Radius of safety roller to be 4/7 of the theoretical impulse radius. The length of horn is to be such that the end would point at least to the center of the ruby pin when the edge of the crescent pa.s.ses the dart; s.p.a.ce between the end of horn and ruby pin is to be 1.

It is well to know that the angles for width of teeth, pallets and drop are measured from the wheel center, while the lifting and locking angles are struck from the pallet center, the draw from the locking corners of the pallets, and the inclination of the teeth from the locking edge.

In the fork and roller action, the angle of motion, the width of slot, the ruby pin and its shake, the freedom between dart and roller, of ruby pin with acting edge of fork and end of horn are all measured from the pallet center, while the impulse angle and the crescent are measured from the balance center. A sensible drawing board measures 17 24 inches, we also require a set of good drawing instruments, the finer the instruments the better; pay special attention to the compa.s.ses, pens and protractor; add to this a straight ruler and set square.

The best all-round drawing paper, both for India ink and colored work has a rough surface; it must be fastened firmly and evenly to the board by means of thumb tacks; the lines must be light and made with a hard pencil. Use Higgins' India ink, which dries rapidly.

[Ill.u.s.tration]

We will begin by drawing the center line A' A B; use the point B for the escape center; place the compa.s.s on it and strike G H, the primitive or geometrical circle of the escape wheel; set the center of the protractor at B and mark off an angle of 30 on each side of the line of centers; this will give us the angles A B E and A B F together, forming the angle F B E of 60, which represents from lock to lock of the pallets. Since the chord of the angle of 60 is equal to the radius of the circle, this gives us an easy means of verifying this angle by placing the compa.s.s at the points of intersection of F B and E B with the primitive circle G H; this distance must be equal to the radius of the circle. At these points we will construct right angles to E B and F B, thus forming the tangents C A and D A to the primitive circle G H. These tangents meet on the line of centers at A, which will be the pallet center. Place the compa.s.s at A and draw the locking circle M N at the points of intersection of E B and F B with the primitive circle G H. The locking edges of the pallets will always stand on this circle no matter in what relation the pallets stand to the wheel. Place the center of the protractor at B and draw the angle of width of pallets of 6; I B E being for the engaging and J B F for the disengaging pallet. In the equidistant pallet I B is drawn on the side towards the center, while J B is drawn further from the center.

If we were drawing a circular pallet, one-half the width of pallets would be placed on each side of E B and F B. At the points of intersection of I B and J B with the primitive circle G H we draw the path O for the discharging edge of the engaging and P for that of the disengaging pallet. The total lock being 1, we construct V' A at this angle from C A; the point of intersection of V' A with the locking circle M N, is the position of the locking corner of the engaging pallet. The pallet having 12 draw when locked we place the center of the protractor on this corner and draw the angle Q M E. Q M will be the locking face of the engaging pallet. If the face of the pallet were on the line E B there would be no draw, and if placed to the opposite side of E B the tooth would repel the pallet, forming what is known as the repellant escapement.

[Ill.u.s.tration: Fig. 28.]

Having shown how to delineate the locking face of the engaging pallet when locked, we will now consider how to draft both it and the disengaging pallet in correct positions when unlocked; to do so we direct our attention until further notice to Fig. 28. The locking faces Q M of the engaging and S N of the disengaging pallets are shown in dotted lines _when locked_. We must now consider the relation which the locking faces will bear to E B in the engaging, and to F B in the disengaging pallets when unlocked. This is a question of some importance; it is easy enough to represent the 12 from the 30 angles when locked; we must be certain that they would occupy exactly that position and yet show them unlocked; we shall take pains to do so. In due time we shall show that there is no appreciable loss of lift on the engaging pallet in the escapement ill.u.s.trated; the angle T A V therefore shows the total lift; we have not shown the corresponding angles on the disengaging side because the angles are somewhat different, but the total lift is still the same. G H represents the primitive circle of the escape wheel, and X Z that of the real, while M N represents the circular course which the locking corners of the pallets take in an equidistant escapement. At a convenient position we will construct the circle C C' D from the pallet center A. Notice the points _e_ and _c_, where V A and T A intersect this circle; the s.p.a.ce between _e_ and _c_ represents the extent of the motion of the pallets at this particular distance from the center A; this being so, then let us apply it to the engaging pallet. At the point of intersection _o_ of the dotted line Q M (which is an extended line on which the face of the pallet lies when locked), with the circle C C' D, we will plant our dividers and transfer _e c_ to _o n_. By setting our dividers on _o_ M and transferring to _n_ M', we will obtain the location of Q' M', the locking face when unlocked. Let us now turn our attention to the disengaging pallet. The dotted line S N represents the location of the locking face of the disengaging pallet when locked at an angle of 12 from F B. At the intersection of S N with the circle C C' D we obtain the point _j_. The motion of the two pallets being equal, we transfer the distance _e c_ with the dividers from _j_ and obtain the point _l_.

By setting the dividers on _j_ N and transferring to _l_ N' we draw the line S' N' on which the locking face of the disengaging pallet will be located when unlocked. It will be perfectly clear to anyone that through these means we can correctly represent the pallets in any desired position.

We will notice that the face Q' M' of the engaging pallet when unlocked stands at a greater angle to E B than it did when locked, while the opposite is the case on the disengaging pallet, in which the angle S' N' F is much less than S N F. This shows that the _deeper_ the engaging pallet locks, the lighter will the draw be, while the opposite holds good with the disengaging pallet; also, that the draw increases during the unlocking of the engaging, and decreases during the unlocking of the disengaging pallet. These points show that the draw should be measured with the _fork standing against the bank_; not when the locking corner of the pallet stands on the primitive circle, as is so often done. The recoil of the wheel (which determines the draw), is ill.u.s.trated by the difference between the locking circle M N and the face Q M for the engaging, and S N for the disengaging pallet, and along the _acting_ surface it is alike on each pallet, showing that the draft angle should be the same on each pallet.

A number of years ago we constructed the escapement model which we herewith ill.u.s.trate. All the parts are adjustable; the pallets can be moved in any direction, the draft angles can be changed at will. Through this model we can practically demonstrate the points of which we have spoken. Such a model can be made by workmen after studying these papers.

[Ill.u.s.tration]

In both the equidistant and circular pallets the locking face S N of the disengaging pallet deviates more from the locking circle M N than does the locking face Q M of the engaging pallet, as will be seen in the diagram. This is because the draft angle is struck from E B which deviates from the locking circle in such a manner, that if the face of a pallet were planted on it and _locked deep enough_ to show it, the wheel would actually _repel_ the pallet, whereas with the disengaging pallet if it were planted on F B, it would actually produce draw if locked very deep; this is on account of the natural deviation of the 30 lines from the locking circle. This difference is more p.r.o.nounced in the circular than in the equidistant pallet, because in the former we have two locking circles, the larger one being for the engaging pallet, and as an arc of a large circle does not deviate as much from a straight line as does that of a smaller circle, it will be easily understood that the natural difference before spoken of is only enhanced thereby. For this reason in order to produce an _actual_ draw of 12, the engaging pallet may be set at a slightly greater angle from E B in the circular escapement; the amount depends upon the width of the pallets; the requirements are that the recoil of the wheel will be the same on each pallet. We must, however, repeat that one of the most important points is to measure the draw when the fork stands against the bank, thereby _increasing_ the draw on the engaging and _decreasing_ that of the disengaging pallet _during_ the unlocking action, thus _naturally_ balancing one fault with another.

We will again proceed with the delineation of the escapement here ill.u.s.trated. After having drawn the locking face Q M, we draw the angle of width of teeth of 4, by planting the protractor on the escape center B. We measure the angle E B K, from the locking face of the pallet; the line E B does not touch the locking face of the pallet at the present time of contact with the tooth, therefore a line must be drawn from the point of contact to the center B. We did so in our drawing but do not ill.u.s.trate it, as in a reduced engraving of this kind it would be too close to E B and would only cause confusion. We will now draw in the lifting angle of 3 for the tooth. From the tangent C A we draw T A at the required angle; at the point of intersection of T A with the 30 line E B we have the real circ.u.mference of the escape wheel. It will only be necessary to connect the locking edge of the tooth with the line K B, where the real or outer circle intersects it. It must be drawn in the same manner in the circular escapement; if the tooth were drawn up to the intersection of K B with T A, the lift would be too great, as that point is further from the center A than the points of contact are.

If the real or outer circle of the wheel intersects both the locking circle M N and the path O of the discharging edge at the points where T A intersects them, then there will be _no loss_ of lift on the engaging pallet. This is precisely how it is in the diagram; but if there is any deviation, then the angle of loss must be measured on the _real_ diameter of the wheel and not on the primitive, as is usually done, as the real diameter of the wheel, or in other words the heel of the tooth, forms the last point of contact. With a wider tooth and a greater lifting angle there will even be a _gain_ of lift on the engaging pallet; the pallet in such a case would actually require a smaller lifting angle, according to the amount of gain. We gave full directions for measuring the loss when describing its effects in Fig. 8.

Whatever the loss amounts to, it is added to the lifting plane of the pallet. In the diagram under discussion there is no loss, consequently the lifting angle on the pallet is to be 5. From V' A we draw V A at the required angle; the point of intersection of V A with the path O will be the discharging edge O. It will now only be necessary to connect the locking corner M with it, and we have the lifting plane of the pallet; the discharging side of the pallet is then drawn parallel to the locking face and made a suitable length. We will now draw the locking edges of the tooth by placing the center of the protractor on the locking edge M and construct the angle B M M' of 24 and draw a circle from the scape center B, to which the line M M' will be a tangent. We will utilize this circle in drawing in the faces of the other teeth after having s.p.a.ced them off 24 apart, by simply putting a ruler on the locking edges and on the periphery of the circle.

We now construct W' A as a tangent to the outer circle of the wheel, thus forming the lifting angle D A W' of 3 for the teeth; this corresponds to the angle T A C on the engaging side. W' A touches the outer circle of the wheel at the intersection of F B with it. We will notice that there is considerable deviation of W' A from the circle at the intersection of J B with it. At the intersecting of this point we draw U A; the angle U A W' is the loss of lift. This angle must be added to the lifting angle of the pallets; we see that in this action there is no loss on the engaging pallet, but on the disengaging the loss amounts to approximately ? in the action ill.u.s.trated. As we have allowed of run for the pallets, the discharging edge P is removed at this angle from U A; we do not ill.u.s.trate it, as the lines would cause confusion being so close together. The lifting angle on the pallet is measured from the point P and amounts to 5 + the angle of the loss; the angle W A U embraces the above angles besides for run. If the locks are equal on each pallet, it proves that the lifts are also equal. This gives us a practical method of proving the correctness of the drawing; to do so, place the dividers on the locking circle M N at the intersection of T A and V A with it, as this is the extent of motion; transfer this measurement to N, if the _actual_ lift is the same on each pallet, the dividers will locate the point which the locking corner N will occupy _when locked_; this, in the present case, will be at an angle of 1 below the tangent D A. By this simple method, the correctness of our proposition that the loss of lift should be measured from the outside circle of the wheel, can be proven. We often see the loss measured for the engaging pallet on the primitive circ.u.mference G H, and on the real circ.u.mference for the disengaging; if one is right then the other must be wrong, as there is a noticeable deviation of the tangent C A from the primitive circle G H at the intersection of the locking circle M N; had we added this amount to the lifting angle V' A V of the engaging pallet, the result would have been that the discharging edge O would be over 1 below its present location, thus showing that by the time the lift on the engaging pallet had been completed, the locking corner N of the disengaging pallet would be locked at an angle of 2 instead of only 1. Many watches contain precisely this fault. If we wish to make a draft showing the pallets at any desired position, at the center of motion for instance, with the fork standing on the line of centers, we would proceed in the following manner: 10 being the total motion, one-half would equal 5?; as the total lock equals 1, we deduct this amount from it which leaves 5? - 1 = 3?, which is the angle at which the locking corner M should be shown above the tangent C A. Now let us see where the locking corner N should stand; M having moved up 5?, therefore N moved down by that amount, the lift on the pallet being 5 and on the tooth 3 (which is added to the tangent D A), it follows that N should stand 5 + 3 - 5? = 3? above D A. We can prove it by the lock, namely: 3? + 1 = 5?, half the remaining motion.

This shows how simple it is to draft pallets in various positions, remembering always to use the tangents to the primitive circle as measuring points. We have fully explained how to draw in the draft angle on the pallets when unlocked, and do not require to repeat it, except to say, that most authorities draw a tangent R N to the locking circle M N, forming in other words, the right angle R N A, then construct an angle of 12 from R N. We have drawn ours in by our own method, which is the correct one. While we here ill.u.s.trate S N R at an angle of 12 it is in reality _less_ than that amount; had we constructed S N at an angle of 12 from R N, then the draw would be 12 from F B, when the primitive circ.u.mference of the wheel is reached, but _more_ than 12 when the fork is against the bank.

The s.p.a.ce between the discharging edge P and the heel of the tooth forms the angle of drop J B I of 1; the definition for drop is that it is the freedom for wheel and pallet. This is not, strictly speaking, perfectly correct, as, during the unlocking action there will be a recoil of the wheel to the extent of the draft angle; the heel of the tooth will therefore approach the edge P, and the discharging side of the pallet approaches the tooth, as only the discharging edge moves on the path P.

A good length for the teeth is 1/10 the diameter of the wheel, measured from the primitive diameter and from the locking edge of the tooth.

The backs of the teeth are hollowed out so as not to interfere with the pallets, and are given a nice form; likewise the rim and arms are drawn in as light and as neat as possible, consistent with strength.

Having explained the delineation of the wheel and pallet action we will now turn our attention to that of the fork and roller. We tried to explain these actions in such a manner that by the time we came to delineate them no difficulty would be found, as in our a.n.a.lysis we discussed the subject sufficiently to enable any one of ordinary intelligence to obtain a correct knowledge of them. The fork and roller action in straight line, right, or any other angle is delineated after the methods we are about to give.

We specified that the acting length of fork was to be equal to the center distance of wheel and pallets; this gives a fork of a fair length.

Having drawn the line of centers A' A we will construct an angle equal to half the angular motion of the pallets; the latter in the case under consideration being 10, therefore 5? is s.p.a.ced off on each side of the line of centers, forming the angles _m_ A _k_ of 10. Placing our dividers on A B the center distance of 'scape wheel and pallets, we plant them on A and construct _c c_; thus we will have the acting length of fork and its path. We saw in our a.n.a.lysis that the impulse angle should be as small as possible. We will use one of 28 in our draft of the double roller; we might however remark that this angle should vary with the construction of the escapements in different watches; if too small, the balance may be stopped when the escapement is locked, while if too great it can be stopped during the lift; both these defects are to be avoided. The angles being respectively 10 and 28 it follows they are of the following proportions: 28 10.25 = 2.7316. The impulse radius therefore bears this relation (but in the inverse ratio to the angles), to the acting length of fork.

We will put it in the following proportion; let A_c_ equal acting length of fork, and _x_ the unknown quant.i.ty; 28:10.25 :: A_c_:_x_; the answer will be the theoretical impulse radius. Having found the required radius we plant one jaw of our measuring instrument on the point of intersection of _c c_ with _k_ A or _m_ A and locate the other jaw on the line of centers; we thus obtain A' the balance center. Through the points of intersection before designated we will draft X A' and Y A'

forming the impulse angle X A' Y of 28. At the intersection of this angle with the fork angle _k_ A' _m_, we draw _i i_ from the center A; this gives us the theoretical impulse circle. The total lock being 1 it follows that the angle described by the balance in unlocking = 1 2.7316 = 4.788. According to the specifications the width of slot is to be 5?; placing the center of the protractor on A we construct half of this angle on each side of _k_ A, which pa.s.ses through the center of the fork when it rests against the bank; this gives us the angle _s_ A _n_ of 5?. If the disengaging pallet were shown locked then _m_ A would represent the center of the fork. The slot is to be made of sufficient depth so there will be no possibility of the ruby pin touching the bottom of it. The ruby pin is to have 1 freedom in pa.s.sing the acting edge of the fork; from the center A we construct the angle _t_ A _n_ of 1; at the point of intersection of _t_ A with _c c_ the acting radius of the fork, we locate the real impulse radius and draw the arc _ri ri_ which describes the path made by the face of the ruby pin. The ruby pin is to have of shake in the slot; it will therefore have a width of 4?; this width is drawn in with the ruby pin imagined as standing over the line of centers and is then transferred to the position which the ruby pin is to occupy in the drawing.

The radius of the safety roller was given as 4/7 of the theoretical impulse radius. They may be made of various proportions; thus ? is often used. Remember that the smaller we make it, the less the friction during accidental contact with the guard pin, the greater must the pa.s.sing hollow be and the horn of fork and guard point must be longer, which increases the weight of the fork.

Having drawn in the safety roller, and having specified that the freedom between the dart and safety roller was to be 1, the dart being in the center of the fork, consequently _k_ A is the center of it; therefore we construct the angle _k_ A X of 1. At the point of intersection of X A with the safety roller we draw the arc _g g_; this locates the point of the dart which we will now draw in. We will next draw _d_ A' from the balance center and touching the point of the dart; we now construct _b_ A' at an angle of 5 to it. This is to allow the necessary freedom for the dart when entering the crescent; from A' we draw a line through the center of the ruby pin. We do not show it in the drawing, as it would be indiscernible, coming very close to A' X. This line will also pa.s.s through the center of the crescent. At the point of intersection of A' _b_ with the safety roller we have one of the edges of the crescent. By placing our compa.s.s at the center of the crescent on the periphery of the roller and on the edge which we have just found, it follows that our compa.s.s will span the radius of the crescent. We now sweep the arc for the latter, thus also drawing in the remaining half of the crescent on the other side of A' X and bringing the crescent of sufficient depth that no possibility exists of the dart touching in or on the edges of it. We will now draw in the impulse roller and make it as light as possible consistent with strength. A hole is shown through the impulse roller to counterbalance the reduced weight at the crescent. When describing Fig. 24, we gave instructions for finding the dimensions of crescent and position of guard pin for the single roller. We will find the length of horn; to do so we must closely follow directions given for Fig. 25. In locating the end of the horn, we must find the location of the center of the crescent and ruby pin _after_ the edge of the crescent has pa.s.sed the dart. From the point of intersection of A' _b_ with the safety roller we transfer the radius of the crescent on the periphery of the safety roller towards the side against the bank, then draw a line from A' through the point so found. At point of intersection of this line with the real impulse circle _r i r i_ we draw an arc radiating from the pallet center; the end of the horn will be located on this arc.

In our drawing the arc spoken of coincides with the dart radius _g g_.

As before pointed out, we gave particulars when treating on Fig. 25, therefore considered it unnecessary to further complicate the draft by the addition of all the constructional lines. We specified that the freedom between ruby pin and end of horn was to be 1; these lines, (which we do not show) are drawn from the pallet center. Having located the end of the horn on the side standing against the bank, we place the dividers on it and on the point of intersection of _k_ A with _g g_--which in this case is on the point of the dart,--and transfer this measurement along _g g_ which will locate the end of the horn on the opposite side.

We have the acting edges of the fork on _cc_ and have also found the position of the ends of the horns; their curvature is drawn in the following manner: We place our compa.s.ses on A and _r i_, spanning therefore the real impulse radius; the compa.s.s is now set on the acting edge of the fork and an arc swept with it which is then to be intersected by another arc swept from the end of the horn, on the same side of the fork. At the point of intersection of the arcs the compa.s.s is planted and the curvature of the horn drawn in, the same operation is to be repeated with the other horn. We will now draw in the sides of the horn of such a form that should the watch rebank, the side of the ruby pin will squarely strike the fork. If the back of the ruby pin strikes the fork there will be a greater tendency of breaking it and injuring the pivots on account of acting like a wedge. The fork and pallets are now drawn in as lightly as possible and of such form as to admit of their being readily poised. The banks are to be drawn at equal distances from the line of centers. In delineating the fork and roller action in any desired position, it must be remembered that the points of location of the real impulse radius, the end of horn, the dart or guard pin and crescent, must _all_ be obtained _when standing against the bank_, and the arcs drawn which they describe; the parts are then located according to the angle at which they are removed from the banks.

We think the instructions given are ample to enable any one to master the subject. We may add that when one becomes well acquainted with the escapement, many of the angles radiating from a common center, may be drawn in at once. We had intended describing the mechanical construction of the escapement, which does unmistakably present some difficulties on account of the small dimensions of the parts, but nevertheless it can be mechanically executed true to the principles enumerated. We have evolved a method of so producing them that young men in a comparatively short period have made them from their drafts (without automatic machinery) that their watches start off when run down the moment the crown is touched. Perhaps later on we will write up the subject. It is our intention of doing so, as we make use of such explanations in our regular work.