable form of pallet made. We shall next consider the
+ratchet-tooth lever escapement with circular pallets and ten degrees of
+pallet action.</p>
+
+
+<h4>DELINEATING CIRCULAR PALLETS.</h4>
+
+<p>To delineate "circular pallets" for a ratchet-tooth lever escapement, we
+proceed very much as in the former drawing, by locating the point <i>A</i>,
+which represents the center of the escape wheel, at some convenient
+point, and with the dividers set at five inches, sweep the arc <i>m</i>, to
+represent the periphery of the escape wheel, and then draw the vertical
+line <i>A B'</i>, Fig. 19. We (as before) lay off thirty degrees on the arc
+<i>m</i> each side of the intersection of said arc with the line <i>A B'</i>, and
+thus establish on the arc <i>m</i> the points <i>a b</i>, and from <i>A</i> as a center
+draw through the points so established the radial lines <i>A a'</i> and <i>A
+b'</i>.</p>
+
+<p>We erect from the point <i>a</i> a perpendicular to the line <i>A a</i>, and, as
+previously explained, establish the pallet center at <i>B</i>. Inasmuch as we
+are to employ circular pallets, we lay off to the left on the arc <i>m</i>,
+from the point <i>a</i>, five degrees, said five degrees being half of the
+angular motion of the escape wheel utilized in the present drawing, and
+thus establish the point <i>c</i>, and from <i>A</i> as a center draw through this
+point the radial line <i>A c'</i>. To the right of the point <i>a</i> we lay off
+five degrees and establish the point <i>d</i>. To illustrate the underlying
+principle of our circular pallets: with one leg of the dividers set at
+<i>B</i> we sweep through the points <i>c a d</i> the arcs <i>c'' a'' d''</i>.</p>
+
+<p>From <i>B</i> as a center, we continue the line <i>B a</i> to <i>f</i>, and with the
+dividers set at five inches, sweep the short arc <i>e e</i>. From the
+intersection of this arc with the line <i>B f</i> we lay off one and a half
+degrees and draw the line <i>B g</i>, which establishes the extent of the
+<a name="Page_28" id="Page_28"></a>lock on the entrance pallet. It will be noticed the linear extent of
+the locking face of the entrance pallet is greater than that of the
+exit, although both represent an angle of one and a half degrees.
+Really, in practice, this discrepancy is of little importance, as the
+same side-shake in banking would secure safety in either case.</p>
+
+<div class="figcenter"><a href="images/pict019.jpg"><img src="images/pict019-tb.jpg" alt="Fig. 19" title="Fig. 19" /></a></div>
+
+<p>The fault we previously pointed out, of the generally accepted method of
+delineating a detached lever escapement, is not as conspicuous here as
+it is where the pallets are drawn with equidistant locking faces; that
+is, the inner angle of the entrance pallet (shown at <i>s</i>) does not have
+to be carried down on the arc <i>d'</i> as far to insure a continuous pallet
+action of ten degrees, as with the pallets with equidistant locking
+faces. Still, even here we have carried the angle <i>s</i> down about half a
+degree on the arc <i>d'</i>, to secure a safe lock on the exit pallet.</p>
+
+
+<h4>THE AMOUNT OF LOCK.</h4>
+
+<p>If we study the large drawing, where we delineate the escape wheel ten
+inches in diameter, it will readily be seen that although we claim one
+and a half degrees lock, we really have only about one degree, inasmuch
+as the curve of the peripheral line <i>m</i> diverges from the line <i>B f</i>,
+and, as a consequence, the absolute lock of the tooth <i>C</i> on the locking
+face of the entrance pallet <i>E</i> is but about <a name="Page_29" id="Page_29"></a>one degree. Under these
+conditions, if we did not extend the outer angle of the exit pallet at
+<i>t</i> down to the peripheral line <i>m</i>, we would scarcely secure one-half a
+degree of lock. This is true of both pallets. We must carry the pallet
+angles at <i>r s n t</i> down on the circles <i>c'' d'</i> if we would secure the
+lock and impulse we claim; that is, one and a half degrees lock and
+eight and a half degrees impulse.</p>
+
+<p>Now, while the writer is willing to admit that a one-degree lock in a
+sound, well-made escapement is ample, still he is not willing to allow
+of a looseness of drawing to incorporate to the extent of one degree in
+any mechanical matter demanding such extreme accuracy as the parts of a
+watch. It has been claimed that such defects can, to a great extent, be
+remedied by setting the escapement closer; that is, by bringing the
+centers of the pallet staff and escape wheel nearer together. We hold
+that such a course is not mechanical and, further, that there is not the
+slightest necessity for such a policy.</p>
+
+
+<h4>ADVANTAGE OF MAKING LARGE DRAWINGS.</h4>
+
+<p>By making the drawings large, as we have already suggested and insisted
+upon, we can secure an accuracy closely approximating perfection. As,
+for instance, if we wish to get a lock of one and a half degrees on the
+locking face of the entrance pallet <i>E</i>, we measure down on the arc
+<i>c''</i> from its intersection with the peripheral line <i>m</i> one and a half
+degrees, and establish the point <i>r</i> and thus locate the outer angle of
+the entrance pallet <i>E</i>, so there will really be one and a half degrees
+of lock; and by measuring down on the arc <i>d'</i> ten degrees from its
+intersection with the peripheral line <i>m</i>, we locate the point <i>s</i>,
+which determines the position of the inner angle of the entrance pallet,
+and we know for a certainty that when this inner angle is freed from the
+tooth it will be after the pallet (and, of course, the lever) has passed
+through exactly ten degrees of angular motion.</p>
+
+<p>For locating the inner angle of the exit pallet, we measure on the arc
+<i>d'</i>, from its intersection with the peripheral line <i>m</i>, eight and a
+half degrees, and establish the point <i>n</i>, which locates the position of
+this inner angle; and, of course, one and a half degrees added on the
+arc <i>d'</i> indicates the extent of the lock on this pallet. Such drawings
+not only enable us to theorize to extreme exactness, but also give us
+proportionate measurements, which can be carried into actual
+construction.</p>
+
+<h4><a name="Page_30" id="Page_30"></a>THE CLUB-TOOTH LEVER ESCAPEMENT.</h4>
+
+<p>We will now take up the club-tooth form of the lever escapement. This
+form of tooth has in the United States and in Switzerland almost
+entirely superceded the ratchet tooth. The principal reason for its
+finding so much favor is, we think, chiefly owing to the fact that this
+form of tooth is better able to stand the manipulations of the
+able-bodied watchmaker, who possesses more strength than skill. We will
+not pause now, however, to consider the comparative merits of the
+ratchet and club-tooth forms of the lever escapement, but leave this
+part of the theme for discussion after we have given full instructions
+for delineating both forms.</p>
+
+<p>With the ratchet-tooth lever escapement all of the impulse must be
+derived from the pallets, but in the club-tooth escapement we can divide
+the impulse planes between the pallets and the teeth to suit our fancy;
+or perhaps it would be better to say carry out theories, because we have
+it in our power, in this form of the lever escapement, to indulge
+ourselves in many changes of the relations of the several parts. With
+the ratchet tooth the principal changes we could make would be from
+pallets with equidistant lockings to circular pallets. The club-tooth
+escape wheel not only allows of circular pallets and equidistant
+lockings, but we can divide the impulse between the pallets and the
+teeth in such a way as will carry out many theoretical advantages which,
+after a full knowledge of the escapement action is acquired, will
+naturally suggest themselves. In the escapement shown at Fig. 20 we have
+selected, as a very excellent example of this form of tooth, circular
+pallets of ten degrees fork action and ten and a half degrees of
+escape-wheel action.</p>
+
+<p>It will be noticed that the pallets here are comparatively thin to those
+in general use; this condition is accomplished by deriving the principal
+part of the impulse from driving planes placed on the teeth. As relates
+to the escape-wheel action of the ten and one-half degrees, which gives
+impulse to the escapement, five and one-half degrees are utilized by the
+driving planes on the teeth and five by the impulse face of the pallet.
+Of the ten degrees of fork action, four and a half degrees relate to the
+impulse face of the teeth, one and a half degrees to lock, and four
+degrees to the driving plane of the pallets.</p>
+
+<p>In delineating such a club-tooth escapement, we commence, as in former
+examples, by first assuming the center of the escape wheel <a name="Page_31" id="Page_31"></a>at <i>A</i>, and
+with the dividers set at five inches sweeping the arc <i>a a</i>. Through <i>A</i>
+we draw the vertical line <i>A B'</i>. On the arc <i>a a</i>, and each side of its
+intersection with the line <i>A B'</i>, we lay off thirty degrees, as in
+former drawings, and through the points so established on the arc <i>a a</i>
+we draw the radial lines <i>A b</i> and <i>A c</i>. From the intersection of the
+radial line <i>A b</i> with the arc <i>a</i> we draw the line <i>h h</i> at right
+angles to <i>A b</i>. Where the line <i>h</i> intersects the radial lines <i>A B'</i>
+is located the center of the pallet staff, as shown at <i>B</i>. Inasmuch as
+we decided to let the pallet utilize five degrees of escape-wheel
+action, we take a space of two and a half degrees in the dividers, and
+on the arc <i>a a</i> lay off the said two and a half degrees to the left of
+this intersection, and through the point so established draw the radial
+line <i>A g</i>. From <i>B</i> as a center we sweep the arc <i>d d</i> so it passes
+through the point of intersection of the arc <i>a</i> with the line <i>A g</i>.</p>
+
+<div class="figcenter"><a href="images/pict020.jpg"><img src="images/pict020-tb.jpg" alt="Fig. 20" title="Fig. 20" /></a></div>
+
+<p>We again lay off two and a half degrees from the intersection of the
+line <i>A b</i> with the arc <i>a</i>, but this time to the right of said
+intersection, and through the point so established, and from <i>B</i> as a
+center, we sweep the arc <i>e</i>. From the intersection of the radial line
+<i>A g</i> with the arc <i>a</i> we lay off to the left five and a half degrees on
+said arc, and through the point so established draw the radial line <i>A
+f</i>. With the dividers set at five inches we sweep the short arc <i>m</i> from
+<i>B</i> as a center. From the intersection of the line <i>h B h'</i><a name="Page_32" id="Page_32"></a> with the
+arc <i>m</i> we lay off on said arc and above the line <i>h'</i> four and a half
+degrees, and through the point so established draw the line <i>B j</i>.</p>
+
+<p>We next set the dividers so they embrace the space on the radial line <i>A
+b</i> between its intersection with the line <i>B j</i> and the center <i>A</i>, and
+from <i>A</i> as a center sweep the arc <i>i</i>, said arc defining the <i>addendum</i>
+of the escape-wheel teeth. We draw a line from the intersection of the
+radial line <i>A f</i> with the arc <i>i</i> to the intersection of the radial
+line <i>A g</i> with the arc <i>a</i>, and thus define the impulse face of the
+escape-wheel tooth <i>D</i>. For defining the locking face of the tooth we
+draw a line at an angle of twenty-four degrees to the line <i>A g</i>, as
+previously described. The back of the tooth is defined with a curve
+swept from some point on the addendum circle <i>i</i>, such as our judgment
+will dictate.</p>
+
+<p>In the drawing shown at Fig. 20 the radius of this curve was obtained by
+taking eleven and a half degrees from the degree arc of 5" radius in the
+dividers, and setting one leg at the intersection of the radial line <i>A
+f</i> with the arc <i>i</i>, and placing the other on the line <i>i</i>, and allowing
+the point so established to serve as a center, the arc was swept for the
+back of the tooth, the small circle at <i>n</i> denoting one of the centers
+just described. The length for the face of the tooth was obtained by
+taking eleven degrees from the degree arc just referred to and laying
+that space off on the line <i>p</i>, which defined the face of the tooth. The
+line <i>B k</i> is laid off one and a half degrees below <i>B h</i> on the arc
+<i>m</i>. The extent of this arc on the arc <i>d</i> defines the locking face of
+the entrance pallet. We set off four degrees on the arc <i>m</i> below the
+line <i>B k</i>, and through the point so established draw the line <i>B l</i>. We
+draw a line from the intersection of the line <i>A g</i> with the line <i>c h</i>
+to the intersection of the arc <i>e</i> with the line <i>c l</i>, and define the
+impulse face of the entrance pallet.</p>
+
+
+<h4>RELATIONS OF THE SEVERAL PARTS.</h4>
+
+<p>Before we proceed to delineate the exit pallet of our escapement, let us
+reason on the relations of the several parts.</p>
+
+<p>The club-tooth lever escapement is really the most complicated
+escapement made. We mean by this that there are more factors involved in
+the problem of designing it correctly than in any other known
+escapement. Most&mdash;we had better say all, for there are no exceptions
+which occur to us&mdash;writers on the lever escapement lay down certain
+empirical rules for delineating the several parts, <a name="Page_33" id="Page_33"></a>without giving
+reasons for this or that course. For illustration, it is an established
+practice among escapement makers to employ tangential lockings, as we
+explained and illustrated in Fig. 16.</p>
+
+<p>Now, when we adopt circular pallets and carry the locking face of the
+entrance pallet around to the left two and a half degrees, the true
+center for the pallet staff, if we employ tangent lockings, would be
+located on a line drawn tangent to the circle <i>a a</i> from its
+intersection with the radial line <i>A k</i>, Fig. 21. Such a tangent is
+depicted at the line <i>s l'</i>. If we reason on the situation, we will see
+that the line <i>A k</i> is not at right angles to the line <i>s l</i>; and,
+consequently, the locking face of the entrance pallet <i>E</i> has not really
+the twelve-degree lock we are taught to believe it has.</p>
+
+<div class="figcenter"><a href="images/pict021.jpg"><img src="images/pict021-tb.jpg" alt="Fig. 21" title="Fig. 21" /></a></div>
+
+<p>We will not discuss these minor points further at present, but leave
+them for subsequent consideration. We will say, however, that we could
+locate the center of the pallet action at the small circle <i>B'</i> above
+the center <i>B</i>, which we have selected as our fork-and-pallet action,
+and secure a perfectly sound escapement, with several claimed
+advantages.</p>
+
+<p>Let us now take up the delineation of the exit pallet. It is very easy
+to locate the outer angle of this pallet, as this must be situated at
+the intersection of the addendum circle <i>i</i> and the arc <i>g</i>, and located
+at <i>o</i>. It is also self-evident that the inner or locking <a name="Page_34" id="Page_34"></a>angle must be
+situated at some point on the arc <i>h</i>. To determine this location we
+draw the line <i>B c</i> from <i>B</i> (the pallet center) through the
+intersection of the arc <i>h</i> with the pitch circle <i>a</i>.</p>
+
+<p>Again, it follows as a self-evident fact, if the pallet we are dealing
+with was locked, that is, engaged with the tooth <i>D''</i>, the inner angle
+<i>n</i> of the exit pallet would be one and a half degrees inside the pitch
+circle <i>a</i>. With the dividers set at 5", we sweep the short arc <i>b b</i>,
+and from the intersection of this arc with the line <i>B c</i> we lay off ten
+degrees, and through the point so established, from <i>B</i>, we draw the
+line <i>B d</i>. Below the point of intersection of the line <i>B d</i> with the
+short arc <i>b b</i> we lay off one and a half degrees, and through the point
+thus established we draw the line <i>B e</i>.</p>
+
+
+<h4>LOCATING THE INNER ANGLE OF THE EXIT PALLET.</h4>
+
+<p>The intersection of the line <i>B e</i> with the arc <i>h</i>, which we will term
+the point <i>n</i>, represents the location of the inner angle of the exit
+pallet. We have already explained how we located the position of the
+outer angle at <i>o</i>. We draw the line <i>n o</i> and define the impulse face
+of the exit pallet. If we mentally analyze the problem in hand, we will
+see that as the exit pallet vibrates through its ten degrees of arc the
+line <i>B d</i> and <i>B c</i> change places, and the tooth <i>D''</i> locks one and a
+half degrees. To delineate the locking face of the exit pallet, we erect
+a perpendicular to the line <i>B e</i> from the point <i>n</i>, as shown by the
+line <i>n p</i>.</p>
+
+<p>From <i>n</i> as a center we sweep the short arc <i>t t</i>, and from its
+intersection with the line <i>n p</i> we lay off twelve degrees, and through
+the point so established we draw the line <i>n u</i>, which defines the
+locking face of the exit pallet. We draw the line <i>o o'</i> parallel with
+<i>n u</i> and define the outer face of said pallet. In Fig. 21 we have not
+made any attempt to show the full outline of the pallets, as they are
+delineated in precisely the same manner as those previously shown.</p>
+
+<p>We shall next describe the delineation of a club-tooth escapement with
+pallets having equidistant locking faces; and in Fig. 22 we shall show
+pallets with much wider arms, because, in this instance, we shall derive
+more of the impulse from the pallets than from the teeth. We do this to
+show the horological student the facility with which the club-tooth
+lever escapement can be manipulated. We wish also to impress on his mind
+the facts that the employment of thick pallet arms and thin pallet arms
+depends on <a name="Page_35" id="Page_35"></a>the teeth of the escape wheel for its efficiency, and that
+he must have knowledge enough of the principles of action to tell at a
+glance on what lines the escapement was constructed.</p>
+
+<p>Suppose, for illustration, we get hold of a watch which has thin pallet
+arms, or stones, if they are exposed pallets, and the escape was
+designed for pallets with thick arms. There is no sort of tinkering we
+can do to give such a watch a good motion, except to change either the
+escape wheel or the pallets. If we know enough of the lever escapement
+to set about it with skill and judgment, the matter is soon put to
+rights; but otherwise we can look and squint, open and close the
+bankings, and tinker about till doomsday, and the watch be none the
+better.</p>
+
+
+<h4>CLUB-TOOTH LEVER WITH EQUIDISTANT LOCKING FACES.</h4>
+
+<p>In drawing a club-tooth lever escapement with equidistant locking, we
+commence, as on former occasions, by producing the vertical line <i>A k</i>,
+Fig. 22, and establishing the center of the escape wheel at <i>A</i>, and
+with the dividers set at 5" sweep the pitch circle <i>a</i>. On each side of
+the intersection of the vertical line <i>A k</i> with the arc <i>a</i> we set off
+thirty degrees on said arc, and through the points so established draw
+the radial lines <i>A b</i> and <i>A c</i>.</p>
+
+<p>From the intersection of the radial line <i>A b</i> with the arc <i>a</i> lay off
+three and a half degrees to the left of said intersection on the arc
+<i>a</i>, and through the point so established draw the radial line <i>A e</i>.
+From the intersection of the radial line <i>A b</i> with the arc <i>a</i> erect
+the perpendicular line <i>f</i>, and at the crossing or intersection of said
+line with the vertical line <i>A k</i> establish the center of the pallet
+staff, as indicated by the small circle <i>B</i>. From <i>B</i> as a center sweep
+the short arc <i>l</i> with a 5" radius; and from the intersection of the
+radial line <i>A b</i> with the arc <i>a</i> continue the line <i>f</i> until it
+crosses the short arc <i>l</i>, as shown at <i>f'</i>. Lay off one and a half
+degrees on the arc <i>l</i> below its intersection with the line <i>f'</i>, and
+from <i>B</i> as a center draw the line <i>B</i> <i>i</i> through said intersection.
+From <i>B</i> as a center, through the intersection of the radial line <i>A b</i>
+and the arc <i>a</i>, sweep the arc <i>g</i>.</p>
+
+<p>The space between the lines <i>B f'</i> and <i>B i</i> on the arc <i>g</i> defines the
+extent of the locking face of the entrance pallet <i>C</i>. The intersection
+of the line <i>B f'</i> with the arc <i>g</i> we denominate the point <i>o</i>, and
+from this point as a center sweep the short arc <i>p</i> with a 5" radius;
+and on this arc, from its intersection with the radial line <i>A b</i>, lay
+off twelve degrees, and through the point so established, <a name="Page_36" id="Page_36"></a>from <i>o</i> as a
+center, draw the radial line <i>o m</i>, said line defining the locking face
+of the entrance pallet <i>C</i>.</p>
+
+<div class="figcenter"><a href="images/pict022.jpg"><img src="images/pict022-tb.jpg" alt="Fig. 22" title="Fig. 22" /></a></div>
+
+<p>It will be seen that this gives a positive "draw" of twelve degrees to
+the entrance pallet; that is, counting to the line <i>B f'</i>. In this
+escapement as delineated there is perfect tangential locking. If the
+locking face of the entrance-pallet stone at <i>C</i> was made to conform to
+the radial line <i>A b</i>, the lock of the tooth <i>D</i> at <i>o</i> would be "dead";
+that is, absolutely neutral. The tooth <i>D</i> would press the pallet <i>C</i> in
+the direction of the arrow <i>x</i>, toward the center of the pallet staff
+<i>B</i>, with no tendency on the part of the pallet to turn on its axis <i>B</i>.
+Theoretically, the pallet with the locking face cut to coincide with the
+line <i>A b</i> would resist movement on the center <i>B</i> in either direction
+indicated by the double-headed arrow <i>y</i>.</p>
+
+<p>A pallet at <i>C</i> with a circular locking face made to conform to the arc
+<i>g</i>, would permit movement in the direction of the double-headed arrow
+<i>y</i> with only mechanical effort enough to overcome friction. But it is
+evident on inspection that a locking face on the line <i>A b</i> would cause
+a retrograde motion of the escape wheel, and consequent resistance, if
+said pallet was moved in either direction indicated by the double-headed
+arrow <i>y</i>. Precisely the same conditions obtain at the point <i>u</i>, which
+holds the same relations to the exit pallet as the point <i>o</i> does to the
+entrance pallet <i>C</i>.</p>
+
+<h4><a name="Page_37" id="Page_37"></a>ANGULAR MOTION OF ESCAPE WHEEL DETERMINED.</h4>
+
+<p>The arc (three and a half degrees) of the circle <i>a</i> embraced between
+the radial lines <i>A b</i> and <i>A e</i> determines the angular motion of the
+escape wheel utilized by the escape-wheel tooth. To establish and define
+the extent of angular motion of the escape wheel utilized by the pallet,
+we lay off seven degrees on the arc <i>a</i> from the point <i>o</i> and establish
+the point <i>n</i>, and through the point <i>n</i>, from <i>B</i> as a center, we sweep
+the short arc <i>n'</i>. Now somewhere on this arc <i>n'</i> will be located the
+inner angle of the entrance pallet. With a carefully-made drawing,
+having the escape wheel 10" in diameter, it will be seen that the arc
+<i>a</i> separates considerably from the line, <i>B f'</i> where it crosses the
+arc <i>n'</i>.</p>
+
+<p>It will be remembered that when drawing the ratchet-tooth lever
+escapement a measurement of eight and a half degrees was made on the arc
+<i>n'</i> down from its intersection with the pitch circle, and thus the
+inner angle of the pallet was located. In the present instance the
+addendum line <i>w</i> becomes the controlling arc, and it will be further
+noticed on the large drawing that the line <i>B h</i> at its intersection
+with the arc <i>n'</i> approaches nearer to the arc <i>w</i> than does the line <i>B
+f'</i> to the pitch circle <i>a</i>; consequently, the inner angle of the pallet
+should not in this instance be carried down on the arc <i>n'</i> so far to
+correct the error as in the ratchet tooth.</p>
+
+<p>Reason tells us that if we measure ten degrees down on the arc <i>n'</i> from
+its intersection with the addendum circle <i>w</i> we must define the
+position of the inner angle of the entrance pallet. We name the point so
+established the point <i>r</i>. The outer angle of this pallet is located at
+the intersection of the radial line <i>A b</i> with the line <i>B i</i>; said
+intersection we name the point <i>v</i>. Draw a line from the point <i>v</i> to
+the point <i>r</i>, and we define the impulse face of the entrance pallet;
+and the angular motion obtained from it as relates to the pallet staff
+embraces six degrees.</p>
+
+<p>Measured on the arc <i>l</i>, the entire ten degrees of angular motion is as
+follows: Two and a half degrees from the impulse face of the tooth, and
+indicated between the lines <i>B h</i> and <i>B f</i>; one and a half degrees lock
+between the lines <i>B f'</i> and <i>B i</i>; six degrees impulse from pallet
+face, entrance between the lines <i>B i</i> and <i>B j</i>.</p>
+
+
+<h4>A DEPARTURE FROM FORMER PRACTICES.</h4>
+
+<p>Grossmann and Britten, in all their delineations of the club-tooth
+escapement, show the exit pallet as disengaged. To vary from this
+<a name="Page_38" id="Page_38"></a>beaten track we will draw our exit pallet as locked. There are other
+reasons which prompt us to do this, one of which is, pupils are apt to
+fall into a rut and only learn to do things a certain way, and that way
+just as they are instructed.</p>
+
+<p>To illustrate, the writer has met several students of the lever
+escapement who could make drawings of either club or ratchet-tooth
+escapement with the lock on the entrance pallet; but when required to
+draw a pallet as illustrated at Fig. 23, could not do it correctly.
+Occasionally one could do it, but the instances were rare. A still
+greater poser was to request them to delineate a pallet and tooth when
+the action of escaping was one-half or one-third performed; and it is
+easy to understand that only by such studies the master workman can
+thoroughly comprehend the complications involved in the club-tooth lever
+escapement.</p>
+
+
+<h4>AN APT ILLUSTRATION.</h4>
+
+<p>As an illustration: Two draughtsmen, employed by two competing watch
+factories, each designs a club-tooth escapement. We will further suppose
+the trains and mainspring power used by each concern to be precisely
+alike. But in practice the escapement of the watches made by one factory
+would "set," that is, if you stopped the balance dead still, with the
+pin in the fork, the watch would not start of itself; while the
+escapement designed by the other draughtsman would not "set"&mdash;stop the
+balance dead as often as you choose, the watch would start of itself.
+Yet even to experienced workmen the escape wheels and pallets <i>looked</i>
+exactly alike. Of course, there was a difference, and still none of the
+text-books make mention of it.</p>
+
+<p>For the present we will go on with delineating our exit pallet. The
+preliminaries are the same as with former drawings, the instructions for
+which we need not repeat. Previous to drawing the exit pallet, let us
+reason on the matter. The point <i>r</i> in Fig. 23 is located at the
+intersection of pitch circle <i>a</i> and the radial line <i>A c</i>; and this
+will also be the point at which the tooth <i>C</i> will engage the locking
+face of the exit pallet.</p>
+
+<p>This point likewise represents the advance angle of the engaging tooth.
+Now if we measure on the arc <i>k</i> (which represents the locking faces of
+both pallets) downward one and a half degrees, we establish the lock of
+the pallet <i>E</i>. To get this one and a half degrees defined on the arc
+<i>k</i>, we set the dividers at 5", and from <i>B</i><a name="Page_39" id="Page_39"></a> as a center sweep the
+short arc <i>i</i>, and from the intersection of the arc <i>i</i> with the line <i>B
+e</i> we lay off on said arc <i>i</i> one and a half degrees, and through the
+point so established draw the line <i>B f</i>.</p>
+
+<p>Now the space on the arc <i>k</i> between the lines <i>B e</i> and <i>B f</i> defines
+the angular extent of the locking face. With the dividers set at 5" and
+one leg resting at the point <i>r</i>, we sweep the short arc <i>t</i>, and from
+the intersection of said arc with the line <i>A c</i> we draw the line <i>n p</i>;
+but in doing so we extend it (the line) so that it intersects the line
+<i>B f</i>, and at said intersection is located the inner angle of the exit
+pallet. This intersection we will name the point <i>n</i>.</p>
+
+<div class="figcenter"><a href="images/pict023.jpg"><img src="images/pict023-tb.jpg" alt="Fig. 23" title="Fig. 23" /></a></div>
+
+<p>From the intersection of the line <i>B e</i> with the arc <i>i</i> we lay off two
+and a half degrees on said arc, and through the point so established we
+draw the line <i>B g</i>. The intersection of this line with the arc <i>k</i> we
+name the point <i>z</i>. With one leg of our dividers set at <i>A</i> we sweep the
+arc <i>l</i> so it passes through the point <i>z</i>. This last arc defines the
+addendum of the escape-wheel teeth. From the point <i>r</i> on the arc <i>a</i> we
+lay off three and a half degrees, and through the point so established
+draw the line <i>A j</i>.</p>
+
+
+<h4>LOCATING THE OUTER ANGLE OF THE IMPULSE PLANES.</h4>
+
+<p>The intersection of this line with the addendum arc <i>l</i> locates the
+outer angle of the impulse planes of the teeth, and we name it the point
+<i>x</i>. From the point <i>r</i> we lay off on the arc <i>a</i> seven degrees <a name="Page_40" id="Page_40"></a>and
+establish the point <i>v</i>, which defines the extent of the angular motion
+of the escape wheel utilized by pallet. Through the point <i>v</i>, from <i>B</i>
+as a center, we sweep the short arc <i>m</i>. It will be evident on a
+moment's reflection that this arc <i>m</i> must represent the path of
+movement of the outer angle of the exit pallet, and if we measure down
+ten degrees from the intersection of the arc <i>l</i> with the arc <i>m</i>, the
+point so established (which we name the point <i>s</i>) must be the exact
+position of the outer angle of the pallet during locking. We have a
+measure of ten degrees on the arc <i>m</i>, between the lines <i>B g</i> and <i>B
+h</i>, and by taking this space in the dividers and setting one leg at the
+intersection of the arc <i>l</i> with the arc <i>m</i>, and measuring down on <i>m</i>,
+we establish the point <i>s</i>. Drawing a line from point <i>n</i> to point <i>s</i>
+we define the impulse face of the pallet.</p>
+
+
+<h4>MAKING AN ESCAPEMENT MODEL.</h4>
+
+<div class="figcenter"><a href="images/pict024.jpg"><img src="images/pict024-tb.jpg" alt="Fig. 24" title="Fig. 24" /></a></div>
+
+<p>It is next proposed we apply the theories we have been considering and
+make an enlarged model of an escapement, as shown at Figs. 24 and 25.
+This model is supposed to have an escape wheel one-fifth the size of the
+10" one we have been drawing. In the accompanying cuts are shown only
+the main plate and bridges <a name="Page_41" id="Page_41"></a>in full lines, while the positions of the
+escape wheel and balance are indicated by the dotted circles <i>I B</i>. The
+cuts are to no precise scale, but were reduced from a full-size drawing
+for convenience in printing. We shall give exact dimensions, however, so
+there will be no difficulty in carrying out our instructions in
+construction.</p>
+
+<div class="figcenter"><img src="images/pict025.jpg" alt="Fig. 25" title="Fig. 25" /></div>
+
+<p>Perhaps it would be as well to give a general description of the model
+before taking up the details. A reduced side view of the complete model
+is given at Fig. 26. In this cut the escapement model shown at Figs. 24
+and 25 is sketched in a rough way at <i>R</i>, while <i>N</i> shows a glass cover,
+and <i>M</i> a wooden base of polished oak or walnut. This base is recessed
+on the lower side to receive an eight-day spring clock movement, which
+supplies the motive power for the model. This base is recessed on top to
+receive the main plate <i>A</i>, Fig. 24, and also to hold the glass shade
+<i>N</i> in position. The base <i>M</i> is 2&frac12;" high and 8" diameter. The glass
+cover <i>N</i> can have either a high and spherical top, as shown, or, as
+most people prefer, a flattened oval.</p>
+
+<div class="figright"><img src="images/pict026.jpg" alt="Fig. 26" title="Fig. 26" /></div>
+
+<p>The main plate <i>A</i> is of hard spring brass, 1/10" thick and 6" in
+diameter; in fact, a simple disk of the size named, with slightly
+rounded edges. The top plate, shown at <i>C</i>, Figs. 24 and 25, is 1/8"
+thick and shaped as shown. This plate (<i>C</i>) is supported on two pillars
+1/2" in diameter and 1-1/4" high. Fig. 25 is a side view of Fig. 24 seen
+in the direction of the arrow <i>p</i>. The cock <i>D</i> is also of 1/8" spring
+brass shaped as shown, and attached by the screw <i>f</i> and steady pins <i>s
+s</i> to the top plate <i>C</i>. The bridge <i>F G</i> carries the top pivots of
+escape wheel and pallet staff, and is shaped as shown at the full
+outline. This bridge is supported on two pillars 1/2" high and 1/2" in
+diameter, one of which is shown at <i>E</i>, Fig. 25, and both at the dotted
+circles <i>E E'</i>, Fig. 24.</p>
+
+<p>To lay out the lower plate we draw the line <i>a a</i> so it passes through
+the center of <i>A</i> at <i>m</i>. At 1.3" from one edge of <i>A</i> we <a name="Page_42" id="Page_42"></a>establish on
+the line <i>a</i> the point <i>d</i>, which locates the center of the escape
+wheel. On the same line <i>a</i> at 1.15" from <i>d</i> we establish the point
+<i>b</i>, which represents the center of the pallet staff. At the distance of
+1.16" from <i>b</i> we establish the point <i>c</i>, which represents the center
+of the balance staff. To locate the pillars <i>H</i>, which support the top
+plate <i>C</i>, we set the dividers at 2.58", and from the center <i>m</i> sweep
+the arc <i>n</i>.</p>
+
+<p>From the intersection of this arc with the line <i>a</i> (at <i>r</i>) we lay off
+on said arc <i>n</i> 2.1" and establish the points <i>g g'</i>, which locate the
+center of the pillars <i>H H</i>. With the dividers set so one leg rests at
+the center <i>m</i> and the other leg at the point <i>d</i>, we sweep the arc <i>t</i>.
+With the dividers set at 1.33" we establish on the arc <i>t</i>, from the
+point <i>d</i>, the points <i>e e'</i>, which locate the position of the pillars
+<i>E E'</i>. The outside diameter of the balance <i>B</i> is 3-5/8" with the rim
+3/16" wide and 5/16" deep, with screws in the rim in imitation of the
+ordinary compensation balance.</p>
+
+<p>Speaking of a balance of this kind suggests to the writer the trouble he
+experienced in procuring material for a model of this kind&mdash;for the
+balance, a pattern had to be made, then a casting made, then a machinist
+turned the casting up, as it was too large for an American lathe. A
+hairspring had to be specially made, inasmuch as a mainspring was too
+short, the coils too open and, more particularly, did not look well.
+Pallet jewels had to be made, and lapidists have usually poor ideas of
+close measurements. Present-day conditions, however, will, no doubt,
+enable the workman to follow our instructions much more readily.</p>
+
+
+<h4>MAKING THE BRIDGES.</h4>
+
+<p>In case the reader makes the bridges <i>C</i> and <i>F</i>, as shown in Fig. 27,
+he should locate small circles on them to indicate the position of the
+screws for securing these bridges to the pillars which support them, and
+also other small circles to indicate the position of the pivot holes <i>d
+b</i> for the escape wheel and pallet staff. In practice it will be well to
+draw the line <i>a a</i> through the center of the main plate <i>A</i>, as
+previously directed, and also establish the point <i>d</i> as therein
+directed.</p>
+
+<div class="figright"><a href="images/pict027.jpg"><img src="images/pict027-tb.jpg" alt="Fig. 27" title="Fig. 27" /></a></div>
+
+<p>The pivot hole <i>d'</i> for the escape wheel, and also the holes at <i>e e</i>
+and <i>b</i>, are now drilled in the bridge <i>F</i>. These holes should be about
+1/16" in diameter. The same sized hole is also drilled in the main plate
+<i>A</i> at <i>d</i>. We now place a nicely-fitting steel pin in the <a name="Page_43" id="Page_43"></a>hole <i>d'</i> in
+the bridge <i>F</i> and let it extend into the hole <i>d</i> in the main plate. We
+clamp the bridge <i>F</i> to <i>A</i> so the hole <i>b</i> comes central on the line
+<i>a</i>, and using the holes <i>e e</i> in <i>F</i> as guides, drill or mark the
+corresponding holes <i>e' e'</i> and <i>b</i> in the main plate for the pillars <i>E
+E'</i> and the pallet staff.</p>
+
+<p>This plan will insure the escape wheel and pallet staff being perfectly
+upright. The same course pursued with the plate <i>C</i> will insure the
+balance being upright. The pillars which support the bridges are shaped
+as shown at Fig. 28, which shows a side view of one of the pillars which
+support the top plate or bridge <i>C</i>. The ends are turned to 1/4" in
+diameter and extend half through the plate, where they are held by
+screws, the same as in American movements.</p>
+
+<div class="figleft"><img src="images/pict028.jpg" alt="Fig. 28" title="Fig. 28" /></div>
+<div class="figright"><img src="images/pict029.jpg" alt="Fig. 29" title="Fig. 29" /></div>
+<p>The pillars (like <i>H</i>) can be riveted in the lower plate <i>A</i>, but we
+think most workmen will find it more satisfactory to employ screws, as
+shown at Fig. 29. The heads of such screws should be about 3/8" in
+diameter and nicely rounded, polished and blued. We would not advise
+jeweling the pivot holes, because there is but slight friction, except
+to the foot of the balance pivot, which should be jeweled with a
+plano-convex garnet.</p>
+
+
+<h4>IMITATION RUBIES FOR CAPPING THE TOP PIVOTS.</h4>
+
+<p>The top pivots to the escape wheel should be capped with imitation
+rubies for appearance sake only, letting the cap settings be red gold,
+or brass red gilded. If real twelve-karat gold is employed the cost will
+not be much, as the settings are only about 3/8" across and can be
+turned very thin, so they will really contain but very little gold. The
+reason why we recommend imitation ruby cap jewels for the upper holes,
+is that such jewels are much more brilliant than any real stone we can
+get for a moderate cost. Besides, there is no wear on them.</p>
+
+<div class="figleft"><img src="images/pict030.jpg" alt="Fig. 30" title="Fig. 30" /></div>
+<div class="figright"><img src="images/pict031.jpg" alt="Fig. 31" title="Fig. 31" /></div>
+
+<p>The pallet jewels are also best made of glass, as garnet or any red
+stone will look almost black in such large pieces. Red carnelian has a
+sort of brick-red color, which has a cheap appearance. There <a name="Page_44" id="Page_44"></a>is a new
+phosphorus glass used by optical instrument makers which is intensely
+hard, and if colored ruby-red makes a beautiful pallet jewel, which will
+afford as much service as if real stones were used; they are no cheaper
+than carnelian pallets, but much richer looking. The prettiest cap for
+the balance is one of those foilback stones in imitation of a rose-cut
+diamond.</p>
+
+<div class="figleft"><img src="images/pict032.jpg" alt="Fig. 32" title="Fig. 32" /></div>
+
+<div class="figright"><img src="images/pict033.jpg" alt="Fig. 33" title="Fig. 33" /></div>
+
+
+<p>In turning the staffs it is the best plan to use double centers, but a
+piece of Stubs steel wire that will go into a No. 40 wire chuck, will
+answer; in case such wire is used, a brass collet must be provided. This
+will be understood by inspecting Fig. 30, where <i>L</i> represents the Stubs
+wire and <i>B N</i> the brass collet, with the balance seat shown at <i>k</i>. The
+escape-wheel arbor and pallet staff can be made in the same way. The
+lower end of the escape wheel pivot is made about 1/4" long, so that a
+short piece of brass wire can be screwed upon it, as shown in Fig. 31,
+where <i>h</i> represents the pivot, <i>A</i> the lower plate, and the dotted line
+at <i>p</i> the brass piece screwed on the end of the pivot. This piece <i>p</i>
+is simply a short bit of brass wire with a female screw tapped into the
+end, which screws on to the pivot. An arm is attached to <i>p</i>, as shown
+at <i>T</i>. The idea is, the pieces <i>T p</i> act like a lathe dog to convey the
+power from one of the pivots of an old eight-day spring clock movement,
+which is secured by screws to the lower side of the main plate <i>A</i>. The
+plan is illustrated at Fig. 32, where <i>l</i> represents pivot of the
+eight-day clock employed to run the model. Counting the escape-wheel
+pivot of the clock as one, we take the third pivot from this in the
+clock train, placing the movement so this point comes opposite the
+escape-wheel pivot of the model, and screw the clock movement fast to
+the lower side of the plate <i>A</i>. The parts <i>T</i>, Fig. 33, are alike on
+both pivots.</p>
+
+
+<h4>PROFITABLE FOR EXPLAINING TO A CUSTOMER.</h4>
+
+<p>To fully appreciate such a large escapement model as we have been
+describing, a person must see it with its great balance, nearly 4"
+across, flashing and sparkling in the show window in the evening, and
+the brilliant imitation ruby pallets dipping in and out of the escape
+wheel. A model of this kind is far more attractive than if the entire
+train were shown, the mystery of "What makes it go?"<a name="Page_45" id="Page_45"></a> being one of the
+attractions. Such a model is, further, of great value in explaining to a
+customer what you mean when you say the escapement of his watch is out
+of order. Any practical workman can easily make an even $100 extra in a
+year by making use of such a model.</p>
+
+<p>For explaining to customers an extra balance cock can be used to show
+how the jewels (hole and cap) are arranged. Where the parts are as large
+as they are in the model, the customer can see and understand for
+himself what is necessary to be done.</p>
+
+<p>It is not to be understood that our advice to purchase the jewels for an
+extra balance cock conflicts with our recommending the reader not to
+jewel the holes of his model. The extra cock is to be shown, not for
+use, and is employed solely for explaining to a customer what is
+required when a pivot or jewel is found to be broken.</p>
+
+
+<h4>HOW LARGE SCREWS ARE MADE.</h4>
+
+<div class="figleft"><img src="images/pict034.jpg" alt="Fig. 34" title="Fig. 34" /></div>
+
+<div class="figright"><img src="images/pict035.jpg" alt="Fig. 35" title="Fig. 35" /></div>
+
+<p>The screws which hold the plates in place should have heads about 3/8"
+in diameter, to be in proportion to the scale on which the balance and
+escape wheel are gotten up. There is much in the manner in which the
+screw heads are finished as regards the elegance of such a model. A
+perfectly flat head, no matter how highly polished, does not look well,
+neither does a flattened conehead, like Fig. 35. The best head for this
+purpose is a cupped head with chamfered edges, as shown at Fig. 34 in
+vertical section. The center <i>b</i> is ground and polished into a perfect
+concave by means of a metal ball. The face, between the lines <i>a a</i>, is
+polished dead flat, and the chamfered edge <i>a c</i> finished a trifle
+convex. The flat surface at <i>a</i> is bright, but the concave <i>b</i> and
+chamfer at <i>c</i> are beautifully blued. For a gilt-edged, double extra
+head, the chamfer at <i>c</i> can be "snailed," that is, ground with a
+suitable lap before bluing, like the stem-wind wheels on some watches.</p>
+
+
+<h4>FANCY SCREWHEADS.</h4>
+
+<div class="figleft"><img src="images/pict036.jpg" alt="Fig. 36" title="Fig. 36" /></div>
+
+<p>There are two easy methods of removing the blue from the flat part of
+the screwhead at <i>a</i>. (1) Make a special holder for the screw in the end
+of a cement brass, as shown at <i>E</i>, Fig. 36, and while it is slowly
+revolving in the lathe touch the flat surface <i>a</i> with a sharpened
+pegwood wet with muriatic acid, which dissolves the <a name="Page_46" id="Page_46"></a>blue coating of
+oxide of iron. (2) The surface of the screwhead is coated with a very
+thin coating of shellac dissolved in alcohol and thoroughly dried, or a
+thin coating of collodion, which is also dried. The screw is placed in
+the ordinary polishing triangle and the flat face at <i>a</i> polished on a
+tin lap with diamantine and oil. In polishing such surfaces the thinnest
+possible coating of diamantine and oil is smeared on the lap&mdash;in fact,
+only enough to dim the surface of the tin. It is, of course, understood
+that it is necessary to move only next to nothing of the material to
+restore the polish of the steel. The polishing of the other steel parts
+is done precisely like any other steel work.</p>
+
+<div class="figright"><img src="images/pict037.jpg" alt="Fig. 37" title="Fig. 37" /></div>
+
+<p>The regulator is of the Howard pattern. The hairspring stud is set in
+the cock like the Elgin three-quarter-plate movement. The richest finish
+for such a model is frosted plates and bridges. The frosting should not
+be a fine mat, like a watch movement, but coarse-grained&mdash;in fact, the
+grain of the frosting should be proportionate to the size of the
+movement. The edges of the bridges and balance cock can be left smooth.
+The best process for frosting is by acid. Details for doing the work
+will now be given.</p>
+
+<div class="figleft"><img src="images/pict038.jpg" alt="Fig. 38" title="Fig. 38" /></div>
+
+<p>To do this frosting by acid nicely, make a sieve by tacking and gluing
+four pieces of thin wood together, to make a rectangular box without a
+bottom. Four pieces of cigar-box wood, 8" long by 1-1/2" wide, answer
+first rate. We show at <i>A A A A</i>, Fig. 37, such a box as if seen from
+above; with a side view, as if seen in the direction of the arrow <i>a</i>,
+at Fig. 38. A piece of India muslin is glued across the bottom, as shown
+at the dotted lines <i>b b</i>. By turning up the edges on the outside of the
+box, the muslin bottom can be drawn as tight as a drum head.</p>
+
+
+<h4>HOW TO DO ACID FROSTING.</h4>
+
+<div class="figright"><img src="images/pict039.jpg" alt="Fig. 39" title="Fig. 39" /></div>
+<p>To do acid frosting, we procure two ounces of gum mastic and place in
+the square sieve, shown at Fig. 37. Usually more than half the weight of
+gum mastic is in fine dust, and if not, that is, if the gum is in the
+shape of small round pellets called "mastic tears," crush these into
+dust and place the dust in <i>A</i>. Let us next <a name="Page_47" id="Page_47"></a>suppose we wish to frost
+the cock on the balance, shown at Fig. 39. Before we commence to frost,
+the cock should be perfectly finished, with all the holes made, the
+regulator cap in position, the screw hole made for the Howard regulator
+and the index arc engraved with the letters S and F.</p>
+
+<p>It is not necessary the brass should be polished, but every file mark
+and scratch should be stoned out with a Scotch stone; in fact, be in the
+condition known as "in the gray." It is not necessary to frost any
+portion of the cock <i>C</i>, except the upper surface. To protect the
+portion of the cock not to be frosted, like the edges and the back, we
+"stop out" by painting over with shellac dissolved in alcohol, to which
+a little lampblack is added. It is not necessary the coating of shellac
+should be very thick, but it is important it should be well dried.</p>
+
+
+<h4>HOW TO PREPARE THE SURFACE.</h4>
+
+<p>For illustration, let us suppose the back and edges of the cock at Fig.
+39 are coated with shellac and it is laid flat on a piece of paper about
+a foot square to catch the excess of mastic. Holes should be made in
+this paper and also in the board on which the paper rests to receive the
+steady pins of the cock. We hold the sieve containing the mastic over
+the cock and, gently tapping the box <i>A</i> with a piece of wood like a
+medium-sized file handle, shake down a little snowstorm of mastic dust
+over the face of the cock <i>C</i>.</p>
+
+<p>Exactly how much mastic dust is required to produce a nice frosting is
+only to be determined by practice. The way to obtain the knack is to
+frost a few scraps to "get your hand in." Nitric acid of full strength
+is used, dipping the piece into a shallow dish for a few seconds. A
+good-sized soup plate would answer very nicely for frosting the bottom
+plate, which, it will be remembered, is 6" in diameter.</p>
+
+
+<h4>HOW TO ETCH THE SURFACE.</h4>
+
+<p>After the mastic is sifted on, the cock should be heated up to about
+250&deg; F., to cause the particles of mastic to adhere to the surface. The
+philosophy of the process is, the nitric acid eats or dissolves the
+brass, leaving a little brass island the size of the particle of mastic
+which was attached to the surface. After heating to attach the particles
+of mastic, the dipping in nitric acid is <a name="Page_48" id="Page_48"></a>done as just described. Common
+commercial nitric acid is used, it not being necessary to employ
+chemically pure acid. For that matter, for such purposes the commercial
+acid is the best.</p>
+
+<p>After the acid has acted for fifteen or twenty seconds the brass is
+rinsed in pure water to remove the acid, and dried by patting with an
+old soft towel, and further dried by waving through the air. A little
+turpentine on a rag will remove the mastic, but turpentine will not
+touch the shellac coating. The surface of the brass will be found
+irregularly acted upon, producing a sort of mottled look. To obtain a
+nice frosting the process of applying the mastic and etching must be
+repeated three or four times, when a beautiful coarse-grain mat or
+frosting will be produced.</p>
+
+<p>The shellac protection will not need much patching up during the three
+or four bitings of acid, as the turpentine used to wash off the mastic
+does not much affect the shellac coating. All the screw holes like <i>s s</i>
+and <i>d</i>, also the steady pins on the back, are protected by varnishing
+with shellac. The edges of the cocks and bridges should be polished by
+rubbing lengthwise with willow charcoal or a bit of chamois skin
+saturated with oil and a little hard rouge scattered upon it. The
+frosting needs thorough scratch-brushing.</p>
+
+<div class="figleft"><img src="images/pict040.jpg" alt="Fig. 40" title="Fig. 40" /></div>
+
+<p>At Fig. 40 we show the balance cock of our model with modified form of
+Howard regulator. The regulator bar <i>A</i> and spring <i>B</i> should be ground
+smooth on one side and deeply outlined to perfect form. The regulator
+cap <i>C</i> is cut out to the correct size. These parts are of decarbonized
+cast steel, annealed until almost as soft as sheet brass. It is not so
+much work to finish these parts as one might imagine. Let us take the
+regulator bar for an example and carry it through the process of making.
+The strip of soft sheet steel on which the regulator bar is outlined is
+represented by the dotted outline <i>b</i>, Fig. 41.</p>
+
+<div class="figright"><img src="images/pict041.jpg" alt="Fig. 41" title="Fig. 41" /></div>
+
+<p>To cut out sheet steel rapidly we take a piece of smooth clock
+mainspring about 3/4" and 10" long and double it together, softening the
+bending point with the lamp until the piece of mainspring <a name="Page_49" id="Page_49"></a>assumes the
+form shown at Fig. 42, where <i>c</i> represents the piece of spring and <i>H
+H</i> the bench-vise jaws. The piece of soft steel is placed between the
+limbs of <i>c c'</i> of the old mainspring up to the line <i>a</i>, Fig. 41, and
+clamped in the vise jaws. The superfluous steel is cut away with a sharp
+and rather thin cold chisel.</p>
+
+<div class="figright"><img src="images/pict042.jpg" alt="Fig. 42" title="Fig. 42" /></div>
+
+<p>The chisel is presented as shown at <i>G</i>, Fig. 43 (which is an end view
+of the vise jaws <i>H H</i> and regulator bar), and held to cut obliquely and
+with a sort of shearing action, as illustrated in Fig. 42, where <i>A''</i>
+represents the soft steel and <i>G</i> the cold chisel. We might add that
+Fig. 42 is a view of Fig. 43 seen in the direction of the arrow <i>f</i>. It
+is well to cut in from the edge <i>b</i> on the line <i>d</i>, Fig. 41, with a
+saw, in order to readily break out the surplus steel and not bend the
+regulator bar. By setting the pieces of steel obliquely in the vise, or
+so the line <i>e</i> comes even with the vise jaws, we can cut to more nearly
+conform to the circular loop <i>A''</i> of the regulator <i>A</i>.</p>
+
+<div class="figleft"><img src="images/pict043.jpg" alt="Fig. 43" title="Fig. 43" /></div>
+
+<p>The smooth steel surface of the bent mainspring <i>c</i> prevents the vise
+jaws from marking the soft steel of the regulator bar. A person who has
+not tried this method of cutting out soft steel would not believe with
+what facility pieces can be shaped. Any workman who has a universal face
+plate to his lathe can turn out the center of the regulator bar to
+receive the disk <i>C</i>, and also turn out the center of the regulator
+spring <i>B</i>. What we have said about the regulator bar applies also to
+the regulator spring <i>B</i>. This spring is attached to the cock <i>D</i> by
+means of two small screws at <i>n</i>.</p>
+
+<p>The micrometer screw <i>F</i> is tapped through <i>B''</i> as in the ordinary
+Howard regulator, and the screw should be about No. 6 of a Swiss
+screw-plate. The wire from which such screw is made should be 1/10" in
+diameter. The steel cap <i>C</i> is fitted like the finer forms of Swiss
+watches. The hairspring stud <i>E</i> is of steel, shaped as shown, and comes
+outlined with the other parts.</p>
+
+
+<h4>TO TEMPER AND POLISH STEEL.</h4>
+
+<div class="figleft"><img src="images/pict044.jpg" alt="Fig. 44" title="Fig. 44" /></div>
+<div class="figright"><img src="images/pict046.jpg" alt="Fig. 46" title="Fig. 46" /></div>
+<div class="figleft"><img src="images/pict045.jpg" alt="Fig. 45" title="Fig. 45" /></div>
+<p>The regulator bar should be hardened by being placed in a folded piece
+of sheet iron and heated red hot, and thrown into cold water. The
+regulator bar <i>A A'</i> is about 3" long; and for <a name="Page_50" id="Page_50"></a>holding it for
+hardening, cut a piece of thin sheet iron 2-1/2" by 3-1/4" and fold it
+through the middle lengthwise, as indicated by the dotted line <i>g</i>, Fig.
+44. The sheet iron when folded will appear as shown at Fig. 45. A piece
+of flat sheet metal of the same thickness as the regulator bar should be
+placed between the iron leaves <i>I I</i>, and the leaves beaten down with a
+hammer, that the iron may serve as a support for the regulator during
+heating and hardening. A paste made of castile soap and water applied to
+the regulator bar in the iron envelope will protect it from oxidizing
+much during the heating. The portions of the regulator bar marked <i>h</i>
+are intended to be rounded, while the parts marked <i>m</i> are intended to
+be dead flat. The rounding is carefully done, first with a file and
+finished with emery paper. The outer edge of the loop <i>A''</i> is a little
+rounded, also the inner edge next the cap <i>C</i>. This will be understood
+by inspecting Fig. 46, where we show a magnified vertical section of the
+regulator on line <i>l</i>, Fig. 40. The curvature should embrace that
+portion of <i>A''</i> between the radial lines <i>o o'</i>, and should, on the
+model, not measure more than 1/40". It will be seen that the curved
+surface of the regulator is sunk so it meets only the vertical edge of
+the loop <i>A''</i>. For the average workman, polishing the flat parts <i>m</i> is
+the most difficult to do, and for this reason we will give entire
+details. It is to be expected that the regulator bar will spring a
+little in hardening, but if only a little we need pay no attention to
+it.</p>
+
+<h4>HOW FLAT STEEL POLISHING IS DONE.</h4>
+<div class="figleft"><img src="images/pict047.jpg" alt="Fig. 47" title="Fig. 47" /></div>
+<div class="figright"><img src="images/pict048.jpg" alt="Fig. 48" title="Fig. 48" /></div>
+<p>Polishing a regulator bar for a large model, such as we are building, is
+only a heavy job of flat steel work, a little larger but no more
+difficult than to polish a regulator for a sixteen-size watch. We would
+ask permission here to say that really nice flat steel work is something
+which only a comparatively few workmen can do, and, still, the process
+is quite simple and the accessories few and inexpensive. First,
+ground-glass slab 6" by 6" by 1/4"; second, flat zinc piece 3-1/4" by
+3-1/4" by 1/4"; third, a piece of thick sheet brass 3" by 2" by 1/8";
+and a bottle of Vienna lime. The glass slab is only a piece of plate
+glass cut to the size given above. The zinc slab is pure zinc planed
+dead flat, and the glass ground to a dead surface with another piece of
+plate glass and some medium fine <a name="Page_51" id="Page_51"></a>emery and water, the whole surface
+being gone over with emery and water until completely depolished. The
+regulator bar, after careful filing and dressing up on the edges with an
+oilstone slip or a narrow emery buff, is finished as previously
+described. We would add to the details already given a few words on
+polishing the edges.</p>
+
+
+<div class="figleft"><img src="images/pict049.jpg" alt="Fig. 49" title="Fig. 49" /></div>
+<div class="figright"><img src="images/pict050.jpg" alt="Fig. 50" title="Fig. 50" /></div>
+<p>It is not necessary that the edges of steelwork, like the regulator bar
+<i>B</i>, Fig. 47, should be polished to a flat surface; indeed, they look
+better to be nicely rounded. Perhaps we can convey the idea better by
+referring to certain parts: say, spring to the regulator, shown at <i>D</i>,
+Fig. 40, and also the hairspring stud <i>E</i>. The edges of these parts look
+best beveled in a rounded manner.</p>
+
+<p>It is a little difficult to convey in words what is meant by "rounded"
+manner. To aid in understanding our meaning, we refer to Figs. 48 and
+49, which are transverse sections of <i>D</i>, Fig. 50, on the line <i>f</i>. The
+edges of <i>D</i>, in Fig. 48, are simply rounded. There are no rules for
+such rounding&mdash;only good judgment and an eye for what looks well. The
+edges of <i>D</i> as shown in Fig. 49 are more on the beveled order. In
+smoothing and polishing such edges, an ordinary jeweler's steel burnish
+can be used.</p>
+
+<h4>SMOOTHING AND POLISHING.</h4>
+
+<div class="figleft"><img src="images/pict051.jpg" alt="Fig. 51" title="Fig. 51" /></div>
+<p>The idea in smoothing and polishing such edges is to get a fair gloss
+without much attention to perfect form, inasmuch as it is the flat
+surface <i>d</i> on top which produces the impression of fine finish. If this
+is flat and brilliant, the rounded edges, like <i>g c</i> can really have
+quite an inferior polish and still look well. For producing the flat
+polish on the upper surface of the regulator bar <i>B</i> and spring <i>D</i>, the
+flat surface <i>d</i>, Figs. 48, 49, 51 and 52, we must attach the regulator
+bar to a plate of heavy brass, as shown at Fig. 47, where <i>A</i> represents
+the brass plate, and <i>B</i> the regulator bar, arranged for grinding and
+polishing flat.</p>
+
+<div class="figright"><img src="images/pict052.jpg" alt="Fig. 52" title="Fig. 52" /></div>
+
+<p>For attaching the regulator bar <i>B</i> to the brass plate <i>A</i>, a good plan
+is to cement it fast with lathe wax; but a better plan is to make the
+plate <i>A</i> of heavy sheet iron, something about<a name="Page_52" id="Page_52"></a> 1/8" thick, and secure
+the two together with three or four little catches of soft solder. It is
+to be understood the edges of the regulator bar or the regulator spring
+are polished, and all that remains to be done is to grind and polish the
+flat face.</p>
+
+<p>Two pieces <i>a a</i> of the same thickness as the regulator bar are placed
+as shown and attached to <i>A</i> to prevent rocking. After <i>B</i> is securely
+attached to <i>A</i>, the regulator should be coated with shellac dissolved
+in alcohol and well dried. The object of this shellac coating is to keep
+the angles formed at the meeting of the face and side clean in the
+process of grinding with oilstone dust and oil. The face of the
+regulator is now placed on the ground glass after smearing it with oil
+and oilstone dust. It requires but a very slight coating to do the work.</p>
+
+<p>The grinding is continued until the required surface is dead flat, after
+which the work is washed with soap and water and the shellac dissolved
+away with alcohol. The final polish is obtained on the zinc lap with
+Vienna lime and alcohol. Where lathe cement is used for securing the
+regulator to the plate <i>A</i>, the alcohol used with the Vienna lime
+dissolves the cement and smears the steel. Diamantine and oil are the
+best materials for polishing when the regulator bar is cemented to the
+plate <i>A</i>.</p>
+
+
+<h4>KNOWLEDGE THAT IS MOST ESSENTIAL.</h4>
+
+<p><i>The knowledge most important for a practical working watchmaker to
+possess is how to get the watches he has to repair in a shape to give
+satisfaction to his customers.</i> No one will dispute the truth of the
+above italicised statement. It is only when we seek to have limits set,
+and define what such knowledge should consist of, that disagreement
+occurs.</p>
+
+<p>One workman who has read Grossmann or Saunier, or both, would insist on
+all watches being made to a certain standard, and, according to their
+ideas, all such lever watches as we are now dealing with should have
+club-tooth escapements with equidistant lockings, ten degrees lever and
+pallet action, with one and one-half degrees lock and one and one-half
+degrees drop. Another workman would insist on circular pallets, his
+judgment being based chiefly on what he had read as stated by some
+author. Now the facts of the situation are that lever escapements vary
+as made by different manufacturers, one concern using circular pallets
+and another using pallets with equidistant lockings.</p>
+
+<h4><a name="Page_53" id="Page_53"></a>WHAT A WORKMAN SHOULD KNOW TO REPAIR A WATCH.</h4>
+
+<p>One escapement maker will divide the impulse equally between the tooth
+and pallet; another will give an excess to the tooth. Now while these
+matters demand our attention in the highest degree in a theoretical
+sense, still, for such "know hows" as count in a workshop, they are of
+but trivial importance in practice.</p>
+
+<p>We propose to deal in detail with the theoretical consideration of
+"thick" and "thin" pallets, and dwell exhaustively on circular pallets
+and those with equidistant locking faces; but before we do so we wish to
+impress on our readers the importance of being able to free themselves
+of the idea that all lever escapements should conform to the rigid rules
+of any dictum.</p>
+
+
+<h4>EDUCATE THE EYE TO JUDGE OF ANGULAR AS WELL AS LINEAR EXTENT.</h4>
+
+<p>For illustration: It would be easy to design a lever escapement that
+would have locking faces which were based on the idea of employing
+neither system, but a compromise between the two, and still give a good,
+sound action. All workmen should learn to estimate accurately the extent
+of angular motion, so as to be able to judge correctly of escapement
+actions. It is not only necessary to know that a club-tooth escapement
+should have one and one-half degrees drop, but the eye should be
+educated, so to speak, as to be able to judge of angular as well as
+linear extent.</p>
+
+<div class="figright"><img src="images/pict053.jpg" alt="Fig. 53" title="Fig. 53" /></div>
+
+<p>Most mechanics will estimate the size of any object measured in inches
+or parts of inches very closely; but as regards angular extent, except
+in a few instances, we will find mechanics but indifferent judges. To
+illustrate, let us refer to Fig. 53. Here we have the base line <i>A A'</i>
+and the perpendicular line <i>a B</i>. Now almost any person would be able to
+see if the angle <i>A a B</i> was equal to <i>B a A'</i>; but not five in one
+hundred practical mechanics would be able to estimate with even
+tolerable accuracy the measure the angles made to the base by the lines
+<i>b c d</i>; and still watchmakers are required in the daily practice of
+their craft to work to angular motions and movements almost as important
+as to results as diameters.</p>
+
+<p>What is the use of our knowing that in theory an escape-wheel tooth
+should have one and one-half degrees drop, when in reality it <a name="Page_54" id="Page_54"></a>has three
+degrees? It is only by educating the eye from carefully-made drawings;
+or, what is better, constructing a model on a large scale, that we can
+learn to judge of proper proportion and relation of parts, especially as
+we have no convenient tool for measuring the angular motion of the fork
+or escape wheel. Nor is it important that we should have, if the workman
+is thoroughly "booked up" in the principles involved.</p>
+
+<p>As we explained early in this treatise, there is no imperative necessity
+compelling us to have the pallets and fork move through ten degrees any
+more than nine and one-half degrees, except that experience has proven
+that ten degrees is about the right thing for good results. In this day,
+when such a large percentage of lever escapements have exposed pallets,
+we can very readily manipulate the pallets to match the fork and roller
+action. For that matter, in many instances, with a faulty lever
+escapement, the best way to go about putting it to rights is to first
+set the fork and roller so they act correctly, and then bring the
+pallets to conform to the angular motion of the fork so adjusted.</p>
+
+
+<h4>FORK AND ROLLER ACTION.</h4>
+
+<p>Although we could say a good deal more about pallets and pallet action,
+still we think it advisable to drop for the present this particular part
+of the lever escapement and take up fork and roller action, because, as
+we have stated, frequently the fork and roller are principally at fault.
+In considering the action and relation of the parts of the fork and
+roller, we will first define what is considered necessary to constitute
+a good, sound construction where the fork vibrates through ten degrees
+of angular motion and is supposed to be engaged with the roller by means
+of the jewel pin for thirty degrees of angular motion of the balance.</p>
+
+<p>There is no special reason why thirty degrees of roller action should be
+employed, except that experience in practical construction has come to
+admit this as about the right arc for watches of ordinary good, sound
+construction. Manufacturers have made departures from this standard, but
+in almost every instance have finally come back to pretty near these
+proportions. In deciding on the length of fork and size of roller, we
+first decide on the distance apart at which to place the center of the
+balance and the center of the pallet staff. These two points
+established, we have the length of the fork and diameter of the roller
+defined at once.</p>
+
+<h4><a name="Page_55" id="Page_55"></a>HOW TO FIND THE ROLLER DIAMETER FROM THE LENGTH OF THE FORK.</h4>
+
+<p>To illustrate, let us imagine the small circles <i>A B</i>, Fig. 54, to
+represent the center of a pallet staff and balance staff in the order
+named. We divide this space into four equal parts, as shown, and the
+third space will represent the point at which the pitch circles of the
+fork and roller will intersect, as shown by the arc <i>a</i> and circle <i>b</i>.
+Now if the length of the radii of these circles stand to each other as
+three to one, and the fork vibrates through an arc of ten degrees, the
+jewel pin engaging such fork must remain in contact with said fork for
+thirty degrees of angular motion of the balance.</p>
+
+<div class="figright"><img src="images/pict054.jpg" alt="Fig. 54" title="Fig. 54" /></div>
+
+<p>Or, in other words, the ratio of angular motion of two <i>mobiles</i> acting
+on each must be in the same ratio as the length of their radii at the
+point of contact. If we desire to give the jewel pin, or, in ordinary
+horological phraseology, have a greater arc of roller action, we would
+extend the length of fork (say) to the point <i>c</i>, which would be
+one-fifth of the space between <i>A</i> and <i>B</i>, and the ratio of fork to
+roller action would be four to one, and ten degrees of fork action would
+give forty degrees of angular motion to the roller&mdash;and such escapements
+have been constructed.</p>
+
+
+<h4>WHY THIRTY DEGREES OF ROLLER ACTION IS ABOUT RIGHT.</h4>
+
+<p>Now we have two sound reasons why we should not extend the arc of
+vibration of the balance: (<i>a</i>) If there is an advantage to be derived
+from a detached escapement, it would surely be policy to have the arc of
+contact, that is, for the jewel pin to engage the fork, as short an arc
+as is compatible with a sound action. (<i>b</i>) It will be evident to any
+thinking mechanic that the acting force of a fork which would carry the
+jewel pin against the force exerted by the balance spring through an arc
+of fifteen degrees, or half of an arc of thirty degrees, would fail to
+do so through an arc of twenty degrees, which is the condition imposed
+when we adopt forty degrees of roller action.</p>
+
+<p>For the present we will accept thirty degrees of roller action as the
+standard. Before we proceed to delineate our fork and roller we will
+devote a brief consideration to the size and shape of a jewel pin to
+perform well. In this matter there has been a broad field <a name="Page_56" id="Page_56"></a>gone over,
+both theoretically and in practical construction. Wide jewel pins, round
+jewel pins, oval jewel pins have been employed, but practical
+construction has now pretty well settled on a round jewel pin with about
+two-fifths cut away. And as regards size, if we adopt the linear extent
+of four degrees of fork or twelve degrees of roller action, we will find
+it about right.</p>
+
+
+<h4>HOW TO SET A FORK AND ROLLER ACTION RIGHT.</h4>
+
+<p>As previously stated, frequently the true place to begin to set a lever
+escapement right is with the roller and fork. But to do this properly we
+should know when such fork and roller action is right and safe in all
+respects. We will see on analysis of the actions involved that there are
+three important actions in the fork and roller functions: (<i>a</i>) The fork
+imparting perfect impulse through the jewel pin to the balance. (<i>b</i>)
+Proper unlocking action. (<i>c</i>) Safety action. The last function is in
+most instances sadly neglected and, we regret to add, by a large
+majority of even practical workmen it is very imperfectly understood. In
+most American watches we have ample opportunity afforded to inspect the
+pallet action, but the fork and roller action is placed so that rigid
+inspection is next to impossible.</p>
+
+<p>The Vacheron concern of Swiss manufacturers were acute enough to see the
+importance of such inspection, and proceeded to cut a circular opening
+in the lower plate, which permitted, on the removal of the dial, a
+careful scrutiny of the action of the roller and fork. While writing on
+this topic we would suggest the importance not only of knowing how to
+draw a correct fork and roller action, but letting the workman who
+desires to be <i>au fait</i> in escapements delineate and study the action of
+a faulty fork and roller action&mdash;say one in which the fork, although of
+the proper form, is too short, or what at first glance would appear to
+amount to the same thing, a roller too small.</p>
+
+<p>Drawings help wonderfully in reasoning out not only correct actions, but
+also faulty ones, and our readers are earnestly advised to make such
+faulty drawings in several stages of action. By this course they will
+educate the eye to discriminate not only as to correct actions, but also
+to detect those which are imperfect, and we believe most watchmakers
+will admit that in many instances it takes much longer to locate a fault
+than to remedy it after it has been found.</p>
+
+<p><a name="Page_57" id="Page_57"></a></p>
+<div class="figcenter"><a href="images/pict055.jpg"><img src="images/pict055-tb.jpg" alt="Fig. 55" title="Fig. 55" /></a></div>
+<p>Let us now proceed to delineate a fork and roller. It is not imperative
+that we should draw the parts to any scale, but it is a rule among
+English makers to let the distance between the center of the pallet
+staff and the center of the balance staff equal in length the chord of
+ninety-six degrees of the pitch circle of the escape wheel, which, in
+case we employ a pitch circle of 5" radius, would make the distance
+between <i>A</i> and <i>B</i>, Fig. 55, approximately 7-1/2", which is a very fair
+scale for study drawings.</p>
+
+
+<h4>HOW TO DELINEATE A FORK AND ROLLER.</h4>
+
+<p>To arrive at the proper proportions of the several parts, we divide the
+space <i>A B</i> into four equal parts, as previously directed, and draw the
+circle <i>a</i> and short arc <i>b</i>. With our dividers set at 5", from <i>B</i> as a
+center we sweep the short arc <i>c</i>. From our arc of sixty degrees, with a
+5" radius, we take five degrees, and from the intersection of the right
+line <i>A B</i> with the arc <i>c</i> we lay off on each side five degrees and
+establish the points <i>d e</i>; and from <i>B</i> as a center, through these
+points draw the lines <i>B d'</i> and <i>B e'</i>. Now the arc embraced between
+these lines represents the angular extent of our fork action.</p>
+
+<p>From <i>A</i> as a center and with our dividers set at 5", we sweep the arc
+<i>f</i>. From the scale of degrees we just used we lay off fifteen degrees
+on each side of the line <i>A B</i> on the arc <i>f</i>, and establish the points
+<i>g h</i>. From <i>A</i> as a center, through the points just established we draw
+the radial lines <i>A g'</i> and <i>A h'</i>. The angular extent between these
+lines defines the limit of our roller action.</p>
+
+<p>Now if we lay off on the arc <i>f</i> six degrees each side of its
+intersection with the line <i>A B</i>, we define the extent of the jewel pin;
+that is, on the arc <i>f</i> we establish the points <i>l m</i> at six degrees
+<a name="Page_58" id="Page_58"></a>from the line <i>A B</i>, and through the points <i>l m</i> draw, from <i>A</i> as a
+center, the radial lines <i>A l'</i> and <i>A m'</i>. The extent of the space
+between the lines <i>A l'</i> and <i>A m'</i> on the circle <i>a</i> defines the size
+of our jewel pin.</p>
+
+
+<h4>TO DETERMINE THE SIZE OF A JEWEL PIN.</h4>
+
+<div class="figleft"><img src="images/pict056.jpg" alt="Fig. 56" title="Fig. 56" /></div>
+
+<p>To make the situation better understood, we make an enlarged drawing of
+the lines defining the jewel pin at Fig. 56. At the intersection of the
+line <i>A B</i> with the arc <i>a</i> we locate the point <i>k</i>, and from it as a
+center we sweep the circle <i>i</i> so it passes through the intersection of
+the lines <i>A l'</i> and <i>A m'</i> with the arc <i>a</i>. We divide the radius of
+the circle <i>i</i> on the line <i>A B</i> into five equal parts, as shown by the
+vertical lines <i>j</i>. Of these five spaces we assume three as the extent
+of the jewel pin, cutting away that portion to the right of the heavy
+vertical line at <i>k</i>.</p>
+
+<p>We will now proceed to delineate a fork and roller as the parts are
+related on first contact of jewel pin with fork and initial with the
+commencing of the act of unlocking a pallet. The position and relations
+are also the same as at the close of the act of impulse. We commence the
+drawing at Fig. 57, as before, by drawing the line <i>A B</i> and the arcs
+<i>a</i> and <i>b</i> to represent the pitch circles. We also sweep the arc <i>f</i> to
+enable us to delineate the line <i>A g'</i>. Next in order we draw our jewel
+pin as shown at <i>D</i>. In drawing the jewel pin we proceed as at Fig. 56,
+except we let the line <i>A g'</i>, Fig. 57, assume the same relations to the
+jewel pin as <i>A B</i> in Fig. 56; that is, we delineate the jewel pin as if
+extending on the arc <i>a</i> six degrees on each side of the line <i>A g'</i>,
+Fig. 57.</p>
+
+<div class="figcenter"><a href="images/pict057.jpg"><img src="images/pict057-tb.jpg" alt="Fig. 57" title="Fig. 57" /></a></div>
+
+
+<h4><a name="Page_59" id="Page_59"></a>THE THEORY OF THE FORK ACTION.</h4>
+
+<p>To aid us in reasoning, we establish the point <i>m</i>, as in Fig. 55, at
+<i>m</i>, Fig. 57, and proceed to delineate another and imaginary jewel pin
+at <i>D'</i> (as we show in dotted outline). A brief reasoning will show that
+in allowing thirty degrees of contact of the fork with the jewel pin,
+the center of the jewel pin will pass through an arc of thirty degrees,
+as shown on the arcs <i>a</i> and <i>f</i>. Now here is an excellent opportunity
+to impress on our minds the true value of angular motion, inasmuch as
+thirty degrees on the arc <i>f</i> is of more than twice the linear extent as
+on the arc <i>a</i>.</p>
+
+
+
+<p>Before we commence to draw the horn of the fork engaging the jewel pin
+<i>D</i>, shown at full line in Fig. 57, we will come to perfectly understand
+what mechanical relations are required. As previously stated, we assume
+the jewel pin, as shown at <i>D</i>, Fig. 57, is in the act of encountering
+the inner face of the horn of the fork for the end or purpose of
+unlocking the engaged pallet. Now if the inner face of the horn of the
+fork was on a radial line, such radial line would be <i>p B</i>, Fig. 57. We
+repeat this line at <i>p</i>, Fig. 56, where the parts are drawn on a larger
+scale.</p>
+
+<p>To delineate a fork at the instant the last effort of impulse has been
+imparted to the jewel pin, and said jewel pin is in the act of
+separating from the inner face of the prong of the fork&mdash;we would also
+call attention to the fact that relations of parts are precisely the
+same as if the jewel pin had just returned from an excursion of
+vibration and was in the act of encountering the inner face of the prong
+of the fork in the act of unlocking the escapement.</p>
+
+<p>We mentioned this matter previously, but venture on the repetition to
+make everything clear and easily understood. We commence by drawing the
+line <i>A B</i> and dividing it in four equal parts, as on previous
+occasions, and from <i>A</i> and <i>B</i> as centers draw the pitch circles <i>c d</i>.
+By methods previously described, we draw the lines <i>A a</i> and <i>A a'</i>,
+also <i>B b</i> and <i>B b'</i> to represent the angular motion of the two
+mobiles, viz., fork and roller action. As already shown, the roller
+occupies twelve degrees of angular extent. To get at this conveniently,
+we lay off on the arc by which we located the lines <i>A a</i> and <i>A a'</i> six
+degrees above the line <i>A a</i> and draw the line <i>A h</i>.</p>
+
+<p>Now the angular extent on the arc <i>c</i> between the lines <i>A a</i> and <i>A h</i>
+represents the radius of the circle defining the jewel pin. From the
+intersection of the line <i>A a</i> with the arc <i>c</i> as a center, and with
+<a name="Page_60" id="Page_60"></a>the radius just named, we sweep the small circle <i>D</i>, Fig. 58, which
+represents our jewel pin; we afterward cut away two-fifths and draw the
+full line <i>D</i>, as shown. We show at Fig. 59 a portion of Fig. 58,
+enlarged four times, to show certain portions of our delineations more
+distinctly. If we give the subject a moment's consideration we will see
+that the length of the prong <i>E</i> of the lever fork is limited to such a
+length as will allow the jewel pin <i>D</i> to pass it.</p>
+
+
+<h4>HOW TO DELINEATE THE PRONGS OF A LEVER FORK.</h4>
+
+<div class="figcenter"><a href="images/pict058-59.jpg"><img src="images/pict058-59-tb.jpg" alt="Fig. 58-59" title="Fig. 58-59" /></a></div>
+
+<p>To delineate this length, from <i>B</i> as a center we sweep the short arc
+<i>f</i> so it passes through the outer angle <i>n</i>, Fig. 59, of the jewel pin.
+This arc, carried across the jewel pin <i>D</i>, limits the length of the
+opposite prong of the fork. The outer face of the prong of the fork can
+be drawn as a line tangent to a circle drawn from <i>A</i> as a center
+through the angle <i>n</i> of the jewel pin. Such a circle or arc is shown at
+<i>o</i>, Figs. 58 and 59. There has been a good deal said as to whether the
+outer edge of the prong of a fork should be straight or curved.</p>
+
+<p>To the writer's mind, a straight-faced prong, like from <i>s</i> to <i>m</i>, is
+what is required for a fork with a single roller, while a fork with a
+curved prong will be best adapted for a double roller. This subject will
+be taken up again when we consider double-roller action. The extent or
+length of the outer face of the prong is also an open subject, but as
+there is but one factor of the problem of lever escapement construction
+depending on it, when we name this and see this requirement satisfied we
+have made an end of this question. The function performed by the outer
+face of the prong of a fork <a name="Page_61" id="Page_61"></a>is to prevent the engaged pallet from
+unlocking while the guard pin is opposite to the passing hollow.</p>
+
+<p>The inner angle <i>s</i> of the horn of the fork must be so shaped and
+located that the jewel pin will just clear it as it passes out of the
+fork, or when it passes into the fork in the act of unlocking the
+escapement. In escapements with solid bankings a trifle is allowed, that
+is, the fork is made enough shorter than the absolute theoretical length
+to allow for safety in this respect.</p>
+
+
+<h4>THE PROPER LENGTH OF A LEVER.</h4>
+
+<p>We will now see how long a lever must be to perform its functions
+perfectly. Now let us determine at what point on the inner face of the
+prong <i>E'</i> the jewel pin parts from the fork, or engages on its return.
+To do this we draw a line from the center <i>r</i> (Fig. 59) of the jewel
+pin, so as to meet the line <i>e</i> at right angles, and the point <i>t</i> so
+established on the line <i>e</i> is where contact will take place between the
+jewel pin and fork.</p>
+
+<p>It will be seen this point (<i>t</i>) of contact is some distance back of the
+angle <i>u</i> which terminates the inner face of the prong <i>E'</i>;
+consequently, it will be seen the prongs <i>E E'</i> of the fork can with
+safety be shortened enough to afford a safe ingress or egress to the
+jewel pin to the slot in the fork. As regards the length of the outer
+face of the prong of the fork, a good rule is to make it one and a half
+times the diameter of the jewel pin. The depth of the slot need be no
+more than to free the jewel in its passage across the ten degrees of
+fork action. A convenient rule as to the depth of the slot in a fork is
+to draw the line <i>k</i>, which, it will be seen, coincides with the circle
+which defines the jewel pin.</p>
+
+
+<h4>HOW TO DELINEATE THE SAFETY ACTION.</h4>
+
+<div class="figright"><img src="images/pict060.jpg" alt="Fig. 60" title="Fig. 60" /></div>
+
+<p>We will next consider a safety action of the single roller type. The
+active or necessary parts of such safety action consist of a roller or
+disk of metal, usually steel, shaped as shown in plan at <i>A</i>, Fig. 60.
+In the edge of this disk is cut in front of the jewel pin a circular
+recess shown at <i>a</i> called the passing hollow. The remaining part of the
+safety action is the guard pin shown at <i>N</i> Figs. 61 and 62, which is
+placed in the lever. Now it is to be understood that the sole function
+performed by the guard pin is to strike the edge of the <a name="Page_62" id="Page_62"></a>roller <i>A</i> at
+any time when the fork starts to unlock the engaged pallet, except when
+the jewel pin is in the slot of the fork. To avoid extreme care in
+fitting up the passing hollow, the horns of the fork are arranged to
+strike the jewel pin and prevent unlocking in case the passing hollow is
+made too wide. To delineate the safety action we first draw the fork and
+jewel pin as previously directed and as shown at Fig. 63. The position
+of the guard pin should be as close to the bottom of the slot of the
+fork as possible and be safe. As to the size of the guard pin, it is
+usual to make it about one-third or half the diameter of the jewel pin.
+The size and position of the guard pin decided on and the small circle
+<i>N</i> drawn, to define the size and position of the roller we set our
+dividers so that a circle drawn from the center <i>A</i> will just touch the
+edge of the small circle <i>N</i>, and thus define the outer boundary of our
+roller, or roller table, as it is frequently called.</p>
+
+<div class="figleft"><img src="images/pict061.jpg" alt="Fig. 61" title="Fig. 61" /></div>
+
+<div class="figright"><img src="images/pict062.jpg" alt="Fig. 62" title="Fig. 62" /></div>
+
+<p>For deciding the angular extent of the passing hollow we have no fixed
+rule, but if we make it to occupy about half more angular extent on the
+circle <i>y</i> than will coincide with the angular extent of the jewel pin,
+it will be perfectly safe and effectual. We previously stated that the
+jewel pin should occupy about twelve degrees of angular extent on the
+circle <i>c</i>, and if we make the passing hollow occupy eighteen degrees
+(which is one and a half the angular extent of the jewel pin) it will do
+nicely. But if we should extend the width of the passing hollow to
+twenty-four degrees it would do no harm, as the jewel pin would be well
+inside the horn of the fork before the guard pin could enter the passing
+hollow.</p>
+
+<div class="figcenter"><a href="images/pict063.jpg"><img src="images/pict063-tb.jpg" alt="Fig. 63" title="Fig. 63" /></a></div>
+
+<p>We show in Fig. 61 the fork as separated from the roller, but in Fig.
+62, which is a side view, we show the fork and jewel pin as <a name="Page_63" id="Page_63"></a>engaged.
+When drawing a fork and roller action it is safe to show the guard pin
+as if in actual contact with the roller. Then in actual construction, if
+the parts are made to measure and agree with the drawing in the gray,
+that is, before polishing, the process of polishing will reduce the
+convex edge of the roller enough to free it.</p>
+
+<p>It is evident if thought is given to the matter, that if the guard pin
+is entirely free and does not touch the roller in any position, a
+condition and relation of parts exist which is all we can desire. We are
+aware that it is usual to give a considerable latitude in this respect
+even by makers, and allow a good bit of side shake to the lever, but our
+judgment would condemn the practice, especially in high-grade watches.</p>
+
+
+<h4>RESTRICT THE FRICTIONAL SURFACES.</h4>
+
+<p>Grossmann, in his essay on the detached lever escapement, adopts one and
+a half degrees lock. Now, we think that one degree is ample; and we are
+sure that every workman experienced in the construction of the finer
+watches will agree with us in the assertion that we should in all
+instances seek to reduce the extent of all frictional surfaces, no
+matter how well jeweled. Acting under such advice, if we can reduce the
+surface friction on the lock from one and a half degrees to one degree
+or, better, to three-fourths of a degree, it is surely wise policy to do
+so. And as regards the extent of angular motion of the lever, if we
+reduce this to six degrees, exclusive of the lock, we would undoubtedly
+obtain better results in timing.</p>
+
+<p>We shall next consider the effects of opening the bankings too wide, and
+follow with various conditions which are sure to come in the experience
+of the practical watch repairer. It is to be supposed in this problem
+that the fork and roller action is all right. The reader may say to
+this, why not close the banking? In reply we would offer the supposition
+that some workman had bent the guard pin forward or set a pallet stone
+too far out.</p>
+
+<p>We have now instructed our readers how to draw and construct a lever
+escapement complete, of the correct proportions, and will next take up
+defective construction and consider faults existing to a lesser or
+greater degree in almost every watch. Faults may also be those arising
+from repairs by some workman not fully posted in the correct form and
+relation of the several parts which go to make up a lever escapement. It
+makes no difference to the artisan <a name="Page_64" id="Page_64"></a>called upon to put a watch in
+perfect order as to whom he is to attribute the imperfection, maker or
+former repairer; all the workman having the job in hand has to do is to
+know positively that such a fault actually exists, and that it devolves
+upon him to correct it properly.</p>
+
+
+<h4>BE FEARLESS IN REPAIRS, IF SURE YOU ARE RIGHT.</h4>
+
+<p>Hence the importance of the workman being perfectly posted on such
+matters and, knowing that he is right, can go ahead and make the watch
+as it should be. The writer had an experience of this kind years ago in
+Chicago. A Jules Jurgensen watch had been in the hands of several good
+workmen in that city, but it would stop. It was then brought to him with
+a statement of facts given above. He knew there must be a fault
+somewhere and searched for it, and found it in the exit pallet&mdash;a
+certain tooth of the escape wheel under the right conditions would
+sometimes not escape. It might go through a great many thousand times
+and yet it might, and did sometimes, hold enough to stop the watch.</p>
+
+<p>Now probably most of my fellow-workmen in this instance would have been
+afraid to alter a "Jurgensen," or even hint to the owner that such a
+thing could exist as a fault in construction in a watch of this
+justly-celebrated maker. The writer removed the stone, ground a little
+from the base of the offending pallet stone, replaced it, and all
+trouble ended&mdash;no stops from that on.</p>
+
+
+<h4>STUDY OF AN ESCAPEMENT ERROR.</h4>
+
+<div class="figleft"><img src="images/pict064.jpg" alt="Fig. 64" title="Fig. 64" /></div>
+
+<p>Now let us suppose a case, and imagine a full-plate American movement in
+which the ingress or entrance pallet extends out too far, and in order
+to have it escape, the banking on that side is opened too wide. We show
+at Fig. 64 a drawing of the parts in their proper relations under the
+conditions named. It will be seen by careful inspection that the jewel
+pin <i>D</i> will not enter the fork, which is absolutely necessary. This
+condition very frequently exists in watches where a new pallet stone has
+been put in by an inexperienced workman. Now this is one of the
+instances in which workmen complain of hearing a "scraping" sound when
+the watch is placed to the ear. The remedy, of course, lies in warming
+up the pallet arms and <a name="Page_65" id="Page_65"></a>pushing the stone in a trifle, "But how much?"
+say some of our readers. There is no definite rule, but we will tell
+such querists how they can test the matter.</p>
+
+<p>Remove the hairspring, and after putting the train in place and securing
+the plates together, give the winding arbor a turn or two to put power
+on the train; close the bankings well in so the watch cannot escape on
+either pallet. Put the balance in place and screw down the cock.
+Carefully turn back the banking on one side so the jewel pin will just
+pass out of the slot in the fork. Repeat this process with the opposite
+banking; the jewel pin will now pass out on each side. Be sure the guard
+pin does not interfere with the fork action in any way. The fork is now
+in position to conform to the conditions required.</p>
+
+
+<h4>HOW TO ADJUST THE PALLETS TO MATCH THE FORK.</h4>
+
+<p>If the escapement is all right, the teeth will have one and a half
+degrees lock and escape correctly; but in the instance we are
+considering, the stone will not permit the teeth to pass, and must be
+pushed in until they will. It is not a very difficult matter after we
+have placed the parts together so we can see exactly how much the pallet
+protrudes beyond what is necessary, to judge how far to push it back
+when we have it out and heated. There is still an "if" in the problem we
+are considering, which lies in the fact that the fork we are
+experimenting with may be too short for the jewel pin to engage it for
+ten degrees of angular motion.</p>
+
+<p>This condition a man of large experience will be able to judge of very
+closely, but the better plan for the workman is to make for himself a
+test gage for the angular movement of the fork. Of course it will be
+understood that with a fork which engages the roller for eight degrees
+of fork action, such fork will not give good results with pallets ground
+for ten degrees of pallet action; still, in many instances, a compromise
+can be effected which will give results that will satisfy the owner of a
+watch of moderate cost, and from a financial point of view it stands the
+repairer in hand to do no more work than is absolutely necessary to keep
+him well pleased.</p>
+
+<p>We have just made mention of a device for testing the angular motion of
+the lever. Before we take up this matter, however, we will devote a
+little time and attention to the subject of jewel pins and how to set
+them. We have heretofore only considered jewel pins of one form, that
+is, a round jewel pin with two-fifths cut away.<a name="Page_66" id="Page_66"></a> We assumed this form
+from the fact that experience has demonstrated that it is the most
+practicable and efficient form so far devised or applied. Subsequently
+we shall take up the subject of jewel pins of different shapes.</p>
+
+
+<h4>HOW TO SET A JEWEL PIN AS IT SHOULD BE.</h4>
+
+<p>Many workmen have a mortal terror of setting a jewel pin and seem to
+fancy that they must have a specially-devised instrument for
+accomplishing this end. Most American watches have the hole for the
+jewel pin "a world too wide" for it, and we have heard repeated
+complaints from this cause. Probably the original object of this
+accommodating sort of hole was to favor or obviate faults of pallet
+action. Let us suppose, for illustration, that we have a roller with the
+usual style of hole for a jewel pin which will take almost anything from
+the size of a No. 12 sewing needle up to a round French clock pallet.</p>
+
+<div class="figleft"><img src="images/pict065.jpg" alt="Fig. 65" title="Fig. 65" /></div>
+
+<p>We are restricted as regards the proper size of jewel pin by the width
+of the slot in the fork. Selecting a jewel which just fits the fork, we
+can set it as regards its relation to the staff so it will cause the
+pitch circle of the jewel pin to coincide with either of dotted circles
+<i>a</i> or <i>a'</i>, Fig. 65. This will perhaps be better understood by
+referring to Fig. 66, which is a view of Fig. 65 seen in the direction
+of the arrow <i>c</i>. Here we see the roller jewel at <i>D</i>, and if we bring
+it forward as far as the hole in the roller will permit, it will occupy
+the position indicated at the dotted lines; and if we set it in (toward
+the staff) as far as the hole will allow, it will occupy the position
+indicated by the full outline.</p>
+
+<div class="figright"><img src="images/pict066.jpg" alt="Fig. 66" title="Fig. 66" /></div>
+
+<p>Now such other condition might very easily exist, that bringing the
+jewel pin forward to the position indicated by the dotted lines at <i>D</i>,
+Fig. 66, would remedy the defect described and illustrated at Fig. 64
+without any other change being necessary. We do not assert, understand,
+that a hole too large for the jewel pin is either necessary or
+desirable&mdash;what we wish to convey to the reader is the necessary
+knowledge so that he can profit by such a state if necessary. A hole
+which just fits the jewel pin so the merest film of cement will hold it
+in place is the way it should be; but we think it will be some time
+before such rollers are made, inasmuch as economy appears to be a chief
+consideration.</p>
+
+<h4><a name="Page_67" id="Page_67"></a>ABOUT JEWEL-PIN SETTERS.</h4>
+
+<div class="figright"><img src="images/pict067.jpg" alt="Fig. 67" title="Fig. 67" /></div>
+<div class="figleft"><img src="images/pict068.jpg" alt="Fig. 68" title="Fig. 68" /></div>
+<p>To make a jewel-pin setter which will set a jewel pin straight is easy
+enough, but to devise any such instrument which will set a jewel so as
+to perfectly accord with the fork action is probably not practicable.
+What the workman needs is to know from examination when the jewel pin is
+in the proper position to perform its functions correctly, and he can
+only arrive at this knowledge by careful study and thought on the
+matter. If we make up our minds on examining a watch that a jewel pin is
+"set too wide," that is, so it carries the fork over too far and
+increases the lock to an undue degree, take out the balance, remove the
+hairspring, warm the roller with a small alcohol lamp, and then with the
+tweezers move the jewel pin in toward the staff.</p>
+
+<div class="figleft"><img src="images/pict069.jpg" alt="Fig. 69" title="Fig. 69" /></div>
+
+<div class="figright"><img src="images/pict070.jpg" alt="Fig. 70" title="Fig. 70" /></div>
+<p>No attempt should be made to move a jewel pin unless the cement which
+holds the jewel is soft, so that when the parts cool off the jewel is as
+rigid as ever. A very little practice will enable any workman who has
+the necessary delicacy of touch requisite to ever become a good
+watchmaker, to manipulate a jewel pin to his entire satisfaction with no
+other setter than a pair of tweezers and his eye, with a proper
+knowledge of what he wants to accomplish. To properly heat a roller for
+truing up the jewel pin, leave it on the staff, and after removing the
+hairspring hold the balance by the rim in a pair of tweezers, "flashing
+it" back and forth through the flame of a rather small alcohol lamp
+until the rim of the balance is so hot it can just be held between the
+thumb and finger, and while at this temperature the jewel pin can be
+pressed forward or backward, as illustrated in Fig. 66, and then a touch
+or two will set the pin straight or parallel with the staff. Figs. 68
+and 69 are self-explanatory. For cementing in a jewel pin a very
+convenient tool is shown at Figs. 67 and 70. It is made of a piece of
+copper wire about 1/16" in diameter, bent to the form shown at Fig. 67.
+The ends <i>b b</i> of the copper wire are flattened a little and recessed on
+their inner faces, as shown in Fig. 70, to grasp the edges of the roller
+<i>A</i>. The heat of an alcohol lamp is applied to the loop of the wire at
+<i>g</i> until the small bit of shellac placed in the hole <i>h</i> melts. The
+necessary small pieces of shellac are made by <a name="Page_68" id="Page_68"></a>warming a bit of the gum
+to near the melting point and then drawing the softened gum into a
+filament the size of horse hair. A bit of this broken off and placed in
+the hole <i>h</i> supplies the cement necessary to fasten the jewel pin.
+Figs. 68 and 69 will, no doubt, assist in a clear understanding of the
+matter.</p>
+
+
+<h4>HOW TO MAKE AN ANGLE-MEASURING DEVICE.</h4>
+
+<p>We will now resume the consideration of the device for measuring the
+extent of the angular motion of the fork and pallets. Now, before we
+take this matter up in detail we wish to say, or rather repeat what we
+have said before, which is to the effect that ten degrees of fork and
+lever action is not imperative, as we can get just as sound an action
+and precisely as good results with nine and a half or even nine degrees
+as with ten, if other acting parts are in unison with such an arc of
+angular motion. The chief use of such an angle-measuring device is to
+aid in comparing the relative action of the several parts with a known
+standard.</p>
+
+<div class="figcenter"><img src="images/pict071.jpg" alt="Fig. 71" title="Fig. 71" /></div>
+
+<p>For use with full-plate movements about the best plan is a spring clip
+or clasp to embrace the pallet staff below the pallets. We show at Fig.
+71 such a device. To make it, take a rather large size of sewing
+needle&mdash;the kind known as a milliner's needle is about the best. The
+diameter of the needle should be about No. 2, so that at <i>b</i> we can
+drill and put in a small screw. It is important that the whole affair
+should be very light. The length of the needle should be about 1-5/8",
+in order that from the notch <i>a</i> to the end of the needle <i>A'</i> should be
+1-1/2". The needle should be annealed and flattened a little, to give a
+pretty good grasp to the notch <i>a</i> on the pallet staff.</p>
+
+<p>Good judgment is important in making this clamp, as it is nearly
+impossible to give exact measurements. About 1/40" in width when seen in
+the direction of the arrow <i>j</i> will be found to be about the right
+width. The spring <i>B</i> can be made of a bit of mainspring, annealed and
+filed down to agree in width with the part <i>A</i>. In connection with the
+device shown at Fig. 71 we need a movement-holder to hold the movement
+as nearly a constant height as possible <a name="Page_69" id="Page_69"></a>above the bench. The idea is,
+when the clamp <i>A B</i> is slipped on the pallet staff the index hand <i>A'</i>
+will extend outward, as shown in Fig. 72, where the circle <i>C</i> is
+supposed to represent the top plate of a watch, and <i>A'</i> the index hand.</p>
+
+
+<h4>HOW THE ANGULAR MOTION IS MEASURED.</h4>
+
+<div class="figright"><img src="images/pict072.jpg" alt="Fig. 72" title="Fig. 72" /></div>
+
+<p>Fig. 72 is supposed to be seen from above. It is evident that if we
+remove the balance from the movement shown at <i>C</i>, leaving power on the
+train, and with an oiling tool or hair broach move the lever back and
+forth, the index hand <i>A'</i> will show in a magnified manner the angular
+motion of the lever. Now if we provide an index arc, as shown at <i>D</i>, we
+can measure the extent of such motion from bank to bank.</p>
+
+<div class="figleft"><img src="images/pict073.jpg" alt="Fig. 73" title="Fig. 73" /></div>
+<div class="figright"><img src="images/pict074.jpg" alt="Fig. 74" title="Fig. 74" /></div>
+<p>To get up such an index arc we first make a stand as shown at <i>E F</i>,
+Fig. 73. The arc <i>D</i> is made to 1-1/2" radius, to agree with the index
+hand <i>A'</i>, and is divided into twelve degree spaces, six each side of a
+zero, as shown at Fig. 74, which is an enlarged view of the index <i>D</i> in
+Fig. 72. The index arc is attached to a short bit of wire extending down
+into the support <i>E</i>, and made adjustable as to height by the set-screw
+<i>l</i>. Let us suppose the index arc is adjusted to the index hand <i>A'</i>,
+and we move the fork as suggested; you see the hand would show exactly
+the arc passed through from bank to bank, and by moving the stand <i>E F</i>
+we can arrange so the zero mark on the scale stands in the center of
+such arc. This, of course, gives the angular motion from bank to bank.
+As an experiment, let us close the bankings so they arrest the fork at
+the instant the tooth drops from each pallet. If this arc is ten
+degrees, the pallet action is as it should be with the majority of
+modern watches.</p>
+
+
+<h4>TESTING LOCK AND DROP WITH OUR NEW DEVICE.</h4>
+
+<p>Let us try another experiment: We carefully move the fork away from the
+bank, and if after the index hand has passed through one and a half
+degrees the fork flies over, we know the lock is right. We repeat the
+experiment from the opposite bank, and in the same manner determine if
+the lock is right on the other pallets.<a name="Page_70" id="Page_70"></a> You see we have now the means
+of measuring not only the angular motion of the lever, but the angular
+extent of the lock. At first glance one would say that if now we bring
+the roller and fork action to coincide and act in unison with the pallet
+action, we would be all right; and so we would, but frequently this
+bringing of the roller and fork to agree is not so easily accomplished.</p>
+
+<p>It is chiefly toward this end the Waltham fork is made adjustable, so it
+can be moved to or from the roller, and also that we can allow the
+pallet arms to be moved, as we will try and explain. As we set the
+bankings the pallets are all right; but to test matters, let us remove
+the hairspring and put the balance in place. Now, if the jewel pin
+passes in and out of the fork, it is to be supposed the fork and roller
+action is all right. To test the fork and roller action we close the
+banking a little on one side. If the fork and jewel pin are related to
+each other as they should be, the jewel pin will not pass out of the
+fork, nor will the engaged tooth drop from that pallet. This condition
+should obtain on both pallets, that is, if the jewel pin will not pass
+out of the fork on a given bank the tooth engaged on its pallet should
+not drop.</p>
+
+<p>We have now come to the most intricate and important problems which
+relate to the lever escapement. However, we promise our readers that if
+they will take the pains to follow closely our elucidations, to make
+these puzzles plain. But we warn them that they are no easy problems to
+solve, but require good, hard thinking. The readiest way to master this
+matter is by means of such a model escapement as we have described. With
+such a model, and the pallets made to clamp with small set-screws, and
+roller constructed so the jewel pin could be set to or from the staff,
+this matter can be reduced to object lessons. But study of the due
+relation of the parts in good drawings will also master the situation.</p>
+
+
+<h4>A FEW EXPERIMENTS WITH OUR ANGLE-MEASURING DEVICE.</h4>
+
+<p>In using the little instrument for determining angular motion that we
+have just described, care must be taken that the spring clamp which
+embraces the pallet staff does not slip. In order to thoroughly
+understand the methods of using this angle-measuring device, let us take
+a further lesson or two.</p>
+
+<p>We considered measuring the amount of lock on each pallet, and advised
+the removal of the balance, because if we left the balance in we could
+not readily tell exactly when the tooth passed <a name="Page_71" id="Page_71"></a>on to the impulse plane;
+but if we touch the fork lightly with an oiling tool or a hair broach,
+moving it (the fork) carefully away from the bank and watching the arc
+indicated by the hand <i>A</i>, Fig. 72, we can determine with great
+exactness the angular extent of lock. The diagram at Fig. 75 illustrates
+how this experiment is conducted. We apply the hair broach to the end of
+the fork <i>M</i>, as shown at <i>L</i>, and gently move the fork in the direction
+of the arrow <i>i</i>, watching the hand <i>A</i> and note the number of degrees,
+or parts of degrees, indicated by the hand as passed over before the
+tooth is unlocked and passes on to the impulse plane and the fork flies
+forward to the opposite bank. Now, the quick movement of the pallet and
+fork may make the hand mark more or less of an arc on the index than one
+of ten degrees, as the grasp may slip on the pallet staff; but the arc
+indicated by the slow movement in unlocking will be correct.</p>
+
+<div class="figright"><img src="images/pict075.jpg" alt="Fig. 75" title="Fig. 75" /></div>
+
+<p>By taking a piece of sharpened pegwood and placing the point in the slot
+of the fork, we can test the fork to see if the drop takes place much
+before the lever rests against the opposite bank. As we have previously
+stated, the drop from the pallet should not take place until the lever
+<i>almost</i> rests on the banking pin. What the reader should impress on his
+mind is that the lever should pass through about one and a half degrees
+arc to unlock, and the remainder (eight and a half degrees) of the ten
+degrees are to be devoted to impulse. But, understand, if the impulse
+angle is only seven and a half degrees, and the jewel pin acts in
+accordance with the rules previously given, do not alter the pallet
+until you know for certain you will gain by it. An observant workman
+will, after a little practice, be able to determine this matter.</p>
+
+<p>We will next take up the double roller and fork action, and also
+consider in many ways the effect of less angles of action than ten
+degrees. This matter now seems of more importance, from the fact that we
+are desirous to impress on our readers that <i>there is no valid reason
+for adopting ten degrees of fork and roller action with the table
+roller, except that about this number of degrees of action are required
+to secure a reliable safety action</i>. With the double roller, as low as
+six degrees fork and pallet action can be safely employed. In fork and
+pallet actions below six degrees of angular motion, side-shake in pivot
+holes becomes a dangerous factor, as will be explained further on. It is
+perfectly comprehending the action of <a name="Page_72" id="Page_72"></a>the lever escapement and then
+being able to remedy defects, that constitute the master workman.</p>
+
+
+<h4>HOW TO MEASURE THE ANGULAR MOTION OF AN ESCAPE WHEEL.</h4>
+
+<div class="figleft"><img src="images/pict076.jpg" alt="Fig. 76" title="Fig. 76" /></div>
+
+<p>We can also make use of our angle-testing device for measuring our
+escape-wheel action, by letting the clasp embrace the arbor of the
+escape wheel, instead of the pallet staff. We set the index arc as in
+our former experiments, except we place the movable index <i>D</i>, Fig. 76,
+so that when the engaged tooth rests on the locking face of a pallet,
+the index hand stands at the extreme end of our arc of twelve degrees.
+We next, with our pointed pegwood, start to move the fork away from the
+bank, as before, we look sharp and see the index hand move backward a
+little, indicating the "draw" on the locking face. As soon as the pallet
+reaches the impulse face, the hand <i>A</i> moves rapidly forward, and if the
+escapement is of the club-tooth order and closely matched, the hand <i>A</i>
+will pass over ten and a half degrees of angular motion before the drop
+takes place.</p>
+
+<div class="figright"><img src="images/pict077.jpg" alt="Fig. 77" title="Fig. 77" /></div>
+
+<p>We will warn our readers in advance, that if they make such a testing
+device they will be astonished at the inaccuracy which they will find in
+the escapements of so-called fine watches. The lock, in many instances,
+instead of being one and a half degrees, will oftener be found to be
+from two to four degrees, and the impulse derived from the escape wheel,
+as illustrated at Fig. 76, will often fall below eight degrees. Such
+watches will have a poor motion and tick loud enough to keep a policeman
+awake. Trials with actual watches, with such a device as we have just
+described, in conjunction with a careful study of the acting parts,
+especially if aided by a large model, such as we have described, will
+soon bring the student to a degree of skill unknown to the old-style
+workman, who, if a poor escapement bothered him, would bend back the
+banking pins or widen the slot in the fork.</p>
+
+<div class="figright"><img src="images/pict078.jpg" alt="Fig. 78" title="Fig. 78" /></div>
+
+<p>We hold that educating our repair workmen up to a high knowledge of what
+is required to constitute a high-grade escapement, will have a
+beneficial effect on manufacturers. When we wish to apply our device to
+the measurement of the escapement of <a name="Page_73" id="Page_73"></a>three-quarter-plate watches, we
+will require another index hand, with the grasping end bent downward, as
+shown at Fig. 77. The idea with this form of index hand is, the
+bent-down jaws <i>B'</i>, Fig. 77, grasp the fork as close to the pallet
+staff as possible, making an allowance for the acting center by so
+placing the index arc that the hand <i>A</i> will read correctly on the index
+<i>D</i>. Suppose, for instance, we place the jaws <i>B'</i> inside the pallet
+staff, we then place the index arc so the hand reads to the arc
+indicated by the dotted arc <i>m</i>, Fig. 78, and if set outside of the
+pallet staff, read by the arc <i>o</i>.</p>
+
+
+<h4>HOW A BALANCE CONTROLS THE TIMEKEEPING OF A WATCH.</h4>
+
+<p>We think a majority of the fine lever escapements made abroad in this
+day have what is termed double-roller safety action. The chief gains to
+be derived from this form of safety action are: (1) Reducing the arc of
+fork and roller action; (2) reducing the friction of the guard point to
+a minimum. While it is entirely practicable to use a table roller for
+holding the jewel pin with a double-roller action, still a departure
+from that form is desirable, both for looks and because as much of the
+aggregate weight of a balance should be kept as far from the axis of
+rotation as possible.</p>
+
+<p>We might as well consider here as elsewhere, the relation the balance
+bears to the train as a controlling power. Strictly speaking, <i>the
+balance and hairspring are the time measurers</i>, the train serving only
+two purposes: (<i>a</i>) To keep the balance in motion; (<i>b</i>) to classify and
+record the number of vibrations of the balance. Hence, it is of
+paramount importance that the vibrations of the balance should be as
+untrammeled as possible; this is why we urge reducing the arc of
+connection between the balance and fork to one as brief as is consistent
+with sound results. With a double-roller safety action we can easily
+reduce the fork action to eight degrees and the roller action to
+twenty-four degrees.</p>
+
+<p>Inasmuch as satisfactory results in adjustment depend very much on the
+perfection of construction, we shall now dwell to some extent on the
+necessity of the several parts being made on correct principles. For
+instance, by reducing the arc of engagement between the fork and roller,
+we lessen the duration of any disturbing influence of escapement action.</p>
+
+<p>To resume the explanation of why it is desirable to make the staff and
+all parts near the axis of the balance as light as possible, <a name="Page_74" id="Page_74"></a>we would
+say it is the moving portion of the balance which controls the
+regularity of the intervals of vibration. To illustrate, suppose we have
+a balance only 3/8" in diameter, but of the same weight as one in an
+ordinary eighteen-size movement. We can readily see that such a balance
+would require but a very light hairspring to cause it to give the usual
+18,000 vibrations to the hour. We can also understand, after a little
+thought, that such a balance would exert as much breaking force on its
+pivots as a balance of the same weight, but 3/4" in diameter acting
+against a very much stronger hairspring. There is another factor in the
+balance problem which deserves our attention, which factor is
+atmospheric resistance. This increases rapidly in proportion to the
+velocity.</p>
+
+
+<h4>HOW BAROMETRIC PRESSURE AFFECTS A WATCH.</h4>
+
+<p>The most careful investigators in horological mechanics have decided
+that a balance much above 75/100" in diameter, making 18,000 vibrations
+per hour, is not desirable, because of the varying atmospheric
+disturbances as indicated by barometric pressure. A balance with all of
+its weight as near the periphery as is consistent with strength, is what
+is to be desired for best results. It is the moving matter composing the
+balance, pitted against the elastic force of the hairspring, which we
+have to depend upon for the regularity of the timekeeping of a watch,
+and if we can take two grains' weight of matter from our roller table
+and place them in the rim or screws of the balance, so as to act to
+better advantage against the hairspring, we have disposed of these two
+grains so as to increase the efficiency of the controlling power and not
+increase the stress on the pivots.</p>
+
+<div class="figleft"><img src="images/pict079.jpg" alt="Fig. 79" title="Fig. 79" /></div>
+
+<p>We have deduced from the facts set forth, two axioms: (<i>a</i>) That we
+should keep the weight of our balance as much in the periphery as
+possible, consistent with due strength; (<i>b</i>) avoid excessive size from
+the disturbing effect of the air. We show at <i>A</i>, Fig. 79, the shape of
+the piece which carries the jewel pin. As shown, it consists of three
+parts: (1) The socket <i>A</i>, which receives the jewel pin <i>a</i>; (2) the
+part <i>A''</i> and hole <i>b</i>, which goes on the balance staff; (3) the
+counterpoise <i>A'''</i>, which makes up for the weight of the jewel socket
+<i>A</i>, neck <i>A'</i> and jewel pin. This counterpoise also makes up for the
+passing hollow <i>C</i> in the guard roller <i>B</i>, Fig. 80. As the <a name="Page_75" id="Page_75"></a>piece <i>A</i>
+is always in the same relation to the roller <i>B</i>, the poise of the
+balance must always remain the same, no matter how the roller action is
+placed on the staff. We once saw a double roller of nearly the shape
+shown at Fig. 79, which had a small gold screw placed at <i>d</i>, evidently
+for the purpose of poising the double rollers; but, to our thinking, it
+was a sort of hairsplitting hardly worth the extra trouble. Rollers for
+very fine watches should be poised on the staff before the balance is
+placed upon it.</p>
+
+<div class="figright"><img src="images/pict080.jpg" alt="Fig. 80" title="Fig. 80" /></div>
+
+<p>We shall next give detailed instructions for drawing such a double
+roller as will be adapted for the large model previously described,
+which, as the reader will remember, was for ten degrees of roller
+action. We will also point out the necessary changes required to make it
+adapted for eight degrees of fork action. We would beg to urge again the
+advantages to be derived from constructing such a model, even for
+workmen who have had a long experience in escapements, our word for it
+they will discover a great many new wrinkles they never dreamed of
+previously.</p>
+
+<p>It is important that every practical watchmaker should thoroughly master
+the theory of the lever escapement and be able to comprehend and
+understand at sight the faults and errors in such escapements, which, in
+the every-day practice of his profession, come to his notice. In no
+place is such knowledge more required than in fork and roller action. We
+are led to say the above chiefly for the benefit of a class of workmen
+who think there is a certain set of rules which, if they could be
+obtained, would enable them to set to rights any and all escapements. It
+is well to understand that no such system exists and that, practically,
+we must make one error balance another; and it is the "know how" to make
+such faults and errors counteract each other that enables one workman to
+earn more for himself or his employer in two days than another workman,
+who can file and drill as well as he can, will earn in a week.</p>
+
+
+<h4>PROPORTIONS OF THE DOUBLE-ROLLER ESCAPEMENT.</h4>
+
+<p>The proportion in size between the two rollers in a double-roller
+escapement is an open question, or, at least, makers seldom agree on it.
+Grossmann shows, in his work on the lever escapement, two sizes: (1)
+Half the diameter of the acting roller; (2) two-thirds of the size of
+the acting roller. The chief fault urged against a smaller safety roller
+is, that it necessitates longer horns <a name="Page_76" id="Page_76"></a>to the fork to carry out the
+safety action. Longer horns mean more metal in the lever, and it is the
+conceded policy of all recent makers to have the fork and pallets as
+light as possible. Another fault pertaining to long horns is, when the
+horn does have to act as safety action, a greater friction ensues.</p>
+
+<p>In all soundly-constructed lever escapements the safety action is only
+called into use in exceptional cases, and if the watch was lying still
+would theoretically never be required. Where fork and pallets are poised
+on their arbor, pocket motion (except torsional) should but very little
+affect the fork and pallet action of a watch, and torsional motion is
+something seldom brought to act on a watch to an extent to make it
+worthy of much consideration. In the double-roller action which we shall
+consider, we shall adopt three-fifths of the pitch diameter of the
+jewel-pin action as the proper size. Not but what the proportions given
+by Grossmann will do good service; but we adopt the proportions named
+because it enables us to use a light fork, and still the friction of the
+guard point on the roller is but little more than where a guard roller
+of half the diameter of the acting roller is employed.</p>
+
+<p>The fork action we shall consider at present is ten degrees, but
+subsequently we shall consider a double-roller action in which the fork
+and pallet action is reduced to eight degrees. We shall conceive the
+play between the guard point and the safety roller as one degree, which
+will leave half a degree of lock remaining in action on the engaged
+pallet.</p>
+
+
+<h4>THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED.</h4>
+
+<p>In the drawing at Fig. 81 we show a diagram of the action of the
+double-roller escapement. The small circle at <i>A</i> represents the center
+of the pallet staff, and the one at <i>B</i> the center of the balance staff.
+The radial lines <i>A d</i> and <i>A d'</i> represent the arc of angular motion of
+fork action. The circle <i>b b</i> represents the pitch circle of the jewel
+pin, and the circle at <i>c c</i> the periphery of the guard or safety
+roller. The points established on the circle <i>c c</i> by intersection of
+the radial lines <i>A d</i> and <i>A d'</i> we will denominate the points <i>h</i> and
+<i>h'</i>. It is at these points the end of the guard point of the fork will
+terminate. In construction, or in delineating for construction, we show
+the guard enough short of the points <i>h h'</i> to allow the fork an angular
+motion of one degree, from <i>A</i> as a center, before said point would come
+in contact with the safety roller.<a name="Page_77" id="Page_77"></a></p>
+
+<div class="figright"><a href="images/pict081.jpg"><img src="images/pict081-tb.jpg" alt="Fig. 81" title="Fig. 81" /></a></div>
+
+<p>We draw through the points <i>h h'</i>, from <i>B</i> as a center, the radial
+lines <i>B g</i> and <i>B g'</i>. We measure this angle by sweeping the short arc
+<i>i</i> with any of the radii we have used for arc measurement in former
+delineations, and find it to be a trifle over sixty degrees. To give
+ourselves a practical object lesson, let us imagine that a real guard
+point rests on the circle <i>c</i> at <i>h</i>. Suppose we make a notch in the
+guard roller represented by the circle <i>c</i>, to admit such imaginary
+guard point, and then commence to revolve the circle <i>c</i> in the
+direction of the arrow <i>j</i>, letting the guard point rest constantly in
+such notch. When the notch <i>n</i> in <i>c</i> has been carried through thirty
+degrees of arc, counting from <i>B</i> as a center, the guard point, as
+relates to <i>A</i> as a center, would only have passed through an arc of
+five degrees. We show such a guard point and notch at <i>o n</i>. In fact, if
+a jewel pin was set to engage the fork on the pitch circle <i>b a</i>, the
+escapement would lock. To obviate such lock we widen the notch <i>n</i> to
+the extent indicated by the dotted lines <i>n'</i>, allowing the guard point
+to fall back, so to speak, into the notch <i>n</i>, which really represents
+the passing hollow. It is not to be understood that the extended notch
+at <i>n</i> is correctly drawn as regards position, because when the guard
+point was on the line <i>A f</i> the point <i>o</i> would be in the center of the
+extended notch, or passing hollow. We shall next give the details of
+drawing the double roller, but before doing so we deemed it important to
+explain the action of such guard points more fully than has been done
+heretofore.</p>
+
+
+<h4>HOW TO DESIGN A DOUBLE-ROLLER ESCAPEMENT.</h4>
+
+<p>We have already given very desirable forms for the parts of a
+double-roller escapement, consequently we shall now deal chiefly with
+acting principles as regards the rollers, but will give, at Fig. 82, a
+very well proportioned and practical form of fork. The pitch circle of
+the jewel pin is indicated by the dotted circle <i>a</i>, and the jewel pin
+of the usual cylindrical form, with two-fifths cut away. The safety
+roller is three-fifths of the diameter of the pitch diameter of the
+jewel-pin action, as indicated by the dotted circle <i>a</i>.</p>
+
+<p><a name="Page_78" id="Page_78"></a>The safety roller is shown in full outline at <i>B'</i>, and the passing
+hollow at <i>E</i>. It will be seen that the arc of intersection embraced
+between the radial lines <i>B c</i> and <i>B d</i> is about sixty-one and a half
+degrees for the roller, but the angular extent of the passing hollow is
+only a little over thirty-two degrees. The passing hollow <i>E</i> is located
+and defined by drawing the radial line <i>B c</i> from the center <i>B</i> through
+the intersection of radial line <i>A i</i> with the dotted arc <i>b</i>, which
+represents the pitch circle of the safety roller. We will name this
+intersection the point <i>l</i>. Now the end of the guard point <i>C</i>
+terminates at the point <i>l</i>, and the passing hollow <i>E</i> extends on <i>b</i>
+sixteen degrees on each side of the radial line <i>B c</i>.</p>
+
+<div class="figcenter"><a href="images/pict082.jpg"><img src="images/pict082-tb.jpg" alt="Fig. 82" title="Fig. 82" /></a></div>
+
+<p>The roller action is supposed to continue through thirty degrees of
+angular motion of the balance staff, and is embraced on the circle <i>a</i>
+between the radial line <i>B k</i> and <i>B o</i>. To delineate the inner face of
+the horn <i>p</i> of the fork <i>F</i> we draw the short arc <i>g</i>, from <i>A</i> as a
+center, and on said arc locate at two degrees from the center at <i>B</i> the
+point <i>f</i>. We will designate the upper angle of the outer face of the
+jewel pin <i>D</i> as the point <i>s</i> and, from <i>A</i> as a center, sweep through
+this point <i>s</i> the short arc <i>n n</i>. Parallel with the line <i>A i</i> and at
+the distance of half the diameter of the jewel pin <i>D</i>, we draw the
+short lines <i>t t'</i>, which define the inner faces of the fork.</p>
+
+<p>The intersection of the short line <i>t</i> with the arc <i>n</i> we will
+designate the point <i>r</i>. With our dividers set to embrace the space
+between the point <i>r</i> and the point <i>f</i>, we sweep the arc which defines
+the inner face of the prong of the fork. The space we just made use of
+is practically the same as the radius of the circle <i>a</i>, and
+consequently of the same curvature. Practically, the length of the guard
+point <i>C'</i> is made as long as will, with certainty, clear <a name="Page_79" id="Page_79"></a>the safety
+roller <i>B</i> in all positions. While we set the point <i>f</i> at two degrees
+from the center <i>B</i>, still, in a well-constructed escapement, one and a
+half degrees should be sufficient, but the extra half degree will do no
+harm. If the roller <i>B'</i> is accurately made and the guard point <i>C'</i>
+properly fitted, the fork will not have half a degree of play.</p>
+
+<p>The reader will remember that in the escapement model we described we
+cut down the drop to one degree, being less by half a degree than
+advised by Grossmann and Saunier. We also advised only one degree of
+lock. In the perfected lever escapement, which we shall describe and
+give working drawings for the construction of, we shall describe a
+detached lever escapement with only eight degrees fork and pallet
+action, with only three-fourths of a degree drop and three-fourths of a
+degree lock, which we can assure our readers is easily within the limits
+of practical construction by modern machinery.</p>
+
+
+<h4>HOW THE GUARD POINT IS MADE.</h4>
+
+<div class="figright"><img src="images/pict083.jpg" alt="Fig. 83" title="Fig. 83" /></div>
+
+<p>The guard point <i>C'</i>, as shown at Fig. 82, is of extremely simple
+construction. Back of the slot of the fork, which is three-fifths of the
+diameter of the jewel pin in depth, is made a square hole, as shown at
+<i>u</i>, and the back end of the guard point <i>C</i> is fitted to this hole so
+that it is rigid in position. This manner of fastening the guard point
+is equally efficient as that of attaching it with a screw, and much
+lighter&mdash;a matter of the highest importance in escapement construction,
+as we have already urged. About the best material for such guard points
+is either aluminum or phosphor bronze, as such material is lighter than
+gold and very rigid and strong. At Fig. 83 we show a side view of the
+essential parts depicted in Fig. 82, as if seen in the direction of the
+arrow <i>v</i>, but we have added the piece which holds the jewel pin <i>D</i>. A
+careful study of the cut shown at Fig. 82 will soon give the horological
+student an excellent idea of the double-roller action.</p>
+
+<p>We will now take up and consider at length why Saunier draws his
+entrance pallet with fifteen degrees draw and his exit pallet with only
+twelve degrees draw. To make ourselves more conversant with Saunier's
+method of delineating the lever escapement, <a name="Page_80" id="Page_80"></a>we reproduce the essential
+features of his drawing, Fig. 1, plate VIII, of his "Modern Horology,"
+in which he makes the draw of the locking face of the entrance pallet
+fifteen degrees and his exit pallet twelve degrees. In the cut shown at
+Fig. 84 we use the same letters of reference as he employs. We do not
+quote his description or directions for delineation because he refers to
+so much matter which he has previously given in the book just referred
+to. Besides we cannot entirely endorse his methods of delineations for
+many reasons, one of which appears in the drawing at Fig. 84.</p>
+
+<div class="figcenter"><a href="images/pict084.jpg"><img src="images/pict084-tb.jpg" alt="Fig. 84" title="Fig. 84" /></a></div>
+
+
+<h4>MORE ABOUT TANGENTIAL LOCKINGS.</h4>
+
+<p>Most writers endorse the idea of tangential lockings, and Saunier speaks
+of the escapement as shown at Fig. 84 as having such tangential
+lockings, which is not the case. He defines the position of the pallet
+staff from the circle <i>t</i>, which represents the extreme length of the
+teeth; drawing the radial lines <i>A D</i> and <i>A E</i> to embrace an arc of
+sixty degrees, and establishing the center of his pallet staff <i>C</i> at
+the intersection of the lines <i>D C</i> and <i>E C</i>, which are drawn at right
+angles to the radial lines <i>A D</i> and <i>A E</i>, and tangential to the circle
+<i>t</i>.</p>
+
+<p>Here is an error; the lines defining the center of the pallet staff
+should have been drawn tangent to the circle <i>s</i>, which represents the
+locking angle of the teeth. This would have placed the <a name="Page_81" id="Page_81"></a>center of the
+pallet staff farther in, or closer to the wheel. Any person can see at a
+glance that the pallets as delineated are not tangential in a true
+sense.</p>
+
+<div class="figcenter"><a href="images/pict085.jpg"><img src="images/pict085-tb.jpg" alt="Fig. 85" title="Fig. 85" /></a></div>
+
+<p>We have previously considered engaging friction and also repeatedly have
+spoken of tangential lockings, but will repeat the idea of tangential
+lockings at Fig. 85. A tangential locking is neutral, or nearly so, as
+regards engaging friction. For illustration we refer to Fig. 85, where
+<i>A</i> represents the center of an escape wheel. We draw the radial lines
+<i>A y</i> and <i>A z</i> so that they embrace sixty degrees of the arcs <i>s</i> or
+<i>t</i>, which correspond to similar circles in Fig. 84, and represent the
+extreme extent of the teeth and likewise the locking angle of such
+teeth. In fact, with the club-tooth escapement all that part of a tooth
+which extends beyond the line <i>s</i> should be considered the same as the
+addendum in gear wheels. Consequently, a tangential locking made to
+coincide with the center of the impulse plane, as recommended by
+Saunier, would require the pallet staff to be located at <i>C'</i> instead of
+<i>C</i>, as he draws it. If the angle <i>k'</i> of the tooth <i>k</i> in Fig. 84 was
+extended outward from the center <i>A</i> so it would engage or rest on the
+locking face of the entrance pallet as shown at Fig. 84, then the draw
+of the locking angle would not be quite fifteen degrees; but it is
+evident no lock can take place until the angle <i>a</i> of the entrance
+pallet has passed inside the circle <i>s</i>. We would say here that we have
+added the letters <i>s</i> and <i>t</i> to the original drawings, as we have
+frequently to <a name="Page_82" id="Page_82"></a>refer to these circles, and without letters had no means
+of designation. Before the locking angle <i>k'</i> of the tooth can engage
+the pallet, as shown in Fig. 84, the pallet must turn on the center <i>C</i>
+through an angular movement of at least four degrees. We show the
+situation in the diagram at Fig. 86, using the same letters of reference
+for similar parts as in Fig. 84.</p>
+
+<div class="figleft"><a href="images/pict086.jpg"><img src="images/pict086-tb.jpg" alt="Fig. 86" title="Fig. 86" /></a></div>
+
+<p>As drawn in Fig. 84 the angle of draft <i>G a I</i> is equal to fifteen
+degrees, but when brought in a position to act as shown at <i>G a' I'</i>,
+Fig. 86, the draw is less even than twelve degrees. The angle <i>C a I</i>
+remains constant, as shown at <i>C a' I'</i>, but the relation to the radial
+<i>A G</i> changes when the pallet moves through the angle <i>w C w'</i>, as it
+must when locked. A tangential locking in the true sense of the meaning
+of the phrase is a locking set so that a pallet with its face coinciding
+with a radial line like <i>A G</i> would be neutral, and the thrust of the
+tooth would be tangent to the circle described by the locking angle of
+the tooth. Thus the center <i>C</i>, Fig. 86, is placed on the line <i>w'</i>
+which is tangent to the circle <i>s</i>; said line <i>w'</i> also being at right
+angles to the radial line <i>A G</i>.</p>
+
+<p>The facts are, the problems relating to the club-tooth lever escapement
+are very intricate and require very careful analysis, and without such
+care the horological student can very readily be misled. Faulty
+drawings, when studying such problems, lead to no end of errors, and
+practical men who make imperfect drawings lead to the popular phrase,
+"Oh, such a matter may be all right in theory, but will not work in
+practice." We should always bear in mind that <i>theory, if right, must
+lead practice</i>.</p>
+
+
+<h4>CORRECT DRAWING REQUIRED.</h4>
+
+<p>If we delineate our entrance pallet to have a draw of twelve degrees
+when in actual contact with the tooth, and then construct in exact
+conformity with such drawings, we will find our lever to "hug the banks"
+in every instance. It is inattention to such details which produces the
+errors of makers complained of by Saunier in section 696 of his "Modern
+Horology," and which <a name="Page_83" id="Page_83"></a>he attempts to correct by drawing the locking face
+at fifteen degrees draw.</p>
+
+<p>We shall show that neither <i>C</i> nor <i>C'</i>, Fig. 85, is the theoretically
+correct position for the pallet center for a tangential locking.</p>
+
+<p>We will now take up the consideration of a club-tooth lever escapement
+with circular pallets and tangential lockings; but previous to making
+the drawings we must decide several points, among which are the
+thickness of the pallet arms, which establishes the angular motion of
+the escape wheel utilized by such pallet arms, and also the angular
+motion imparted to the pallets by the impulse faces of the teeth. We
+will, for the present, accept the thickness of the arms as being
+equivalent to five degrees of angular extent of the pitch circle of the
+escape wheel.</p>
+
+<div class="figcenter"><a href="images/pict087-88.jpg"><img src="images/pict087-88-tb.jpg" alt="Fig. 87-88" title="Fig. 87-88" /></a></div>
+
+<p>In making our drawings we commence, as on former occasions, by
+establishing the center of our escape wheel at <i>A</i>, Fig. 87, and
+sweeping the arc <i>a a</i> to represent the pitch circle of such wheel.
+Through the center <i>A</i> we draw the vertical line <i>A B</i>, which is
+supposed to also pass through the center of the pallet staff. The
+intersection of the line <i>A B</i> with the arc <i>a</i> we term the point <i>d</i>,
+and from this point we lay off on said arc <i>a</i> thirty degrees each side
+of said intersection, and thus establish the points <i>c b</i>. From <i>A</i>,
+through the point <i>c</i>, we draw the line <i>A c c'</i>. On the arc <i>a a</i> and
+two and a half degrees to the left of the point <i>c</i> we establish the
+point <i>f</i>, which space represents half of the thickness of the entrance
+pallet. From<a name="Page_84" id="Page_84"></a> <i>A</i> we draw through the point <i>f</i> the line <i>A f f'</i>. From
+<i>f</i>, and at right angles to said line <i>A f</i>, we draw the line <i>f e</i>
+until it crosses the line <i>A B</i>.</p>
+
+<p>Now this line <i>f e</i> is tangent to the arc <i>a</i> from the point <i>f</i>, and
+consequently a locking placed at the point <i>f</i> is a true tangential
+locking; and if the resting or locking face of a pallet was made to
+coincide with the line <i>A f'</i>, such locking face would be strictly
+"dead" or neutral. The intersection of the line <i>f e</i> with the line <i>A
+B</i> we call the point <i>C</i>, and locate at this point the center of our
+pallet staff. According to the method of delineating the lever
+escapement by Moritz Grossmann the tangent line for locating the center
+of the pallet staff is drawn from the point <i>c</i>, which would locate the
+center of the pallet staff at the point <i>h</i> on the line <i>A B</i>.</p>
+
+<p>Grossmann, in delineating his locking face for the draw, shows such face
+at an angle of twelve degrees to the radial line <i>A f'</i>, when he should
+have drawn it twelve degrees to an imaginary line shown at <i>f i</i>, which
+is at right angles to the line <i>f h</i>. To the writer's mind this is not
+just as it should be, and may lead to misunderstanding and bad
+construction. We should always bear in mind the fact that the basis of a
+locking face is a neutral plane placed at right angles to the line of
+thrust, and the "draw" comes from a locking face placed at an angle to
+such neutral plane. A careful study of the diagram at Fig. 88 will give
+the reader correct ideas. If a tooth locks at the point <i>c</i>, the
+tangential thrust would be on the line <i>c h'</i>, and a neutral locking
+face would be on the line <i>A c</i>.</p>
+
+
+<h4>NEUTRAL LOCKINGS.</h4>
+
+<p>To aid in explanation, let us remove the pallet center to <i>D</i>; then the
+line of thrust would be <i>c D</i> and a neutral locking face would coincide
+with the line <i>m m</i>, which is at right angles to the line <i>c D</i>. If we
+should now make a locking face with a "draw" and at an angle to the line
+<i>c D</i>, say, for illustration, to correspond to the line <i>c c'</i> (leaving
+the pallet center at <i>D</i>), we would have a strong draw and also a cruel
+engaging friction.</p>
+
+<p>If, however, we removed the engaging tooth, which we have just conceived
+to be at <i>c</i>, to the point <i>k</i> on the arc <i>a' a'</i>, Fig. 88, the pallet
+center <i>D</i> would then represent a tangential locking, and a neutral
+pallet face would coincide with the radial line <i>A k'</i>; and a locking
+face with twelve degrees draw would coincide nearly with <a name="Page_85" id="Page_85"></a>the line <i>l</i>.
+Let us next analyze what the effect would be if we changed the pallet
+center to <i>h'</i>, Fig. 88, leaving the engaging tooth still at <i>k</i>. In
+this instance the line <i>l l</i> would then coincide with a neutral locking
+face, and to obtain the proper draw we should delineate the locking face
+to correspond to the line <i>k n</i>, which we assume to be twelve degrees
+from <i>k l</i>.</p>
+
+<p>It is not to be understood that we insist on precisely twelve degrees
+draw from a neutral plane for locking faces for lever pallets. What we
+do insist upon, however, is a "safe and sure draw" for a lever pallet
+which will hold a fork to the banks and will also return it to such
+banks if by accident the fork is moved away. We are well aware that it
+takes lots of patient, hard study to master the complications of the
+club-tooth lever escapement, but it is every watchmaker's duty to
+conquer the problem. The definition of "lock," in the detached lever
+escapement, is the stoppage or arrest of the escape wheel of a watch
+while the balance is left free or detached to perform the greater
+portion of its arc of vibration. "Draw" is a function of the locking
+parts to preserve the fork in the proper position to receive and act on
+the jewel pin of the balance.</p>
+
+<p>It should be borne in mind in connection with "lock" and "draw," that
+the line of thrust as projected from the locked tooth of the escape
+wheel should be as near tangential as practicable. This maxim applies
+particularly to the entrance pallet. We would beg to add that
+practically it will make but little odds whether we plant the center of
+our pallet staff at <i>C</i> or <i>h</i>, Fig. 87, provided we modify the locking
+and impulse angles of our pallets to conform to such pallet center. But
+it will not do to arrange the parts for one center and then change to
+another.</p>
+
+
+<h4>PRACTICAL HINTS FOR LEVER ESCAPEMENTS.</h4>
+
+<p>Apparently there seems to be a belief with very many watchmakers that
+there is a set of shorthand rules for setting an escapement, especially
+in American watches, which, if once acquired, conquers all
+imperfections. Now we wish to disabuse the minds of our readers of any
+such notions. Although the lever escapement, as adopted by our American
+factories, is constructed on certain "lines," still these lines are
+subject to modifications, such as may be demanded for certain defects of
+construction. If we could duplicate every part of a watch movement
+perfectly, then we could have <a name="Page_86" id="Page_86"></a>certain rules to go by, and fixed
+templets could be used for setting pallet stones and correcting other
+escapement faults.</p>
+
+<p>Let us now make an analysis of the action of a lever escapement. We show
+at Fig. 89 an ordinary eighteen-size full-plate lever with fork and
+pallets. The dotted lines <i>a b</i> are supposed to represent an angular
+movement of ten degrees. Now, it is the function of the fork to carry
+the power of the train to the balance. How well the fork performs its
+office we will consider subsequently; for the present we are dealing
+with the power as conveyed to the fork by the pallets as shown at Fig.
+89.</p>
+
+<div class="figcenter"><a href="images/pict089.jpg"><img src="images/pict089-tb.jpg" alt="Fig. 89" title="Fig. 89" /></a></div>
+
+<p>The angular motion between the lines <i>a c</i> (which represents the lock)
+is not only absolutely lost&mdash;wasted&mdash;but during this movement the train
+has to retrograde; that is, the dynamic force stored in the momentum of
+the balance has to actually turn the train backward and against the
+force of the mainspring. True, it is only through a very short arc, but
+the necessary force to effect this has to be discounted from the power
+stored in the balance from a former impulse. For this reason we should
+make the angular motion of unlocking as brief as possible. Grossmann, in
+his essay, endorses one and a half degrees as the proper lock.</p>
+
+<p>In the description which we employed in describing the large model for
+illustrating the action of the detached lever escapement, we cut the
+lock to one degree, and in the description of the up-to-date lever
+escapement, which we shall hereafter give, we shall cut the lock down to
+three-quarters of a degree, a perfection easily to be attained by modern
+tools and appliances. We shall also cut the drop down to three-quarters
+of a degree. By these two economies we more than make up for the power
+lost in unlocking. With highly polished ruby or sapphire pallets ten
+degrees of draw is ample. But such draw must positively be ten degrees
+from a <a name="Page_87" id="Page_87"></a>neutral locking face, not an escapement drawn on paper and
+called ten degrees, but when actually measured would only show eight and
+a half or nine degrees.</p>
+
+
+<h4>THE PERFECTED LEVER ESCAPEMENT.</h4>
+
+<p>With ten degrees angular motion of the lever and one and a half degrees
+lock, we should have eight and a half degrees impulse. The pith of the
+problem, as regards pallet action, for the practical workman can be
+embodied in the following question: What proportion of the power derived
+from the twelve degrees of angular motion of the escape wheel is really
+conveyed to the fork? The great leak of power as transmitted by the
+lever escapement to the balance is to be found in the pallet action, and
+we shall devote special attention to finding and stopping such leaks.</p>
+
+
+<h4>WHEN POWER IS LOST IN THE LEVER ESCAPEMENT.</h4>
+
+<p>If we use a ratchet-tooth escape wheel we must allow at least one and a
+half degrees drop to free the back of the tooth; but with a club-tooth
+escape wheel made as can be constructed by proper skill and care, the
+drop can be cut down to three-quarters of a degree, or one-half of the
+loss with the ratchet tooth. We do not wish our readers to imagine that
+such a condition exists in most of the so-called fine watches, because
+if we take the trouble to measure the actual drop with one of the little
+instruments we have described, it will be found that the drop is seldom
+less than two, or even three degrees.</p>
+
+<p>If we measure the angular movement of the fork while locked, it will
+seldom be found less than two or three degrees. Now, we can all
+understand that the friction of the locking surface has to be counted as
+well as the recoil of the draw. Locking friction is seldom looked after
+as carefully as the situation demands. Our factories make the impulse
+face of the pallets rounded, but leave the locking face flat. We are
+aware this condition is, in a degree, necessary from the use of exposed
+pallets. In many of the English lever watches with ratchet teeth, the
+locking faces are made cylindrical, but with such watches the pallet
+stones, as far as the writer has seen, are set "close"; that is, with
+steel pallet arms extending above and below the stone.</p>
+
+<p>There is another feature of the club-tooth lever escapement that next
+demands our attention which we have never seen discussed.<a name="Page_88" id="Page_88"></a> We refer to
+arranging and disposing of the impulse of the escape wheel to meet the
+resistance of the hairspring. Let us imagine the dotted line <i>A d</i>, Fig.
+89, to represent the center of action of the fork. We can readily see
+that the fork in a state of rest would stand half way between the two
+banks from the action of the hairspring, and in the pallet action the
+force of the escape wheel, one tooth of which rests on the impulse face
+of a pallet, would be exerted against the elastic force of the
+hairspring. If the force of the mainspring, as represented by the
+escape-wheel tooth, is superior to the power of the hairspring, the
+watch starts itself. The phases of this important part of the detached
+lever escapement will be fully discussed.</p>
+
+
+<h4>ABOUT THE CLUB-TOOTH ESCAPEMENT.</h4>
+
+<p>We will now take up a study of the detached lever escapement as relates
+to pallet action, with the point specially in view of constructing an
+escapement which cannot "set" in the pocket, or, in other words, an
+escapement which will start after winding (if run down) without shaking
+or any force other than that supplied by the train as impelled by the
+mainspring. In the drawing at Fig. 90 we propose to utilize eleven
+degrees of escape-wheel action, against ten and a half, as laid down by
+Grossmann. Of this eleven degrees we propose to divide the impulse arc
+of the escape wheel in six and five degrees, six to be derived from the
+impulse face of the club tooth and five from the impulse plane of the
+pallet.</p>
+
+<p>The pallet action we divide into five and four, with one degree of lock.
+Five degrees of pallet action is derived from the impulse face of the
+tooth and four from the impulse face of the pallet. The reader will
+please bear in mind that we do not give these proportions as imperative,
+because we propose to give the fullest evidence into the reader's hands
+and enable him to judge for himself, as we do not believe in laying down
+imperious laws that the reader must accept on our assertion as being
+correct. Our idea is rather to furnish the proper facts and put him in a
+situation to know for himself.</p>
+
+<p>The reader is urged to make the drawings for himself on a large scale,
+say, an escape wheel 10" pitch diameter. Such drawings will enable him
+to realize small errors which have been tolerated too much in drawings
+of this kind. The drawings, as they appear in the cut, are one-fourth
+the size recommended, and many of the <a name="Page_89" id="Page_89"></a>lines fail to show points we
+desire to call attention to. As for instance, the pallet center at <i>B</i>
+is tangential to the pitch circle <i>a</i> from the point of tooth contact at
+<i>f</i>. To establish this point we draw the radial lines <i>A c</i> and <i>A d</i>
+from the escape-wheel center <i>A</i>, as shown, by laying off thirty degrees
+on each side of the intersection of the vertical line <i>i</i> (passing
+through the centers <i>A B</i>) with the arc <i>a</i>, and then laying off two and
+a half degrees on <i>a</i> and establishing the point <i>f</i>, and through <i>f</i>
+from the center <i>A</i> draw the radial line <i>A f'</i>. Through the point <i>f</i>
+we draw the tangent line <i>b' b b''</i>, and at the intersection of the line
+<i>b</i> with <i>i</i> we establish the center of our pallet staff at <i>B</i>. At two
+and a half degrees from the point <i>c</i> we lay off two and a half degrees
+to the right of said point and establish the point <i>n</i>, and draw the
+radial line <i>A n n'</i>, which establishes the extent of the arc of angular
+motion of the escape wheel utilized by the pallet arm.</p>
+
+<div class="figcenter"><a href="images/pict090.jpg"><img src="images/pict090-tb.jpg" alt="Fig. 90" title="Fig. 90" /></a></div>
+
+<p>We have now come to the point where we must exercise our reasoning
+powers a little. We know the locking angle of the escape-wheel tooth
+passes on the arc <i>a</i>, and if we utilize the impulse face of the tooth
+for five degrees of pallet or lever motion we must shape it to this end.
+We draw the short arc <i>k</i> through the point <i>n</i>, knowing that the inner
+angle of the pallet stone must rest on this arc wherever it is situated.
+As, for instance, when the locking face of the pallet is engaged, the
+inner angle of the pallet stone must rest somewhere on this arc (<i>k</i>)
+inside of <i>a</i>, and the extreme <a name="Page_90" id="Page_90"></a>outer angle of the impulse face of the
+tooth must part with the pallet on this arc <i>k</i>.</p>
+
+
+<h4>HOW TO LOCATE THE PALLET ACTION.</h4>
+
+<p>With the parts related to each other as shown in the cut, to establish
+where the inner angle of the pallet stone is located in the drawing, we
+measure down on the arc <i>k</i> five degrees from its intersection with <i>a</i>,
+and establish the point <i>s</i>. The line <i>B b</i>, Fig. 90, as the reader will
+see, does not coincide with the intersection of the arcs <i>a</i> and <i>k</i>,
+and to conveniently get at the proper location for the inner angle of
+our pallet stone, we draw the line <i>B b'</i>, which passes through the
+point <i>n</i> located at the intersection of the arc <i>a</i> with the arc <i>k</i>.
+From <i>B</i> as a center we sweep the short arc <i>j</i> with any convenient
+radius of which we have a sixty-degree scale, and from the intersection
+of <i>B b'</i> with <i>j</i> we lay off five degrees and draw the line <i>B s'</i>,
+which establishes the point <i>s</i> on the arc <i>k</i>. As stated above, we
+allow one degree for lock, which we establish on the arc <i>o</i> by laying
+off one degree on the arc <i>j</i> below its intersection with the line <i>B
+b</i>. We do not show this line in the drawing, from the fact that it comes
+so near to <i>B b'</i> that it would confuse the reader. Above the arc <i>a</i> on
+the arc <i>k</i> at five degrees from the point <i>n</i> we establish the point
+<i>l</i>, by laying off five degrees on the arc <i>j</i> above the intersection of
+the line <i>B b</i> with <i>j</i>.</p>
+
+<p>The point <i>l</i>, Fig. 90, establishes where the outer angle of the tooth
+will pass the arc <i>k</i> to give five degrees of angular motion to the
+lever. From <i>A</i> as a center we sweep the arc <i>m</i>, passing through the
+point <i>l</i>. The intersection of the arc <i>m</i> with the line <i>A h</i> we call
+the point <i>r</i>, and by drawing the right line <i>r f</i> we delineate the
+impulse face of the tooth. On the arc <i>o</i> and one degree below its
+intersection with the line <i>B b</i> we establish the point <i>t</i>, and by
+drawing a right line from <i>t</i> to <i>s</i> we delineate the impulse face of
+our entrance pallet.</p>
+
+
+<h4>"ACTION" DRAWINGS.</h4>
+
+<p>One great fault with most of our text books on horology lies in the fact
+that when dealing with the detached lever escapement the drawings show
+only the position of the pallets when locked, and many of the conditions
+assumed are arrived at by mental processes, without making the proper
+drawings to show the actual relation of the parts at the time such
+conditions exist. For illustration, it is often urged that there is a
+time in the action of the club-tooth lever <a name="Page_91" id="Page_91"></a>escapement action when the
+incline on the tooth and the incline on the pallet present parallel
+surfaces, and consequently endure excessive friction, especially if the
+oil is a little thickened.</p>
+
+<p>We propose to make drawings to show the exact position and relation of
+the entrance pallet and tooth at three intervals viz: (1) Locked; (2)
+the position of the parts when the lever has performed one-half of its
+angular motion; (3) when half of the impulse face of the tooth has
+passed the pallet. The position of the entrance pallet when locked is
+sufficiently well shown in Fig. 90 to give a correct idea of the
+relations with the entrance pallet; and to conform to statement (2), as
+above. We will now delineate the entrance pallet, not in actual contact,
+however, with the pallet, because if we did so the lines we employed
+would become confused. The methods we use are such that <i>we can
+delineate with absolute correctness either a pallet or tooth at any
+point in its angular motion</i>.</p>
+
+<p>We have previously given instructions for drawing the pallet locked; and
+to delineate the pallet after five degrees of angular motion, we have
+only to conceive that we substitute the line <i>s'</i> for the line <i>b'</i>. All
+angular motions and measurements for pallet actions are from the center
+of the pallet staff at <i>B</i>. As we desire to now delineate the entrance
+pallet, it has passed through five degrees of angular motion and the
+inner angle <i>s</i> now lies on the pitch circle of the escape wheel, the
+angular space between the lines <i>b' s'</i> being five degrees, the line
+<i>b''</i>[**note: check this against the diagram-most other lines nave a
+two-letter identification] reducing the impulse face to four degrees.</p>
+
+
+<h4>DRAWING AN ESCAPEMENT TO SHOW ANGULAR MOTION.</h4>
+
+<p>To delineate our locking face we draw a line at right angles to the line
+<i>B b''</i> from the point <i>t</i>, said point being located at the intersection
+of the arc <i>o</i> with the line <i>B b''</i>. To draw a line perpendicular to <i>B
+b''</i> from the point <i>t</i>, we take a convenient space in our dividers and
+establish on the line <i>B b''</i> the points <i>x x'</i> at equal distances from
+the point <i>t</i>. We open the dividers a little (no special distance) and
+sweep the short arcs <i>x'' x'''</i>, as shown at Fig. 91. Through the
+intersection of the short arcs <i>x'' x'''</i> and to the point <i>t</i> we draw
+the line <i>t y</i>. The reader will see from our former explanations that
+the line <i>t y</i> represents the neutral plane of the locking face, and
+that to have the proper draw we must delineate the locking face of our
+pallet at twelve degrees. To do this we draw the line <i>t x'</i> at twelve
+degrees to the line <i>t y</i>, <a name="Page_92" id="Page_92"></a>and proceed to outline our pallet faces as
+shown. We can now understand, after a moment's thought, that we can
+delineate the impulse face of a tooth at any point or place we choose by
+laying off six degrees on the arc <i>m</i>, and drawing radial lines from <i>A</i>
+to embrace such arc. To illustrate, suppose we draw the radial lines <i>w'
+w''</i> to embrace six degrees on the arc <i>a</i>. We make these lines
+contiguous to the entrance pallet <i>C</i> for convenience only. To delineate
+the impulse face of the tooth, we draw a line extending from the
+intersection of the radial line <i>A' w'</i> with the arc <i>m</i> to the
+intersection of the arc <i>a</i> with the radial line <i>A w''</i>.</p>
+
+<div class="figcenter"><a href="images/pict091.jpg"><img src="images/pict091-tb.jpg" alt="Fig. 91" title="Fig. 91" /></a></div>
+
+<p>We next desire to know where contact will take place between the
+wheel-tooth <i>D</i> and pallet <i>C</i>. To determine this we sweep, with our
+dividers set so one leg rests at the escape-wheel center <i>A</i> and the
+other at the outer angle <i>t</i> of the entrance pallet, the short arc <i>t'
+w</i>. Where this arc intersects the line <i>w</i> (which represents the impulse
+face of the tooth) is where the outer angle <i>t</i> of the entrance pallet
+<i>C</i> will touch the impulse face of the tooth. To prove this we draw the
+radial line <i>A v</i> through the point where the short arc <i>t t'</i> passes
+through the impulse face <i>w</i> of the tooth <i>D</i>. Then we continue the line
+<i>w</i> to <i>n</i>, to represent the impulse face of the tooth, and then measure
+the angle <i>A w n</i> between the lines <i>w n</i> and <i>v A</i>, and find it to be
+approximately sixty-four degrees. We then, by a similar process, measure
+the angle <i>A t s'</i> and find it to be approximately sixty-six degrees.
+When contact ensues between the tooth <i>D</i> and pallet <i>C</i> the tooth <i>D</i>
+will attack the pallet at the point where the radial line <i>A v</i> crosses
+the tooth face. We have now explained <a name="Page_93" id="Page_93"></a>how we can delineate a tooth or
+pallet at any point of its angular motion, and will next explain how to
+apply this knowledge in actual practice.</p>
+
+
+<h4>PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT.</h4>
+
+<p>To delineate our entrance pallet after one-half of the engaged tooth has
+passed the inner angle of the entrance pallet, we proceed, as in former
+illustrations, to establish the escape-wheel center at <i>A</i>, and from it
+sweep the arc <i>b</i>, to represent the pitch circle. We next sweep the
+short arcs <i>p s</i>, to represent the arcs through which the inner and
+outer angles of the entrance pallet move. Now, to comply with our
+statement as above, we must draw the tooth as if half of it has passed
+the arc <i>s</i>.</p>
+
+<p>To do this we draw from <i>A</i> as a center the radial line <i>A j</i>, passing
+through the point <i>s</i>, said point <i>s</i> being located at the intersection
+of the arcs <i>s</i> and <i>b</i>. The tooth <i>D</i> is to be shown as if one half of
+it has passed the point <i>s</i>; and, consequently, if we lay off three
+degrees on each side of the point <i>s</i> and establish the points <i>d m</i>, we
+have located on the arc <i>b</i> the angular extent of the tooth to be drawn.
+To aid in our delineations we draw from the center <i>A</i> the radial lines
+<i>A d'</i> and <i>A m'</i>, passing through the points <i>d m</i>. The arc <i>a</i> is next
+drawn as in former instructions and establishes the length of the
+addendum of the escape-wheel teeth, the outer angle of our escape-wheel
+tooth being located at the intersection of the arc <i>a</i> with the radial
+line <i>A d'</i>.</p>
+
+<p>As shown in Fig. 92, the impulse planes of the tooth <i>D</i> and pallet <i>C</i>
+are in contact and, consequently, in parallel planes, as mentioned on
+page 91. It is not an easy matter to determine at exactly what degree of
+angular motion of the escape wheel such condition takes place; because
+to determine such relation mathematically requires a knowledge of higher
+mathematics, which would require more study than most practical men
+would care to bestow, especially as they would have but very little use
+for such knowledge except for this problem and a few others in dealing
+with epicycloidal curves for the teeth of wheels.</p>
+
+<p>For all practical purposes it will make no difference whether such
+parallelism takes place after eight or nine degrees of angular motion of
+the escape wheel subsequent to the locking action. The great point, as
+far as practical results go, is to determine if it takes place at or
+near the time the escape wheel meets the greatest <a name="Page_94" id="Page_94"></a>resistance from the
+hairspring. We find by analysis of our drawing that parallelism takes
+place about the time when the tooth has three degrees of angular motion
+to make, and the pallet lacks about two degrees of angular movement for
+the tooth to escape. It is thus evident that the relations, as shown in
+our drawing, are in favor of the train or mainspring power over
+hairspring resistance as three is to two, while the average is only as
+eleven to ten; that is, the escape wheel in its entire effort passes
+through eleven degrees of angular motion, while the pallets and fork
+move through ten degrees. The student will thus see we have arranged to
+give the train-power an advantage where it is most needed to overcome
+the opposing influence of the hairspring.</p>
+
+<div class="figcenter"><a href="images/pict092.jpg"><img src="images/pict092-tb.jpg" alt="Fig. 92" title="Fig. 92" /></a></div>
+
+<p>As regards the exalted adhesion of the parallel surfaces, we fancy there
+is more harm feared than really exists, because, to take the worst view
+of the situation, such parallelism only exists for the briefest
+duration, in a practical sense, because theoretically these surfaces
+never slide on each other as parallel planes. Mathematically
+<a name="Page_95" id="Page_95"></a>considered, the theoretical plane represented by the impulse face of
+the tooth approaches parallelism with the plane represented by the
+impulse face of the pallet, arrives at parallelism and instantly passes
+away from such parallelism.</p>
+
+
+<h4>TO DRAW A PALLET IN ANY POSITION.</h4>
+
+<p>As delineated in Fig. 92, the impulse planes of the tooth and pallet are
+in contact; but we have it in our power to delineate the pallet at any
+point we choose between the arcs <i>p s</i>. To describe and illustrate the
+above remark, we say the lines <i>B e</i> and <i>B f</i> embrace five degrees of
+angular motion of the pallet. Now, the impulse plane of the pallet
+occupies four of these five degrees. We do not draw a radial line from
+<i>B</i> inside of the line <i>B e</i> to show where the outer angle of the
+impulse plane commences, but the reader will see that the impulse plane
+is drawn one degree on the arc <i>p</i> below the line <i>B e</i>. We continue the
+line <i>h h</i> to represent the impulse face of the tooth, and measure the
+angle <i>B n h</i> and find it to be twenty-seven degrees. Now suppose we
+wish to delineate the entrance pallet as if not in contact with the
+escape-wheel tooth&mdash;for illustration, say, we wish the inner angle of
+the pallet to be at the point <i>v</i> on the arc <i>s</i>. We draw the radial
+line <i>B l</i> through <i>v</i>; and if we draw another line so it passes through
+the point <i>v</i> at an angle of twenty-seven degrees to <i>B l</i>, and continue
+said line so it crosses the arc <i>p</i>, we delineate the impulse face of
+our pallet.</p>
+
+<p>We measure the angle <i>i n B</i>, Fig. 92, and find it to be seventy-four
+degrees; we draw the line <i>v t</i> to the same angle with <i>v B</i>, and we
+define the inner face of our pallet in the new position. We draw a line
+parallel with <i>v t</i> from the intersection of the line <i>v y</i> with the arc
+<i>p</i>, and we define our locking face. If now we revolve the lines we have
+just drawn on the center <i>B</i> until the line <i>l B</i> coincides with the
+line <i>f B</i>, we will find the line <i>y y</i> to coincide with <i>h h</i>, and the
+line <i>v v'</i> with <i>n i</i>.</p>
+
+
+<h4>HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT.</h4>
+
+<p>We have now instructed the reader how to delineate either tooth or
+pallet in any conceivable position in which they can be related to each
+other. Probably nothing has afforded more efficient aid to practical
+mechanics than has been afforded by the graphic solution of abstruce
+mathematical problems; and if we add to this the means of correction by
+mathematical calculations which do not <a name="Page_96" id="Page_96"></a>involve the highest mathematical
+acquirements, we have approached pretty close to the actual requirements
+of the practical watchmaker.</p>
+
+<div class="figcenter"><a href="images/pict093.jpg"><img src="images/pict093-tb.jpg" alt="Fig. 93" title="Fig. 93" /></a></div>
+
+<p>To better explain what we mean, we refer the reader to Fig. 93, where we
+show preliminary drawings for delineating a lever escapement. We wish to
+ascertain by the graphic method the distance between the centers of
+action of the escape wheel and the pallet staff. We make our drawing
+very carefully to a given scale, as, for instance, the radius of the arc
+<i>a</i> is 5". After the drawing is in the condition shown at Fig. 93 we
+measure the distance on the line <i>b</i> between the points (centers) <i>A B</i>,
+and we thus by graphic means obtain a measure of the distance between <i>A
+B</i>. Now, by the use of trigonometry, we have the length of the line <i>A
+f</i> (radius of the arc <i>a</i>) and all the angles given, to find the length
+of <i>f B</i>, or <i>A B</i>, or both <i>f B</i> and <i>A B</i>. By adopting this policy we
+can verify the measurements taken from our drawings. Suppose we find by
+the graphic method that the distance between the points <i>A B</i> is 5.78",
+and by trigonometrical computation find the distance to be 5.7762". We
+know from this that there is .0038" to be accounted for somewhere; but
+for all practical purposes either measurement should be satisfactory,
+because our drawing is about thirty-eight times the actual size of the
+escape wheel of an eighteen-size movement.</p>
+
+
+<h4>HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED.</h4>
+
+<p>Let us further suppose the diameter of our actual escape wheel to be
+.26", and we were constructing a watch after the lines of our drawing.
+By "lines," in this case, we mean in the same general form and ratio of
+parts; as, for illustration, if the distance from the intersection of
+the arc <i>a</i> with the line <i>b</i> to the point <i>B</i> was one-fifteenth of the
+diameter of the escape wheel, this ratio would hold good in the actual
+watch, that is, it would be the one-fifteenth part of .26". Again,
+suppose the diameter of the escape wheel in the large drawing is 10" and
+the distance between the centers <i>A B</i> is 5.78"; to obtain the actual
+distance for the watch with the escape <a name="Page_97" id="Page_97"></a>wheel .26" diameter, we make a
+statement in proportion, thus: 10 : 5.78 :: .26 to the actual distance
+between the pivot holes of the watch. By computation we find the
+distance to be .15". These proportions will hold good in every part of
+actual construction.</p>
+
+<p>All parts&mdash;thickness of the pallet stones, length of pallet arms,
+etc.&mdash;bear the same ratio of proportion. We measure the thickness of the
+entrance pallet stone on the large drawing and find it to be .47"; we
+make a similar statement to the one above, thus: 10 : .47 :: .26 to the
+actual thickness of the real pallet stone. By computation we find it to
+be .0122". All angular relations are alike, whether in the large drawing
+or the small pallets to match the actual escape wheel .26" in diameter.
+Thus, in the pallet <i>D</i>, Fig. 93, the impulse face, as reckoned from <i>B</i>
+as a center, would occupy four degrees.</p>
+
+
+<h4>MAKE A LARGE ESCAPEMENT MODEL.</h4>
+
+<p>Reason would suggest the idea of having the theoretical keep pace and
+touch with the practical. It has been a grave fault with many writers on
+horological matters that they did not make and measure the abstractions
+which they delineated on paper. We do not mean by this to endorse the
+cavil we so often hear&mdash;"Oh, that is all right in theory, but it will
+not work in practice." If theory is right, practice must conform to it.
+The trouble with many theories is, they do not contain all the elements
+or factors of the problem.</p>
+
+<div class="figleft"><img src="images/pict094.jpg" alt="Fig. 94" title="Fig. 94" /></div>
+
+<p>Near the beginning of this treatise we advised our readers to make a
+large model, and described in detail the complete parts for such a
+model. What we propose now is to make adjustable the pallets and fork to
+such a model, in order that we can set them both right and wrong, and
+thus practically demonstrate a perfect action and also the various
+faults to which the lever escapement is subject. The pallet arms are
+shaped as shown at <i>A</i>, Fig. 94. The pallets <i>B B'</i> can be made of steel
+or stone, and for all practical purposes those made of steel answer
+quite as well, and have the advantage of being cheaper. A plate of sheet
+brass should be obtained, shaped as shown at <i>C</i>, Fig. 95. This plate is
+of thin brass, about No. 18, and on it are outlined the pallet arms
+shown at Fig. 94.<a name="Page_98" id="Page_98"></a></p>
+
+<div class="figleft"><img src="images/pict095.jpg" alt="Fig. 95" title="Fig. 95" /></div>
+<div class="figcenter"><img src="images/pict096.jpg" alt="Fig. 96" title="Fig. 96" /></div>
+
+<div class="figright"><img src="images/pict097.jpg" alt="Fig. 97" title="Fig. 97" /></div>
+<p>To make the pallets adjustable, they are set in thick disks of sheet
+brass, as shown at <i>D</i>, Figs. 95, 96 and 97. At the center of the plate
+<i>C</i> is placed a brass disk <i>E</i>, Fig. 98, which serves to support the
+lever shown at Fig. 99. This disk <i>E</i> is permanently attached to the
+plate <i>C</i>. The lever shown at Fig. 99 is attached to the disk <i>E</i> by two
+screws, which pass through the holes <i>h h</i>. If we now place the brass
+pieces <i>D D'</i> on the plate <i>C</i> in such a way that the pallets set in
+them correspond exactly to the pallets as outlined on the plate <i>C</i>, we
+will find the action of the pallets to be precisely the same as if the
+pallet arms <i>A A'</i>, Fig. 94, were employed.</p>
+
+<div class="figleft"><img src="images/pict098.jpg" alt="Fig. 98" title="Fig. 98" /></div>
+<div class="figright"><img src="images/pict099.jpg" alt="Fig. 99" title="Fig. 99" /></div>
+<p>To enable us to practically experiment with and to fully demonstrate all
+the problems of lock, draw, drop, etc., we make quite a large hole in
+<i>C</i> where the screws <i>b</i> come. To explain, if the screws <i>b b</i> were
+tapped directly into <i>C</i>, as they are shown at Fig. 95, we could only
+turn the disk <i>D</i> on the screw <i>b</i>; but if we enlarge the screw hole in
+<i>C</i> to three or four times the natural diameter, and then place the nut
+<i>e</i> under <i>C</i> to receive the screw <i>b</i>, we can then set the disks <i>D D'</i>
+and pallets <i>B B'</i> in almost any relation we choose to the escape wheel,
+and clamp the pallets fast and try the action. We show at Fig. 97 a view
+of the pallet <i>B'</i>, disk <i>D'</i> and plate <i>C</i> (seen in the direction of
+the arrow <i>c</i>) as shown in Fig. 95.</p>
+
+
+
+<h4>PRACTICAL LESSONS WITH FORK AND PALLET ACTION.</h4>
+
+<p>It will be noticed in Fig. 99 that the hole <i>g</i> for the pallet staff in
+the lever is oblong; this is to allow the lever to be shifted back and
+forth as relates to roller and fork action. We will not bother about
+this now, and only call attention to the capabilities of such
+adjustments when required. At the outset we will conceive the fork <i>F</i>
+attached to the piece <i>E</i> by two screws passing through the holes <i>h h</i>,
+Fig. 99. Such an arrangement will insure the fork and <a name="Page_99" id="Page_99"></a>roller action
+keeping right if they are put right at first. Fig. 100 will do much to
+aid in conveying a clear impression to the reader.</p>
+
+<p>The idea of the adjustable features of our escapement model is to show
+the effects of setting the pallets wrong or having them of bad form. For
+illustration, we make use of a pallet with the angle too acute, as shown
+at <i>B'''</i>, Fig. 101. The problem in hand is to find out by mechanical
+experiments and tests the consequences of such a change. It is evident
+that the angular motion of the pallet staff will be increased, and that
+we shall have to open one of the banking pins to allow the engaging
+tooth to escape. To trace out <i>all</i> the consequences of this one little
+change would require a considerable amount of study, and many drawings
+would have to be made to illustrate the effects which would naturally
+follow only one such slight change.</p>
+
+<div class="figright"><img src="images/pict100.jpg" alt="Fig. 100" title="Fig. 100" /></div>
+<p>Suppose, for illustration, we should make such a change in the pallet
+stone of the entrance pallet; we have increased the angle between the
+lines <i>k l</i> by (say) one and a half degrees; by so doing we would
+increase the lock on the exit pallet to three degrees, provided we were
+working on a basis of one and a half degrees lock; and if we pushed back
+the exit pallet so as to have the proper degree of lock (one and a half)
+on it, the tooth which would next engage the entrance pallet would not
+lock at all, but would strike the pallet on the impulse instead of on
+the locking face. Again, such a change might cause the jewel pin to
+strike the horn of the fork, as indicated at the dotted line <i>m</i>, Fig.
+99.</p>
+
+<div class="figleft"><img src="images/pict101.jpg" alt="Fig. 101" title="Fig. 101" /></div>
+<p>Dealing with such and similar abstractions by mental process requires
+the closest kind of reasoning; and if we attempt to delineate all the
+complications which follow even such a small change, we will find the
+job a lengthy one. But with a large model having adjustable parts we
+provide ourselves with the means for the very best practical solution,
+and the workman who makes and manipulates such a model will soon master
+the lever escapement.</p>
+
+
+<h4>QUIZ PROBLEMS IN THE DETACHED LEVER ESCAPEMENT.</h4>
+
+<p>Some years ago a young watchmaker friend of the writer made, at his
+suggestion, a model of the lever escapement similar to the one
+described, which he used to "play with," as he termed it&mdash;that is, <a name="Page_100" id="Page_100"></a>he
+would set the fork and pallets (which were adjustable) in all sorts of
+ways, right ways and wrong ways, so he could watch the results. A
+favorite pastime was to set every part for the best results, which was
+determined by the arc of vibration of the balance. By this sort of
+training he soon reached that degree of proficiency where one could no
+more puzzle him with a bad lever escapement than you could spoil a meal
+for him by disarranging his knife, fork and spoon.</p>
+
+<div class="figleft"><img src="images/pict102.jpg" alt="Fig. 102" title="Fig. 102" /></div>
+<p>Let us, as a practical example, take up the consideration of a short
+fork. To represent this in our model we take a lever as shown at Fig.
+99, with the elongated slot for the pallet staff at <i>g</i>. To facilitate
+the description we reproduce at Fig. 102 the figure just mentioned, and
+also employ the same letters of reference. We fancy everybody who has
+any knowledge of the lever escapement has an idea of exactly what a
+"short fork" is, and at the same time it would perhaps puzzle them a
+good deal to explain the difference between a short fork and a roller
+too small.</p>
+
+<div class="figright"><img src="images/pict103.jpg" alt="Fig. 103" title="Fig. 103" /></div>
+<p>In our practical problems, as solved on a large escapement model, say we
+first fit our fork of the proper length, and then by the slot <i>g</i> move
+the lever back a little, leaving the bankings precisely as they were.
+What are the consequences of this slight change? One of the first
+results which would display itself would be discovered by the guard pin
+failing to perform its proper functions. For instance, the guard pin
+pushed inward against the roller would cause the engaged tooth to pass
+off the locking face of the pallet, and the fork, instead of returning
+against the banking, would cause the guard pin to "ride the roller"
+during the entire excursion of the jewel pin. This fault produces a
+scraping sound in a watch. Suppose we attempt to remedy the fault by
+bending forward the guard pin <i>b</i>, as indicated by the dotted outline
+<i>b'</i> in Fig. 103, said figure being a side view of Fig. 102 seen in the
+direction of the arrow <i>a</i>. This policy would prevent the engaged pallet
+from passing off of the locking face of the pallet, but would be
+followed by the jewel pin not passing fully into the fork, but striking
+the inside face of the prong of the fork at about the point indicated by
+the dotted line <i>m</i>. We can see that if the <a name="Page_101" id="Page_101"></a>prong of the fork was
+extended to about the length indicated by the outline at <i>c</i>, the action
+would be as it should be.</p>
+
+<p>To practically investigate this matter to the best advantage, we need
+some arrangement by which we can determine the angular motion of the
+lever and also of the roller and escape wheel. To do this, we provide
+ourselves with a device which has already been described, but of smaller
+size, for measuring fork and pallet action. The device to which we
+allude is shown at Figs. 104, 105 and 106. Fig. 104 shows only the index
+hand, which is made of steel about 1/20" thick and shaped as shown. The
+jaws <i>B''</i> are intended to grasp the pallet staff by the notches <i>e</i>,
+and hold by friction. The prongs <i>l l</i> are only to guard the staff so it
+will readily enter the notch <i>e</i>. The circle <i>d</i> is only to enable us to
+better hold the hand <i>B</i> flat.</p>
+
+<div class="figcenter"><img src="images/pict104.jpg" alt="Fig. 104" title="Fig. 104" /></div>
+
+
+<h4>HOW TO MEASURE ESCAPEMENT ANGLES.</h4>
+
+<p>From the center of the notches <i>e</i> to the tip of the index hand <i>B'</i> the
+length is 2". This distance is also the radius of the index arc <i>C</i>.
+This index arc is divided into thirty degrees, with three or four
+supplementary degrees on each side, as shown. For measuring pallet
+action we only require ten degrees, and for roller action thirty
+degrees. The arc <i>C</i>, Fig. 105, can be made of brass and is about 1-1/2"
+long by 1/4" wide; said arc is mounted on a brass wire about 1/8"
+diameter, as shown at <i>k</i>, Fig. 106, which is a view of Fig. 105 seen in
+the direction of the arrow <i>i</i>. This wire <i>k</i> enters a base shown at <i>D
+E</i>, Fig. 106, which is provided with a set-screw at <i>j</i> for holding the
+index arc at the proper height to coincide with the hand <i>B</i>.</p>
+
+<div class="figleft"><img src="images/pict105.jpg" alt="Fig. 105" title="Fig. 105" /></div>
+<p>A good way to get up the parts shown in Fig. 106 is to take a disk of
+thick sheet brass about 1" in diameter and insert in it a piece of brass
+wire about 1/4" diameter and 3/8" long, through which drill axially a
+hole to receive the wire <i>k</i>. After the jaws <i>B''</i> are clamped on the
+pallet staff, we set the index arc <i>C</i> so the hand <i>B'</i> will indicate
+<a name="Page_102" id="Page_102"></a>the angular motion of the pallet staff. By placing the index hand <i>B</i>
+on the balance staff we can get at the exact angular duration of the
+engagement of the jewel pin in the fork.</p>
+
+<div class="figright"><img src="images/pict106.jpg" alt="Fig. 106" title="Fig. 106" /></div>
+<p>Of course, it is understood that this instrument will also measure the
+angles of impulse and lock. Thus, suppose the entire angular motion of
+the lever from bank to bank is ten degrees; to determine how much of
+this is lock and how much impulse, we set the index arc <i>C</i> so that the
+hand <i>B'</i> marks ten degrees for the entire motion of the fork, and when
+the escapement is locked we move the fork from its bank and notice by
+the arc <i>C</i> how many degrees the hand indicated before it passed of its
+own accord to the opposite bank. If we have more than one and a half
+degrees of lock we have too much and should seek to remedy it. How? It
+is just the answers to such questions we propose to give by the aid of
+our big model.</p>
+
+
+<h4>DETERMINATION OF "RIGHT" METHODS.</h4>
+
+<p>"Be sure you are right, then go ahead," was the advice of the celebrated
+Davie Crockett. The only trouble in applying this motto to watchmaking
+is to know when you are right. We have also often heard the remark that
+there was only one right way, but any number of wrong ways. Now we are
+inclined to think that most of the people who hold to but one right way
+are chiefly those who believe all ways but their own ways are wrong.
+Iron-bound rules are seldom sound even in ethics, and are utterly
+impracticable in mechanics.</p>
+
+<p>We have seen many workmen who had learned to draw a lever escapement of
+a given type, and lived firm in the belief that all lever escapements
+were wrong which were not made so as to conform to this certain method.
+One workman believes in equidistant lockings, another in circular
+pallets; each strong in the idea that their particular and peculiar
+method of designing a lever escapement was the only one to be tolerated.
+The writer is free to confess that he has seen lever escapements of both
+types, that is, circular pallets and equidistant lockings, which gave
+excellent results.</p>
+
+<p>Another mooted point in the lever escapement is, to decide between the
+merits of the ratchet and the club-tooth escape wheel. English makers,
+as a rule, hold to the ratchet tooth, while Continental and American
+manufacturers favor the club tooth. The chief arguments in favor of the
+ratchet tooth are: (<i>a</i>) It will run without oiling the pallets; (<i>b</i>)
+in case the escape wheel is lost or broken it <a name="Page_103" id="Page_103"></a>is more readily replaced,
+as all ratchet-tooth escape wheels are alike, either for circular
+pallets or equidistant lockings. The objections urged against it are:
+(<i>a</i>) Excessive drop; (<i>b</i>) the escape wheel, being frail, is liable to
+be injured by incompetent persons handling it; (<i>c</i>) this escapement in
+many instances does require to have the pallets oiled.</p>
+
+
+<h4>ESCAPEMENTS COMPARED.</h4>
+
+<p>(<i>a</i>) That a ratchet-tooth escape wheel requires more drop than a club
+tooth must be admitted without argument, as this form of tooth requires
+from one-half to three-fourths of a degree more drop than a club tooth;
+(<i>b</i>) as regards the frailty of the teeth we hold this as of small
+import, as any workman who is competent to repair watches would never
+injure the delicate teeth of an escape wheel; (<i>c</i>) ratchet-tooth lever
+escapements will occasionally need to have the pallets oiled. The writer
+is inclined to think that this defect could be remedied by proper care
+in selecting the stone (ruby or sapphire) and grinding the pallets in
+such a way that the escape-wheel teeth will not act against the
+foliations with which all crystalline stones are built up.</p>
+
+<p>All workmen who have had an extended experience in repair work are well
+aware that there are some lever escapements in which the pallets
+absolutely require oil; others will seem to get along very nicely
+without. This applies also to American brass club-tooth escapements;
+hence, we have so much contention about oiling pallets. The writer does
+not claim to know positively that the pallet stones are at fault because
+some escapements need oiling, but the fact must admit of explanation
+some way, and is this not at least a rational solution? All persons who
+have paid attention to crystallography are aware that crystals are built
+up, and have lines of cleavage. In the manufacture of hole jewels, care
+must be taken to work with the axis of crystallization, or a smooth hole
+cannot be obtained.</p>
+
+<p>The advantages claimed for the club-tooth escapement are many; among
+them may be cited (<i>a</i>) the fact that it utilizes a greater arc of
+impulse of the escape wheel; (<i>b</i>) the impulse being divided between the
+tooth and the pallet, permits greater power to be utilized at the close
+of the impulse. This feature we have already explained. It is no doubt
+true that it is more difficult to match a set of pallets with an escape
+wheel of the club-tooth order than with a ratchet tooth; still the
+writer thinks that this objection <a name="Page_104" id="Page_104"></a>is of but little consequence where a
+workman knows exactly what to do and how to do it; in other words, is
+sure he is right, and can then go ahead intelligently.</p>
+
+<p>It is claimed by some that all American escape wheels of a given grade
+are exact duplicates; but, as we have previously stated, this is not
+exactly the case, as they vary a trifle. So do the pallet jewels vary a
+little in thickness and in the angles. Suppose we put in a new escape
+wheel and find we have on the entrance pallet too much drop, that is,
+the tooth which engaged this pallet made a decided movement forward
+before the tooth which engaged the exit pallet encountered the locking
+face of said pallet. If we thoroughly understand the lever escapement we
+can see in an instant if putting in a thicker pallet stone for entrance
+pallet will remedy the defect. Here again we can study the effects of a
+change in our large model better than in an escapement no larger than is
+in an ordinary watch.</p>
+
+
+<h4>HOW TO SET PALLET STONES.</h4>
+
+<p>There have been many devices brought forward to aid the workman in
+adjusting the pallet stones to lever watches. Before going into the
+details of any such device we should thoroughly understand exactly what
+we desire to accomplish. In setting pallet stones we must take into
+consideration the relation of the roller and fork action. As has already
+been explained, the first thing to do is to set the roller and fork
+action as it should be, without regard in a great degree to pallet
+action.</p>
+
+<div class="figleft"><img src="images/pict107.jpg" alt="Fig. 107" title="Fig. 107" /></div>
+
+<p>To explain, suppose we have a pallet stone to set in a full-plate
+movement. The first thing to do is to close the bankings so that the
+jewel pin will not pass out of the slot in the fork on either side; then
+gradually open the bankings until the jewel pin will pass out. This will
+be understood by inspecting Fig. 107, where <i>A A'</i> shows a lever fork as
+if in contact with both banks, and the jewel pin, represented at <i>B
+B''</i>, just passes the angle <i>a c'</i> of the fork. The circle described by
+the jewel pin <i>B</i> is indicated by the arc <i>e</i>. It is well to put a
+slight friction under the balance rim, in order that we can try the
+freedom of the guard pin. As a rule, all the guard pin needs is to be
+free and not touch the roller. The entire point, as far as setting the
+fork and bankings is concerned, is to have the <a name="Page_105" id="Page_105"></a>fork and roller action
+sound. For all ordinary lever escapements the angular motion of the
+lever banked in as just described should be <i>about</i> ten degrees. As
+explained in former examples, if the fork action is entirely sound and
+the lever only vibrates through an arc of nine degrees, it is quite as
+well to make the pallets conform to this arc as to make the jewel pin
+carry the fork through full ten degrees. Again, if the lever vibrates
+through eleven degrees, it is as well to make the pallets conform to
+this arc.</p>
+
+<p>The writer is well aware that many readers will cavil at this idea and
+insist that the workman should bring all the parts right on the basis of
+ten degrees fork and lever action. In reply we would say that no
+escapement is perfect, and it is the duty of the workman to get the best
+results he can for the money he gets for the job. In the instance given
+above, of the escapement with nine degrees of lever action, when the
+fork worked all right, if we undertook to give the fork the ten degrees
+demanded by the stickler for accuracy we would have to set out the jewel
+pin or lengthen the fork, and to do either would require more time than
+it would to bring the pallets to conform to the fork and roller action.
+It is just this knowing how and the decision to act that makes the
+difference in the workman who is worth to his employer twelve or
+twenty-five dollars per week.</p>
+
+<p>We have described instruments for measuring the angle of fork and pallet
+action, but after one has had experience he can judge pretty nearly and
+then it is seldom necessary to measure the angle of fork action as long
+as it is near the proper thing, and then bring the pallets to match the
+escape wheel after the fork and roller action is as it should be&mdash;that
+is, the jewel pin and fork work free, the guard pin has proper freedom,
+and the fork vibrates through an arc of about ten degrees.</p>
+
+<p>Usually the workman can manipulate the pallets to match the escape wheel
+so that the teeth will have the proper lock and drop at the right
+instant, and again have the correct lock on the next succeeding pallet.
+The tooth should fall but a slight distance before the tooth next in
+action locks it, because all the angular motion the escape wheel makes
+except when in contact with the pallets is just so much lost power,
+which should go toward giving motion to the balance.</p>
+
+<div class="figleft"><img src="images/pict108.jpg" alt="Fig. 108" title="Fig. 108" /></div>
+
+<p>There seems to be a little confusion in the use of the word "drop" in
+horological phrase, as it is used to express the act of <a name="Page_106" id="Page_106"></a>parting of the
+tooth with the pallet. The idea will be seen by inspecting Fig. 108,
+where we show the tooth <i>D</i> and pallet <i>C</i> as about parting or dropping.
+When we speak of "banking up to the drop" we mean we set the banking
+screws so that the teeth will just escape from each pallet. By the term
+"fall" we mean the arc the tooth passes through before the next pallet
+is engaged. This action is also illustrated at Fig. 108, where the tooth
+<i>D</i>, after dropping from the pallet <i>C</i>, is arrested at the position
+shown by the dotted outline. We designate this arc by the term "fall,"
+and we measure this motion by its angular extent, as shown by the dotted
+radial lines <i>i f</i> and <i>i g</i>. As we have explained, this fall should
+only extend through an arc of one and a half degrees, but by close
+escapement matching this arc can be reduced to one degree, or even a
+trifle less.</p>
+
+<p>We shall next describe an instrument for holding the escape wheel and
+pallets while adjusting them. As shown at Fig. 107, the fork <i>A'</i> is
+banked a little close and the jewel pin as shown would, in some
+portions, rub on <i>C'</i>, making a scraping sound.</p>
+
+
+<h4>HOW TO MAKE AN ESCAPEMENT MATCHING TOOL.</h4>
+
+<div class="figright"><img src="images/pict109.jpg" alt="Fig. 109" title="Fig. 109" /></div>
+
+<p>A point has now been reached where we can use an escapement matcher to
+advantage. There are several good ones on the market, but we can make
+one very cheaply and also add our own improvements. In making one, the
+first thing to be provided is a movement holder. Any of the three-jaw
+types of such holders will answer, provided the jaws hold a movement
+plate perfectly parallel with the bed of the holder. This will be better
+understood by inspecting Fig. 109, which is a side view of a device of
+this kind seen edgewise in elevation. In this <i>B</i> represents the bed
+plate, which supports three swing jaws, shown at <i>C</i>, Figs. 109 and 110.
+The watch plate is indicated by the parallel dotted lines <i>A</i>, Fig. 109.
+The seat <i>a</i> of the swing jaws <i>C</i> must hold the watch plate <i>A</i> exactly
+parallel with the bed plate <i>B</i>. In the cheap movement holders these
+seats (<i>a</i>) are apt to be of irregular heights, and <a name="Page_107" id="Page_107"></a>must be corrected
+for our purpose. We will take it for granted that all the seats <i>a</i> are
+of precisely the same height, measured from <i>B</i>, and that a watch plate
+placed in the jaws <i>C</i> will be held exactly parallel with the said bed
+<i>B</i>. We must next provide two pillars, shown at <i>D E</i>, Figs. 109 and
+111. These pillars furnish support for sliding centers which hold the
+top pivots of the escape wheel and pallet staff while we are testing the
+depths and adjusting the pallet stones. It will be understood that these
+pillars <i>D E</i> are at right angles to the plane of the bed <i>B</i>, in order
+that the slides like <i>G N</i> on the pillars <i>D E</i> move exactly vertical.
+In fact, all the parts moving up and down should be accurately made, so
+as not to destroy the depths taken from the watch plate <i>A</i>. Suppose, to
+illustrate, that we place the plate <i>A</i> in position as shown, and insert
+the cone point <i>n</i>, Figs. 109 and 112, in the pivot hole for the pallet
+staff, adjusting the slide <i>G N</i> so that the cone point rests accurately
+in said pivot hole. It is further demanded that the parts <i>I H F G N D</i>
+be so constructed and adjusted that the sliding center <i>I</i> moves truly
+vertical, and that we can change ends with said center <i>I</i> and place the
+hollow cone end <i>m</i>, Fig. 112, so it will receive the top pivot of the
+pallet staff and hold it exactly upright.</p>
+<div class="figcenter"><img src="images/pict110.jpg" alt="Fig. 110" title="Fig. 110" /></div>
+
+
+
+
+<div class="figleft"><img src="images/pict111.jpg" alt="Fig. 111" title="Fig. 111" /></div>
+<div class="figright"><img src="images/pict112.jpg" alt="Fig. 112" title="Fig. 112" /></div>
+<p>The idea of the sliding center <i>I</i> is to perfectly supply the place of
+the opposite plate of the watch and give us exactly the same practical
+depths as if the parts were in their place between the plates of the
+movement. The foot of the pillar <i>D</i> has a flange attached, as shown at
+<i>f</i>, which aids in holding it perfectly upright. It is well to cut a
+screw on <i>D</i> at <i>D'</i>, and screw the flange <i>f</i> on such screw and then
+turn the lower face of <i>f</i> flat to aid in having the pillar <i>D</i>
+perfectly upright.</p>
+
+
+<h4>DETAILS OF FITTING UP ESCAPEMENT MATCHER.</h4>
+
+<div class="figleft"><img src="images/pict113.jpg" alt="Fig. 113" title="Fig. 113" /></div>
+<div class="figright"><img src="images/pict114.jpg" alt="Fig. 114" title="Fig. 114" /></div>
+
+<p>It is well to fit the screw <i>D'</i> loosely, so that the flange <i>f</i> will
+come perfectly flat with the upper surface of the base plate <i>B</i>. The
+slide <i>G N</i> on the pillar <i>D</i> can be made of two pieces of small brass
+tube, one fitting the pillar <i>D</i> and the other the bar <i>F</i>. The slide <i>G
+N</i> is held in position by the set screw <i>g</i>, and the rod <i>F</i> by the set
+screw <i>h</i>.<a name="Page_108" id="Page_108"></a></p>
+
+<p>The piece <i>H</i> can be permanently attached to the rod <i>F</i>. We show
+separate at Figs. 113 and 114 the slide <i>G N</i> on an enlarged scale from
+Fig. 109. Fig. 114 is a view of Fig. 113 seen in the direction of the
+arrow <i>e</i>. All joints and movable parts should work free, in order that
+the center <i>I</i> may be readily and accurately set. The parts <i>H F</i> are
+shown separate and enlarged at Figs. 115 and 116. The piece <i>H</i> can be
+made of thick sheet brass securely attached to <i>F</i> in such a way as to
+bring the V-shaped groove at right angles to the axis of the rod <i>F</i>. It
+is well to make the rod <i>F</i> about 1/8" in diameter, while the sliding
+center <i>I</i> need not be more than 1/16" in diameter. The cone point <i>n</i>
+should be hardened to a spring temper and turned to a true cone in an
+accurately running wire chuck.</p>
+
+<div class="figleft"><img src="images/pict115.jpg" alt="Fig. 115" title="Fig. 115" /></div>
+<div class="figright"><img src="images/pict116.jpg" alt="Fig. 116" title="Fig. 116" /></div>
+
+
+<p>The hollow cone end <i>m</i> of <i>I</i> should also be hardened, but this is best
+done after the hollow cone is turned in. The hardening of both ends
+should only be at the tips. The sliding center <i>I</i> can be held in the
+V-shaped groove by two light friction springs, as indicated at the
+dotted lines <i>s s</i>, Fig. 115, or a flat plate of No. 24 or 25 sheet
+brass of the size of <i>H</i> can be employed, as shown at Figs. 116 and 117,
+where <i>o</i> represents the plate of No. 24 brass, <i>p p</i> the small screws
+attaching the plate <i>o</i> to <i>H</i>, and <i>k</i> a clamping screw to fasten <i>I</i>
+in position. It will be found that the two light springs <i>s s</i>, Fig. 115
+will be the most satisfactory. The wire legs, shown at <i>L</i>, will aid in
+making the device set steady. The pillar <i>E</i> is provided with the same
+slides and other parts as described and illustrated as attached to <i>D</i>.
+The position of the pillars <i>D</i> and <i>E</i> are indicated at Fig. 110.</p>
+
+<div class="figcenter"><img src="images/pict118.jpg" alt="Fig. 118" title="Fig. 118" /></div>
+
+<div class="figleft"><img src="images/pict117.jpg" alt="Fig. 117" title="Fig. 117" /></div>
+<div class="figright"><img src="images/pict119.jpg" alt="Fig. 119" title="Fig. 119" /></div>
+<p>We will next tell how to flatten <i>F</i> to keep <i>H</i> exactly vertical. To
+aid in explanation, we will show (enlarged) at Fig. 118 the bar <i>F</i>
+shown in Fig. 109. In flattening <a name="Page_109" id="Page_109"></a>such pieces to prevent turning, we
+should cut away about two-fifths, as shown at Fig. 119, which is an end
+view of Fig. 118 seen in the direction of the arrow <i>c</i>. In such
+flattening we should not only cut away two-fifths at one end, but we
+must preserve this proportion from end to end. To aid in this operation
+we make a fixed gage of sheet metal, shaped as shown at <i>I</i>, Fig. 120.</p>
+
+
+<h4>ESCAPEMENT MATCHING DEVICE DESCRIBED.</h4>
+
+<div class="figleft"><img src="images/pict120.jpg" alt="Fig. 120" title="Fig. 120" /></div>
+<div class="figright"><img src="images/pict121.jpg" alt="Fig. 121" title="Fig. 121" /></div>
+
+<p>In practical construction we first file away about two-fifths of <i>F</i> and
+then grind the flat side on a glass slab to a flat, even surface and, of
+course, equal thickness from end to end. We reproduce the sleeve <i>G</i> as
+shown at Fig. 113 as if seen from the left and in the direction of the
+axis of the bar <i>F</i>. To prevent the bar <i>F</i> turning on its axis, we
+insert in the sleeve <i>G</i> a piece of wire of the same size as <i>F</i> but
+with three-fifths cut away, as shown at <i>y</i>, Fig. 121. This piece <i>y</i> is
+soldered in the sleeve <i>G</i> so its flat face stands vertical. To give
+service and efficiency to the screw <i>h</i>, we thicken the side of the
+sleeve <i>F</i> by adding the stud <i>w</i>, through which the screw <i>h</i> works. A
+soft metal plug goes between the screw <i>h</i> and the bar <i>F</i>, to prevent
+<i>F</i> being cut up and marred. It will be seen that we can place the top
+plate of a full-plate movement in the device shown at Fig. 109 and set
+the vertical centers <i>I</i> so the cone points <i>n</i> will rest in the pivot
+holes of the escape wheel and pallets. It is to be understood that the
+lower side of the top plate is placed uppermost in the movement holder.</p>
+
+<p>If we now reverse the ends of the centers <i>I</i> and let the pivots of the
+escape wheel and pallet staff rest in the hollow cones of these centers
+<i>I</i>, we have the escape wheel and pallets in precisely the same position
+and relation to each other as if the lower plate was in position. It is
+further to be supposed that the balance is in place and the cock screwed
+down, although the presence of the balance is not absolutely necessary
+if the banking screws are set as directed, that is, so the jewel pin
+will just freely pass in and out of the fork.</p>
+
+
+<h4>HOW TO SET PALLET STONES.</h4>
+
+<p>We have now come to setting or manipulating the pallet stones so they
+will act in exact conjunction with the fork and roller. To do this we
+need to have the shellac which holds the pallet stones <a name="Page_110" id="Page_110"></a>heated enough to
+make it plastic. The usual way is to heat a piece of metal and place it
+in close proximity to the pallets, or to heat a pair of pliers and clamp
+the pallet arms to soften the cement.</p>
+
+<p>Of course, it is understood that the movement holder cannot be moved
+about while the stones are being manipulated. The better way is to set
+the movement holder on a rather heavy plate of glass or metal, so that
+the holder will not jostle about; then set the lamp so it will do its
+duty, and after a little practice the setting of a pair of pallet stones
+to perfectly perform their functions will take but a few minutes. In
+fact, if the stones will answer at all, three to five minutes is as much
+time as one could well devote to the adjustment. The reader will see
+that if the lever is properly banked all he has to do is to set the
+stones so the lock, draw and drop are right, when the entire escapement
+is as it should be, and will need no further trial or manipulating.</p>
+
+
+
+<hr style="width: 65%;" /><p><a name="Page_111" id="Page_111"></a></p>
+<h2>CHAPTER II.</h2>
+
+<h3>THE CYLINDER ESCAPEMENT.</h3>
+
+
+<p>There is always in mechanical matters an underlying combination of
+principles and relations of parts known as "theory." We often hear the
+remark made that such a thing may be all right in theory, but will not
+work in practice. This statement has no foundation in fact. If a given
+mechanical device accords strictly with theory, it will come out all
+right practically. <i>Mental conceptions</i> of a machine are what we may
+term their theoretical existence.</p>
+
+<p>When we make drawings of a machine mentally conceived, we commence its
+mechanical construction, and if we make such drawings to scale, and add
+a specification stating the materials to be employed, we leave only the
+merest mechanical details to be carried out; the brain work is done and
+only finger work remains to be executed.</p>
+
+<p>With these preliminary remarks we will take up the consideration of the
+cylinder escapement invented by Robert Graham about the year 1720. It is
+one of the two so-called frictional rest dead-beat escapements which
+have come into popular use, the other being the duplex. Usage, or, to
+put it in other words, experience derived from the actual manufacture of
+the cylinder escapement, settled the best forms and proportions of the
+several parts years ago. Still, makers vary slightly on certain lines,
+which are important for a man who repairs such watches to know and be
+able to carry out, in order to put them in a condition to perform as
+intended by the manufacturers. It is not knowing these lines which
+leaves the average watchmaker so much at sea. He cuts and moves and
+shifts parts about to see if dumb luck will not supply the correction he
+does not know how to make. This requisite knowledge does not consist so
+much in knowing how to file or grind as it does in discriminating where
+such application of manual dexterity is to be applied. And right here
+let us make a remark to which we will call attention again later on. The
+point of this remark lies in the question&mdash;How many of the so-called
+practical watchmakers could tell you what proportion of a cylinder
+should be cut away from the half shell? How many could explain the
+difference between the<a name="Page_112" id="Page_112"></a> "real" and "apparent" lift? Comparatively few,
+and yet a knowledge of these things is as important for a watchmaker as
+it is for a surgeon to understand the action of a man's heart or the
+relations of the muscles to the bones.</p>
+
+<h4>ESSENTIAL PARTS OF THE CYLINDER ESCAPEMENT.</h4>
+
+<p>The cylinder escapement is made up of two essential parts, viz.: the
+escape wheel and the cylinder. The cylinder escape wheel in all modern
+watches has fifteen teeth, although Saunier, in his "Modern Horology,"
+delineates a twelve-tooth wheel for apparently no better reason than
+because it was more easily drawn. We, in this treatise, will consider
+both the theoretical action and the practical construction, but more
+particularly the repair of this escapement in a thorough and complete
+manner.</p>
+
+<p>At starting out, we will first agree on the names of the several parts
+of this escapement, and to aid us in this we will refer to the
+accompanying drawings, in which Fig. 122 is a side elevation of a
+cylinder complete and ready to have a balance staked on to it. Fig. 123
+shows the cylinder removed from the balance collet. Figs. 124 and 125
+show the upper and lower plugs removed from the cylinder. Fig. 126 is a
+horizontal section of Fig. 122 on the line <i>i</i>. Fig. 127 is a side view
+of one tooth of a cylinder escape wheel as if seen in the direction of
+the arrow <i>f</i> in Fig. 126. Fig. 128 is a top view of two teeth of a
+cylinder escape wheel. The names of the several parts usually employed
+are as follows:</p>
+
+
+<table border="0" width="60%" cellpadding="4" cellspacing="0" summary="Naming of the parts of the cylinder escapement">
+<tr><td align='right'><i>A.</i></td><td align='left'>&mdash;Upper or Main Shell.</td></tr>
+<tr><td align='right'><i>A'.</i></td><td align='left'>&mdash;Half Shell.</td></tr>
+<tr><td align='right'><i>A''.</i></td><td align='left'>&mdash;Column.</td></tr>
+<tr><td align='right'><i>A'''.</i></td><td align='left'>&mdash;Small Shell.</td></tr>
+<tr><td align='right'><i>B B' B''.</i></td><td align='left'>&mdash;Balance Collet.</td></tr>
+<tr><td align='right'><i>G.</i></td><td align='left'>&mdash;Upper Plug.</td></tr>
+<tr><td align='right'><i>H.</i></td><td align='left'>&mdash;Lower Plug.</td></tr>
+<tr><td align='right'><i>g.</i></td><td align='left'>&mdash;Entrance Lip of Cylinder.</td></tr>
+<tr><td align='right'><i>h.</i></td><td align='left'>&mdash;Exit Lip of Cylinder.</td></tr>
+<tr><td align='right'><i>c.</i></td><td align='left'>&mdash;Banking Slot.</td></tr>
+<tr><td align='right'><i>C.</i></td><td align='left'>&mdash;Tooth.</td></tr>
+<tr><td align='right'><i>D.</i></td><td align='left'>&mdash;U arm.</td></tr>
+<tr><td align='right'><i>E.</i></td><td align='left'>&mdash;Stalk of Pillar.</td></tr>
+<tr><td align='right'><i>I.</i></td><td align='left'>&mdash;U space</td></tr>
+<tr><td align='right'><i>l.</i></td><td align='left'>&mdash;Point of Tooth.</td></tr>
+<tr><td align='right'><i>k.</i></td><td align='left'>&mdash;Heel of Tooth.</td></tr>
+</table>
+
+<p>The cylinder escapement has two engagements or actions, during the
+passage of each tooth; that is, one on the outside of the cylinder and
+one on the inside of the shell. As we shall show later on, the cylinder
+escapement is the only positively dead-beat escapement in use, all
+others, even the duplex, having a slight recoil during the process of
+escaping.</p>
+
+<p>When the tooth of a cylinder escape wheel while performing its
+functions, strikes the cylinder shell, it rests dead on the outer or
+<a name="Page_113" id="Page_113"></a>inner surface of the half shell until the action of the balance spring
+has brought the lip of the cylinder so that the impulse face of the
+tooth commences to impart motion or power to the balance.</p>
+
+<hr style="width: 65%;" />
+
+<div class="figleft"><img src="images/pict122.jpg" alt="Fig. 122" title="Fig. 122" /></div>
+<div class="figright"><img src="images/pict123.jpg" alt="Fig. 123" title="Fig. 123" /></div>
+
+<div class="figleft"><img src="images/pict124.jpg" alt="Fig. 124" title="Fig. 124" /></div>
+<div class="figright"><img src="images/pict125.jpg" alt="Fig. 125" title="Fig. 125" /></div>
+
+
+<div class="figleft"><img src="images/pict126.jpg" alt="Fig. 126" title="Fig. 126" /></div>
+<div class="figright"><img src="images/pict127.jpg" alt="Fig. 127" title="Fig. 127" /></div>
+<div class="figleft"><img src="images/pict128.jpg" alt="Fig. 128" title="Fig. 128" /></div>
+
+<hr style="width: 65%;" />
+
+<p>Most writers on horological matters term this act the "lift," which name
+was no doubt acquired when escapements were chiefly confined to pendulum
+clocks. Very little thought on the matter will show any person who
+inspects Fig. 126 that if the tooth <i>C</i> is released or escapes from the
+inside of the half shell of the cylinder <i>A</i>, said cylinder must turn or
+revolve a little in the direction of the arrow <i>j</i>, and also that the
+next succeeding tooth of the escape wheel will engage the cylinder on
+the outside of the half shell, falling on the dead or neutral portion of
+said cylinder, to rest until the hairspring causes the cylinder to turn
+in the opposite direction and permitting the tooth now resting on the
+outside of the cylinder to assume the position shown on the drawing.</p>
+
+<p>The first problem in our consideration of the theoretical action of the
+cylinder escapement, is to arrange the parts we have described so as to
+have these two movements of the escape wheel of like angular values. To
+explain what we mean by this, we must premise by <a name="Page_114" id="Page_114"></a>saying, that as our
+escape wheel has fifteen teeth and we make each tooth give two impulses
+in alternate directions we must arrange to have these half-tooth
+movements exactly alike, or, as stated above, of equal angular values;
+and also each impulse must convey the same power or force to the
+balance. All escape wheels of fifteen teeth acting by half impulses must
+impel the balance during twelve degrees (minus the drop) of escape-wheel
+action; or, in other words, when a tooth passes out of the cylinder from
+the position shown at Fig. 126, the form of the impulse face of the
+tooth and the shape of the exit lip of the cylinder must be such during
+twelve degrees (less the drop) of the angular motion of the escape
+wheel. The entire power of such an escape wheel is devoted to giving
+impulse to the balance.</p>
+
+<p>The extent of angular motion of the balance during such impulse is, as
+previously stated, termed the "lifting angle." This "lifting angle" is
+by horological writers again divided into real and apparent lifts. This
+last division is only an imaginary one, as the real lift is the one to
+be studied and expresses the arc through which the impulse face of the
+tooth impels the balance during the act of escaping, and so, as we shall
+subsequently show, should no more be counted than in the detached lever
+escapement, where a precisely similar condition exists, but is never
+considered or discussed.</p>
+
+<p>We shall for the present take no note of this lifting angle, but confine
+ourselves to the problem just named, of so arranging and designing our
+escape-wheel teeth and cylinder that each half of the tooth space shall
+give equal impulses to the balance with the minimum of drop. To do this
+we will make a careful drawing of an escape-wheel tooth and cylinder on
+an enlarged scale; our method of making such drawings will be on a new
+and original system, which is very simple yet complete.</p>
+
+
+<h4>DRAWING THE CYLINDER ESCAPEMENT.</h4>
+
+<p>All horological&mdash;and for that matter all mechanical&mdash;drawings are based
+on two systems of measurements: (1) Linear extent; (2) angular movement.
+For the first measurement we adopt the inch and its decimals; for the
+second we adopt degrees, minutes and seconds. For measuring the latter
+the usual plan is to employ a protractor, which serves the double
+purpose of enabling us to lay off and delineate any angle and also to
+measure any angle obtained by the graphic method, and it is thus by this
+graphic method we <a name="Page_115" id="Page_115"></a>propose to solve very simply some of the most
+abstruce problems in horological delineations. As an instance, we
+propose to draw our cylinder escapement with no other instruments than a
+steel straight-edge, showing one-hundredths of an inch, and a pair of
+dividers; the degree measurement being obtained from arcs of sixty
+degrees of radii, as will be explained further on.</p>
+
+<p>In describing the method for drawing the cylinder escapement we shall
+make a radical departure from the systems usually laid down in
+text-books, and seek to simplify the formulas which have heretofore been
+given for such delineations. In considering the cylinder escapement we
+shall pursue an analytical course and strive to build up from the
+underlying principles. In the drawings for this purpose we shall
+commence with one having an escape wheel of 10" radius, and our first
+effort will be the primary drawing shown at Fig. 129. Here we establish
+the point <i>A</i> for the center of our escape wheel, and from this center
+sweep the short arc <i>a a</i> with a 10" radius, to represent the
+circumference of our escape wheel. From <i>A</i> we draw the vertical line <i>A
+B</i>, and from the intersection of said line with the arc <i>a a</i> we lay off
+twelve degree spaces on each side of the line <i>A B</i> on said arc <i>a</i> and
+establish the points <i>b c</i>. From <i>A</i> as a center we draw through the
+points <i>b c</i> the radial lines <i>b' c'</i>.</p>
+
+<p>To define the face of the incline to the teeth we set our dividers to
+the radius of any of the convenient arcs of sixty degrees which we have
+provided, and sweep the arc <i>t t</i>. From the intersection of said arc
+with the line <i>A b'</i> we lay off on said arc sixty-four degrees and
+establish the point <i>g</i> and draw the line <i>b g</i>. Why we take sixty-four
+degrees for the angle <i>A b g</i> will be explained later on, when we are
+discussing the angular motion of the cylinder. By dividing the eleventh
+degree from the point <i>b</i> on the arc <i>a a</i> into thirds and taking two of
+them, we establish the point <i>y</i> and draw the radial line <i>A y'</i>. Where
+this line <i>A y'</i> intersects the line <i>b g</i> we name the point <i>n</i>, and in
+it is located the point of the escape-wheel tooth. That portion of the
+line <i>b g</i> which lies between the points <i>b</i> and <i>n</i> represents the
+measure of the inner diameter of the cylinder, and also the length of
+the chord of the arc which rounds the impulse face of the tooth. We
+divide the space <i>b n</i> into two equal portions and establish the point
+<i>e</i>, which locates the position of the center of the cylinder. From <i>A</i>
+as a center and through the point <i>e</i> we sweep the arc <i>e' e'</i>, and it
+is on this line that the points establishing the center of the cylinder
+will in every instance be located. From <i>A</i> as <a name="Page_116" id="Page_116"></a>a center, through the
+point <i>n</i> we sweep the arc <i>k</i>, and on this line we locate the points of
+the escape-wheel teeth. For delineating the curved impulse faces of the
+escape-wheel teeth we draw from the point <i>e</i> and at right angles to the
+line <i>b g</i> the line <i>e o</i>. We next take in our dividers the radius of
+the arc <i>k</i>, and setting one leg at either of the points <i>b</i> or <i>n</i>,
+establish with the other leg the point <i>p'</i> on the line <i>e o</i>, and from
+the point <i>p'</i> as a center we sweep the arc <i>b v n</i>, which defines the
+curve of the impulse faces of the teeth. From <i>A</i> as a center through
+the point <i>p'</i> we sweep the arc <i>p</i>, and in all instances where we
+desire to delineate the curved face of a tooth we locate either the
+position of the point or the heel of such tooth, and setting one leg of
+our dividers at such point, the other leg resting on the arc <i>p</i>, we
+establish the center from which to sweep the arc defining the face of
+said tooth.</p>
+
+
+<h4>ADVANTAGES GAINED IN SHAPING.</h4>
+
+<p>The reason for giving a curved form to the impulse face of the teeth of
+cylinder escape wheels are somewhat intricate, and the problem involves
+several factors. That there are advantages in so shaping the incline or
+impulse face is conceded, we believe, by all recent manufacturers. The
+chief benefit derived from such curved impulse faces will be evident
+after a little thought and study of the situation and relation of parts
+as shown in Fig. 129. It will be seen on inspection that the angular
+motion imparted to the cylinder by the impulse face of the tooth when
+curved as shown, is greater during the first half of the twelve degrees
+of escape-wheel action than during the last half, thus giving the escape
+wheel the advantage at the time the balance spring increases its
+resistance to the passage of the escape-wheel tooth across the lip of
+the cylinder. Or, in other words, as the ratio of resistance of the
+balance spring increases, in a like ratio the curved form of the impulse
+face of the tooth gives greater power to the escape-wheel action in
+proportion to the angular motion of the escape wheel. Hence, in actual
+service it is found that cylinder watches with curved impulse planes to
+the escape-wheel teeth are less liable to set in the pocket than the
+teeth having straight impulse faces.</p>
+
+
+<h4>THE OUTER DIAMETER OF THE CYLINDER.</h4>
+
+<div class="figcenter"><a href="images/pict129.jpg"><img src="images/pict129-tb.jpg" alt="Fig. 129" title="Fig. 129" /></a></div>
+<p>To define the remainder of the form of our escape-wheel tooth we will
+next delineate the heel. To do this we first define the outer <a name="Page_117" id="Page_117"></a><a name="Page_118" id="Page_118"></a>diameter
+of our cylinder, which is the extent from the point <i>n</i> to <i>c</i>, and
+after drawing the line <i>n c</i> we halve the space and establish the point
+<i>x</i>, from which point as a center we sweep the circle <i>w w</i>, which
+defines the outer circumference of our cylinder. With our dividers set
+to embrace the extent from the point <i>n</i> to the point <i>c</i> we set one leg
+at the point <i>b</i>, and with the other leg establish on the arc <i>k</i> the
+point <i>h</i>. We next draw the line <i>b h</i>, and from the point <i>b</i> draw the
+line <i>b f</i> at right angle to the line <i>b h</i>. Our object for drawing
+these lines is to define the heel of our escape-wheel tooth by a right
+angle line tangent to the circle <i>w</i>, from the point <i>b</i>; which circle
+<i>w</i> represents the curve of the outer circumference of the cylinder. We
+shape the point of the tooth as shown to give it the proper stability,
+and draw the full line <i>j</i> to a curve from the center <i>A</i>. We have now
+defined the form of the upper face of the tooth. How to delineate the U
+arms will be taken up later on, as, in the present case, the necessary
+lines would confuse our drawing.</p>
+
+<p>We would here take the opportunity to say that there is a great latitude
+taken by makers as regards the extent of angular impulse given to the
+cylinder, or, as it is termed, the "actual lift." This latitude governs
+to a great extent the angle <i>A b g</i>, which we gave as sixty-four degrees
+in our drawing. It is well to understand that the use of sixty-four
+degrees is based on no hard-and-fast rules, but varies back and forth,
+according as a greater or lesser angle of impulse or lift is employed.</p>
+
+<p>In practical workshop usage the impulse angle is probably more easily
+estimated by the ratio between the diameter of the cylinder and the
+measured (by lineal measure) height of the impulse plane. Or, to be more
+explicit, we measure the radial extent from the center <i>A</i> between the
+arcs <i>a k</i> on the line <i>A b</i>, and use this for comparison with the outer
+diameter of the cylinder.</p>
+
+<p>We can readily see that as we increase the height of the heel of the
+impulse face of our tooth we must also increase the angle of impulse
+imparted to the cylinder. With the advantages of accurate micrometer
+calipers now possessed by the horological student it is an easy matter
+to get at the angular extent of the real lift of any cylinder. The
+advantage of such measuring instruments is also made manifest in
+determining when the proper proportion of the cylinder is cut away for
+the half shell.</p>
+
+<div class="figcenter"><a href="images/pict130.jpg"><img src="images/pict130-tb.jpg" alt="Fig. 130" title="Fig. 130" /></a></div>
+
+<p>In the older methods of watchmaking it was a very common rule to say,
+let the height of the incline of the tooth be one-seventh <a name="Page_119" id="Page_119"></a><a name="Page_120" id="Page_120"></a>of the outer
+diameter of the cylinder, and at the same time the trade was furnished
+with no tools except a clumsy douzieme gage; but with micrometer
+calipers which read to one-thousandths of an inch such rules can be
+definitely carried into effect and not left to guess work. Let us
+compare the old method with the new: Suppose we have a new cylinder to
+put in; we have the old escape wheel, but the former cylinder is gone.
+The old-style workman would take a round broach and calculate the size
+of the cylinder by finding a place where the broach would just go
+between the teeth, and the size of the broach at this point was supposed
+to be the outer diameter of the cylinder. By our method we measure the
+diameter of the escape wheel in thousandths of an inch, and from this
+size calculate exactly what the diameter of the new cylinder should be
+in thousandths of an inch. Suppose, to further carry out our comparison,
+the escape wheel which is in the watch has teeth which have been stoned
+off to permit the use of a cylinder which was too small inside, or, in
+fact, of a cylinder too small for the watch: in this case the broach
+system would only add to the trouble and give us a cylinder which would
+permit too much inside drop.</p>
+
+
+<h4>DRAWING A CYLINDER.</h4>
+
+<p>We have already instructed the pupil how to delineate a cylinder escape
+wheel tooth and we will next describe how to draw a cylinder. As already
+stated, the center of the cylinder is placed to coincide with the center
+of the chord of the arc which defines the impulse face of the tooth.
+Consequently, if we design a cylinder escape wheel tooth as previously
+described, and setting one leg of our compasses at the point <i>e</i> which
+is situated at the center of the chord of the arc which defines the
+impulse face of the tooth and through the points <i>d</i> and <i>b</i> we define
+the inside of our cylinder. We next divide the chord <i>d b</i> into eight
+parts and set our dividers to five of these parts, and from <i>e</i> as a
+center sweep the circle <i>h</i> and define the outside of our cylinder. From
+<i>A</i> as a center we draw the radial line <i>A e'</i>. At right angles to the
+line <i>A e'</i> and through the point <i>e</i> we draw the line from <i>e</i> as a
+center, and with our dividers set to the radius of any of the convenient
+arcs which we have divided into sixty degrees, we sweep the arc <i>i</i>.
+Where this arc intersects the line <i>f</i> we term the point <i>k</i>, and from
+this point we lay off on the arc <i>i</i> 220 degrees, and draw the line <i>l e
+l'</i>, which we see coincides with the chord of the impulse face of the
+tooth. We set our <a name="Page_121" id="Page_121"></a>dividers to the same radius by which we sweep the arc
+<i>i</i> and set one leg at the point <i>b</i> for a center and sweep the arc
+<i>j'</i>. If we measure this arc from the point <i>j'</i> to intersection of said
+arc <i>j'</i> with the line <i>l</i> we will find it to be sixty-four degrees,
+which accounts for our taking this number of degrees when we defined the
+face of our escape-wheel tooth, Fig. 129.</p>
+
+<p>There is no reason why we should take twenty-degrees for the angle <i>k e
+l</i> except that the practical construction of the larger sizes of
+cylinder watches has established the fact that this is about the right
+angle to employ, while in smaller watches it frequently runs up as high
+as twenty-five. Although the cylinder is seemingly a very simple
+escapement, it is really a very abstruce one to follow out so as to
+become familiar with all of its actions.</p>
+
+
+<h4>THE CYLINDER PROPER CONSIDERED.</h4>
+
+<div class="figcenter"><a href="images/pict131.jpg"><img src="images/pict131-tb.jpg" alt="Fig. 131" title="Fig. 131" /></a></div>
+
+<p>We will now proceed and consider the cylinder proper, and to aid us in
+understanding the position and relation of the parts we refer to Fig.
+131, where we repeat the circles <i>d</i> and <i>h</i>, shown in Fig. 130, which
+represents the inside and outside of the cylinder. We have here also
+repeated the line <i>f</i> of Fig. 130 as it cuts the cylinder in half, that
+is, divides it into two segments of 180 degrees each. If we conceive of
+a cylinder in which just one-half is cut away, that is, the lips are
+bounded by straight radial lines, we can also conceive of the relation
+and position of the parts shown in Fig. 130. The first position of which
+we should take cognizance is, the tooth <i>D</i> is moved back to the left so
+as to rest on the outside of our cylinder. The cylinder is also supposed
+to stand so that the lips correspond to the line <i>f</i>. On pressing the
+tooth <i>D</i> forward <a name="Page_122" id="Page_122"></a>the incline of the tooth would attack the entrance
+lip of the cylinder at just about the center of the curved impulse face,
+imparting to the cylinder twenty degrees of angular motion, but the
+point of the tooth at <i>d</i> would exactly encounter the inner angle of the
+exit lip, and of course the cylinder would afford no rest for the tooth;
+hence, we see the importance of not cutting away too much of the half
+shell of the cylinder.</p>
+
+<p>But before we further consider the action of the tooth <i>D</i> in its action
+as it passes the exit lip of the cylinder we must finish with the action
+of the tooth on the entrance lip. A very little thought and study of
+Fig. 130 will convince us that the incline of the tooth as it enters the
+cylinder will commence at <i>t</i>, Fig. 130, but at the close of the action
+the tooth parts from the lip on the inner angle. Now it is evident that
+it would require greater force to propel the cylinder by its inner angle
+than by the outer one. To compensate for this we round the edge of the
+entrance lip so that the action of the tooth instead of commencing on
+the outer angle commences on the center of the edge of the entrance lip
+and also ends its action on the center of the entrance lip. To give
+angular extent enough to the shell of the cylinder to allow for rounding
+and also to afford a secure rest for the tooth inside the cylinder, we
+add six degrees to the angular extent of the entrance lip of the
+cylinder shell, as indicated on the arc <i>o'</i>, Fig. 131, three of these
+degrees being absorbed for rounding and three to insure a dead rest for
+the tooth when it enters the cylinder.</p>
+
+
+<h4>WHY THE ANGULAR EXTENT IS INCREASED.</h4>
+
+<p>Without rounding the exit lip the action of the tooth on its exit would
+be entirely on the inner angle of the shell. To obviate this it is the
+usual practice to increase the angular extent of the cylinder ten
+degrees, as shown on the arc <i>o'</i> between the lines <i>f</i> and <i>p</i>, Fig.
+131. Why we should allow ten degrees on the exit lip and but six degrees
+on the entrance lip will be understood by observing Fig. 130, where the
+radial lines <i>s</i> and <i>r</i> show the extent of angular motion of the
+cylinder, which would be lost if the tooth commenced to act on the inner
+angle and ended on the outer angle of the exit lip. This arc is a little
+over six degrees, and if we add a trifle over three degrees for rounding
+we would account for the ten degrees between the lines <i>f</i> and <i>p</i>, Fig.
+131. It will now be seen that the angular extent is 196 degrees. If we
+draw the line <i>w</i> we can see in <a name="Page_123" id="Page_123"></a>what proportion the measurement should
+be made between the outer diameter of the cylinder and the measure of
+the half shell. It will be seen on measurement that the distance between
+the center <i>e</i> and the line <i>w</i> is about one-fifteenth part of the outer
+diameter of the cylinder and consequently with a cylinder which measures
+45/1000 of an inch in diameter, now the half shell should measure half
+of the entire diameter of the cylinder plus one-fifteenth part of such
+diameter, or 25-1/2 thousandths of an inch.</p>
+
+<p>After these proportions are understood and the drawing made, the eye
+will get accustomed to judging pretty near what is required; but much
+the safer plan is to measure, where we have the proper tools for doing
+so. Most workmen have an idea that the depth or distance at which the
+cylinder is set from the escape wheel is a matter of adjustment; while
+this is true to a certain extent, still there is really only one
+position for the center of the cylinder, and that is so that the center
+of the pivot hole coincides exactly with the center of the chord to the
+curve of the impulse face of the tooth or the point <i>e</i>, Fig. 130. Any
+adjustment or moving back and forth of the chariot to change the depth
+could only be demanded where there was some fault existing in the
+cylinder or where it had been moved out of its proper place by some
+genius as an experiment in cylinder depths. It will be evident on
+observing the drawing at Fig. 131 that when the cylinder is performing
+an arc of vibration, as soon as the entrance lip has passed the point
+indicated by the radial line <i>e x</i> the point of the escape-wheel tooth
+will commence to act on the cylinder lip and continue to do so through
+an arc of forty degrees, or from the lines <i>x</i> to <i>l</i>.</p>
+
+
+<h4>MAKING A WORKING MODEL.</h4>
+
+<p>To practically study the action of the cylinder escapement it is well to
+make a working model. It is not necessary that such a model should
+contain an entire escape wheel; all that is really required is two teeth
+cut out of brass of the proper forms and proportions and attached to the
+end of an arm 4-7/8" long with studs riveted to the U arms to support
+the teeth. This U arm is attached to the long arm we have just
+mentioned. A flat ring of heavy sheet brass is shaped to represent a
+short transverse section of a cylinder. This segment is mounted on a
+yoke which turns on pivots. In making such a model we can employ all the
+proportions and exact forms of the larger drawings made on a ten-inch
+radius.<a name="Page_124" id="Page_124"></a> Such a model becomes of great service in learning the
+importance of properly shaping the lips of the cylinder. And right here
+we beg to call attention to the fact that in the ordinary repair shop
+the proper shape of cylinder lips is entirely neglected.</p>
+
+
+<h4>PROPER SHAPE OF CYLINDER LIPS.</h4>
+
+<p>The workman buys a cylinder and whether the proper amount is cut away
+from the half shell, or the lips, the correct form is entirely ignored,
+and still careful attention to the form of the cylinder lips adds full
+ten per cent. to the efficiency of the motive force as applied to the
+cylinder. In making study drawings of the cylinder escapement it is not
+necessary to employ paper so large that we can establish upon it the
+center of the arc which represents the periphery of our escape wheel, as
+we have at our disposal two plans by which this can be obviated. First,
+placing a bit of bristol board on our drawing-board in which we can set
+one leg of our dividers or compasses when we sweep the peripheral arc
+which we use in our delineations; second, making three arcs in brass or
+other sheet metal, viz.: the periphery of the escape wheel, the arc
+passing through the center of the chord of the arc of the impulse face
+of the tooth, and the arc passing through the point of the escape-wheel
+tooth. Of these plans we favor the one of sticking a bit of cardboard on
+the drawing board outside of the paper on which we are making our
+drawing.</p>
+
+<div class="figcenter"><a href="images/pict132.jpg"><img src="images/pict132-tb.jpg" alt="Fig. 132" title="Fig. 132" /></a></div>
+
+<p>At Fig. 132 we show the position and relation of the several parts just
+as the tooth passes into the shell of the cylinder, leaving the lip of
+the cylinder just as the tooth parted with it. The half <a name="Page_125" id="Page_125"></a>shell of the
+cylinder as shown occupies 196 degrees or the larger arc embraced
+between the radial lines <i>k</i> and <i>l</i>. In drawing the entrance lip the
+acting face is made almost identical with a radial line except to round
+the corners for about one-third the thickness of the cylinder shell. No
+portion, however, of the lip can be considered as a straight line, but
+might be described as a flattened curve.</p>
+
+<div class="figcenter"><a href="images/pict133.jpg"><img src="images/pict133-tb.jpg" alt="Fig. 133" title="Fig. 133" /></a></div>
+
+<p>A little study of what would be required to get the best results after
+making such a drawing will aid the pupil in arriving at the proper
+shape, especially when he remembers that the thickness of the cylinder
+shell of a twelve-line watch is only about five one-thousandths of an
+inch. But because the parts are small we should not shirk the problem of
+getting the most we possibly can out of a cylinder watch.</p>
+
+<p>The extent of arc between the radial lines <i>k f</i>, as shown in Fig. 132,
+is four degrees. Although in former drawings we showed the angular
+extent added as six degrees, as we show the lip <i>m</i> in Fig. 132, two
+degrees are lost in rounding. The space <i>k f</i> on the egress or exit side
+is intended to be about four degrees, which shows the extent of lock. We
+show at Fig. 133 the tooth <i>D</i> just having passed out of the cylinder,
+having parted with the exit lip <i>p</i>.</p>
+
+<p>In making this drawing we proceed as with Fig. 132 by establishing a
+center for our radius of 10" outside of our drawing paper and drawing
+the line <i>A A</i> to such center and sweeping the arcs <i>a b c</i>. We
+establish the point <i>e</i>, which represents the center of our cylinder, as
+before. We take the space to represent the radial extent of the outside
+of our cylinder in our dividers and from <i>e</i> as a center sweep a fine
+pencil line, represented by the dotted line <i>t</i> in our drawing; <a name="Page_126" id="Page_126"></a>and
+where this circle intersects the arc <i>a</i> we name it the point <i>s</i>; and
+it is at this point the heel of our escape-wheel tooth must part with
+the exit lip of the cylinder. From <i>e</i> as a center and through the point
+<i>s</i> we draw the line <i>e l''</i>. With our dividers set to the radius of any
+convenient arc which we have divided into degrees, we sweep the short
+arc <i>d'</i>. The intersection of this arc with the line <i>e l''</i> we name the
+point <i>u</i>; and from <i>e</i> as a center we draw the radial line <i>e u f'</i>. We
+place the letter <i>f''</i> in connection with this line because it (the
+line) bears the same relations to the half shell of the cylinder shown
+in Fig. 133 that the line <i>f</i> does to the half shell (<i>D</i>) shown in Fig.
+132. We draw the line <i>f'' f'''</i>, Fig. 133, which divides the cylinder
+into two segments of 180 degrees each. We take the same space in our
+dividers with which we swept the interior of the cylinder in Fig. 132
+and sweep the circle <i>v</i>, Fig. 133. From <i>e</i> as a center we sweep the
+short arc <i>d''</i>, Fig. 133, and from its intersection of the line <i>f''</i>
+we lay off six degrees on said arc <i>d''</i> and draw the line <i>e' k''</i>,
+which defines the angular extent of our entrance lip to the half shell
+of the cylinder in Fig. 133. We draw the full lines of the cylinder as
+shown.</p>
+
+<p>We next delineate the heel of the tooth which has just passed out of the
+cylinder, as shown at <i>D'</i>, Fig. 133. We now have a drawing showing the
+position of the half shell of the cylinder just as the tooth has passed
+the exit lip. This drawing also represents the position of the half
+shell of the cylinder when the tooth rests against it on the outside. If
+we should make a drawing of an escape-wheel tooth shaped exactly as the
+one shown at Fig. 132 and the point of the tooth resting at <i>x</i>, we
+would show the position of a tooth encountering the cylinder after a
+tooth which has been engaged in the inside of the shell has passed out.
+By following the instructions now given, we can delineate a tooth in any
+of its relations with the cylinder shell.</p>
+
+
+<h4>DELINEATING AN ESCAPE-WHEEL TOOTH WHILE IN ACTION.</h4>
+
+<p>We will now go through the operation of delineating an escape-wheel
+tooth while in action. The position we shall assume is the one in which
+the cylinder and escape-wheel tooth are in the relation of the passage
+of half the impulse face of the tooth into the cylinder. To do this is
+simple enough: We first produce the arcs <i>a b c</i>, Fig. 133, as directed,
+and then proceed to delineate a tooth as in previous instances. To
+delineate our cylinder in the <a name="Page_127" id="Page_127"></a>position we have assumed above, we take
+the space between the points <i>e d</i> in our dividers and setting one leg
+at <i>d</i> establish the point <i>g</i>, to represent the center of our cylinder.
+If we then sweep the circle <i>h</i> from the center of <i>g</i> we define the
+inner surface of the shell of our cylinder.</p>
+
+<p>Strictly speaking, we have not assumed the position we stated, that is,
+the impulse face of the tooth as passing half way into the cylinder. To
+comply strictly with our statement, we divide the chord of the impulse
+face of the tooth <i>A</i> into eight equal spaces, as shown. Now as each of
+these spaces represent the thickness of the cylinder, if we take in our
+dividers four of these spaces and half of another, we have the radius of
+a circle passing the center of the cylinder shell. Consequently, if with
+this space in our dividers we set the leg at <i>d</i>, we establish on the
+arc <i>b</i> the point <i>i</i>. We locate the center of our cylinder when
+one-half of an entering tooth has passed into the cylinder. If now from
+the new center with our dividers set at four of the spaces into which we
+have divided the line <i>e f</i> we can sweep a circle representing the inner
+surface of the cylinder shell, and by setting our dividers to five of
+these spaces we can, from <i>i</i> as a center, sweep an arc representing the
+outside of the cylinder shell. For all purposes of practical study the
+delineation we show at Fig. 133 is to be preferred, because, if we carry
+out all the details we have described, the lines would become confused.
+We set our dividers at five of the spaces on the line <i>e f</i> and from <i>g</i>
+as a center sweep the circle <i>j</i>, which delineates the outer surface of
+our cylinder shell.</p>
+
+<p>Let us now, as we directed in our former instructions, draw a flattened
+curve to represent the acting surface of the entrance lip of our
+cylinder as if it were in direct contact with the impulse face of the
+tooth. To delineate the exit lip we draw from the center <i>g</i>, Fig. 134,
+to the radial line <i>g k</i>, said line passing through the point of contact
+between the tooth and entrance lip of the cylinder. Let us next continue
+this line on the opposite side of the point <i>g</i>, as shown at <i>g k'</i>, and
+we thus bisect the cylinder shell into two equal parts of 180 degrees
+each. As we previously explained, the entire extent of the cylinder half
+shell is 196 degrees. We now set our dividers to the radius of any
+convenient arc which we have divided into degrees, and from <i>g</i> as a
+center sweep the short arc <i>l l</i>, and from the intersection of this arc
+with the line <i>g k'</i> we lay off sixteen degrees on the said arc <i>l</i> and
+establish the point <i>n</i>, from <i>g</i> as a <a name="Page_128" id="Page_128"></a>center draw the radial line <i>g
+n'</i>. Take ten degrees from the same parent arc and establish the point
+<i>m</i>, then draw the line <i>g m'</i>. Now the arc on the circles <i>h j</i> between
+the lines <i>g n'</i> and <i>g m</i> limits the extent of the exit lip of the
+cylinder and the arc between the lines <i>g k'</i> and <i>g m'</i> represents the
+locking surface of the cylinder shell.</p>
+
+<div class="figcenter"><a href="images/pict134.jpg"><img src="images/pict134-tb.jpg" alt="Fig. 134" title="Fig. 134" /></a></div>
+
+<p>To delineate the U arms we refer to Fig. 135. Here, again, we draw the
+arc <i>a b c</i> and delineate a tooth as before. From the point <i>e</i> located
+at the heel of the tooth we draw the radial line <i>e e'</i>. From the point
+<i>e</i> we lay off on the arc <i>a</i> five degrees and establish the point <i>p</i>;
+we halve this space and draw the short radial line <i>p' s'</i> and <i>p s</i>.
+From the point <i>e</i> on the arc <i>A</i> we lay off twenty-four degrees and
+establish the point <i>t</i>, which locates the heel of the next tooth in
+advance of <i>A</i>. At two and a half degrees to the right of the point <i>t</i>
+we locate the point <i>r</i> and draw the short radial line <i>r s</i>. On the arc
+<i>b</i> and half way between the lines <i>p s</i> and <i>r s</i>, we establish the
+point <i>u</i>, and from it as a center we sweep the arc <i>v</i> defining the
+curve of the U arms.</p>
+
+<p>We have now given minute instructions for drawing a cylinder escapement
+in all its details except the extent of the banking slot of the
+cylinder, which is usually made to embrace an angular extent of 270
+degrees; consequently, the pillar of the cylinder will not measure more
+than ninety degrees of angular extent.</p>
+
+<p>There is no escapement constructed where carefully-made drawings tend
+more to perfect knowledge of the action than the <a name="Page_129" id="Page_129"></a>cylinder. But it is
+necessary with the pupil to institute a careful analysis of the actions
+involved. In writing on a subject of this kind it is extremely
+perplexing to know when to stop; not that there is so much danger of
+saying too much as there is not having the words read with attention.</p>
+
+<p>As an illustration, let us consider the subject of depth between the
+cylinder and the escape wheel. As previously stated, 196 degrees of
+cylinder shell should be employed; but suppose we find a watch in which
+the half shell has had too much cut away, so the tooth on entering the
+half shell after parting with the entrance lip does not strike dead on
+the inside of the shell, but encounters the edge of the exit lip. In
+this case the impulse of the balance would cause the tooth to slightly
+retrograde and the watch would go but would lack a good motion. In such
+an instance a very slight advance of the chariot would remedy the
+fault&mdash;not perfectly remedy it, but patch up, so to speak&mdash;and the watch
+would run.</p>
+
+<div class="figcenter"><a href="images/pict135.jpg"><img src="images/pict135-tb.jpg" alt="Fig. 135" title="Fig. 135" /></a></div>
+
+<p>In this day, fine cylinder watches are not made, and only the common
+kind are met with, and for this reason the student should familiarize
+himself with all the imaginary faults which could occur from bad
+construction. The best way to do this is to delineate what he (the
+student) knows to be a faulty escapement, as, for instance, a cylinder
+in which too much of the half shell is cut away; but in every instance
+let the tooth be of the correct form. Then delineate an escapement in
+which the cylinder is correct but the teeth faulty; also change the
+thickness of the cylinder shell, so as to make the teeth too short. This
+sort of practice makes the pupil think and study and he will acquire a
+knowledge which will never <a name="Page_130" id="Page_130"></a>be forgotten, but always be present to aid
+him in the puzzles to which the practical watchmaker is every day
+subject.</p>
+
+<p>The ability to solve these perplexing problems determines in a great
+degree the worth of a man to his employer, in addition to establishing
+his reputation as a skilled workman. The question is frequently asked,
+"How can I profitably employ myself in spare time?" It would seem that a
+watchmaker could do no better than to carefully study matters
+horological, striving constantly to attain a greater degree of
+perfection, for by so doing his earning capacity will undoubtedly be
+increased.</p>
+
+
+
+<hr style="width: 65%;" /><p><a name="Page_131" id="Page_131"></a></p>
+<h2>CHAPTER III.</h2>
+
+<h3>THE CHRONOMETER ESCAPEMENT.</h3>
+
+
+<p>Undoubtedly "the detent," or, as it is usually termed, "the chronometer
+escapement," is the most perfect of any of our portable time measurers.
+Although the marine chronometer is in a sense a portable timepiece,
+still it is not, like a pocket watch, capable of being adjusted to
+positions. As we are all aware, the detent escapement is used in fine
+pocket watches, still the general feeling of manufacturers is not
+favorable to it. Much of this feeling no doubt is owing to the
+mechanical difficulties presented in repairing the chronometer
+escapements when the detent is broken, and the fact that the spring
+detent could not be adjusted to position. We shall have occasion to
+speak of position adjustments as relate to the chronometer escapement
+later on.</p>
+
+
+<h4>ADVANTAGES OF THE CHRONOMETER.</h4>
+
+<p>We will proceed now to consider briefly the advantages the detent
+escapement has over all others. It was soon discovered in constructing
+portable timepieces, that to obtain the best results the vibrations of
+the balance should be as free as possible from any control or influence
+except at such times as it received the necessary impulse to maintain
+the vibrations at a constant arc. This want undoubtedly led to the
+invention of the detent escapement. The early escapements were all
+frictional escapements, <i>i.e.</i>, the balance staff was never free from
+the influence of the train. The verge escapement, which was undoubtedly
+the first employed, was constantly in contact with the escape wheel, and
+was what is known as a "recoiling beat," that is, the contact of the
+pallets actually caused the escape wheel to recoil or turn back. Such
+escapements were too much influenced by the train, and any increase in
+power caused the timepiece to gain. The first attempt to correct this
+imperfection led to the invention and introduction of the fusee, which
+enabled the watchmaker to obtain from a coiled spring nearly equal power
+during the entire period of action. The next step in advance was the
+"dead-beat escapement," which included the cylinder and duplex. In these
+frictional escapements the balance staff locked the train while the
+balance performed its arc of vibration.</p>
+
+<h4><a name="Page_132" id="Page_132"></a>FRICTIONAL ESCAPEMENTS IN HIGH FAVOR.</h4>
+
+<p>These frictional escapements held favor with many eminent watchmakers
+even after the introduction of the detached escapements. It is no more
+than natural we should inquire, why? The idea with the advocates of the
+frictional rest escapements was, the friction of the tooth acted as a
+<i>corrective</i>, and led no doubt to the introduction of going-barrel
+watches. To illustrate, suppose in a cylinder watch we increase the
+motive power, such increase of power would not, as in the verge
+escapement, increase the rapidity of the vibrations; it might, in fact,
+cause the timepiece to run slower from the increased friction of the
+escape-wheel tooth on the cylinder; also, in the duplex escapement the
+friction of the locking tooth on the staff retards the vibrations.</p>
+
+<p>Dr. Hooke, the inventor of the balance spring, soon discovered it could
+be manipulated to isochronism, <i>i.e.</i>, so arcs of different extent would
+be formed in equal time. Of course, the friction-rest escapement
+requiring a spring to possess different properties from one which would
+be isochronal with a perfectly detached escapement, these two frictional
+escapements also differing, the duplex requiring other properties from
+what would isochronize a spring for a cylinder escapement. Although
+pocket watches with duplex and cylinder escapements having balances
+compensated for heat and cold and balance springs adjusted to
+isochronism gave very good results, careful makers were satisfied that
+an escapement in which the balance was detached and free to act during
+the greater proportion of the arc of vibration and uncontrolled by any
+cause, would do still better, and this led to the detent escapement.</p>
+
+
+<h4>FAULTS IN THE DETENT ESCAPEMENT.</h4>
+
+<p>As stated previously, the detent escapement having pronounced faults in
+positions which held it back, it is probable it would never have been
+employed in pocket watches to any extent if it had not acquired such a
+high reputation in marine chronometers. Let us now analyze the
+influences which surround the detent escapement in a marine chronometer
+and take account of the causes which are combined to make it an accurate
+time measurer, and also take cognizance of other interfering causes
+which have a tendency to prevent desired results. First, we will imagine
+a balance with its spring such as we find in fine marine chronometers.
+It has small pivots running in highly-polished jewels; such pivots are
+perfectly <a name="Page_133" id="Page_133"></a>cylindrical, and no larger than are absolutely necessary to
+endure the task imposed upon them&mdash;of carrying the weight of the balance
+and endure careful handling.</p>
+
+<p>To afford the necessary vibrations a spring is fitted, usually of a
+helical form, so disposed as to cause the balance to vibrate in arcs
+back and forth in equal time, <i>provided these arcs are of equal extent</i>.
+It is now to be taken note of that we have it at our disposal and option
+to make these arcs equal in time duration, <i>i.e.</i>, to make the long or
+short arcs the quickest or to synchronize them. We can readily
+comprehend we have now established a very perfect measure of short
+intervals of time. We can also see if we provide the means of
+maintaining these vibrations and counting them we should possess the
+means of counting the flights of time with great accuracy. The
+conditions which surround our balance are very constant, the small
+pivots turning in fine hard jewels lubricated with an oil on which
+exposure to the action of the air has little effect, leaves but few
+influences which can interfere with the regular action of our balance.
+We add to the influences an adjustable correction for the disturbances
+of heat and cold, and we are convinced that but little could be added.</p>
+
+
+<h4>ANTAGONISTIC INFLUENCES.</h4>
+
+<p>In this combination we have pitted two antagonistic forces against each
+other, viz., the elasticity of the spring and the weight and inertia of
+the balance; both forces are theoretically constant and should produce
+constant results. The mechanical part of the problem is simply to afford
+these two forces perfect facilities to act on each other and compel each
+to realize its full effect. We must also devise mechanical means to
+record the duration of each conflict, that is, the time length of each
+vibration. Many years have been spent in experimenting to arrive at the
+best propositions to employ for the several parts to obtain the best
+practical results. Consequently, in designing a chronometer escapement
+we must not only draw the parts to a certain form, but consider the
+quality and weight of material to employ.</p>
+
+<p>To illustrate what we have just said, suppose, in drawing an escape
+wheel, we must not only delineate the proper angle for the acting face
+of the tooth, but must also take cognizance of the thickness of the
+tooth. By thickness we mean the measurement of extent of the tooth in
+the direction of the axis of the escape wheel. An escape-wheel tooth
+might be of the best form to act in conveying <a name="Page_134" id="Page_134"></a>power to the balance and
+yet by being too thin soon wear or produce excessive friction. How thick
+an escape wheel should be to produce best results, is one of the many
+matters settled only by actual workshop experience.</p>
+
+
+<h4>FACTORS THAT MUST BE CONSIDERED.</h4>
+
+<p>Even this experience is in every instance modified by other influences.
+To illustrate: Let us suppose in the ordinary to-day marine chronometer
+the escape-wheel teeth exerted a given average force, which we set down
+as so many grains. Now, if we should employ other material than
+hammer-hardened brass for an escape wheel it would modify the thickness;
+also, if we should decrease the motive power and increase the arc of
+impulse. Or, if we should diminish the extent of the impulse arc and add
+to the motive force, every change would have a controlling influence. In
+the designs we shall employ, it is our purpose to follow such
+proportions as have been adopted by our best makers, in all respects,
+including form, size and material. We would say, however, there has been
+but little deviation with our principal manufacturers of marine
+chronometers for the last twenty years as regards the general principle
+on which they were constructed, the chief aim being to excel in the
+perfection of the several parts and the care taken in the several
+adjustments.</p>
+
+<p>Before we proceed to take up the details of constructing a chronometer
+escapement we had better master the names for the several parts. We show
+at Fig. 136 a complete plan of a chronometer escapement as if seen from
+the back, which is in reality the front or dial side of the "top plate."
+The chronometer escapement consists of four chief or principal parts,
+viz.: The escape wheel, a portion of which is shown at <i>A</i>; the impulse
+roller <i>B</i>; unlocking or discharging roller <i>C</i>, and the detent <i>D</i>.
+These principal parts are made up of sub-parts: thus, the escape wheel
+is composed of arms, teeth, recess and collet, the recess being the
+portion of the escape wheel sunk, to enable us to get wide teeth actions
+on the impulse pallet. The collet is a brass bush on which the wheel is
+set to afford better support to the escape wheel than could be obtained
+by the thinned wheel if driven directly on the pinion arbor. The impulse
+roller is composed of a cylindrical steel collet <i>B</i>, the impulse pallet
+<i>d</i> (some call it the impulse stone), the safety recess <i>b b</i>. The
+diameter of the impulse collet is usually <a name="Page_135" id="Page_135"></a><a name="Page_136" id="Page_136"></a>one-half that of the escape
+wheel. This impulse roller is staked directly on the balance staff, and
+its perfection of position assured by resting against the foot of the
+shoulder to which the balance is secured. This will be understood by
+inspecting Fig. 137, which is a vertical longitudinal section of a
+chronometer balance staff, the lower side of the impulse roller being
+cupped out at <i>c</i> with a ball grinder and finished a ball polish.</p>
+
+<div class="figcenter"><a href="images/pict136.jpg"><img src="images/pict136-tb.jpg" alt="Fig. 136" title="Fig. 136" /></a></div>
+
+<p>It will be seen the impulse roller is staked flat against the hub <i>E</i> of
+the balance staff. The unlocking roller, or, as it is also called, the
+discharging roller, <i>C</i>, is usually thinner than the impulse roller and
+has a jewel similar to the impulse jewel <i>a</i> shown at <i>f</i>. This roller
+is fitted by friction to the lower part of the balance staff and for
+additional security has a pipe or short socket <i>e</i> which embraces the
+balance staff at <i>g</i>. The pipe <i>e</i> is usually flattened on opposite
+sides to admit of employing a special wrench for turning the discharging
+roller in adjusting the jewel for opening the escapement at the proper
+instant to permit the escape wheel to act on the impulse jewel <i>a</i>. The
+parts which go to make up the detent <i>D</i> consist of the "detent foot"
+<i>F</i>, the detent spring <i>h</i>, the detent blade <i>i</i>, the jewel pipe <i>j</i>,
+the locking jewel (or stone) <i>s</i>, the "horn" of the detent <i>k</i>, the
+"gold spring" (also called the auxiliary and lifting spring) <i>m</i>. This
+lifting or gold spring <i>m</i> should be made as light and thin as possible
+and stand careful handling.</p>
+
+<div class="figcenter"><img src="images/pict137.jpg" alt="Fig. 137" title="Fig. 137" /></div>
+
+<p>We cannot impress on our readers too much the importance of making a
+chronometer detent light. Very few detents, even from <a name="Page_137" id="Page_137"></a>the hands of our
+best makers, are as light as they might be. We should in such
+construction have very little care for clumsy workmen who may have to
+repair such mechanism. This feature should not enter into consideration.</p>
+
+<p>We should only be influenced by the feeling that we are working for best
+results, and it is acting under this influence that we devote so much
+time to establishing a correct idea of the underlying principles
+involved in a marine chronometer, instead of proceeding directly to the
+drawing of such an escapement and give empirical rules for the length of
+this or the diameter of that. As, for instance, in finishing the detent
+spring <i>h</i>, suppose we read in text books the spring should be reduced
+in thickness, so that a weight of one pennyweight suspended from the
+pipe <i>j</i> will deflect the detent &frac14;". This is a rule well enough for
+people employed in a chronometer factory, but for the horological
+student such fixed rules (even if remembered) would be of small use.
+What the student requires is sound knowledge of the "whys," in order
+that he may be able to thoroughly master this escapement.</p>
+
+
+<h4>FUNCTIONS OF THE DETENT.</h4>
+
+<p>We can see, after a brief analysis of the principles involved, that the
+functions required of the detent <i>D</i> are to lock the escape wheel <i>A</i>
+and hold it while the balance performs its excursion, and that the
+detent or recovering spring <i>h</i> must have sufficient strength and power
+to perform two functions: (1) Return the locking stone <i>s</i> back to the
+proper position to arrest and hold the escape wheel; (2) the spring <i>h</i>
+must also be able to resist, without buckling or cockling, the thrust of
+the escape wheel, represented by the arrows <i>p o</i>. Now we can readily
+understand that the lighter we make the parts <i>i j k m</i>, the weaker the
+spring <i>h</i> can be. You say, perhaps, if we make it too weak it will be
+liable to buckle under the pressure of the escape wheel; this, in turn,
+will depend in a great measure on the condition of the spring <i>h</i>.
+Suppose we have it straight when we put it in position, it will then
+have no stress to keep it pressed to the holding, stop or banking screw,
+which regulates the lock of the tooth. To obtain this stress we set the
+foot <i>F</i> of the detent around to the position indicated by the dotted
+lines <i>r</i> and <i>n</i>, and we get the proper tension on the detent spring to
+effect the lock, or rather of the detent in time to lock the escape
+wheel; but the spring <i>h</i>, instead of being perfectly straight, <a name="Page_138" id="Page_138"></a>is bent
+and consequently not in a condition to stand the thrust of the escape
+wheel, indicated by the arrows <i>o p</i>.</p>
+
+
+<h4>OBTAINING THE BEST CONDITIONS.</h4>
+
+<p>Now the true way to obtain the best conditions is to give the spring <i>h</i>
+a set curvature before we put it in place, and then when the detent is
+in the proper position the spring <i>h</i> will have tension enough on it to
+bring the jewel <i>s</i> against the stop screw, which regulates the lock,
+and still be perfectly straight. This matter is of so much importance
+that we will give further explanation. Suppose we bend the detent spring
+<i>h</i> so it is curved to the dotted line <i>t</i>, Fig. 136, and then the foot
+<i>F</i> would assume the position indicated at the dotted line <i>r</i>. We next
+imagine the foot <i>F</i> to be put in the position shown by the full lines,
+the spring <i>h</i> will become straight again and in perfect shape to resist
+the thrust of the escape wheel.</p>
+
+<p>Little "ways and methods" like the above have long been known to the
+trade, but for some reason are never mentioned in our text books. A
+detent spring 2/1000" thick and 80/1000" wide will stand the thrust for
+any well-constructed marine chronometer in existence, and yet it will
+not require half a pennyweight to deflect it one-fourth of an inch. It
+is a good rule to make the length of the detent from the foot <i>F</i> to the
+center of the locking jewel pipe <i>j</i> equal to the diameter of the escape
+wheel, and the length of the detent spring <i>h</i> two-sevenths of this
+distance. The length of the horn <i>k</i> is determined by the graphic plan
+and can be taken from the plotted plan. The end, however, should
+approach as near to the discharging jewel as possible and not absolutely
+touch. The discharging (gold) spring <i>m</i> is attached to the blade <i>i</i> of
+the detent with a small screw <i>l</i> cut in a No. 18 hole of a Swiss plate.
+While there should be a slight increase in thickness in the detent blade
+at <i>w</i>, where the gold spring is attached, still it should be no more
+than to separate the gold spring <i>m</i> from the detent blade <i>i</i>.</p>
+
+
+<h4>IMPORTANT CONSIDERATIONS.</h4>
+
+<p>It is important the spring should be absolutely free and not touch the
+detent except at its point of attachment at <i>w</i> and to rest against the
+end of the horn <i>k</i>, and the extreme end of <i>k</i>, where the gold spring
+rests, should only be what we may term a dull or thick edge. The end of
+the horn <i>k</i> (shown at <i>y</i>) is best made, for convenience of elegant
+construction, square&mdash;that is, the part <i>y</i> turns at <a name="Page_139" id="Page_139"></a>right angles to
+<i>k</i> and is made thicker than <i>k</i> and at the same time deeper; or, to
+make a comparison to a clumsy article, <i>y</i> is like the head of a nail,
+which is all on one side. Some makers bend the horn <i>k</i> to a curve and
+allow the end of the horn to arrest or stop the gold spring; but as it
+is important the entire detent should be as light as possible, the
+square end best answers this purpose. The banking placed at <i>j</i> should
+arrest the detent as thrown back by the spring <i>h</i> at the "point of
+percussion." This point of percussion is a certain point in a moving
+mass where the greatest effort is produced and would be somewhere near
+the point <i>x</i>, in a bar <i>G</i> turning on a pivot at <i>z</i>, Fig. 138. It will
+be evident, on inspection of this figure, if the bar <i>G</i> was turning on
+the center <i>z</i> it would not give the hardest impact at the end <i>v</i>, as
+parts of its force would be expended at the center <i>z</i>.</p>
+
+<div class="figcenter"><img src="images/pict138.jpg" alt="Fig. 138" title="Fig. 138" /></div>
+
+
+<h4>DECISIONS ARRIVED AT BY EXPERIENCE.</h4>
+
+<p>Experience has decided that the impulse roller should be about half the
+diameter of the escape wheel, and experience has also decided that an
+escape wheel of fifteen teeth has the greatest number of advantages;
+also, that the balance should make 14,400 vibrations in one hour. We
+will accept these proportions and conditions as best, from the fact that
+they are now almost universally adopted by our best chronometer makers.
+Although it would seem as if these proportions should have established
+themselves earlier among practical men, we shall in these drawings
+confine ourselves to the graphic plan, considering it preferable. In the
+practical detail drawing we advise the employment of the scale given,
+<i>i.e.</i>, delineating an escape wheel 10" in diameter. The drawings which
+accompany the description are one-fourth of this size, for the sake of
+convenience in copying.</p>
+
+<p>With an escape wheel of fifteen teeth the impulse arc is exactly
+twenty-four degrees, and of course the periphery of the impulse roller
+must intersect the periphery of the escape wheel for <a name="Page_140" id="Page_140"></a>this arc (24&deg;).
+The circles <i>A B</i>, Fig. 139, represent the peripheries of these two
+mobiles, and the problem in hand is to locate and define the position of
+the two centers <i>a c</i>. These, of course, are not separated, the sum of
+the two radii, <i>i.e.</i>, 5" + 2-1/2" (in the large drawing), as these
+circles intersect, as shown at <i>d</i>. Arithmetically considered, the
+problem is quite difficult, but graphically, simple enough. After we
+have swept the circle <i>A</i> with a radius of 5", we draw the radial line
+<i>a f</i>, said line extending beyond the circle <i>A</i>.</p>
+
+
+<h4>LOCATING THE CENTER OF THE BALANCE STAFF.</h4>
+
+<p>Somewhere on this line is located the center of the balance staff, and
+it is the problem in hand to locate or establish this center. Now, it is
+known the circles which define the peripheries of the escape wheel and
+the impulse roller intersect at <i>e e<sup>2</sup></i>. We can establish on our
+circle <i>A</i> where these intersections take place by laying off twelve
+degrees, one-half of the impulse arc on each side of the line of centers
+<i>a f</i> on this circle and establishing the points <i>e e<sup>2</sup></i>. These points
+<i>e e<sup>2</sup></i> being located at the intersection of the circles <i>A</i> and <i>B</i>,
+must be at the respective distances of 5" and 2-1/2" distance from the
+center of the circles <i>A B</i>; consequently, if we set our dividers at
+2-1/2" and place one leg at <i>e</i> and sweep the short arc <i>g<sup>2</sup></i>, and
+repeat this process when one leg of the dividers is set at <i>e<sup>2</sup></i>, the
+intersection of the short arcs <i>g</i> and <i>g<sup>2</sup></i> will locate the center of
+our balance staff. We have now our two centers established, whose
+peripheries are in the relation of 2 to 1.</p>
+
+<p>To know, in the chronometer which we are supposed to be constructing,
+the exact distance apart at which to plant the hole jewels for our two
+mobiles, <i>i.e.</i>, escape wheel and balance staff, we measure carefully on
+our drawing the distance from <i>a</i> to <i>c</i> (the latter we having just
+established) and make our statement in the rule of three, as follows: As
+(10) the diameter of drawn escape wheel is to our real escape wheel so
+is the measured distance on our drawing to the real distance in the
+chronometer we are constructing.</p>
+
+<p>It is well to use great care in the large drawing to obtain great
+accuracy, and make said large drawing on a sheet of metal. This course
+is justified by the degree of perfection to which measuring tools have
+arrived in this day. It will be found on measurement of the arc of the
+circle <i>B</i>, embraced between the intersections <i>e e<sup>2</sup></i>, that it is
+about forty-eight degrees. How much of this we can <a name="Page_141" id="Page_141"></a>utilize in our
+escapement will depend very much on the perfection and accuracy of
+construction.</p>
+
+<div class="figcenter"><a href="images/pict139.jpg"><img src="images/pict139-tb.jpg" alt="Fig. 139" title="Fig. 139" /></a></div>
+
+<p>We show at Fig. 140 three teeth of an escape wheel, together with the
+locking jewel <i>E</i> and impulse jewel <i>D</i>. Now, while theoretically we
+could commence the impulse as soon as the impulse jewel <i>D</i> was inside
+of the circle representing the periphery of the escape wheel, still, in
+practical construction, we must allow for <a name="Page_142" id="Page_142"></a>contingencies. Before it is
+safe for the escape wheel to attack the impulse jewel, said jewel must
+be safely inside of said escape wheel periphery, in order that the
+attacking tooth shall act with certainty and its full effect. A good
+deal of thought and study can be bestowed to great advantage on the
+"action" of a chronometer escapement. Let us examine the conditions
+involved. We show in Fig. 140 the impulse jewel <i>D</i> just passing inside
+the circle of the periphery of the escape wheel. Now the attendant
+conditions are these: The escape wheel is locked fast and perfectly
+dead, and in the effort of unlocking it has to first turn backward
+against the effort of the mainspring; the power of force required for
+this effort is derived from the balance in which is stored up, so to
+speak, power from impulses imparted to the balance by former efforts of
+the escape wheel. In actual fact, the balance at the time the unlocking
+takes place is moving with nearly its greatest peripheral velocity and,
+as stated above, the escape wheel is at rest.</p>
+
+<p>Here comes a very delicate problem as regards setting the unlocking or
+discharging jewel. Let us first suppose we set the discharging jewel so
+the locking jewel frees its tooth at the exact instant the impulse jewel
+is inside the periphery of the escape wheel. As just stated, the escape
+wheel is not only dead but actually moving back at the time the release
+takes place. Now, it is evident that the escape wheel requires an
+appreciable time to move forward and attack the impulse jewel, and
+during this appreciable time the impulse jewel has been moving forward
+inside of the arc <i>A A</i>, which represents the periphery of the escape
+wheel. The proper consideration of this problem is of more importance in
+chronometer making than we might at first thought have imagined,
+consequently, we shall dwell upon it at some length.</p>
+
+
+<h4>HOW TO SET THE DISCHARGING JEWEL.</h4>
+
+<div class="figcenter"><a href="images/pict140.jpg"><img src="images/pict140-tb.jpg" alt="Fig. 140" title="Fig. 140" /></a></div>
+
+<p>Theoretically, the escape-wheel tooth should encounter the impulse jewel
+at the time&mdash;instant&mdash;both are moving with the same velocity. It is
+evident then that there can be no special rule given for this, <i>i.e.</i>,
+how to set the discharging jewel so it will free the tooth at exactly
+the proper instant, from the fact that one chronometer train may be much
+slower in getting to move forward from said train being heavy and clumsy
+in construction. Let us make an experiment with a real chronometer in
+illustration of our problem. To do so we remove our balance spring and
+place the balance <a name="Page_143" id="Page_143"></a>in position. If we start the balance revolving in the
+direction of the arrow <i>y</i>, Fig. 140, it will cause the escapement to be
+unlocked and the balance to turn rapidly in one direction and with
+increasing velocity until, in fact, the escape wheel has but very little
+effect on the impulse jewel; in fact, we could, by applying some outside
+source of power&mdash;like blowing with a blow pipe on the balance&mdash;cause the
+impulse jewel to pass in advance of the escape wheel; that is, the
+escape-wheel tooth would not be able to catch the impulse jewel during
+the entire impulse arc. Let us suppose, now, we set our unlocking or
+discharging jewel in advance, <a name="Page_144" id="Page_144"></a>that is, so the escapement is really
+unlocked a little before the setting parts are in the positions and
+relations shown in Fig. 141. Under the new conditions the escape wheel
+would commence to move and get sufficient velocity on it to act on the
+impulse jewel as soon as it was inside of the periphery of the escape
+wheel. If the balance was turned slowly now the tooth of the escape
+wheel would not encounter the impulse jewel at all, but fall into the
+passing hollow <i>n</i>; but if we give the balance a high velocity, the
+tooth would again encounter and act upon the jewel in the proper manner.
+Experienced adjusters of chronometers can tell by listening if the
+escape-wheel tooth attacks the impulse jewel properly, <i>i.e.</i>, when both
+are moving with similar velocities. The true sound indicating correct
+action is only given when the balance has its maximum arc of vibration,
+which should be about 1-1/4 revolutions, or perform an arc of 225
+degrees on each excursion.</p>
+
+
+<p>Fig. 142 is a side view of Fig. 141 seen in the direction of the arrow
+<i>y</i>. We have mentioned a chariot to which the detent is attached, but we
+shall make no attempt to show it in the accompanying drawings, as it
+really has no relation to the problem in hand; <i>i.e.</i>, explaining the
+action of the chronometer escapement, as the chariot relates entirely to
+the convenience of setting and adjusting the relation of the second
+parts. The size, or better, say, the inside diameter of the pipe at <i>C</i>,
+Fig. 143, which holds the locking jewel, should be about one-third of a
+tooth space, and the jewel made to fit perfectly. Usually, jewelmakers
+have a tendency to make this jewel too frail, cutting away the jewel
+back of the releasing angle (<i>n</i>, Fig. 143) too much.</p>
+
+
+<h4>A GOOD FORM OF LOCKING STONE.</h4>
+
+<p>A very practical form for a locking stone is shown in transverse section
+at Fig. 143. In construction it is a piece of ruby, or, better, sapphire
+cut to coincide to its axis of crystallization, into first a solid
+cylinder nicely fitting the pipe <i>C</i> and finished with an
+after-grinding, cutting away four-tenths of the cylinder, as shown at
+<i>I</i>, Fig. 143. Here the line <i>m</i> represents the locking face of the
+jewel and the line <i>o</i> the clearance to free the escaping tooth, the
+angle at <i>n</i> being about fifty-four degrees. This angle (<i>n</i>) should
+leave the rounding of the stone intact, that is, the rounding of the
+angle should be left and not made after the flat faces <i>m o</i> are ground
+and polished. The circular space at <i>I</i> is filled with an aluminum
+<a name="Page_145" id="Page_145"></a><a name="Page_146" id="Page_146"></a>pin. The sizes shown are of about the right relative proportions; but
+we feel it well to repeat the statement made previously, to the effect
+that the detent to a chronometer cannot well be made too light.</p>
+
+<div class="figcenter"><a href="images/pict141-142.jpg"><img src="images/pict141-142-tb.jpg" alt="Fig. 141-142" title="Fig. 141-142" /></a></div>
+
+<p>The so-called gold spring shown at <i>H</i>, Figs. 141 and 142, should also
+be as light as is consistent with due strength and can be made of the
+composite metal used for gold filled goods, as the only real benefit to
+be derived from employing gold is to avoid the necessity of applying oil
+to any part of the escapement. If such gold metal is employed, after
+hammering to obtain the greatest possible elasticity to the spring, the
+gold is filed away, except where the spring is acted upon by the
+discharging jewel <i>h</i>. We have previously mentioned the importance of
+avoiding wide, flat contacts between all acting surfaces, like where the
+gold spring rests on the horn of the detent at <i>p</i>; also where the
+detent banks on the banking screw, shown at <i>G</i>, Fig. 142. Under this
+principle the impact of the face of the discharging jewel with the end
+of the gold spring should be confined to as small a surface as is
+consistent with what will not produce abrasive action. The gold spring
+is shaped as shown at Fig. 142 and loses, in a measure, under the pipe
+of the locking jewel, a little more than one-half of the pipe below the
+blade of the detent being cut away, as shown in Fig. 143, where the
+lines <i>r r</i> show the extent of the part of the pipe which banks against
+the banking screw <i>G</i>. In this place even, only the curved surface of
+the outside of the pipe touches the screw <i>G</i>, again avoiding contact of
+broad surfaces.</p>
+
+<div class="figleft"><img src="images/pict143.jpg" alt="Fig. 143" title="Fig. 143" /></div>
+
+<p>We show the gold spring separate at Fig. 144. A slight torsion or twist
+is given to the gold spring to cause it to bend with a true curvature in
+the act of allowing the discharging pallet to pass back after unlocking.
+If the gold spring is filed and stoned to the right flexure, that is,
+the thinnest point properly placed or, say, located, the gold spring
+will not continue in contact with the discharging pallet any longer time
+or through a greater arc than during the process of unlocking. To make
+this statement better understood, let us suppose the weakest part of the
+gold spring <i>H</i> is opposite the arrow <i>y</i>, Fig. 141, it will readily be
+understood the contact of the discharging stone <i>h</i> would continue
+longer than if the point of greatest (or easiest) flexure was nearer to
+the pipe <i>C</i>. If the end <i>D<sup>2</sup></i> of the horn of the detent is as near as
+it should be to the discharging <a name="Page_147" id="Page_147"></a>stone there need be no fear but the
+escapement will be unlocked. The horn <i>D<sup>2</sup></i> of the detent should be
+bent until five degrees of angular motion of the balance will unlock the
+escape, and the contact of discharging jewel <i>h</i> should be made without
+engaging friction. This condition can be determined by observing if the
+jewel seems to slide up (toward the pipe <i>C</i>) on the gold spring after
+contact. Some adjusters set the jewel <i>J</i>, Figs. 143 and 141, in such a
+way that the tooth rests close to the base; such adjusters claiming this
+course has a tendency to avoid cockling or buckling of the detent spring
+<i>E</i>. Such adjusters also set the impulse jewel slightly oblique, so as
+to lean on the opposite angle of the tooth. Our advice is to set both
+stones in places corresponding to the axis of the balance staff, and the
+escape-wheel mobiles.</p>
+
+
+<h4>THE DETENT SPRING.</h4>
+
+<div class="figcenter"><img src="images/pict144.jpg" alt="Fig. 144" title="Fig. 144" /></div>
+<p>It will be noticed we have made the detent spring <i>E</i> pretty wide and
+extended it well above the blade of the detent. By shaping the detent in
+this way nearly all the tendency of the spring <i>E</i> to cockle is
+annulled. We would beg to add to what we said in regard to setting
+jewels obliquely. We are unable to understand the advantage of
+wide-faced stones and deep teeth when we do not take advantage of the
+wide surfaces which we assert are important. We guarantee that with a
+detent and spring made as we show, there will be no tendency to cockle,
+or if there is, it will be too feeble to even display itself. Those who
+have had extended experience with chronometers cannot fail to have
+noticed a gummy secretion which accumulates on the impulse and
+discharging stones of a chronometer, although no oil is ever applied to
+them. We imagine this coating is derived from the oil applied to the
+pivots, which certainly evaporates, passes into vapor, or the remaining
+oil could not become gummy. We would advise, when setting jewels (we
+mean the locking, impulse and discharging jewels), to employ no more
+shellac than is absolutely necessary, depending chiefly on metallic
+contact for security.</p>
+
+<h4><a name="Page_148" id="Page_148"></a>DETAILS OF CONSTRUCTION.</h4>
+
+<p>We will now say a few words about the number of beats to the hour for a
+box or marine chronometer to make to give the best results. Experience
+shows that slow but most perfect construction has settled that 14,400,
+or four vibrations of the balance to a second, as the proper number, the
+weight of balance, including balance proper and movable weights, to be
+about 5-1/2 pennyweights, and the compensating curb about 1-2/10" in
+diameter. The escape wheel, 55/100" in diameter and recessed so as to be
+as light as possible, should have sufficient strength to perform its
+functions properly. The thickness or, more properly, the face extent of
+the tooth, measured in the direction of the axis of the escape wheel,
+should be about 1/20". The recessing should extend half way up the
+radial back of the tooth at <i>t</i>. The curvature of the back of the teeth
+is produced with the same radii as the impulse roller. To locate the
+center from which the arc which defines the back of the teeth is swept,
+we halve the space between the teeth <i>A<sup>2</sup></i> and <i>a<sup>4</sup></i> and establish
+the point <i>n</i>, Fig. 141, and with our dividers set to sweep the circle
+representing the impulse roller, we sweep an arc passing the point of
+the tooth <i>A<sup>3</sup></i> and <i>u</i>, thus locating the center <i>w</i>. From the center
+<i>k</i> of the escape wheel we sweep a complete circle, a portion of which
+is represented by the arc <i>w v</i>. For delineating other teeth we set one
+leg of our dividers to agree with the point of the tooth and the other
+leg on the circle <i>w v</i> and produce an arc like <i>z u</i>.</p>
+
+
+<h4>ORIGINAL DESIGNING OF THE ESCAPEMENT.</h4>
+
+<p>On delineating our chronometer escapement shown at Fig. 141 we have
+followed no text-book authority, but have drawn it according to such
+requirements as are essential to obtain the best results. An escapement
+of any kind is only a machine, and merely requires in its construction a
+combination of sound mechanical principles. Neither Saunier nor Britten,
+in their works, give instructions for drawing this escapement which will
+bear close analysis. It is not our intention, however, to criticise
+these authors, except we can present better methods and give correct
+systems.</p>
+
+
+<h4>TANGENTIAL LOCKINGS.</h4>
+
+<p>It has been a matter of great contention with makers of chronometer and
+also lever escapements as to the advantages of "tangential lockings." By
+this term is meant a locking the <a name="Page_149" id="Page_149"></a>same as is shown at <i>C</i>, Fig. 141, and
+means a detent planted at right angles to a line radial to the
+escape-wheel axis, said radial line passing through the point of the
+escape-wheel tooth resting on the locking jewel. In escapements not set
+tangential, the detent is pushed forward in the direction of the arrow
+<i>x</i> about half a tooth space. Britten, in his "Hand-Book," gives a
+drawing of such an escapement. We claim the chief advantage of
+tangential locking to lie in the action of the escape-wheel teeth, both
+on the impulse stone and also on the locking stone of the detent.
+Saunier, in his "Modern Horology," gives the inclination of the front
+fan of the escape-wheel teeth as being at an angle of twenty-seven
+degrees to a radial line. Britten says twenty degrees, and also employs
+a non-tangential locking.</p>
+
+<p>Our drawing is on an angle of twenty-eight degrees, which is as low as
+is safe, as we shall proceed to demonstrate. For establishing the angle
+of an escape-wheel tooth we draw the line <i>C d</i>, from the point of the
+escape-wheel tooth resting on the locking stone shown at <i>C</i> at an angle
+of twenty-eight degrees to radial line <i>C k</i>. We have already discussed
+how to locate and plant the center of the balance staff.</p>
+
+<p>We shall not show in this drawing the angular motion of the escape
+wheel, but delineate at the radial lines <i>c e</i> and <i>c f</i> of the arc of
+the balance during the extent of its implication with the periphery of
+the escape wheel, which arc is one of about forty-eight degrees. Of this
+angle but forty-three degrees is attempted to be utilized for the
+purpose of impulse, five degrees being allowed for the impulse jewel to
+pass inside of the arc of periphery of the escape wheel before the
+locking jewel releases the tooth of the escape wheel resting upon it. At
+this point it is supposed the escape wheel attacks the impulse jewel,
+because, as we just explained, the locking jewel has released the tooth
+engaging it. Now, if the train had no weight, no inertia to overcome,
+the escape wheel tooth <i>A<sup>2</sup></i> would move forward and attack the impulse
+pallet instantly; but, in fact, as we have already explained, there will
+be an appreciable time elapse before the tooth overtakes the
+rapidly-moving impulse jewel. It will, of course, be understood that the
+reference letters used herein refer to the illustrations that have
+appeared on preceding pages.</p>
+
+<p>If we reason carefully on the matter, we will readily comprehend that we
+can move the locking jewel, <i>i.e.</i>, set it so the unlocking will take
+place in reality before the impulse jewel has passed <a name="Page_150" id="Page_150"></a>through the entire
+five degrees of arc embraced between the radial lines <i>c e</i> and <i>c g</i>,
+Fig. 141, and yet have the tooth attack the jewel after the five degrees
+of arc. In practice it is safe to set the discharging jewel <i>h</i> so the
+release of the held tooth <i>A<sup>1</sup></i> will take place as soon as the tooth
+<i>A<sup>2</sup></i> is inside the principal line of the escape wheel. As we
+previously explained, the contact between <i>A<sup>2</sup></i> and the impulse jewel
+<i>i</i> would not in reality occur until the said jewel <i>i</i> had fully passed
+through the arc (five degrees) embraced between the radial lines <i>c e</i>
+and <i>c g</i>.</p>
+
+<p>At this point we will explain why we drew the front fan of the
+escape-wheel teeth at the angle of twenty-eight degrees. If the fan of
+impulse jewel <i>i</i> is set radial to the axis of the balance, the
+engagement of the tooth <i>A<sup>2</sup></i> would be at a disadvantage if it took
+place prior to this jewel passing through an arc of five degrees inside
+the periphery of the escape wheel. It will be evident on thought that if
+an escape-wheel tooth engaged the impulse stone before the five-degrees
+angle had passed, the contact would not be on its flat face, but the
+tooth would strike the impulse jewel on its outer angle. A continued
+inspection will also reveal the fact that in order to have the point of
+the tooth engage the flat surface of the impulse pallet the impulse
+jewel must coincide with the radial line <i>c g</i>. If we seek to remedy
+this condition by setting the impulse jewel so the face is not radial,
+but inclined backward, we encounter a bad engaging friction, because,
+during the first part of the impulse action, the tooth has to slide up
+the face of the impulse jewel. All things considered, the best action is
+obtained with the impulse jewel set so the acting face is radial to the
+balance staff and the engagement takes place between the tooth and the
+impulse jewel when both are moving with equal velocities, <i>i.e.</i>, when
+the balance is performing with an arc (or motion) of 1-1/4 revolutions
+or 225 degrees each way from a point of rest. Under such conditions the
+actual contact will not take place before some little time after the
+impulse jewel has passed the five-degree arc between the lines <i>c e</i> and
+<i>c g</i>.</p>
+
+
+<h4>THE DROP AND DRAW CONSIDERED.</h4>
+
+<p>Exactly how much drop must be allowed from the time the tooth leaves the
+impulse jewel before the locking tooth engages the locking jewel will
+depend in a great measure on the perfection of workmanship, but should
+in no instance be more than what is absolutely required to make the
+escapement safe. The amount of <a name="Page_151" id="Page_151"></a>draw given to the locking stone <i>c</i> is
+usually about twelve degrees to the radial line <i>k a</i>. Much of the
+perfection of the chronometer escapement will always depend on the skill
+of the escapement adjuster and not on the mechanical perfection of the
+parts.</p>
+
+<p>The jewels all have to be set by hand after they are made, and the
+distance to which the impulse jewel protrudes beyond the periphery of
+the impulse roller is entirely a matter for hand and eye, but should
+never exceed 2/1000". After the locking jewel <i>c</i> is set, we can set the
+foot <i>F</i> of the detent <i>D</i> forward or back, to perfect and correct the
+engagement of the escape-wheel teeth with the impulse roller <i>B</i>. If we
+set this too far forward, the tooth <i>A<sup>3</sup></i> will encounter the roller
+while the tooth <i>A<sup>2</sup></i> will be free.</p>
+
+<p>We would beg to say here there is no escape wheel made which requires
+the same extreme accuracy as the chronometer, as the tooth spaces and
+the equal radial extent of each tooth should be only limited by our
+powers toward perfection. It is usual to give the detent a locking of
+about two degrees; that is, it requires about two degrees to open it,
+counting the center of fluxion of the detent spring <i>E</i> and five degrees
+of balance arc.</p>
+
+
+<h4>FITTING UP OF THE FOOT.</h4>
+
+<p>Several attempts have been made by chronometer makers to have the foot
+<i>F</i> adjustable; that is, so it could be moved back and forth with a
+screw, but we have never known of anything satisfactory being
+accomplished in this direction. About the best way of fitting up the
+foot <i>F</i> seems to be to provide it with two soft iron steady pins (shown
+at <i>j</i>) with corresponding holes in the chariot, said holes being
+conically enlarged so they (the pins) can be bent and manipulated so the
+detent not only stands in the proper position as regards the escape
+wheel, but also to give the detent spring <i>E</i> the proper elastic force
+to return in time to afford a secure locking to the arresting tooth of
+the escape wheel after an impulse has been given.</p>
+
+<p>If these pins <i>j</i> are bent properly by the adjuster, whoever afterwards
+cleans the chronometer needs only to gently push the foot <i>F</i> forward so
+as to cause the pins <i>j</i> to take the correct positions as determined by
+the adjuster and set the screw <i>l</i> up to hold the foot <i>F</i> when all the
+other relations are as they should be, except such as we can control by
+the screw <i>G</i>, which prevents the locking jewel from entering too deeply
+into the escape wheel.</p>
+
+<p><a name="Page_152" id="Page_152"></a>In addition to being a complete master of the technical part of his
+business, it is also desirable that the up-to-date workman should be
+familiar with the subject from a historical point of view. To aid in
+such an understanding of the matter we have translated from "L'Almanach
+de l'Horologerie et de la Bijouterie" the matter contained in the
+following chapter.</p>
+
+
+
+<hr style="width: 65%;" /><p><a name="Page_153" id="Page_153"></a></p>
+<h2>CHAPTER IV.</h2>
+
+<h3>HISTORY OF ESCAPEMENTS.</h3>
+
+
+<p>It could not have been long after man first became cognizant of his
+reasoning faculties that he began to take more or less notice of the
+flight of time. The motion of the sun by day and of the moon and stars
+by night served to warn him of the recurring periods of light and
+darkness. By noting the position of these stellar bodies during his
+lonely vigils, he soon became proficient in roughly dividing up the
+cycle into sections, which he denominated the hours of the day and of
+the night. Primitive at first, his methods were simple, his needs few
+and his time abundant. Increase in numbers, multiplicity of duties, and
+division of occupation began to make it imperative that a more
+systematic following of these occupations should be instituted, and with
+this end in view he contrived, by means of burning lights or by
+restricting the flowing of water or the falling of weights, to subdivide
+into convenient intervals and in a tolerably satisfactory manner the
+periods of light.</p>
+
+<p>These modest means then were the first steps toward the exact
+subdivisions of time which we now enjoy. Unrest, progress, discontent
+with things that be, we must acknowledge, have, from the appearance of
+the first clock to the present hour, been the powers which have driven
+on the inventive genius of watch and clockmakers to designate some new
+and more acceptable system for regulating the course of the movement. In
+consequence of this restless search after the best, a very considerable
+number of escapements have been invented and made up, both for clocks
+and watches; only a few, however, of the almost numberless systems have
+survived the test of time and been adopted in the manufacture of the
+timepiece as we know it now. Indeed, many such inventions never passed
+the experimental stage, and yet it would be very interesting to the
+professional horologist, the apprentice and even the layman to become
+more intimately acquainted with the vast variety of inventions made upon
+this domain since the inception of horological science. Undoubtedly, a
+complete collection of all the escapements invented would constitute a
+most instructive work for the progressive watchmaker, and while we are
+waiting for a competent author <a name="Page_154" id="Page_154"></a>to take such an exhaustive work upon his
+hands, we shall endeavor to open the way and trust that a number of
+voluntary collaborators will come forward and assist us to the extent of
+their ability in filling up the chinks.</p>
+
+
+<h4>PROBLEMS TO BE SOLVED.</h4>
+
+<p>The problem to be solved by means of the escapement has always been to
+govern, within limits precise and perfectly regular, if it be possible,
+the flow of the motive force; that means the procession of the
+wheel-work and, as a consequence, of the hands thereto attached. At
+first blush it seems as if a continually-moving governor, such as is in
+use on steam engines, for example, ought to fulfil the conditions, and
+attempts have accordingly been made upon this line with results which
+have proven entirely unsatisfactory.</p>
+
+<p>Having thoroughly sifted the many varieties at hand, it has been finally
+determined that the only means known to provide the most regular flow of
+power consists in intermittently interrupting the procession of the
+wheel-work, and thereby gaining a periodically uniform movement.
+Whatever may be the system or kind of escapement employed, the
+functioning of the mechanism is characterized by the suspension, at
+regular intervals, of the rotation of the last wheel of the train and in
+transmitting to a regulator, be it a balance or a pendulum, the power
+sent into that wheel.</p>
+
+
+<h4>ESCAPEMENT THE MOST ESSENTIAL PART.</h4>
+
+<p>Of all the parts of the timepiece the escapement is then the most
+essential; it is the part which assures regularity in the running of the
+watch or clock, and that part of parts that endows the piece with real
+value. The most perfect escapement would be that one which should
+perform its duty with the least influence upon the time of oscillation
+or vibration of the regulating organ. The stoppage of the train by the
+escapement is brought about in different ways, which may be gathered
+under three heads or categories. In the two which we shall mention
+first, the stop is effected directly upon the axis of the regulator, or
+against a piece which forms a part of that axis; the tooth of the escape
+wheel at the moment of its disengagement remains supported upon or
+against that stop.</p>
+
+<p>In the first escapement invented and, indeed, in some actually employed
+to-day for certain kinds of timekeepers, we notice during the locking a
+retrograde movement of the escape wheel; to this kind of movement has
+been given the name of <i>recoil escapement</i>.<a name="Page_155" id="Page_155"></a> It was recognized by the
+fraternity that this recoil was prejudicial to the regularity of the
+running of the mechanism and, after the invention of the pendulum and
+the spiral, inventive makers succeeded in replacing this sort of
+escapement with one which we now call the <i>dead-beat escapement</i>. In
+this latter the wheel, stopped by the axis of the regulator, remains
+immovable up to the instant of its disengagement or unlocking.</p>
+
+<p>In the third category have been collected all those forms of escapement
+wherein the escape wheel is locked by an intermediate piece, independent
+of the regulating organ. This latter performs its vibrations of
+oscillation quite without interference, and it is only in contact with
+the train during the very brief moment of impulse which is needful to
+keep the regulating organ in motion. This category constitutes what is
+known as the <i>detached escapement</i> class.</p>
+
+<p>Of the <i>recoil escapement</i> the principal types are: the <i>verge
+escapement</i> or <i>crown-wheel escapement</i> for both watches and clocks, and
+the <i>recoil anchor escapement</i> for clocks. The <i>cylinder</i> and <i>duplex
+escapements</i> for watches and the <i>Graham anchor escapement</i> for clocks
+are styles of the <i>dead-beat escapement</i> most often employed. Among the
+<i>detached escapements</i> we have the <i>lever</i> and <i>detent</i> or <i>chronometer
+escapements</i> for watches; for clocks there is no fixed type of detached
+lever and it finds no application to-day.</p>
+
+
+<h4>THE VERGE ESCAPEMENT.</h4>
+
+<p>The <i>verge escapement</i>, called also the <i>crown-wheel escapement</i>, is by
+far the simplest and presents the least difficulty in construction. We
+regret that the world does not know either the name of its originator
+nor the date at which the invention made its first appearance, but it
+seems to have followed very closely upon the birth of mechanical
+horology.</p>
+
+<p>Up to 1750 it was employed to the exclusion of almost all the others. In
+1850 a very large part of the ordinary commercial watches were still
+fitted with the verge escapement, and it is still used under the form of
+<i>recoil anchor</i> in clocks, eighty years after the invention of the
+cylinder escapement, or in 1802. Ferdinand Berthoud, in his "History of
+the Measurement of Time," says of the balance-wheel escapement: "Since
+the epoch of its invention an infinite variety of escapements have been
+constructed, but the one which is employed in ordinary watches for
+every-day use is still the best." In referring to our illustrations, we
+beg first to call <a name="Page_156" id="Page_156"></a>attention to the plates marked Figs. 145 and 146.
+This plate gives us two views of a verge escapement; that is, a balance
+wheel and a verge formed by its two opposite pallets. The views are
+intentionally presented in this manner to show that the verge <i>V</i> may be
+disposed either horizontally, as in Fig. 146, or vertically, as in Fig.
+145.</p>
+
+<hr style="width: 65%;" />
+
+<div class="figleft"><img src="images/pict145-146.jpg" alt="Fig. 145-146" title="Fig. 145-146" /></div>
+<div class="figright"><img src="images/pict147.jpg" alt="Fig. 147" title="Fig. 147" /></div>
+
+<hr style="width: 65%;" />
+<p>Let us imagine that our drawing is in motion, then will the tooth <i>d</i>,
+of the crown wheel <i>R</i>, be pushing against the pallet <i>P</i>, and just upon
+the point of slipping by or escaping, while the opposite tooth <i>e</i> is
+just about to impinge upon the advancing pallet <i>P'</i>. This it does, and
+will at first, through the impulse received from the tooth <i>d</i> be forced
+back by the momentum of the pallet, that is, suffer a recoil; but on the
+return journey of the pallet <i>P'</i>, the tooth <i>e</i> will then add its
+impulse to the receding pallet. The tooth <i>e</i> having thus accomplished
+its mission, will now slip by and the tooth <i>c</i> will come in lock with
+the pallet <i>P</i> and, after the manner just described for <i>e</i>, continue
+the escapement. Usually these escape wheels are provided with teeth to
+the number of 11, 13 or 15, and always uneven. A great advantage
+possessed by this form of escapement is that it does not require any
+oil, and it may be made to work even under very inferior construction.</p>
+
+<h4><a name="Page_157" id="Page_157"></a>OLDEST ARRANGEMENT OF A CROWN-WHEEL ESCAPEMENT.</h4>
+
+<div class="figright"><img src="images/pict148.jpg" alt="Fig. 148" title="Fig. 148" /></div>
+
+<p>Plate 147 shows us the oldest known arrangement of a crown-wheel
+escapement in a clock. <i>R</i> is the crown wheel or balance wheel acting
+upon the pallets <i>P</i> and <i>P'</i>, which form part of the verge <i>V</i>. This
+verge is suspended as lightly as possible upon a pliable cord <i>C</i> and
+carries at its upper end two arms, <i>B</i> and <i>B</i>, called adjusters,
+forming the balance. Two small weights <i>D D</i>, adapted to movement along
+the rules or adjusters serve to regulate the duration of a vibration. In
+Fig. 148 we have the arrangement adopted in small timepieces and
+watches: <i>B</i> represents the regulator in the form of a circular balance,
+but not yet furnished with a spiral regulating spring; <i>c</i> is the last
+wheel of the train and called the <i>fourth wheel</i>, it being that number
+distant from the great wheel. As will be seen, the verge provided with
+its pallets is vertically placed, as in the preceding plate.</p>
+
+<div class="figright"><img src="images/pict149.jpg" alt="Fig. 149" title="Fig. 149" /></div>
+
+<p>Here it will quickly be seen that regarded from the standpoint of
+regularity of motion, this arrangement can be productive of but meager
+results. Subjected as it is to the influence of the slightest variation
+in the motive power and of the least jar or shaking, a balance wheel
+escapement improvided with a regulator containing within itself a
+regulating force, could not possibly give forth anything else than an
+unsteady movement. However, mechanical clocks fitted with this
+escapement offer indisputable advantages over the ancient clepsydra; in
+spite of their imperfections they rendered important services,
+especially after the striking movement had been added. For more than
+three centuries both this crude escapement and the cruder regulator were
+suffered to continue in this state without a thought of improvement;
+even <a name="Page_158" id="Page_158"></a>in 1600, when Galileo discovered the law governing the oscillation
+of the pendulum, they did not suspect how important this discovery was
+for the science of time measurement.</p>
+
+
+<h4>GALILEO'S EXPERIMENTS.</h4>
+
+<div class="figleft"><img src="images/pict150.jpg" alt="Fig. 150" title="Fig. 150" /></div>
+
+<p>Galileo, himself, in spite of his genius for investigation, was so
+engrossed in his researches that he could not seem to disengage the
+simple pendulum from the compound pendulums to which he devoted his
+attention; besides, he attributed to the oscillation an absolute
+generality of isochronism, which they did not possess; nor did he know
+how to apply his famous discovery to the measurement of time. In fact,
+it was not till after more than half a century had elapsed, in 1657, to
+be exact, that the celebrated Dutch mathematician and astronomer,
+Huygens, published his memoirs in which he made known to the world the
+degree of perfection which would accrue to clocks if the pendulum were
+adopted to regulate their movement.</p>
+
+<div class="figright"><img src="images/pict151.jpg" alt="Fig. 151" title="Fig. 151" /></div>
+
+<p>An attempt was indeed made to snatch from Huygens and confer upon
+Galileo the glory of having first applied the pendulum to a clock, but
+this attempt not having been made until some time after the publication
+of "Huygens' Memoirs," it was impossible to place any faith in the
+contention. If Galileo had indeed solved the beautiful problem, both in
+the conception and the fact, the honor of the discovery was lost to him
+by the laziness and negligence of his pupil, Viviani, upon whom he had
+placed such high hopes. One thing is certain, that the right of priority
+of the discovery and the recognition of the entire world has been
+incontestably bestowed upon Huygens. The escapement which Galileo is
+supposed to have conceived and to which he applied the pendulum, is
+shown in Fig. 149. The wheel <i>R</i> is supplied with teeth, which lock
+against the piece <i>D</i> attached to a lever pivoted at <i>a</i>, and also with
+pins calculated to impart impulses <a name="Page_159" id="Page_159"></a>to the pendulum through the pallet
+<i>P</i>. The arm <i>L</i> serves to disengage or unlock the wheel by lifting the
+lever <i>D</i> upon the return oscillation of the pendulum.</p>
+
+<hr style="width: 65%;" />
+
+<div class="figleft"><img src="images/pict152.jpg" alt="Fig. 152" title="Fig. 152" /></div>
+<div class="figright"><img src="images/pict153.jpg" alt="Fig. 153" title="Fig. 153" /></div>
+
+<hr style="width: 65%;" />
+
+<p>A careful study of Fig. 150 will discover a simple transposition which
+it became necessary to make in the clocks, for the effectual adaptation
+of the pendulum to their regulation. The verge <i>V</i> was set up
+horizontally and the pendulum <i>B</i>, suspended freely from a flexible
+cord, received the impulses through the intermediation of the forked arm
+<i>F</i>, which formed a part of the verge. At first this forked arm was not
+thought of, for the pendulum itself formed a part of the verge. A
+far-reaching step had been taken, but it soon became apparent that
+perfection was still a long way off. The crown-wheel escapement forcibly
+incited the pendulum to wider oscillations; these oscillations not being
+as Galileo had believed, of unvaried durations, but they varied sensibly
+with the intensity of the motive power.</p>
+
+
+<h4>THE ATTAINMENT OF ISOCHRONISM BY HUYGENS.</h4>
+
+<div class="figleft"><img src="images/pict154.jpg" alt="Fig. 154" title="Fig. 154" /></div>
+<p>Huygens rendered his pendulum <i>isochronous</i>; that is, compelled it to
+make its oscillations of equal duration, whatever might be the arc
+described, by suspending the pendulum between two metallic curves <i>c
+c'</i>, each one formed by an arc of a cycloid and against which the
+suspending cord must lie upon each forward or <a name="Page_160" id="Page_160"></a>backward oscillation. We
+show this device in Fig. 151. In great oscillations, and by that we mean
+oscillations under a greater impulse, the pendulum would thus be
+shortened and the shortening would correct the time of the oscillation.
+However, the application of an exact cycloidal arc was a matter of no
+little difficulty, if not an impossibility in practice, and practical
+men began to grope about in search of an escapement which would permit
+the use of shorter arcs of oscillation. At London the horologist, G.
+Clement, solved the problem in 1675 with his rack escapement and recoil
+anchor. In the interval other means were invented, especially the
+addition of a second pendulum to correct the irregularities of the
+first. Such an escapement is pictured in Fig. 152. The verge is again
+vertical and carries near its upper end two arms <i>D D</i>, which are each
+connected by a cord with a pendulum. The two pendulums oscillate
+constantly in the inverse sense the one to the other.</p>
+
+
+<h4>ANOTHER TWO-PENDULUM ESCAPEMENT.</h4>
+
+<div class="figright"><img src="images/pict155.jpg" alt="Fig. 155" title="Fig. 155" /></div>
+<p>We show another escapement with two pendulums in Fig. 153. These are
+fixed directly upon two axes, each one carrying a pallet <i>P P'</i> and a
+segment of a toothed wheel <i>D D</i>, which produces the effect of
+solidarity between them. The two pendulums oscillate inversely one to
+the other, and one after the other receives an impulse. This escapement
+was constructed by Jean Baptiste Dutertre, of Paris.</p>
+
+<p>Fig. 154 shows another disposition of a double pendulum. While the
+pendulum here is double, it has but one bob; it receives the impulse by
+means of a double fork <i>F</i>. <i>C C</i> represents the cycloidal curves and
+are placed with a view of correcting the <a name="Page_161" id="Page_161"></a>inequality in the duration of
+the oscillations. In watches the circular balances did not afford any
+better results than the regulating rods or rules of the clocks, and the
+pendulum, of course, was out of the question altogether; it therefore
+became imperative to invent some other regulating system.</p>
+
+<hr style="width: 65%;" />
+
+<div class="figleft"><img src="images/pict156.jpg" alt="Fig. 156" title="Fig. 156" /></div>
+<div class="figright"><img src="images/pict157.jpg" alt="Fig. 157" title="Fig. 157" /></div>
+
+<hr style="width: 65%;" />
+
+<p>It occured to the Abb&eacute; d'Hautefeuille to form a sort of resilient
+mechanism by attaching one end of a hog's bristle to the plate and the
+other to the balance near the axis. Though imperfect in results, this
+was nevertheless a brilliant idea, and it was but a short step to
+replace the bristle with a straight and very flexible spring, which
+later was supplanted by one coiled up like a serpent; but in spite of
+this advancement, the watches did not keep much better time. Harrison,
+the celebrated English horologist, had recourse to two artifices, of
+which the one consisted in giving to the pallets of the escapement such
+a curvature that the balance could be led back with a velocity
+corresponding to the extension of the oscillation; the second consisted
+of an accessory piece, the resultant action of which was analogous to
+that of the cycloidal curves in connection with the pendulum.</p>
+
+
+<h4>CORRECTING IRREGULARITIES IN THE VERGE ESCAPEMENT.</h4>
+
+
+<div class="figleft"><img src="images/pict158.jpg" alt="Fig. 158" title="Fig. 158" /></div>
+<p>Huygens attempted to correct these irregularities in the verge
+escapement in watches by amplifying the arc of oscillation of the
+balance itself. He constructed for that purpose a pirouette escapement
+shown in Fig. 155, in which a toothed wheel <i>A</i> adjusted upon <a name="Page_162" id="Page_162"></a>the verge
+<i>V</i> serves as an intermediary between that and the balance <i>B</i>, upon the
+axis of which was fixed a pinion <i>D</i>. By this method he obtained
+extended arcs of vibration, but the vibrations were, as a consequence,
+very slow, and they still remained subject to all the irregularities
+arising from the variation in the motive power as well as from shocks. A
+little later, but about the same epoch, a certain Dr. Hook, of the Royal
+Society of London, contrived another arrangement by means of which he
+succeeded, so it appeared to him at least, in greatly diminishing the
+influence of shock upon the escapement; but many other, perhaps greater,
+inconveniences caused his invention to be speedily rejected. We shall
+give our readers an idea of what Dr. Hook's escapement was like.</p>
+
+<div class="figright"><img src="images/pict159.jpg" alt="Fig. 159" title="Fig. 159" /></div>
+
+<p>On looking at Fig. 156 we see the escape wheel <i>R</i>, which was flat and
+in the form of a ratchet; it was provided with two balances. <i>B B</i>
+engaging each other in teeth, each one carrying a pallet <i>P P'</i> upon its
+axis; the axes of the three wheels being parallel. Now, in our drawing,
+the tooth <i>a</i> of the escape wheel exerts its lift upon the pallet <i>P'</i>;
+when this tooth escapes the tooth <i>b</i> will fall upon the pallet <i>P'</i> on
+the opposite side, a recoil will be produced upon the action of the two
+united balances, then the tooth <i>b</i> will give its impulse in the
+contrary direction. Considerable analogy exists between this form of
+escapement and that shown in Fig. 153 and intended for clocks. This was
+the busy era in the watchmaker's line. All the great heads were
+pondering upon the subject and everyone was on the <i>qui vive</i> for the
+newest thing in the art.</p>
+
+<p>In 1674 Huygens brought out the first watch having a regulating spring
+in the form of a spiral; the merit of this invention was disputed by the
+English savant, Dr. Hook, who pretended, as <a name="Page_163" id="Page_163"></a>did Galileo, in the
+application of the pendulum, to have priority in the idea. Huygens, who
+had discovered and corrected the irregularities in the oscillations of
+the pendulum, did not think of those of the balance with the spiral
+spring. And it was not until the close of the year 1750 that Pierre Le
+Roy and Ferdinand Berthoud studied the conditions of isochronism
+pertaining to the spiral.</p>
+
+
+<h4>AN INVENTION THAT CREATED MUCH ENTHUSIASM.</h4>
+
+<p>However that may be, this magnificent invention, like the adaptation of
+the pendulum, was welcomed with general enthusiasm throughout the
+scientific world: without spiral and without pendulum, no other
+escapement but the recoil escapement was possible; a new highway was
+thus opened to the searchers. The water clocks (clepsydr&aelig;) and the hour
+glasses disappeared completely, and the timepieces which had till then
+only marked the hours, having been perfected up to the point of keeping
+more exact time, were graced with the addition of another hand to tell
+off the minutes.</p>
+
+<hr style="width: 65%;" />
+
+<div class="figleft"><img src="images/pict160.jpg" alt="Fig. 160" title="Fig. 160" /></div>
+<div class="figright"><img src="images/pict161.jpg" alt="Fig. 161" title="Fig. 161" /></div>
+
+<hr style="width: 65%;" />
+
+<p>It was not until 1695 that the first <i>dead-beat escapement</i> appeared
+upon the scene; during the interval of over twenty years all thought had
+been directed toward the one goal, viz.: the perfecting of the <i>verge
+escapement</i>; but practice demonstrated that no other arrangement of the
+parts was superior to the original idea. For the benefit of our readers
+we shall give a few of these attempts at betterment, and you may see for
+yourselves wherein the trials failed.</p>
+
+<p>Fig. 157 represents a <i>verge escapement</i> with a ratchet wheel, the
+pallets <i>P P'</i> being carried upon separate axes. The two axes are
+rigidly connected, the one to the other, by means of the arms <i>o o'</i>.
+One of the axes carries besides the fork <i>F</i>, which transmits the
+<a name="Page_164" id="Page_164"></a>impulse to the pendulum <i>B</i>. In the front view, at the right of the
+plate, for the sake of clearness the fork and the pendulum are not
+shown, but one may easily see the jointure of the arms <i>o o'</i> and their
+mode of operation.</p>
+
+<p>Another very peculiar arrangement of the <i>verge escapement</i> we show at
+Fig. 158. In this there are two wheels, one, <i>R'</i>, a small one in the
+form of a ratchet; the other, <i>R</i>, somewhat larger, called the balance
+wheel, but being supplied with straight and slender teeth. The verge <i>V</i>
+carrying the two pallets is pivoted in the vertical diameter of the
+larger wheel. The front view shows the <i>modus operandi</i> of this
+combination, which is practically the same as the others. The tooth <i>a</i>
+of the large wheel exerts its force upon the pallet <i>P</i>, and the tooth
+<i>b</i> of the ratchet will encounter the pallet <i>P'</i>. This pallet, after
+suffering its recoil, will receive the impulse communicated by the tooth
+<i>b</i>. This escapement surely could not have given much satisfaction, for
+it offers no advantage over the others, besides it is of very difficult
+construction.</p>
+
+<hr style="width: 65%;" />
+
+<div class="figleft"><img src="images/pict162.jpg" alt="Fig. 162" title="Fig. 162" /></div>
+<div class="figright"><img src="images/pict163.jpg" alt="Fig. 163" title="Fig. 163" /></div>
+<hr style="width: 65%;" />
+
+<h4>INGENIOUS ATTEMPTS AT SOLUTION OF A DIFFICULT PROBLEM.</h4>
+
+<p>Much ingenuity to a worthy end, but of little practical value, is
+displayed in these various attempts at the solution of a very difficult
+problem. In Fig. 159 we have a mechanism combining two escape wheels
+engaging each other in gear; of the two wheels, <i>R R'</i>, one alone is
+driven directly by the train, the other being turned in the opposite
+direction by its comrade. Both are furnished with pins <i>c c'</i>, which act
+alternately upon the pallets <i>P P'</i> disposed in the same plane upon the
+verge <i>V</i> and pivoted between the wheels. Our drawing represents the
+escapement at the moment when the pin <i>C'</i> delivers its impulse, and
+this having been accomplished, the locking <a name="Page_165" id="Page_165"></a>takes place upon the pin <i>C</i>
+of the other wheel upon the pallet <i>P'</i>. Another system of two escape
+wheels is shown in Fig. 160, but in this case the two wheels <i>R R</i> are
+driven in a like direction by the last wheel <i>A</i> of the train. The
+operation of the escapement is the same as in Fig. 159.</p>
+
+<hr style="width: 65%;" />
+
+<div class="figleft"><img src="images/pict164.jpg" alt="Fig. 164" title="Fig. 164" /></div>
+<div class="figright"><img src="images/pict165.jpg" alt="Fig. 165" title="Fig. 165" /></div>
+
+<hr style="width: 65%;" />
+
+<p>In Fig. 161 we have a departure from the road ordinarily pursued. Here
+we see an escapement combining two levers, invented by the Chevalier de
+B&eacute;thune and applied by M. Thiout, master-horologist, at Paris in 1727.
+<i>P P'</i> are the two levers or pallets separately pivoted. Upon the axis
+<i>V</i>, of the lever <i>P</i>, is fixed a fork which communicates the motion to
+the pendulum. The two levers are intimately connected by the two arms <i>B
+B'</i>, of which the former carries an adjusting screw, a well-conceived
+addition for regulating the opening between the pallets. The
+counter-weight <i>C</i> compels constant contact between the arms <i>B B'</i>. The
+function is always the same, the recoil and the impulsion operate upon
+the two pallets simultaneously. This escapement enjoyed a certain degree
+of success, having been employed by a number of horologists who modified
+it in various ways.</p>
+
+
+<h4>VARIOUS MODIFICATIONS</h4>
+
+<p>Some of these modifications we shall show. For the first example, then,
+let Fig. 162 illustrate. In this arrangement the fork is carried upon
+the axis of the pallet <i>P'</i>, which effectually does away with the
+counter-weight <i>C</i>, as shown. Somewhat more complicated, but of the same
+intrinsic nature, is the arrangement displayed in Fig. 163. We should
+not imagine that it enjoyed a very extensive application. Here the two
+levers are completely independent of each other; they act upon the piece
+<i>B B</i> upon the axis <i>V</i> of the fork. The counter-weights <i>C C'</i> maintain
+the arms <a name="Page_166" id="Page_166"></a>carrying the rollers <i>D D'</i> in contact with the piece <i>B B'</i>
+which thus receives the impulse from the wheel <i>R</i>. Two adjusting screws
+serve to place the escapement upon the center. By degrees these
+fantastic constructions were abandoned to make way for the anchor recoil
+escapement, which was invented, as we have said, in 1675, by G. Clement,
+a horologist, of London. In Fig. 164 we have the disposition of the
+parts as first arranged by this artist. Here the pallets are replaced by
+the inclines <i>A</i> and <i>B</i> of the anchor, which is pivoted at <i>V</i> upon an
+axis to which is fixed also the fork. The tooth <i>a</i> escapes from the
+incline or lever <i>A</i>, and the tooth <i>b</i> immediately rests upon the lever
+<i>B</i>; by the action of the pendulum the escape wheel suffers a recoil as
+in the pallet escapement, and on the return of the pendulum the tooth
+<i>c</i> gives out its impulse in the contrary direction. With this new
+system it became possible to increase the weight of the bob and at the
+same time lessen the effective motor power. The travel of the pendulum,
+or arc of oscillation, being reduced in a marked degree, an accuracy of
+rate was obtained far superior to that of the crown-wheel escapement.
+However, this new application of the recoil escapement was not adopted
+in France until 1695.</p>
+
+<hr style="width: 65%;" />
+<div class="figleft"><img src="images/pict166.jpg" alt="Fig. 166" title="Fig. 166" /></div>
+<div class="figright"><img src="images/pict167.jpg" alt="Fig. 167" title="Fig. 167" /></div>
+<hr style="width: 65%;" />
+
+<p>The travel of the pendulum, though greatly reduced, still surpassed in
+breadth the arc in which it is isochronous, and repeated efforts were
+made to give such shape to the levers as would compel its oscillation
+within the arc of equal time; a motion which is, as was recognized even
+at that epoch, the prime requisite to a precise rating. Thus, in 1720,
+Julien Leroy occupied himself working out the proper shapes for the
+inclines to produce this desired isochronism. Searching along the same
+path, Ferd. Berthoud constructed an <a name="Page_167" id="Page_167"></a>escapement represented by the Fig.
+165. In it we see the same inclines <i>A B</i> of the former construction,
+but the locking is effected against the slides <i>C</i> and <i>D</i>, the curved
+faces of which produce isochronous oscillations of the pendulum. The
+tooth <i>b</i> imparts its lift and the tooth <i>c</i> will lock against the face
+<i>C</i>; after having passed through its recoil motion this tooth <i>c</i> will
+butt against the incline <i>A</i> and work out its lift or impulse upon it.</p>
+
+
+<h4>THE GABLE ESCAPEMENT.</h4>
+
+<hr style="width: 65%;" />
+<div class="figleft"><img src="images/pict168.jpg" alt="Fig. 168" title="Fig. 168" /></div>
+<div class="figright"><img src="images/pict169.jpg" alt="Fig. 169" title="Fig. 169" /></div>
+<hr style="width: 65%;" />
+
+<p>The <i>gable escapement</i>, shown in Fig. 166, allows the use of a heavier
+pendulum, at the same time the anchor embraces within its jaws a greater
+number of the escape-wheel teeth; an arrangement after this manner leads
+to the conclusion that with these long levers of the anchor the friction
+will be considerably increased and the recoil faces will, as a
+consequence, be quickly worn away. Without doubt, this was invented to
+permit of opening and closing the contact points of the anchor more
+easily. Under the name of the <i>English recoil anchor</i> there came into
+use an escapement with a <i>reduced gable</i>, which embraced fewer teeth
+between the pallets or inclines; we give a representation of this in
+Fig. 167. This system seems to have been moderately successful. The
+anchor recoil escapement in use in Germany to-day is demonstrated in
+Fig. 168; this arrangement is also found in the American clocks. As we
+see, the anchor is composed of a single piece of curved steel bent to
+the desired curves. Clocks provided with this escapement keep reasonably
+good time; the resistance of the recoils compensate in a measure for the
+want of isochronism in the oscillations of the pendulum. Ordinary clocks
+require considerably more power to drive them than finer clocks and, as
+a consequence, their ticking <a name="Page_168" id="Page_168"></a>is very noisy. Several means have been
+employed to dampen this noise, one of which we show in Fig. 169.</p>
+
+<div class="figleft"><img src="images/pict170.jpg" alt="Fig. 170" title="Fig. 170" /></div>
+
+<p>Here the anchor is composed of two pieces, <i>A B</i>, screwed upon a plate
+<i>H</i> pivoting at <i>V</i>. In their arrangement the two pieces represent, as
+to distance and curvature, the counterpart of Fig. 168. At the moment of
+impact their extreme ends recoil or spring back from the shock of the
+escape teeth, but the resiliency of the metal is calculated to be strong
+enough to return them immediately to the contact studs <i>e e</i>.</p>
+
+<p>As a termination to this chapter, we shall mention the use made at the
+present day of the recoil lever escapement in repeating watches. We give
+a diagram of this construction in Fig. 170. The lever here is intended
+to restrain and regulate the motion of the small striking work. It is
+pivoted at <i>V</i> and is capable of a very rapid oscillatory motion, the
+arc of which may, however, be fixed by the stud or stop <i>D</i>, which
+limits the swing of the fly <i>C</i>. This fly is of one piece with the lever
+and, together with the stud <i>D</i>, determines the angular motion of the
+lever. If the angle be large that means the path of the fly be long,
+then the striking train will move slowly; but if the teeth of the escape
+wheel <i>R</i> can just pass by without causing the lever to describe a
+supplementary or extended arc, the striking work will run off rapidly.</p>
+
+
+
+<hr style="width: 65%;" /><p><a name="Page_169" id="Page_169"></a></p>
+<h2>CHAPTER V.</h2>
+
+<h3>PUTTING IN A NEW CYLINDER.</h3>
+
+
+<p>Putting in a new cylinder is something most watchmakers fancy they can
+do, and do well; but still it is a job very few workmen can do and
+fulfill all the requirements a job of this kind demands under the
+ever-varying conditions and circumstances presented in repairs of this
+kind. It is well to explain somewhat at this point: Suppose we have five
+watches taken in with broken cylinders. Out of this number probably two
+could be pivoted to advantage and make the watches as good as ever. As
+to the pivoting of a cylinder, we will deal with this later on. The
+first thing to do is to make an examination of the cylinder, not only to
+see if it is broken, but also to determine if pivoting is going to bring
+it out all right. Let us imagine that some workman has, at some previous
+time, put in a new cylinder, and instead of putting in one of the proper
+size he has put one in too large or too small. Now, in either case he
+would have to remove a portion of the escape-wheel tooth, that is,
+shorten the tooth: because, if the cylinder was too large it would not
+go in between the teeth, and consequently the teeth would have to be cut
+or stoned away. If the cylinder was too small, again the teeth would
+have to be cut away to allow them to enter the cylinder. All workmen
+have traditions, rules some call them, that they go by in relation to
+the right way to dress a cylinder tooth; some insisting that the toe or
+point of the tooth is the only place which should be tampered with.
+Other workmen insist that the heel of the tooth is the proper place.
+Now, with all due consideration, we would say that in ninety-nine cases
+out of a hundred the proper thing to do is to let the escape-wheel teeth
+entirely alone. As we can understand, after a moment's thought, that it
+is impossible to have the teeth of the escape wheel too long and have
+the watch run at all; hence, the idea of stoning a cylinder escape-wheel
+tooth should not be tolerated.</p>
+
+
+<h4>ESCAPE-WHEEL TEETH <i>vs.</i> CYLINDER.</h4>
+
+<p>It will not do, however, to accept, and take it for granted that the
+escape-wheel teeth are all right, because in many instances they have
+been stoned away and made too short; but if we accept this <a name="Page_170" id="Page_170"></a>condition as
+being the case, that is, that the escape-wheel teeth are too short, what
+is the workman going to do about it? The owner of the watch will not pay
+for a new escape wheel as well as a new cylinder. The situation can be
+summed up about in this way, that we will have to make the best we can
+out of a bad job, and pick out and fit a cylinder on a compromise idea.</p>
+
+<p>In regard to picking out a new cylinder, it may not do to select one of
+the same size as the old one, from the fact that the old one may not
+have been of the proper size for the escape wheel, because, even in new,
+cheap watches, the workmen who "run in" the escapement knew very well
+the cylinder and escape wheel were not adapted for each other, but they
+were the best he had. Chapter II, on the cylinder escapement, will
+enable our readers to master the subject and hence be better able to
+judge of allowances to be made in order to permit imperfect material to
+be used.</p>
+
+<p>In illustration, let us imagine that we have to put in a new cylinder,
+and we have none of precisely the proper size, but we have them both a
+mere trifle too large and too small, and the question is which to use.
+Our advice is to use the smaller one if it does not require the
+escape-wheel teeth to be "dressed," that is, made smaller. Why we make
+this choice is based on the fact that the smaller cylinder shell gives
+less friction, and the loss from "drop"&mdash;that is, side play between the
+escape-wheel teeth and the cylinder&mdash;will be the same in both instances
+except to change the lost motion from inside to outside drop.</p>
+
+<p>In devising a system to be applied to selecting a new cylinder, we meet
+the same troubles encountered throughout all watchmakers' repair work,
+and chief among these are good and convenient measuring tools. But even
+with perfect measuring tools we would have to exercise good judgment, as
+just explained. In Chapter II we gave a rule for determining the outside
+diameter of a cylinder from the diameter of the escape wheel; but such
+rules and tables will, in nine instances out of ten, have to be modified
+by attendant circumstances&mdash;as, for instance, the thickness of the shell
+of the cylinder, which should be one-tenth of the outer diameter of the
+shell, but the shell is usually thicker. A tolerably safe practical rule
+and one also depending very much on the workman's good judgment is, when
+the escape-wheel teeth have been shortened, to select a cylinder giving
+ample clearance inside the shell to the tooth, but by no means large
+enough to fill the space between the teeth.<a name="Page_171" id="Page_171"></a> After studying carefully
+the instructions just given we think the workman will have no difficulty
+in selecting a cylinder of the right diameter.</p>
+
+
+<h4>MEASURING THE HEIGHTS.</h4>
+
+<div class="figright"><img src="images/pict171.jpg" alt="Fig. 171" title="Fig. 171" /></div>
+<p>The next thing is to get the proper heights. This is much more easily
+arrived at: the main measurement being to have the teeth of the escape
+wheel clear the upper face of the lower plug. In order to talk
+intelligently we will make a drawing of a cylinder and agree on the
+proper names for the several parts to be used in this chapter. Such
+drawing is shown at Fig. 171. The names are: The hollow cylinder, made
+up of the parts <i>A A' A'' A'''</i>, called the shell&mdash;<i>A</i> is the great
+shell, <i>A'</i> the half shell, <i>A''</i> the banking slot, and <i>A'''</i> the small
+shell. The brass part <i>D</i> is called the collet and consists of three
+parts&mdash;the hairspring seat <i>D</i>, the balance seat <i>D'</i> and the shoulder
+<i>D''</i>, against which the balance is riveted.</p>
+
+<p>The first measurement for fitting a new cylinder is to determine the
+height of the lower plug face, which corresponds to the line <i>x</i> <i>x</i>,
+Fig. 171. The height of this face is such as to permit the escape wheel
+to pass freely over it. In selecting a new cylinder it is well to choose
+one which is as wide at the banking slot <i>A''</i> as is consistent with
+safety. The width of the banking slot is represented by the dotted lines
+<i>x u</i>. The dotted line <i>v</i> represents the length to which the lower
+pivot <i>y</i> is to be cut.</p>
+
+<div class="figleft"><img src="images/pict172.jpg" alt="Fig. 172" title="Fig. 172" /></div>
+<div class="figright"><img src="images/pict173.jpg" alt="Fig. 173" title="Fig. 173" /></div>
+
+<p>There are several little tools on the market used for making the
+necessary measurements, but we will describe a very simple one which can
+readily be made. To do so, take about a No. 5 sewing needle and, after
+annealing, cut a screw thread on it, as shown at Fig, 172, where <i>E</i>
+represents the needle and <i>t t</i> the screw cut upon it. After the screw
+is cut, the needle is again hardened and tempered to a spring temper and
+a long, thin pivot turned upon it. The needle is now shaped as shown at
+Fig. 173. The pivot at <i>s</i> should be small enough to go easily through
+the smallest hole jewel to be found in cylinder watches, and should be
+about 1/16" long. The part at <i>r</i> should be about 3/16" long and <a name="Page_172" id="Page_172"></a>only
+reduced in size enough to fully remove the screw threads shown at <i>t</i>.</p>
+
+<div class="figleft"><img src="images/pict174.jpg" alt="Fig. 174" title="Fig. 174" /></div>
+<div class="figright"><img src="images/pict175.jpg" alt="Fig. 175" title="Fig. 175" /></div>
+
+<div class="figleft"><img src="images/pict176.jpg" alt="Fig. 176" title="Fig. 176" /></div>
+<div class="figright"><img src="images/pict177.jpg" alt="Fig. 177" title="Fig. 177" /></div>
+
+<p>We next provide a sleeve or guard for our gage. To do this we take a
+piece of hard brass bushing wire about 1/2" long and, placing it in a
+wire chuck, center and drill it nearly the entire length, leaving, say,
+1/10" at one end to be carried through with a small drill. We show at
+<i>F</i>, Fig. 174, a magnified longitudinal section of such a sleeve. The
+piece <i>F</i> is drilled from the end <i>l</i> up to the line <i>q</i> with a drill of
+such a size that a female screw can be cut in it to fit the screw on the
+needle, and <i>F</i> is tapped out to fit such a screw from <i>l</i> up to the
+dotted line <i>p</i>. The sleeve <i>F</i> is run on the screw <i>t</i> and now appears
+as shown at Fig. 175, with the addition of a handle shown at <i>G G'</i>. It
+is evident that we can allow the pivot <i>s</i> to protrude from the sleeve
+<i>F</i> any portion of its length, and regulate such protrusion by the screw
+<i>t</i>. To employ this tool for getting the proper length to which to cut
+the pivot <i>y</i>, Fig. 171, we remove the lower cap jewel to the cylinder
+pivot and, holding, the movement in the left hand, pass the pivot <i>s</i>,
+Fig. 175, up through the hole jewel, regulate the length by turning the
+sleeve <i>F</i> until the arm of the escape wheel <i>I</i>, Fig. 176, will just
+turn free over it. Now the length of the pivot <i>s</i>, which protrudes
+beyond the sleeve <i>F</i>, coincides with the length to which we must cut
+the pivot <i>y</i>, Fig. 171. To hold a cylinder for reducing the length of
+the pivot <i>y</i>, we hold said pivot in a pair of thin-edged cutting
+pliers, as shown at Fig. 177, where <i>N N'</i> represent the jaws of a pair
+of cutting pliers and <i>y</i> the pivot to be cut. The measurement is made
+by putting the pivot <i>s</i> between the jaws <i>N N'</i> as they hold the pivot.
+The cutting is done by simply filing back the pivot until of the right
+length.</p>
+
+
+<h4>TURNING THE PIVOTS.</h4>
+
+<p>We have now the pivot <i>y</i> of the proper length, and what remains to be
+done is to turn it to the right size. We do not think it advisable to
+try to use a split chuck, although we have seen workmen drive the shell
+<i>A A'''</i> out of the collet <i>D</i> and then turn up the pivots <i>y z</i> in said
+wire chuck. To our judgment there is <a name="Page_173" id="Page_173"></a>but one chuck for turning pivots,
+and this is the cement chuck provided with all American lathes. Many
+workmen object to a cement chuck, but we think no man should lay claim
+to the name of watchmaker until he masters the mystery of the cement
+chuck. It is not such a very difficult matter, and the skill once
+acquired would not be parted with cheaply. One thing has served to put
+the wax or cement chuck into disfavor, and that is the abominable stuff
+sold by some material houses for lathe cement. The original cement, made
+and patented by James Bottum for his cement chuck, was made up of a
+rather complicated mixture; but all the substances really demanded in
+such cement are ultramarine blue and a good quality of shellac. These
+ingredients are compounded in the proportion of 8 parts of shellac and 1
+part of ultramarine&mdash;all by weight.</p>
+
+
+<h4>HOW TO USE A CEMENT CHUCK.</h4>
+
+<p>The shellac is melted in an iron vessel, and the ultramarine added and
+stirred to incorporate the parts. Care should be observed not to burn
+the shellac. While warm, the melted mass is poured on to a cold slab of
+iron or stone, and while plastic made into sticks about 1/2" in
+diameter.</p>
+
+<div class="figleft"><img src="images/pict178.jpg" alt="Fig. 178" title="Fig. 178" /></div>
+<div class="figright"><img src="images/pict179.jpg" alt="Fig. 179" title="Fig. 179" /></div>
+
+<p>We show at Fig. 178 a side view of the outer end of a cement chuck with
+a cylinder in position. We commence to turn the lower pivot of a
+cylinder, allowing the pivot <i>z</i> to rest at the apex of the hollow cone
+<i>a</i>, as shown. There is something of a trick in turning such a hollow
+cone and leaving no "tit" or protuberance in the center, but it is
+important it should be done. A little practice will soon enable one to
+master the job. A graver for this purpose should be cut to rather an
+oblique point, as shown at <i>L</i>, Fig. 179. The slope of the sides to the
+recess <i>a</i>, Fig. 178, should be to about forty-five degrees, making the
+angle at <i>a</i> about ninety degrees. The only way to insure perfect
+accuracy of centering of a cylinder in a cement chuck is center by the
+shell, which is done by cutting a piece of pegwood to a wedge shape and
+letting it rest on the T-rest; then hold the edge of the pegwood to the
+cylinder as the lathe revolves and the cement soft and plastic. A
+cylinder so centered will be absolutely true. The outline curve at <i>c</i>,
+Fig. 178, represents the surface of the cement.</p>
+
+<p><a name="Page_174" id="Page_174"></a>The next operation is turning the pivot to the proper size to fit the
+jewel. This is usually done by trial, that is, trying the pivot into the
+hole in the jewel. A quicker way is to gage the hole jewel and then turn
+the pivot to the right size, as measured by micrometer calipers. In some
+cylinder watches the end stone stands at some distance from the outer
+surface of the hole jewel; consequently, if the measurement for the
+length of the pivot is taken by the tool shown at Fig. 175, the pivot
+will apparently be too short. When the lower end stone is removed we
+should take note if any allowance is to be made for such extra space.
+The trouble which would ensue from not providing for such extra end
+shake would be that the lower edge of the half shell, shown at <i>e</i>, Fig.
+171, would strike the projection on which the "stalk" of the tooth is
+planted. After the lower pivot is turned to fit the jewel the cylinder
+is to be removed from the cement chuck and the upper part turned. The
+measurements to be looked to now are, first, the entire length of the
+cylinder, which is understood to be the entire distance between the
+inner faces of the two end stones, and corresponds to the distance
+between the lines <i>v d</i>, Fig. 171. This measurement can be got by
+removing both end stones and taking the distance with a Boley gage or a
+douzieme caliper.</p>
+
+
+<h4>A CONVENIENT TOOL FOR LENGTH MEASUREMENT.</h4>
+
+<div class="figleft"><img src="images/pict180.jpg" alt="Fig. 180" title="Fig. 180" /></div>
+
+<p>A pair of common pinion calipers slightly modified makes as good a pair
+of calipers for length measurement as one can desire. This instrument is
+made by inserting a small screw in one of the blades&mdash;the head on the
+inner side, as shown at <i>f</i>, Fig. 180. The idea of the tool is, the
+screw head <i>f</i> rests in the sink of the cap jewel or end stone, while
+the other blade rests on the cock over the balance. After the adjusting
+screw to the caliper is set, the spring of the blades allows of their
+removal. The top pivot <i>z</i> of the cylinder is next cut to the proper
+length, as indicated by the space between the screwhead <i>f</i> and the
+other blade of the pinion caliper. The upper pinion <i>z</i> is held in the
+jaws of the cutting pliers, as shown in Fig. 177, the same as the lower
+one was held, until the proper length between the lines <i>d v</i>, Fig. 171,
+is secured, after which the cylinder is put back into the cement chuck,
+as shown at Fig. 178, except this time the top portion of the cylinder
+is allowed to protrude so that we can turn the top pivot and the balance
+collet <i>D</i>, Fig. 171.</p>
+
+<p><a name="Page_175" id="Page_175"></a>The sizes we have now to look to is to fit the pivot <i>z</i> to the top
+hole jewel in the cock, also the hairspring seat <i>D</i> and balance seat
+<i>D'</i>. These are turned to diameters, and are the most readily secured by
+the use of the micrometer calipers to be had of any large watchmakers'
+tool and supply house. In addition to the diameters named, we must get
+the proper height for the balance, which is represented by the dotted
+line <i>b</i>. The measurement for this can usually be obtained from the old
+cylinder by simply comparing it with the new one as it rests in the
+cement chuck. The true tool for such measurements is a height gage. We
+have made no mention of finishing and polishing the pivots, as these
+points are generally well understood by the trade.</p>
+
+
+<h4>REMOVING THE LATHE CEMENT.</h4>
+
+<p>One point perhaps we might well say a few words on, and this is in
+regard to removing the lathe cement. Such cement is usually removed by
+boiling in a copper dish with alcohol. But there are several objections
+to the practice. In the first place, it wastes a good deal of alcohol,
+and also leaves the work stained. We can accomplish this operation
+quicker, and save alcohol, by putting the cylinder with the wax on it in
+a very small homeopathic bottle and corking it tight. The bottle is then
+boiled in water, and in a few seconds the shellac is dissolved away. The
+balance to most cylinder watches is of red brass, and in some instances
+of low karat gold; in either case the balance should be repolished. To
+do this dip in a strong solution of cyanide of potassium dissolved in
+water; one-fourth ounce of cyanide in half pint of water is about the
+proper strength. Dip and rinse, then polish with a chamois buff and
+rouge.</p>
+
+<div class="figright"><img src="images/pict181.jpg" alt="Fig. 181" title="Fig. 181" /></div>
+
+<p>In staking on the balance, care should be observed to set the banking
+pin in the rim so it will come right; this is usually secured by setting
+said pin so it stands opposite to the opening in the half shell. The
+seat of the balance on the collet <i>D</i> should be undercut so that there
+is only an edge to rivet down on the balance. This will be better
+understood by inspecting Fig. 181, where we show a vertical section of
+the collet <i>D</i> and cylinder <i>A</i>. At <i>g g</i> is shown the undercut edge of
+the balance seat, which is folded over as the balance is rivetted fast.</p>
+
+<p>About all that remains now to be done is to true up the balance and
+bring it to poise. The practice frequently adopted to poise a <a name="Page_176" id="Page_176"></a>plain
+balance is to file it with a half-round file on the inside, in order not
+to show any detraction when looking at the outer edge of the rim. A
+better and quicker plan is to place the balance in a split chuck, and
+with a diamond or round-pointed tool scoop out a little piece of metal
+as the balance revolves. In doing this, the spindle of the lathe is
+turned by the hand grasping the pulley between the finger and thumb. The
+so-called diamond and round-pointed tools are shown at <i>o o'</i>, Fig. 182.
+The idea of this plan of reducing the weight of a balance is, one of the
+tools <i>o</i> is rested on the T-rest and pressed forward until a chip is
+started and allowed to enter until sufficient metal is engaged, then, by
+swinging down on the handle of the tool, the chip is taken out.</p>
+
+<div class="figleft"><img src="images/pict182.jpg" alt="Fig. 182" title="Fig. 182" /></div>
+<div class="figright"><img src="images/pict183.jpg" alt="Fig. 183" title="Fig. 183" /></div>
+
+<p>In placing a balance in a step chuck, the banking pin is caused to enter
+one of the three slots in the chuck, so as not to be bent down on to the
+rim of the balance. It is seldom the depth between the cylinder and
+escape wheel will need be changed after putting in a new cylinder; if
+such is the case, however, move the chariot&mdash;we mean the cock attached
+to the lower plate. Do not attempt to change the depth by manipulating
+the balance cock. Fig. 183 shows, at <i>h h</i>, the form of chip taken out
+by the tool <i>o o'</i>, Fig. 182.</p>
+
+
+
+<hr style="width: 65%;" /><p><a name="Page_177" id="Page_177"></a></p>
+<h2>INDEX</h2>
+
+
+<table border="0" cellpadding="4" width="60%" cellspacing="0" summary="INDEX">
+<tr><td align='left'>A</td></tr>
+<tr><td align='left'>Acid frosting,</td><td align='left'><a href='#Page_46'>46</a></td></tr>
+<tr><td align='left'>"Action" drawings,</td><td align='left'><a href='#Page_90'>90</a></td></tr>
+<tr><td align='left'>Action of a chronometer escapement,</td><td align='left'><a href='#Page_142'>142</a></td></tr>
+<tr><td align='left'>Acting surface of entrance lip,</td><td align='left'><a href='#Page_127'>127</a></td></tr>
+<tr><td align='left'>Actions of cylinder escapement,</td><td align='left'><a href='#Page_112'>112</a></td></tr>
+<tr><td align='left'>Adhesion of parallel surfaces,</td><td align='left'><a href='#Page_94'>94</a></td></tr>
+<tr><td align='left'>Adjustable pallets,</td><td align='left'><a href='#Page_98'>98</a></td></tr>
+<tr><td align='left'>Adjusting screw for drawing instruments,</td><td align='left'><a href='#Page_21'>21</a></td></tr>
+<tr><td align='left'>Analysis of principles involved in detent,</td><td align='left'><a href='#Page_137'>137</a></td></tr>
+<tr><td align='left'>Analysis of the action of a lever escapement,</td><td align='left'><a href='#Page_86'>86</a></td></tr>
+<tr><td align='left'>Angle-measuring device,</td><td align='left'><a href='#Page_68'>68</a></td></tr>
+<tr><td align='left'>Angular extent of shell of cylinder,</td><td align='left'><a href='#Page_122'>122</a></td></tr>
+<tr><td align='left'>Angular motion, drawing an escapement to show,</td><td align='left'><a href='#Page_91'>91</a></td></tr>
+<tr><td align='left'>----How measured,</td><td align='left'><a href='#Page_69'>69</a></td></tr>
+<tr><td align='left'>----Of escape wheel,</td><td align='left'><a href='#Page_37'>37</a></td></tr>
+<tr><td align='left'>Antagonistic influences,</td><td align='left'><a href='#Page_133'>133</a></td></tr>
+<tr><td align='left'>Arc of degrees,</td><td align='left'><a href='#Page_9'>9</a></td></tr>
+<tr><td align='left'>Atmospheric disturbances,</td><td align='left'><a href='#Page_74'>74</a></td></tr>
+<tr><td align='left'>Attainment of isochronism,</td><td align='left'><a href='#Page_159'>159</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>B</td></tr>
+<tr><td align='left'>Balance, how it controls timekeeping,</td><td align='left'><a href='#Page_73'>73</a></td></tr>
+<tr><td align='left'>----Weight and inertia of,</td><td align='left'><a href='#Page_133'>133</a></td></tr>
+<tr><td align='left'>Balance spring, inventor of,</td><td align='left'><a href='#Page_132'>132</a></td></tr>
+<tr><td align='left'>Banking slot of cylinder,</td><td align='left'><a href='#Page_112'>112</a></td></tr>
+<tr><td align='left'>Bankings, effect of opening too wide,</td><td align='left'><a href='#Page_63'>63</a></td></tr>
+<tr><td align='left'>Bar compasses,</td><td align='left'><a href='#Page_21'>21</a></td></tr>
+<tr><td align='left'>Barometric pressure,</td><td align='left'><a href='#Page_74'>74</a></td></tr>
+<tr><td align='left'>Basis for close measurements,</td><td align='left'><a href='#Page_96'>96</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>C</td></tr>
+<tr><td align='left'>Cement chuck, how to use,</td><td align='left'><a href='#Page_173'>173</a></td></tr>
+<tr><td align='left'>Chronometer detent, importance of light construction,</td><td align='left'><a href='#Page_136'>136</a></td></tr>
+<tr><td align='left'>Chronometer escapement,</td><td align='left'><a href='#Page_131'>131</a>, <a href='#Page_155'>155</a></td></tr>
+<tr><td align='left'>----Four principal parts of,</td><td align='left'><a href='#Page_134'>134</a></td></tr>
+<tr><td align='left'>Circular pallets,</td><td align='left'><a href='#Page_27'>27</a></td></tr>
+<tr><td align='left'>Club-tooth escapement,</td><td align='left'><a href='#Page_30'>30</a>, <a href='#Page_34'>34</a></td></tr>
+<tr><td align='left'>Club-tooth lever escapement with circular pallets and tangential lockings,</td><td align='left'><a href='#Page_83'>83</a></td></tr>
+<tr><td align='left'>Crown-wheel escapement,</td><td align='left'><a href='#Page_155'>155</a></td></tr>
+<tr><td align='left'>Cylinder, drawing a,</td><td align='left'><a href='#Page_120'>120</a></td></tr>
+<tr><td align='left'>----Outer diameter of,</td><td align='left'><a href='#Page_116'>116</a></td></tr>
+<tr><td align='left'>----Putting in a new,</td><td align='left'><a href='#Page_169'>169</a></td></tr>
+<tr><td align='left'>Cylinder escapement,</td><td align='left'><a href='#Page_155'>155</a></td></tr>
+<tr><td align='left'>----Date of invention, etc.,</td><td align='left'><a href='#Page_111'>111</a></td></tr>
+<tr><td align='left'>----Forms and proportions of several parts of,</td><td align='left'><a href='#Page_111'>111</a></td></tr>
+<tr><td align='left'>----Names of various parts,</td><td align='left'><a href='#Page_112'>112</a></td></tr>
+<tr><td align='left'>Cylinder lips, proper shape of,</td><td align='left'><a href='#Page_124'>124</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>D</td></tr>
+<tr><td align='left'>Dead-beat escapement,</td><td align='left'><a href='#Page_131'>131</a>, <a href='#Page_135'>135</a></td></tr>
+<tr><td align='left'>----Only one true,</td><td align='left'><a href='#Page_112'>112</a></td></tr>
+<tr><td align='left'>Depth, between cylinder and escape wheel,</td><td align='left'><a href='#Page_129'>129</a></td></tr>
+<tr><td align='left'>----Effect of changing,</td><td align='left'><a href='#Page_176'>176</a></td></tr>
+<tr><td align='left'>Designing a double roller,</td><td align='left'><a href='#Page_77'>77</a></td></tr>
+<tr><td align='left'>Detached escapement,</td><td align='left'><a href='#Page_155'>155</a></td></tr>
+<tr><td align='left'>Detent, functions of the,</td><td align='left'><a href='#Page_137'>137</a></td></tr>
+<tr><td align='left'>Detent escapement,</td><td align='left'><a href='#Page_131'>131</a>, <a href='#Page_155'>155</a></td></tr>
+<tr><td align='left'>----Faults in,</td><td align='left'><a href='#Page_132'>132</a></td></tr>
+<tr><td align='left'>Detent spring dimensions,</td><td align='left'><a href='#Page_138'>138</a></td></tr>
+<tr><td align='left'>Detent springs, width of,</td><td align='left'><a href='#Page_147'>147</a></td></tr>
+<tr><td align='left'>Discharging jewel, setting the,</td><td align='left'><a href='#Page_142'>142</a></td></tr>
+<tr><td align='left'>Discharging roller,</td><td align='left'><a href='#Page_136'>136</a></td></tr>
+<tr><td align='left'>Dividers,</td><td align='left'><a href='#Page_9'>9</a></td></tr>
+<tr><td align='left'>----Making,</td><td align='left'><a href='#Page_10'>10</a></td></tr>
+<tr><td align='left'>Double pendulum,</td><td align='left'><a href='#Page_160'>160</a></td></tr>
+<tr><td align='left'>Double-roller escapement,</td><td align='left'><a href='#Page_75'>75</a></td></tr>
+<tr><td align='left'>Draw defined,</td><td align='left'><a href='#Page_85'>85</a></td></tr>
+<tr><td align='left'>Drawing-board,</td><td align='left'><a href='#Page_11'>11</a></td></tr>
+<tr><td align='left'>Drawing instruments,</td><td align='left'><a href='#Page_9'>9</a></td></tr>
+<tr><td align='left'>Drawings, advantage of large,</td><td align='left'><a href='#Page_29'>29</a></td></tr>
+<tr><td align='left'>Drop and draw,</td><td align='left'><a href='#Page_150'>150</a></td></tr>
+<tr><td align='left'>Duplex escapement,</td><td align='left'><a href='#Page_131'>131</a>, <a href='#Page_155'>155</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>E</td></tr>
+<tr><td align='left'>Elasticity of spring,</td><td align='left'><a href='#Page_133'>133</a></td></tr>
+<tr><td align='left'>Engaging friction,</td><td align='left'><a href='#Page_81'>81</a></td></tr>
+<tr><td align='left'>English recoil anchor,</td><td align='left'><a href='#Page_167'>167</a></td></tr>
+<tr><td align='left'>Entrance lip of cylinder escapement,</td><td align='left'><a href='#Page_125'>125</a></td></tr>
+<tr><td align='left'>Escapement angles, measuring,</td><td align='left'><a href='#Page_101'>101</a></td></tr>
+<tr><td align='left'>Escapement error, study of,</td><td align='left'><a href='#Page_64'>64</a></td></tr>
+<tr><td align='left'>Escapement matching tool,</td><td align='left'><a href='#Page_106'>106</a></td></tr>
+<tr><td align='left'>Escapement model,</td><td align='left'><a href='#Page_40'>40</a></td></tr>
+<tr><td align='left'>----Balance,</td><td align='left'><a href='#Page_42'>42</a></td></tr>
+<tr><td align='left'>----Balance staff,</td><td align='left'><a href='#Page_44'>44</a></td></tr>
+<tr><td align='left'>----Bridges,</td><td align='left'><a href='#Page_41'>41</a>, <a href='#Page_42'>42</a></td></tr>
+<tr><td align='left'>----Escape wheel,</td><td align='left'><a href='#Page_43'>43</a></td></tr>
+<tr><td align='left'>----Extra balance cock,</td><td align='left'><a href='#Page_45'>45</a></td></tr>
+<tr><td align='left'>----"Frosting",</td><td align='left'><a href='#Page_46'>46</a></td></tr>
+<tr><td align='left'>----Hairspring,</td><td align='left'><a href='#Page_42'>42</a></td></tr>
+<tr><td align='left'>----Jewel for,</td><td align='left'><a href='#Page_43'>43</a></td></tr>
+<tr><td align='left'>----Lower plate,</td><td align='left'><a href='#Page_41'>41</a></td></tr>
+<tr><td align='left'>----Main plate,</td><td align='left'><a href='#Page_41'>41</a></td></tr>
+<tr><td align='left'>----Movement for,</td><td align='left'><a href='#Page_41'>41</a><a name="Page_178" id="Page_178"></a></td></tr>
+<tr><td align='left'>----Pallet staff,</td><td align='left'><a href='#Page_42'>42</a></td></tr>
+<tr><td align='left'>----Pillars,</td><td align='left'><a href='#Page_43'>43</a></td></tr>
+<tr><td align='left'>----Regulator,</td><td align='left'><a href='#Page_46'>46</a></td></tr>
+<tr><td align='left'>----Uses of,</td><td align='left'><a href='#Page_44'>44</a></td></tr>
+<tr><td align='left'>----Wood base for,</td><td align='left'><a href='#Page_41'>41</a></td></tr>
+<tr><td align='left'>Escapements compared,</td><td align='left'><a href='#Page_103'>103</a></td></tr>
+<tr><td align='left'>Escapement of Dutertre,</td><td align='left'><a href='#Page_160'>160</a></td></tr>
+<tr><td align='left'>Escape-wheel action,</td><td align='left'><a href='#Page_30'>30</a></td></tr>
+<tr><td align='left'>Escape-wheel, delineating an,</td><td align='left'><a href='#Page_11'>11</a></td></tr>
+<tr><td align='left'>Escape-wheel teeth vs. cylinder,</td><td align='left'><a href='#Page_169'>169</a></td></tr>
+<tr><td align='left'>Escape-wheel tooth in action, delineating an,</td><td align='left'><a href='#Page_126'>126</a></td></tr>
+<tr><td align='left'>Exit pallet,</td><td align='left'><a href='#Page_26'>26</a></td></tr>
+<tr><td align='left'>Experiments of Galileo,</td><td align='left'><a href='#Page_158'>158</a></td></tr>
+<tr><td align='left'>Experiments with a chronometer,</td><td align='left'><a href='#Page_142'>142</a></td></tr>
+<tr><td align='left'>Extent of angular impulse,</td><td align='left'><a href='#Page_118'>118</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>F</td></tr>
+<tr><td align='left'>"Fall" defined,</td><td align='left'><a href='#Page_106'>106</a></td></tr>
+<tr><td align='left'>Faults in the detent escapement,</td><td align='left'><a href='#Page_132'>132</a></td></tr>
+<tr><td align='left'>Fixed rules, of little value to student,</td><td align='left'><a href='#Page_137'>137</a></td></tr>
+<tr><td align='left'>Flexure of gold spring,</td><td align='left'><a href='#Page_146'>146</a></td></tr>
+<tr><td align='left'>Foot, fitting up the,</td><td align='left'><a href='#Page_151'>151</a></td></tr>
+<tr><td align='left'>Fork, testing the,</td><td align='left'><a href='#Page_71'>71</a></td></tr>
+<tr><td align='left'>Fork action,</td><td align='left'><a href='#Page_30'>30</a></td></tr>
+<tr><td align='left'>----Theory of,</td><td align='left'><a href='#Page_59'>59</a></td></tr>
+<tr><td align='left'>Fork and roller action,</td><td align='left'><a href='#Page_54'>54</a></td></tr>
+<tr><td align='left'>Formulas for delineating cylinder escapement,</td><td align='left'><a href='#Page_115'>115</a></td></tr>
+<tr><td align='left'>Frictions,</td><td align='left'><a href='#Page_24'>24</a></td></tr>
+<tr><td align='left'>Frictional escapement,</td><td align='left'><a href='#Page_131'>131</a>, <a href='#Page_132'>132</a></td></tr>
+<tr><td align='left'>Frictional surfaces,</td><td align='left'><a href='#Page_63'>63</a></td></tr>
+<tr><td align='left'>Fusee,</td><td align='left'><a href='#Page_131'>131</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>G</td></tr>
+<tr><td align='left'>Gable escapement,</td><td align='left'><a href='#Page_167'>167</a></td></tr>
+<tr><td align='left'>Gage, a new,</td><td align='left'><a href='#Page_172'>172</a></td></tr>
+<tr><td align='left'>Graham anchor escapement,</td><td align='left'><a href='#Page_155'>155</a></td></tr>
+<tr><td align='left'>Gold spring,</td><td align='left'><a href='#Page_146'>146</a></td></tr>
+<tr><td align='left'>Guard point,</td><td align='left'><a href='#Page_79'>79</a></td></tr>
+<tr><td align='left'>----Material for,</td><td align='left'><a href='#Page_79'>79</a></td></tr>
+<tr><td align='left'>Gummy secretion on impulse and discharging stones,</td><td align='left'><a href='#Page_147'>147</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>H</td></tr>
+<tr><td align='left'>Heights in cylinders, how obtained,</td><td align='left'><a href='#Page_171'>171</a></td></tr>
+<tr><td align='left'>Hole jewels, distance apart,</td><td align='left'><a href='#Page_140'>140</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>I</td></tr>
+<tr><td align='left'>Imaginary faults in cylinders,</td><td align='left'><a href='#Page_129'>129</a></td></tr>
+<tr><td align='left'>Impulse angle,</td><td align='left'><a href='#Page_118'>118</a></td></tr>
+<tr><td align='left'>Impulse arc, extent of,</td><td align='left'><a href='#Page_134'>134</a></td></tr>
+<tr><td align='left'>Impulse jewel set oblique,</td><td align='left'><a href='#Page_147'>147</a></td></tr>
+<tr><td align='left'>Impulse planes, locating outer angle of,</td><td align='left'><a href='#Page_39'>39</a></td></tr>
+<tr><td align='left'>Impulse roller,</td><td align='left'><a href='#Page_136'>136</a></td></tr>
+<tr><td align='left'>Incline of teeth,</td><td align='left'><a href='#Page_122'>122</a></td></tr>
+<tr><td align='left'>Inertia of balance,</td><td align='left'><a href='#Page_133'>133</a></td></tr>
+<tr><td align='left'>Inventions of</td></tr>
+<tr><td align='left'>----Berthoud,</td><td align='left'><a href='#Page_163'>163</a></td></tr>
+<tr><td align='left'>----Béthune,</td><td align='left'><a href='#Page_165'>165</a></td></tr>
+<tr><td align='left'>----Clement,</td><td align='left'><a href='#Page_166'>166</a></td></tr>
+<tr><td align='left'>----Dr. Hook,</td><td align='left'><a href='#Page_162'>162</a></td></tr>
+<tr><td align='left'>----Harrison,</td><td align='left'><a href='#Page_161'>161</a></td></tr>
+<tr><td align='left'>----Hautefeuille,</td><td align='left'><a href='#Page_161'>161</a></td></tr>
+<tr><td align='left'>----Huygens,</td><td align='left'><a href='#Page_158'>158</a></td></tr>
+<tr><td align='left'>----Leroy,</td><td align='left'><a href='#Page_163'>163</a></td></tr>
+<tr><td align='left'>----Thiout,</td><td align='left'><a href='#Page_165'>165</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>J</td></tr>
+<tr><td align='left'>Jewel pin, determining size,</td><td align='left'><a href='#Page_58'>58</a></td></tr>
+<tr><td align='left'>----Cementing in,</td><td align='left'><a href='#Page_67'>67</a></td></tr>
+<tr><td align='left'>----Settings,</td><td align='left'><a href='#Page_66'>66</a></td></tr>
+<tr><td align='left'>Jewel-pin setters,</td><td align='left'><a href='#Page_67'>67</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>L</td></tr>
+<tr><td align='left'>Lathe cement,</td><td align='left'><a href='#Page_173'>173</a></td></tr>
+<tr><td align='left'>----Removing,</td><td align='left'><a href='#Page_175'>175</a></td></tr>
+<tr><td align='left'>Lever, proper length of,</td><td align='left'><a href='#Page_61'>61</a></td></tr>
+<tr><td align='left'>Lever fork, horn of,</td><td align='left'><a href='#Page_61'>61</a></td></tr>
+<tr><td align='left'>----prongs of,</td><td align='left'><a href='#Page_60'>60</a></td></tr>
+<tr><td align='left'>Lift, real and apparent,</td><td align='left'><a href='#Page_112'>112</a></td></tr>
+<tr><td align='left'>Lifting angle,</td><td align='left'><a href='#Page_114'>114</a></td></tr>
+<tr><td align='left'>Lock, amount of,</td><td align='left'><a href='#Page_28'>28</a></td></tr>
+<tr><td align='left'>----Defined,</td><td align='left'><a href='#Page_85'>85</a></td></tr>
+<tr><td align='left'>Lock and drop testing,</td><td align='left'><a href='#Page_69'>69</a></td></tr>
+<tr><td align='left'>Locking jewel, moving the,</td><td align='left'><a href='#Page_149'>149</a></td></tr>
+<tr><td align='left'>Locking stone, good form of,</td><td align='left'><a href='#Page_144'>144</a></td></tr>
+<tr><td align='left'>Lower plate, circular opening in,</td><td align='left'><a href='#Page_56'>56</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>M</td></tr>
+<tr><td align='left'>Marine chronometer, number of beats to hour,</td><td align='left'><a href='#Page_148'>148</a></td></tr>
+<tr><td align='left'>Mathematics,</td><td align='left'><a href='#Page_95'>95</a></td></tr>
+<tr><td align='left'>Measuring tools,</td><td align='left'><a href='#Page_171'>171</a></td></tr>
+<tr><td align='left'>Metal drawings, advantages of,</td><td align='left'><a href='#Page_140'>140</a></td></tr>
+<tr><td align='left'>Motion, how obtained,</td><td align='left'><a href='#Page_16'>16</a></td></tr>
+<tr><td align='left'>Movement holder,</td><td align='left'><a href='#Page_110'>110</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>N</td></tr>
+<tr><td align='left'>Neutral lockings,</td><td align='left'><a href='#Page_84'>84</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>O</td></tr>
+<tr><td align='left'>Original designing,</td><td align='left'><a href='#Page_148'>148</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>P</td></tr>
+<tr><td align='left'>Pallet action, locating the,</td><td align='left'><a href='#Page_90'>90</a></td></tr>
+<tr><td align='left'>Pallet-and-fork action,</td><td align='left'><a href='#Page_12'>12</a>, <a href='#Page_13'>13</a>, <a href='#Page_17'>17</a>, <a href='#Page_18'>18</a></td></tr>
+<tr><td align='left'>Pallet stones, how to set,</td><td align='left'><a href='#Page_104'>104</a></td></tr>
+<tr><td align='left'>Pallets, adjusting to match the fork,</td><td align='left'><a href='#Page_65'>65</a></td></tr>
+<tr><td align='left'>Paper for drawing,</td><td align='left'><a href='#Page_11'>11</a></td></tr>
+<tr><td align='left'>Parts, relations of the,</td><td align='left'><a href='#Page_32'>32</a></td></tr>
+<tr><td align='left'>Passing hollow,</td><td align='left'><a href='#Page_62'>62</a><a name="Page_179" id="Page_179"></a></td></tr>
+<tr><td align='left'>Perfected lever escapement,</td><td align='left'><a href='#Page_87'>87</a></td></tr>
+<tr><td align='left'>Pivots, turning,</td><td align='left'><a href='#Page_172'>172</a></td></tr>
+<tr><td align='left'>Point of percussion,</td><td align='left'><a href='#Page_139'>139</a></td></tr>
+<tr><td align='left'>Points for drawing instruments,</td><td align='left'><a href='#Page_20'>20</a></td></tr>
+<tr><td align='left'>Polishing materials,</td><td align='left'><a href='#Page_52'>52</a></td></tr>
+<tr><td align='left'>Power leaks,</td><td align='left'><a href='#Page_16'>16</a></td></tr>
+<tr><td align='left'>Power lost in lever escapement,</td><td align='left'><a href='#Page_87'>87</a></td></tr>
+<tr><td align='left'>Practical problems in the lever escapement,</td><td align='left'><a href='#Page_98'>98</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>R</td></tr>
+<tr><td align='left'>Radial extent of outside of cylinder,</td><td align='left'><a href='#Page_125'>125</a></td></tr>
+<tr><td align='left'>Ratchet-tooth escape wheel,</td><td align='left'><a href='#Page_12'>12</a></td></tr>
+<tr><td align='left'>Recoil anchor escapement,</td><td align='left'><a href='#Page_155'>155</a></td></tr>
+<tr><td align='left'>Recoil escapement,</td><td align='left'><a href='#Page_154'>154</a></td></tr>
+<tr><td align='left'>Reduced gable escapement,</td><td align='left'><a href='#Page_167'>167</a></td></tr>
+<tr><td align='left'>Retrograde motion,</td><td align='left'><a href='#Page_36'>36</a></td></tr>
+<tr><td align='left'>Roller action, why <a href='#Page_30'>30</a> degrees,</td><td align='left'><a href='#Page_55'>55</a></td></tr>
+<tr><td align='left'>----Of double roller,</td><td align='left'><a href='#Page_78'>78</a></td></tr>
+<tr><td align='left'>Roller diameter, determining the,</td><td align='left'><a href='#Page_55'>55</a></td></tr>
+<tr><td align='left'>Ruling pen,</td><td align='left'><a href='#Page_9'>9</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>S</td></tr>
+<tr><td align='left'>Safety action,</td><td align='left'><a href='#Page_56'>56</a></td></tr>
+<tr><td align='left'>Scale of inches,</td><td align='left'><a href='#Page_9'>9</a></td></tr>
+<tr><td align='left'>Screws, making extra large,</td><td align='left'><a href='#Page_45'>45</a></td></tr>
+<tr><td align='left'>Screwheads, fancy,</td><td align='left'><a href='#Page_45'>45</a></td></tr>
+<tr><td align='left'>Selecting new cylinder,</td><td align='left'><a href='#Page_170'>170</a></td></tr>
+<tr><td align='left'>Shaping, advantages gained in,</td><td align='left'><a href='#Page_116'>116</a></td></tr>
+<tr><td align='left'>Sheet steel, cutting,</td><td align='left'><a href='#Page_48'>48</a></td></tr>
+<tr><td align='left'>Short fork,</td><td align='left'><a href='#Page_100'>100</a></td></tr>
+<tr><td align='left'>Sound as indicator of correct action,</td><td align='left'><a href='#Page_144'>144</a></td></tr>
+<tr><td align='left'>Spring, elasticity of,</td><td align='left'><a href='#Page_133'>133</a></td></tr>
+<tr><td align='left'>Staking on a balance,</td><td align='left'><a href='#Page_175'>175</a></td></tr>
+<tr><td align='left'>Steel, polishing,</td><td align='left'><a href='#Page_49'>49</a></td></tr>
+<tr><td align='left'>----Tempering,</td><td align='left'><a href='#Page_49'>49</a></td></tr>
+<tr><td align='left'>Study drawings,</td><td align='left'><a href='#Page_124'>124</a></td></tr>
+<tr><td align='left'>Systems of measurements,</td><td align='left'><a href='#Page_114'>114</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>T</td></tr>
+<tr><td align='left'>Tangential lockings,</td><td align='left'><a href='#Page_80'>80</a>, <a href='#Page_148'>148</a></td></tr>
+<tr><td align='left'>Test gage for angular movement,</td><td align='left'><a href='#Page_65'>65</a></td></tr>
+<tr><td align='left'>Theoretical action of double roller,</td><td align='left'><a href='#Page_76'>76</a></td></tr>
+<tr><td align='left'>Timekeeping, controlled by balance,</td><td align='left'><a href='#Page_73'>73</a></td></tr>
+<tr><td align='left'>Tool for length measurement,</td><td align='left'><a href='#Page_174'>174</a></td></tr>
+<tr><td align='left'>Tools, measuring,</td><td align='left'><a href='#Page_171'>171</a></td></tr>
+<tr><td align='left'>Triangle,</td><td align='left'><a href='#Page_18'>18</a></td></tr>
+<tr><td align='left'>T-square,</td><td align='left'><a href='#Page_9'>9</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>U</td></tr>
+<tr><td align='left'>Unlocking action,</td><td align='left'><a href='#Page_56'>56</a></td></tr>
+<tr><td align='left'>Unlocking roller,</td><td align='left'><a href='#Page_136'>136</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>V</td></tr>
+<tr><td align='left'>Verge escapement,</td><td align='left'><a href='#Page_131'>131</a>, <a href='#Page_155'>155</a></td></tr>
+<tr><td colspan="2">&nbsp;</td></tr>
+<tr><td align='left'>W</td></tr>
+<tr><td align='left'>Weight and inertia of balance,</td><td align='left'><a href='#Page_133'>133</a></td></tr>
+<tr><td align='left'>Working model of cylinder escapement,</td><td align='left'><a href='#Page_123'>123</a></td></tr>
+</table>
+<p><a name="Page_180" id="Page_180"></a><a name="Page_181" id="Page_181"></a></p>
+
+
+<hr style="width: 65%;" />
+
+
+<p><b>THE WATCH ADJUSTER'S MANUAL</b></p>
+
+
+<p><b>A Complete and Practical Guide for Watchmakers in Adjusting Watches and
+Chronometers for Isochronism, Position, Heat and Cold.</b></p>
+
+
+<p><span class="smcap"><b>By Charles Edgar Fritts (Excelsior)</b>,</span></p>
+
+<p>Author of "Practical Hints on Watch Repairing," "Practical Treatise on
+Balance Spring," "Electricity and Magnetism for Watchmakers," etc., etc.</p>
+
+<p>This well-known work is now recognized as the standard authority on the
+adjustments and kindred subjects, both here and in England. It contains
+an exhaustive consideration of the various theories proposed, the
+mechanical principles on which the adjustments are based, and the
+different methods followed in actual practice, giving all that is
+publicly known in the trade, with a large amount of entirely new
+practical matter not to be found elsewhere, obtained from the best
+manufacturers and workmen, as well as from the author's own studies and
+experiences.</p>
+
+<p><b>Sent postpaid to any part of the world on receipt of $2.50 (10s. 5d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_182" id="Page_182"></a><b>THE ART OF ENGRAVING</b></p>
+
+<p><b>A Complete Treatise on the Engraver's Art, with Special Reference to
+Letter and Monogram Engraving. Specially Compiled as a Standard
+Text-Book for Students and a Reliable Reference Book for Engravers.</b></p>
+
+<p>This work is the only thoroughly reliable and exhaustive treatise
+published on this important subject. It is an ideal text-book, beginning
+with the rudiments and leading the student step by step to a complete
+and practical mastery of the art. Back of the authorship is a long
+experience as a successful engraver, also a successful career as an
+instructor in engraving. These qualifications ensure accuracy and
+reliability of matter, and such a course of instruction as is best for
+the learner and qualified engraver.</p>
+
+<p>The most notable feature of the new treatise is the instructive
+character of the illustrations. There are over 200 original
+illustrations by the author. A very complete index facilitates reference
+to any required topic.</p>
+
+<p><b>Bound in Silk Cloth&mdash;208 Pages and 216 Illustrations.</b></p>
+
+<p><b>Sent postpaid to any part of the world on receipt of price, $1.50 (6s.
+3d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><b>THE KEYSTONE PORTFOLIO OF MONOGRAMS</b><br /><br /></p>
+
+<div class="figleft"><img src="images/ad003.jpg" alt="Monogram" title="Monogram" /></div>
+
+<div class="figright"><img src="images/ad004.jpg" alt="Monograms" title="Monograms" /></div>
+
+<p>This portfolio contains 121 combination designs. These designs were
+selected from the best of those submitted in a prize competition held by
+The Keystone, and will be found of value to every one doing
+engraving.</p>
+
+<p>The designs are conceded to be the best in the market, excelling in
+art and novelty of combination and skill in execution.</p>
+
+<p>They are printed from steel plates on stiff, durable paper, and
+contain sample monograms in a variety of combinations.</p>
+
+<p>The portfolio is a bench requirement that no jeweler can afford to be
+without. It is a necessary supplement to any text-book on letter
+engraving.</p>
+
+<p class='center'>
+<b>Price, 50 Cents (2s.)</b><br /><br />
+</p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_184" id="Page_184"></a><b>THE OPTICIAN'S MANUAL</b></p>
+
+<p><b>VOL. I.</b></p>
+
+<p><span class="smcap"><b>By C.H. Brown, M.D.</b></span></p>
+
+<p><b>Graduate University of Pennsylvania; Professor of Optics and Refraction;
+formerly Physician in Philadelphia Hospital; Member of Philadelphia
+County, Pennsylvania State and American Medical Societies.</b></p>
+
+<p>The Optician's Manual, Vol. I., has proved to be the most popular work
+on practical refraction ever published. The knowledge it contains has
+been more effective in building up the optical profession than any other
+educational factor. A study of it is essential to an intelligent
+appreciation of Vol. II., for it lays the foundation structure of all
+optical knowledge, as the titles of its ten chapters show:</p>
+
+
+<table border="0" cellpadding="4" width="60%" cellspacing="0" summary="TOC for the Opticians Manual">
+<tr><td align='right'>Chapter I.</td><td align='left'>&mdash;Introductory Remarks.</td></tr>
+<tr><td align='right'>Chapter II.</td><td align='left'>&mdash;The Eye Anatomically.</td></tr>
+<tr><td align='right'>Chapter III.</td><td align='left'>&mdash;The Eye Optically; or, The Physiology of Vision.</td></tr>
+<tr><td align='right'>Chapter IV.</td><td align='left'>&mdash;Optics.</td></tr>
+<tr><td align='right'>Chapter V.</td><td align='left'>&mdash;Lenses.</td></tr>
+<tr><td align='right'>Chapter VI.</td><td align='left'>&mdash;Numbering of Lenses.</td></tr>
+<tr><td align='right'>Chapter VII.</td><td align='left'>&mdash;The Use and Value of Glasses.</td></tr>
+<tr><td align='right'>Chapter VIII.</td><td align='left'>&mdash;Outfit Required.</td></tr>
+<tr><td align='right'>Chapter IX.</td><td align='left'>&mdash;Method of Examination.</td></tr>
+<tr><td align='right'>Chapter X.</td><td align='left'>&mdash;Presbyopia.</td></tr>
+</table>
+
+
+<p>The Optician's Manual, Vol. I., is complete in itself, and has been the
+entire optical education of many successful opticians. For student and
+teacher it is the best treatise of its kind, being simple in style,
+accurate in statement and comprehensive in its treatment of refractive
+procedure and problems. It merits the place of honor beside Vol. II. in
+every optical library.</p>
+
+<p><b>Bound in Cloth&mdash;422 pages&mdash;colored plates and Illustrations.</b></p>
+
+<p><b>Sent postpaid on receipt of $2.00 (8s. 4d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_185" id="Page_185"></a><b>THE OPTICIAN'S MANUAL</b></p>
+
+<p><b>VOL. II.</b></p>
+
+<p><span class="smcap"><b>By C.H. Brown, M.D.</b></span></p>
+
+<p>Graduate University of Pennsylvania; Professor of Optics and Refraction;
+formerly Physician in Philadelphia Hospital; Member of Philadelphia
+County, Pennsylvania State and American Medical Societies.</p>
+
+<p>The Optician's Manual, Vol. II., is a direct continuation of The
+Optician's Manual, Vol. I., being a much more advanced and comprehensive
+treatise. It covers in minutest detail the four great subdivisions of
+practical eye refraction, viz:</p>
+
+<p>
+<span style="margin-left: 1em;">Myopia.</span><br />
+<span style="margin-left: 1em;">Hypermetropia.</span><br />
+<span style="margin-left: 1em;">Astigmatism.</span><br />
+<span style="margin-left: 1em;">Muscular Anomalies.</span><br />
+</p>
+
+<p>It contains the most authoritative and complete researches up to date on
+these subjects, treated by the master hand of an eminent oculist and
+optical teacher. It is thoroughly practical, explicit in statement and
+accurate as to fact. All refractive errors and complications are clearly
+explained, and the methods of correction thoroughly elucidated.</p>
+
+<p>This book fills the last great want in higher refractive optics, and the
+knowledge contained in it marks the standard of professionalism.</p>
+
+<p><b>Bound in Cloth&mdash;408 pages&mdash;with illustrations.</b></p>
+
+<p><b>Sent postpaid on receipt of $2.00 (8s. 4d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_186" id="Page_186"></a><b>SKIASCOPY AND THE USE OF THE RETINOSCOPE</b></p>
+
+
+<p><b>A Treatise on the Shadow Test in its Practical Application to the Work
+of Refraction, with an Explanation in Detail of the Optical Principles
+on which the Science is Based.</b></p>
+
+<p>This new work, the sale of which has already necessitated a second
+edition, far excels all previous treatises on the subject in
+comprehensiveness and practical value to the refractionist. It not only
+explains the test, but expounds fully and explicitly the principles
+underlying it&mdash;not only the phenomena revealed by the test, but the why
+and wherefore of such phenomena.</p>
+
+<p>It contains a full description of skiascopic apparatus, including the
+latest and most approved instruments.</p>
+
+<p>In depth of research, wealth of illustration and scientific completeness
+this work is unique.</p>
+
+<p><b>Bound in cloth; contains 231 pages and 73 illustrations and colored
+plates.</b></p>
+
+<p><b>Sent postpaid to any part of the world on receipt of $1.00 (4s. 2d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_187" id="Page_187"></a><b>PHYSIOLOGIC OPTICS</b></p>
+
+<p><b>Ocular Dioptrics&mdash;Functions of the Retina&mdash;Ocular Movements and
+Binocular Vision</b></p>
+
+<p><span class="smcap"><b>By Dr. M. Tscherning</b></span></p>
+
+<p><b>Adjunct-Director of the Laboratory of Ophthalmology at the Sorbonne,
+Paris</b></p>
+
+<p>AUTHORIZED TRANSLATION</p>
+
+<p><span class="smcap">By Carl Weiland, M.D.</span></p>
+
+<p>Former Chief of Clinic in the Eye Department of the Jefferson College
+Hospital, Philadelphia, Pa.</p>
+
+<p>This is the crowning work on physiologic optics, and will mark a new era
+in optical study. Its distinguished author is recognized in the world of
+science as the greatest living authority on this subject, and his book
+embodies not only his own researches, but those of the several hundred
+investigators who, in the past hundred years, made the eye their
+specialty and life study.</p>
+
+<p>Tscherning has sifted the gold of all optical research from the dross,
+and his book, as now published in English with many additions, is the
+most valuable mine of reliable optical knowledge within reach of
+ophthalmologists. It contains 380 pages and 212 illustrations, and its
+reference list comprises the entire galaxy of scientists who have made
+the century famous in the world of optics.</p>
+
+<p>The chapters on Ophthalmometry, Ophthalmoscopy, Accommodation,
+Astigmatism, Aberration and Entoptic Phenomena, etc.&mdash;in fact, the
+entire book contains so much that is new, practical and necessary that
+no refractionist can afford to be without it.</p>
+
+<p><b>Bound in Cloth. 380 Pages, 212 Illustrations.</b></p>
+
+<p><b>Price, $3.50 (14s. 7d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_188" id="Page_188"></a><b>OPHTHALMIC LENSES</b></p>
+
+<p><b>Dioptric Formul&aelig; for Combined Cylindrical Lenses, The Prism-Dioptry and
+Other Original Papers</b></p>
+
+<p><span class="smcap"><b>By Charles F. Prentice, M.E.</b></span></p>
+
+<p>A new and revised edition of all the original papers of this noted
+author, combined in one volume. In this revised form, with the addition
+of recent research, these standard papers are of increased value.
+Combined for the first time in one volume, they are the greatest
+compilation on the subject of lenses extant.</p>
+
+<p>This book of over 200 pages contains the following papers:</p>
+
+<p>
+<span style="margin-left: 1em;">Ophthalmic Lenses.</span><br />
+<span style="margin-left: 1em;">Dioptric Formul&aelig; for Combined Cylindrical Lenses.</span><br />
+<span style="margin-left: 1em;">The Prism-Dioptry.</span><br />
+<span style="margin-left: 1em;">A Metric System of Numbering and Measuring Prisms.</span><br />
+<span style="margin-left: 2em;">The Relation of the Prism-Dioptry to the Meter Angle.</span><br />
+<span style="margin-left: 2em;">The Relation of the Prism-Dioptry to the Lens-Dioptry.</span><br />
+<span style="margin-left: 1em;">The Perfected Prismometer.</span><br />
+<span style="margin-left: 1em;">The Prismometric Scale.</span><br />
+<span style="margin-left: 1em;">On the Practical Execution of Ophthalmic Prescriptions involving Prisms.</span><br />
+<span style="margin-left: 1em;">A Problem in Cemented Bi-Focal Lenses, Solved by the Prism-Dioptry.</span><br />
+<span style="margin-left: 1em;">Why Strong Contra-Generic Lenses of Equal Power Fail to Neutralize Each Other.</span><br />
+<span style="margin-left: 1em;">The Advantages of the Sphero-Toric Lens.</span><br />
+<span style="margin-left: 1em;">The Iris, as Diaphragm and Photostat.</span><br />
+<span style="margin-left: 1em;">The Typoscope.</span><br />
+<span style="margin-left: 1em;">The Correction of Depleted Dynamic Refraction (Presbyopia).</span><br />
+</p>
+
+<p><i>Press Notices on the Original Edition:</i><br /><br /></p>
+
+<p><b>OPHTHALMIC LENSES.</b></p>
+
+<p>"The work stands alone, in its present form, a compendium of the various
+laws of physics relative to this subject that are so difficult of access
+in scattered treatises."&mdash;<i>New England Medical Gazette.</i></p>
+
+<p>"It is the most complete and best illustrated book on this special
+subject ever published."&mdash;<i>Horological Review</i>, New York.</p>
+
+<p>"Of all the simple treatises on the properties of lenses that we have
+seen, this is incomparably the best.... The teacher of the average
+medical student will hail this little work as a great boon."&mdash;<i>Archives
+of Ophthalmology, edited by H. Knapp, M.D.</i><br /><br /></p>
+
+<p><b>DIOPTRIC FORMUL&AElig; FOR COMBINED CYLINDRICAL LENSES.</b></p>
+
+<p>"This little brochure solves the problem of combined cylinders in all
+its aspects, and in a manner simple enough for the comprehension of the
+average student of ophthalmology. The author is to be congratulated upon
+the success that has crowned his labors, for nowhere is there to be
+found so simple and yet so complete an explanation as is contained in
+these pages."&mdash;<i>Archives of Ophthalmology, edited by H. Knapp, M.D.</i></p>
+
+<p>"This exhaustive work of Mr. Prentice is a solution of one of the most
+difficult problems in ophthalmological optics. Thanks are due to Mr.
+Prentice for the excellent manner in which he has elucidated a subject
+which has not hitherto been satisfactorily explained."&mdash;<i>The Ophthalmic
+Review</i>, London.</p>
+
+<p><b>The book contains 110 Original Diagrams. Bound in cloth.</b></p>
+
+<p><b>Price, $1.50 (6s. 3d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_189" id="Page_189"></a><b>OPTOMETRIC RECORD BOOK</b></p>
+
+
+<p>A record book, wherein to record optometric examinations, is an
+indispensable adjunct of an optician's outfit.</p>
+
+<p>The Keystone Optometric Record Book was specially prepared for this
+purpose. It excels all others in being not only a record book, but an
+invaluable guide in examination.</p>
+
+<p>The book contains two hundred record forms with printed headings,
+suggesting, in the proper order, the course of examination that should
+be pursued to obtain most accurate results.</p>
+
+<p>Each book has an index, which enables the optician to refer instantly to
+the case of any particular patient.</p>
+
+<p>The Keystone Record Book diminishes the time and labor required for
+examinations, obviates possible oversights from carelessness and assures
+a systematic and thorough examination of the eye, as well as furnishes a
+permanent record of all examinations.</p>
+
+<p><b>Sent postpaid on receipt of $1.00 (4s. 2d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_190" id="Page_190"></a><b>THE KEYSTONE BOOK OF MONOGRAMS</b></p>
+
+<p>This book contains 2400 designs and over 6000 different combinations of
+two and three letters.</p>
+
+<p>Is an essential to every jeweler's outfit. It is not only necessary for
+the jeweler's own use and guidance, but also to enable customers to
+indicate exactly what they want, thus saving time and possible
+dissatisfaction.</p>
+
+<p>The Monograms are purposely left in outline, in order to show clearly
+how the letters are intertwined or woven together. This permits such
+enlargement or reduction of the Monogram as may be desired, and as much
+shading, ornamentation and artistic finish as the jeweler may wish to
+add.</p>
+
+<p>This comprehensive compilation of Monograms is especially available as a
+reference book in busy seasons. Its use saves time, thought and labor,
+and ensures quick and satisfactory work.</p>
+
+<p>Monograms are the fad of the time, and there's money for the jeweler in
+Monogram engraving. The knowledge in this book can be turned into cash.
+All the various styles of letters are illustrated.</p>
+
+<p><b>Price, $1.00 (4s. 2d.)</b></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><a name="Page_191" id="Page_191"></a><b><span class="smcap">The Keystone Record Book of Watch Repairs</span></b></p>
+
+<p>This book is 9 &times; 11 inches, has 120 pages, and space for recording
+sixteen hundred jobs in detail. It is made of linen ledger paper, bound
+in cloth with leather back and corners.</p>
+
+<p><b>Price, $1.00 (4s. 2d.), prepaid.</b></p>
+
+<p>No other record book on the market is so complete, and all cost more.<br /><br /></p>
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span><br /><br />
+</p>
+
+<hr style='width: 45%;' />
+
+<p><span class="smcap"><b>The Keystone Book of Guarantees of Watch Repairs</b></span></p>
+
+<p>This book contains two hundred printed guarantees, and is handsomely
+bound. Each guarantee is 3-1/4 x 7-1/2 inches, and most carefully
+worded. Jewelers have discovered that the use of these guarantees is a
+most effective way to secure and cultivate public confidence. We sell a
+book of two hundred for</p>
+
+<p><b>$1.00 (4s. 2d.), prepaid,</b></p>
+
+<p>which is one-third less than the price charged by others for a
+similar book.<br /><br /></p>
+
+
+<p class='center'>
+Published by <span class="smcap">The Keystone,<br />
+the organ of the jewelry and optical trades,<br />
+19th &amp; Brown Sts., Philadelphia, U.S.A.</span>
+</p>
+
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+<hr class="full" />
+<p>***END OF THE PROJECT GUTENBERG EBOOK WATCH AND CLOCK ESCAPEMENTS***</p>
+<p>******* This file should be named 17021-h.txt or 17021-h.zip *******</p>
+<p>This and all associated files of various formats will be found in:<br />
+<a href="https://www.gutenberg.org/dirs/1/7/0/2/17021">https://www.gutenberg.org/1/7/0/2/17021</a></p>
+<p>Updated editions will replace the previous one--the old editions
+will be renamed.</p>
+
+<p>Creating the works from public domain print editions means that no
+one owns a United States copyright in these works, so the Foundation
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+The Project Gutenberg eBook, Watch and Clock Escapements, by Anonymous
+
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+
+
+
+Title: Watch and Clock Escapements
+       A Complete Study in Theory and Practice of the Lever, Cylinder and Chronometer Escapements, Together with a Brief Account of the Origin and Evolution of the Escapement in Horology
+
+
+Author: Anonymous
+
+
+
+Release Date: November 6, 2005  [eBook #17021]
+
+Language: English
+
+Character set encoding: ISO-646-US (US-ASCII)
+
+
+***START OF THE PROJECT GUTENBERG EBOOK WATCH AND CLOCK ESCAPEMENTS***
+
+
+E-text prepared by Robert Cicconetti, Janet Blenkinship, and the Project
+Gutenberg Online Distributed Proofreading Team (https://www.pgdp.net/).
+Book provided by the New York University Library.
+
+
+
+Note: Project Gutenberg also has an HTML version of this file which
+      includes the original more than 180 illustrations.
+      See 17021-h.htm or 17021-h.zip:
+      (https://www.gutenberg.org/dirs/1/7/0/2/17021/17021-h/17021-h.htm)
+      or
+      (https://www.gutenberg.org/dirs/1/7/0/2/17021/17021-h.zip)
+
+
+
+
+
+WATCH AND CLOCK ESCAPEMENTS
+
+A Complete Study in Theory and Practice of the Lever, Cylinder and
+Chronometer Escapements, Together with a Brief Account of the Origin
+and Evolution of the Escapement in Horology
+
+Compiled from the well-known Escapement Serials
+published in The Keystone
+
+Nearly Two Hundred Original Illustrations
+
+
+
+
+
+
+
+Published by
+The Keystone
+The Organ of the Jewelry and Optical Trades
+19th & Brown Sts., Philadelphia, U.S.A.
+
+1904
+
+All Rights Reserved
+Copyright, 1904, By B. Thorpe,
+Publisher of the Keystone.
+
+
+
+
+PREFACE
+
+
+Especially notable among the achievements of The Keystone in the field
+of horology were the three serials devoted to the lever, cylinder and
+chronometer escapements. So highly valued were these serials when
+published that on the completion of each we were importuned to republish
+it in book form, but we deemed it advisable to postpone such publication
+until the completion of all three, in order that the volume should be a
+complete treatise on the several escapements in use in horology. The
+recent completion of the third serial gave us the opportunity to
+republish in book form, and the present volume is the result. We present
+it to the trade and students of horology happy in the knowledge that its
+contents have already received their approval. An interesting addition
+to the book is the illustrated story of the escapements, from the first
+crude conceptions to their present perfection.
+
+
+
+
+  CONTENTS
+
+
+  CHAPTER I.
+
+  THE DETACHED LEVER ESCAPEMENT      9
+
+
+  CHAPTER II.
+
+  THE CYLINDER ESCAPEMENT          111
+
+
+  CHAPTER III.
+
+  THE CHRONOMETER ESCAPEMENT       131
+
+
+  CHAPTER IV.
+
+  HISTORY OF ESCAPEMENTS           153
+
+
+  CHAPTER V.
+
+  PUTTING IN A NEW CYLINDER        169
+
+
+  INDEX                            177
+
+
+
+
+
+
+WATCH AND CLOCK ESCAPEMENTS
+
+
+
+
+CHAPTER I.
+
+THE DETACHED LEVER ESCAPEMENT.
+
+
+In this treatise we do not propose to go into the history of this
+escapement and give a long dissertation on its origin and evolution, but
+shall confine ourselves strictly to the designing and construction as
+employed in our best watches. By designing, we mean giving full
+instructions for drawing an escapement of this kind to the best
+proportions. The workman will need but few drawing instruments, and a
+drawing-board about 15" by 18" will be quite large enough. The necessary
+drawing-instruments are a T-square with 15" blade; a scale of inches
+divided into decimal parts; two pairs dividers with pen and pencil
+points--one pair of these dividers to be 5" and the other 6"; one ruling
+pen. Other instruments can be added as the workman finds he needs them.
+Those enumerated above, however, will be all that are absolutely
+necessary.
+
+[Illustration: Fig. 1]
+
+We shall, in addition, need an arc of degrees, which we can best make
+for ourselves. To construct one, we procure a piece of No. 24 brass,
+about 51/2" long by 11/4" wide. We show such a piece of brass at _A_,
+Fig. 1. On this piece of brass we sweep two arcs with a pair of dividers
+set at precisely 5", as shown (reduced) at _a a_ and _b b_. On these
+arcs we set off the space held in our dividers--that is 5"--as shown at
+the short radial lines at each end of the two arcs. Now it is a
+well-known fact that the space embraced by our dividers contains exactly
+sixty degrees of the arcs _a a_ and _b b_, or one-sixth of the entire
+circle; consequently, we divide the arcs _a a_ and _b b_ into sixty
+equal parts, to represent degrees, and at one end of these arcs we
+halve five spaces so we can get at half degrees.
+
+[Illustration: Fig. 2]
+
+Before we take up the details of drawing an escapement we will say a few
+words about "degrees," as this seems to be something difficult to
+understand by most pupils in horology when learning to draw parts of
+watches to scale. At Fig. 2 we show several short arcs of fifteen
+degrees, all having the common center _g_. Most learners seem to have an
+idea that a degree must be a specific space, like an inch or a foot. Now
+the first thing in learning to draw an escapement is to fix in our minds
+the fact that the extent of a degree depends entirely on the radius of
+the arc we employ. To aid in this explanation we refer to Fig. 2. Here
+the arcs _c_, _d_, _e_ and _f_ are all fifteen degrees, although the
+linear extent of the degree on the arc _c_ is twice that of the degree
+on the arc _f_. When we speak of a degree in connection with a circle we
+mean the one-three-hundred-and-sixtieth part of the periphery of such a
+circle. In dividing the arcs _a a_ and _b b_ we first divide them into
+six spaces, as shown, and each of these spaces into ten minor spaces, as
+is also shown. We halve five of the degree spaces, as shown at _h_. We
+should be very careful about making the degree arcs shown at Fig. 1, as
+the accuracy of our drawings depends a great deal on the perfection of
+the division on the scale _A_. In connection with such a fixed scale of
+degrees as is shown at Fig. 1, a pair of small dividers, constantly set
+to a degree space, is very convenient.
+
+
+MAKING A PAIR OF DIVIDERS.
+
+[Illustration: Fig. 3]
+
+To make such a pair of small dividers, take a piece of hard sheet brass
+about 1/20" thick, 1/4" wide, 11/2" long, and shape it as shown at Fig.
+3. It should be explained, the part cut from the sheet brass is shown
+below the dotted line _k_, the portion above (_C_) being a round handle
+turned from hard wood or ivory. The slot _l_ is sawn in, and two holes
+drilled in the end to insert the needle points _i i_. In making the slot
+_l_ we arrange to have the needle points come a little too close
+together to agree with the degree spaces on the arcs _a a_ and _b b_. We
+then put the small screw _j_ through one of the legs _D''_, and by
+turning _j_, set the needle points _i i_ to exactly agree with the
+degree spaces. As soon as the points _i i_ are set correctly, _j_ should
+be soft soldered fast.
+
+The degree spaces on _A_ are set off with these dividers and the spaces
+on _A_ very carefully marked. The upper and outer arc _a a_ should have
+the spaces cut with a graver line, while the lower one, _b b_ is best
+permanently marked with a carefully-made prick punch. After the arc _a a_
+is divided, the brass plate _A_ is cut back to this arc so the
+divisions we have just made are on the edge. The object of having two
+arcs on the plate _A_ is, if we desire to get at the number of degrees
+contained in any arc of a 5" radius we lay the scale _A_ so the edge
+agrees with the arc _a a_, and read off the number of degrees from the
+scale. In setting dividers we employ the dotted spaces on the arc _b b_.
+
+
+DELINEATING AN ESCAPE WHEEL.
+
+[Illustration: Fig. 4]
+
+We will now proceed to delineate an escape wheel for a detached lever.
+We place a piece of good drawing-paper on our drawing-board and provide
+ourselves with a very hard (HHH) drawing-pencil and a bottle of liquid
+India ink. After placing our paper on the board, we draw, with the aid
+of our T-square, a line through the center of the paper, as shown at
+_m m_, Fig. 4. At 51/2" from the lower margin of the paper we establish
+the point _p_ and sweep the circle _n n_ with a radius of 5". We have
+said nothing about stretching our paper on the drawing-board; still,
+carefully-stretched paper is an important part of nice and correct
+drawing. We shall subsequently give directions for properly stretching
+paper, but for the present we will suppose the paper we are using is
+nicely tacked to the face of the drawing-board with the smallest tacks
+we can procure. The paper should not come quite to the edge of the
+drawing-board, so as to interfere with the head of the T-square. We are
+now ready to commence delineating our escape wheel and a set of pallets
+to match.
+
+The simplest form of the detached lever escapement in use is the one
+known as the "ratchet-tooth lever escapement," and generally found in
+English lever watches. This form of escapement gives excellent results
+when well made; and we can only account for it not being in more general
+use from the fact that the escape-wheel teeth are not so strong and
+capable of resisting careless usage as the club-tooth escape wheel.
+
+It will be our aim to convey broad ideas and inculcate general
+principles, rather than to give specific instructions for doing "one
+thing one way." The ratchet-tooth lever escapements of later dates
+have almost invariably been constructed on the ten-degree
+lever-and-pallet-action plan; that is, the fork and pallets were
+intended to act through this arc. Some of the other specimens of this
+escapement have larger arcs--some as high as twelve degrees.
+
+
+PALLET-AND-FORK ACTION.
+
+[Illustration: Fig. 5]
+
+We illustrate at Fig. 5 what we mean by ten degrees of pallet-and-fork
+action. If we draw a line through the center of the pallet staff, and
+also through the center of the fork slot, as shown at _a b_, Fig. 5, and
+allow the fork to vibrate five degrees each side of said lines _a b_, to
+the lines _a c_ and _a c'_, the fork has what we term ten-degree pallet
+action. If the fork and pallets vibrate six degrees on each side of the
+line _a b_--that is, to the lines _a d_ and _a d'_--we have twelve
+degrees pallet action. If we cut the arc down so the oscillation is only
+four and one-quarter degrees on each side of _a b_, as indicated by the
+lines _a s_ and _a s'_, we have a pallet-and-fork action of eight and
+one-half degrees; which, by the way, is a very desirable arc for a
+carefully-constructed escapement.
+
+The controlling idea which would seem to rule in constructing a detached
+lever escapement, would be to make it so the balance is free of the
+fork; that is, detached, during as much of the arc of the vibration of
+the balance as possible, and yet have the action thoroughly sound and
+secure. Where a ratchet-tooth escapement is thoroughly well-made of
+eight and one-half degrees of pallet-and-fork action, ten and one-half
+degrees of escape-wheel action can be utilized, as will be explained
+later on.
+
+We will now resume the drawing of our escape wheel, as illustrated at
+Fig. 4. In the drawing at Fig. 6 we show the circle _n n_, which
+represents the periphery of our escape wheel; and in the drawing we are
+supposed to be drawing it ten inches in diameter.
+
+We produce the vertical line _m_ passing through the center _p_ of the
+circle _n_. From the intersection of the circle _n_ with the line _m_
+at _i_ we lay off thirty degrees on each side, and establish the points
+_e f_; and from the center _p_, through these points, draw the radial
+lines _p e'_ and _p f'_. The points _f e_, Fig. 6, are, of course, just
+sixty degrees apart and represent the extent of two and one-half teeth
+of the escape wheel. There are two systems on which pallets for lever
+escapements are made, viz., equidistant lockings and circular pallets.
+The advantages claimed for each system will be discussed subsequently.
+For the first and present illustration we will assume we are to employ
+circular pallets and one of the teeth of the escape wheel resting on the
+pallet at the point _f_; and the escape wheel turning in the direction
+of the arrow _j_. If we imagine a tooth as indicated at the dotted
+outline at _D_, Fig. 6, pressing against a surface which coincides with
+the radial line _p f_, the action would be in the direction of the line
+_f h_ and at right angles to _p f_. If we reason on the action of the
+tooth _D_, as it presses against a pallet placed at _f_, we see the
+action is neutral.
+
+[Illustration: Fig. 6]
+
+
+ESTABLISHING THE CENTER OF PALLET STAFF.
+
+[Illustration: Fig. 7]
+
+With a fifteen-tooth escape wheel each tooth occupies twenty-four
+degrees, and from the point _f_ to _e_ would be two and one-half
+tooth-spaces. We show the dotted points of four teeth at _D D' D''D'''_.
+To establish the center of the pallet staff we draw a line at
+right angles to the line _p e'_ from the point _e_ so it intersects the
+line _f h_ at _k_. For drawing a line at right angles to another line,
+as we have just done, a hard-rubber triangle, shaped as shown at _C_,
+Fig. 7, can be employed. To use such a triangle, we place it so the
+right, or ninety-degrees angle, rests at _e_, as shown at the dotted
+triangle _C_, Fig. 6, and the long side coincides with the radial line
+_p e'_. If the short side of the hard-rubber triangle is too short, as
+indicated, we place a short ruler so it rests against the edge, as shown
+at the dotted line _g e_, Fig. 7, and while holding it securely down on
+the drawing we remove the triangle, and with a fine-pointed pencil draw
+the line _e g_, Fig. 6, by the short rule. Let us imagine a flat surface
+placed at _e_ so its face was at right angles to the line _g e_, which
+would arrest the tooth _D''_ after the tooth _D_ resting on _f_ had been
+released and passed through an arc of twelve degrees. A tooth resting on
+a flat surface, as imagined above, would also rest dead. As stated
+previously, the pallets we are considering have equidistant locking
+faces and correspond to the arc _l l_, Fig. 6.
+
+In order to realize any power from our escape-wheel tooth, we must
+provide an impulse face to the pallets faced at _f e_; and the problem
+before us is to delineate these pallets so that the lever will be
+propelled through an arc of eight and one-half degrees, while the escape
+wheel is moving through an arc of ten and one-half degrees. We make the
+arc of fork action eight and one-half degrees for two reasons--(1)
+because most text-books have selected ten degrees of fork-and-pallet
+action; (2) because most of the finer lever escapements of recent
+construction have a lever action of less than ten degrees.
+
+
+LAYING OUT ESCAPE-WHEEL TEETH.
+
+To "lay out" or delineate our escape-wheel teeth, we continue our
+drawing shown at Fig. 6, and reproduce this cut very nearly at Fig. 8.
+With our dividers set at five inches, we sweep the short arc _a a'_ from
+_f_ as a center. It is to be borne in mind that at the point _f_ is
+located the extreme point of an escape-wheel tooth. On the arc _a a_ we
+lay off from _p_ twenty-four degrees, and establish the point _b_; at
+twelve degrees beyond _b_ we establish the point _c_. From _f_ we draw
+the lines _f b_ and _f c_; these lines establishing the form and
+thickness of the tooth _D_. To get the length of the tooth, we take in
+our dividers one-half a tooth space, and on the radial line _p f_
+establish the point _d_ and draw circle _d' d'_.
+
+To facilitate the drawing of the other teeth, we draw the circles _d' c'_,
+to which the lines _f b_ and _f c_ are tangent, as shown. We divide
+the circle _n n_, representing the periphery of our escape wheel, into
+fifteen spaces, to represent teeth, commencing at _f_ and continued as
+shown at _o o_ until the entire wheel is divided. We only show four
+teeth complete, but the same methods as produced these will produce them
+all. To briefly recapitulate the instructions for drawing the teeth for
+the ratchet-tooth lever escapement: We draw the face of the teeth at an
+angle of twenty-four degrees to a radial line; the back of the tooth at
+an angle of thirty-six degrees to the same radial line; and make teeth
+half a tooth-space deep or long.
+
+[Illustration: Fig. 8]
+
+We now come to the consideration of the pallets and how to delineate
+them. To this we shall add a careful analysis of their action. Let us,
+before proceeding further, "think a little" over some of the factors
+involved. To aid in this thinking or reasoning on the matter, let us
+draw the heavy arc _l_ extending from a little inside of the circle _n_
+at _f_ to the circle _n_ at _e_. If now we imagine our escape wheel to
+be pressed forward in the direction of the arrow _j_, the tooth _D_
+would press on the arc _l_ and be held. If, however, we should revolve
+the arc _l_ on the center _k_ in the direction of the arrow _i_, the
+tooth _D_ would _escape_ from the edge of _l_ and the tooth _D''_ would
+pass through an arc (reckoning from the center _p_) of twelve degrees,
+and be arrested by the inside of the arc _l_ at _e_. If we now should
+reverse the motion and turn the arc _l_ backward, the tooth at _e_
+would, in turn, be released and the tooth following after _D_ (but not
+shown) would engage _l_ at _f_. By supplying motive to revolve the
+escape wheel (_E_) represented by the circle _n_, and causing the arc
+_l_ to oscillate back and forth in exact intervals of time, we should
+have, in effect, a perfect escapement. To accomplish automatically such
+oscillations is the problem we have now on hand.
+
+
+HOW MOTION IS OBTAINED.
+
+In clocks, the back-and-forth movement, or oscillating motion, is
+obtained by employing a pendulum; in a movable timepiece we make use of
+an equally-poised wheel of some weight on a pivoted axle, which device
+we term a balance; the vibrations or oscillations being obtained by
+applying a coiled spring, which was first called a "pendulum spring,"
+then a "balance spring," and finally, from its diminutive size and coil
+form, a "hairspring." We are all aware that for the motive power for
+keeping up the oscillations of the escaping circle _l_ we must contrive
+to employ power derived from the teeth _D_ of the escape wheel. About
+the most available means of conveying power from the escape wheel to the
+oscillating arc _l_ is to provide the lip of said arc with an inclined
+plane, along which the tooth which is disengaged from _l_ at _f_ to
+slide and move said arc _l_ through--in the present instance an arc of
+eight and one-half degrees, during the time the tooth _D_ is passing
+through ten and one-half degrees. This angular motion of the arc _l_ is
+represented by the radial lines _k f'_ and _k r_, Fig. 8. We desire to
+impress on the reader's mind the idea that each of these angular motions
+is not only required to be made, but the motion of one mobile must
+convey power to another mobile.
+
+In this case the power conveyed from the mainspring to the escape wheel
+is to be conveyed to the lever, and by the lever transmitted to the
+balance. We know it is the usual plan adopted by text-books to lay down
+a certain formula for drawing an escapement, leaving the pupil to work
+and reason out the principles involved in the action. In the plan we
+have adopted we propose to induct the reader into the why and how, and
+point out to him the rules and methods of analysis of the problem, so
+that he can, if required, calculate mathematically exactly how many
+grains of force the fork exerts on the jewel pin, and also how much (or,
+rather, what percentage) of the motive power is lost in various "power
+leaks," like "drop" and lost motion. In the present case the mechanical
+result we desire to obtain is to cause our lever pivoted at _k_ to
+vibrate back and forth through an arc of eight and one-half degrees;
+this lever not only to vibrate back and forth, but also to lock and hold
+the escape wheel during a certain period of time; that is, through the
+period of time the balance is performing its excursion and the jewel pin
+free and detached from the fork.
+
+We have spoken of paper being employed for drawings, but for very
+accurate delineations we would recommend the horological student to make
+drawings on a flat metal plate, after perfectly smoothing the surface
+and blackening it by oxidizing.
+
+
+PALLET-AND-FORK ACTION.
+
+By adopting eight and one-half degrees pallet-and-fork action we can
+utilize ten and one-half degrees of escape-wheel action. We show at _A A'_,
+Fig. 9, two teeth of a ratchet-tooth escape wheel reduced one-half;
+that is, the original drawing was made for an escape wheel ten inches in
+diameter. We shall make a radical departure from the usual practice in
+making cuts on an enlarged scale, for only such parts as we are talking
+about. To explain, we show at Fig. 10 about one-half of an escape wheel
+one eighth the size of our large drawing; and when we wish to show some
+portion of such drawing on a larger scale we will designate such
+enlargement by saying one-fourth, one-half or full size.
+
+[Illustration: Fig. 9]
+
+At Fig. 9 we show at half size that portion of our escapement embraced
+by the dotted lines _d_, Fig. 10. This plan enables us to show very
+minutely such parts as we have under consideration, and yet occupy but
+little space. The arc _a_, Fig. 9, represents the periphery of the
+escape wheel. On this line, ten and one-half degrees from the point of
+the tooth _A_, we establish the point _c_ and draw the radial line
+_c c'_. It is to be borne in mind that the arc embraced between the points
+_b_ and _c_ represents the duration of contact between the tooth _A_ and
+the entrance pallet of the lever. The space or short arc _c n_
+represents the "drop" of the tooth.
+
+This arc of one and one-half degrees of escape-wheel movement is a
+complete loss of six and one-fourth per cent. of the entire power of the
+mainspring, as brought down to the escapement; still, up to the present
+time, no remedy has been devised to overcome it. All the other
+escapements, including the chronometer, duplex and cylinder, are quite
+as wasteful of power, if not more so. It is usual to construct
+ratchet-tooth pallets so as to utilize but ten degrees of escape-wheel
+action; but we shall show that half a degree more can be utilized by
+adopting the eight and one-half degree fork action and employing a
+double-roller safety action to prevent over-banking.
+
+[Illustration: Fig. 10]
+
+From the point _e_, which represents the center of the pallet staff, we
+draw through _b_ the line _e f_. At one degree below _e f_ we draw the
+line _e g_, and seven and one-half degrees below the line _e g_ we draw
+the line _e h_. For delineating the lines _e g_, etc., correctly, we
+employ a degree-arc; that is, on the large drawing we are making we
+first draw the line _e b f_, Fig. 10, and then, with our dividers set at
+five inches, sweep the short arc _i_, and on this lay off first one
+degree from the intersection of _f e_ with the arc _i_, and through this
+point draw the line _e g_.
+
+From the intersection of the line _f e_ with the arc _i_ we lay off
+eight and one-half degrees, and through this point draw the line _e h_.
+Bear in mind that we are drawing the pallet at _B_ to represent one with
+eight and one-half degrees fork-and-pallet action, and with equidistant
+lockings. If we reason on the matter under consideration, we will see
+the tooth _A_ and the pallet _B_, against which it acts, part or
+separate when the tooth arrives at the point _c_; that is, after the
+escape wheel has moved through ten and one-half degrees of angular
+motion, the tooth drops from the impulse face of the pallet and falls
+through one and one-half degrees of arc, when the tooth _A''_, Fig. 10,
+is arrested by the exit pallet.
+
+To locate the position of the inner angle of the pallet _B_, sweep the
+short arc _l_ by setting the dividers so one point or leg rests at the
+center _e_ and the other at the point _c_. Somewhere on this arc _l_ is
+to be located the inner angle of our pallet. In delineating this angle,
+Moritz Grossman, in his "Prize Essay on the Detached Lever Escapement,"
+makes an error, in Plate III of large English edition, of more than his
+entire lock, or about two degrees. We make no apologies for calling
+attention to this mistake on the part of an authority holding so high a
+position on such matters as Mr. Grossman, because a mistake is a
+mistake, no matter who makes it.
+
+We will say no more of this error at present, but will farther on show
+drawings of Mr. Grossman's faulty method, and also the correct method of
+drawing such a pallet. To delineate the locking face of our pallet, from
+the point formed by the intersection of the lines _e g b b'_, Fig. 9, as
+a center, we draw the line _j_ at an angle of twelve degrees to _b b''_.
+In doing this we employ the same method of establishing the angle as we
+made use of in drawing the lines _e g_ and _e h_, Fig. 10. The line _j_
+establishes the locking face of the pallet _B_. Setting the locking face
+of the pallet at twelve degrees has been found in practice to give a
+safe "draw" to the pallet and keep the lever secure against the bank. It
+will be remembered the face of the escape-wheel tooth was drawn at
+twenty-four degrees to a radial line of the escape wheel, which, in this
+instance, is the line _b b'_, Fig. 9. It will now be seen that the angle
+of the pallet just halves this angle, and consequently the tooth _A_
+only rests with its point on the locking face of the pallet. We do not
+show the outlines of the pallet _B_, because we have not so far pointed
+out the correct method of delineating it.
+
+
+METHODS OF MAKING GOOD DRAWING INSTRUMENTS.
+
+Perhaps we cannot do our readers a greater favor than to digress from
+the study of the detached lever escapement long enough to say a few
+words about drawing instruments and tablets or surfaces on which to
+delineate, with due precision, mechanical designs or drawings. Ordinary
+drawing instruments, even of the higher grades, and costing a good deal
+of money, are far from being satisfactory to a man who has the proper
+idea of accuracy to be rated as a first-class mechanic. Ordinary
+compasses are obstinate when we try to set them to the hundredth of an
+inch; usually the points are dull and ill-shapen; if they make a
+puncture in the paper it is unsightly.
+
+Watchmakers have one advantage, however, because they can very easily
+work over a cheap set of drawing instruments and make them even superior
+to anything they can buy at the art stores. To illustrate, let us take a
+cheap pair of brass or German-silver five-inch dividers and make them
+over into needle points and "spring set." To do this the points are cut
+off at the line _a a_, Fig 11, and a steel tube is gold-soldered on each
+leg. The steel tube is made by taking a piece of steel wire which will
+fit a No. 16 chuck of a Whitcomb lathe, and drilling a hole in the end
+about one-fourth of an inch deep and about the size of a No. 3 sewing
+needle. We Show at Fig. 12 a view of the point _A'_, Fig. 11, enlarged,
+and the steel tube we have just drilled out attached at _C_. About the
+best way to attach _C_ is to solder. After the tube _C_ is attached a
+hole is drilled through _A'_ at _d_, and the thumb-screw _d_ inserted.
+This thumb-screw should be of steel, and hardened and tempered. The use
+of this screw is to clamp the needle point. With such a device as the
+tube _C_ and set-screw _d_, a No. 3 needle is used for a point; but for
+drawings on paper a turned point, as shown at Fig 13, is to be
+preferred. Such points can be made from a No. 3 needle after softening
+enough to be turned so as to form the point _c_. This point at the
+shoulder _f_ should be about 12/1000 of an inch, or the size of a
+fourth-wheel pivot to an eighteen size movement.
+
+[Illustration: Fig. 11]
+
+[Illustration: Fig. 12]
+
+[Illustration: Fig. 13]
+
+[Illustration: Fig. 14]
+
+The idea is, when drawing on paper the point _c_ enters the paper. For
+drawing on metal the form of the point is changed to a simple cone, as
+shown at _B'_ _c_, Fig. 13. such cones can be turned carefully, then
+hardened and tempered to a straw color; and when they become dull, can
+be ground by placing the points in a wire chuck and dressing them up
+with an emery buff or an Arkansas slip. The opposite leg of the dividers
+is the one to which is attached the spring for close setting of the
+points.
+
+In making this spring, we take a piece of steel about two and
+one-fourth inches long and of the same width as the leg of the divider,
+and attach it to the inside of the leg as shown at Fig. 14, where _D_
+represents the spring and _A_ the leg of the dividers. The spring _D_
+has a short steel tube _C''_ and set-screw _d''_ for a fine point like
+_B_ or _B'_. In the lower end of the leg _A_, Fig. 14, is placed the
+milled-head screw _g_, which serves to adjust the two points of the
+dividers to very close distances. The spring _D_ is, of course, set so
+it would press close to the leg _A_ if the screw _g_ did not force it
+away.
+
+
+SPRING AND ADJUSTING SCREW FOR DRAWING INSTRUMENTS.
+
+[Illustration: Fig. 15]
+
+It will be seen that we can apply a spring _D_ and adjusting screw
+opposite to the leg which carries the pen or pencil point of all our
+dividers if we choose to do so; but it is for metal drawing that such
+points are of the greatest advantage, as we can secure an accuracy very
+gratifying to a workman who believes in precision. For drawing circles
+on metal, "bar compasses" are much the best, as they are almost entirely
+free from spring, which attends the jointed compass. To make (because
+they cannot be bought) such an instrument, take a piece of flat steel,
+one-eighth by three-eighths of an inch and seven inches long, and after
+turning and smoothing it carefully, make a slide half an inch wide, as
+shown at Fig. 15, with a set-screw _h_ on top to secure it at any point
+on the bar _E_. In the lower part of the slide _F_ is placed a steel
+tube like _C_, shown in Figs. 12 and 14, with set-screw for holding
+points like _B B'_, Fig. 13. At the opposite end of the bar _E_ is
+placed a looped spring _G_, which carries a steel tube and point like
+the spring _D_, Fig. 14. Above this tube and point, shown at _j_, Fig.
+15, is placed an adjustment screw _k_ for fine adjustment. The inner end
+of the screw _k_ rests against the end of the bar _E_. The tendency of
+the spring _G_ is to close upon the end of _E_; consequently if we make
+use of the screw _k_ to force away the lower end of _G_, we can set the
+fine point in _j_ to the greatest exactness.
+
+The spring _G_ is made of a piece of steel one-eighth of an inch
+square, and secured to the bar _E_ with a screw and steady pins at _m_.
+A pen and pencil point attachment can be added to the spring _G_; but in
+case this is done it would be better to make another spring like _G_
+without the point _j_, and with the adjusting screw placed at _l_. In
+fitting pen and pencil points to a spring like _G_ it would probably be
+economical to make them outright; that is, make the blades and screw for
+the ruling pen and a spring or clamping tube for the pencil point.
+
+
+CONSIDERATION OF DETACHED LEVER ESCAPEMENT RESUMED.
+
+We will now, with our improved drawing instruments, resume the
+consideration of the ratchet-tooth lever escapement. We reproduce at
+Fig. 16 a portion of diagram III, from Moritz Grossmann's "Prize Essay
+on the Detached Lever Escapement," in order to point out the error in
+delineating the entrance pallet to which we previously called attention.
+The cut, as we give it, is not quite one-half the size of Mr.
+Grossmann's original plate.
+
+In the cut we give the letters of reference employed the same as on the
+original engraving, except where we use others in explanation. The
+angular motion of the lever and pallet action as shown in the cut is ten
+degrees; but in our drawing, where we only use eight and one-half
+degrees, the same mistake would give proportionate error if we did not
+take the means to correct it. The error to which we refer lies in
+drawing the impulse face of the entrance pallet. The impulse face of
+this pallet as drawn by Mr. Grossmann would not, from the action of the
+engaging tooth, carry this pallet through more than eight degrees of
+angular motion; consequently, the tooth which should lock on the exit
+pallet would fail to do so, and strike the impulse face.
+
+We would here beg to add that nothing will so much instruct a person
+desiring to acquire sound ideas on escapements as making a large model.
+The writer calls to mind a wood model of a lever escapement made by one
+of the "boys" in the Elgin factory about a year or two after Mr.
+Grossmann's prize essay was published. It went from hand to hand and did
+much toward establishing sound ideas as regards the correct action of
+the lever escapement in that notable concern.
+
+If a horological student should construct a large model on the lines
+laid down in Mr. Grossmann's work, the entrance pallet would be faulty
+in form and would not properly perform its functions. Why? perhaps says
+our reader. In reply let us analyze the action of the tooth _B_ as it
+rests on the pallet _A_. Now, if we move this pallet through an angular
+motion of one and one-half degrees on the center _g_ (which also
+represents the center of the pallet staff), the tooth _B_ is disengaged
+from the locking face and commences to slide along the impulse face of
+the pallet and "drops," that is, falls from the pallet, when the inner
+angle of the pallet is reached.
+
+[Illustration: Fig. 16]
+
+This inner angle, as located by Mr. Grossmann, is at the intersection of
+the short arc _i_ with the line _g n_, which limits the ten-degree
+angular motion of the pallets. If we carefully study the drawing, we
+will see the pallet has only to move through eight degrees of angular
+motion of the pallet staff for the tooth to escape, _because the tooth
+certainly must be disengaged when the inner angle of the pallet reaches
+the peripheral line a_. The true way to locate the position of the inner
+angle of the pallet, is to measure down on the arc _i_ ten degrees from
+its intersection with the peripheral line _a_ and locate a point to
+which a line is drawn from the intersection of the line _g m_ with the
+radial line _a c_, thus defining the inner angle of the entrance pallet.
+We will name this point the point _x_.
+
+It may not be amiss to say the arc _i_ is swept from the center _g_
+through the point _u_, said point being located ten degrees from the
+intersection of the radial _a c_ with the peripheral line _a_. It will
+be noticed that the inner angle of the entrance pallet _A_ seems to
+extend inward, beyond the radial line _a j_, that is, toward the pallet
+center _g_, and gives the appearance of being much thicker than the exit
+pallet _A'_; but we will see on examination that the extreme angle _x_
+of the entrance pallet must move on the arc _i_ and, consequently, cross
+the peripheral line _a_ at the point _u_. If we measure the impulse
+faces of the two pallets _A A'_, we will find them nearly alike in
+linear extent.
+
+Mr. Grossmann, in delineating his exit pallet, brings the extreme angle
+(shown at _4_) down to the periphery of the escape, as shown in the
+drawing, where it extends beyond the intersection of the line _g f_ with
+the radial line _a 3_. The correct form for the entrance pallet should
+be to the dotted line _z x y_.
+
+[Illustration: Fig. 17]
+
+We have spoken of engaging and disengaging frictions; we do not know how
+we can better explain this term than by illustrating the idea with a
+grindstone. Suppose two men are grinding on the same stone; each has,
+say, a cold chisel to grind, as shown at Fig. 17, where _G_ represents
+the grindstone and _N N'_ the cold chisels. The grindstone is supposed
+to be revolving in the direction of the arrow. The chisels _N_ and _N'_
+are both being ground, but the chisel _N'_ is being cut much the more
+rapidly, as each particle of grit of the stone as it catches on the
+steel causes the chisel to hug the stone and bite in deeper and deeper;
+while the chisel shown at _N_ is thrust away by the action of the grit.
+Now, friction of any kind is only a sort of grinding operation, and the
+same principles hold good.
+
+
+THE NECESSITY FOR GOOD INSTRUMENTS.
+
+It is to be hoped the reader who intends to profit by this treatise has
+fitted up such a pair of dividers as those we have described, because it
+is only with accurate instruments he can hope to produce drawings on
+which any reliance can be placed. The drawing of a ratchet-tooth lever
+escapement of eight and one-half degrees pallet action will now be
+resumed. In the drawing at Fig. 18 is shown a complete delineation of
+such an escapement with eight and one-half degrees of pallet action and
+equidistant locking faces. It is, of course, understood the escape wheel
+is to be drawn ten inches in diameter, and that the degree arcs shown in
+Fig. 1 will be used.
+
+We commence by carefully placing on the drawing-board a sheet of paper
+about fifteen inches square, and then vertically through the center
+draw the line _a' a''_. At some convenient position on this line is
+established the point _a_, which represents the center of the escape
+wheel. In this drawing it is not important that the entire escape wheel
+be shown, inasmuch as we have really to do with but a little over sixty
+degrees of the periphery of the escape wheel. With the dividers
+carefully set at five inches, from _a_, as a center, we sweep the arc
+_n n_, and from the intersection of the perpendicular line _a' a''_ with
+the arc _n_ we lay off on each side thirty degrees from the brass degree
+arc, and through the points thus established are drawn the radial lines
+_a b'_ and _a d'_.
+
+
+[Illustration: Fig. 18]
+
+The point on the arc _n_ where it intersects with the line _b'_ is
+termed the point _b_. At the intersection of the radial line _a d'_ is
+established the point _d_. We take ten and one-half degrees in the
+dividers, and from the point _b_ establish the point _c_, which embraces
+the arc of the escape wheel which is utilized by the pallet action.
+Through the point _b_ the line _h' h_ is drawn at right angles to the
+line _a b'_. The line _j j'_ is also drawn at right angles to the line
+_a d'_ through the point _d_. We now have an intersection of the lines
+just drawn in common with the line _a a'_ at the point _g_, said point
+indicating the center of the pallet action.
+
+The dividers are now set to embrace the space between the points _b_ and
+_g_ on the line _h' h_, and the arc _f f_ is swept; which, in proof of
+the accuracy of the work, intersects the arc _n_ at the point _d_. This
+arc coincides with the locking faces of both pallets. To lay out the
+entrance pallet, the dividers are set to five inches, and from _g_ as a
+center the short arc _o o_ is swept. On this arc one degree is laid off
+below the line _h' h_, and the line _g i_ drawn. The space embraced
+between the lines _h_ and _i_ on the arc _f_ represents the locking face
+of the entrance pallet, and the point formed at the intersection of the
+line _g i_ with the arc _f_ is called the point _p_. To give the proper
+lock to the face of the pallet, from the point _p_ as a center is swept
+the short arc _r r_, and from its intersection with the line _a b'_
+twelve degrees are laid off and the line _b s_ drawn, which defines the
+locking face of the entrance pallet. From _g_ as a center is swept the
+arc _c' c'_, intersecting the arc _n n_ at _c_. On this arc (_c_) is
+located the inner angle of the entrance pallet. The dividers are set to
+embrace the space on the arc _c'_ between the lines _g h'_ and _g k_.
+With this space in the dividers one leg is set at the point _c_,
+measuring down on the arc _c'_ and establishing the point _t_. The
+points _p_ and _t_ are then connected, and thus the impulse face of the
+entrance pallet _B_ is defined. From the point _t_ is drawn the line
+_t t'_, parallel to the line _b s_, thus defining the inner face of the
+entrance pallet.
+
+
+DELINEATING THE EXIT PALLET.
+
+To delineate the exit pallet, sweep the short arc _u u_ (from _g_ as a
+center) with the dividers set at five inches, and from the intersection
+of this arc with the line _g j'_ set off eight and one-half degrees and
+draw the line _g l_. At one degree below this line is drawn the line _g m_.
+The space on the arc _f_ between these lines defines the locking
+face of the exit pallet. The point where the line _g m_ intersects the
+arc _f_ is named the point _x_. From the point _x_ is erected the line
+_x w_, perpendicular to the line _g m_. From _x_ as a center, and with
+the dividers set at five inches, the short arc _y y_ is swept, and on
+this arc are laid off twelve degrees, and the line _x z_ is drawn, which
+line defines the locking face of the exit pallet.
+
+Next is taken ten and one-half degrees from the brass degree-scale, and
+from the point _d_ on the arc _n_ the space named is laid off, and thus
+is established the point _v_; and from _g_ as a center is swept the arc
+_v' v'_ through the point _v_. It will be evident on a little thought,
+that if the tooth _A'_ impelled the exit pallet to the position shown,
+the outer angle of the pallet must extend down to the point _v_, on the
+arc _v' v'_; consequently, we define the impulse face of this pallet by
+drawing a line from point _x_ to _v_. To define the outer face of the
+exit pallet, we draw the line _v e_ parallel to the line _x z_.
+
+There are no set rules for drawing the general form of the pallet arms,
+only to be governed by and conforming to about what we would deem
+appropriate, and to accord with a sense of proportion and mechanical
+elegance. Ratchet-tooth pallets are usually made in what is termed
+"close pallets"; that is, the pallet jewel is set in a slot sawed in the
+steel pallet arm, which is undoubtedly the strongest and most
+serviceable form of pallet made. We shall next consider the
+ratchet-tooth lever escapement with circular pallets and ten degrees of
+pallet action.
+
+
+DELINEATING CIRCULAR PALLETS.
+
+To delineate "circular pallets" for a ratchet-tooth lever escapement, we
+proceed very much as in the former drawing, by locating the point _A_,
+which represents the center of the escape wheel, at some convenient
+point, and with the dividers set at five inches, sweep the arc _m_, to
+represent the periphery of the escape wheel, and then draw the vertical
+line _A B'_, Fig. 19. We (as before) lay off thirty degrees on the arc
+_m_ each side of the intersection of said arc with the line _A B'_, and
+thus establish on the arc _m_ the points _a b_, and from _A_ as a center
+draw through the points so established the radial lines _A a'_ and _A b'_.
+
+We erect from the point _a_ a perpendicular to the line _A a_, and, as
+previously explained, establish the pallet center at _B_. Inasmuch as we
+are to employ circular pallets, we lay off to the left on the arc _m_,
+from the point _a_, five degrees, said five degrees being half of the
+angular motion of the escape wheel utilized in the present drawing, and
+thus establish the point _c_, and from _A_ as a center draw through this
+point the radial line _A c'_. To the right of the point _a_ we lay off
+five degrees and establish the point _d_. To illustrate the underlying
+principle of our circular pallets: with one leg of the dividers set at
+_B_ we sweep through the points _c a d_ the arcs _c'' a'' d''_.
+
+From _B_ as a center, we continue the line _B a_ to _f_, and with the
+dividers set at five inches, sweep the short arc _e e_. From the
+intersection of this arc with the line _B f_ we lay off one and a half
+degrees and draw the line _B g_, which establishes the extent of the
+lock on the entrance pallet. It will be noticed the linear extent of
+the locking face of the entrance pallet is greater than that of the
+exit, although both represent an angle of one and a half degrees.
+Really, in practice, this discrepancy is of little importance, as the
+same side-shake in banking would secure safety in either case.
+
+[Illustration: Fig. 19]
+
+The fault we previously pointed out, of the generally accepted method of
+delineating a detached lever escapement, is not as conspicuous here as
+it is where the pallets are drawn with equidistant locking faces; that
+is, the inner angle of the entrance pallet (shown at _s_) does not have
+to be carried down on the arc _d'_ as far to insure a continuous pallet
+action of ten degrees, as with the pallets with equidistant locking
+faces. Still, even here we have carried the angle _s_ down about half a
+degree on the arc _d'_, to secure a safe lock on the exit pallet.
+
+
+THE AMOUNT OF LOCK.
+
+If we study the large drawing, where we delineate the escape wheel ten
+inches in diameter, it will readily be seen that although we claim one
+and a half degrees lock, we really have only about one degree, inasmuch
+as the curve of the peripheral line _m_ diverges from the line _B f_,
+and, as a consequence, the absolute lock of the tooth _C_ on the locking
+face of the entrance pallet _E_ is but about one degree. Under these
+conditions, if we did not extend the outer angle of the exit pallet at
+_t_ down to the peripheral line _m_, we would scarcely secure one-half a
+degree of lock. This is true of both pallets. We must carry the pallet
+angles at _r s n t_ down on the circles _c'' d'_ if we would secure the
+lock and impulse we claim; that is, one and a half degrees lock and
+eight and a half degrees impulse.
+
+Now, while the writer is willing to admit that a one-degree lock in a
+sound, well-made escapement is ample, still he is not willing to allow
+of a looseness of drawing to incorporate to the extent of one degree in
+any mechanical matter demanding such extreme accuracy as the parts of a
+watch. It has been claimed that such defects can, to a great extent, be
+remedied by setting the escapement closer; that is, by bringing the
+centers of the pallet staff and escape wheel nearer together. We hold
+that such a course is not mechanical and, further, that there is not the
+slightest necessity for such a policy.
+
+
+ADVANTAGE OF MAKING LARGE DRAWINGS.
+
+By making the drawings large, as we have already suggested and insisted
+upon, we can secure an accuracy closely approximating perfection. As,
+for instance, if we wish to get a lock of one and a half degrees on the
+locking face of the entrance pallet _E_, we measure down on the arc
+_c''_ from its intersection with the peripheral line _m_ one and a half
+degrees, and establish the point _r_ and thus locate the outer angle of
+the entrance pallet _E_, so there will really be one and a half degrees
+of lock; and by measuring down on the arc _d'_ ten degrees from its
+intersection with the peripheral line _m_, we locate the point _s_,
+which determines the position of the inner angle of the entrance pallet,
+and we know for a certainty that when this inner angle is freed from the
+tooth it will be after the pallet (and, of course, the lever) has passed
+through exactly ten degrees of angular motion.
+
+For locating the inner angle of the exit pallet, we measure on the arc
+_d'_, from its intersection with the peripheral line _m_, eight and a
+half degrees, and establish the point _n_, which locates the position of
+this inner angle; and, of course, one and a half degrees added on the
+arc _d'_ indicates the extent of the lock on this pallet. Such drawings
+not only enable us to theorize to extreme exactness, but also give us
+proportionate measurements, which can be carried into actual
+construction.
+
+
+THE CLUB-TOOTH LEVER ESCAPEMENT.
+
+We will now take up the club-tooth form of the lever escapement. This
+form of tooth has in the United States and in Switzerland almost
+entirely superceded the ratchet tooth. The principal reason for its
+finding so much favor is, we think, chiefly owing to the fact that this
+form of tooth is better able to stand the manipulations of the
+able-bodied watchmaker, who possesses more strength than skill. We will
+not pause now, however, to consider the comparative merits of the
+ratchet and club-tooth forms of the lever escapement, but leave this
+part of the theme for discussion after we have given full instructions
+for delineating both forms.
+
+With the ratchet-tooth lever escapement all of the impulse must be
+derived from the pallets, but in the club-tooth escapement we can divide
+the impulse planes between the pallets and the teeth to suit our fancy;
+or perhaps it would be better to say carry out theories, because we have
+it in our power, in this form of the lever escapement, to indulge
+ourselves in many changes of the relations of the several parts. With
+the ratchet tooth the principal changes we could make would be from
+pallets with equidistant lockings to circular pallets. The club-tooth
+escape wheel not only allows of circular pallets and equidistant
+lockings, but we can divide the impulse between the pallets and the
+teeth in such a way as will carry out many theoretical advantages which,
+after a full knowledge of the escapement action is acquired, will
+naturally suggest themselves. In the escapement shown at Fig. 20 we have
+selected, as a very excellent example of this form of tooth, circular
+pallets of ten degrees fork action and ten and a half degrees of
+escape-wheel action.
+
+It will be noticed that the pallets here are comparatively thin to those
+in general use; this condition is accomplished by deriving the principal
+part of the impulse from driving planes placed on the teeth. As relates
+to the escape-wheel action of the ten and one-half degrees, which gives
+impulse to the escapement, five and one-half degrees are utilized by the
+driving planes on the teeth and five by the impulse face of the pallet.
+Of the ten degrees of fork action, four and a half degrees relate to the
+impulse face of the teeth, one and a half degrees to lock, and four
+degrees to the driving plane of the pallets.
+
+In delineating such a club-tooth escapement, we commence, as in former
+examples, by first assuming the center of the escape wheel at _A_, and
+with the dividers set at five inches sweeping the arc _a a_. Through _A_
+we draw the vertical line _A B'_. On the arc _a a_, and each side of its
+intersection with the line _A B'_, we lay off thirty degrees, as in
+former drawings, and through the points so established on the arc _a a_
+we draw the radial lines _A b_ and _A c_. From the intersection of the
+radial line _A b_ with the arc _a_ we draw the line _h h_ at right
+angles to _A b_. Where the line _h_ intersects the radial lines _A B'_
+is located the center of the pallet staff, as shown at _B_. Inasmuch as
+we decided to let the pallet utilize five degrees of escape-wheel
+action, we take a space of two and a half degrees in the dividers, and
+on the arc _a a_ lay off the said two and a half degrees to the left of
+this intersection, and through the point so established draw the radial
+line _A g_. From _B_ as a center we sweep the arc _d d_ so it passes
+through the point of intersection of the arc _a_ with the line _A g_.
+
+[Illustration: Fig. 20]
+
+We again lay off two and a half degrees from the intersection of the
+line _A b_ with the arc _a_, but this time to the right of said
+intersection, and through the point so established, and from _B_ as a
+center, we sweep the arc _e_. From the intersection of the radial line
+_A g_ with the arc _a_ we lay off to the left five and a half degrees on
+said arc, and through the point so established draw the radial line _A f_.
+With the dividers set at five inches we sweep the short arc _m_ from
+_B_ as a center. From the intersection of the line _h B h'_ with the
+arc _m_ we lay off on said arc and above the line _h'_ four and a half
+degrees, and through the point so established draw the line _B j_.
+
+We next set the dividers so they embrace the space on the radial line _A b_
+between its intersection with the line _B j_ and the center _A_, and
+from _A_ as a center sweep the arc _i_, said arc defining the _addendum_
+of the escape-wheel teeth. We draw a line from the intersection of the
+radial line _A f_ with the arc _i_ to the intersection of the radial
+line _A g_ with the arc _a_, and thus define the impulse face of the
+escape-wheel tooth _D_. For defining the locking face of the tooth we
+draw a line at an angle of twenty-four degrees to the line _A g_, as
+previously described. The back of the tooth is defined with a curve
+swept from some point on the addendum circle _i_, such as our judgment
+will dictate.
+
+In the drawing shown at Fig. 20 the radius of this curve was obtained by
+taking eleven and a half degrees from the degree arc of 5" radius in the
+dividers, and setting one leg at the intersection of the radial line _A f_
+with the arc _i_, and placing the other on the line _i_, and allowing
+the point so established to serve as a center, the arc was swept for the
+back of the tooth, the small circle at _n_ denoting one of the centers
+just described. The length for the face of the tooth was obtained by
+taking eleven degrees from the degree arc just referred to and laying
+that space off on the line _p_, which defined the face of the tooth. The
+line _B k_ is laid off one and a half degrees below _B h_ on the arc
+_m_. The extent of this arc on the arc _d_ defines the locking face of
+the entrance pallet. We set off four degrees on the arc _m_ below the
+line _B k_, and through the point so established draw the line _B l_. We
+draw a line from the intersection of the line _A g_ with the line _c h_
+to the intersection of the arc _e_ with the line _c l_, and define the
+impulse face of the entrance pallet.
+
+
+RELATIONS OF THE SEVERAL PARTS.
+
+Before we proceed to delineate the exit pallet of our escapement, let us
+reason on the relations of the several parts.
+
+The club-tooth lever escapement is really the most complicated
+escapement made. We mean by this that there are more factors involved in
+the problem of designing it correctly than in any other known
+escapement. Most--we had better say all, for there are no exceptions
+which occur to us--writers on the lever escapement lay down certain
+empirical rules for delineating the several parts, without giving
+reasons for this or that course. For illustration, it is an established
+practice among escapement makers to employ tangential lockings, as we
+explained and illustrated in Fig. 16.
+
+Now, when we adopt circular pallets and carry the locking face of the
+entrance pallet around to the left two and a half degrees, the true
+center for the pallet staff, if we employ tangent lockings, would be
+located on a line drawn tangent to the circle _a a_ from its
+intersection with the radial line _A k_, Fig. 21. Such a tangent is
+depicted at the line _s l'_. If we reason on the situation, we will see
+that the line _A k_ is not at right angles to the line _s l_; and,
+consequently, the locking face of the entrance pallet _E_ has not really
+the twelve-degree lock we are taught to believe it has.
+
+[Illustration: Fig. 21]
+
+We will not discuss these minor points further at present, but leave
+them for subsequent consideration. We will say, however, that we could
+locate the center of the pallet action at the small circle _B'_ above
+the center _B_, which we have selected as our fork-and-pallet action,
+and secure a perfectly sound escapement, with several claimed
+advantages.
+
+Let us now take up the delineation of the exit pallet. It is very easy
+to locate the outer angle of this pallet, as this must be situated at
+the intersection of the addendum circle _i_ and the arc _g_, and located
+at _o_. It is also self-evident that the inner or locking angle must be
+situated at some point on the arc _h_. To determine this location we
+draw the line _B c_ from _B_ (the pallet center) through the
+intersection of the arc _h_ with the pitch circle _a_.
+
+Again, it follows as a self-evident fact, if the pallet we are dealing
+with was locked, that is, engaged with the tooth _D''_, the inner angle
+_n_ of the exit pallet would be one and a half degrees inside the pitch
+circle _a_. With the dividers set at 5", we sweep the short arc _b b_,
+and from the intersection of this arc with the line _B c_ we lay off ten
+degrees, and through the point so established, from _B_, we draw the
+line _B d_. Below the point of intersection of the line _B d_ with the
+short arc _b b_ we lay off one and a half degrees, and through the point
+thus established we draw the line _B e_.
+
+
+LOCATING THE INNER ANGLE OF THE EXIT PALLET.
+
+The intersection of the line _B e_ with the arc _h_, which we will term
+the point _n_, represents the location of the inner angle of the exit
+pallet. We have already explained how we located the position of the
+outer angle at _o_. We draw the line _n o_ and define the impulse face
+of the exit pallet. If we mentally analyze the problem in hand, we will
+see that as the exit pallet vibrates through its ten degrees of arc the
+line _B d_ and _B c_ change places, and the tooth _D''_ locks one and a
+half degrees. To delineate the locking face of the exit pallet, we erect
+a perpendicular to the line _B e_ from the point _n_, as shown by the
+line _n p_.
+
+From _n_ as a center we sweep the short arc _t t_, and from its
+intersection with the line _n p_ we lay off twelve degrees, and through
+the point so established we draw the line _n u_, which defines the
+locking face of the exit pallet. We draw the line _o o'_ parallel with
+_n u_ and define the outer face of said pallet. In Fig. 21 we have not
+made any attempt to show the full outline of the pallets, as they are
+delineated in precisely the same manner as those previously shown.
+
+We shall next describe the delineation of a club-tooth escapement with
+pallets having equidistant locking faces; and in Fig. 22 we shall show
+pallets with much wider arms, because, in this instance, we shall derive
+more of the impulse from the pallets than from the teeth. We do this to
+show the horological student the facility with which the club-tooth
+lever escapement can be manipulated. We wish also to impress on his mind
+the facts that the employment of thick pallet arms and thin pallet arms
+depends on the teeth of the escape wheel for its efficiency, and that
+he must have knowledge enough of the principles of action to tell at a
+glance on what lines the escapement was constructed.
+
+Suppose, for illustration, we get hold of a watch which has thin pallet
+arms, or stones, if they are exposed pallets, and the escape was
+designed for pallets with thick arms. There is no sort of tinkering we
+can do to give such a watch a good motion, except to change either the
+escape wheel or the pallets. If we know enough of the lever escapement
+to set about it with skill and judgment, the matter is soon put to
+rights; but otherwise we can look and squint, open and close the
+bankings, and tinker about till doomsday, and the watch be none the
+better.
+
+
+CLUB-TOOTH LEVER WITH EQUIDISTANT LOCKING FACES.
+
+In drawing a club-tooth lever escapement with equidistant locking, we
+commence, as on former occasions, by producing the vertical line _A k_,
+Fig. 22, and establishing the center of the escape wheel at _A_, and
+with the dividers set at 5" sweep the pitch circle _a_. On each side of
+the intersection of the vertical line _A k_ with the arc _a_ we set off
+thirty degrees on said arc, and through the points so established draw
+the radial lines _A b_ and _A c_.
+
+From the intersection of the radial line _A b_ with the arc _a_ lay off
+three and a half degrees to the left of said intersection on the arc
+_a_, and through the point so established draw the radial line _A e_.
+From the intersection of the radial line _A b_ with the arc _a_ erect
+the perpendicular line _f_, and at the crossing or intersection of said
+line with the vertical line _A k_ establish the center of the pallet
+staff, as indicated by the small circle _B_. From _B_ as a center sweep
+the short arc _l_ with a 5" radius; and from the intersection of the
+radial line _A b_ with the arc _a_ continue the line _f_ until it
+crosses the short arc _l_, as shown at _f'_. Lay off one and a half
+degrees on the arc _l_ below its intersection with the line _f'_, and
+from _B_ as a center draw the line _B_ _i_ through said intersection.
+From _B_ as a center, through the intersection of the radial line _A b_
+and the arc _a_, sweep the arc _g_.
+
+The space between the lines _B f'_ and _B i_ on the arc _g_ defines the
+extent of the locking face of the entrance pallet _C_. The intersection
+of the line _B f'_ with the arc _g_ we denominate the point _o_, and
+from this point as a center sweep the short arc _p_ with a 5" radius;
+and on this arc, from its intersection with the radial line _A b_, lay
+off twelve degrees, and through the point so established, from _o_ as a
+center, draw the radial line _o m_, said line defining the locking face
+of the entrance pallet _C_.
+
+[Illustration: Fig. 22]
+
+It will be seen that this gives a positive "draw" of twelve degrees to
+the entrance pallet; that is, counting to the line _B f'_. In this
+escapement as delineated there is perfect tangential locking. If the
+locking face of the entrance-pallet stone at _C_ was made to conform to
+the radial line _A b_, the lock of the tooth _D_ at _o_ would be "dead";
+that is, absolutely neutral. The tooth _D_ would press the pallet _C_ in
+the direction of the arrow _x_, toward the center of the pallet staff
+_B_, with no tendency on the part of the pallet to turn on its axis _B_.
+Theoretically, the pallet with the locking face cut to coincide with the
+line _A b_ would resist movement on the center _B_ in either direction
+indicated by the double-headed arrow _y_.
+
+A pallet at _C_ with a circular locking face made to conform to the arc
+_g_, would permit movement in the direction of the double-headed arrow
+_y_ with only mechanical effort enough to overcome friction. But it is
+evident on inspection that a locking face on the line _A b_ would cause
+a retrograde motion of the escape wheel, and consequent resistance, if
+said pallet was moved in either direction indicated by the double-headed
+arrow _y_. Precisely the same conditions obtain at the point _u_, which
+holds the same relations to the exit pallet as the point _o_ does to the
+entrance pallet _C_.
+
+
+ANGULAR MOTION OF ESCAPE WHEEL DETERMINED.
+
+The arc (three and a half degrees) of the circle _a_ embraced between
+the radial lines _A b_ and _A e_ determines the angular motion of the
+escape wheel utilized by the escape-wheel tooth. To establish and define
+the extent of angular motion of the escape wheel utilized by the pallet,
+we lay off seven degrees on the arc _a_ from the point _o_ and establish
+the point _n_, and through the point _n_, from _B_ as a center, we sweep
+the short arc _n'_. Now somewhere on this arc _n'_ will be located the
+inner angle of the entrance pallet. With a carefully-made drawing,
+having the escape wheel 10" in diameter, it will be seen that the arc
+_a_ separates considerably from the line, _B f'_ where it crosses the
+arc _n'_.
+
+It will be remembered that when drawing the ratchet-tooth lever
+escapement a measurement of eight and a half degrees was made on the arc
+_n'_ down from its intersection with the pitch circle, and thus the
+inner angle of the pallet was located. In the present instance the
+addendum line _w_ becomes the controlling arc, and it will be further
+noticed on the large drawing that the line _B h_ at its intersection
+with the arc _n'_ approaches nearer to the arc _w_ than does the line
+_B f'_ to the pitch circle _a_; consequently, the inner angle of the pallet
+should not in this instance be carried down on the arc _n'_ so far to
+correct the error as in the ratchet tooth.
+
+Reason tells us that if we measure ten degrees down on the arc _n'_ from
+its intersection with the addendum circle _w_ we must define the
+position of the inner angle of the entrance pallet. We name the point so
+established the point _r_. The outer angle of this pallet is located at
+the intersection of the radial line _A b_ with the line _B i_; said
+intersection we name the point _v_. Draw a line from the point _v_ to
+the point _r_, and we define the impulse face of the entrance pallet;
+and the angular motion obtained from it as relates to the pallet staff
+embraces six degrees.
+
+Measured on the arc _l_, the entire ten degrees of angular motion is as
+follows: Two and a half degrees from the impulse face of the tooth, and
+indicated between the lines _B h_ and _B f_; one and a half degrees lock
+between the lines _B f'_ and _B i_; six degrees impulse from pallet
+face, entrance between the lines _B i_ and _B j_.
+
+
+A DEPARTURE FROM FORMER PRACTICES.
+
+Grossmann and Britten, in all their delineations of the club-tooth
+escapement, show the exit pallet as disengaged. To vary from this
+beaten track we will draw our exit pallet as locked. There are other
+reasons which prompt us to do this, one of which is, pupils are apt to
+fall into a rut and only learn to do things a certain way, and that way
+just as they are instructed.
+
+To illustrate, the writer has met several students of the lever
+escapement who could make drawings of either club or ratchet-tooth
+escapement with the lock on the entrance pallet; but when required to
+draw a pallet as illustrated at Fig. 23, could not do it correctly.
+Occasionally one could do it, but the instances were rare. A still
+greater poser was to request them to delineate a pallet and tooth when
+the action of escaping was one-half or one-third performed; and it is
+easy to understand that only by such studies the master workman can
+thoroughly comprehend the complications involved in the club-tooth lever
+escapement.
+
+
+AN APT ILLUSTRATION.
+
+As an illustration: Two draughtsmen, employed by two competing watch
+factories, each designs a club-tooth escapement. We will further suppose
+the trains and mainspring power used by each concern to be precisely
+alike. But in practice the escapement of the watches made by one factory
+would "set," that is, if you stopped the balance dead still, with the
+pin in the fork, the watch would not start of itself; while the
+escapement designed by the other draughtsman would not "set"--stop the
+balance dead as often as you choose, the watch would start of itself.
+Yet even to experienced workmen the escape wheels and pallets _looked_
+exactly alike. Of course, there was a difference, and still none of the
+text-books make mention of it.
+
+For the present we will go on with delineating our exit pallet. The
+preliminaries are the same as with former drawings, the instructions for
+which we need not repeat. Previous to drawing the exit pallet, let us
+reason on the matter. The point _r_ in Fig. 23 is located at the
+intersection of pitch circle _a_ and the radial line _A c_; and this
+will also be the point at which the tooth _C_ will engage the locking
+face of the exit pallet.
+
+This point likewise represents the advance angle of the engaging tooth.
+Now if we measure on the arc _k_ (which represents the locking faces of
+both pallets) downward one and a half degrees, we establish the lock of
+the pallet _E_. To get this one and a half degrees defined on the arc
+_k_, we set the dividers at 5", and from _B_ as a center sweep the
+short arc _i_, and from the intersection of the arc _i_ with the line
+_B e_ we lay off on said arc _i_ one and a half degrees, and through the
+point so established draw the line _B f_.
+
+Now the space on the arc _k_ between the lines _B e_ and _B f_ defines
+the angular extent of the locking face. With the dividers set at 5" and
+one leg resting at the point _r_, we sweep the short arc _t_, and from
+the intersection of said arc with the line _A c_ we draw the line _n p_;
+but in doing so we extend it (the line) so that it intersects the line
+_B f_, and at said intersection is located the inner angle of the exit
+pallet. This intersection we will name the point _n_.
+
+[Illustration: Fig. 23]
+
+From the intersection of the line _B e_ with the arc _i_ we lay off two
+and a half degrees on said arc, and through the point so established we
+draw the line _B g_. The intersection of this line with the arc _k_ we
+name the point _z_. With one leg of our dividers set at _A_ we sweep the
+arc _l_ so it passes through the point _z_. This last arc defines the
+addendum of the escape-wheel teeth. From the point _r_ on the arc _a_ we
+lay off three and a half degrees, and through the point so established
+draw the line _A j_.
+
+
+LOCATING THE OUTER ANGLE OF THE IMPULSE PLANES.
+
+The intersection of this line with the addendum arc _l_ locates the
+outer angle of the impulse planes of the teeth, and we name it the point
+_x_. From the point _r_ we lay off on the arc _a_ seven degrees and
+establish the point _v_, which defines the extent of the angular motion
+of the escape wheel utilized by pallet. Through the point _v_, from _B_
+as a center, we sweep the short arc _m_. It will be evident on a
+moment's reflection that this arc _m_ must represent the path of
+movement of the outer angle of the exit pallet, and if we measure down
+ten degrees from the intersection of the arc _l_ with the arc _m_, the
+point so established (which we name the point _s_) must be the exact
+position of the outer angle of the pallet during locking. We have a
+measure of ten degrees on the arc _m_, between the lines _B g_ and _B
+h_, and by taking this space in the dividers and setting one leg at the
+intersection of the arc _l_ with the arc _m_, and measuring down on _m_,
+we establish the point _s_. Drawing a line from point _n_ to point _s_
+we define the impulse face of the pallet.
+
+
+MAKING AN ESCAPEMENT MODEL.
+
+[Illustration: Fig. 24]
+
+It is next proposed we apply the theories we have been considering and
+make an enlarged model of an escapement, as shown at Figs. 24 and 25.
+This model is supposed to have an escape wheel one-fifth the size of the
+10" one we have been drawing. In the accompanying cuts are shown only
+the main plate and bridges in full lines, while the positions of the
+escape wheel and balance are indicated by the dotted circles _I B_. The
+cuts are to no precise scale, but were reduced from a full-size drawing
+for convenience in printing. We shall give exact dimensions, however, so
+there will be no difficulty in carrying out our instructions in
+construction.
+
+[Illustration: Fig. 25]
+
+Perhaps it would be as well to give a general description of the model
+before taking up the details. A reduced side view of the complete model
+is given at Fig. 26. In this cut the escapement model shown at Figs. 24
+and 25 is sketched in a rough way at _R_, while _N_ shows a glass cover,
+and _M_ a wooden base of polished oak or walnut. This base is recessed
+on the lower side to receive an eight-day spring clock movement, which
+supplies the motive power for the model. This base is recessed on top to
+receive the main plate _A_, Fig. 24, and also to hold the glass shade
+_N_ in position. The base _M_ is 21/2" high and 8" diameter. The glass
+cover _N_ can have either a high and spherical top, as shown, or, as
+most people prefer, a flattened oval.
+
+[Illustration: Fig. 26]
+
+The main plate _A_ is of hard spring brass, 1/10" thick and 6" in
+diameter; in fact, a simple disk of the size named, with slightly
+rounded edges. The top plate, shown at _C_, Figs. 24 and 25, is 1/8"
+thick and shaped as shown. This plate (_C_) is supported on two pillars
+1/2" in diameter and 11/4" high. Fig. 25 is a side view of Fig. 24 seen
+in the direction of the arrow _p_. The cock _D_ is also of 1/8" spring
+brass shaped as shown, and attached by the screw _f_ and steady pins _s s_
+to the top plate _C_. The bridge _F G_ carries the top pivots of
+escape wheel and pallet staff, and is shaped as shown at the full
+outline. This bridge is supported on two pillars 1/2" high and 1/2" in
+diameter, one of which is shown at _E_, Fig. 25, and both at the dotted
+circles _E E'_, Fig. 24.
+
+To lay out the lower plate we draw the line _a a_ so it passes through
+the center of _A_ at _m_. At 1.3" from one edge of _A_ we establish on
+the line _a_ the point _d_, which locates the center of the escape
+wheel. On the same line _a_ at 1.15" from _d_ we establish the point
+_b_, which represents the center of the pallet staff. At the distance of
+1.16" from _b_ we establish the point _c_, which represents the center
+of the balance staff. To locate the pillars _H_, which support the top
+plate _C_, we set the dividers at 2.58", and from the center _m_ sweep
+the arc _n_.
+
+From the intersection of this arc with the line _a_ (at _r_) we lay off
+on said arc _n_ 2.1" and establish the points _g g'_, which locate the
+center of the pillars _H H_. With the dividers set so one leg rests at
+the center _m_ and the other leg at the point _d_, we sweep the arc _t_.
+With the dividers set at 1.33" we establish on the arc _t_, from the
+point _d_, the points _e e'_, which locate the position of the pillars
+_E E'_. The outside diameter of the balance _B_ is 3-5/8" with the rim
+3/16" wide and 5/16" deep, with screws in the rim in imitation of the
+ordinary compensation balance.
+
+Speaking of a balance of this kind suggests to the writer the trouble he
+experienced in procuring material for a model of this kind--for the
+balance, a pattern had to be made, then a casting made, then a machinist
+turned the casting up, as it was too large for an American lathe. A
+hairspring had to be specially made, inasmuch as a mainspring was too
+short, the coils too open and, more particularly, did not look well.
+Pallet jewels had to be made, and lapidists have usually poor ideas of
+close measurements. Present-day conditions, however, will, no doubt,
+enable the workman to follow our instructions much more readily.
+
+
+MAKING THE BRIDGES.
+
+In case the reader makes the bridges _C_ and _F_, as shown in Fig. 27,
+he should locate small circles on them to indicate the position of the
+screws for securing these bridges to the pillars which support them, and
+also other small circles to indicate the position of the pivot holes _d b_
+for the escape wheel and pallet staff. In practice it will be well to
+draw the line _a a_ through the center of the main plate _A_, as
+previously directed, and also establish the point _d_ as therein
+directed.
+
+The pivot hole _d'_ for the escape wheel, and also the holes at _e e_
+and _b_, are now drilled in the bridge _F_. These holes should be about
+1/16" in diameter. The same sized hole is also drilled in the main plate
+_A_ at _d_. We now place a nicely-fitting steel pin in the hole _d'_ in
+the bridge _F_ and let it extend into the hole _d_ in the main plate. We
+clamp the bridge _F_ to _A_ so the hole _b_ comes central on the line
+_a_, and using the holes _e e_ in _F_ as guides, drill or mark the
+corresponding holes _e' e'_ and _b_ in the main plate for the pillars
+_E E'_ and the pallet staff.
+
+[Illustration: Fig. 27]
+
+This plan will insure the escape wheel and pallet staff being perfectly
+upright. The same course pursued with the plate _C_ will insure the
+balance being upright. The pillars which support the bridges are shaped
+as shown at Fig. 28, which shows a side view of one of the pillars which
+support the top plate or bridge _C_. The ends are turned to 1/4" in
+diameter and extend half through the plate, where they are held by
+screws, the same as in American movements.
+
+[Illustration: Fig. 28]
+
+The pillars (like _H_) can be riveted in the lower plate _A_, but we
+think most workmen will find it more satisfactory to employ screws, as
+shown at Fig. 29. The heads of such screws should be about 3/8" in
+diameter and nicely rounded, polished and blued. We would not advise
+jeweling the pivot holes, because there is but slight friction, except
+to the foot of the balance pivot, which should be jeweled with a
+plano-convex garnet.
+
+[Illustration: Fig. 29]
+
+IMITATION RUBIES FOR CAPPING THE TOP PIVOTS.
+
+The top pivots to the escape wheel should be capped with imitation
+rubies for appearance sake only, letting the cap settings be red gold,
+or brass red gilded. If real twelve-karat gold is employed the cost will
+not be much, as the settings are only about 3/8" across and can be
+turned very thin, so they will really contain but very little gold. The
+reason why we recommend imitation ruby cap jewels for the upper holes,
+is that such jewels are much more brilliant than any real stone we can
+get for a moderate cost. Besides, there is no wear on them.
+
+The pallet jewels are also best made of glass, as garnet or any red
+stone will look almost black in such large pieces. Red carnelian has a
+sort of brick-red color, which has a cheap appearance. There is a new
+phosphorus glass used by optical instrument makers which is intensely
+hard, and if colored ruby-red makes a beautiful pallet jewel, which will
+afford as much service as if real stones were used; they are no cheaper
+than carnelian pallets, but much richer looking. The prettiest cap for
+the balance is one of those foilback stones in imitation of a rose-cut
+diamond.
+
+[Illustration: Fig. 30]
+
+[Illustration: Fig. 31]
+
+In turning the staffs it is the best plan to use double centers, but a
+piece of Stubs steel wire that will go into a No. 40 wire chuck, will
+answer; in case such wire is used, a brass collet must be provided. This
+will be understood by inspecting Fig. 30, where _L_ represents the Stubs
+wire and _B N_ the brass collet, with the balance seat shown at _k_. The
+escape-wheel arbor and pallet staff can be made in the same way. The
+lower end of the escape wheel pivot is made about 1/4" long, so that a
+short piece of brass wire can be screwed upon it, as shown in Fig. 31,
+where _h_ represents the pivot, _A_ the lower plate, and the dotted line
+at _p_ the brass piece screwed on the end of the pivot. This piece _p_
+is simply a short bit of brass wire with a female screw tapped into the
+end, which screws on to the pivot. An arm is attached to _p_, as shown
+at _T_. The idea is, the pieces _T p_ act like a lathe dog to convey the
+power from one of the pivots of an old eight-day spring clock movement,
+which is secured by screws to the lower side of the main plate _A_. The
+plan is illustrated at Fig. 32, where _l_ represents pivot of the
+eight-day clock employed to run the model. Counting the escape-wheel
+pivot of the clock as one, we take the third pivot from this in the
+clock train, placing the movement so this point comes opposite the
+escape-wheel pivot of the model, and screw the clock movement fast to
+the lower side of the plate _A_. The parts _T_, Fig. 33, are alike on
+both pivots.
+
+[Illustration: Fig. 32]
+
+[Illustration: Fig. 33]
+
+
+PROFITABLE FOR EXPLAINING TO A CUSTOMER.
+
+To fully appreciate such a large escapement model as we have been
+describing, a person must see it with its great balance, nearly 4"
+across, flashing and sparkling in the show window in the evening, and
+the brilliant imitation ruby pallets dipping in and out of the escape
+wheel. A model of this kind is far more attractive than if the entire
+train were shown, the mystery of "What makes it go?" being one of the
+attractions. Such a model is, further, of great value in explaining to a
+customer what you mean when you say the escapement of his watch is out
+of order. Any practical workman can easily make an even $100 extra in a
+year by making use of such a model.
+
+For explaining to customers an extra balance cock can be used to show
+how the jewels (hole and cap) are arranged. Where the parts are as large
+as they are in the model, the customer can see and understand for
+himself what is necessary to be done.
+
+It is not to be understood that our advice to purchase the jewels for an
+extra balance cock conflicts with our recommending the reader not to
+jewel the holes of his model. The extra cock is to be shown, not for
+use, and is employed solely for explaining to a customer what is
+required when a pivot or jewel is found to be broken.
+
+
+HOW LARGE SCREWS ARE MADE.
+
+The screws which hold the plates in place should have heads about 3/8"
+in diameter, to be in proportion to the scale on which the balance and
+escape wheel are gotten up. There is much in the manner in which the
+screw heads are finished as regards the elegance of such a model. A
+perfectly flat head, no matter how highly polished, does not look well,
+neither does a flattened conehead, like Fig. 35. The best head for this
+purpose is a cupped head with chamfered edges, as shown at Fig. 34 in
+vertical section. The center _b_ is ground and polished into a perfect
+concave by means of a metal ball. The face, between the lines _a a_, is
+polished dead flat, and the chamfered edge _a c_ finished a trifle
+convex. The flat surface at _a_ is bright, but the concave _b_ and
+chamfer at _c_ are beautifully blued. For a gilt-edged, double extra
+head, the chamfer at _c_ can be "snailed," that is, ground with a
+suitable lap before bluing, like the stem-wind wheels on some watches.
+
+[Illustration: Fig. 34]
+
+[Illustration: Fig. 35]
+
+
+FANCY SCREWHEADS.
+
+There are two easy methods of removing the blue from the flat part of
+the screwhead at _a_. (1) Make a special holder for the screw in the end
+of a cement brass, as shown at _E_, Fig. 36, and while it is slowly
+revolving in the lathe touch the flat surface _a_ with a sharpened
+pegwood wet with muriatic acid, which dissolves the blue coating of
+oxide of iron. (2) The surface of the screwhead is coated with a very
+thin coating of shellac dissolved in alcohol and thoroughly dried, or a
+thin coating of collodion, which is also dried. The screw is placed in
+the ordinary polishing triangle and the flat face at _a_ polished on a
+tin lap with diamantine and oil. In polishing such surfaces the thinnest
+possible coating of diamantine and oil is smeared on the lap--in fact,
+only enough to dim the surface of the tin. It is, of course, understood
+that it is necessary to move only next to nothing of the material to
+restore the polish of the steel. The polishing of the other steel parts
+is done precisely like any other steel work.
+
+[Illustration: Fig. 36]
+
+The regulator is of the Howard pattern. The hairspring stud is set in
+the cock like the Elgin three-quarter-plate movement. The richest finish
+for such a model is frosted plates and bridges. The frosting should not
+be a fine mat, like a watch movement, but coarse-grained--in fact, the
+grain of the frosting should be proportionate to the size of the
+movement. The edges of the bridges and balance cock can be left smooth.
+The best process for frosting is by acid. Details for doing the work
+will now be given.
+
+[Illustration: Fig. 37]
+
+[Illustration: Fig. 38]
+
+To do this frosting by acid nicely, make a sieve by tacking and gluing
+four pieces of thin wood together, to make a rectangular box without a
+bottom. Four pieces of cigar-box wood, 8" long by 11/2" wide, answer
+first rate. We show at _A A A A_, Fig. 37, such a box as if seen from
+above; with a side view, as if seen in the direction of the arrow _a_,
+at Fig. 38. A piece of India muslin is glued across the bottom, as shown
+at the dotted lines _b b_. By turning up the edges on the outside of the
+box, the muslin bottom can be drawn as tight as a drum head.
+
+
+HOW TO DO ACID FROSTING.
+
+To do acid frosting, we procure two ounces of gum mastic and place in
+the square sieve, shown at Fig. 37. Usually more than half the weight of
+gum mastic is in fine dust, and if not, that is, if the gum is in the
+shape of small round pellets called "mastic tears," crush these into
+dust and place the dust in _A_. Let us next suppose we wish to frost
+the cock on the balance, shown at Fig. 39. Before we commence to frost,
+the cock should be perfectly finished, with all the holes made, the
+regulator cap in position, the screw hole made for the Howard regulator
+and the index arc engraved with the letters S and F.
+
+[Illustration: Fig. 39]
+
+It is not necessary the brass should be polished, but every file mark
+and scratch should be stoned out with a Scotch stone; in fact, be in the
+condition known as "in the gray." It is not necessary to frost any
+portion of the cock _C_, except the upper surface. To protect the
+portion of the cock not to be frosted, like the edges and the back, we
+"stop out" by painting over with shellac dissolved in alcohol, to which
+a little lampblack is added. It is not necessary the coating of shellac
+should be very thick, but it is important it should be well dried.
+
+
+HOW TO PREPARE THE SURFACE.
+
+For illustration, let us suppose the back and edges of the cock at Fig.
+39 are coated with shellac and it is laid flat on a piece of paper about
+a foot square to catch the excess of mastic. Holes should be made in
+this paper and also in the board on which the paper rests to receive the
+steady pins of the cock. We hold the sieve containing the mastic over
+the cock and, gently tapping the box _A_ with a piece of wood like a
+medium-sized file handle, shake down a little snowstorm of mastic dust
+over the face of the cock _C_.
+
+Exactly how much mastic dust is required to produce a nice frosting is
+only to be determined by practice. The way to obtain the knack is to
+frost a few scraps to "get your hand in." Nitric acid of full strength
+is used, dipping the piece into a shallow dish for a few seconds. A
+good-sized soup plate would answer very nicely for frosting the bottom
+plate, which, it will be remembered, is 6" in diameter.
+
+
+HOW TO ETCH THE SURFACE.
+
+After the mastic is sifted on, the cock should be heated up to about
+250 deg. F., to cause the particles of mastic to adhere to the surface. The
+philosophy of the process is, the nitric acid eats or dissolves the
+brass, leaving a little brass island the size of the particle of mastic
+which was attached to the surface. After heating to attach the particles
+of mastic, the dipping in nitric acid is done as just described. Common
+commercial nitric acid is used, it not being necessary to employ
+chemically pure acid. For that matter, for such purposes the commercial
+acid is the best.
+
+After the acid has acted for fifteen or twenty seconds the brass is
+rinsed in pure water to remove the acid, and dried by patting with an
+old soft towel, and further dried by waving through the air. A little
+turpentine on a rag will remove the mastic, but turpentine will not
+touch the shellac coating. The surface of the brass will be found
+irregularly acted upon, producing a sort of mottled look. To obtain a
+nice frosting the process of applying the mastic and etching must be
+repeated three or four times, when a beautiful coarse-grain mat or
+frosting will be produced.
+
+The shellac protection will not need much patching up during the three
+or four bitings of acid, as the turpentine used to wash off the mastic
+does not much affect the shellac coating. All the screw holes like _s s_
+and _d_, also the steady pins on the back, are protected by varnishing
+with shellac. The edges of the cocks and bridges should be polished by
+rubbing lengthwise with willow charcoal or a bit of chamois skin
+saturated with oil and a little hard rouge scattered upon it. The
+frosting needs thorough scratch-brushing.
+
+[Illustration: Fig. 40]
+
+At Fig. 40 we show the balance cock of our model with modified form of
+Howard regulator. The regulator bar _A_ and spring _B_ should be ground
+smooth on one side and deeply outlined to perfect form. The regulator
+cap _C_ is cut out to the correct size. These parts are of decarbonized
+cast steel, annealed until almost as soft as sheet brass. It is not so
+much work to finish these parts as one might imagine. Let us take the
+regulator bar for an example and carry it through the process of making.
+The strip of soft sheet steel on which the regulator bar is outlined is
+represented by the dotted outline _b_, Fig. 41.
+
+[Illustration: Fig. 41]
+
+To cut out sheet steel rapidly we take a piece of smooth clock
+mainspring about 3/4" and 10" long and double it together, softening the
+bending point with the lamp until the piece of mainspring assumes the
+form shown at Fig. 42, where _c_ represents the piece of spring and
+_H H_ the bench-vise jaws. The piece of soft steel is placed between the
+limbs of _c c'_ of the old mainspring up to the line _a_, Fig. 41, and
+clamped in the vise jaws. The superfluous steel is cut away with a sharp
+and rather thin cold chisel.
+
+[Illustration: Fig. 42]
+
+The chisel is presented as shown at _G_, Fig. 43 (which is an end view
+of the vise jaws _H H_ and regulator bar), and held to cut obliquely and
+with a sort of shearing action, as illustrated in Fig. 42, where _A''_
+represents the soft steel and _G_ the cold chisel. We might add that
+Fig. 42 is a view of Fig. 43 seen in the direction of the arrow _f_. It
+is well to cut in from the edge _b_ on the line _d_, Fig. 41, with a
+saw, in order to readily break out the surplus steel and not bend the
+regulator bar. By setting the pieces of steel obliquely in the vise, or
+so the line _e_ comes even with the vise jaws, we can cut to more nearly
+conform to the circular loop _A''_ of the regulator _A_.
+
+[Illustration: Fig. 43]
+
+The smooth steel surface of the bent mainspring _c_ prevents the vise
+jaws from marking the soft steel of the regulator bar. A person who has
+not tried this method of cutting out soft steel would not believe with
+what facility pieces can be shaped. Any workman who has a universal face
+plate to his lathe can turn out the center of the regulator bar to
+receive the disk _C_, and also turn out the center of the regulator
+spring _B_. What we have said about the regulator bar applies also to
+the regulator spring _B_. This spring is attached to the cock _D_ by
+means of two small screws at _n_.
+
+The micrometer screw _F_ is tapped through _B''_ as in the ordinary
+Howard regulator, and the screw should be about No. 6 of a Swiss
+screw-plate. The wire from which such screw is made should be 1/10" in
+diameter. The steel cap _C_ is fitted like the finer forms of Swiss
+watches. The hairspring stud _E_ is of steel, shaped as shown, and comes
+outlined with the other parts.
+
+
+TO TEMPER AND POLISH STEEL.
+
+The regulator bar should be hardened by being placed in a folded piece
+of sheet iron and heated red hot, and thrown into cold water. The
+regulator bar _A A'_ is about 3" long; and for holding it for
+hardening, cut a piece of thin sheet iron 21/2" by 31/4" and fold it
+through the middle lengthwise, as indicated by the dotted line _g_, Fig.
+44. The sheet iron when folded will appear as shown at Fig. 45. A piece
+of flat sheet metal of the same thickness as the regulator bar should be
+placed between the iron leaves _I I_, and the leaves beaten down with a
+hammer, that the iron may serve as a support for the regulator during
+heating and hardening. A paste made of castile soap and water applied to
+the regulator bar in the iron envelope will protect it from oxidizing
+much during the heating. The portions of the regulator bar marked _h_
+are intended to be rounded, while the parts marked _m_ are intended to
+be dead flat. The rounding is carefully done, first with a file and
+finished with emery paper. The outer edge of the loop _A''_ is a little
+rounded, also the inner edge next the cap _C_. This will be understood
+by inspecting Fig. 46, where we show a magnified vertical section of the
+regulator on line _l_, Fig. 40. The curvature should embrace that
+portion of _A''_ between the radial lines _o o'_, and should, on the
+model, not measure more than 1/40". It will be seen that the curved
+surface of the regulator is sunk so it meets only the vertical edge of
+the loop _A''_. For the average workman, polishing the flat parts _m_ is
+the most difficult to do, and for this reason we will give entire
+details. It is to be expected that the regulator bar will spring a
+little in hardening, but if only a little we need pay no attention to
+it.
+
+[Illustration: Fig. 44]
+
+[Illustration: Fig. 45]
+
+[Illustration: Fig. 46]
+
+
+HOW FLAT STEEL POLISHING IS DONE.
+
+Polishing a regulator bar for a large model, such as we are building, is
+only a heavy job of flat steel work, a little larger but no more
+difficult than to polish a regulator for a sixteen-size watch. We would
+ask permission here to say that really nice flat steel work is something
+which only a comparatively few workmen can do, and, still, the process
+is quite simple and the accessories few and inexpensive. First,
+ground-glass slab 6" by 6" by 1/4"; second, flat zinc piece 31/4" by
+31/4" by 1/4"; third, a piece of thick sheet brass 3" by 2" by 1/8";
+and a bottle of Vienna lime. The glass slab is only a piece of plate
+glass cut to the size given above. The zinc slab is pure zinc planed
+dead flat, and the glass ground to a dead surface with another piece of
+plate glass and some medium fine emery and water, the whole surface
+being gone over with emery and water until completely depolished. The
+regulator bar, after careful filing and dressing up on the edges with an
+oilstone slip or a narrow emery buff, is finished as previously
+described. We would add to the details already given a few words on
+polishing the edges.
+
+[Illustration: Fig. 47]
+
+It is not necessary that the edges of steelwork, like the regulator bar
+_B_, Fig. 47, should be polished to a flat surface; indeed, they look
+better to be nicely rounded. Perhaps we can convey the idea better by
+referring to certain parts: say, spring to the regulator, shown at _D_,
+Fig. 40, and also the hairspring stud _E_. The edges of these parts look
+best beveled in a rounded manner.
+
+[Illustration: Fig. 48]
+
+[Illustration: Fig. 49]
+
+It is a little difficult to convey in words what is meant by "rounded"
+manner. To aid in understanding our meaning, we refer to Figs. 48 and
+49, which are transverse sections of _D_, Fig. 50, on the line _f_. The
+edges of _D_, in Fig. 48, are simply rounded. There are no rules for
+such rounding--only good judgment and an eye for what looks well. The
+edges of _D_ as shown in Fig. 49 are more on the beveled order. In
+smoothing and polishing such edges, an ordinary jeweler's steel burnish
+can be used.
+
+[Illustration: Fig. 50]
+
+
+SMOOTHING AND POLISHING.
+
+The idea in smoothing and polishing such edges is to get a fair gloss
+without much attention to perfect form, inasmuch as it is the flat
+surface _d_ on top which produces the impression of fine finish. If this
+is flat and brilliant, the rounded edges, like _g c_ can really have
+quite an inferior polish and still look well. For producing the flat
+polish on the upper surface of the regulator bar _B_ and spring _D_, the
+flat surface _d_, Figs. 48, 49, 51 and 52, we must attach the regulator
+bar to a plate of heavy brass, as shown at Fig. 47, where _A_ represents
+the brass plate, and _B_ the regulator bar, arranged for grinding and
+polishing flat.
+
+[Illustration: Fig. 51]
+
+[Illustration: Fig. 52]
+
+For attaching the regulator bar _B_ to the brass plate _A_, a good plan
+is to cement it fast with lathe wax; but a better plan is to make the
+plate _A_ of heavy sheet iron, something about 1/8" thick, and secure
+the two together with three or four little catches of soft solder. It is
+to be understood the edges of the regulator bar or the regulator spring
+are polished, and all that remains to be done is to grind and polish the
+flat face.
+
+Two pieces _a a_ of the same thickness as the regulator bar are placed
+as shown and attached to _A_ to prevent rocking. After _B_ is securely
+attached to _A_, the regulator should be coated with shellac dissolved
+in alcohol and well dried. The object of this shellac coating is to keep
+the angles formed at the meeting of the face and side clean in the
+process of grinding with oilstone dust and oil. The face of the
+regulator is now placed on the ground glass after smearing it with oil
+and oilstone dust. It requires but a very slight coating to do the work.
+
+The grinding is continued until the required surface is dead flat, after
+which the work is washed with soap and water and the shellac dissolved
+away with alcohol. The final polish is obtained on the zinc lap with
+Vienna lime and alcohol. Where lathe cement is used for securing the
+regulator to the plate _A_, the alcohol used with the Vienna lime
+dissolves the cement and smears the steel. Diamantine and oil are the
+best materials for polishing when the regulator bar is cemented to the
+plate _A_.
+
+
+KNOWLEDGE THAT IS MOST ESSENTIAL.
+
+_The knowledge most important for a practical working watchmaker to
+possess is how to get the watches he has to repair in a shape to give
+satisfaction to his customers._ No one will dispute the truth of the
+above italicised statement. It is only when we seek to have limits set,
+and define what such knowledge should consist of, that disagreement
+occurs.
+
+One workman who has read Grossmann or Saunier, or both, would insist on
+all watches being made to a certain standard, and, according to their
+ideas, all such lever watches as we are now dealing with should have
+club-tooth escapements with equidistant lockings, ten degrees lever and
+pallet action, with one and one-half degrees lock and one and one-half
+degrees drop. Another workman would insist on circular pallets, his
+judgment being based chiefly on what he had read as stated by some
+author. Now the facts of the situation are that lever escapements vary
+as made by different manufacturers, one concern using circular pallets
+and another using pallets with equidistant lockings.
+
+WHAT A WORKMAN SHOULD KNOW TO REPAIR A WATCH.
+
+One escapement maker will divide the impulse equally between the tooth
+and pallet; another will give an excess to the tooth. Now while these
+matters demand our attention in the highest degree in a theoretical
+sense, still, for such "know hows" as count in a workshop, they are of
+but trivial importance in practice.
+
+We propose to deal in detail with the theoretical consideration of
+"thick" and "thin" pallets, and dwell exhaustively on circular pallets
+and those with equidistant locking faces; but before we do so we wish to
+impress on our readers the importance of being able to free themselves
+of the idea that all lever escapements should conform to the rigid rules
+of any dictum.
+
+
+EDUCATE THE EYE TO JUDGE OF ANGULAR AS WELL AS LINEAR EXTENT.
+
+For illustration: It would be easy to design a lever escapement that
+would have locking faces which were based on the idea of employing
+neither system, but a compromise between the two, and still give a good,
+sound action. All workmen should learn to estimate accurately the extent
+of angular motion, so as to be able to judge correctly of escapement
+actions. It is not only necessary to know that a club-tooth escapement
+should have one and one-half degrees drop, but the eye should be
+educated, so to speak, as to be able to judge of angular as well as
+linear extent.
+
+[Illustration: Fig. 53]
+
+Most mechanics will estimate the size of any object measured in inches
+or parts of inches very closely; but as regards angular extent, except
+in a few instances, we will find mechanics but indifferent judges. To
+illustrate, let us refer to Fig. 53. Here we have the base line _A A'_
+and the perpendicular line _a B_. Now almost any person would be able to
+see if the angle _A a B_ was equal to _B a A'_; but not five in one
+hundred practical mechanics would be able to estimate with even
+tolerable accuracy the measure the angles made to the base by the lines
+_b c d_; and still watchmakers are required in the daily practice of
+their craft to work to angular motions and movements almost as important
+as to results as diameters.
+
+What is the use of our knowing that in theory an escape-wheel tooth
+should have one and one-half degrees drop, when in reality it has three
+degrees? It is only by educating the eye from carefully-made drawings;
+or, what is better, constructing a model on a large scale, that we can
+learn to judge of proper proportion and relation of parts, especially as
+we have no convenient tool for measuring the angular motion of the fork
+or escape wheel. Nor is it important that we should have, if the workman
+is thoroughly "booked up" in the principles involved.
+
+As we explained early in this treatise, there is no imperative necessity
+compelling us to have the pallets and fork move through ten degrees any
+more than nine and one-half degrees, except that experience has proven
+that ten degrees is about the right thing for good results. In this day,
+when such a large percentage of lever escapements have exposed pallets,
+we can very readily manipulate the pallets to match the fork and roller
+action. For that matter, in many instances, with a faulty lever
+escapement, the best way to go about putting it to rights is to first
+set the fork and roller so they act correctly, and then bring the
+pallets to conform to the angular motion of the fork so adjusted.
+
+
+FORK AND ROLLER ACTION.
+
+Although we could say a good deal more about pallets and pallet action,
+still we think it advisable to drop for the present this particular part
+of the lever escapement and take up fork and roller action, because, as
+we have stated, frequently the fork and roller are principally at fault.
+In considering the action and relation of the parts of the fork and
+roller, we will first define what is considered necessary to constitute
+a good, sound construction where the fork vibrates through ten degrees
+of angular motion and is supposed to be engaged with the roller by means
+of the jewel pin for thirty degrees of angular motion of the balance.
+
+There is no special reason why thirty degrees of roller action should be
+employed, except that experience in practical construction has come to
+admit this as about the right arc for watches of ordinary good, sound
+construction. Manufacturers have made departures from this standard, but
+in almost every instance have finally come back to pretty near these
+proportions. In deciding on the length of fork and size of roller, we
+first decide on the distance apart at which to place the center of the
+balance and the center of the pallet staff. These two points
+established, we have the length of the fork and diameter of the roller
+defined at once.
+
+
+HOW TO FIND THE ROLLER DIAMETER FROM THE LENGTH OF THE FORK.
+
+To illustrate, let us imagine the small circles _A B_, Fig. 54, to
+represent the center of a pallet staff and balance staff in the order
+named. We divide this space into four equal parts, as shown, and the
+third space will represent the point at which the pitch circles of the
+fork and roller will intersect, as shown by the arc _a_ and circle _b_.
+Now if the length of the radii of these circles stand to each other as
+three to one, and the fork vibrates through an arc of ten degrees, the
+jewel pin engaging such fork must remain in contact with said fork for
+thirty degrees of angular motion of the balance.
+
+[Illustration: Fig. 54]
+
+Or, in other words, the ratio of angular motion of two _mobiles_ acting
+on each must be in the same ratio as the length of their radii at the
+point of contact. If we desire to give the jewel pin, or, in ordinary
+horological phraseology, have a greater arc of roller action, we would
+extend the length of fork (say) to the point _c_, which would be
+one-fifth of the space between _A_ and _B_, and the ratio of fork to
+roller action would be four to one, and ten degrees of fork action would
+give forty degrees of angular motion to the roller--and such escapements
+have been constructed.
+
+
+WHY THIRTY DEGREES OF ROLLER ACTION IS ABOUT RIGHT.
+
+Now we have two sound reasons why we should not extend the arc of
+vibration of the balance: (_a_) If there is an advantage to be derived
+from a detached escapement, it would surely be policy to have the arc of
+contact, that is, for the jewel pin to engage the fork, as short an arc
+as is compatible with a sound action. (_b_) It will be evident to any
+thinking mechanic that the acting force of a fork which would carry the
+jewel pin against the force exerted by the balance spring through an arc
+of fifteen degrees, or half of an arc of thirty degrees, would fail to
+do so through an arc of twenty degrees, which is the condition imposed
+when we adopt forty degrees of roller action.
+
+For the present we will accept thirty degrees of roller action as the
+standard. Before we proceed to delineate our fork and roller we will
+devote a brief consideration to the size and shape of a jewel pin to
+perform well. In this matter there has been a broad field gone over,
+both theoretically and in practical construction. Wide jewel pins, round
+jewel pins, oval jewel pins have been employed, but practical
+construction has now pretty well settled on a round jewel pin with about
+two-fifths cut away. And as regards size, if we adopt the linear extent
+of four degrees of fork or twelve degrees of roller action, we will find
+it about right.
+
+
+HOW TO SET A FORK AND ROLLER ACTION RIGHT.
+
+As previously stated, frequently the true place to begin to set a lever
+escapement right is with the roller and fork. But to do this properly we
+should know when such fork and roller action is right and safe in all
+respects. We will see on analysis of the actions involved that there are
+three important actions in the fork and roller functions: (_a_) The fork
+imparting perfect impulse through the jewel pin to the balance. (_b_)
+Proper unlocking action. (_c_) Safety action. The last function is in
+most instances sadly neglected and, we regret to add, by a large
+majority of even practical workmen it is very imperfectly understood. In
+most American watches we have ample opportunity afforded to inspect the
+pallet action, but the fork and roller action is placed so that rigid
+inspection is next to impossible.
+
+The Vacheron concern of Swiss manufacturers were acute enough to see the
+importance of such inspection, and proceeded to cut a circular opening
+in the lower plate, which permitted, on the removal of the dial, a
+careful scrutiny of the action of the roller and fork. While writing on
+this topic we would suggest the importance not only of knowing how to
+draw a correct fork and roller action, but letting the workman who
+desires to be _au fait_ in escapements delineate and study the action of
+a faulty fork and roller action--say one in which the fork, although of
+the proper form, is too short, or what at first glance would appear to
+amount to the same thing, a roller too small.
+
+Drawings help wonderfully in reasoning out not only correct actions, but
+also faulty ones, and our readers are earnestly advised to make such
+faulty drawings in several stages of action. By this course they will
+educate the eye to discriminate not only as to correct actions, but also
+to detect those which are imperfect, and we believe most watchmakers
+will admit that in many instances it takes much longer to locate a fault
+than to remedy it after it has been found.
+
+[Illustration: Fig. 55]
+
+Let us now proceed to delineate a fork and roller. It is not imperative
+that we should draw the parts to any scale, but it is a rule among
+English makers to let the distance between the center of the pallet
+staff and the center of the balance staff equal in length the chord of
+ninety-six degrees of the pitch circle of the escape wheel, which, in
+case we employ a pitch circle of 5" radius, would make the distance
+between _A_ and _B_, Fig. 55, approximately 71/2", which is a very fair
+scale for study drawings.
+
+
+HOW TO DELINEATE A FORK AND ROLLER.
+
+To arrive at the proper proportions of the several parts, we divide the
+space _A B_ into four equal parts, as previously directed, and draw the
+circle _a_ and short arc _b_. With our dividers set at 5", from _B_ as a
+center we sweep the short arc _c_. From our arc of sixty degrees, with a
+5" radius, we take five degrees, and from the intersection of the right
+line _A B_ with the arc _c_ we lay off on each side five degrees and
+establish the points _d e_; and from _B_ as a center, through these
+points draw the lines _B d'_ and _B e'_. Now the arc embraced between
+these lines represents the angular extent of our fork action.
+
+From _A_ as a center and with our dividers set at 5", we sweep the arc
+_f_. From the scale of degrees we just used we lay off fifteen degrees
+on each side of the line _A B_ on the arc _f_, and establish the points
+_g h_. From _A_ as a center, through the points just established we draw
+the radial lines _A g'_ and _A h'_. The angular extent between these
+lines defines the limit of our roller action.
+
+Now if we lay off on the arc _f_ six degrees each side of its
+intersection with the line _A B_, we define the extent of the jewel pin;
+that is, on the arc _f_ we establish the points _l m_ at six degrees
+from the line _A B_, and through the points _l m_ draw, from _A_ as a
+center, the radial lines _A l'_ and _A m'_. The extent of the space
+between the lines _A l'_ and _A m'_ on the circle _a_ defines the size
+of our jewel pin.
+
+
+TO DETERMINE THE SIZE OF A JEWEL PIN.
+
+[Illustration: Fig. 56]
+
+To make the situation better understood, we make an enlarged drawing of
+the lines defining the jewel pin at Fig. 56. At the intersection of the
+line _A B_ with the arc _a_ we locate the point _k_, and from it as a
+center we sweep the circle _i_ so it passes through the intersection of
+the lines _A l'_ and _A m'_ with the arc _a_. We divide the radius of
+the circle _i_ on the line _A B_ into five equal parts, as shown by the
+vertical lines _j_. Of these five spaces we assume three as the extent
+of the jewel pin, cutting away that portion to the right of the heavy
+vertical line at _k_.
+
+[Illustration: Fig. 57]
+
+We will now proceed to delineate a fork and roller as the parts are
+related on first contact of jewel pin with fork and initial with the
+commencing of the act of unlocking a pallet. The position and relations
+are also the same as at the close of the act of impulse. We commence the
+drawing at Fig. 57, as before, by drawing the line _A B_ and the arcs
+_a_ and _b_ to represent the pitch circles. We also sweep the arc _f_ to
+enable us to delineate the line _A g'_. Next in order we draw our jewel
+pin as shown at _D_. In drawing the jewel pin we proceed as at Fig. 56,
+except we let the line _A g'_, Fig. 57, assume the same relations to the
+jewel pin as _A B_ in Fig. 56; that is, we delineate the jewel pin as if
+extending on the arc _a_ six degrees on each side of the line _A g'_,
+Fig. 57.
+
+
+THE THEORY OF THE FORK ACTION.
+
+To aid us in reasoning, we establish the point _m_, as in Fig. 55, at
+_m_, Fig. 57, and proceed to delineate another and imaginary jewel pin
+at _D'_ (as we show in dotted outline). A brief reasoning will show that
+in allowing thirty degrees of contact of the fork with the jewel pin,
+the center of the jewel pin will pass through an arc of thirty degrees,
+as shown on the arcs _a_ and _f_. Now here is an excellent opportunity
+to impress on our minds the true value of angular motion, inasmuch as
+thirty degrees on the arc _f_ is of more than twice the linear extent as
+on the arc _a_.
+
+Before we commence to draw the horn of the fork engaging the jewel pin
+_D_, shown at full line in Fig. 57, we will come to perfectly understand
+what mechanical relations are required. As previously stated, we assume
+the jewel pin, as shown at _D_, Fig. 57, is in the act of encountering
+the inner face of the horn of the fork for the end or purpose of
+unlocking the engaged pallet. Now if the inner face of the horn of the
+fork was on a radial line, such radial line would be _p B_, Fig. 57. We
+repeat this line at _p_, Fig. 56, where the parts are drawn on a larger
+scale.
+
+To delineate a fork at the instant the last effort of impulse has been
+imparted to the jewel pin, and said jewel pin is in the act of
+separating from the inner face of the prong of the fork--we would also
+call attention to the fact that relations of parts are precisely the
+same as if the jewel pin had just returned from an excursion of
+vibration and was in the act of encountering the inner face of the prong
+of the fork in the act of unlocking the escapement.
+
+We mentioned this matter previously, but venture on the repetition to
+make everything clear and easily understood. We commence by drawing the
+line _A B_ and dividing it in four equal parts, as on previous
+occasions, and from _A_ and _B_ as centers draw the pitch circles _c d_.
+By methods previously described, we draw the lines _A a_ and _A a'_,
+also _B b_ and _B b'_ to represent the angular motion of the two
+mobiles, viz., fork and roller action. As already shown, the roller
+occupies twelve degrees of angular extent. To get at this conveniently,
+we lay off on the arc by which we located the lines _A a_ and _A a'_ six
+degrees above the line _A a_ and draw the line _A h_.
+
+Now the angular extent on the arc _c_ between the lines _A a_ and _A h_
+represents the radius of the circle defining the jewel pin. From the
+intersection of the line _A a_ with the arc _c_ as a center, and with
+the radius just named, we sweep the small circle _D_, Fig. 58, which
+represents our jewel pin; we afterward cut away two-fifths and draw the
+full line _D_, as shown. We show at Fig. 59 a portion of Fig. 58,
+enlarged four times, to show certain portions of our delineations more
+distinctly. If we give the subject a moment's consideration we will see
+that the length of the prong _E_ of the lever fork is limited to such a
+length as will allow the jewel pin _D_ to pass it.
+
+
+HOW TO DELINEATE THE PRONGS OF A LEVER FORK.
+
+[Illustration: Fig. 58]
+
+[Illustration: Fig. 59]
+
+To delineate this length, from _B_ as a center we sweep the short arc
+_f_ so it passes through the outer angle _n_, Fig. 59, of the jewel pin.
+This arc, carried across the jewel pin _D_, limits the length of the
+opposite prong of the fork. The outer face of the prong of the fork can
+be drawn as a line tangent to a circle drawn from _A_ as a center
+through the angle _n_ of the jewel pin. Such a circle or arc is shown at
+_o_, Figs. 58 and 59. There has been a good deal said as to whether the
+outer edge of the prong of a fork should be straight or curved.
+
+To the writer's mind, a straight-faced prong, like from _s_ to _m_, is
+what is required for a fork with a single roller, while a fork with a
+curved prong will be best adapted for a double roller. This subject will
+be taken up again when we consider double-roller action. The extent or
+length of the outer face of the prong is also an open subject, but as
+there is but one factor of the problem of lever escapement construction
+depending on it, when we name this and see this requirement satisfied we
+have made an end of this question. The function performed by the outer
+face of the prong of a fork is to prevent the engaged pallet from
+unlocking while the guard pin is opposite to the passing hollow.
+
+The inner angle _s_ of the horn of the fork must be so shaped and
+located that the jewel pin will just clear it as it passes out of the
+fork, or when it passes into the fork in the act of unlocking the
+escapement. In escapements with solid bankings a trifle is allowed, that
+is, the fork is made enough shorter than the absolute theoretical length
+to allow for safety in this respect.
+
+
+THE PROPER LENGTH OF A LEVER.
+
+We will now see how long a lever must be to perform its functions
+perfectly. Now let us determine at what point on the inner face of the
+prong _E'_ the jewel pin parts from the fork, or engages on its return.
+To do this we draw a line from the center _r_ (Fig. 59) of the jewel
+pin, so as to meet the line _e_ at right angles, and the point _t_ so
+established on the line _e_ is where contact will take place between the
+jewel pin and fork.
+
+It will be seen this point (_t_) of contact is some distance back of the
+angle _u_ which terminates the inner face of the prong _E'_;
+consequently, it will be seen the prongs _E E'_ of the fork can with
+safety be shortened enough to afford a safe ingress or egress to the
+jewel pin to the slot in the fork. As regards the length of the outer
+face of the prong of the fork, a good rule is to make it one and a half
+times the diameter of the jewel pin. The depth of the slot need be no
+more than to free the jewel in its passage across the ten degrees of
+fork action. A convenient rule as to the depth of the slot in a fork is
+to draw the line _k_, which, it will be seen, coincides with the circle
+which defines the jewel pin.
+
+
+HOW TO DELINEATE THE SAFETY ACTION.
+
+[Illustration: Fig. 60]
+
+We will next consider a safety action of the single roller type. The
+active or necessary parts of such safety action consist of a roller or
+disk of metal, usually steel, shaped as shown in plan at _A_, Fig. 60.
+In the edge of this disk is cut in front of the jewel pin a circular
+recess shown at _a_ called the passing hollow. The remaining part of the
+safety action is the guard pin shown at _N_ Figs. 61 and 62, which is
+placed in the lever. Now it is to be understood that the sole function
+performed by the guard pin is to strike the edge of the roller _A_ at
+any time when the fork starts to unlock the engaged pallet, except when
+the jewel pin is in the slot of the fork. To avoid extreme care in
+fitting up the passing hollow, the horns of the fork are arranged to
+strike the jewel pin and prevent unlocking in case the passing hollow is
+made too wide. To delineate the safety action we first draw the fork and
+jewel pin as previously directed and as shown at Fig. 63. The position
+of the guard pin should be as close to the bottom of the slot of the
+fork as possible and be safe. As to the size of the guard pin, it is
+usual to make it about one-third or half the diameter of the jewel pin.
+The size and position of the guard pin decided on and the small circle
+_N_ drawn, to define the size and position of the roller we set our
+dividers so that a circle drawn from the center _A_ will just touch the
+edge of the small circle _N_, and thus define the outer boundary of our
+roller, or roller table, as it is frequently called.
+
+[Illustration: Fig. 61]
+
+[Illustration: Fig. 62]
+
+For deciding the angular extent of the passing hollow we have no fixed
+rule, but if we make it to occupy about half more angular extent on the
+circle _y_ than will coincide with the angular extent of the jewel pin,
+it will be perfectly safe and effectual. We previously stated that the
+jewel pin should occupy about twelve degrees of angular extent on the
+circle _c_, and if we make the passing hollow occupy eighteen degrees
+(which is one and a half the angular extent of the jewel pin) it will do
+nicely. But if we should extend the width of the passing hollow to
+twenty-four degrees it would do no harm, as the jewel pin would be well
+inside the horn of the fork before the guard pin could enter the passing
+hollow.
+
+[Illustration: Fig. 63]
+
+We show in Fig. 61 the fork as separated from the roller, but in Fig.
+62, which is a side view, we show the fork and jewel pin as engaged.
+When drawing a fork and roller action it is safe to show the guard pin
+as if in actual contact with the roller. Then in actual construction, if
+the parts are made to measure and agree with the drawing in the gray,
+that is, before polishing, the process of polishing will reduce the
+convex edge of the roller enough to free it.
+
+It is evident if thought is given to the matter, that if the guard pin
+is entirely free and does not touch the roller in any position, a
+condition and relation of parts exist which is all we can desire. We are
+aware that it is usual to give a considerable latitude in this respect
+even by makers, and allow a good bit of side shake to the lever, but our
+judgment would condemn the practice, especially in high-grade watches.
+
+
+RESTRICT THE FRICTIONAL SURFACES.
+
+Grossmann, in his essay on the detached lever escapement, adopts one and
+a half degrees lock. Now, we think that one degree is ample; and we are
+sure that every workman experienced in the construction of the finer
+watches will agree with us in the assertion that we should in all
+instances seek to reduce the extent of all frictional surfaces, no
+matter how well jeweled. Acting under such advice, if we can reduce the
+surface friction on the lock from one and a half degrees to one degree
+or, better, to three-fourths of a degree, it is surely wise policy to do
+so. And as regards the extent of angular motion of the lever, if we
+reduce this to six degrees, exclusive of the lock, we would undoubtedly
+obtain better results in timing.
+
+We shall next consider the effects of opening the bankings too wide, and
+follow with various conditions which are sure to come in the experience
+of the practical watch repairer. It is to be supposed in this problem
+that the fork and roller action is all right. The reader may say to
+this, why not close the banking? In reply we would offer the supposition
+that some workman had bent the guard pin forward or set a pallet stone
+too far out.
+
+We have now instructed our readers how to draw and construct a lever
+escapement complete, of the correct proportions, and will next take up
+defective construction and consider faults existing to a lesser or
+greater degree in almost every watch. Faults may also be those arising
+from repairs by some workman not fully posted in the correct form and
+relation of the several parts which go to make up a lever escapement. It
+makes no difference to the artisan called upon to put a watch in
+perfect order as to whom he is to attribute the imperfection, maker or
+former repairer; all the workman having the job in hand has to do is to
+know positively that such a fault actually exists, and that it devolves
+upon him to correct it properly.
+
+
+BE FEARLESS IN REPAIRS, IF SURE YOU ARE RIGHT.
+
+Hence the importance of the workman being perfectly posted on such
+matters and, knowing that he is right, can go ahead and make the watch
+as it should be. The writer had an experience of this kind years ago in
+Chicago. A Jules Jurgensen watch had been in the hands of several good
+workmen in that city, but it would stop. It was then brought to him with
+a statement of facts given above. He knew there must be a fault
+somewhere and searched for it, and found it in the exit pallet--a
+certain tooth of the escape wheel under the right conditions would
+sometimes not escape. It might go through a great many thousand times
+and yet it might, and did sometimes, hold enough to stop the watch.
+
+Now probably most of my fellow-workmen in this instance would have been
+afraid to alter a "Jurgensen," or even hint to the owner that such a
+thing could exist as a fault in construction in a watch of this
+justly-celebrated maker. The writer removed the stone, ground a little
+from the base of the offending pallet stone, replaced it, and all
+trouble ended--no stops from that on.
+
+
+STUDY OF AN ESCAPEMENT ERROR.
+
+[Illustration: Fig. 64]
+
+Now let us suppose a case, and imagine a full-plate American movement in
+which the ingress or entrance pallet extends out too far, and in order
+to have it escape, the banking on that side is opened too wide. We show
+at Fig. 64 a drawing of the parts in their proper relations under the
+conditions named. It will be seen by careful inspection that the jewel
+pin _D_ will not enter the fork, which is absolutely necessary. This
+condition very frequently exists in watches where a new pallet stone has
+been put in by an inexperienced workman. Now this is one of the
+instances in which workmen complain of hearing a "scraping" sound when
+the watch is placed to the ear. The remedy, of course, lies in warming
+up the pallet arms and pushing the stone in a trifle, "But how much?"
+say some of our readers. There is no definite rule, but we will tell
+such querists how they can test the matter.
+
+Remove the hairspring, and after putting the train in place and securing
+the plates together, give the winding arbor a turn or two to put power
+on the train; close the bankings well in so the watch cannot escape on
+either pallet. Put the balance in place and screw down the cock.
+Carefully turn back the banking on one side so the jewel pin will just
+pass out of the slot in the fork. Repeat this process with the opposite
+banking; the jewel pin will now pass out on each side. Be sure the guard
+pin does not interfere with the fork action in any way. The fork is now
+in position to conform to the conditions required.
+
+
+HOW TO ADJUST THE PALLETS TO MATCH THE FORK.
+
+If the escapement is all right, the teeth will have one and a half
+degrees lock and escape correctly; but in the instance we are
+considering, the stone will not permit the teeth to pass, and must be
+pushed in until they will. It is not a very difficult matter after we
+have placed the parts together so we can see exactly how much the pallet
+protrudes beyond what is necessary, to judge how far to push it back
+when we have it out and heated. There is still an "if" in the problem we
+are considering, which lies in the fact that the fork we are
+experimenting with may be too short for the jewel pin to engage it for
+ten degrees of angular motion.
+
+This condition a man of large experience will be able to judge of very
+closely, but the better plan for the workman is to make for himself a
+test gage for the angular movement of the fork. Of course it will be
+understood that with a fork which engages the roller for eight degrees
+of fork action, such fork will not give good results with pallets ground
+for ten degrees of pallet action; still, in many instances, a compromise
+can be effected which will give results that will satisfy the owner of a
+watch of moderate cost, and from a financial point of view it stands the
+repairer in hand to do no more work than is absolutely necessary to keep
+him well pleased.
+
+We have just made mention of a device for testing the angular motion of
+the lever. Before we take up this matter, however, we will devote a
+little time and attention to the subject of jewel pins and how to set
+them. We have heretofore only considered jewel pins of one form, that
+is, a round jewel pin with two-fifths cut away. We assumed this form
+from the fact that experience has demonstrated that it is the most
+practicable and efficient form so far devised or applied. Subsequently
+we shall take up the subject of jewel pins of different shapes.
+
+
+HOW TO SET A JEWEL PIN AS IT SHOULD BE.
+
+Many workmen have a mortal terror of setting a jewel pin and seem to
+fancy that they must have a specially-devised instrument for
+accomplishing this end. Most American watches have the hole for the
+jewel pin "a world too wide" for it, and we have heard repeated
+complaints from this cause. Probably the original object of this
+accommodating sort of hole was to favor or obviate faults of pallet
+action. Let us suppose, for illustration, that we have a roller with the
+usual style of hole for a jewel pin which will take almost anything from
+the size of a No. 12 sewing needle up to a round French clock pallet.
+
+[Illustration: Fig. 65]
+
+We are restricted as regards the proper size of jewel pin by the width
+of the slot in the fork. Selecting a jewel which just fits the fork, we
+can set it as regards its relation to the staff so it will cause the
+pitch circle of the jewel pin to coincide with either of dotted circles
+_a_ or _a'_, Fig. 65. This will perhaps be better understood by
+referring to Fig. 66, which is a view of Fig. 65 seen in the direction
+of the arrow _c_. Here we see the roller jewel at _D_, and if we bring
+it forward as far as the hole in the roller will permit, it will occupy
+the position indicated at the dotted lines; and if we set it in (toward
+the staff) as far as the hole will allow, it will occupy the position
+indicated by the full outline.
+
+[Illustration: Fig. 66]
+
+Now such other condition might very easily exist, that bringing the
+jewel pin forward to the position indicated by the dotted lines at _D_,
+Fig. 66, would remedy the defect described and illustrated at Fig. 64
+without any other change being necessary. We do not assert, understand,
+that a hole too large for the jewel pin is either necessary or
+desirable--what we wish to convey to the reader is the necessary
+knowledge so that he can profit by such a state if necessary. A hole
+which just fits the jewel pin so the merest film of cement will hold it
+in place is the way it should be; but we think it will be some time
+before such rollers are made, inasmuch as economy appears to be a chief
+consideration.
+
+
+ABOUT JEWEL-PIN SETTERS.
+
+To make a jewel-pin setter which will set a jewel pin straight is easy
+enough, but to devise any such instrument which will set a jewel so as
+to perfectly accord with the fork action is probably not practicable.
+What the workman needs is to know from examination when the jewel pin is
+in the proper position to perform its functions correctly, and he can
+only arrive at this knowledge by careful study and thought on the
+matter. If we make up our minds on examining a watch that a jewel pin is
+"set too wide," that is, so it carries the fork over too far and
+increases the lock to an undue degree, take out the balance, remove the
+hairspring, warm the roller with a small alcohol lamp, and then with the
+tweezers move the jewel pin in toward the staff.
+
+[Illustration: Fig. 67]
+
+[Illustration: Fig. 68]
+
+[Illustration: Fig. 69]
+
+[Illustration: Fig. 70]
+
+No attempt should be made to move a jewel pin unless the cement which
+holds the jewel is soft, so that when the parts cool off the jewel is as
+rigid as ever. A very little practice will enable any workman who has
+the necessary delicacy of touch requisite to ever become a good
+watchmaker, to manipulate a jewel pin to his entire satisfaction with no
+other setter than a pair of tweezers and his eye, with a proper
+knowledge of what he wants to accomplish. To properly heat a roller for
+truing up the jewel pin, leave it on the staff, and after removing the
+hairspring hold the balance by the rim in a pair of tweezers, "flashing
+it" back and forth through the flame of a rather small alcohol lamp
+until the rim of the balance is so hot it can just be held between the
+thumb and finger, and while at this temperature the jewel pin can be
+pressed forward or backward, as illustrated in Fig. 66, and then a touch
+or two will set the pin straight or parallel with the staff. Figs. 68
+and 69 are self-explanatory. For cementing in a jewel pin a very
+convenient tool is shown at Figs. 67 and 70. It is made of a piece of
+copper wire about 1/16" in diameter, bent to the form shown at Fig. 67.
+The ends _b b_ of the copper wire are flattened a little and recessed on
+their inner faces, as shown in Fig. 70, to grasp the edges of the roller
+_A_. The heat of an alcohol lamp is applied to the loop of the wire at
+_g_ until the small bit of shellac placed in the hole _h_ melts. The
+necessary small pieces of shellac are made by warming a bit of the gum
+to near the melting point and then drawing the softened gum into a
+filament the size of horse hair. A bit of this broken off and placed in
+the hole _h_ supplies the cement necessary to fasten the jewel pin.
+Figs. 68 and 69 will, no doubt, assist in a clear understanding of the
+matter.
+
+
+HOW TO MAKE AN ANGLE-MEASURING DEVICE.
+
+We will now resume the consideration of the device for measuring the
+extent of the angular motion of the fork and pallets. Now, before we
+take this matter up in detail we wish to say, or rather repeat what we
+have said before, which is to the effect that ten degrees of fork and
+lever action is not imperative, as we can get just as sound an action
+and precisely as good results with nine and a half or even nine degrees
+as with ten, if other acting parts are in unison with such an arc of
+angular motion. The chief use of such an angle-measuring device is to
+aid in comparing the relative action of the several parts with a known
+standard.
+
+[Illustration: Fig. 71]
+
+For use with full-plate movements about the best plan is a spring clip
+or clasp to embrace the pallet staff below the pallets. We show at Fig.
+71 such a device. To make it, take a rather large size of sewing
+needle--the kind known as a milliner's needle is about the best. The
+diameter of the needle should be about No. 2, so that at _b_ we can
+drill and put in a small screw. It is important that the whole affair
+should be very light. The length of the needle should be about 1-5/8",
+in order that from the notch _a_ to the end of the needle _A'_ should be
+11/2". The needle should be annealed and flattened a little, to give a
+pretty good grasp to the notch _a_ on the pallet staff.
+
+Good judgment is important in making this clamp, as it is nearly
+impossible to give exact measurements. About 1/40" in width when seen in
+the direction of the arrow _j_ will be found to be about the right
+width. The spring _B_ can be made of a bit of mainspring, annealed and
+filed down to agree in width with the part _A_. In connection with the
+device shown at Fig. 71 we need a movement-holder to hold the movement
+as nearly a constant height as possible above the bench. The idea is,
+when the clamp _A B_ is slipped on the pallet staff the index hand _A'_
+will extend outward, as shown in Fig. 72, where the circle _C_ is
+supposed to represent the top plate of a watch, and _A'_ the index hand.
+
+
+HOW THE ANGULAR MOTION IS MEASURED.
+
+[Illustration: Fig. 72]
+
+Fig. 72 is supposed to be seen from above. It is evident that if we
+remove the balance from the movement shown at _C_, leaving power on the
+train, and with an oiling tool or hair broach move the lever back and
+forth, the index hand _A'_ will show in a magnified manner the angular
+motion of the lever. Now if we provide an index arc, as shown at _D_, we
+can measure the extent of such motion from bank to bank.
+
+[Illustration: Fig. 73]
+
+[Illustration: Fig. 74]
+
+To get up such an index arc we first make a stand as shown at _E F_,
+Fig. 73. The arc _D_ is made to 11/2" radius, to agree with the index
+hand _A'_, and is divided into twelve degree spaces, six each side of a
+zero, as shown at Fig. 74, which is an enlarged view of the index _D_ in
+Fig. 72. The index arc is attached to a short bit of wire extending down
+into the support _E_, and made adjustable as to height by the set-screw
+_l_. Let us suppose the index arc is adjusted to the index hand _A'_,
+and we move the fork as suggested; you see the hand would show exactly
+the arc passed through from bank to bank, and by moving the stand _E F_
+we can arrange so the zero mark on the scale stands in the center of
+such arc. This, of course, gives the angular motion from bank to bank.
+As an experiment, let us close the bankings so they arrest the fork at
+the instant the tooth drops from each pallet. If this arc is ten
+degrees, the pallet action is as it should be with the majority of
+modern watches.
+
+
+TESTING LOCK AND DROP WITH OUR NEW DEVICE.
+
+Let us try another experiment: We carefully move the fork away from the
+bank, and if after the index hand has passed through one and a half
+degrees the fork flies over, we know the lock is right. We repeat the
+experiment from the opposite bank, and in the same manner determine if
+the lock is right on the other pallets. You see we have now the means
+of measuring not only the angular motion of the lever, but the angular
+extent of the lock. At first glance one would say that if now we bring
+the roller and fork action to coincide and act in unison with the pallet
+action, we would be all right; and so we would, but frequently this
+bringing of the roller and fork to agree is not so easily accomplished.
+
+It is chiefly toward this end the Waltham fork is made adjustable, so it
+can be moved to or from the roller, and also that we can allow the
+pallet arms to be moved, as we will try and explain. As we set the
+bankings the pallets are all right; but to test matters, let us remove
+the hairspring and put the balance in place. Now, if the jewel pin
+passes in and out of the fork, it is to be supposed the fork and roller
+action is all right. To test the fork and roller action we close the
+banking a little on one side. If the fork and jewel pin are related to
+each other as they should be, the jewel pin will not pass out of the
+fork, nor will the engaged tooth drop from that pallet. This condition
+should obtain on both pallets, that is, if the jewel pin will not pass
+out of the fork on a given bank the tooth engaged on its pallet should
+not drop.
+
+We have now come to the most intricate and important problems which
+relate to the lever escapement. However, we promise our readers that if
+they will take the pains to follow closely our elucidations, to make
+these puzzles plain. But we warn them that they are no easy problems to
+solve, but require good, hard thinking. The readiest way to master this
+matter is by means of such a model escapement as we have described. With
+such a model, and the pallets made to clamp with small set-screws, and
+roller constructed so the jewel pin could be set to or from the staff,
+this matter can be reduced to object lessons. But study of the due
+relation of the parts in good drawings will also master the situation.
+
+
+A FEW EXPERIMENTS WITH OUR ANGLE-MEASURING DEVICE.
+
+In using the little instrument for determining angular motion that we
+have just described, care must be taken that the spring clamp which
+embraces the pallet staff does not slip. In order to thoroughly
+understand the methods of using this angle-measuring device, let us take
+a further lesson or two.
+
+We considered measuring the amount of lock on each pallet, and advised
+the removal of the balance, because if we left the balance in we could
+not readily tell exactly when the tooth passed on to the impulse plane;
+but if we touch the fork lightly with an oiling tool or a hair broach,
+moving it (the fork) carefully away from the bank and watching the arc
+indicated by the hand _A_, Fig. 72, we can determine with great
+exactness the angular extent of lock. The diagram at Fig. 75 illustrates
+how this experiment is conducted. We apply the hair broach to the end of
+the fork _M_, as shown at _L_, and gently move the fork in the direction
+of the arrow _i_, watching the hand _A_ and note the number of degrees,
+or parts of degrees, indicated by the hand as passed over before the
+tooth is unlocked and passes on to the impulse plane and the fork flies
+forward to the opposite bank. Now, the quick movement of the pallet and
+fork may make the hand mark more or less of an arc on the index than one
+of ten degrees, as the grasp may slip on the pallet staff; but the arc
+indicated by the slow movement in unlocking will be correct.
+
+[Illustration: Fig. 75]
+
+By taking a piece of sharpened pegwood and placing the point in the slot
+of the fork, we can test the fork to see if the drop takes place much
+before the lever rests against the opposite bank. As we have previously
+stated, the drop from the pallet should not take place until the lever
+_almost_ rests on the banking pin. What the reader should impress on his
+mind is that the lever should pass through about one and a half degrees
+arc to unlock, and the remainder (eight and a half degrees) of the ten
+degrees are to be devoted to impulse. But, understand, if the impulse
+angle is only seven and a half degrees, and the jewel pin acts in
+accordance with the rules previously given, do not alter the pallet
+until you know for certain you will gain by it. An observant workman
+will, after a little practice, be able to determine this matter.
+
+We will next take up the double roller and fork action, and also
+consider in many ways the effect of less angles of action than ten
+degrees. This matter now seems of more importance, from the fact that we
+are desirous to impress on our readers that _there is no valid reason
+for adopting ten degrees of fork and roller action with the table
+roller, except that about this number of degrees of action are required
+to secure a reliable safety action_. With the double roller, as low as
+six degrees fork and pallet action can be safely employed. In fork and
+pallet actions below six degrees of angular motion, side-shake in pivot
+holes becomes a dangerous factor, as will be explained further on. It is
+perfectly comprehending the action of the lever escapement and then
+being able to remedy defects, that constitute the master workman.
+
+
+HOW TO MEASURE THE ANGULAR MOTION OF AN ESCAPE WHEEL.
+
+[Illustration: Fig. 76]
+
+We can also make use of our angle-testing device for measuring our
+escape-wheel action, by letting the clasp embrace the arbor of the
+escape wheel, instead of the pallet staff. We set the index arc as in
+our former experiments, except we place the movable index _D_, Fig. 76,
+so that when the engaged tooth rests on the locking face of a pallet,
+the index hand stands at the extreme end of our arc of twelve degrees.
+We next, with our pointed pegwood, start to move the fork away from the
+bank, as before, we look sharp and see the index hand move backward a
+little, indicating the "draw" on the locking face. As soon as the pallet
+reaches the impulse face, the hand _A_ moves rapidly forward, and if the
+escapement is of the club-tooth order and closely matched, the hand _A_
+will pass over ten and a half degrees of angular motion before the drop
+takes place.
+
+[Illustration: Fig. 77]
+
+We will warn our readers in advance, that if they make such a testing
+device they will be astonished at the inaccuracy which they will find in
+the escapements of so-called fine watches. The lock, in many instances,
+instead of being one and a half degrees, will oftener be found to be
+from two to four degrees, and the impulse derived from the escape wheel,
+as illustrated at Fig. 76, will often fall below eight degrees. Such
+watches will have a poor motion and tick loud enough to keep a policeman
+awake. Trials with actual watches, with such a device as we have just
+described, in conjunction with a careful study of the acting parts,
+especially if aided by a large model, such as we have described, will
+soon bring the student to a degree of skill unknown to the old-style
+workman, who, if a poor escapement bothered him, would bend back the
+banking pins or widen the slot in the fork.
+
+We hold that educating our repair workmen up to a high knowledge of what
+is required to constitute a high-grade escapement, will have a
+beneficial effect on manufacturers. When we wish to apply our device to
+the measurement of the escapement of three-quarter-plate watches, we
+will require another index hand, with the grasping end bent downward, as
+shown at Fig. 77. The idea with this form of index hand is, the
+bent-down jaws _B'_, Fig. 77, grasp the fork as close to the pallet
+staff as possible, making an allowance for the acting center by so
+placing the index arc that the hand _A_ will read correctly on the index
+_D_. Suppose, for instance, we place the jaws _B'_ inside the pallet
+staff, we then place the index arc so the hand reads to the arc
+indicated by the dotted arc _m_, Fig. 78, and if set outside of the
+pallet staff, read by the arc _o_.
+
+[Illustration: Fig. 78]
+
+
+HOW A BALANCE CONTROLS THE TIMEKEEPING OF A WATCH.
+
+We think a majority of the fine lever escapements made abroad in this
+day have what is termed double-roller safety action. The chief gains to
+be derived from this form of safety action are: (1) Reducing the arc of
+fork and roller action; (2) reducing the friction of the guard point to
+a minimum. While it is entirely practicable to use a table roller for
+holding the jewel pin with a double-roller action, still a departure
+from that form is desirable, both for looks and because as much of the
+aggregate weight of a balance should be kept as far from the axis of
+rotation as possible.
+
+We might as well consider here as elsewhere, the relation the balance
+bears to the train as a controlling power. Strictly speaking, _the
+balance and hairspring are the time measurers_, the train serving only
+two purposes: (_a_) To keep the balance in motion; (_b_) to classify and
+record the number of vibrations of the balance. Hence, it is of
+paramount importance that the vibrations of the balance should be as
+untrammeled as possible; this is why we urge reducing the arc of
+connection between the balance and fork to one as brief as is consistent
+with sound results. With a double-roller safety action we can easily
+reduce the fork action to eight degrees and the roller action to
+twenty-four degrees.
+
+Inasmuch as satisfactory results in adjustment depend very much on the
+perfection of construction, we shall now dwell to some extent on the
+necessity of the several parts being made on correct principles. For
+instance, by reducing the arc of engagement between the fork and roller,
+we lessen the duration of any disturbing influence of escapement action.
+
+To resume the explanation of why it is desirable to make the staff and
+all parts near the axis of the balance as light as possible, we would
+say it is the moving portion of the balance which controls the
+regularity of the intervals of vibration. To illustrate, suppose we have
+a balance only 3/8" in diameter, but of the same weight as one in an
+ordinary eighteen-size movement. We can readily see that such a balance
+would require but a very light hairspring to cause it to give the usual
+18,000 vibrations to the hour. We can also understand, after a little
+thought, that such a balance would exert as much breaking force on its
+pivots as a balance of the same weight, but 3/4" in diameter acting
+against a very much stronger hairspring. There is another factor in the
+balance problem which deserves our attention, which factor is
+atmospheric resistance. This increases rapidly in proportion to the
+velocity.
+
+
+HOW BAROMETRIC PRESSURE AFFECTS A WATCH.
+
+The most careful investigators in horological mechanics have decided
+that a balance much above 75/100" in diameter, making 18,000 vibrations
+per hour, is not desirable, because of the varying atmospheric
+disturbances as indicated by barometric pressure. A balance with all of
+its weight as near the periphery as is consistent with strength, is what
+is to be desired for best results. It is the moving matter composing the
+balance, pitted against the elastic force of the hairspring, which we
+have to depend upon for the regularity of the timekeeping of a watch,
+and if we can take two grains' weight of matter from our roller table
+and place them in the rim or screws of the balance, so as to act to
+better advantage against the hairspring, we have disposed of these two
+grains so as to increase the efficiency of the controlling power and not
+increase the stress on the pivots.
+
+[Illustration: Fig. 79]
+
+We have deduced from the facts set forth, two axioms: (_a_) That we
+should keep the weight of our balance as much in the periphery as
+possible, consistent with due strength; (_b_) avoid excessive size from
+the disturbing effect of the air. We show at _A_, Fig. 79, the shape of
+the piece which carries the jewel pin. As shown, it consists of three
+parts: (1) The socket _A_, which receives the jewel pin _a_; (2) the
+part _A''_ and hole _b_, which goes on the balance staff; (3) the
+counterpoise _A'''_, which makes up for the weight of the jewel socket
+_A_, neck _A'_ and jewel pin. This counterpoise also makes up for the
+passing hollow _C_ in the guard roller _B_, Fig. 80. As the piece _A_
+is always in the same relation to the roller _B_, the poise of the
+balance must always remain the same, no matter how the roller action is
+placed on the staff. We once saw a double roller of nearly the shape
+shown at Fig. 79, which had a small gold screw placed at _d_, evidently
+for the purpose of poising the double rollers; but, to our thinking, it
+was a sort of hairsplitting hardly worth the extra trouble. Rollers for
+very fine watches should be poised on the staff before the balance is
+placed upon it.
+
+[Illustration: Fig. 80]
+
+We shall next give detailed instructions for drawing such a double
+roller as will be adapted for the large model previously described,
+which, as the reader will remember, was for ten degrees of roller
+action. We will also point out the necessary changes required to make it
+adapted for eight degrees of fork action. We would beg to urge again the
+advantages to be derived from constructing such a model, even for
+workmen who have had a long experience in escapements, our word for it
+they will discover a great many new wrinkles they never dreamed of
+previously.
+
+It is important that every practical watchmaker should thoroughly master
+the theory of the lever escapement and be able to comprehend and
+understand at sight the faults and errors in such escapements, which, in
+the every-day practice of his profession, come to his notice. In no
+place is such knowledge more required than in fork and roller action. We
+are led to say the above chiefly for the benefit of a class of workmen
+who think there is a certain set of rules which, if they could be
+obtained, would enable them to set to rights any and all escapements. It
+is well to understand that no such system exists and that, practically,
+we must make one error balance another; and it is the "know how" to make
+such faults and errors counteract each other that enables one workman to
+earn more for himself or his employer in two days than another workman,
+who can file and drill as well as he can, will earn in a week.
+
+
+PROPORTIONS OF THE DOUBLE-ROLLER ESCAPEMENT.
+
+The proportion in size between the two rollers in a double-roller
+escapement is an open question, or, at least, makers seldom agree on it.
+Grossmann shows, in his work on the lever escapement, two sizes: (1)
+Half the diameter of the acting roller; (2) two-thirds of the size of
+the acting roller. The chief fault urged against a smaller safety roller
+is, that it necessitates longer horns to the fork to carry out the
+safety action. Longer horns mean more metal in the lever, and it is the
+conceded policy of all recent makers to have the fork and pallets as
+light as possible. Another fault pertaining to long horns is, when the
+horn does have to act as safety action, a greater friction ensues.
+
+In all soundly-constructed lever escapements the safety action is only
+called into use in exceptional cases, and if the watch was lying still
+would theoretically never be required. Where fork and pallets are poised
+on their arbor, pocket motion (except torsional) should but very little
+affect the fork and pallet action of a watch, and torsional motion is
+something seldom brought to act on a watch to an extent to make it
+worthy of much consideration. In the double-roller action which we shall
+consider, we shall adopt three-fifths of the pitch diameter of the
+jewel-pin action as the proper size. Not but what the proportions given
+by Grossmann will do good service; but we adopt the proportions named
+because it enables us to use a light fork, and still the friction of the
+guard point on the roller is but little more than where a guard roller
+of half the diameter of the acting roller is employed.
+
+The fork action we shall consider at present is ten degrees, but
+subsequently we shall consider a double-roller action in which the fork
+and pallet action is reduced to eight degrees. We shall conceive the
+play between the guard point and the safety roller as one degree, which
+will leave half a degree of lock remaining in action on the engaged
+pallet.
+
+
+THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED.
+
+In the drawing at Fig. 81 we show a diagram of the action of the
+double-roller escapement. The small circle at _A_ represents the center
+of the pallet staff, and the one at _B_ the center of the balance staff.
+The radial lines _A d_ and _A d'_ represent the arc of angular motion of
+fork action. The circle _b b_ represents the pitch circle of the jewel
+pin, and the circle at _c c_ the periphery of the guard or safety
+roller. The points established on the circle _c c_ by intersection of
+the radial lines _A d_ and _A d'_ we will denominate the points _h_ and
+_h'_. It is at these points the end of the guard point of the fork will
+terminate. In construction, or in delineating for construction, we show
+the guard enough short of the points _h h'_ to allow the fork an angular
+motion of one degree, from _A_ as a center, before said point would come
+in contact with the safety roller.
+
+[Illustration: Fig. 81]
+
+We draw through the points _h h'_, from _B_ as a center, the radial
+lines _B g_ and _B g'_. We measure this angle by sweeping the short arc
+_i_ with any of the radii we have used for arc measurement in former
+delineations, and find it to be a trifle over sixty degrees. To give
+ourselves a practical object lesson, let us imagine that a real guard
+point rests on the circle _c_ at _h_. Suppose we make a notch in the
+guard roller represented by the circle _c_, to admit such imaginary
+guard point, and then commence to revolve the circle _c_ in the
+direction of the arrow _j_, letting the guard point rest constantly in
+such notch. When the notch _n_ in _c_ has been carried through thirty
+degrees of arc, counting from _B_ as a center, the guard point, as
+relates to _A_ as a center, would only have passed through an arc of
+five degrees. We show such a guard point and notch at _o n_. In fact, if
+a jewel pin was set to engage the fork on the pitch circle _b a_, the
+escapement would lock. To obviate such lock we widen the notch _n_ to
+the extent indicated by the dotted lines _n'_, allowing the guard point
+to fall back, so to speak, into the notch _n_, which really represents
+the passing hollow. It is not to be understood that the extended notch
+at _n_ is correctly drawn as regards position, because when the guard
+point was on the line _A f_ the point _o_ would be in the center of the
+extended notch, or passing hollow. We shall next give the details of
+drawing the double roller, but before doing so we deemed it important to
+explain the action of such guard points more fully than has been done
+heretofore.
+
+
+HOW TO DESIGN A DOUBLE-ROLLER ESCAPEMENT.
+
+We have already given very desirable forms for the parts of a
+double-roller escapement, consequently we shall now deal chiefly with
+acting principles as regards the rollers, but will give, at Fig. 82, a
+very well proportioned and practical form of fork. The pitch circle of
+the jewel pin is indicated by the dotted circle _a_, and the jewel pin
+of the usual cylindrical form, with two-fifths cut away. The safety
+roller is three-fifths of the diameter of the pitch diameter of the
+jewel-pin action, as indicated by the dotted circle _a_.
+
+The safety roller is shown in full outline at _B'_, and the passing
+hollow at _E_. It will be seen that the arc of intersection embraced
+between the radial lines _B c_ and _B d_ is about sixty-one and a half
+degrees for the roller, but the angular extent of the passing hollow is
+only a little over thirty-two degrees. The passing hollow _E_ is located
+and defined by drawing the radial line _B c_ from the center _B_ through
+the intersection of radial line _A i_ with the dotted arc _b_, which
+represents the pitch circle of the safety roller. We will name this
+intersection the point _l_. Now the end of the guard point _C_
+terminates at the point _l_, and the passing hollow _E_ extends on _b_
+sixteen degrees on each side of the radial line _B c_.
+
+[Illustration: Fig. 82]
+
+The roller action is supposed to continue through thirty degrees of
+angular motion of the balance staff, and is embraced on the circle _a_
+between the radial line _B k_ and _B o_. To delineate the inner face of
+the horn _p_ of the fork _F_ we draw the short arc _g_, from _A_ as a
+center, and on said arc locate at two degrees from the center at _B_ the
+point _f_. We will designate the upper angle of the outer face of the
+jewel pin _D_ as the point _s_ and, from _A_ as a center, sweep through
+this point _s_ the short arc _n n_. Parallel with the line _A i_ and at
+the distance of half the diameter of the jewel pin _D_, we draw the
+short lines _t t'_, which define the inner faces of the fork.
+
+The intersection of the short line _t_ with the arc _n_ we will
+designate the point _r_. With our dividers set to embrace the space
+between the point _r_ and the point _f_, we sweep the arc which defines
+the inner face of the prong of the fork. The space we just made use of
+is practically the same as the radius of the circle _a_, and
+consequently of the same curvature. Practically, the length of the guard
+point _C'_ is made as long as will, with certainty, clear the safety
+roller _B_ in all positions. While we set the point _f_ at two degrees
+from the center _B_, still, in a well-constructed escapement, one and a
+half degrees should be sufficient, but the extra half degree will do no
+harm. If the roller _B'_ is accurately made and the guard point _C'_
+properly fitted, the fork will not have half a degree of play.
+
+The reader will remember that in the escapement model we described we
+cut down the drop to one degree, being less by half a degree than
+advised by Grossmann and Saunier. We also advised only one degree of
+lock. In the perfected lever escapement, which we shall describe and
+give working drawings for the construction of, we shall describe a
+detached lever escapement with only eight degrees fork and pallet
+action, with only three-fourths of a degree drop and three-fourths of a
+degree lock, which we can assure our readers is easily within the limits
+of practical construction by modern machinery.
+
+
+HOW THE GUARD POINT IS MADE.
+
+[Illustration: Fig. 83]
+
+The guard point _C'_, as shown at Fig. 82, is of extremely simple
+construction. Back of the slot of the fork, which is three-fifths of the
+diameter of the jewel pin in depth, is made a square hole, as shown at
+_u_, and the back end of the guard point _C_ is fitted to this hole so
+that it is rigid in position. This manner of fastening the guard point
+is equally efficient as that of attaching it with a screw, and much
+lighter--a matter of the highest importance in escapement construction,
+as we have already urged. About the best material for such guard points
+is either aluminum or phosphor bronze, as such material is lighter than
+gold and very rigid and strong. At Fig. 83 we show a side view of the
+essential parts depicted in Fig. 82, as if seen in the direction of the
+arrow _v_, but we have added the piece which holds the jewel pin _D_. A
+careful study of the cut shown at Fig. 82 will soon give the horological
+student an excellent idea of the double-roller action.
+
+We will now take up and consider at length why Saunier draws his
+entrance pallet with fifteen degrees draw and his exit pallet with only
+twelve degrees draw. To make ourselves more conversant with Saunier's
+method of delineating the lever escapement, we reproduce the essential
+features of his drawing, Fig. 1, plate VIII, of his "Modern Horology,"
+in which he makes the draw of the locking face of the entrance pallet
+fifteen degrees and his exit pallet twelve degrees. In the cut shown at
+Fig. 84 we use the same letters of reference as he employs. We do not
+quote his description or directions for delineation because he refers to
+so much matter which he has previously given in the book just referred
+to. Besides we cannot entirely endorse his methods of delineations for
+many reasons, one of which appears in the drawing at Fig. 84.
+
+[Illustration: Fig. 84]
+
+
+MORE ABOUT TANGENTIAL LOCKINGS.
+
+Most writers endorse the idea of tangential lockings, and Saunier speaks
+of the escapement as shown at Fig. 84 as having such tangential
+lockings, which is not the case. He defines the position of the pallet
+staff from the circle _t_, which represents the extreme length of the
+teeth; drawing the radial lines _A D_ and _A E_ to embrace an arc of
+sixty degrees, and establishing the center of his pallet staff _C_ at
+the intersection of the lines _D C_ and _E C_, which are drawn at right
+angles to the radial lines _A D_ and _A E_, and tangential to the circle
+_t_.
+
+Here is an error; the lines defining the center of the pallet staff
+should have been drawn tangent to the circle _s_, which represents the
+locking angle of the teeth. This would have placed the center of the
+pallet staff farther in, or closer to the wheel. Any person can see at a
+glance that the pallets as delineated are not tangential in a true
+sense.
+
+[Illustration: Fig. 85]
+
+We have previously considered engaging friction and also repeatedly have
+spoken of tangential lockings, but will repeat the idea of tangential
+lockings at Fig. 85. A tangential locking is neutral, or nearly so, as
+regards engaging friction. For illustration we refer to Fig. 85, where
+_A_ represents the center of an escape wheel. We draw the radial lines
+_A y_ and _A z_ so that they embrace sixty degrees of the arcs _s_ or
+_t_, which correspond to similar circles in Fig. 84, and represent the
+extreme extent of the teeth and likewise the locking angle of such
+teeth. In fact, with the club-tooth escapement all that part of a tooth
+which extends beyond the line _s_ should be considered the same as the
+addendum in gear wheels. Consequently, a tangential locking made to
+coincide with the center of the impulse plane, as recommended by
+Saunier, would require the pallet staff to be located at _C'_ instead of
+_C_, as he draws it. If the angle _k'_ of the tooth _k_ in Fig. 84 was
+extended outward from the center _A_ so it would engage or rest on the
+locking face of the entrance pallet as shown at Fig. 84, then the draw
+of the locking angle would not be quite fifteen degrees; but it is
+evident no lock can take place until the angle _a_ of the entrance
+pallet has passed inside the circle _s_. We would say here that we have
+added the letters _s_ and _t_ to the original drawings, as we have
+frequently to refer to these circles, and without letters had no means
+of designation. Before the locking angle _k'_ of the tooth can engage
+the pallet, as shown in Fig. 84, the pallet must turn on the center _C_
+through an angular movement of at least four degrees. We show the
+situation in the diagram at Fig. 86, using the same letters of reference
+for similar parts as in Fig. 84.
+
+[Illustration: Fig. 86]
+
+As drawn in Fig. 84 the angle of draft _G a I_ is equal to fifteen
+degrees, but when brought in a position to act as shown at _G a' I'_,
+Fig. 86, the draw is less even than twelve degrees. The angle _C a I_
+remains constant, as shown at _C a' I'_, but the relation to the radial
+_A G_ changes when the pallet moves through the angle _w C w'_, as it
+must when locked. A tangential locking in the true sense of the meaning
+of the phrase is a locking set so that a pallet with its face coinciding
+with a radial line like _A G_ would be neutral, and the thrust of the
+tooth would be tangent to the circle described by the locking angle of
+the tooth. Thus the center _C_, Fig. 86, is placed on the line _w'_
+which is tangent to the circle _s_; said line _w'_ also being at right
+angles to the radial line _A G_.
+
+The facts are, the problems relating to the club-tooth lever escapement
+are very intricate and require very careful analysis, and without such
+care the horological student can very readily be misled. Faulty
+drawings, when studying such problems, lead to no end of errors, and
+practical men who make imperfect drawings lead to the popular phrase,
+"Oh, such a matter may be all right in theory, but will not work in
+practice." We should always bear in mind that _theory, if right, must
+lead practice_.
+
+
+CORRECT DRAWING REQUIRED.
+
+If we delineate our entrance pallet to have a draw of twelve degrees
+when in actual contact with the tooth, and then construct in exact
+conformity with such drawings, we will find our lever to "hug the banks"
+in every instance. It is inattention to such details which produces the
+errors of makers complained of by Saunier in section 696 of his "Modern
+Horology," and which he attempts to correct by drawing the locking face
+at fifteen degrees draw.
+
+We shall show that neither _C_ nor _C'_, Fig. 85, is the theoretically
+correct position for the pallet center for a tangential locking.
+
+We will now take up the consideration of a club-tooth lever escapement
+with circular pallets and tangential lockings; but previous to making
+the drawings we must decide several points, among which are the
+thickness of the pallet arms, which establishes the angular motion of
+the escape wheel utilized by such pallet arms, and also the angular
+motion imparted to the pallets by the impulse faces of the teeth. We
+will, for the present, accept the thickness of the arms as being
+equivalent to five degrees of angular extent of the pitch circle of the
+escape wheel.
+
+[Illustration: Fig. 87]
+
+[Illustration: Fig. 88]
+
+In making our drawings we commence, as on former occasions, by
+establishing the center of our escape wheel at _A_, Fig. 87, and
+sweeping the arc _a a_ to represent the pitch circle of such wheel.
+Through the center _A_ we draw the vertical line _A B_, which is
+supposed to also pass through the center of the pallet staff. The
+intersection of the line _A B_ with the arc _a_ we term the point _d_,
+and from this point we lay off on said arc _a_ thirty degrees each side
+of said intersection, and thus establish the points _c b_. From _A_,
+through the point _c_, we draw the line _A c c'_. On the arc _a a_ and
+two and a half degrees to the left of the point _c_ we establish the
+point _f_, which space represents half of the thickness of the entrance
+pallet. From _A_ we draw through the point _f_ the line _A f f'_. From
+_f_, and at right angles to said line _A f_, we draw the line _f e_
+until it crosses the line _A B_.
+
+Now this line _f e_ is tangent to the arc _a_ from the point _f_, and
+consequently a locking placed at the point _f_ is a true tangential
+locking; and if the resting or locking face of a pallet was made to
+coincide with the line _A f'_, such locking face would be strictly
+"dead" or neutral. The intersection of the line _f e_ with the line _A
+B_ we call the point _C_, and locate at this point the center of our
+pallet staff. According to the method of delineating the lever
+escapement by Moritz Grossmann the tangent line for locating the center
+of the pallet staff is drawn from the point _c_, which would locate the
+center of the pallet staff at the point _h_ on the line _A B_.
+
+Grossmann, in delineating his locking face for the draw, shows such face
+at an angle of twelve degrees to the radial line _A f'_, when he should
+have drawn it twelve degrees to an imaginary line shown at _f i_, which
+is at right angles to the line _f h_. To the writer's mind this is not
+just as it should be, and may lead to misunderstanding and bad
+construction. We should always bear in mind the fact that the basis of a
+locking face is a neutral plane placed at right angles to the line of
+thrust, and the "draw" comes from a locking face placed at an angle to
+such neutral plane. A careful study of the diagram at Fig. 88 will give
+the reader correct ideas. If a tooth locks at the point _c_, the
+tangential thrust would be on the line _c h'_, and a neutral locking
+face would be on the line _A c_.
+
+
+NEUTRAL LOCKINGS.
+
+To aid in explanation, let us remove the pallet center to _D_; then the
+line of thrust would be _c D_ and a neutral locking face would coincide
+with the line _m m_, which is at right angles to the line _c D_. If we
+should now make a locking face with a "draw" and at an angle to the line
+_c D_, say, for illustration, to correspond to the line _c c'_ (leaving
+the pallet center at _D_), we would have a strong draw and also a cruel
+engaging friction.
+
+If, however, we removed the engaging tooth, which we have just conceived
+to be at _c_, to the point _k_ on the arc _a' a'_, Fig. 88, the pallet
+center _D_ would then represent a tangential locking, and a neutral
+pallet face would coincide with the radial line _A k'_; and a locking
+face with twelve degrees draw would coincide nearly with the line _l_.
+Let us next analyze what the effect would be if we changed the pallet
+center to _h'_, Fig. 88, leaving the engaging tooth still at _k_. In
+this instance the line _l l_ would then coincide with a neutral locking
+face, and to obtain the proper draw we should delineate the locking face
+to correspond to the line _k n_, which we assume to be twelve degrees
+from _k l_.
+
+It is not to be understood that we insist on precisely twelve degrees
+draw from a neutral plane for locking faces for lever pallets. What we
+do insist upon, however, is a "safe and sure draw" for a lever pallet
+which will hold a fork to the banks and will also return it to such
+banks if by accident the fork is moved away. We are well aware that it
+takes lots of patient, hard study to master the complications of the
+club-tooth lever escapement, but it is every watchmaker's duty to
+conquer the problem. The definition of "lock," in the detached lever
+escapement, is the stoppage or arrest of the escape wheel of a watch
+while the balance is left free or detached to perform the greater
+portion of its arc of vibration. "Draw" is a function of the locking
+parts to preserve the fork in the proper position to receive and act on
+the jewel pin of the balance.
+
+It should be borne in mind in connection with "lock" and "draw," that
+the line of thrust as projected from the locked tooth of the escape
+wheel should be as near tangential as practicable. This maxim applies
+particularly to the entrance pallet. We would beg to add that
+practically it will make but little odds whether we plant the center of
+our pallet staff at _C_ or _h_, Fig. 87, provided we modify the locking
+and impulse angles of our pallets to conform to such pallet center. But
+it will not do to arrange the parts for one center and then change to
+another.
+
+
+PRACTICAL HINTS FOR LEVER ESCAPEMENTS.
+
+Apparently there seems to be a belief with very many watchmakers that
+there is a set of shorthand rules for setting an escapement, especially
+in American watches, which, if once acquired, conquers all
+imperfections. Now we wish to disabuse the minds of our readers of any
+such notions. Although the lever escapement, as adopted by our American
+factories, is constructed on certain "lines," still these lines are
+subject to modifications, such as may be demanded for certain defects of
+construction. If we could duplicate every part of a watch movement
+perfectly, then we could have certain rules to go by, and fixed
+templets could be used for setting pallet stones and correcting other
+escapement faults.
+
+Let us now make an analysis of the action of a lever escapement. We show
+at Fig. 89 an ordinary eighteen-size full-plate lever with fork and
+pallets. The dotted lines _a b_ are supposed to represent an angular
+movement of ten degrees. Now, it is the function of the fork to carry
+the power of the train to the balance. How well the fork performs its
+office we will consider subsequently; for the present we are dealing
+with the power as conveyed to the fork by the pallets as shown at Fig.
+89.
+
+[Illustration: Fig. 89]
+
+The angular motion between the lines _a c_ (which represents the lock)
+is not only absolutely lost--wasted--but during this movement the train
+has to retrograde; that is, the dynamic force stored in the momentum of
+the balance has to actually turn the train backward and against the
+force of the mainspring. True, it is only through a very short arc, but
+the necessary force to effect this has to be discounted from the power
+stored in the balance from a former impulse. For this reason we should
+make the angular motion of unlocking as brief as possible. Grossmann, in
+his essay, endorses one and a half degrees as the proper lock.
+
+In the description which we employed in describing the large model for
+illustrating the action of the detached lever escapement, we cut the
+lock to one degree, and in the description of the up-to-date lever
+escapement, which we shall hereafter give, we shall cut the lock down to
+three-quarters of a degree, a perfection easily to be attained by modern
+tools and appliances. We shall also cut the drop down to three-quarters
+of a degree. By these two economies we more than make up for the power
+lost in unlocking. With highly polished ruby or sapphire pallets ten
+degrees of draw is ample. But such draw must positively be ten degrees
+from a neutral locking face, not an escapement drawn on paper and
+called ten degrees, but when actually measured would only show eight and
+a half or nine degrees.
+
+
+THE PERFECTED LEVER ESCAPEMENT.
+
+With ten degrees angular motion of the lever and one and a half degrees
+lock, we should have eight and a half degrees impulse. The pith of the
+problem, as regards pallet action, for the practical workman can be
+embodied in the following question: What proportion of the power derived
+from the twelve degrees of angular motion of the escape wheel is really
+conveyed to the fork? The great leak of power as transmitted by the
+lever escapement to the balance is to be found in the pallet action, and
+we shall devote special attention to finding and stopping such leaks.
+
+
+WHEN POWER IS LOST IN THE LEVER ESCAPEMENT.
+
+If we use a ratchet-tooth escape wheel we must allow at least one and a
+half degrees drop to free the back of the tooth; but with a club-tooth
+escape wheel made as can be constructed by proper skill and care, the
+drop can be cut down to three-quarters of a degree, or one-half of the
+loss with the ratchet tooth. We do not wish our readers to imagine that
+such a condition exists in most of the so-called fine watches, because
+if we take the trouble to measure the actual drop with one of the little
+instruments we have described, it will be found that the drop is seldom
+less than two, or even three degrees.
+
+If we measure the angular movement of the fork while locked, it will
+seldom be found less than two or three degrees. Now, we can all
+understand that the friction of the locking surface has to be counted as
+well as the recoil of the draw. Locking friction is seldom looked after
+as carefully as the situation demands. Our factories make the impulse
+face of the pallets rounded, but leave the locking face flat. We are
+aware this condition is, in a degree, necessary from the use of exposed
+pallets. In many of the English lever watches with ratchet teeth, the
+locking faces are made cylindrical, but with such watches the pallet
+stones, as far as the writer has seen, are set "close"; that is, with
+steel pallet arms extending above and below the stone.
+
+There is another feature of the club-tooth lever escapement that next
+demands our attention which we have never seen discussed. We refer to
+arranging and disposing of the impulse of the escape wheel to meet the
+resistance of the hairspring. Let us imagine the dotted line _A d_, Fig.
+89, to represent the center of action of the fork. We can readily see
+that the fork in a state of rest would stand half way between the two
+banks from the action of the hairspring, and in the pallet action the
+force of the escape wheel, one tooth of which rests on the impulse face
+of a pallet, would be exerted against the elastic force of the
+hairspring. If the force of the mainspring, as represented by the
+escape-wheel tooth, is superior to the power of the hairspring, the
+watch starts itself. The phases of this important part of the detached
+lever escapement will be fully discussed.
+
+
+ABOUT THE CLUB-TOOTH ESCAPEMENT.
+
+We will now take up a study of the detached lever escapement as relates
+to pallet action, with the point specially in view of constructing an
+escapement which cannot "set" in the pocket, or, in other words, an
+escapement which will start after winding (if run down) without shaking
+or any force other than that supplied by the train as impelled by the
+mainspring. In the drawing at Fig. 90 we propose to utilize eleven
+degrees of escape-wheel action, against ten and a half, as laid down by
+Grossmann. Of this eleven degrees we propose to divide the impulse arc
+of the escape wheel in six and five degrees, six to be derived from the
+impulse face of the club tooth and five from the impulse plane of the
+pallet.
+
+The pallet action we divide into five and four, with one degree of lock.
+Five degrees of pallet action is derived from the impulse face of the
+tooth and four from the impulse face of the pallet. The reader will
+please bear in mind that we do not give these proportions as imperative,
+because we propose to give the fullest evidence into the reader's hands
+and enable him to judge for himself, as we do not believe in laying down
+imperious laws that the reader must accept on our assertion as being
+correct. Our idea is rather to furnish the proper facts and put him in a
+situation to know for himself.
+
+The reader is urged to make the drawings for himself on a large scale,
+say, an escape wheel 10" pitch diameter. Such drawings will enable him
+to realize small errors which have been tolerated too much in drawings
+of this kind. The drawings, as they appear in the cut, are one-fourth
+the size recommended, and many of the lines fail to show points we
+desire to call attention to. As for instance, the pallet center at _B_
+is tangential to the pitch circle _a_ from the point of tooth contact at
+_f_. To establish this point we draw the radial lines _A c_ and _A d_
+from the escape-wheel center _A_, as shown, by laying off thirty degrees
+on each side of the intersection of the vertical line _i_ (passing
+through the centers _A B_) with the arc _a_, and then laying off two and
+a half degrees on _a_ and establishing the point _f_, and through _f_
+from the center _A_ draw the radial line _A f'_. Through the point _f_
+we draw the tangent line _b' b b''_, and at the intersection of the line
+_b_ with _i_ we establish the center of our pallet staff at _B_. At two
+and a half degrees from the point _c_ we lay off two and a half degrees
+to the right of said point and establish the point _n_, and draw the
+radial line _A n n'_, which establishes the extent of the arc of angular
+motion of the escape wheel utilized by the pallet arm.
+
+[Illustration: Fig. 90]
+
+We have now come to the point where we must exercise our reasoning
+powers a little. We know the locking angle of the escape-wheel tooth
+passes on the arc _a_, and if we utilize the impulse face of the tooth
+for five degrees of pallet or lever motion we must shape it to this end.
+We draw the short arc _k_ through the point _n_, knowing that the inner
+angle of the pallet stone must rest on this arc wherever it is situated.
+As, for instance, when the locking face of the pallet is engaged, the
+inner angle of the pallet stone must rest somewhere on this arc (_k_)
+inside of _a_, and the extreme outer angle of the impulse face of the
+tooth must part with the pallet on this arc _k_.
+
+
+HOW TO LOCATE THE PALLET ACTION.
+
+With the parts related to each other as shown in the cut, to establish
+where the inner angle of the pallet stone is located in the drawing, we
+measure down on the arc _k_ five degrees from its intersection with _a_,
+and establish the point _s_. The line _B b_, Fig. 90, as the reader will
+see, does not coincide with the intersection of the arcs _a_ and _k_,
+and to conveniently get at the proper location for the inner angle of
+our pallet stone, we draw the line _B b'_, which passes through the
+point _n_ located at the intersection of the arc _a_ with the arc _k_.
+From _B_ as a center we sweep the short arc _j_ with any convenient
+radius of which we have a sixty-degree scale, and from the intersection
+of _B b'_ with _j_ we lay off five degrees and draw the line _B s'_,
+which establishes the point _s_ on the arc _k_. As stated above, we
+allow one degree for lock, which we establish on the arc _o_ by laying
+off one degree on the arc _j_ below its intersection with the line _B
+b_. We do not show this line in the drawing, from the fact that it comes
+so near to _B b'_ that it would confuse the reader. Above the arc _a_ on
+the arc _k_ at five degrees from the point _n_ we establish the point
+_l_, by laying off five degrees on the arc _j_ above the intersection of
+the line _B b_ with _j_.
+
+The point _l_, Fig. 90, establishes where the outer angle of the tooth
+will pass the arc _k_ to give five degrees of angular motion to the
+lever. From _A_ as a center we sweep the arc _m_, passing through the
+point _l_. The intersection of the arc _m_ with the line _A h_ we call
+the point _r_, and by drawing the right line _r f_ we delineate the
+impulse face of the tooth. On the arc _o_ and one degree below its
+intersection with the line _B b_ we establish the point _t_, and by
+drawing a right line from _t_ to _s_ we delineate the impulse face of
+our entrance pallet.
+
+
+"ACTION" DRAWINGS.
+
+One great fault with most of our text books on horology lies in the fact
+that when dealing with the detached lever escapement the drawings show
+only the position of the pallets when locked, and many of the conditions
+assumed are arrived at by mental processes, without making the proper
+drawings to show the actual relation of the parts at the time such
+conditions exist. For illustration, it is often urged that there is a
+time in the action of the club-tooth lever escapement action when the
+incline on the tooth and the incline on the pallet present parallel
+surfaces, and consequently endure excessive friction, especially if the
+oil is a little thickened.
+
+We propose to make drawings to show the exact position and relation of
+the entrance pallet and tooth at three intervals viz: (1) Locked; (2)
+the position of the parts when the lever has performed one-half of its
+angular motion; (3) when half of the impulse face of the tooth has
+passed the pallet. The position of the entrance pallet when locked is
+sufficiently well shown in Fig. 90 to give a correct idea of the
+relations with the entrance pallet; and to conform to statement (2), as
+above. We will now delineate the entrance pallet, not in actual contact,
+however, with the pallet, because if we did so the lines we employed
+would become confused. The methods we use are such that _we can
+delineate with absolute correctness either a pallet or tooth at any
+point in its angular motion_.
+
+We have previously given instructions for drawing the pallet locked; and
+to delineate the pallet after five degrees of angular motion, we have
+only to conceive that we substitute the line _s'_ for the line _b'_. All
+angular motions and measurements for pallet actions are from the center
+of the pallet staff at _B_. As we desire to now delineate the entrance
+pallet, it has passed through five degrees of angular motion and the
+inner angle _s_ now lies on the pitch circle of the escape wheel, the
+angular space between the lines _b' s'_ being five degrees, the line
+_b''_ reducing the impulse face to four degrees.
+
+
+DRAWING AN ESCAPEMENT TO SHOW ANGULAR MOTION.
+
+To delineate our locking face we draw a line at right angles to the line
+_B b''_ from the point _t_, said point being located at the intersection
+of the arc _o_ with the line _B b''_. To draw a line perpendicular to
+_B b''_ from the point _t_, we take a convenient space in our dividers and
+establish on the line _B b''_ the points _x x'_ at equal distances from
+the point _t_. We open the dividers a little (no special distance) and
+sweep the short arcs _x'' x'''_, as shown at Fig. 91. Through the
+intersection of the short arcs _x'' x'''_ and to the point _t_ we draw
+the line _t y_. The reader will see from our former explanations that
+the line _t y_ represents the neutral plane of the locking face, and
+that to have the proper draw we must delineate the locking face of our
+pallet at twelve degrees. To do this we draw the line _t x'_ at twelve
+degrees to the line _t y_, and proceed to outline our pallet faces as
+shown. We can now understand, after a moment's thought, that we can
+delineate the impulse face of a tooth at any point or place we choose by
+laying off six degrees on the arc _m_, and drawing radial lines from _A_
+to embrace such arc. To illustrate, suppose we draw the radial lines
+_w' w''_ to embrace six degrees on the arc _a_. We make these lines
+contiguous to the entrance pallet _C_ for convenience only. To delineate
+the impulse face of the tooth, we draw a line extending from the
+intersection of the radial line _A' w'_ with the arc _m_ to the
+intersection of the arc _a_ with the radial line _A w''_.
+
+[Illustration: Fig. 91]
+
+We next desire to know where contact will take place between the
+wheel-tooth _D_ and pallet _C_. To determine this we sweep, with our
+dividers set so one leg rests at the escape-wheel center _A_ and the
+other at the outer angle _t_ of the entrance pallet, the short arc _t' w_.
+Where this arc intersects the line _w_ (which represents the impulse
+face of the tooth) is where the outer angle _t_ of the entrance pallet
+_C_ will touch the impulse face of the tooth. To prove this we draw the
+radial line _A v_ through the point where the short arc _t t'_ passes
+through the impulse face _w_ of the tooth _D_. Then we continue the line
+_w_ to _n_, to represent the impulse face of the tooth, and then measure
+the angle _A w n_ between the lines _w n_ and _v A_, and find it to be
+approximately sixty-four degrees. We then, by a similar process, measure
+the angle _A t s'_ and find it to be approximately sixty-six degrees.
+When contact ensues between the tooth _D_ and pallet _C_ the tooth _D_
+will attack the pallet at the point where the radial line _A v_ crosses
+the tooth face. We have now explained how we can delineate a tooth or
+pallet at any point of its angular motion, and will next explain how to
+apply this knowledge in actual practice.
+
+
+PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT.
+
+To delineate our entrance pallet after one-half of the engaged tooth has
+passed the inner angle of the entrance pallet, we proceed, as in former
+illustrations, to establish the escape-wheel center at _A_, and from it
+sweep the arc _b_, to represent the pitch circle. We next sweep the
+short arcs _p s_, to represent the arcs through which the inner and
+outer angles of the entrance pallet move. Now, to comply with our
+statement as above, we must draw the tooth as if half of it has passed
+the arc _s_.
+
+To do this we draw from _A_ as a center the radial line _A j_, passing
+through the point _s_, said point _s_ being located at the intersection
+of the arcs _s_ and _b_. The tooth _D_ is to be shown as if one half of
+it has passed the point _s_; and, consequently, if we lay off three
+degrees on each side of the point _s_ and establish the points _d m_, we
+have located on the arc _b_ the angular extent of the tooth to be drawn.
+To aid in our delineations we draw from the center _A_ the radial lines
+_A d'_ and _A m'_, passing through the points _d m_. The arc _a_ is next
+drawn as in former instructions and establishes the length of the
+addendum of the escape-wheel teeth, the outer angle of our escape-wheel
+tooth being located at the intersection of the arc _a_ with the radial
+line _A d'_.
+
+As shown in Fig. 92, the impulse planes of the tooth _D_ and pallet _C_
+are in contact and, consequently, in parallel planes, as mentioned on
+page 91. It is not an easy matter to determine at exactly what degree of
+angular motion of the escape wheel such condition takes place; because
+to determine such relation mathematically requires a knowledge of higher
+mathematics, which would require more study than most practical men
+would care to bestow, especially as they would have but very little use
+for such knowledge except for this problem and a few others in dealing
+with epicycloidal curves for the teeth of wheels.
+
+For all practical purposes it will make no difference whether such
+parallelism takes place after eight or nine degrees of angular motion of
+the escape wheel subsequent to the locking action. The great point, as
+far as practical results go, is to determine if it takes place at or
+near the time the escape wheel meets the greatest resistance from the
+hairspring. We find by analysis of our drawing that parallelism takes
+place about the time when the tooth has three degrees of angular motion
+to make, and the pallet lacks about two degrees of angular movement for
+the tooth to escape. It is thus evident that the relations, as shown in
+our drawing, are in favor of the train or mainspring power over
+hairspring resistance as three is to two, while the average is only as
+eleven to ten; that is, the escape wheel in its entire effort passes
+through eleven degrees of angular motion, while the pallets and fork
+move through ten degrees. The student will thus see we have arranged to
+give the train-power an advantage where it is most needed to overcome
+the opposing influence of the hairspring.
+
+[Illustration: Fig. 92]
+
+As regards the exalted adhesion of the parallel surfaces, we fancy there
+is more harm feared than really exists, because, to take the worst view
+of the situation, such parallelism only exists for the briefest
+duration, in a practical sense, because theoretically these surfaces
+never slide on each other as parallel planes. Mathematically
+considered, the theoretical plane represented by the impulse face of
+the tooth approaches parallelism with the plane represented by the
+impulse face of the pallet, arrives at parallelism and instantly passes
+away from such parallelism.
+
+
+TO DRAW A PALLET IN ANY POSITION.
+
+As delineated in Fig. 92, the impulse planes of the tooth and pallet are
+in contact; but we have it in our power to delineate the pallet at any
+point we choose between the arcs _p s_. To describe and illustrate the
+above remark, we say the lines _B e_ and _B f_ embrace five degrees of
+angular motion of the pallet. Now, the impulse plane of the pallet
+occupies four of these five degrees. We do not draw a radial line from
+_B_ inside of the line _B e_ to show where the outer angle of the
+impulse plane commences, but the reader will see that the impulse plane
+is drawn one degree on the arc _p_ below the line _B e_. We continue the
+line _h h_ to represent the impulse face of the tooth, and measure the
+angle _B n h_ and find it to be twenty-seven degrees. Now suppose we
+wish to delineate the entrance pallet as if not in contact with the
+escape-wheel tooth--for illustration, say, we wish the inner angle of
+the pallet to be at the point _v_ on the arc _s_. We draw the radial
+line _B l_ through _v_; and if we draw another line so it passes through
+the point _v_ at an angle of twenty-seven degrees to _B l_, and continue
+said line so it crosses the arc _p_, we delineate the impulse face of
+our pallet.
+
+We measure the angle _i n B_, Fig. 92, and find it to be seventy-four
+degrees; we draw the line _v t_ to the same angle with _v B_, and we
+define the inner face of our pallet in the new position. We draw a line
+parallel with _v t_ from the intersection of the line _v y_ with the arc
+_p_, and we define our locking face. If now we revolve the lines we have
+just drawn on the center _B_ until the line _l B_ coincides with the
+line _f B_, we will find the line _y y_ to coincide with _h h_, and the
+line _v v'_ with _n i_.
+
+
+HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT.
+
+We have now instructed the reader how to delineate either tooth or
+pallet in any conceivable position in which they can be related to each
+other. Probably nothing has afforded more efficient aid to practical
+mechanics than has been afforded by the graphic solution of abstruce
+mathematical problems; and if we add to this the means of correction by
+mathematical calculations which do not involve the highest mathematical
+acquirements, we have approached pretty close to the actual requirements
+of the practical watchmaker.
+
+[Illustration: Fig. 93]
+
+To better explain what we mean, we refer the reader to Fig. 93, where we
+show preliminary drawings for delineating a lever escapement. We wish to
+ascertain by the graphic method the distance between the centers of
+action of the escape wheel and the pallet staff. We make our drawing
+very carefully to a given scale, as, for instance, the radius of the arc
+_a_ is 5". After the drawing is in the condition shown at Fig. 93 we
+measure the distance on the line _b_ between the points (centers) _A B_,
+and we thus by graphic means obtain a measure of the distance between _A
+B_. Now, by the use of trigonometry, we have the length of the line _A
+f_ (radius of the arc _a_) and all the angles given, to find the length
+of _f B_, or _A B_, or both _f B_ and _A B_. By adopting this policy we
+can verify the measurements taken from our drawings. Suppose we find by
+the graphic method that the distance between the points _A B_ is 5.78",
+and by trigonometrical computation find the distance to be 5.7762". We
+know from this that there is .0038" to be accounted for somewhere; but
+for all practical purposes either measurement should be satisfactory,
+because our drawing is about thirty-eight times the actual size of the
+escape wheel of an eighteen-size movement.
+
+
+HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED.
+
+Let us further suppose the diameter of our actual escape wheel to be
+.26", and we were constructing a watch after the lines of our drawing.
+By "lines," in this case, we mean in the same general form and ratio of
+parts; as, for illustration, if the distance from the intersection of
+the arc _a_ with the line _b_ to the point _B_ was one-fifteenth of the
+diameter of the escape wheel, this ratio would hold good in the actual
+watch, that is, it would be the one-fifteenth part of .26". Again,
+suppose the diameter of the escape wheel in the large drawing is 10" and
+the distance between the centers _A B_ is 5.78"; to obtain the actual
+distance for the watch with the escape wheel .26" diameter, we make a
+statement in proportion, thus: 10 : 5.78 :: .26 to the actual distance
+between the pivot holes of the watch. By computation we find the
+distance to be .15". These proportions will hold good in every part of
+actual construction.
+
+All parts--thickness of the pallet stones, length of pallet arms,
+etc.--bear the same ratio of proportion. We measure the thickness of the
+entrance pallet stone on the large drawing and find it to be .47"; we
+make a similar statement to the one above, thus: 10 : .47 :: .26 to the
+actual thickness of the real pallet stone. By computation we find it to
+be .0122". All angular relations are alike, whether in the large drawing
+or the small pallets to match the actual escape wheel .26" in diameter.
+Thus, in the pallet _D_, Fig. 93, the impulse face, as reckoned from _B_
+as a center, would occupy four degrees.
+
+
+MAKE A LARGE ESCAPEMENT MODEL.
+
+Reason would suggest the idea of having the theoretical keep pace and
+touch with the practical. It has been a grave fault with many writers on
+horological matters that they did not make and measure the abstractions
+which they delineated on paper. We do not mean by this to endorse the
+cavil we so often hear--"Oh, that is all right in theory, but it will
+not work in practice." If theory is right, practice must conform to it.
+The trouble with many theories is, they do not contain all the elements
+or factors of the problem.
+
+[Illustration: Fig. 94]
+
+Near the beginning of this treatise we advised our readers to make a
+large model, and described in detail the complete parts for such a
+model. What we propose now is to make adjustable the pallets and fork to
+such a model, in order that we can set them both right and wrong, and
+thus practically demonstrate a perfect action and also the various
+faults to which the lever escapement is subject. The pallet arms are
+shaped as shown at _A_, Fig. 94. The pallets _B B'_ can be made of steel
+or stone, and for all practical purposes those made of steel answer
+quite as well, and have the advantage of being cheaper. A plate of sheet
+brass should be obtained, shaped as shown at _C_, Fig. 95. This plate is
+of thin brass, about No. 18, and on it are outlined the pallet arms
+shown at Fig. 94.
+
+[Illustration: Fig. 95]
+
+[Illustration: Fig. 96]
+
+[Illustration: Fig. 97]
+
+[Illustration: Fig. 98]
+
+To make the pallets adjustable, they are set in thick disks of sheet
+brass, as shown at _D_, Figs. 95, 96 and 97. At the center of the plate
+_C_ is placed a brass disk _E_, Fig. 98, which serves to support the
+lever shown at Fig. 99. This disk _E_ is permanently attached to the
+plate _C_. The lever shown at Fig. 99 is attached to the disk _E_ by two
+screws, which pass through the holes _h h_. If we now place the brass
+pieces _D D'_ on the plate _C_ in such a way that the pallets set in
+them correspond exactly to the pallets as outlined on the plate _C_, we
+will find the action of the pallets to be precisely the same as if the
+pallet arms _A A'_, Fig. 94, were employed.
+
+[Illustration: Fig. 99]
+
+To enable us to practically experiment with and to fully demonstrate all
+the problems of lock, draw, drop, etc., we make quite a large hole in
+_C_ where the screws _b_ come. To explain, if the screws _b b_ were
+tapped directly into _C_, as they are shown at Fig. 95, we could only
+turn the disk _D_ on the screw _b_; but if we enlarge the screw hole in
+_C_ to three or four times the natural diameter, and then place the nut
+_e_ under _C_ to receive the screw _b_, we can then set the disks _D D'_
+and pallets _B B'_ in almost any relation we choose to the escape wheel,
+and clamp the pallets fast and try the action. We show at Fig. 97 a view
+of the pallet _B'_, disk _D'_ and plate _C_ (seen in the direction of
+the arrow _c_) as shown in Fig. 95.
+
+
+PRACTICAL LESSONS WITH FORK AND PALLET ACTION.
+
+It will be noticed in Fig. 99 that the hole _g_ for the pallet staff in
+the lever is oblong; this is to allow the lever to be shifted back and
+forth as relates to roller and fork action. We will not bother about
+this now, and only call attention to the capabilities of such
+adjustments when required. At the outset we will conceive the fork _F_
+attached to the piece _E_ by two screws passing through the holes _h h_,
+Fig. 99. Such an arrangement will insure the fork and roller action
+keeping right if they are put right at first. Fig. 100 will do much to
+aid in conveying a clear impression to the reader.
+
+The idea of the adjustable features of our escapement model is to show
+the effects of setting the pallets wrong or having them of bad form. For
+illustration, we make use of a pallet with the angle too acute, as shown
+at _B'''_, Fig. 101. The problem in hand is to find out by mechanical
+experiments and tests the consequences of such a change. It is evident
+that the angular motion of the pallet staff will be increased, and that
+we shall have to open one of the banking pins to allow the engaging
+tooth to escape. To trace out _all_ the consequences of this one little
+change would require a considerable amount of study, and many drawings
+would have to be made to illustrate the effects which would naturally
+follow only one such slight change.
+
+[Illustration: Fig. 100]
+
+[Illustration: Fig. 101]
+
+Suppose, for illustration, we should make such a change in the pallet
+stone of the entrance pallet; we have increased the angle between the
+lines _k l_ by (say) one and a half degrees; by so doing we would
+increase the lock on the exit pallet to three degrees, provided we were
+working on a basis of one and a half degrees lock; and if we pushed back
+the exit pallet so as to have the proper degree of lock (one and a half)
+on it, the tooth which would next engage the entrance pallet would not
+lock at all, but would strike the pallet on the impulse instead of on
+the locking face. Again, such a change might cause the jewel pin to
+strike the horn of the fork, as indicated at the dotted line _m_, Fig.
+99.
+
+Dealing with such and similar abstractions by mental process requires
+the closest kind of reasoning; and if we attempt to delineate all the
+complications which follow even such a small change, we will find the
+job a lengthy one. But with a large model having adjustable parts we
+provide ourselves with the means for the very best practical solution,
+and the workman who makes and manipulates such a model will soon master
+the lever escapement.
+
+
+QUIZ PROBLEMS IN THE DETACHED LEVER ESCAPEMENT.
+
+Some years ago a young watchmaker friend of the writer made, at his
+suggestion, a model of the lever escapement similar to the one
+described, which he used to "play with," as he termed it--that is, he
+would set the fork and pallets (which were adjustable) in all sorts of
+ways, right ways and wrong ways, so he could watch the results. A
+favorite pastime was to set every part for the best results, which was
+determined by the arc of vibration of the balance. By this sort of
+training he soon reached that degree of proficiency where one could no
+more puzzle him with a bad lever escapement than you could spoil a meal
+for him by disarranging his knife, fork and spoon.
+
+Let us, as a practical example, take up the consideration of a short
+fork. To represent this in our model we take a lever as shown at Fig.
+99, with the elongated slot for the pallet staff at _g_. To facilitate
+the description we reproduce at Fig. 102 the figure just mentioned, and
+also employ the same letters of reference. We fancy everybody who has
+any knowledge of the lever escapement has an idea of exactly what a
+"short fork" is, and at the same time it would perhaps puzzle them a
+good deal to explain the difference between a short fork and a roller
+too small.
+
+[Illustration: Fig. 102]
+
+[Illustration: Fig. 103]
+
+In our practical problems, as solved on a large escapement model, say we
+first fit our fork of the proper length, and then by the slot _g_ move
+the lever back a little, leaving the bankings precisely as they were.
+What are the consequences of this slight change? One of the first
+results which would display itself would be discovered by the guard pin
+failing to perform its proper functions. For instance, the guard pin
+pushed inward against the roller would cause the engaged tooth to pass
+off the locking face of the pallet, and the fork, instead of returning
+against the banking, would cause the guard pin to "ride the roller"
+during the entire excursion of the jewel pin. This fault produces a
+scraping sound in a watch. Suppose we attempt to remedy the fault by
+bending forward the guard pin _b_, as indicated by the dotted outline
+_b'_ in Fig. 103, said figure being a side view of Fig. 102 seen in the
+direction of the arrow _a_. This policy would prevent the engaged pallet
+from passing off of the locking face of the pallet, but would be
+followed by the jewel pin not passing fully into the fork, but striking
+the inside face of the prong of the fork at about the point indicated by
+the dotted line _m_. We can see that if the prong of the fork was
+extended to about the length indicated by the outline at _c_, the action
+would be as it should be.
+
+To practically investigate this matter to the best advantage, we need
+some arrangement by which we can determine the angular motion of the
+lever and also of the roller and escape wheel. To do this, we provide
+ourselves with a device which has already been described, but of smaller
+size, for measuring fork and pallet action. The device to which we
+allude is shown at Figs. 104, 105 and 106. Fig. 104 shows only the index
+hand, which is made of steel about 1/20" thick and shaped as shown. The
+jaws _B''_ are intended to grasp the pallet staff by the notches _e_,
+and hold by friction. The prongs _l l_ are only to guard the staff so it
+will readily enter the notch _e_. The circle _d_ is only to enable us to
+better hold the hand _B_ flat.
+
+[Illustration: Fig. 104]
+
+
+HOW TO MEASURE ESCAPEMENT ANGLES.
+
+From the center of the notches _e_ to the tip of the index hand _B'_ the
+length is 2". This distance is also the radius of the index arc _C_.
+This index arc is divided into thirty degrees, with three or four
+supplementary degrees on each side, as shown. For measuring pallet
+action we only require ten degrees, and for roller action thirty
+degrees. The arc _C_, Fig. 105, can be made of brass and is about 11/2"
+long by 1/4" wide; said arc is mounted on a brass wire about 1/8"
+diameter, as shown at _k_, Fig. 106, which is a view of Fig. 105 seen in
+the direction of the arrow _i_. This wire _k_ enters a base shown at
+_D E_, Fig. 106, which is provided with a set-screw at _j_ for holding
+the index arc at the proper height to coincide with the hand _B_.
+
+[Illustration: Fig. 105]
+
+[Illustration: Fig. 106]
+
+A good way to get up the parts shown in Fig. 106 is to take a disk of
+thick sheet brass about 1" in diameter and insert in it a piece of brass
+wire about 1/4" diameter and 3/8" long, through which drill axially a
+hole to receive the wire _k_. After the jaws _B''_ are clamped on the
+pallet staff, we set the index arc _C_ so the hand _B'_ will indicate
+the angular motion of the pallet staff. By placing the index hand _B_
+on the balance staff we can get at the exact angular duration of the
+engagement of the jewel pin in the fork.
+
+Of course, it is understood that this instrument will also measure the
+angles of impulse and lock. Thus, suppose the entire angular motion of
+the lever from bank to bank is ten degrees; to determine how much of
+this is lock and how much impulse, we set the index arc _C_ so that the
+hand _B'_ marks ten degrees for the entire motion of the fork, and when
+the escapement is locked we move the fork from its bank and notice by
+the arc _C_ how many degrees the hand indicated before it passed of its
+own accord to the opposite bank. If we have more than one and a half
+degrees of lock we have too much and should seek to remedy it. How? It
+is just the answers to such questions we propose to give by the aid of
+our big model.
+
+
+DETERMINATION OF "RIGHT" METHODS.
+
+"Be sure you are right, then go ahead," was the advice of the celebrated
+Davie Crockett. The only trouble in applying this motto to watchmaking
+is to know when you are right. We have also often heard the remark that
+there was only one right way, but any number of wrong ways. Now we are
+inclined to think that most of the people who hold to but one right way
+are chiefly those who believe all ways but their own ways are wrong.
+Iron-bound rules are seldom sound even in ethics, and are utterly
+impracticable in mechanics.
+
+We have seen many workmen who had learned to draw a lever escapement of
+a given type, and lived firm in the belief that all lever escapements
+were wrong which were not made so as to conform to this certain method.
+One workman believes in equidistant lockings, another in circular
+pallets; each strong in the idea that their particular and peculiar
+method of designing a lever escapement was the only one to be tolerated.
+The writer is free to confess that he has seen lever escapements of both
+types, that is, circular pallets and equidistant lockings, which gave
+excellent results.
+
+Another mooted point in the lever escapement is, to decide between the
+merits of the ratchet and the club-tooth escape wheel. English makers,
+as a rule, hold to the ratchet tooth, while Continental and American
+manufacturers favor the club tooth. The chief arguments in favor of the
+ratchet tooth are: (_a_) It will run without oiling the pallets; (_b_)
+in case the escape wheel is lost or broken it is more readily replaced,
+as all ratchet-tooth escape wheels are alike, either for circular
+pallets or equidistant lockings. The objections urged against it are:
+(_a_) Excessive drop; (_b_) the escape wheel, being frail, is liable to
+be injured by incompetent persons handling it; (_c_) this escapement in
+many instances does require to have the pallets oiled.
+
+
+ESCAPEMENTS COMPARED.
+
+(_a_) That a ratchet-tooth escape wheel requires more drop than a club
+tooth must be admitted without argument, as this form of tooth requires
+from one-half to three-fourths of a degree more drop than a club tooth;
+(_b_) as regards the frailty of the teeth we hold this as of small
+import, as any workman who is competent to repair watches would never
+injure the delicate teeth of an escape wheel; (_c_) ratchet-tooth lever
+escapements will occasionally need to have the pallets oiled. The writer
+is inclined to think that this defect could be remedied by proper care
+in selecting the stone (ruby or sapphire) and grinding the pallets in
+such a way that the escape-wheel teeth will not act against the
+foliations with which all crystalline stones are built up.
+
+All workmen who have had an extended experience in repair work are well
+aware that there are some lever escapements in which the pallets
+absolutely require oil; others will seem to get along very nicely
+without. This applies also to American brass club-tooth escapements;
+hence, we have so much contention about oiling pallets. The writer does
+not claim to know positively that the pallet stones are at fault because
+some escapements need oiling, but the fact must admit of explanation
+some way, and is this not at least a rational solution? All persons who
+have paid attention to crystallography are aware that crystals are built
+up, and have lines of cleavage. In the manufacture of hole jewels, care
+must be taken to work with the axis of crystallization, or a smooth hole
+cannot be obtained.
+
+The advantages claimed for the club-tooth escapement are many; among
+them may be cited (_a_) the fact that it utilizes a greater arc of
+impulse of the escape wheel; (_b_) the impulse being divided between the
+tooth and the pallet, permits greater power to be utilized at the close
+of the impulse. This feature we have already explained. It is no doubt
+true that it is more difficult to match a set of pallets with an escape
+wheel of the club-tooth order than with a ratchet tooth; still the
+writer thinks that this objection is of but little consequence where a
+workman knows exactly what to do and how to do it; in other words, is
+sure he is right, and can then go ahead intelligently.
+
+It is claimed by some that all American escape wheels of a given grade
+are exact duplicates; but, as we have previously stated, this is not
+exactly the case, as they vary a trifle. So do the pallet jewels vary a
+little in thickness and in the angles. Suppose we put in a new escape
+wheel and find we have on the entrance pallet too much drop, that is,
+the tooth which engaged this pallet made a decided movement forward
+before the tooth which engaged the exit pallet encountered the locking
+face of said pallet. If we thoroughly understand the lever escapement we
+can see in an instant if putting in a thicker pallet stone for entrance
+pallet will remedy the defect. Here again we can study the effects of a
+change in our large model better than in an escapement no larger than is
+in an ordinary watch.
+
+
+HOW TO SET PALLET STONES.
+
+There have been many devices brought forward to aid the workman in
+adjusting the pallet stones to lever watches. Before going into the
+details of any such device we should thoroughly understand exactly what
+we desire to accomplish. In setting pallet stones we must take into
+consideration the relation of the roller and fork action. As has already
+been explained, the first thing to do is to set the roller and fork
+action as it should be, without regard in a great degree to pallet
+action.
+
+[Illustration: Fig. 107]
+
+To explain, suppose we have a pallet stone to set in a full-plate
+movement. The first thing to do is to close the bankings so that the
+jewel pin will not pass out of the slot in the fork on either side; then
+gradually open the bankings until the jewel pin will pass out. This will
+be understood by inspecting Fig. 107, where _A A'_ shows a lever fork as
+if in contact with both banks, and the jewel pin, represented at _B
+B''_, just passes the angle _a c'_ of the fork. The circle described by
+the jewel pin _B_ is indicated by the arc _e_. It is well to put a
+slight friction under the balance rim, in order that we can try the
+freedom of the guard pin. As a rule, all the guard pin needs is to be
+free and not touch the roller. The entire point, as far as setting the
+fork and bankings is concerned, is to have the fork and roller action
+sound. For all ordinary lever escapements the angular motion of the
+lever banked in as just described should be _about_ ten degrees. As
+explained in former examples, if the fork action is entirely sound and
+the lever only vibrates through an arc of nine degrees, it is quite as
+well to make the pallets conform to this arc as to make the jewel pin
+carry the fork through full ten degrees. Again, if the lever vibrates
+through eleven degrees, it is as well to make the pallets conform to
+this arc.
+
+The writer is well aware that many readers will cavil at this idea and
+insist that the workman should bring all the parts right on the basis of
+ten degrees fork and lever action. In reply we would say that no
+escapement is perfect, and it is the duty of the workman to get the best
+results he can for the money he gets for the job. In the instance given
+above, of the escapement with nine degrees of lever action, when the
+fork worked all right, if we undertook to give the fork the ten degrees
+demanded by the stickler for accuracy we would have to set out the jewel
+pin or lengthen the fork, and to do either would require more time than
+it would to bring the pallets to conform to the fork and roller action.
+It is just this knowing how and the decision to act that makes the
+difference in the workman who is worth to his employer twelve or
+twenty-five dollars per week.
+
+We have described instruments for measuring the angle of fork and pallet
+action, but after one has had experience he can judge pretty nearly and
+then it is seldom necessary to measure the angle of fork action as long
+as it is near the proper thing, and then bring the pallets to match the
+escape wheel after the fork and roller action is as it should be--that
+is, the jewel pin and fork work free, the guard pin has proper freedom,
+and the fork vibrates through an arc of about ten degrees.
+
+Usually the workman can manipulate the pallets to match the escape wheel
+so that the teeth will have the proper lock and drop at the right
+instant, and again have the correct lock on the next succeeding pallet.
+The tooth should fall but a slight distance before the tooth next in
+action locks it, because all the angular motion the escape wheel makes
+except when in contact with the pallets is just so much lost power,
+which should go toward giving motion to the balance.
+
+There seems to be a little confusion in the use of the word "drop" in
+horological phrase, as it is used to express the act of parting of the
+tooth with the pallet. The idea will be seen by inspecting Fig. 108,
+where we show the tooth _D_ and pallet _C_ as about parting or dropping.
+When we speak of "banking up to the drop" we mean we set the banking
+screws so that the teeth will just escape from each pallet. By the term
+"fall" we mean the arc the tooth passes through before the next pallet
+is engaged. This action is also illustrated at Fig. 108, where the tooth
+_D_, after dropping from the pallet _C_, is arrested at the position
+shown by the dotted outline. We designate this arc by the term "fall,"
+and we measure this motion by its angular extent, as shown by the dotted
+radial lines _i f_ and _i g_. As we have explained, this fall should
+only extend through an arc of one and a half degrees, but by close
+escapement matching this arc can be reduced to one degree, or even a
+trifle less.
+
+[Illustration: Fig. 108]
+
+We shall next describe an instrument for holding the escape wheel and
+pallets while adjusting them. As shown at Fig. 107, the fork _A'_ is
+banked a little close and the jewel pin as shown would, in some
+portions, rub on _C'_, making a scraping sound.
+
+
+HOW TO MAKE AN ESCAPEMENT MATCHING TOOL.
+
+[Illustration: Fig. 109]
+
+A point has now been reached where we can use an escapement matcher to
+advantage. There are several good ones on the market, but we can make
+one very cheaply and also add our own improvements. In making one, the
+first thing to be provided is a movement holder. Any of the three-jaw
+types of such holders will answer, provided the jaws hold a movement
+plate perfectly parallel with the bed of the holder. This will be better
+understood by inspecting Fig. 109, which is a side view of a device of
+this kind seen edgewise in elevation. In this _B_ represents the bed
+plate, which supports three swing jaws, shown at _C_, Figs. 109 and 110.
+The watch plate is indicated by the parallel dotted lines _A_, Fig. 109.
+The seat _a_ of the swing jaws _C_ must hold the watch plate _A_ exactly
+parallel with the bed plate _B_. In the cheap movement holders these
+seats (_a_) are apt to be of irregular heights, and must be corrected
+for our purpose. We will take it for granted that all the seats _a_ are
+of precisely the same height, measured from _B_, and that a watch plate
+placed in the jaws _C_ will be held exactly parallel with the said bed
+_B_. We must next provide two pillars, shown at _D E_, Figs. 109 and
+111. These pillars furnish support for sliding centers which hold the
+top pivots of the escape wheel and pallet staff while we are testing the
+depths and adjusting the pallet stones. It will be understood that these
+pillars _D E_ are at right angles to the plane of the bed _B_, in order
+that the slides like _G N_ on the pillars _D E_ move exactly vertical.
+In fact, all the parts moving up and down should be accurately made, so
+as not to destroy the depths taken from the watch plate _A_. Suppose, to
+illustrate, that we place the plate _A_ in position as shown, and insert
+the cone point _n_, Figs. 109 and 112, in the pivot hole for the pallet
+staff, adjusting the slide _G N_ so that the cone point rests accurately
+in said pivot hole. It is further demanded that the parts _I H F G N D_
+be so constructed and adjusted that the sliding center _I_ moves truly
+vertical, and that we can change ends with said center _I_ and place the
+hollow cone end _m_, Fig. 112, so it will receive the top pivot of the
+pallet staff and hold it exactly upright.
+
+[Illustration: Fig. 110]
+
+[Illustration: Fig. 111]
+
+[Illustration: Fig. 112]
+
+The idea of the sliding center _I_ is to perfectly supply the place of
+the opposite plate of the watch and give us exactly the same practical
+depths as if the parts were in their place between the plates of the
+movement. The foot of the pillar _D_ has a flange attached, as shown at
+_f_, which aids in holding it perfectly upright. It is well to cut a
+screw on _D_ at _D'_, and screw the flange _f_ on such screw and then
+turn the lower face of _f_ flat to aid in having the pillar _D_
+perfectly upright.
+
+
+DETAILS OF FITTING UP ESCAPEMENT MATCHER.
+
+It is well to fit the screw _D'_ loosely, so that the flange _f_ will
+come perfectly flat with the upper surface of the base plate _B_. The
+slide _G N_ on the pillar _D_ can be made of two pieces of small brass
+tube, one fitting the pillar _D_ and the other the bar _F_. The slide _G
+N_ is held in position by the set screw _g_, and the rod _F_ by the set
+screw _h_.
+
+[Illustration: Fig. 113]
+
+[Illustration: Fig. 114]
+
+The piece _H_ can be permanently attached to the rod _F_. We show
+separate at Figs. 113 and 114 the slide _G N_ on an enlarged scale from
+Fig. 109. Fig. 114 is a view of Fig. 113 seen in the direction of the
+arrow _e_. All joints and movable parts should work free, in order that
+the center _I_ may be readily and accurately set. The parts _H F_ are
+shown separate and enlarged at Figs. 115 and 116. The piece _H_ can be
+made of thick sheet brass securely attached to _F_ in such a way as to
+bring the V-shaped groove at right angles to the axis of the rod _F_. It
+is well to make the rod _F_ about 1/8" in diameter, while the sliding
+center _I_ need not be more than 1/16" in diameter. The cone point _n_
+should be hardened to a spring temper and turned to a true cone in an
+accurately running wire chuck.
+
+[Illustration: Fig. 115]
+
+[Illustration: Fig. 116]
+
+The hollow cone end _m_ of _I_ should also be hardened, but this is best
+done after the hollow cone is turned in. The hardening of both ends
+should only be at the tips. The sliding center _I_ can be held in the
+V-shaped groove by two light friction springs, as indicated at the
+dotted lines _s s_, Fig. 115, or a flat plate of No. 24 or 25 sheet
+brass of the size of _H_ can be employed, as shown at Figs. 116 and 117,
+where _o_ represents the plate of No. 24 brass, _p p_ the small screws
+attaching the plate _o_ to _H_, and _k_ a clamping screw to fasten _I_
+in position. It will be found that the two light springs _s s_, Fig. 115
+will be the most satisfactory. The wire legs, shown at _L_, will aid in
+making the device set steady. The pillar _E_ is provided with the same
+slides and other parts as described and illustrated as attached to _D_.
+The position of the pillars _D_ and _E_ are indicated at Fig. 110.
+
+[Illustration: Fig. 117]
+
+[Illustration: Fig. 118]
+
+We will next tell how to flatten _F_ to keep _H_ exactly vertical. To
+aid in explanation, we will show (enlarged) at Fig. 118 the bar _F_
+shown in Fig. 109. In flattening such pieces to prevent turning, we
+should cut away about two-fifths, as shown at Fig. 119, which is an end
+view of Fig. 118 seen in the direction of the arrow _c_. In such
+flattening we should not only cut away two-fifths at one end, but we
+must preserve this proportion from end to end. To aid in this operation
+we make a fixed gage of sheet metal, shaped as shown at _I_, Fig. 120.
+
+[Illustration: Fig. 119]
+
+
+ESCAPEMENT MATCHING DEVICE DESCRIBED.
+
+[Illustration: Fig. 120]
+
+In practical construction we first file away about two-fifths of _F_ and
+then grind the flat side on a glass slab to a flat, even surface and, of
+course, equal thickness from end to end. We reproduce the sleeve _G_ as
+shown at Fig. 113 as if seen from the left and in the direction of the
+axis of the bar _F_. To prevent the bar _F_ turning on its axis, we
+insert in the sleeve _G_ a piece of wire of the same size as _F_ but
+with three-fifths cut away, as shown at _y_, Fig. 121. This piece _y_ is
+soldered in the sleeve _G_ so its flat face stands vertical. To give
+service and efficiency to the screw _h_, we thicken the side of the
+sleeve _F_ by adding the stud _w_, through which the screw _h_ works. A
+soft metal plug goes between the screw _h_ and the bar _F_, to prevent
+_F_ being cut up and marred. It will be seen that we can place the top
+plate of a full-plate movement in the device shown at Fig. 109 and set
+the vertical centers _I_ so the cone points _n_ will rest in the pivot
+holes of the escape wheel and pallets. It is to be understood that the
+lower side of the top plate is placed uppermost in the movement holder.
+
+[Illustration: Fig. 121]
+
+If we now reverse the ends of the centers _I_ and let the pivots of the
+escape wheel and pallet staff rest in the hollow cones of these centers
+_I_, we have the escape wheel and pallets in precisely the same position
+and relation to each other as if the lower plate was in position. It is
+further to be supposed that the balance is in place and the cock screwed
+down, although the presence of the balance is not absolutely necessary
+if the banking screws are set as directed, that is, so the jewel pin
+will just freely pass in and out of the fork.
+
+
+HOW TO SET PALLET STONES.
+
+We have now come to setting or manipulating the pallet stones so they
+will act in exact conjunction with the fork and roller. To do this we
+need to have the shellac which holds the pallet stones heated enough to
+make it plastic. The usual way is to heat a piece of metal and place it
+in close proximity to the pallets, or to heat a pair of pliers and clamp
+the pallet arms to soften the cement.
+
+Of course, it is understood that the movement holder cannot be moved
+about while the stones are being manipulated. The better way is to set
+the movement holder on a rather heavy plate of glass or metal, so that
+the holder will not jostle about; then set the lamp so it will do its
+duty, and after a little practice the setting of a pair of pallet stones
+to perfectly perform their functions will take but a few minutes. In
+fact, if the stones will answer at all, three to five minutes is as much
+time as one could well devote to the adjustment. The reader will see
+that if the lever is properly banked all he has to do is to set the
+stones so the lock, draw and drop are right, when the entire escapement
+is as it should be, and will need no further trial or manipulating.
+
+
+
+
+CHAPTER II.
+
+THE CYLINDER ESCAPEMENT.
+
+
+There is always in mechanical matters an underlying combination of
+principles and relations of parts known as "theory." We often hear the
+remark made that such a thing may be all right in theory, but will not
+work in practice. This statement has no foundation in fact. If a given
+mechanical device accords strictly with theory, it will come out all
+right practically. _Mental conceptions_ of a machine are what we may
+term their theoretical existence.
+
+When we make drawings of a machine mentally conceived, we commence its
+mechanical construction, and if we make such drawings to scale, and add
+a specification stating the materials to be employed, we leave only the
+merest mechanical details to be carried out; the brain work is done and
+only finger work remains to be executed.
+
+With these preliminary remarks we will take up the consideration of the
+cylinder escapement invented by Robert Graham about the year 1720. It is
+one of the two so-called frictional rest dead-beat escapements which
+have come into popular use, the other being the duplex. Usage, or, to
+put it in other words, experience derived from the actual manufacture of
+the cylinder escapement, settled the best forms and proportions of the
+several parts years ago. Still, makers vary slightly on certain lines,
+which are important for a man who repairs such watches to know and be
+able to carry out, in order to put them in a condition to perform as
+intended by the manufacturers. It is not knowing these lines which
+leaves the average watchmaker so much at sea. He cuts and moves and
+shifts parts about to see if dumb luck will not supply the correction he
+does not know how to make. This requisite knowledge does not consist so
+much in knowing how to file or grind as it does in discriminating where
+such application of manual dexterity is to be applied. And right here
+let us make a remark to which we will call attention again later on. The
+point of this remark lies in the question--How many of the so-called
+practical watchmakers could tell you what proportion of a cylinder
+should be cut away from the half shell? How many could explain the
+difference between the "real" and "apparent" lift? Comparatively few,
+and yet a knowledge of these things is as important for a watchmaker as
+it is for a surgeon to understand the action of a man's heart or the
+relations of the muscles to the bones.
+
+
+ESSENTIAL PARTS OF THE CYLINDER ESCAPEMENT.
+
+The cylinder escapement is made up of two essential parts, viz.: the
+escape wheel and the cylinder. The cylinder escape wheel in all modern
+watches has fifteen teeth, although Saunier, in his "Modern Horology,"
+delineates a twelve-tooth wheel for apparently no better reason than
+because it was more easily drawn. We, in this treatise, will consider
+both the theoretical action and the practical construction, but more
+particularly the repair of this escapement in a thorough and complete
+manner.
+
+At starting out, we will first agree on the names of the several parts
+of this escapement, and to aid us in this we will refer to the
+accompanying drawings, in which Fig. 122 is a side elevation of a
+cylinder complete and ready to have a balance staked on to it. Fig. 123
+shows the cylinder removed from the balance collet. Figs. 124 and 125
+show the upper and lower plugs removed from the cylinder. Fig. 126 is a
+horizontal section of Fig. 122 on the line _i_. Fig. 127 is a side view
+of one tooth of a cylinder escape wheel as if seen in the direction of
+the arrow _f_ in Fig. 126. Fig. 128 is a top view of two teeth of a
+cylinder escape wheel. The names of the several parts usually employed
+are as follows:
+
+         _A._--Upper or Main Shell.
+        _A'._--Half Shell.
+       _A''._--Column.
+      _A'''._--Small Shell.
+  _B B' B''._--Balance Collet.
+         _G._--Upper Plug.
+         _H._--Lower Plug.
+         _g._--Entrance Lip of Cylinder.
+         _h._--Exit Lip of Cylinder.
+         _c._--Banking Slot.
+         _C._--Tooth.
+         _D._--U arm.
+         _E._--Stalk of Pillar.
+         _I._--U space.
+         _l._--Point of Tooth.
+         _k._--Heel of Tooth.
+
+The cylinder escapement has two engagements or actions, during the
+passage of each tooth; that is, one on the outside of the cylinder and
+one on the inside of the shell. As we shall show later on, the cylinder
+escapement is the only positively dead-beat escapement in use, all
+others, even the duplex, having a slight recoil during the process of
+escaping.
+
+When the tooth of a cylinder escape wheel while performing its
+functions, strikes the cylinder shell, it rests dead on the outer or
+inner surface of the half shell until the action of the balance spring
+has brought the lip of the cylinder so that the impulse face of the
+tooth commences to impart motion or power to the balance.
+
+[Illustration: Fig. 122]
+
+[Illustration: Fig. 123]
+
+[Illustration: Fig. 124]
+
+[Illustration: Fig. 125]
+
+[Illustration: Fig. 126]
+
+[Illustration: Fig. 127]
+
+[Illustration: Fig. 128]
+
+Most writers on horological matters term this act the "lift," which name
+was no doubt acquired when escapements were chiefly confined to pendulum
+clocks. Very little thought on the matter will show any person who
+inspects Fig. 126 that if the tooth _C_ is released or escapes from the
+inside of the half shell of the cylinder _A_, said cylinder must turn or
+revolve a little in the direction of the arrow _j_, and also that the
+next succeeding tooth of the escape wheel will engage the cylinder on
+the outside of the half shell, falling on the dead or neutral portion of
+said cylinder, to rest until the hairspring causes the cylinder to turn
+in the opposite direction and permitting the tooth now resting on the
+outside of the cylinder to assume the position shown on the drawing.
+
+The first problem in our consideration of the theoretical action of the
+cylinder escapement, is to arrange the parts we have described so as to
+have these two movements of the escape wheel of like angular values. To
+explain what we mean by this, we must premise by saying, that as our
+escape wheel has fifteen teeth and we make each tooth give two impulses
+in alternate directions we must arrange to have these half-tooth
+movements exactly alike, or, as stated above, of equal angular values;
+and also each impulse must convey the same power or force to the
+balance. All escape wheels of fifteen teeth acting by half impulses must
+impel the balance during twelve degrees (minus the drop) of escape-wheel
+action; or, in other words, when a tooth passes out of the cylinder from
+the position shown at Fig. 126, the form of the impulse face of the
+tooth and the shape of the exit lip of the cylinder must be such during
+twelve degrees (less the drop) of the angular motion of the escape
+wheel. The entire power of such an escape wheel is devoted to giving
+impulse to the balance.
+
+The extent of angular motion of the balance during such impulse is, as
+previously stated, termed the "lifting angle." This "lifting angle" is
+by horological writers again divided into real and apparent lifts. This
+last division is only an imaginary one, as the real lift is the one to
+be studied and expresses the arc through which the impulse face of the
+tooth impels the balance during the act of escaping, and so, as we shall
+subsequently show, should no more be counted than in the detached lever
+escapement, where a precisely similar condition exists, but is never
+considered or discussed.
+
+We shall for the present take no note of this lifting angle, but confine
+ourselves to the problem just named, of so arranging and designing our
+escape-wheel teeth and cylinder that each half of the tooth space shall
+give equal impulses to the balance with the minimum of drop. To do this
+we will make a careful drawing of an escape-wheel tooth and cylinder on
+an enlarged scale; our method of making such drawings will be on a new
+and original system, which is very simple yet complete.
+
+
+DRAWING THE CYLINDER ESCAPEMENT.
+
+All horological--and for that matter all mechanical--drawings are based
+on two systems of measurements: (1) Linear extent; (2) angular movement.
+For the first measurement we adopt the inch and its decimals; for the
+second we adopt degrees, minutes and seconds. For measuring the latter
+the usual plan is to employ a protractor, which serves the double
+purpose of enabling us to lay off and delineate any angle and also to
+measure any angle obtained by the graphic method, and it is thus by this
+graphic method we propose to solve very simply some of the most
+abstruce problems in horological delineations. As an instance, we
+propose to draw our cylinder escapement with no other instruments than a
+steel straight-edge, showing one-hundredths of an inch, and a pair of
+dividers; the degree measurement being obtained from arcs of sixty
+degrees of radii, as will be explained further on.
+
+In describing the method for drawing the cylinder escapement we shall
+make a radical departure from the systems usually laid down in
+text-books, and seek to simplify the formulas which have heretofore been
+given for such delineations. In considering the cylinder escapement we
+shall pursue an analytical course and strive to build up from the
+underlying principles. In the drawings for this purpose we shall
+commence with one having an escape wheel of 10" radius, and our first
+effort will be the primary drawing shown at Fig. 129. Here we establish
+the point _A_ for the center of our escape wheel, and from this center
+sweep the short arc _a a_ with a 10" radius, to represent the
+circumference of our escape wheel. From _A_ we draw the vertical line
+_A B_, and from the intersection of said line with the arc _a a_ we lay
+off twelve degree spaces on each side of the line _A B_ on said arc _a_
+and establish the points _b c_. From _A_ as a center we draw through
+the points _b c_ the radial lines _b' c'_.
+
+To define the face of the incline to the teeth we set our dividers to
+the radius of any of the convenient arcs of sixty degrees which we have
+provided, and sweep the arc _t t_. From the intersection of said arc
+with the line _A b'_ we lay off on said arc sixty-four degrees and
+establish the point _g_ and draw the line _b g_. Why we take sixty-four
+degrees for the angle _A b g_ will be explained later on, when we are
+discussing the angular motion of the cylinder. By dividing the eleventh
+degree from the point _b_ on the arc _a a_ into thirds and taking two of
+them, we establish the point _y_ and draw the radial line _A y'_. Where
+this line _A y'_ intersects the line _b g_ we name the point _n_, and in
+it is located the point of the escape-wheel tooth. That portion of the
+line _b g_ which lies between the points _b_ and _n_ represents the
+measure of the inner diameter of the cylinder, and also the length of
+the chord of the arc which rounds the impulse face of the tooth. We
+divide the space _b n_ into two equal portions and establish the point
+_e_, which locates the position of the center of the cylinder. From _A_
+as a center and through the point _e_ we sweep the arc _e' e'_, and it
+is on this line that the points establishing the center of the cylinder
+will in every instance be located. From _A_ as a center, through the
+point _n_ we sweep the arc _k_, and on this line we locate the points of
+the escape-wheel teeth. For delineating the curved impulse faces of the
+escape-wheel teeth we draw from the point _e_ and at right angles to the
+line _b g_ the line _e o_. We next take in our dividers the radius of
+the arc _k_, and setting one leg at either of the points _b_ or _n_,
+establish with the other leg the point _p'_ on the line _e o_, and from
+the point _p'_ as a center we sweep the arc _b v n_, which defines the
+curve of the impulse faces of the teeth. From _A_ as a center through
+the point _p'_ we sweep the arc _p_, and in all instances where we
+desire to delineate the curved face of a tooth we locate either the
+position of the point or the heel of such tooth, and setting one leg of
+our dividers at such point, the other leg resting on the arc _p_, we
+establish the center from which to sweep the arc defining the face of
+said tooth.
+
+
+ADVANTAGES GAINED IN SHAPING.
+
+The reason for giving a curved form to the impulse face of the teeth of
+cylinder escape wheels are somewhat intricate, and the problem involves
+several factors. That there are advantages in so shaping the incline or
+impulse face is conceded, we believe, by all recent manufacturers. The
+chief benefit derived from such curved impulse faces will be evident
+after a little thought and study of the situation and relation of parts
+as shown in Fig. 129. It will be seen on inspection that the angular
+motion imparted to the cylinder by the impulse face of the tooth when
+curved as shown, is greater during the first half of the twelve degrees
+of escape-wheel action than during the last half, thus giving the escape
+wheel the advantage at the time the balance spring increases its
+resistance to the passage of the escape-wheel tooth across the lip of
+the cylinder. Or, in other words, as the ratio of resistance of the
+balance spring increases, in a like ratio the curved form of the impulse
+face of the tooth gives greater power to the escape-wheel action in
+proportion to the angular motion of the escape wheel. Hence, in actual
+service it is found that cylinder watches with curved impulse planes to
+the escape-wheel teeth are less liable to set in the pocket than the
+teeth having straight impulse faces.
+
+
+THE OUTER DIAMETER OF THE CYLINDER.
+
+[Illustration: Fig. 129]
+
+To define the remainder of the form of our escape-wheel tooth we will
+next delineate the heel. To do this we first define the outer diameter
+of our cylinder, which is the extent from the point _n_ to _c_, and
+after drawing the line _n c_ we halve the space and establish the point
+_x_, from which point as a center we sweep the circle _w w_, which
+defines the outer circumference of our cylinder. With our dividers set
+to embrace the extent from the point _n_ to the point _c_ we set one leg
+at the point _b_, and with the other leg establish on the arc _k_ the
+point _h_. We next draw the line _b h_, and from the point _b_ draw the
+line _b f_ at right angle to the line _b h_. Our object for drawing
+these lines is to define the heel of our escape-wheel tooth by a right
+angle line tangent to the circle _w_, from the point _b_; which circle
+_w_ represents the curve of the outer circumference of the cylinder. We
+shape the point of the tooth as shown to give it the proper stability,
+and draw the full line _j_ to a curve from the center _A_. We have now
+defined the form of the upper face of the tooth. How to delineate the U
+arms will be taken up later on, as, in the present case, the necessary
+lines would confuse our drawing.
+
+We would here take the opportunity to say that there is a great latitude
+taken by makers as regards the extent of angular impulse given to the
+cylinder, or, as it is termed, the "actual lift." This latitude governs
+to a great extent the angle _A b g_, which we gave as sixty-four degrees
+in our drawing. It is well to understand that the use of sixty-four
+degrees is based on no hard-and-fast rules, but varies back and forth,
+according as a greater or lesser angle of impulse or lift is employed.
+
+In practical workshop usage the impulse angle is probably more easily
+estimated by the ratio between the diameter of the cylinder and the
+measured (by lineal measure) height of the impulse plane. Or, to be more
+explicit, we measure the radial extent from the center _A_ between the
+arcs _a k_ on the line _A b_, and use this for comparison with the outer
+diameter of the cylinder.
+
+We can readily see that as we increase the height of the heel of the
+impulse face of our tooth we must also increase the angle of impulse
+imparted to the cylinder. With the advantages of accurate micrometer
+calipers now possessed by the horological student it is an easy matter
+to get at the angular extent of the real lift of any cylinder. The
+advantage of such measuring instruments is also made manifest in
+determining when the proper proportion of the cylinder is cut away for
+the half shell.
+
+[Illustration: Fig. 130]
+
+In the older methods of watchmaking it was a very common rule to say,
+let the height of the incline of the tooth be one-seventh of the outer
+diameter of the cylinder, and at the same time the trade was furnished
+with no tools except a clumsy douzieme gage; but with micrometer
+calipers which read to one-thousandths of an inch such rules can be
+definitely carried into effect and not left to guess work. Let us
+compare the old method with the new: Suppose we have a new cylinder to
+put in; we have the old escape wheel, but the former cylinder is gone.
+The old-style workman would take a round broach and calculate the size
+of the cylinder by finding a place where the broach would just go
+between the teeth, and the size of the broach at this point was supposed
+to be the outer diameter of the cylinder. By our method we measure the
+diameter of the escape wheel in thousandths of an inch, and from this
+size calculate exactly what the diameter of the new cylinder should be
+in thousandths of an inch. Suppose, to further carry out our comparison,
+the escape wheel which is in the watch has teeth which have been stoned
+off to permit the use of a cylinder which was too small inside, or, in
+fact, of a cylinder too small for the watch: in this case the broach
+system would only add to the trouble and give us a cylinder which would
+permit too much inside drop.
+
+
+DRAWING A CYLINDER.
+
+We have already instructed the pupil how to delineate a cylinder escape
+wheel tooth and we will next describe how to draw a cylinder. As already
+stated, the center of the cylinder is placed to coincide with the center
+of the chord of the arc which defines the impulse face of the tooth.
+Consequently, if we design a cylinder escape wheel tooth as previously
+described, and setting one leg of our compasses at the point _e_ which
+is situated at the center of the chord of the arc which defines the
+impulse face of the tooth and through the points _d_ and _b_ we define
+the inside of our cylinder. We next divide the chord _d b_ into eight
+parts and set our dividers to five of these parts, and from _e_ as a
+center sweep the circle _h_ and define the outside of our cylinder. From
+_A_ as a center we draw the radial line _A e'_. At right angles to the
+line _A e'_ and through the point _e_ we draw the line from _e_ as a
+center, and with our dividers set to the radius of any of the convenient
+arcs which we have divided into sixty degrees, we sweep the arc _i_.
+Where this arc intersects the line _f_ we term the point _k_, and from
+this point we lay off on the arc _i_ 220 degrees, and draw the line
+_l e l'_, which we see coincides with the chord of the impulse face of the
+tooth. We set our dividers to the same radius by which we sweep the arc
+_i_ and set one leg at the point _b_ for a center and sweep the arc
+_j'_. If we measure this arc from the point _j'_ to intersection of said
+arc _j'_ with the line _l_ we will find it to be sixty-four degrees,
+which accounts for our taking this number of degrees when we defined the
+face of our escape-wheel tooth, Fig. 129.
+
+There is no reason why we should take twenty-degrees for the angle _k e
+l_ except that the practical construction of the larger sizes of
+cylinder watches has established the fact that this is about the right
+angle to employ, while in smaller watches it frequently runs up as high
+as twenty-five. Although the cylinder is seemingly a very simple
+escapement, it is really a very abstruce one to follow out so as to
+become familiar with all of its actions.
+
+
+THE CYLINDER PROPER CONSIDERED.
+
+[Illustration: Fig. 131]
+
+We will now proceed and consider the cylinder proper, and to aid us in
+understanding the position and relation of the parts we refer to Fig.
+131, where we repeat the circles _d_ and _h_, shown in Fig. 130, which
+represents the inside and outside of the cylinder. We have here also
+repeated the line _f_ of Fig. 130 as it cuts the cylinder in half, that
+is, divides it into two segments of 180 degrees each. If we conceive of
+a cylinder in which just one-half is cut away, that is, the lips are
+bounded by straight radial lines, we can also conceive of the relation
+and position of the parts shown in Fig. 130. The first position of which
+we should take cognizance is, the tooth _D_ is moved back to the left so
+as to rest on the outside of our cylinder. The cylinder is also supposed
+to stand so that the lips correspond to the line _f_. On pressing the
+tooth _D_ forward the incline of the tooth would attack the entrance
+lip of the cylinder at just about the center of the curved impulse face,
+imparting to the cylinder twenty degrees of angular motion, but the
+point of the tooth at _d_ would exactly encounter the inner angle of the
+exit lip, and of course the cylinder would afford no rest for the tooth;
+hence, we see the importance of not cutting away too much of the half
+shell of the cylinder.
+
+But before we further consider the action of the tooth _D_ in its action
+as it passes the exit lip of the cylinder we must finish with the action
+of the tooth on the entrance lip. A very little thought and study of
+Fig. 130 will convince us that the incline of the tooth as it enters the
+cylinder will commence at _t_, Fig. 130, but at the close of the action
+the tooth parts from the lip on the inner angle. Now it is evident that
+it would require greater force to propel the cylinder by its inner angle
+than by the outer one. To compensate for this we round the edge of the
+entrance lip so that the action of the tooth instead of commencing on
+the outer angle commences on the center of the edge of the entrance lip
+and also ends its action on the center of the entrance lip. To give
+angular extent enough to the shell of the cylinder to allow for rounding
+and also to afford a secure rest for the tooth inside the cylinder, we
+add six degrees to the angular extent of the entrance lip of the
+cylinder shell, as indicated on the arc _o'_, Fig. 131, three of these
+degrees being absorbed for rounding and three to insure a dead rest for
+the tooth when it enters the cylinder.
+
+
+WHY THE ANGULAR EXTENT IS INCREASED.
+
+Without rounding the exit lip the action of the tooth on its exit would
+be entirely on the inner angle of the shell. To obviate this it is the
+usual practice to increase the angular extent of the cylinder ten
+degrees, as shown on the arc _o'_ between the lines _f_ and _p_, Fig.
+131. Why we should allow ten degrees on the exit lip and but six degrees
+on the entrance lip will be understood by observing Fig. 130, where the
+radial lines _s_ and _r_ show the extent of angular motion of the
+cylinder, which would be lost if the tooth commenced to act on the inner
+angle and ended on the outer angle of the exit lip. This arc is a little
+over six degrees, and if we add a trifle over three degrees for rounding
+we would account for the ten degrees between the lines _f_ and _p_, Fig.
+131. It will now be seen that the angular extent is 196 degrees. If we
+draw the line _w_ we can see in what proportion the measurement should
+be made between the outer diameter of the cylinder and the measure of
+the half shell. It will be seen on measurement that the distance between
+the center _e_ and the line _w_ is about one-fifteenth part of the outer
+diameter of the cylinder and consequently with a cylinder which measures
+45/1000 of an inch in diameter, now the half shell should measure half
+of the entire diameter of the cylinder plus one-fifteenth part of such
+diameter, or 251/2 thousandths of an inch.
+
+After these proportions are understood and the drawing made, the eye
+will get accustomed to judging pretty near what is required; but much
+the safer plan is to measure, where we have the proper tools for doing
+so. Most workmen have an idea that the depth or distance at which the
+cylinder is set from the escape wheel is a matter of adjustment; while
+this is true to a certain extent, still there is really only one
+position for the center of the cylinder, and that is so that the center
+of the pivot hole coincides exactly with the center of the chord to the
+curve of the impulse face of the tooth or the point _e_, Fig. 130. Any
+adjustment or moving back and forth of the chariot to change the depth
+could only be demanded where there was some fault existing in the
+cylinder or where it had been moved out of its proper place by some
+genius as an experiment in cylinder depths. It will be evident on
+observing the drawing at Fig. 131 that when the cylinder is performing
+an arc of vibration, as soon as the entrance lip has passed the point
+indicated by the radial line _e x_ the point of the escape-wheel tooth
+will commence to act on the cylinder lip and continue to do so through
+an arc of forty degrees, or from the lines _x_ to _l_.
+
+
+MAKING A WORKING MODEL.
+
+To practically study the action of the cylinder escapement it is well to
+make a working model. It is not necessary that such a model should
+contain an entire escape wheel; all that is really required is two teeth
+cut out of brass of the proper forms and proportions and attached to the
+end of an arm 4-7/8" long with studs riveted to the U arms to support
+the teeth. This U arm is attached to the long arm we have just
+mentioned. A flat ring of heavy sheet brass is shaped to represent a
+short transverse section of a cylinder. This segment is mounted on a
+yoke which turns on pivots. In making such a model we can employ all the
+proportions and exact forms of the larger drawings made on a ten-inch
+radius. Such a model becomes of great service in learning the
+importance of properly shaping the lips of the cylinder. And right here
+we beg to call attention to the fact that in the ordinary repair shop
+the proper shape of cylinder lips is entirely neglected.
+
+
+PROPER SHAPE OF CYLINDER LIPS.
+
+The workman buys a cylinder and whether the proper amount is cut away
+from the half shell, or the lips, the correct form is entirely ignored,
+and still careful attention to the form of the cylinder lips adds full
+ten per cent. to the efficiency of the motive force as applied to the
+cylinder. In making study drawings of the cylinder escapement it is not
+necessary to employ paper so large that we can establish upon it the
+center of the arc which represents the periphery of our escape wheel, as
+we have at our disposal two plans by which this can be obviated. First,
+placing a bit of bristol board on our drawing-board in which we can set
+one leg of our dividers or compasses when we sweep the peripheral arc
+which we use in our delineations; second, making three arcs in brass or
+other sheet metal, viz.: the periphery of the escape wheel, the arc
+passing through the center of the chord of the arc of the impulse face
+of the tooth, and the arc passing through the point of the escape-wheel
+tooth. Of these plans we favor the one of sticking a bit of cardboard on
+the drawing board outside of the paper on which we are making our
+drawing.
+
+[Illustration: Fig. 132]
+
+At Fig. 132 we show the position and relation of the several parts just
+as the tooth passes into the shell of the cylinder, leaving the lip of
+the cylinder just as the tooth parted with it. The half shell of the
+cylinder as shown occupies 196 degrees or the larger arc embraced
+between the radial lines _k_ and _l_. In drawing the entrance lip the
+acting face is made almost identical with a radial line except to round
+the corners for about one-third the thickness of the cylinder shell. No
+portion, however, of the lip can be considered as a straight line, but
+might be described as a flattened curve.
+
+[Illustration: Fig. 133]
+
+A little study of what would be required to get the best results after
+making such a drawing will aid the pupil in arriving at the proper
+shape, especially when he remembers that the thickness of the cylinder
+shell of a twelve-line watch is only about five one-thousandths of an
+inch. But because the parts are small we should not shirk the problem of
+getting the most we possibly can out of a cylinder watch.
+
+The extent of arc between the radial lines _k f_, as shown in Fig. 132,
+is four degrees. Although in former drawings we showed the angular
+extent added as six degrees, as we show the lip _m_ in Fig. 132, two
+degrees are lost in rounding. The space _k f_ on the egress or exit side
+is intended to be about four degrees, which shows the extent of lock. We
+show at Fig. 133 the tooth _D_ just having passed out of the cylinder,
+having parted with the exit lip _p_.
+
+In making this drawing we proceed as with Fig. 132 by establishing a
+center for our radius of 10" outside of our drawing paper and drawing
+the line _A A_ to such center and sweeping the arcs _a b c_. We
+establish the point _e_, which represents the center of our cylinder, as
+before. We take the space to represent the radial extent of the outside
+of our cylinder in our dividers and from _e_ as a center sweep a fine
+pencil line, represented by the dotted line _t_ in our drawing; and
+where this circle intersects the arc _a_ we name it the point _s_; and
+it is at this point the heel of our escape-wheel tooth must part with
+the exit lip of the cylinder. From _e_ as a center and through the point
+_s_ we draw the line _e l''_. With our dividers set to the radius of any
+convenient arc which we have divided into degrees, we sweep the short
+arc _d'_. The intersection of this arc with the line _e l''_ we name the
+point _u_; and from _e_ as a center we draw the radial line _e u f'_. We
+place the letter _f''_ in connection with this line because it (the
+line) bears the same relations to the half shell of the cylinder shown
+in Fig. 133 that the line _f_ does to the half shell (_D_) shown in Fig.
+132. We draw the line _f'' f'''_, Fig. 133, which divides the cylinder
+into two segments of 180 degrees each. We take the same space in our
+dividers with which we swept the interior of the cylinder in Fig. 132
+and sweep the circle _v_, Fig. 133. From _e_ as a center we sweep the
+short arc _d''_, Fig. 133, and from its intersection of the line _f''_
+we lay off six degrees on said arc _d''_ and draw the line _e' k''_,
+which defines the angular extent of our entrance lip to the half shell
+of the cylinder in Fig. 133. We draw the full lines of the cylinder as
+shown.
+
+We next delineate the heel of the tooth which has just passed out of the
+cylinder, as shown at _D'_, Fig. 133. We now have a drawing showing the
+position of the half shell of the cylinder just as the tooth has passed
+the exit lip. This drawing also represents the position of the half
+shell of the cylinder when the tooth rests against it on the outside. If
+we should make a drawing of an escape-wheel tooth shaped exactly as the
+one shown at Fig. 132 and the point of the tooth resting at _x_, we
+would show the position of a tooth encountering the cylinder after a
+tooth which has been engaged in the inside of the shell has passed out.
+By following the instructions now given, we can delineate a tooth in any
+of its relations with the cylinder shell.
+
+
+DELINEATING AN ESCAPE-WHEEL TOOTH WHILE IN ACTION.
+
+We will now go through the operation of delineating an escape-wheel
+tooth while in action. The position we shall assume is the one in which
+the cylinder and escape-wheel tooth are in the relation of the passage
+of half the impulse face of the tooth into the cylinder. To do this is
+simple enough: We first produce the arcs _a b c_, Fig. 133, as directed,
+and then proceed to delineate a tooth as in previous instances. To
+delineate our cylinder in the position we have assumed above, we take
+the space between the points _e d_ in our dividers and setting one leg
+at _d_ establish the point _g_, to represent the center of our cylinder.
+If we then sweep the circle _h_ from the center of _g_ we define the
+inner surface of the shell of our cylinder.
+
+Strictly speaking, we have not assumed the position we stated, that is,
+the impulse face of the tooth as passing half way into the cylinder. To
+comply strictly with our statement, we divide the chord of the impulse
+face of the tooth _A_ into eight equal spaces, as shown. Now as each of
+these spaces represent the thickness of the cylinder, if we take in our
+dividers four of these spaces and half of another, we have the radius of
+a circle passing the center of the cylinder shell. Consequently, if with
+this space in our dividers we set the leg at _d_, we establish on the
+arc _b_ the point _i_. We locate the center of our cylinder when
+one-half of an entering tooth has passed into the cylinder. If now from
+the new center with our dividers set at four of the spaces into which we
+have divided the line _e f_ we can sweep a circle representing the inner
+surface of the cylinder shell, and by setting our dividers to five of
+these spaces we can, from _i_ as a center, sweep an arc representing the
+outside of the cylinder shell. For all purposes of practical study the
+delineation we show at Fig. 133 is to be preferred, because, if we carry
+out all the details we have described, the lines would become confused.
+We set our dividers at five of the spaces on the line _e f_ and from _g_
+as a center sweep the circle _j_, which delineates the outer surface of
+our cylinder shell.
+
+Let us now, as we directed in our former instructions, draw a flattened
+curve to represent the acting surface of the entrance lip of our
+cylinder as if it were in direct contact with the impulse face of the
+tooth. To delineate the exit lip we draw from the center _g_, Fig. 134,
+to the radial line _g k_, said line passing through the point of contact
+between the tooth and entrance lip of the cylinder. Let us next continue
+this line on the opposite side of the point _g_, as shown at _g k'_, and
+we thus bisect the cylinder shell into two equal parts of 180 degrees
+each. As we previously explained, the entire extent of the cylinder half
+shell is 196 degrees. We now set our dividers to the radius of any
+convenient arc which we have divided into degrees, and from _g_ as a
+center sweep the short arc _l l_, and from the intersection of this arc
+with the line _g k'_ we lay off sixteen degrees on the said arc _l_ and
+establish the point _n_, from _g_ as a center draw the radial line _g
+n'_. Take ten degrees from the same parent arc and establish the point
+_m_, then draw the line _g m'_. Now the arc on the circles _h j_ between
+the lines _g n'_ and _g m_ limits the extent of the exit lip of the
+cylinder and the arc between the lines _g k'_ and _g m'_ represents the
+locking surface of the cylinder shell.
+
+[Illustration: Fig. 134]
+
+To delineate the U arms we refer to Fig. 135. Here, again, we draw the
+arc _a b c_ and delineate a tooth as before. From the point _e_ located
+at the heel of the tooth we draw the radial line _e e'_. From the point
+_e_ we lay off on the arc _a_ five degrees and establish the point _p_;
+we halve this space and draw the short radial line _p' s'_ and _p s_.
+From the point _e_ on the arc _A_ we lay off twenty-four degrees and
+establish the point _t_, which locates the heel of the next tooth in
+advance of _A_. At two and a half degrees to the right of the point _t_
+we locate the point _r_ and draw the short radial line _r s_. On the arc
+_b_ and half way between the lines _p s_ and _r s_, we establish the
+point _u_, and from it as a center we sweep the arc _v_ defining the
+curve of the U arms.
+
+We have now given minute instructions for drawing a cylinder escapement
+in all its details except the extent of the banking slot of the
+cylinder, which is usually made to embrace an angular extent of 270
+degrees; consequently, the pillar of the cylinder will not measure more
+than ninety degrees of angular extent.
+
+There is no escapement constructed where carefully-made drawings tend
+more to perfect knowledge of the action than the cylinder. But it is
+necessary with the pupil to institute a careful analysis of the actions
+involved. In writing on a subject of this kind it is extremely
+perplexing to know when to stop; not that there is so much danger of
+saying too much as there is not having the words read with attention.
+
+As an illustration, let us consider the subject of depth between the
+cylinder and the escape wheel. As previously stated, 196 degrees of
+cylinder shell should be employed; but suppose we find a watch in which
+the half shell has had too much cut away, so the tooth on entering the
+half shell after parting with the entrance lip does not strike dead on
+the inside of the shell, but encounters the edge of the exit lip. In
+this case the impulse of the balance would cause the tooth to slightly
+retrograde and the watch would go but would lack a good motion. In such
+an instance a very slight advance of the chariot would remedy the
+fault--not perfectly remedy it, but patch up, so to speak--and the watch
+would run.
+
+[Illustration: Fig. 135]
+
+In this day, fine cylinder watches are not made, and only the common
+kind are met with, and for this reason the student should familiarize
+himself with all the imaginary faults which could occur from bad
+construction. The best way to do this is to delineate what he (the
+student) knows to be a faulty escapement, as, for instance, a cylinder
+in which too much of the half shell is cut away; but in every instance
+let the tooth be of the correct form. Then delineate an escapement in
+which the cylinder is correct but the teeth faulty; also change the
+thickness of the cylinder shell, so as to make the teeth too short. This
+sort of practice makes the pupil think and study and he will acquire a
+knowledge which will never be forgotten, but always be present to aid
+him in the puzzles to which the practical watchmaker is every day
+subject.
+
+The ability to solve these perplexing problems determines in a great
+degree the worth of a man to his employer, in addition to establishing
+his reputation as a skilled workman. The question is frequently asked,
+"How can I profitably employ myself in spare time?" It would seem that a
+watchmaker could do no better than to carefully study matters
+horological, striving constantly to attain a greater degree of
+perfection, for by so doing his earning capacity will undoubtedly be
+increased.
+
+
+
+
+CHAPTER III.
+
+THE CHRONOMETER ESCAPEMENT.
+
+
+Undoubtedly "the detent," or, as it is usually termed, "the chronometer
+escapement," is the most perfect of any of our portable time measurers.
+Although the marine chronometer is in a sense a portable timepiece,
+still it is not, like a pocket watch, capable of being adjusted to
+positions. As we are all aware, the detent escapement is used in fine
+pocket watches, still the general feeling of manufacturers is not
+favorable to it. Much of this feeling no doubt is owing to the
+mechanical difficulties presented in repairing the chronometer
+escapements when the detent is broken, and the fact that the spring
+detent could not be adjusted to position. We shall have occasion to
+speak of position adjustments as relate to the chronometer escapement
+later on.
+
+
+ADVANTAGES OF THE CHRONOMETER.
+
+We will proceed now to consider briefly the advantages the detent
+escapement has over all others. It was soon discovered in constructing
+portable timepieces, that to obtain the best results the vibrations of
+the balance should be as free as possible from any control or influence
+except at such times as it received the necessary impulse to maintain
+the vibrations at a constant arc. This want undoubtedly led to the
+invention of the detent escapement. The early escapements were all
+frictional escapements, i.e., the balance staff was never free from
+the influence of the train. The verge escapement, which was undoubtedly
+the first employed, was constantly in contact with the escape wheel, and
+was what is known as a "recoiling beat," that is, the contact of the
+pallets actually caused the escape wheel to recoil or turn back. Such
+escapements were too much influenced by the train, and any increase in
+power caused the timepiece to gain. The first attempt to correct this
+imperfection led to the invention and introduction of the fusee, which
+enabled the watchmaker to obtain from a coiled spring nearly equal power
+during the entire period of action. The next step in advance was the
+"dead-beat escapement," which included the cylinder and duplex. In these
+frictional escapements the balance staff locked the train while the
+balance performed its arc of vibration.
+
+FRICTIONAL ESCAPEMENTS IN HIGH FAVOR.
+
+These frictional escapements held favor with many eminent watchmakers
+even after the introduction of the detached escapements. It is no more
+than natural we should inquire, why? The idea with the advocates of the
+frictional rest escapements was, the friction of the tooth acted as a
+_corrective_, and led no doubt to the introduction of going-barrel
+watches. To illustrate, suppose in a cylinder watch we increase the
+motive power, such increase of power would not, as in the verge
+escapement, increase the rapidity of the vibrations; it might, in fact,
+cause the timepiece to run slower from the increased friction of the
+escape-wheel tooth on the cylinder; also, in the duplex escapement the
+friction of the locking tooth on the staff retards the vibrations.
+
+Dr. Hooke, the inventor of the balance spring, soon discovered it could
+be manipulated to isochronism, i.e., so arcs of different extent would
+be formed in equal time. Of course, the friction-rest escapement
+requiring a spring to possess different properties from one which would
+be isochronal with a perfectly detached escapement, these two frictional
+escapements also differing, the duplex requiring other properties from
+what would isochronize a spring for a cylinder escapement. Although
+pocket watches with duplex and cylinder escapements having balances
+compensated for heat and cold and balance springs adjusted to
+isochronism gave very good results, careful makers were satisfied that
+an escapement in which the balance was detached and free to act during
+the greater proportion of the arc of vibration and uncontrolled by any
+cause, would do still better, and this led to the detent escapement.
+
+
+FAULTS IN THE DETENT ESCAPEMENT.
+
+As stated previously, the detent escapement having pronounced faults in
+positions which held it back, it is probable it would never have been
+employed in pocket watches to any extent if it had not acquired such a
+high reputation in marine chronometers. Let us now analyze the
+influences which surround the detent escapement in a marine chronometer
+and take account of the causes which are combined to make it an accurate
+time measurer, and also take cognizance of other interfering causes
+which have a tendency to prevent desired results. First, we will imagine
+a balance with its spring such as we find in fine marine chronometers.
+It has small pivots running in highly-polished jewels; such pivots are
+perfectly cylindrical, and no larger than are absolutely necessary to
+endure the task imposed upon them--of carrying the weight of the balance
+and endure careful handling.
+
+To afford the necessary vibrations a spring is fitted, usually of a
+helical form, so disposed as to cause the balance to vibrate in arcs
+back and forth in equal time, _provided these arcs are of equal extent_.
+It is now to be taken note of that we have it at our disposal and option
+to make these arcs equal in time duration, i.e., to make the long or
+short arcs the quickest or to synchronize them. We can readily
+comprehend we have now established a very perfect measure of short
+intervals of time. We can also see if we provide the means of
+maintaining these vibrations and counting them we should possess the
+means of counting the flights of time with great accuracy. The
+conditions which surround our balance are very constant, the small
+pivots turning in fine hard jewels lubricated with an oil on which
+exposure to the action of the air has little effect, leaves but few
+influences which can interfere with the regular action of our balance.
+We add to the influences an adjustable correction for the disturbances
+of heat and cold, and we are convinced that but little could be added.
+
+
+ANTAGONISTIC INFLUENCES.
+
+In this combination we have pitted two antagonistic forces against each
+other, viz., the elasticity of the spring and the weight and inertia of
+the balance; both forces are theoretically constant and should produce
+constant results. The mechanical part of the problem is simply to afford
+these two forces perfect facilities to act on each other and compel each
+to realize its full effect. We must also devise mechanical means to
+record the duration of each conflict, that is, the time length of each
+vibration. Many years have been spent in experimenting to arrive at the
+best propositions to employ for the several parts to obtain the best
+practical results. Consequently, in designing a chronometer escapement
+we must not only draw the parts to a certain form, but consider the
+quality and weight of material to employ.
+
+To illustrate what we have just said, suppose, in drawing an escape
+wheel, we must not only delineate the proper angle for the acting face
+of the tooth, but must also take cognizance of the thickness of the
+tooth. By thickness we mean the measurement of extent of the tooth in
+the direction of the axis of the escape wheel. An escape-wheel tooth
+might be of the best form to act in conveying power to the balance and
+yet by being too thin soon wear or produce excessive friction. How thick
+an escape wheel should be to produce best results, is one of the many
+matters settled only by actual workshop experience.
+
+
+FACTORS THAT MUST BE CONSIDERED.
+
+Even this experience is in every instance modified by other influences.
+To illustrate: Let us suppose in the ordinary to-day marine chronometer
+the escape-wheel teeth exerted a given average force, which we set down
+as so many grains. Now, if we should employ other material than
+hammer-hardened brass for an escape wheel it would modify the thickness;
+also, if we should decrease the motive power and increase the arc of
+impulse. Or, if we should diminish the extent of the impulse arc and add
+to the motive force, every change would have a controlling influence. In
+the designs we shall employ, it is our purpose to follow such
+proportions as have been adopted by our best makers, in all respects,
+including form, size and material. We would say, however, there has been
+but little deviation with our principal manufacturers of marine
+chronometers for the last twenty years as regards the general principle
+on which they were constructed, the chief aim being to excel in the
+perfection of the several parts and the care taken in the several
+adjustments.
+
+Before we proceed to take up the details of constructing a chronometer
+escapement we had better master the names for the several parts. We show
+at Fig. 136 a complete plan of a chronometer escapement as if seen from
+the back, which is in reality the front or dial side of the "top plate."
+The chronometer escapement consists of four chief or principal parts,
+viz.: The escape wheel, a portion of which is shown at _A_; the impulse
+roller _B_; unlocking or discharging roller _C_, and the detent _D_.
+These principal parts are made up of sub-parts: thus, the escape wheel
+is composed of arms, teeth, recess and collet, the recess being the
+portion of the escape wheel sunk, to enable us to get wide teeth actions
+on the impulse pallet. The collet is a brass bush on which the wheel is
+set to afford better support to the escape wheel than could be obtained
+by the thinned wheel if driven directly on the pinion arbor. The impulse
+roller is composed of a cylindrical steel collet _B_, the impulse pallet
+_d_ (some call it the impulse stone), the safety recess _b b_. The
+diameter of the impulse collet is usually one-half that of the escape
+wheel. This impulse roller is staked directly on the balance staff, and
+its perfection of position assured by resting against the foot of the
+shoulder to which the balance is secured. This will be understood by
+inspecting Fig. 137, which is a vertical longitudinal section of a
+chronometer balance staff, the lower side of the impulse roller being
+cupped out at _c_ with a ball grinder and finished a ball polish.
+
+[Illustration: Fig. 136]
+
+[Illustration: Fig. 137]
+
+It will be seen the impulse roller is staked flat against the hub _E_ of
+the balance staff. The unlocking roller, or, as it is also called, the
+discharging roller, _C_, is usually thinner than the impulse roller and
+has a jewel similar to the impulse jewel _a_ shown at _f_. This roller
+is fitted by friction to the lower part of the balance staff and for
+additional security has a pipe or short socket _e_ which embraces the
+balance staff at _g_. The pipe _e_ is usually flattened on opposite
+sides to admit of employing a special wrench for turning the discharging
+roller in adjusting the jewel for opening the escapement at the proper
+instant to permit the escape wheel to act on the impulse jewel _a_. The
+parts which go to make up the detent _D_ consist of the "detent foot"
+_F_, the detent spring _h_, the detent blade _i_, the jewel pipe _j_,
+the locking jewel (or stone) _s_, the "horn" of the detent _k_, the
+"gold spring" (also called the auxiliary and lifting spring) _m_. This
+lifting or gold spring _m_ should be made as light and thin as possible
+and stand careful handling.
+
+We cannot impress on our readers too much the importance of making a
+chronometer detent light. Very few detents, even from the hands of our
+best makers, are as light as they might be. We should in such
+construction have very little care for clumsy workmen who may have to
+repair such mechanism. This feature should not enter into consideration.
+
+We should only be influenced by the feeling that we are working for best
+results, and it is acting under this influence that we devote so much
+time to establishing a correct idea of the underlying principles
+involved in a marine chronometer, instead of proceeding directly to the
+drawing of such an escapement and give empirical rules for the length of
+this or the diameter of that. As, for instance, in finishing the detent
+spring _h_, suppose we read in text books the spring should be reduced
+in thickness, so that a weight of one pennyweight suspended from the
+pipe _j_ will deflect the detent 1/4". This is a rule well enough for
+people employed in a chronometer factory, but for the horological
+student such fixed rules (even if remembered) would be of small use.
+What the student requires is sound knowledge of the "whys," in order
+that he may be able to thoroughly master this escapement.
+
+
+FUNCTIONS OF THE DETENT.
+
+We can see, after a brief analysis of the principles involved, that the
+functions required of the detent _D_ are to lock the escape wheel _A_
+and hold it while the balance performs its excursion, and that the
+detent or recovering spring _h_ must have sufficient strength and power
+to perform two functions: (1) Return the locking stone _s_ back to the
+proper position to arrest and hold the escape wheel; (2) the spring _h_
+must also be able to resist, without buckling or cockling, the thrust of
+the escape wheel, represented by the arrows _p o_. Now we can readily
+understand that the lighter we make the parts _i j k m_, the weaker the
+spring _h_ can be. You say, perhaps, if we make it too weak it will be
+liable to buckle under the pressure of the escape wheel; this, in turn,
+will depend in a great measure on the condition of the spring _h_.
+Suppose we have it straight when we put it in position, it will then
+have no stress to keep it pressed to the holding, stop or banking screw,
+which regulates the lock of the tooth. To obtain this stress we set the
+foot _F_ of the detent around to the position indicated by the dotted
+lines _r_ and _n_, and we get the proper tension on the detent spring to
+effect the lock, or rather of the detent in time to lock the escape
+wheel; but the spring _h_, instead of being perfectly straight, is bent
+and consequently not in a condition to stand the thrust of the escape
+wheel, indicated by the arrows _o p_.
+
+
+OBTAINING THE BEST CONDITIONS.
+
+Now the true way to obtain the best conditions is to give the spring _h_
+a set curvature before we put it in place, and then when the detent is
+in the proper position the spring _h_ will have tension enough on it to
+bring the jewel _s_ against the stop screw, which regulates the lock,
+and still be perfectly straight. This matter is of so much importance
+that we will give further explanation. Suppose we bend the detent spring
+_h_ so it is curved to the dotted line _t_, Fig. 136, and then the foot
+_F_ would assume the position indicated at the dotted line _r_. We next
+imagine the foot _F_ to be put in the position shown by the full lines,
+the spring _h_ will become straight again and in perfect shape to resist
+the thrust of the escape wheel.
+
+Little "ways and methods" like the above have long been known to the
+trade, but for some reason are never mentioned in our text books. A
+detent spring 2/1000" thick and 80/1000" wide will stand the thrust for
+any well-constructed marine chronometer in existence, and yet it will
+not require half a pennyweight to deflect it one-fourth of an inch. It
+is a good rule to make the length of the detent from the foot _F_ to the
+center of the locking jewel pipe _j_ equal to the diameter of the escape
+wheel, and the length of the detent spring _h_ two-sevenths of this
+distance. The length of the horn _k_ is determined by the graphic plan
+and can be taken from the plotted plan. The end, however, should
+approach as near to the discharging jewel as possible and not absolutely
+touch. The discharging (gold) spring _m_ is attached to the blade _i_ of
+the detent with a small screw _l_ cut in a No. 18 hole of a Swiss plate.
+While there should be a slight increase in thickness in the detent blade
+at _w_, where the gold spring is attached, still it should be no more
+than to separate the gold spring _m_ from the detent blade _i_.
+
+
+IMPORTANT CONSIDERATIONS.
+
+It is important the spring should be absolutely free and not touch the
+detent except at its point of attachment at _w_ and to rest against the
+end of the horn _k_, and the extreme end of _k_, where the gold spring
+rests, should only be what we may term a dull or thick edge. The end of
+the horn _k_ (shown at _y_) is best made, for convenience of elegant
+construction, square--that is, the part _y_ turns at right angles to
+_k_ and is made thicker than _k_ and at the same time deeper; or, to
+make a comparison to a clumsy article, _y_ is like the head of a nail,
+which is all on one side. Some makers bend the horn _k_ to a curve and
+allow the end of the horn to arrest or stop the gold spring; but as it
+is important the entire detent should be as light as possible, the
+square end best answers this purpose. The banking placed at _j_ should
+arrest the detent as thrown back by the spring _h_ at the "point of
+percussion." This point of percussion is a certain point in a moving
+mass where the greatest effort is produced and would be somewhere near
+the point _x_, in a bar _G_ turning on a pivot at _z_, Fig. 138. It will
+be evident, on inspection of this figure, if the bar _G_ was turning on
+the center _z_ it would not give the hardest impact at the end _v_, as
+parts of its force would be expended at the center _z_.
+
+[Illustration: Fig. 138]
+
+
+DECISIONS ARRIVED AT BY EXPERIENCE.
+
+Experience has decided that the impulse roller should be about half the
+diameter of the escape wheel, and experience has also decided that an
+escape wheel of fifteen teeth has the greatest number of advantages;
+also, that the balance should make 14,400 vibrations in one hour. We
+will accept these proportions and conditions as best, from the fact that
+they are now almost universally adopted by our best chronometer makers.
+Although it would seem as if these proportions should have established
+themselves earlier among practical men, we shall in these drawings
+confine ourselves to the graphic plan, considering it preferable. In the
+practical detail drawing we advise the employment of the scale given,
+i.e., delineating an escape wheel 10" in diameter. The drawings which
+accompany the description are one-fourth of this size, for the sake of
+convenience in copying.
+
+With an escape wheel of fifteen teeth the impulse arc is exactly
+twenty-four degrees, and of course the periphery of the impulse roller
+must intersect the periphery of the escape wheel for this arc (24 deg.).
+The circles _A B_, Fig. 139, represent the peripheries of these two
+mobiles, and the problem in hand is to locate and define the position of
+the two centers _a c_. These, of course, are not separated, the sum of
+the two radii, i.e., 5" + 21/2" (in the large drawing), as these
+circles intersect, as shown at _d_. Arithmetically considered, the
+problem is quite difficult, but graphically, simple enough. After we
+have swept the circle _A_ with a radius of 5", we draw the radial line
+_a f_, said line extending beyond the circle _A_.
+
+
+LOCATING THE CENTER OF THE BALANCE STAFF.
+
+Somewhere on this line is located the center of the balance staff, and
+it is the problem in hand to locate or establish this center. Now, it is
+known the circles which define the peripheries of the escape wheel and
+the impulse roller intersect at _e e^2_. We can establish on our
+circle _A_ where these intersections take place by laying off twelve
+degrees, one-half of the impulse arc on each side of the line of centers
+_a f_ on this circle and establishing the points _e e^2_. These points
+_e e^2_ being located at the intersection of the circles _A_ and _B_,
+must be at the respective distances of 5" and 21/2" distance from the
+center of the circles _A B_; consequently, if we set our dividers at
+21/2" and place one leg at _e_ and sweep the short arc _g^2_, and
+repeat this process when one leg of the dividers is set at _e^2_, the
+intersection of the short arcs _g_ and _g^2_ will locate the center of
+our balance staff. We have now our two centers established, whose
+peripheries are in the relation of 2 to 1.
+
+To know, in the chronometer which we are supposed to be constructing,
+the exact distance apart at which to plant the hole jewels for our two
+mobiles, i.e., escape wheel and balance staff, we measure carefully on
+our drawing the distance from _a_ to _c_ (the latter we having just
+established) and make our statement in the rule of three, as follows: As
+(10) the diameter of drawn escape wheel is to our real escape wheel so
+is the measured distance on our drawing to the real distance in the
+chronometer we are constructing.
+
+It is well to use great care in the large drawing to obtain great
+accuracy, and make said large drawing on a sheet of metal. This course
+is justified by the degree of perfection to which measuring tools have
+arrived in this day. It will be found on measurement of the arc of the
+circle _B_, embraced between the intersections _e e^2_, that it is
+about forty-eight degrees. How much of this we can utilize in our
+escapement will depend very much on the perfection and accuracy of
+construction.
+
+[Illustration: Fig. 139]
+
+We show at Fig. 140 three teeth of an escape wheel, together with the
+locking jewel _E_ and impulse jewel _D_. Now, while theoretically we
+could commence the impulse as soon as the impulse jewel _D_ was inside
+of the circle representing the periphery of the escape wheel, still, in
+practical construction, we must allow for contingencies. Before it is
+safe for the escape wheel to attack the impulse jewel, said jewel must
+be safely inside of said escape wheel periphery, in order that the
+attacking tooth shall act with certainty and its full effect. A good
+deal of thought and study can be bestowed to great advantage on the
+"action" of a chronometer escapement. Let us examine the conditions
+involved. We show in Fig. 140 the impulse jewel _D_ just passing inside
+the circle of the periphery of the escape wheel. Now the attendant
+conditions are these: The escape wheel is locked fast and perfectly
+dead, and in the effort of unlocking it has to first turn backward
+against the effort of the mainspring; the power of force required for
+this effort is derived from the balance in which is stored up, so to
+speak, power from impulses imparted to the balance by former efforts of
+the escape wheel. In actual fact, the balance at the time the unlocking
+takes place is moving with nearly its greatest peripheral velocity and,
+as stated above, the escape wheel is at rest.
+
+Here comes a very delicate problem as regards setting the unlocking or
+discharging jewel. Let us first suppose we set the discharging jewel so
+the locking jewel frees its tooth at the exact instant the impulse jewel
+is inside the periphery of the escape wheel. As just stated, the escape
+wheel is not only dead but actually moving back at the time the release
+takes place. Now, it is evident that the escape wheel requires an
+appreciable time to move forward and attack the impulse jewel, and
+during this appreciable time the impulse jewel has been moving forward
+inside of the arc _A A_, which represents the periphery of the escape
+wheel. The proper consideration of this problem is of more importance in
+chronometer making than we might at first thought have imagined,
+consequently, we shall dwell upon it at some length.
+
+
+HOW TO SET THE DISCHARGING JEWEL.
+
+[Illustration: Fig. 140]
+
+Theoretically, the escape-wheel tooth should encounter the impulse jewel
+at the time--instant--both are moving with the same velocity. It is
+evident then that there can be no special rule given for this, i.e.,
+how to set the discharging jewel so it will free the tooth at exactly
+the proper instant, from the fact that one chronometer train may be much
+slower in getting to move forward from said train being heavy and clumsy
+in construction. Let us make an experiment with a real chronometer in
+illustration of our problem. To do so we remove our balance spring and
+place the balance in position. If we start the balance revolving in the
+direction of the arrow _y_, Fig. 140, it will cause the escapement to be
+unlocked and the balance to turn rapidly in one direction and with
+increasing velocity until, in fact, the escape wheel has but very little
+effect on the impulse jewel; in fact, we could, by applying some outside
+source of power--like blowing with a blow pipe on the balance--cause the
+impulse jewel to pass in advance of the escape wheel; that is, the
+escape-wheel tooth would not be able to catch the impulse jewel during
+the entire impulse arc. Let us suppose, now, we set our unlocking or
+discharging jewel in advance, that is, so the escapement is really
+unlocked a little before the setting parts are in the positions and
+relations shown in Fig. 141. Under the new conditions the escape wheel
+would commence to move and get sufficient velocity on it to act on the
+impulse jewel as soon as it was inside of the periphery of the escape
+wheel. If the balance was turned slowly now the tooth of the escape
+wheel would not encounter the impulse jewel at all, but fall into the
+passing hollow _n_; but if we give the balance a high velocity, the
+tooth would again encounter and act upon the jewel in the proper manner.
+Experienced adjusters of chronometers can tell by listening if the
+escape-wheel tooth attacks the impulse jewel properly, i.e., when both
+are moving with similar velocities. The true sound indicating correct
+action is only given when the balance has its maximum arc of vibration,
+which should be about 11/4 revolutions, or perform an arc of 225
+degrees on each excursion.
+
+
+Fig. 142 is a side view of Fig. 141 seen in the direction of the arrow
+_y_. We have mentioned a chariot to which the detent is attached, but we
+shall make no attempt to show it in the accompanying drawings, as it
+really has no relation to the problem in hand; i.e., explaining the
+action of the chronometer escapement, as the chariot relates entirely to
+the convenience of setting and adjusting the relation of the second
+parts. The size, or better, say, the inside diameter of the pipe at _C_,
+Fig. 143, which holds the locking jewel, should be about one-third of a
+tooth space, and the jewel made to fit perfectly. Usually, jewelmakers
+have a tendency to make this jewel too frail, cutting away the jewel
+back of the releasing angle (_n_, Fig. 143) too much.
+
+
+A GOOD FORM OF LOCKING STONE.
+
+A very practical form for a locking stone is shown in transverse section
+at Fig. 143. In construction it is a piece of ruby, or, better, sapphire
+cut to coincide to its axis of crystallization, into first a solid
+cylinder nicely fitting the pipe _C_ and finished with an
+after-grinding, cutting away four-tenths of the cylinder, as shown at
+_I_, Fig. 143. Here the line _m_ represents the locking face of the
+jewel and the line _o_ the clearance to free the escaping tooth, the
+angle at _n_ being about fifty-four degrees. This angle (_n_) should
+leave the rounding of the stone intact, that is, the rounding of the
+angle should be left and not made after the flat faces _m o_ are ground
+and polished. The circular space at _I_ is filled with an aluminum
+pin. The sizes shown are of about the right relative proportions; but
+we feel it well to repeat the statement made previously, to the effect
+that the detent to a chronometer cannot well be made too light.
+
+[Illustration: Fig. 141]
+
+[Illustration: Fig. 142]
+
+[Illustration: Fig. 143]
+
+The so-called gold spring shown at _H_, Figs. 141 and 142, should also
+be as light as is consistent with due strength and can be made of the
+composite metal used for gold filled goods, as the only real benefit to
+be derived from employing gold is to avoid the necessity of applying oil
+to any part of the escapement. If such gold metal is employed, after
+hammering to obtain the greatest possible elasticity to the spring, the
+gold is filed away, except where the spring is acted upon by the
+discharging jewel _h_. We have previously mentioned the importance of
+avoiding wide, flat contacts between all acting surfaces, like where the
+gold spring rests on the horn of the detent at _p_; also where the
+detent banks on the banking screw, shown at _G_, Fig. 142. Under this
+principle the impact of the face of the discharging jewel with the end
+of the gold spring should be confined to as small a surface as is
+consistent with what will not produce abrasive action. The gold spring
+is shaped as shown at Fig. 142 and loses, in a measure, under the pipe
+of the locking jewel, a little more than one-half of the pipe below the
+blade of the detent being cut away, as shown in Fig. 143, where the
+lines _r r_ show the extent of the part of the pipe which banks against
+the banking screw _G_. In this place even, only the curved surface of
+the outside of the pipe touches the screw _G_, again avoiding contact of
+broad surfaces.
+
+We show the gold spring separate at Fig. 144. A slight torsion or twist
+is given to the gold spring to cause it to bend with a true curvature in
+the act of allowing the discharging pallet to pass back after unlocking.
+If the gold spring is filed and stoned to the right flexure, that is,
+the thinnest point properly placed or, say, located, the gold spring
+will not continue in contact with the discharging pallet any longer time
+or through a greater arc than during the process of unlocking. To make
+this statement better understood, let us suppose the weakest part of the
+gold spring _H_ is opposite the arrow _y_, Fig. 141, it will readily be
+understood the contact of the discharging stone _h_ would continue
+longer than if the point of greatest (or easiest) flexure was nearer to
+the pipe _C_. If the end _D^2_ of the horn of the detent is as near as
+it should be to the discharging stone there need be no fear but the
+escapement will be unlocked. The horn _D^2_ of the detent should be
+bent until five degrees of angular motion of the balance will unlock the
+escape, and the contact of discharging jewel _h_ should be made without
+engaging friction. This condition can be determined by observing if the
+jewel seems to slide up (toward the pipe _C_) on the gold spring after
+contact. Some adjusters set the jewel _J_, Figs. 143 and 141, in such a
+way that the tooth rests close to the base; such adjusters claiming this
+course has a tendency to avoid cockling or buckling of the detent spring
+_E_. Such adjusters also set the impulse jewel slightly oblique, so as
+to lean on the opposite angle of the tooth. Our advice is to set both
+stones in places corresponding to the axis of the balance staff, and the
+escape-wheel mobiles.
+
+
+THE DETENT SPRING.
+
+[Illustration: Fig. 144]
+
+It will be noticed we have made the detent spring _E_ pretty wide and
+extended it well above the blade of the detent. By shaping the detent in
+this way nearly all the tendency of the spring _E_ to cockle is
+annulled. We would beg to add to what we said in regard to setting
+jewels obliquely. We are unable to understand the advantage of
+wide-faced stones and deep teeth when we do not take advantage of the
+wide surfaces which we assert are important. We guarantee that with a
+detent and spring made as we show, there will be no tendency to cockle,
+or if there is, it will be too feeble to even display itself. Those who
+have had extended experience with chronometers cannot fail to have
+noticed a gummy secretion which accumulates on the impulse and
+discharging stones of a chronometer, although no oil is ever applied to
+them. We imagine this coating is derived from the oil applied to the
+pivots, which certainly evaporates, passes into vapor, or the remaining
+oil could not become gummy. We would advise, when setting jewels (we
+mean the locking, impulse and discharging jewels), to employ no more
+shellac than is absolutely necessary, depending chiefly on metallic
+contact for security.
+
+
+DETAILS OF CONSTRUCTION.
+
+We will now say a few words about the number of beats to the hour for a
+box or marine chronometer to make to give the best results. Experience
+shows that slow but most perfect construction has settled that 14,400,
+or four vibrations of the balance to a second, as the proper number, the
+weight of balance, including balance proper and movable weights, to be
+about 51/2 pennyweights, and the compensating curb about 1-2/10" in
+diameter. The escape wheel, 55/100" in diameter and recessed so as to be
+as light as possible, should have sufficient strength to perform its
+functions properly. The thickness or, more properly, the face extent of
+the tooth, measured in the direction of the axis of the escape wheel,
+should be about 1/20". The recessing should extend half way up the
+radial back of the tooth at _t_. The curvature of the back of the teeth
+is produced with the same radii as the impulse roller. To locate the
+center from which the arc which defines the back of the teeth is swept,
+we halve the space between the teeth _A^2_ and _a^4_ and establish
+the point _n_, Fig. 141, and with our dividers set to sweep the circle
+representing the impulse roller, we sweep an arc passing the point of
+the tooth _A^3_ and _u_, thus locating the center _w_. From the center
+_k_ of the escape wheel we sweep a complete circle, a portion of which
+is represented by the arc _w v_. For delineating other teeth we set one
+leg of our dividers to agree with the point of the tooth and the other
+leg on the circle _w v_ and produce an arc like _z u_.
+
+
+ORIGINAL DESIGNING OF THE ESCAPEMENT.
+
+On delineating our chronometer escapement shown at Fig. 141 we have
+followed no text-book authority, but have drawn it according to such
+requirements as are essential to obtain the best results. An escapement
+of any kind is only a machine, and merely requires in its construction a
+combination of sound mechanical principles. Neither Saunier nor Britten,
+in their works, give instructions for drawing this escapement which will
+bear close analysis. It is not our intention, however, to criticise
+these authors, except we can present better methods and give correct
+systems.
+
+
+TANGENTIAL LOCKINGS.
+
+It has been a matter of great contention with makers of chronometer and
+also lever escapements as to the advantages of "tangential lockings." By
+this term is meant a locking the same as is shown at _C_, Fig. 141, and
+means a detent planted at right angles to a line radial to the
+escape-wheel axis, said radial line passing through the point of the
+escape-wheel tooth resting on the locking jewel. In escapements not set
+tangential, the detent is pushed forward in the direction of the arrow
+_x_ about half a tooth space. Britten, in his "Hand-Book," gives a
+drawing of such an escapement. We claim the chief advantage of
+tangential locking to lie in the action of the escape-wheel teeth, both
+on the impulse stone and also on the locking stone of the detent.
+Saunier, in his "Modern Horology," gives the inclination of the front
+fan of the escape-wheel teeth as being at an angle of twenty-seven
+degrees to a radial line. Britten says twenty degrees, and also employs
+a non-tangential locking.
+
+Our drawing is on an angle of twenty-eight degrees, which is as low as
+is safe, as we shall proceed to demonstrate. For establishing the angle
+of an escape-wheel tooth we draw the line _C d_, from the point of the
+escape-wheel tooth resting on the locking stone shown at _C_ at an angle
+of twenty-eight degrees to radial line _C k_. We have already discussed
+how to locate and plant the center of the balance staff.
+
+We shall not show in this drawing the angular motion of the escape
+wheel, but delineate at the radial lines _c e_ and _c f_ of the arc of
+the balance during the extent of its implication with the periphery of
+the escape wheel, which arc is one of about forty-eight degrees. Of this
+angle but forty-three degrees is attempted to be utilized for the
+purpose of impulse, five degrees being allowed for the impulse jewel to
+pass inside of the arc of periphery of the escape wheel before the
+locking jewel releases the tooth of the escape wheel resting upon it. At
+this point it is supposed the escape wheel attacks the impulse jewel,
+because, as we just explained, the locking jewel has released the tooth
+engaging it. Now, if the train had no weight, no inertia to overcome,
+the escape wheel tooth _A^2_ would move forward and attack the impulse
+pallet instantly; but, in fact, as we have already explained, there will
+be an appreciable time elapse before the tooth overtakes the
+rapidly-moving impulse jewel. It will, of course, be understood that the
+reference letters used herein refer to the illustrations that have
+appeared on preceding pages.
+
+If we reason carefully on the matter, we will readily comprehend that we
+can move the locking jewel, i.e., set it so the unlocking will take
+place in reality before the impulse jewel has passed through the entire
+five degrees of arc embraced between the radial lines _c e_ and _c g_,
+Fig. 141, and yet have the tooth attack the jewel after the five degrees
+of arc. In practice it is safe to set the discharging jewel _h_ so the
+release of the held tooth _A^1_ will take place as soon as the tooth
+_A^2_ is inside the principal line of the escape wheel. As we
+previously explained, the contact between _A^2_ and the impulse jewel
+_i_ would not in reality occur until the said jewel _i_ had fully passed
+through the arc (five degrees) embraced between the radial lines _c e_
+and _c g_.
+
+At this point we will explain why we drew the front fan of the
+escape-wheel teeth at the angle of twenty-eight degrees. If the fan of
+impulse jewel _i_ is set radial to the axis of the balance, the
+engagement of the tooth _A^2_ would be at a disadvantage if it took
+place prior to this jewel passing through an arc of five degrees inside
+the periphery of the escape wheel. It will be evident on thought that if
+an escape-wheel tooth engaged the impulse stone before the five-degrees
+angle had passed, the contact would not be on its flat face, but the
+tooth would strike the impulse jewel on its outer angle. A continued
+inspection will also reveal the fact that in order to have the point of
+the tooth engage the flat surface of the impulse pallet the impulse
+jewel must coincide with the radial line _c g_. If we seek to remedy
+this condition by setting the impulse jewel so the face is not radial,
+but inclined backward, we encounter a bad engaging friction, because,
+during the first part of the impulse action, the tooth has to slide up
+the face of the impulse jewel. All things considered, the best action is
+obtained with the impulse jewel set so the acting face is radial to the
+balance staff and the engagement takes place between the tooth and the
+impulse jewel when both are moving with equal velocities, i.e., when
+the balance is performing with an arc (or motion) of 11/4 revolutions
+or 225 degrees each way from a point of rest. Under such conditions the
+actual contact will not take place before some little time after the
+impulse jewel has passed the five-degree arc between the lines _c e_ and
+_c g_.
+
+
+THE DROP AND DRAW CONSIDERED.
+
+Exactly how much drop must be allowed from the time the tooth leaves the
+impulse jewel before the locking tooth engages the locking jewel will
+depend in a great measure on the perfection of workmanship, but should
+in no instance be more than what is absolutely required to make the
+escapement safe. The amount of draw given to the locking stone _c_ is
+usually about twelve degrees to the radial line _k a_. Much of the
+perfection of the chronometer escapement will always depend on the skill
+of the escapement adjuster and not on the mechanical perfection of the
+parts.
+
+The jewels all have to be set by hand after they are made, and the
+distance to which the impulse jewel protrudes beyond the periphery of
+the impulse roller is entirely a matter for hand and eye, but should
+never exceed 2/1000". After the locking jewel _c_ is set, we can set the
+foot _F_ of the detent _D_ forward or back, to perfect and correct the
+engagement of the escape-wheel teeth with the impulse roller _B_. If we
+set this too far forward, the tooth _A^3_ will encounter the roller
+while the tooth _A^2_ will be free.
+
+We would beg to say here there is no escape wheel made which requires
+the same extreme accuracy as the chronometer, as the tooth spaces and
+the equal radial extent of each tooth should be only limited by our
+powers toward perfection. It is usual to give the detent a locking of
+about two degrees; that is, it requires about two degrees to open it,
+counting the center of fluxion of the detent spring _E_ and five degrees
+of balance arc.
+
+
+FITTING UP OF THE FOOT.
+
+Several attempts have been made by chronometer makers to have the foot
+_F_ adjustable; that is, so it could be moved back and forth with a
+screw, but we have never known of anything satisfactory being
+accomplished in this direction. About the best way of fitting up the
+foot _F_ seems to be to provide it with two soft iron steady pins (shown
+at _j_) with corresponding holes in the chariot, said holes being
+conically enlarged so they (the pins) can be bent and manipulated so the
+detent not only stands in the proper position as regards the escape
+wheel, but also to give the detent spring _E_ the proper elastic force
+to return in time to afford a secure locking to the arresting tooth of
+the escape wheel after an impulse has been given.
+
+If these pins _j_ are bent properly by the adjuster, whoever afterwards
+cleans the chronometer needs only to gently push the foot _F_ forward so
+as to cause the pins _j_ to take the correct positions as determined by
+the adjuster and set the screw _l_ up to hold the foot _F_ when all the
+other relations are as they should be, except such as we can control by
+the screw _G_, which prevents the locking jewel from entering too deeply
+into the escape wheel.
+
+In addition to being a complete master of the technical part of his
+business, it is also desirable that the up-to-date workman should be
+familiar with the subject from a historical point of view. To aid in
+such an understanding of the matter we have translated from "L'Almanach
+de l'Horologerie et de la Bijouterie" the matter contained in the
+following chapter.
+
+
+
+
+CHAPTER IV.
+
+HISTORY OF ESCAPEMENTS.
+
+
+It could not have been long after man first became cognizant of his
+reasoning faculties that he began to take more or less notice of the
+flight of time. The motion of the sun by day and of the moon and stars
+by night served to warn him of the recurring periods of light and
+darkness. By noting the position of these stellar bodies during his
+lonely vigils, he soon became proficient in roughly dividing up the
+cycle into sections, which he denominated the hours of the day and of
+the night. Primitive at first, his methods were simple, his needs few
+and his time abundant. Increase in numbers, multiplicity of duties, and
+division of occupation began to make it imperative that a more
+systematic following of these occupations should be instituted, and with
+this end in view he contrived, by means of burning lights or by
+restricting the flowing of water or the falling of weights, to subdivide
+into convenient intervals and in a tolerably satisfactory manner the
+periods of light.
+
+These modest means then were the first steps toward the exact
+subdivisions of time which we now enjoy. Unrest, progress, discontent
+with things that be, we must acknowledge, have, from the appearance of
+the first clock to the present hour, been the powers which have driven
+on the inventive genius of watch and clockmakers to designate some new
+and more acceptable system for regulating the course of the movement. In
+consequence of this restless search after the best, a very considerable
+number of escapements have been invented and made up, both for clocks
+and watches; only a few, however, of the almost numberless systems have
+survived the test of time and been adopted in the manufacture of the
+timepiece as we know it now. Indeed, many such inventions never passed
+the experimental stage, and yet it would be very interesting to the
+professional horologist, the apprentice and even the layman to become
+more intimately acquainted with the vast variety of inventions made upon
+this domain since the inception of horological science. Undoubtedly, a
+complete collection of all the escapements invented would constitute a
+most instructive work for the progressive watchmaker, and while we are
+waiting for a competent author to take such an exhaustive work upon his
+hands, we shall endeavor to open the way and trust that a number of
+voluntary collaborators will come forward and assist us to the extent of
+their ability in filling up the chinks.
+
+
+PROBLEMS TO BE SOLVED.
+
+The problem to be solved by means of the escapement has always been to
+govern, within limits precise and perfectly regular, if it be possible,
+the flow of the motive force; that means the procession of the
+wheel-work and, as a consequence, of the hands thereto attached. At
+first blush it seems as if a continually-moving governor, such as is in
+use on steam engines, for example, ought to fulfil the conditions, and
+attempts have accordingly been made upon this line with results which
+have proven entirely unsatisfactory.
+
+Having thoroughly sifted the many varieties at hand, it has been finally
+determined that the only means known to provide the most regular flow of
+power consists in intermittently interrupting the procession of the
+wheel-work, and thereby gaining a periodically uniform movement.
+Whatever may be the system or kind of escapement employed, the
+functioning of the mechanism is characterized by the suspension, at
+regular intervals, of the rotation of the last wheel of the train and in
+transmitting to a regulator, be it a balance or a pendulum, the power
+sent into that wheel.
+
+
+ESCAPEMENT THE MOST ESSENTIAL PART.
+
+Of all the parts of the timepiece the escapement is then the most
+essential; it is the part which assures regularity in the running of the
+watch or clock, and that part of parts that endows the piece with real
+value. The most perfect escapement would be that one which should
+perform its duty with the least influence upon the time of oscillation
+or vibration of the regulating organ. The stoppage of the train by the
+escapement is brought about in different ways, which may be gathered
+under three heads or categories. In the two which we shall mention
+first, the stop is effected directly upon the axis of the regulator, or
+against a piece which forms a part of that axis; the tooth of the escape
+wheel at the moment of its disengagement remains supported upon or
+against that stop.
+
+In the first escapement invented and, indeed, in some actually employed
+to-day for certain kinds of timekeepers, we notice during the locking a
+retrograde movement of the escape wheel; to this kind of movement has
+been given the name of _recoil escapement_. It was recognized by the
+fraternity that this recoil was prejudicial to the regularity of the
+running of the mechanism and, after the invention of the pendulum and
+the spiral, inventive makers succeeded in replacing this sort of
+escapement with one which we now call the _dead-beat escapement_. In
+this latter the wheel, stopped by the axis of the regulator, remains
+immovable up to the instant of its disengagement or unlocking.
+
+In the third category have been collected all those forms of escapement
+wherein the escape wheel is locked by an intermediate piece, independent
+of the regulating organ. This latter performs its vibrations of
+oscillation quite without interference, and it is only in contact with
+the train during the very brief moment of impulse which is needful to
+keep the regulating organ in motion. This category constitutes what is
+known as the _detached escapement_ class.
+
+Of the _recoil escapement_ the principal types are: the _verge
+escapement_ or _crown-wheel escapement_ for both watches and clocks, and
+the _recoil anchor escapement_ for clocks. The _cylinder_ and _duplex
+escapements_ for watches and the _Graham anchor escapement_ for clocks
+are styles of the _dead-beat escapement_ most often employed. Among the
+_detached escapements_ we have the _lever_ and _detent_ or _chronometer
+escapements_ for watches; for clocks there is no fixed type of detached
+lever and it finds no application to-day.
+
+
+THE VERGE ESCAPEMENT.
+
+The _verge escapement_, called also the _crown-wheel escapement_, is by
+far the simplest and presents the least difficulty in construction. We
+regret that the world does not know either the name of its originator
+nor the date at which the invention made its first appearance, but it
+seems to have followed very closely upon the birth of mechanical
+horology.
+
+Up to 1750 it was employed to the exclusion of almost all the others. In
+1850 a very large part of the ordinary commercial watches were still
+fitted with the verge escapement, and it is still used under the form of
+_recoil anchor_ in clocks, eighty years after the invention of the
+cylinder escapement, or in 1802. Ferdinand Berthoud, in his "History of
+the Measurement of Time," says of the balance-wheel escapement: "Since
+the epoch of its invention an infinite variety of escapements have been
+constructed, but the one which is employed in ordinary watches for
+every-day use is still the best." In referring to our illustrations, we
+beg first to call attention to the plates marked Figs. 145 and 146.
+This plate gives us two views of a verge escapement; that is, a balance
+wheel and a verge formed by its two opposite pallets. The views are
+intentionally presented in this manner to show that the verge _V_ may be
+disposed either horizontally, as in Fig. 146, or vertically, as in Fig.
+145.
+
+[Illustration: Figs. 145 and 146]
+
+[Illustration: Fig. 147]
+
+Let us imagine that our drawing is in motion, then will the tooth _d_,
+of the crown wheel _R_, be pushing against the pallet _P_, and just upon
+the point of slipping by or escaping, while the opposite tooth _e_ is
+just about to impinge upon the advancing pallet _P'_. This it does, and
+will at first, through the impulse received from the tooth _d_ be forced
+back by the momentum of the pallet, that is, suffer a recoil; but on the
+return journey of the pallet _P'_, the tooth _e_ will then add its
+impulse to the receding pallet. The tooth _e_ having thus accomplished
+its mission, will now slip by and the tooth _c_ will come in lock with
+the pallet _P_ and, after the manner just described for _e_, continue
+the escapement. Usually these escape wheels are provided with teeth to
+the number of 11, 13 or 15, and always uneven. A great advantage
+possessed by this form of escapement is that it does not require any
+oil, and it may be made to work even under very inferior construction.
+
+
+OLDEST ARRANGEMENT OF A CROWN-WHEEL ESCAPEMENT.
+
+[Illustration: Fig. 148]
+
+Plate 147 shows us the oldest known arrangement of a crown-wheel
+escapement in a clock. _R_ is the crown wheel or balance wheel acting
+upon the pallets _P_ and _P'_, which form part of the verge _V_. This
+verge is suspended as lightly as possible upon a pliable cord _C_ and
+carries at its upper end two arms, _B_ and _B_, called adjusters,
+forming the balance. Two small weights _D D_, adapted to movement along
+the rules or adjusters serve to regulate the duration of a vibration. In
+Fig. 148 we have the arrangement adopted in small timepieces and
+watches: _B_ represents the regulator in the form of a circular balance,
+but not yet furnished with a spiral regulating spring; _c_ is the last
+wheel of the train and called the _fourth wheel_, it being that number
+distant from the great wheel. As will be seen, the verge provided with
+its pallets is vertically placed, as in the preceding plate.
+
+[Illustration: Fig. 149]
+
+Here it will quickly be seen that regarded from the standpoint of
+regularity of motion, this arrangement can be productive of but meager
+results. Subjected as it is to the influence of the slightest variation
+in the motive power and of the least jar or shaking, a balance wheel
+escapement improvided with a regulator containing within itself a
+regulating force, could not possibly give forth anything else than an
+unsteady movement. However, mechanical clocks fitted with this
+escapement offer indisputable advantages over the ancient clepsydra; in
+spite of their imperfections they rendered important services,
+especially after the striking movement had been added. For more than
+three centuries both this crude escapement and the cruder regulator were
+suffered to continue in this state without a thought of improvement;
+even in 1600, when Galileo discovered the law governing the oscillation
+of the pendulum, they did not suspect how important this discovery was
+for the science of time measurement.
+
+
+GALILEO'S EXPERIMENTS.
+
+[Illustration: Fig. 150]
+
+Galileo, himself, in spite of his genius for investigation, was so
+engrossed in his researches that he could not seem to disengage the
+simple pendulum from the compound pendulums to which he devoted his
+attention; besides, he attributed to the oscillation an absolute
+generality of isochronism, which they did not possess; nor did he know
+how to apply his famous discovery to the measurement of time. In fact,
+it was not till after more than half a century had elapsed, in 1657, to
+be exact, that the celebrated Dutch mathematician and astronomer,
+Huygens, published his memoirs in which he made known to the world the
+degree of perfection which would accrue to clocks if the pendulum were
+adopted to regulate their movement.
+
+[Illustration: Fig. 151]
+
+An attempt was indeed made to snatch from Huygens and confer upon
+Galileo the glory of having first applied the pendulum to a clock, but
+this attempt not having been made until some time after the publication
+of "Huygens' Memoirs," it was impossible to place any faith in the
+contention. If Galileo had indeed solved the beautiful problem, both in
+the conception and the fact, the honor of the discovery was lost to him
+by the laziness and negligence of his pupil, Viviani, upon whom he had
+placed such high hopes. One thing is certain, that the right of priority
+of the discovery and the recognition of the entire world has been
+incontestably bestowed upon Huygens. The escapement which Galileo is
+supposed to have conceived and to which he applied the pendulum, is
+shown in Fig. 149. The wheel _R_ is supplied with teeth, which lock
+against the piece _D_ attached to a lever pivoted at _a_, and also with
+pins calculated to impart impulses to the pendulum through the pallet
+_P_. The arm _L_ serves to disengage or unlock the wheel by lifting the
+lever _D_ upon the return oscillation of the pendulum.
+
+[Illustration: Fig. 152]
+
+[Illustration: Fig. 153]
+
+A careful study of Fig. 150 will discover a simple transposition which
+it became necessary to make in the clocks, for the effectual adaptation
+of the pendulum to their regulation. The verge _V_ was set up
+horizontally and the pendulum _B_, suspended freely from a flexible
+cord, received the impulses through the intermediation of the forked arm
+_F_, which formed a part of the verge. At first this forked arm was not
+thought of, for the pendulum itself formed a part of the verge. A
+far-reaching step had been taken, but it soon became apparent that
+perfection was still a long way off. The crown-wheel escapement forcibly
+incited the pendulum to wider oscillations; these oscillations not being
+as Galileo had believed, of unvaried durations, but they varied sensibly
+with the intensity of the motive power.
+
+
+THE ATTAINMENT OF ISOCHRONISM BY HUYGENS.
+
+Huygens rendered his pendulum _isochronous_; that is, compelled it to
+make its oscillations of equal duration, whatever might be the arc
+described, by suspending the pendulum between two metallic curves _c
+c'_, each one formed by an arc of a cycloid and against which the
+suspending cord must lie upon each forward or backward oscillation. We
+show this device in Fig. 151. In great oscillations, and by that we mean
+oscillations under a greater impulse, the pendulum would thus be
+shortened and the shortening would correct the time of the oscillation.
+However, the application of an exact cycloidal arc was a matter of no
+little difficulty, if not an impossibility in practice, and practical
+men began to grope about in search of an escapement which would permit
+the use of shorter arcs of oscillation. At London the horologist, G.
+Clement, solved the problem in 1675 with his rack escapement and recoil
+anchor. In the interval other means were invented, especially the
+addition of a second pendulum to correct the irregularities of the
+first. Such an escapement is pictured in Fig. 152. The verge is again
+vertical and carries near its upper end two arms _D D_, which are each
+connected by a cord with a pendulum. The two pendulums oscillate
+constantly in the inverse sense the one to the other.
+
+[Illustration: Fig. 154]
+
+[Illustration: Fig. 155]
+
+
+ANOTHER TWO-PENDULUM ESCAPEMENT.
+
+We show another escapement with two pendulums in Fig. 153. These are
+fixed directly upon two axes, each one carrying a pallet _P P'_ and a
+segment of a toothed wheel _D D_, which produces the effect of
+solidarity between them. The two pendulums oscillate inversely one to
+the other, and one after the other receives an impulse. This escapement
+was constructed by Jean Baptiste Dutertre, of Paris.
+
+Fig. 154 shows another disposition of a double pendulum. While the
+pendulum here is double, it has but one bob; it receives the impulse by
+means of a double fork _F_. _C C_ represents the cycloidal curves and
+are placed with a view of correcting the inequality in the duration of
+the oscillations. In watches the circular balances did not afford any
+better results than the regulating rods or rules of the clocks, and the
+pendulum, of course, was out of the question altogether; it therefore
+became imperative to invent some other regulating system.
+
+[Illustration: Fig. 156]
+
+[Illustration: Fig. 157]
+
+It occured to the Abbe d'Hautefeuille to form a sort of resilient
+mechanism by attaching one end of a hog's bristle to the plate and the
+other to the balance near the axis. Though imperfect in results, this
+was nevertheless a brilliant idea, and it was but a short step to
+replace the bristle with a straight and very flexible spring, which
+later was supplanted by one coiled up like a serpent; but in spite of
+this advancement, the watches did not keep much better time. Harrison,
+the celebrated English horologist, had recourse to two artifices, of
+which the one consisted in giving to the pallets of the escapement such
+a curvature that the balance could be led back with a velocity
+corresponding to the extension of the oscillation; the second consisted
+of an accessory piece, the resultant action of which was analogous to
+that of the cycloidal curves in connection with the pendulum.
+
+
+CORRECTING IRREGULARITIES IN THE VERGE ESCAPEMENT.
+
+Huygens attempted to correct these irregularities in the verge
+escapement in watches by amplifying the arc of oscillation of the
+balance itself. He constructed for that purpose a pirouette escapement
+shown in Fig. 155, in which a toothed wheel _A_ adjusted upon the verge
+_V_ serves as an intermediary between that and the balance _B_, upon the
+axis of which was fixed a pinion _D_. By this method he obtained
+extended arcs of vibration, but the vibrations were, as a consequence,
+very slow, and they still remained subject to all the irregularities
+arising from the variation in the motive power as well as from shocks. A
+little later, but about the same epoch, a certain Dr. Hook, of the Royal
+Society of London, contrived another arrangement by means of which he
+succeeded, so it appeared to him at least, in greatly diminishing the
+influence of shock upon the escapement; but many other, perhaps greater,
+inconveniences caused his invention to be speedily rejected. We shall
+give our readers an idea of what Dr. Hook's escapement was like.
+
+[Illustration: Fig. 158]
+
+[Illustration: Fig. 159]
+
+On looking at Fig. 156 we see the escape wheel _R_, which was flat and
+in the form of a ratchet; it was provided with two balances. _B B_
+engaging each other in teeth, each one carrying a pallet _P P'_ upon its
+axis; the axes of the three wheels being parallel. Now, in our drawing,
+the tooth _a_ of the escape wheel exerts its lift upon the pallet _P'_;
+when this tooth escapes the tooth _b_ will fall upon the pallet _P'_ on
+the opposite side, a recoil will be produced upon the action of the two
+united balances, then the tooth _b_ will give its impulse in the
+contrary direction. Considerable analogy exists between this form of
+escapement and that shown in Fig. 153 and intended for clocks. This was
+the busy era in the watchmaker's line. All the great heads were
+pondering upon the subject and everyone was on the _qui vive_ for the
+newest thing in the art.
+
+In 1674 Huygens brought out the first watch having a regulating spring
+in the form of a spiral; the merit of this invention was disputed by the
+English savant, Dr. Hook, who pretended, as did Galileo, in the
+application of the pendulum, to have priority in the idea. Huygens, who
+had discovered and corrected the irregularities in the oscillations of
+the pendulum, did not think of those of the balance with the spiral
+spring. And it was not until the close of the year 1750 that Pierre Le
+Roy and Ferdinand Berthoud studied the conditions of isochronism
+pertaining to the spiral.
+
+
+AN INVENTION THAT CREATED MUCH ENTHUSIASM.
+
+However that may be, this magnificent invention, like the adaptation of
+the pendulum, was welcomed with general enthusiasm throughout the
+scientific world: without spiral and without pendulum, no other
+escapement but the recoil escapement was possible; a new highway was
+thus opened to the searchers. The water clocks (clepsydrae) and the hour
+glasses disappeared completely, and the timepieces which had till then
+only marked the hours, having been perfected up to the point of keeping
+more exact time, were graced with the addition of another hand to tell
+off the minutes.
+
+[Illustration: Fig. 160]
+
+[Illustration: Fig. 161]
+
+It was not until 1695 that the first _dead-beat escapement_ appeared
+upon the scene; during the interval of over twenty years all thought had
+been directed toward the one goal, viz.: the perfecting of the _verge
+escapement_; but practice demonstrated that no other arrangement of the
+parts was superior to the original idea. For the benefit of our readers
+we shall give a few of these attempts at betterment, and you may see for
+yourselves wherein the trials failed.
+
+Fig. 157 represents a _verge escapement_ with a ratchet wheel, the
+pallets _P P'_ being carried upon separate axes. The two axes are
+rigidly connected, the one to the other, by means of the arms _o o'_.
+One of the axes carries besides the fork _F_, which transmits the
+impulse to the pendulum _B_. In the front view, at the right of the
+plate, for the sake of clearness the fork and the pendulum are not
+shown, but one may easily see the jointure of the arms _o o'_ and their
+mode of operation.
+
+Another very peculiar arrangement of the _verge escapement_ we show at
+Fig. 158. In this there are two wheels, one, _R'_, a small one in the
+form of a ratchet; the other, _R_, somewhat larger, called the balance
+wheel, but being supplied with straight and slender teeth. The verge _V_
+carrying the two pallets is pivoted in the vertical diameter of the
+larger wheel. The front view shows the _modus operandi_ of this
+combination, which is practically the same as the others. The tooth _a_
+of the large wheel exerts its force upon the pallet _P_, and the tooth
+_b_ of the ratchet will encounter the pallet _P'_. This pallet, after
+suffering its recoil, will receive the impulse communicated by the tooth
+_b_. This escapement surely could not have given much satisfaction, for
+it offers no advantage over the others, besides it is of very difficult
+construction.
+
+[Illustration: Fig. 162]
+
+[Illustration: Fig. 163]
+
+
+INGENIOUS ATTEMPTS AT SOLUTION OF A DIFFICULT PROBLEM.
+
+Much ingenuity to a worthy end, but of little practical value, is
+displayed in these various attempts at the solution of a very difficult
+problem. In Fig. 159 we have a mechanism combining two escape wheels
+engaging each other in gear; of the two wheels, _R R'_, one alone is
+driven directly by the train, the other being turned in the opposite
+direction by its comrade. Both are furnished with pins _c c'_, which act
+alternately upon the pallets _P P'_ disposed in the same plane upon the
+verge _V_ and pivoted between the wheels. Our drawing represents the
+escapement at the moment when the pin _C'_ delivers its impulse, and
+this having been accomplished, the locking takes place upon the pin _C_
+of the other wheel upon the pallet _P'_. Another system of two escape
+wheels is shown in Fig. 160, but in this case the two wheels _R R_ are
+driven in a like direction by the last wheel _A_ of the train. The
+operation of the escapement is the same as in Fig. 159.
+
+[Illustration: Fig. 164]
+
+[Illustration: Fig. 165]
+
+In Fig. 161 we have a departure from the road ordinarily pursued. Here
+we see an escapement combining two levers, invented by the Chevalier de
+Bethune and applied by M. Thiout, master-horologist, at Paris in 1727.
+_P P'_ are the two levers or pallets separately pivoted. Upon the axis
+_V_, of the lever _P_, is fixed a fork which communicates the motion to
+the pendulum. The two levers are intimately connected by the two arms _B
+B'_, of which the former carries an adjusting screw, a well-conceived
+addition for regulating the opening between the pallets. The
+counter-weight _C_ compels constant contact between the arms _B B'_. The
+function is always the same, the recoil and the impulsion operate upon
+the two pallets simultaneously. This escapement enjoyed a certain degree
+of success, having been employed by a number of horologists who modified
+it in various ways.
+
+
+VARIOUS MODIFICATIONS
+
+Some of these modifications we shall show. For the first example, then,
+let Fig. 162 illustrate. In this arrangement the fork is carried upon
+the axis of the pallet _P'_, which effectually does away with the
+counter-weight _C_, as shown. Somewhat more complicated, but of the same
+intrinsic nature, is the arrangement displayed in Fig. 163. We should
+not imagine that it enjoyed a very extensive application. Here the two
+levers are completely independent of each other; they act upon the piece
+_B B_ upon the axis _V_ of the fork. The counter-weights _C C'_ maintain
+the arms carrying the rollers _D D'_ in contact with the piece _B B'_
+which thus receives the impulse from the wheel _R_. Two adjusting screws
+serve to place the escapement upon the center. By degrees these
+fantastic constructions were abandoned to make way for the anchor recoil
+escapement, which was invented, as we have said, in 1675, by G. Clement,
+a horologist, of London. In Fig. 164 we have the disposition of the
+parts as first arranged by this artist. Here the pallets are replaced by
+the inclines _A_ and _B_ of the anchor, which is pivoted at _V_ upon an
+axis to which is fixed also the fork. The tooth _a_ escapes from the
+incline or lever _A_, and the tooth _b_ immediately rests upon the lever
+_B_; by the action of the pendulum the escape wheel suffers a recoil as
+in the pallet escapement, and on the return of the pendulum the tooth
+_c_ gives out its impulse in the contrary direction. With this new
+system it became possible to increase the weight of the bob and at the
+same time lessen the effective motor power. The travel of the pendulum,
+or arc of oscillation, being reduced in a marked degree, an accuracy of
+rate was obtained far superior to that of the crown-wheel escapement.
+However, this new application of the recoil escapement was not adopted
+in France until 1695.
+
+[Illustration: Fig. 166]
+
+[Illustration: Fig. 167]
+
+The travel of the pendulum, though greatly reduced, still surpassed in
+breadth the arc in which it is isochronous, and repeated efforts were
+made to give such shape to the levers as would compel its oscillation
+within the arc of equal time; a motion which is, as was recognized even
+at that epoch, the prime requisite to a precise rating. Thus, in 1720,
+Julien Leroy occupied himself working out the proper shapes for the
+inclines to produce this desired isochronism. Searching along the same
+path, Ferd. Berthoud constructed an escapement represented by the Fig.
+165. In it we see the same inclines _A B_ of the former construction,
+but the locking is effected against the slides _C_ and _D_, the curved
+faces of which produce isochronous oscillations of the pendulum. The
+tooth _b_ imparts its lift and the tooth _c_ will lock against the face
+_C_; after having passed through its recoil motion this tooth _c_ will
+butt against the incline _A_ and work out its lift or impulse upon it.
+
+
+THE GABLE ESCAPEMENT.
+
+[Illustration: Fig. 168]
+
+[Illustration: Fig. 169]
+
+The _gable escapement_, shown in Fig. 166, allows the use of a heavier
+pendulum, at the same time the anchor embraces within its jaws a greater
+number of the escape-wheel teeth; an arrangement after this manner leads
+to the conclusion that with these long levers of the anchor the friction
+will be considerably increased and the recoil faces will, as a
+consequence, be quickly worn away. Without doubt, this was invented to
+permit of opening and closing the contact points of the anchor more
+easily. Under the name of the _English recoil anchor_ there came into
+use an escapement with a _reduced gable_, which embraced fewer teeth
+between the pallets or inclines; we give a representation of this in
+Fig. 167. This system seems to have been moderately successful. The
+anchor recoil escapement in use in Germany to-day is demonstrated in
+Fig. 168; this arrangement is also found in the American clocks. As we
+see, the anchor is composed of a single piece of curved steel bent to
+the desired curves. Clocks provided with this escapement keep reasonably
+good time; the resistance of the recoils compensate in a measure for the
+want of isochronism in the oscillations of the pendulum. Ordinary clocks
+require considerably more power to drive them than finer clocks and, as
+a consequence, their ticking is very noisy. Several means have been
+employed to dampen this noise, one of which we show in Fig. 169.
+
+[Illustration: Fig. 170]
+
+Here the anchor is composed of two pieces, _A B_, screwed upon a plate
+_H_ pivoting at _V_. In their arrangement the two pieces represent, as
+to distance and curvature, the counterpart of Fig. 168. At the moment of
+impact their extreme ends recoil or spring back from the shock of the
+escape teeth, but the resiliency of the metal is calculated to be strong
+enough to return them immediately to the contact studs _e e_.
+
+As a termination to this chapter, we shall mention the use made at the
+present day of the recoil lever escapement in repeating watches. We give
+a diagram of this construction in Fig. 170. The lever here is intended
+to restrain and regulate the motion of the small striking work. It is
+pivoted at _V_ and is capable of a very rapid oscillatory motion, the
+arc of which may, however, be fixed by the stud or stop _D_, which
+limits the swing of the fly _C_. This fly is of one piece with the lever
+and, together with the stud _D_, determines the angular motion of the
+lever. If the angle be large that means the path of the fly be long,
+then the striking train will move slowly; but if the teeth of the escape
+wheel _R_ can just pass by without causing the lever to describe a
+supplementary or extended arc, the striking work will run off rapidly.
+
+
+
+
+CHAPTER V.
+
+PUTTING IN A NEW CYLINDER.
+
+
+Putting in a new cylinder is something most watchmakers fancy they can
+do, and do well; but still it is a job very few workmen can do and
+fulfill all the requirements a job of this kind demands under the
+ever-varying conditions and circumstances presented in repairs of this
+kind. It is well to explain somewhat at this point: Suppose we have five
+watches taken in with broken cylinders. Out of this number probably two
+could be pivoted to advantage and make the watches as good as ever. As
+to the pivoting of a cylinder, we will deal with this later on. The
+first thing to do is to make an examination of the cylinder, not only to
+see if it is broken, but also to determine if pivoting is going to bring
+it out all right. Let us imagine that some workman has, at some previous
+time, put in a new cylinder, and instead of putting in one of the proper
+size he has put one in too large or too small. Now, in either case he
+would have to remove a portion of the escape-wheel tooth, that is,
+shorten the tooth: because, if the cylinder was too large it would not
+go in between the teeth, and consequently the teeth would have to be cut
+or stoned away. If the cylinder was too small, again the teeth would
+have to be cut away to allow them to enter the cylinder. All workmen
+have traditions, rules some call them, that they go by in relation to
+the right way to dress a cylinder tooth; some insisting that the toe or
+point of the tooth is the only place which should be tampered with.
+Other workmen insist that the heel of the tooth is the proper place.
+Now, with all due consideration, we would say that in ninety-nine cases
+out of a hundred the proper thing to do is to let the escape-wheel teeth
+entirely alone. As we can understand, after a moment's thought, that it
+is impossible to have the teeth of the escape wheel too long and have
+the watch run at all; hence, the idea of stoning a cylinder escape-wheel
+tooth should not be tolerated.
+
+
+ESCAPE-WHEEL TEETH _vs._ CYLINDER.
+
+It will not do, however, to accept, and take it for granted that the
+escape-wheel teeth are all right, because in many instances they have
+been stoned away and made too short; but if we accept this condition as
+being the case, that is, that the escape-wheel teeth are too short, what
+is the workman going to do about it? The owner of the watch will not pay
+for a new escape wheel as well as a new cylinder. The situation can be
+summed up about in this way, that we will have to make the best we can
+out of a bad job, and pick out and fit a cylinder on a compromise idea.
+
+In regard to picking out a new cylinder, it may not do to select one of
+the same size as the old one, from the fact that the old one may not
+have been of the proper size for the escape wheel, because, even in new,
+cheap watches, the workmen who "run in" the escapement knew very well
+the cylinder and escape wheel were not adapted for each other, but they
+were the best he had. Chapter II, on the cylinder escapement, will
+enable our readers to master the subject and hence be better able to
+judge of allowances to be made in order to permit imperfect material to
+be used.
+
+In illustration, let us imagine that we have to put in a new cylinder,
+and we have none of precisely the proper size, but we have them both a
+mere trifle too large and too small, and the question is which to use.
+Our advice is to use the smaller one if it does not require the
+escape-wheel teeth to be "dressed," that is, made smaller. Why we make
+this choice is based on the fact that the smaller cylinder shell gives
+less friction, and the loss from "drop"--that is, side play between the
+escape-wheel teeth and the cylinder--will be the same in both instances
+except to change the lost motion from inside to outside drop.
+
+In devising a system to be applied to selecting a new cylinder, we meet
+the same troubles encountered throughout all watchmakers' repair work,
+and chief among these are good and convenient measuring tools. But even
+with perfect measuring tools we would have to exercise good judgment, as
+just explained. In Chapter II we gave a rule for determining the outside
+diameter of a cylinder from the diameter of the escape wheel; but such
+rules and tables will, in nine instances out of ten, have to be modified
+by attendant circumstances--as, for instance, the thickness of the shell
+of the cylinder, which should be one-tenth of the outer diameter of the
+shell, but the shell is usually thicker. A tolerably safe practical rule
+and one also depending very much on the workman's good judgment is, when
+the escape-wheel teeth have been shortened, to select a cylinder giving
+ample clearance inside the shell to the tooth, but by no means large
+enough to fill the space between the teeth. After studying carefully
+the instructions just given we think the workman will have no difficulty
+in selecting a cylinder of the right diameter.
+
+
+MEASURING THE HEIGHTS.
+
+The next thing is to get the proper heights. This is much more easily
+arrived at: the main measurement being to have the teeth of the escape
+wheel clear the upper face of the lower plug. In order to talk
+intelligently we will make a drawing of a cylinder and agree on the
+proper names for the several parts to be used in this chapter. Such
+drawing is shown at Fig. 171. The names are: The hollow cylinder, made
+up of the parts _A A' A'' A'''_, called the shell--_A_ is the great
+shell, _A'_ the half shell, _A''_ the banking slot, and _A'''_ the small
+shell. The brass part _D_ is called the collet and consists of three
+parts--the hairspring seat _D_, the balance seat _D'_ and the shoulder
+_D''_, against which the balance is riveted.
+
+[Illustration: Fig. 171]
+
+The first measurement for fitting a new cylinder is to determine the
+height of the lower plug face, which corresponds to the line _x x_,
+Fig. 171. The height of this face is such as to permit the escape wheel
+to pass freely over it. In selecting a new cylinder it is well to choose
+one which is as wide at the banking slot _A''_ as is consistent with
+safety. The width of the banking slot is represented by the dotted lines
+_x u_. The dotted line _v_ represents the length to which the lower
+pivot _y_ is to be cut.
+
+[Illustration: Fig. 172]
+
+[Illustration: Fig. 173]
+
+There are several little tools on the market used for making the
+necessary measurements, but we will describe a very simple one which can
+readily be made. To do so, take about a No. 5 sewing needle and, after
+annealing, cut a screw thread on it, as shown at Fig, 172, where _E_
+represents the needle and _t t_ the screw cut upon it. After the screw
+is cut, the needle is again hardened and tempered to a spring temper and
+a long, thin pivot turned upon it. The needle is now shaped as shown at
+Fig. 173. The pivot at _s_ should be small enough to go easily through
+the smallest hole jewel to be found in cylinder watches, and should be
+about 1/16" long. The part at _r_ should be about 3/16" long and only
+reduced in size enough to fully remove the screw threads shown at _t_.
+
+[Illustration: Fig. 174]
+
+[Illustration: Fig. 175]
+
+[Illustration: Fig. 176]
+
+[Illustration: Fig. 177]
+
+We next provide a sleeve or guard for our gage. To do this we take a
+piece of hard brass bushing wire about 1/2" long and, placing it in a
+wire chuck, center and drill it nearly the entire length, leaving, say,
+1/10" at one end to be carried through with a small drill. We show at
+_F_, Fig. 174, a magnified longitudinal section of such a sleeve. The
+piece _F_ is drilled from the end _l_ up to the line _q_ with a drill of
+such a size that a female screw can be cut in it to fit the screw on the
+needle, and _F_ is tapped out to fit such a screw from _l_ up to the
+dotted line _p_. The sleeve _F_ is run on the screw _t_ and now appears
+as shown at Fig. 175, with the addition of a handle shown at _G G'_. It
+is evident that we can allow the pivot _s_ to protrude from the sleeve
+_F_ any portion of its length, and regulate such protrusion by the screw
+_t_. To employ this tool for getting the proper length to which to cut
+the pivot _y_, Fig. 171, we remove the lower cap jewel to the cylinder
+pivot and, holding, the movement in the left hand, pass the pivot _s_,
+Fig. 175, up through the hole jewel, regulate the length by turning the
+sleeve _F_ until the arm of the escape wheel _I_, Fig. 176, will just
+turn free over it. Now the length of the pivot _s_, which protrudes
+beyond the sleeve _F_, coincides with the length to which we must cut
+the pivot _y_, Fig. 171. To hold a cylinder for reducing the length of
+the pivot _y_, we hold said pivot in a pair of thin-edged cutting
+pliers, as shown at Fig. 177, where _N N'_ represent the jaws of a pair
+of cutting pliers and _y_ the pivot to be cut. The measurement is made
+by putting the pivot _s_ between the jaws _N N'_ as they hold the pivot.
+The cutting is done by simply filing back the pivot until of the right
+length.
+
+
+TURNING THE PIVOTS.
+
+We have now the pivot _y_ of the proper length, and what remains to be
+done is to turn it to the right size. We do not think it advisable to
+try to use a split chuck, although we have seen workmen drive the shell
+_A A'''_ out of the collet _D_ and then turn up the pivots _y z_ in said
+wire chuck. To our judgment there is but one chuck for turning pivots,
+and this is the cement chuck provided with all American lathes. Many
+workmen object to a cement chuck, but we think no man should lay claim
+to the name of watchmaker until he masters the mystery of the cement
+chuck. It is not such a very difficult matter, and the skill once
+acquired would not be parted with cheaply. One thing has served to put
+the wax or cement chuck into disfavor, and that is the abominable stuff
+sold by some material houses for lathe cement. The original cement, made
+and patented by James Bottum for his cement chuck, was made up of a
+rather complicated mixture; but all the substances really demanded in
+such cement are ultramarine blue and a good quality of shellac. These
+ingredients are compounded in the proportion of 8 parts of shellac and 1
+part of ultramarine--all by weight.
+
+
+HOW TO USE A CEMENT CHUCK.
+
+The shellac is melted in an iron vessel, and the ultramarine added and
+stirred to incorporate the parts. Care should be observed not to burn
+the shellac. While warm, the melted mass is poured on to a cold slab of
+iron or stone, and while plastic made into sticks about 1/2" in
+diameter.
+
+[Illustration: Fig. 178]
+
+[Illustration: Fig. 179]
+
+We show at Fig. 178 a side view of the outer end of a cement chuck with
+a cylinder in position. We commence to turn the lower pivot of a
+cylinder, allowing the pivot _z_ to rest at the apex of the hollow cone
+_a_, as shown. There is something of a trick in turning such a hollow
+cone and leaving no "tit" or protuberance in the center, but it is
+important it should be done. A little practice will soon enable one to
+master the job. A graver for this purpose should be cut to rather an
+oblique point, as shown at _L_, Fig. 179. The slope of the sides to the
+recess _a_, Fig. 178, should be to about forty-five degrees, making the
+angle at _a_ about ninety degrees. The only way to insure perfect
+accuracy of centering of a cylinder in a cement chuck is center by the
+shell, which is done by cutting a piece of pegwood to a wedge shape and
+letting it rest on the T-rest; then hold the edge of the pegwood to the
+cylinder as the lathe revolves and the cement soft and plastic. A
+cylinder so centered will be absolutely true. The outline curve at _c_,
+Fig. 178, represents the surface of the cement.
+
+The next operation is turning the pivot to the proper size to fit the
+jewel. This is usually done by trial, that is, trying the pivot into the
+hole in the jewel. A quicker way is to gage the hole jewel and then turn
+the pivot to the right size, as measured by micrometer calipers. In some
+cylinder watches the end stone stands at some distance from the outer
+surface of the hole jewel; consequently, if the measurement for the
+length of the pivot is taken by the tool shown at Fig. 175, the pivot
+will apparently be too short. When the lower end stone is removed we
+should take note if any allowance is to be made for such extra space.
+The trouble which would ensue from not providing for such extra end
+shake would be that the lower edge of the half shell, shown at _e_, Fig.
+171, would strike the projection on which the "stalk" of the tooth is
+planted. After the lower pivot is turned to fit the jewel the cylinder
+is to be removed from the cement chuck and the upper part turned. The
+measurements to be looked to now are, first, the entire length of the
+cylinder, which is understood to be the entire distance between the
+inner faces of the two end stones, and corresponds to the distance
+between the lines _v d_, Fig. 171. This measurement can be got by
+removing both end stones and taking the distance with a Boley gage or a
+douzieme caliper.
+
+
+A CONVENIENT TOOL FOR LENGTH MEASUREMENT.
+
+[Illustration: Fig. 180]
+
+A pair of common pinion calipers slightly modified makes as good a pair
+of calipers for length measurement as one can desire. This instrument is
+made by inserting a small screw in one of the blades--the head on the
+inner side, as shown at _f_, Fig. 180. The idea of the tool is, the
+screw head _f_ rests in the sink of the cap jewel or end stone, while
+the other blade rests on the cock over the balance. After the adjusting
+screw to the caliper is set, the spring of the blades allows of their
+removal. The top pivot _z_ of the cylinder is next cut to the proper
+length, as indicated by the space between the screwhead _f_ and the
+other blade of the pinion caliper. The upper pinion _z_ is held in the
+jaws of the cutting pliers, as shown in Fig. 177, the same as the lower
+one was held, until the proper length between the lines _d v_, Fig. 171,
+is secured, after which the cylinder is put back into the cement chuck,
+as shown at Fig. 178, except this time the top portion of the cylinder
+is allowed to protrude so that we can turn the top pivot and the balance
+collet _D_, Fig. 171.
+
+The sizes we have now to look to is to fit the pivot _z_ to the top
+hole jewel in the cock, also the hairspring seat _D_ and balance seat
+_D'_. These are turned to diameters, and are the most readily secured by
+the use of the micrometer calipers to be had of any large watchmakers'
+tool and supply house. In addition to the diameters named, we must get
+the proper height for the balance, which is represented by the dotted
+line _b_. The measurement for this can usually be obtained from the old
+cylinder by simply comparing it with the new one as it rests in the
+cement chuck. The true tool for such measurements is a height gage. We
+have made no mention of finishing and polishing the pivots, as these
+points are generally well understood by the trade.
+
+
+REMOVING THE LATHE CEMENT.
+
+One point perhaps we might well say a few words on, and this is in
+regard to removing the lathe cement. Such cement is usually removed by
+boiling in a copper dish with alcohol. But there are several objections
+to the practice. In the first place, it wastes a good deal of alcohol,
+and also leaves the work stained. We can accomplish this operation
+quicker, and save alcohol, by putting the cylinder with the wax on it in
+a very small homeopathic bottle and corking it tight. The bottle is then
+boiled in water, and in a few seconds the shellac is dissolved away. The
+balance to most cylinder watches is of red brass, and in some instances
+of low karat gold; in either case the balance should be repolished. To
+do this dip in a strong solution of cyanide of potassium dissolved in
+water; one-fourth ounce of cyanide in half pint of water is about the
+proper strength. Dip and rinse, then polish with a chamois buff and
+rouge.
+
+[Illustration: Fig. 181]
+
+In staking on the balance, care should be observed to set the banking
+pin in the rim so it will come right; this is usually secured by setting
+said pin so it stands opposite to the opening in the half shell. The
+seat of the balance on the collet _D_ should be undercut so that there
+is only an edge to rivet down on the balance. This will be better
+understood by inspecting Fig. 181, where we show a vertical section of
+the collet _D_ and cylinder _A_. At _g g_ is shown the undercut edge of
+the balance seat, which is folded over as the balance is rivetted fast.
+
+About all that remains now to be done is to true up the balance and
+bring it to poise. The practice frequently adopted to poise a plain
+balance is to file it with a half-round file on the inside, in order not
+to show any detraction when looking at the outer edge of the rim. A
+better and quicker plan is to place the balance in a split chuck, and
+with a diamond or round-pointed tool scoop out a little piece of metal
+as the balance revolves. In doing this, the spindle of the lathe is
+turned by the hand grasping the pulley between the finger and thumb. The
+so-called diamond and round-pointed tools are shown at _o o'_, Fig. 182.
+The idea of this plan of reducing the weight of a balance is, one of the
+tools _o_ is rested on the T-rest and pressed forward until a chip is
+started and allowed to enter until sufficient metal is engaged, then, by
+swinging down on the handle of the tool, the chip is taken out.
+
+[Illustration: Fig. 182]
+
+[Illustration: Fig. 183]
+
+In placing a balance in a step chuck, the banking pin is caused to enter
+one of the three slots in the chuck, so as not to be bent down on to the
+rim of the balance. It is seldom the depth between the cylinder and
+escape wheel will need be changed after putting in a new cylinder; if
+such is the case, however, move the chariot--we mean the cock attached
+to the lower plate. Do not attempt to change the depth by manipulating
+the balance cock. Fig. 183 shows, at _h h_, the form of chip taken out
+by the tool _o o'_, Fig. 182.
+
+
+
+
+INDEX
+
+
+  A
+
+  Acid frosting, 46
+
+  "Action" drawings, 90
+
+  Action of a chronometer escapement, 142
+
+  Acting surface of entrance lip, 127
+
+  Actions of cylinder escapement, 112
+
+  Adhesion of parallel surfaces, 94
+
+  Adjustable pallets, 98
+
+  Adjusting screw for drawing instruments, 21
+
+  Analysis of principles involved in detent, 137
+
+  Analysis of the action of a lever escapement, 86
+
+  Angle-measuring device, 68
+
+  Angular extent of shell of cylinder, 122
+
+  Angular motion, drawing an escapement to show, 91
+    How measured, 69
+    Of escape wheel, 37
+
+  Antagonistic influences, 133
+
+  Arc of degrees, 9
+
+  Atmospheric disturbances, 74
+
+  Attainment of isochronism, 159
+
+
+  B
+
+  Balance, how it controls timekeeping, 73
+    Weight and inertia of, 133
+
+  Balance spring, inventor of, 132
+
+  Banking slot of cylinder, 112
+
+  Bankings, effect of opening too wide, 63
+
+  Bar compasses, 21
+
+  Barometric pressure, 74
+
+  Basis for close measurements, 96
+
+
+  C
+
+  Cement chuck, how to use, 173
+
+  Chronometer detent, importance of light construction, 136
+
+  Chronometer escapement, 131, 155
+    Four principal parts of, 134
+
+  Circular pallets, 27
+
+  Club-tooth escapement, 30, 34
+
+  Club-tooth lever escapement with circular pallets and
+    tangential lockings, 83
+
+  Crown-wheel escapement, 155
+
+  Cylinder, drawing a, 120
+    Outer diameter of, 116
+    Putting in a new, 169
+
+  Cylinder escapement, 155
+    Date of invention, etc., 111
+    Forms and proportions of several parts of, 111
+    Names of various parts, 112
+
+  Cylinder lips, proper shape of, 124
+
+
+  D
+
+  Dead-beat escapement, 131, 135
+    Only one true, 112
+
+  Depth, between cylinder and escape wheel, 129
+    Effect of changing, 176
+
+  Designing a double roller, 77
+
+  Detached escapement, 155
+
+  Detent, functions of the, 137
+
+  Detent escapement, 131, 155
+    Faults in, 132
+
+  Detent spring dimensions, 138
+
+  Detent springs, width of, 147
+
+  Discharging jewel, setting the, 142
+
+  Discharging roller, 136
+
+  Dividers, 9
+    Making, 10
+
+  Double pendulum, 160
+
+  Double-roller escapement, 75
+
+  Draw defined, 85
+
+  Drawing-board, 11
+
+  Drawing instruments, 9
+
+  Drawings, advantage of large, 29
+
+  Drop and draw, 150
+
+  Duplex escapement, 131, 155
+
+
+  E
+
+  Elasticity of spring, 133
+
+  Engaging friction, 81
+
+  English recoil anchor, 167
+
+  Entrance lip of cylinder escapement, 125
+
+  Escapement angles, measuring, 101
+
+  Escapement error, study of, 64
+
+  Escapement matching tool, 106
+
+  Escapement model, 40
+    Balance, 42
+    Balance staff, 44
+    Bridges, 41, 42
+    Escape wheel, 43
+    Extra balance cock, 45
+    "Frosting", 46
+    Hairspring, 42
+    Jewel for, 43
+    Lower plate, 41
+    Main plate, 41
+    Movement for, 41
+    Pallet staff, 42
+    Pillars, 43
+    Regulator, 46
+    Uses of, 44
+    Wood base for, 41
+
+  Escapements compared, 103
+
+  Escapement of Dutertre, 160
+
+  Escape-wheel action, 30
+
+  Escape-wheel, delineating an, 11
+
+  Escape-wheel teeth vs. cylinder, 169
+
+  Escape-wheel tooth in action, delineating an, 126
+
+  Exit pallet, 26
+
+  Experiments of Galileo, 158
+
+  Experiments with a chronometer, 142
+
+  Extent of angular impulse, 118
+
+
+  F
+
+  "Fall" defined, 106
+
+  Faults in the detent escapement, 132
+
+  Fixed rules, of little value to student, 137
+
+  Flexure of gold spring, 146
+
+  Foot, fitting up the, 151
+
+  Fork, testing the, 71
+
+  Fork action, 30
+    Theory of, 59
+
+  Fork and roller action, 54
+
+  Formulas for delineating cylinder escapement, 115
+
+  Frictions, 24
+
+  Frictional escapement, 131, 132
+
+  Frictional surfaces, 63
+
+  Fusee, 131
+
+
+  G
+
+  Gable escapement, 167
+
+  Gage, a new, 172
+
+  Graham anchor escapement, 155
+
+  Gold spring, 146
+
+  Guard point, 79
+    Material for, 79
+
+  Gummy secretion on impulse and discharging stones, 147
+
+
+  H
+
+  Heights in cylinders, how obtained, 171
+
+  Hole jewels, distance apart, 140
+
+
+  I
+
+  Imaginary faults in cylinders, 129
+
+  Impulse angle, 118
+
+  Impulse arc, extent of, 134
+
+  Impulse jewel set oblique, 147
+
+  Impulse planes, locating outer angle of, 39
+
+  Impulse roller, 136
+
+  Incline of teeth, 122
+
+  Inertia of balance, 133
+
+  Inventions of
+    Berthoud, 163
+    Bethune, 165
+    Clement, 166
+    Dr. Hook, 162
+    Harrison, 161
+    Hautefeuille, 161
+    Huygens, 158
+    Leroy, 163
+    Thiout, 165
+
+
+  J
+
+  Jewel pin, determining size, 58
+    Cementing in, 67
+    Settings, 66
+
+  Jewel-pin setters, 67
+
+
+  L
+
+  Lathe cement, 173
+    Removing, 175
+
+  Lever, proper length of, 61
+
+  Lever fork, horn of, 61
+    prongs of, 60
+
+  Lift, real and apparent, 112
+
+  Lifting angle, 114
+
+  Lock, amount of, 28
+    Defined, 85
+
+  Lock and drop testing, 69
+
+  Locking jewel, moving the, 149
+
+  Locking stone, good form of, 144
+
+  Lower plate, circular opening in, 56
+
+
+  M
+
+  Marine chronometer, number of beats to hour, 148
+
+  Mathematics, 95
+
+  Measuring tools, 171
+
+  Metal drawings, advantages of, 140
+
+  Motion, how obtained, 16
+
+  Movement holder, 110
+
+
+  N
+
+  Neutral lockings, 84
+
+
+  O
+
+  Original designing, 148
+
+
+  P
+
+  Pallet action, locating the, 90
+
+  Pallet-and-fork action, 12, 13, 17, 18
+
+  Pallet stones, how to set, 104
+
+  Pallets, adjusting to match the fork, 65
+
+  Paper for drawing, 11
+
+  Parts, relations of the, 32
+
+  Passing hollow, 62
+
+  Perfected lever escapement, 87
+
+  Pivots, turning, 172
+
+  Point of percussion, 139
+
+  Points for drawing instruments, 20
+
+  Polishing materials, 52
+
+  Power leaks, 16
+
+  Power lost in lever escapement, 87
+
+  Practical problems in the lever escapement, 98
+
+
+  R
+
+  Radial extent of outside of cylinder, 125
+
+  Ratchet-tooth escape wheel, 12
+
+  Recoil anchor escapement, 155
+
+  Recoil escapement, 154
+
+  Reduced gable escapement, 167
+
+  Retrograde motion, 36
+
+  Roller action, why 30 degrees, 55
+    Of double roller, 78
+
+  Roller diameter, determining the, 55
+
+  Ruling pen, 9
+
+
+  S
+
+  Safety action, 56
+
+  Scale of inches, 9
+
+  Screws, making extra large, 45
+
+  Screwheads, fancy, 45
+
+  Selecting new cylinder, 170
+
+  Shaping, advantages gained in, 116
+
+  Sheet steel, cutting, 48
+
+  Short fork, 100
+
+  Sound as indicator of correct action, 144
+
+  Spring, elasticity of, 133
+
+  Staking on a balance, 175
+
+  Steel, polishing, 49
+    Tempering, 49
+
+  Study drawings, 124
+
+  Systems of measurements, 114
+
+
+  T
+
+  Tangential lockings, 80, 148
+
+  Test gage for angular movement, 65
+
+  Theoretical action of double roller, 76
+
+  Timekeeping, controlled by balance, 73
+
+  Tool for length measurement, 174
+
+  Tools, measuring, 171
+
+  Triangle, 18
+
+  T-square, 9
+
+
+  U
+
+  Unlocking action, 56
+
+  Unlocking roller, 136
+
+
+  V
+
+  Verge escapement, 131, 155
+
+
+  W
+
+  Weight and inertia of balance, 133
+
+  Working model of cylinder escapement, 123
+
+
+
+     *     *     *     *     *     *
+
+
+
+THE WATCH ADJUSTER'S MANUAL
+
+[Illustration]
+
+A Complete and Practical Guide for Watchmakers in Adjusting Watches and
+Chronometers for Isochronism, Position, Heat and Cold.
+
+
+BY CHARLES EDGAR FRITTS (EXCELSIOR),
+
+Author of "Practical Hints on Watch Repairing," "Practical Treatise on
+Balance Spring," "Electricity and Magnetism for Watchmakers," etc., etc.
+
+This well-known work is now recognized as the standard authority on the
+adjustments and kindred subjects, both here and in England. It contains
+an exhaustive consideration of the various theories proposed, the
+mechanical principles on which the adjustments are based, and the
+different methods followed in actual practice, giving all that is
+publicly known in the trade, with a large amount of entirely new
+practical matter not to be found elsewhere, obtained from the best
+manufacturers and workmen, as well as from the author's own studies and
+experiences.
+
+Sent postpaid to any part of the world on receipt of $2.50 (10s. 5d.)
+
+  THE KEYSTONE (SOLE AGENT),
+  19TH AND BROWN STREETS, PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE ART OF ENGRAVING
+
+[Illustration]
+
+A Complete Treatise on the Engraver's Art, with Special Reference to
+Letter and Monogram Engraving. Specially Compiled as a Standard
+Text-Book for Students and a Reliable Reference Book for Engravers.
+
+This work is the only thoroughly reliable and exhaustive treatise
+published on this important subject. It is an ideal text-book, beginning
+with the rudiments and leading the student step by step to a complete
+and practical mastery of the art. Back of the authorship is a long
+experience as a successful engraver, also a successful career as an
+instructor in engraving. These qualifications ensure accuracy and
+reliability of matter, and such a course of instruction as is best for
+the learner and qualified engraver.
+
+The most notable feature of the new treatise is the instructive
+character of the illustrations. There are over 200 original
+illustrations by the author. A very complete index facilitates reference
+to any required topic.
+
+Bound in Silk Cloth--208 Pages and 216 Illustrations.
+
+Sent postpaid to any part of the world on receipt of price, $1.50 (6s.
+3d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE KEYSTONE PORTFOLIO OF MONOGRAMS
+
+[Illustration: C.B.R.]
+
+[Illustration: A.O.U.W]
+
+[Illustration: I.R.C.]
+
+[Illustration: G.H.I.]
+
+This portfolio contains 121 combination designs. These designs were
+selected from the best of those submitted in a prize competition held by
+The Keystone, and will be found of value to every one doing engraving.
+
+The designs are conceded to be the best in the market, excelling in art
+and novelty of combination and skill in execution.
+
+They are printed from steel plates on stiff, durable paper, and contain
+sample monograms in a variety of combinations.
+
+The portfolio is a bench requirement that no jeweler can afford to be
+without. It is a necessary supplement to any text-book on letter
+engraving.
+
+  Price,
+  50 Cents (2s.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE OPTICIAN'S MANUAL
+
+VOL. I.
+
+BY C.H. BROWN, M.D.
+
+Graduate University of Pennsylvania; Professor of Optics and Refraction;
+formerly Physician in Philadelphia Hospital; Member of Philadelphia
+County, Pennsylvania State and American Medical Societies.
+
+[Illustration]
+
+The Optician's Manual, Vol. I., has proved to be the most popular work
+on practical refraction ever published. The knowledge it contains has
+been more effective in building up the optical profession than any other
+educational factor. A study of it is essential to an intelligent
+appreciation of Vol. II., for it lays the foundation structure of all
+optical knowledge, as the titles of its ten chapters show:
+
+  Chapter    I.--Introductory Remarks.
+  Chapter   II.--The Eye Anatomically.
+  Chapter  III.--The Eye Optically; or, The Physiology of Vision.
+  Chapter   IV.--Optics.
+  Chapter    V.--Lenses.
+  Chapter   VI.--Numbering of Lenses.
+  Chapter  VII.--The Use and Value of Glasses.
+  Chapter VIII.--Outfit Required.
+  Chapter   IX.--Method of Examination.
+  Chapter    X.--Presbyopia.
+
+The Optician's Manual, Vol. I., is complete in itself, and has been the
+entire optical education of many successful opticians. For student and
+teacher it is the best treatise of its kind, being simple in style,
+accurate in statement and comprehensive in its treatment of refractive
+procedure and problems. It merits the place of honor beside Vol. II. in
+every optical library.
+
+Bound in Cloth--422 pages--colored plates and Illustrations.
+
+Sent postpaid on receipt of $2.00 (8s. 4d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE OPTICIAN'S MANUAL
+
+VOL. II.
+
+BY C.H. BROWN, M.D.
+
+Graduate University of Pennsylvania; Professor of Optics and Refraction;
+formerly Physician in Philadelphia Hospital; Member of Philadelphia
+County, Pennsylvania State and American Medical Societies.
+
+[Illustration]
+
+The Optician's Manual, Vol. II., is a direct continuation of The
+Optician's Manual, Vol. I., being a much more advanced and comprehensive
+treatise. It covers in minutest detail the four great subdivisions of
+practical eye refraction, viz:
+
+  Myopia.
+  Hypermetropia.
+  Astigmatism.
+  Muscular Anomalies.
+
+It contains the most authoritative and complete researches up to date on
+these subjects, treated by the master hand of an eminent oculist and
+optical teacher. It is thoroughly practical, explicit in statement and
+accurate as to fact. All refractive errors and complications are clearly
+explained, and the methods of correction thoroughly elucidated.
+
+This book fills the last great want in higher refractive optics, and the
+knowledge contained in it marks the standard of professionalism.
+
+Bound in Cloth--408 pages--with illustrations.
+
+Sent postpaid on receipt of $2.00 (8s. 4d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+SKIASCOPY AND THE USE OF THE RETINOSCOPE
+
+[Illustration]
+
+A Treatise on the Shadow Test in its Practical Application to the Work
+of Refraction, with an Explanation in Detail of the Optical Principles
+on which the Science is Based.
+
+This new work, the sale of which has already necessitated a second
+edition, far excels all previous treatises on the subject in
+comprehensiveness and practical value to the refractionist. It not only
+explains the test, but expounds fully and explicitly the principles
+underlying it--not only the phenomena revealed by the test, but the why
+and wherefore of such phenomena.
+
+It contains a full description of skiascopic apparatus, including the
+latest and most approved instruments.
+
+In depth of research, wealth of illustration and scientific completeness
+this work is unique.
+
+Bound in cloth; contains 231 pages and 73 illustrations and colored
+plates.
+
+Sent postpaid to any part of the world on receipt of $1.00 (4s. 2d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH AND BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+PHYSIOLOGIC OPTICS
+
+Ocular Dioptrics--Functions of the Retina--Ocular Movements and
+Binocular Vision
+
+BY DR. M. TSCHERNING
+
+Adjunct-Director of the Laboratory of Ophthalmology at the Sorbonne,
+Paris
+
+AUTHORIZED TRANSLATION
+
+BY CARL WEILAND, M.D.
+
+Former Chief of Clinic in the Eye Department of the Jefferson College
+Hospital, Philadelphia, Pa.
+
+This is the crowning work on physiologic optics, and will mark a new era
+in optical study. Its distinguished author is recognized in the world of
+science as the greatest living authority on this subject, and his book
+embodies not only his own researches, but those of the several hundred
+investigators who, in the past hundred years, made the eye their
+specialty and life study.
+
+Tscherning has sifted the gold of all optical research from the dross,
+and his book, as now published in English with many additions, is the
+most valuable mine of reliable optical knowledge within reach of
+ophthalmologists. It contains 380 pages and 212 illustrations, and its
+reference list comprises the entire galaxy of scientists who have made
+the century famous in the world of optics.
+
+The chapters on Ophthalmometry, Ophthalmoscopy, Accommodation,
+Astigmatism, Aberration and Entoptic Phenomena, etc.--in fact, the
+entire book contains so much that is new, practical and necessary that
+no refractionist can afford to be without it.
+
+Bound in Cloth. 380 Pages, 212 Illustrations.
+
+Price, $3.50 (14s. 7d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+OPHTHALMIC LENSES
+
+Dioptric Formulae for Combined Cylindrical Lenses, The Prism-Dioptry and
+Other Original Papers
+
+BY CHARLES F. PRENTICE, M.E.
+
+A new and revised edition of all the original papers of this noted
+author, combined in one volume. In this revised form, with the addition
+of recent research, these standard papers are of increased value.
+Combined for the first time in one volume, they are the greatest
+compilation on the subject of lenses extant.
+
+This book of over 200 pages contains the following papers:
+
+  Ophthalmic Lenses.
+  Dioptric Formulae for Combined Cylindrical Lenses.
+  The Prism-Dioptry.
+  A Metric System of Numbering and Measuring Prisms.
+    The Relation of the Prism-Dioptry to the Meter Angle.
+    The Relation of the Prism-Dioptry to the Lens-Dioptry.
+  The Perfected Prismometer.
+  The Prismometric Scale.
+  On the Practical Execution of Ophthalmic Prescriptions involving Prisms.
+  A Problem in Cemented Bi-Focal Lenses, Solved by the Prism-Dioptry.
+  Why Strong Contra-Generic Lenses of Equal Power Fail to Neutralize
+    Each Other.
+  The Advantages of the Sphero-Toric Lens.
+  The Iris, as Diaphragm and Photostat.
+  The Typoscope.
+  The Correction of Depleted Dynamic Refraction (Presbyopia).
+
+_Press Notices on the Original Edition:_
+
+
+OPHTHALMIC LENSES.
+
+"The work stands alone, in its present form, a compendium of the various
+laws of physics relative to this subject that are so difficult of access
+in scattered treatises."--_New England Medical Gazette._
+
+"It is the most complete and best illustrated book on this special
+subject ever published."--_Horological Review_, New York.
+
+"Of all the simple treatises on the properties of lenses that we have
+seen, this is incomparably the best.... The teacher of the average
+medical student will hail this little work as a great boon."--_Archives
+of Ophthalmology, edited by H. Knapp, M.D._
+
+DIOPTRIC FORMULAE FOR COMBINED CYLINDRICAL LENSES.
+
+"This little brochure solves the problem of combined cylinders in all
+its aspects, and in a manner simple enough for the comprehension of the
+average student of ophthalmology. The author is to be congratulated upon
+the success that has crowned his labors, for nowhere is there to be
+found so simple and yet so complete an explanation as is contained in
+these pages."--_Archives of Ophthalmology, edited by H. Knapp, M.D._
+
+"This exhaustive work of Mr. Prentice is a solution of one of the most
+difficult problems in ophthalmological optics. Thanks are due to Mr.
+Prentice for the excellent manner in which he has elucidated a subject
+which has not hitherto been satisfactorily explained."--_The Ophthalmic
+Review_, London.
+
+The book contains 110 Original Diagrams. Bound in cloth.
+
+Price, $1.50 (6s. 3d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+OPTOMETRIC RECORD BOOK
+
+
+A record book, wherein to record optometric examinations, is an
+indispensable adjunct of an optician's outfit.
+
+The Keystone Optometric Record Book was specially prepared for this
+purpose. It excels all others in being not only a record book, but an
+invaluable guide in examination.
+
+The book contains two hundred record forms with printed headings,
+suggesting, in the proper order, the course of examination that should
+be pursued to obtain most accurate results.
+
+Each book has an index, which enables the optician to refer instantly to
+the case of any particular patient.
+
+The Keystone Record Book diminishes the time and labor required for
+examinations, obviates possible oversights from carelessness and assures
+a systematic and thorough examination of the eye, as well as furnishes a
+permanent record of all examinations.
+
+Sent postpaid on receipt of $1.00 (4s. 2d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE KEYSTONE BOOK OF MONOGRAMS
+
+This book contains 2400 designs and over 6000 different combinations of
+two and three letters.
+
+Is an essential to every jeweler's outfit. It is not only necessary for
+the jeweler's own use and guidance, but also to enable customers to
+indicate exactly what they want, thus saving time and possible
+dissatisfaction.
+
+The Monograms are purposely left in outline, in order to show clearly
+how the letters are intertwined or woven together. This permits such
+enlargement or reduction of the Monogram as may be desired, and as much
+shading, ornamentation and artistic finish as the jeweler may wish to
+add.
+
+This comprehensive compilation of Monograms is especially available as a
+reference book in busy seasons. Its use saves time, thought and labor,
+and ensures quick and satisfactory work.
+
+Monograms are the fad of the time, and there's money for the jeweler in
+Monogram engraving. The knowledge in this book can be turned into cash.
+All the various styles of letters are illustrated.
+
+Price, $1.00 (4s. 2d.)
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+THE KEYSTONE RECORD BOOK OF WATCH REPAIRS
+
+This book is 9 x 11 inches, has 120 pages, and space for recording
+sixteen hundred jobs in detail. It is made of linen ledger paper, bound
+in cloth with leather back and corners.
+
+Price, $1.00 (4s. 2d.), prepaid.
+
+No other record book on the market is so complete, and all cost more.
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+         *       *       *       *       *
+
+  THE KEYSTONE
+  BOOK OF GUARANTEES OF WATCH REPAIRS
+
+  This book contains two hundred printed guarantees, and is
+  handsomely bound. Each guarantee is 31/4 x 71/2 inches, and
+  most carefully worded. Jewelers have discovered that the use
+  of these guarantees is a most effective way to secure and cultivate
+  public confidence. We sell a book of two hundred for
+
+  $1.00 (4s. 2d.), prepaid,
+
+  which is one-third less than the price charged by others for a
+  similar book.
+
+  PUBLISHED BY THE KEYSTONE,
+  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
+  19TH & BROWN STS., PHILADELPHIA, U.S.A.
+
+
+
+***END OF THE PROJECT GUTENBERG EBOOK WATCH AND CLOCK ESCAPEMENTS***
+
+
+******* This file should be named 17021.txt or 17021.zip *******
+
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