Chapter I: The Detached Lever Escapement (1)

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.

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.

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.

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.

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.

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.

ESTABLISHING THE CENTER OF PALLET STAFF.

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.

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.

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.

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.

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.

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.

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_.

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'_.

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.

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_.

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_.