To come back to the impulse angle, some might use a proportion of 3.5, 4 or even 5 to 1, while others for the finest of watches would only use 2.75 to 1. By having a total vibration of the balance of 1 turns, which is equal to 540 a fork angle of 10 and a proportion of 2.75 for the impulse angle which would be equal to 10 2.75 = 27.5. The _free_ vibration of the balance, or as this is called, "the supplemental arc,"

is equal to 540 - 27.5 = 512.50, while with a proportion of 5 to 1, making an impulse angle of 50, it would be equal to 490. To sum up, the finer the watch the lower the proportion, the closer the action to the line of centers, the smaller the friction. On account of leverage the more difficult the unlocking but the more energetic the impulse when it does occur. The velocity of the ruby pin at P; Fig. 14, is much greater than at W, consequently it will not be overtaken as soon by the fork as at W. The velocity of the fork at the latter point is greater than at P; the intersection of _ii_ and _cc_ is also not as great; therefore the lower the proportion the finer and more exact must the workmanship be.

We will notice that the unlocking action has been overruled by the impulse. The only point so far in which the former has been favored is in the diminished action before the line of centers, as previously pointed out at P, Fig. 14.

We will now consider the width of the ruby pin and to get a good insight into the question, we will study Fig. 17. A is the pallet center, A' the balance center, the line AA' being the line of centers; the angle WAA equals half the total motion of the fork, the other half, of course, taking place on the opposite side of the center line. WA is the _center_ of the fork when it rests against the bank. The angle AA'X represents half the impulse angle; the other half, the same as with the fork, is struck on the other side of the center line. At the point of intersection of these angles we will draw _cc_ from the pallet center A, which equals the acting length of the fork, and from the balance center we will draw _ii_, which equals the _theoretical_ impulse radius; some writers use it as the _real_ radius. The wider the ruby pin the greater will the latter be, which we will explain presently.

The ruby pin in entering the fork must have a certain amount of freedom for action, from 1 to 1. Should the watch receive a jar at the moment the guard point enters the crescent or pa.s.sing hollow in the roller, the fork would fly against the ruby pin. It is important that the angular freedom between the fork and ruby pin at the moment it enters into the slot be _less_ than the total locking angle on the pallets. If we employ a locking angle of 1 and run, we would have a total lock on the pallets of 2. By allowing 1 of freedom for the ruby pin at the moment the guard point enters the crescent, in case the fork should strike the face of the ruby pin, the pallets will still be locked and the fork drawn back against the bankings through the draft angle.

We will see what this shake amounts to for a given acting length of fork, which describes an arc of a circle, therefore the acting length is only the radius of that circle and must be multiplied by two in order to get the diameter. The acting length of fork = 4.5 mm., what is the amount of shake when the ruby pin pa.s.ses the acting corner?

4.5 2 3.1416 360 = .0785 1.25 = .0992 mm. The shake of the ruby pin in the slot of the fork must be as slight as possible, consistent with perfect freedom of action. It varies from to , according to length of fork and shape of ruby pin. A square ruby pin requires more shake than any other kind; it enters the fork and receives the impulse in a diagonal direction on the jewel, in which position it is ill.u.s.trated at Z, Fig. 20. This ruby pin acts on a knife edge, but for all that the engaging friction during the unlocking action is considerable.

Our reasoning tells us it matters not if a ruby pin be wide or narrow, it must have _the same_ freedom in pa.s.sing the acting edge of the fork, therefore, to have the impulse radius on the point of intersection of A'X with AW, Fig. 17, we would require a _very_ narrow ruby pin. With 1 of freedom at the edge, and in the slot, we could only have a ruby pin of a width of 1. Applying it to the preceding example it would only have an actual width of .0785 1.5 = .1178 mm., or the size of an ordinary balance pivot. At _n_, Fig. 17, we ill.u.s.trate such a ruby pin; the theoretical and real impulse radius coincide with one another. The intersection of the circle _ii_ and _cc_ is very slight, while the friction in unlocking begins within 1 of half the total movement of the fork from the line of centers; to ill.u.s.trate, if the angular motion is 11 the ruby pin under discussion will begin action 4 before the line of centers, being an engaging, or "uphill" friction of considerable magnitude.

[Ill.u.s.tration: Fig. 17.]

[Ill.u.s.tration: Fig. 18.]

[Ill.u.s.tration: Fig. 19.]

[Ill.u.s.tration: Fig. 20.]

The intersection with the fork is also much less than with the wider ruby pin, making the impulse action very delicate. On the other hand the widest ruby pin for which there is any occasion is one beginning the unlocking action on the line of centers, Fig. 17; this entails a width of slot equal to the angular motion of the fork. We see here the advantage of a wide ruby pin over a narrow one in the unlocking action.

Let us now examine the question from the standpoint of the impulse action.

Fig. 18 ill.u.s.trates the moment the impulse is transmitted; the fork has been moved in the direction of the arrow by the ruby pin; the escapement has been unlocked and the opposite side of the slot has just struck the ruby pin. The exact position in which the impulse is transmitted varies with the locking angle, the width of ruby pin, its shake in the slot, the length of fork, its weight, and the velocity of the ruby pin, which is determined by the vibrations of the balance and the impulse radius.

In an escapement with a total lock of 1 and 1 of shake in the slot, theoretically, the impulse would be transmitted 2 from the bankings.

The narrow ruby pin n receives the impulse on the line _v_, which is closer to the line of centers than the line _u_, on which the large ruby pin receives the impulse. Here then we have an advantage of the narrow ruby pin over a wide one; with a wider ruby pin the balance is also more liable to rebank when it takes a long vibration. Also on account of the greater angle at which the ruby pin stands to the slot when the impulse takes place, the _drop_ of the fork against the jewel will amount to more than its shake in the slot (which is measured when standing on the line of centers). On this account some watches have slots dovetailed in form, being wider at the bottom, others have ruby pins of this form.

They require very exact execution; we think we can do without them by judiciously selecting a width of ruby pin between the two extremes. We would choose a ruby pin of a width equal to half the angular motion of the fork. There is an ingenious arrangement of fork and roller which aims to, and partially does, overcome the difficulty of choosing between a wide and narrow ruby pin, it is known as the Savage pin roller escapement. We intend to describe it later.

If the face of the ruby pin were planted on the theoretical impulse radius _ii_, Fig. 19, the impulse would end in a b.u.t.ting action as shown; hence the great importance of distinguishing between the theoretical and real impulse radius and establishing a reliable data from which to work. We feel that these actions have never been properly and thoroughly treated in simple language; we have tried to make them plain so that anyone can comprehend them with a little study.

Three good forms of ruby pins are the triangular, the oval and the flat faced; for ordinary work the latter is as good as any, but for fine work the triangular pin with the corners slightly rounded off is preferable.

[Ill.u.s.tration: Fig. 21.]

[Ill.u.s.tration: Fig. 23.]

[Ill.u.s.tration: Fig. 22.]

English watches are met with having a cylindrical or round ruby pin.

Such a pin should never be put into a watch. The law of the parallelogram of forces is completely ignored by using such a pin; the friction during the unlocking and impulse actions is too severe, as it is, without the addition of so unmechanical an arrangement. Fig. 21 ill.u.s.trates the action of a round ruby pin; _ii_ is the path of the ruby pin; _cc_ that of the acting length of the fork. It is shown at the moment the impulse is transmitted. It will be seen that the impact takes place _below_ the center of the ruby pin, whereas it should take place at the center, as the motion of the fork is _upwards_ and that of the ruby pin _downwards_ until the line of the centers has been reached.

The same rule applies to the flat-faced pin and it is important that the right quant.i.ty be ground off. We find that 3/7 is approximately the amount which should be ground away. Fig. 22 ill.u.s.trates the fork standing against the bank. The ruby pin touches the side of the slot but has not as yet begun to act; _ri_ is the real impulse circle for which we allow 1 of freedom at the acting edge of the fork; the face of the ruby pin is therefore on this line. The next thing to do is to find the center of the pin. From the side _n_ of the slot we construct the right angle _o n t_; from _n_, we transmit the width of the pin, and plant the center _x_ on the line _n t_. We can have the center of the pin slightly below this line, but in no case above it; but if we put it below, the pin will be thinner and therefore more easily broken.

[Ill.u.s.tration: Fig. 14.]

_The Safety Action._ Although this action is separate from the impulse and unlocking actions, it is still very closely connected with them, much more so in the single than in the double roller escapement. If we were to place the ruby pin at _X_, Fig. 14, we could have a much smaller roller than by placing it at _P_. With the small roller the safety action is more secure, as the intersection at _m_ is greater than at _k_. It is not as liable to "b.u.t.t" and the friction is less when the guard point is thrown against the small roller. Suppose we take two rollers, one with a diameter of 2.5 mm., the other just twice this amount, of 5 mm. By having the guard radius and pressure the same in each case, if the guard point touched the larger roller it would not only have twice, but four times more effect than on the smaller one. We will notice that the smaller the impulse angle the larger the roller, because the ruby pin is necessarily placed farther from the center. The position of the ruby pin should, therefore, govern the size of the roller, which should be as small as possible. There should only be enough metal left between the circ.u.mference of the roller and the face of the jewel to allow for a crescent or pa.s.sing hollow of sufficient depth and an efficient setting for the jewel. For this reason, as well as securing the correct impulse radius and therefore angle, when replacing the ruby pin, and having it set securely and mechanically in the roller, it is necessary that the pin and the hole in the roller be of the same form, and a good fit. Fig. 23 ill.u.s.trates the difference in size of rollers. In the smaller one the conditions imposed are satisfied, while in the larger one they are not. In the single roller the safety action is at the mercy of the impulse and pallet angles. We have noticed that in order to favor the impulse we require a large roller, and for the safety action a small one, therefore escapements made on fine principles are supplied with two rollers, one for each action.

It may be well to say that in our opinion a proportion between the fork and impulse angles in 10 pallets of 3 or 3 to 1, _depending_ upon the size of the escapement, is the lowest which should be made in single roller. We have seen them in proportions of 2 to 1 in single roller--a scientific principle foolishly applied--resulting in an action entirely unsatisfactory.

When the guard point is pressed against the roller the escape tooth must still rest on the locking face of the pallet; if the total lock is 2, by allowing 1 freedom for the guard point between the bank and the roller the escapement will still be locked . How much this shake actually amounts to depends upon the guard radius. Suppose this to be 4 mm., then the freedom would equal 4 2 3.1416 360 1.25 = .0873 mm.

[Ill.u.s.tration: Fig. 24.]

[Ill.u.s.tration: Fig. 25.]

_The Crescent_ in the roller must be large and deep enough so it will be impossible for the guard point to touch in or on the corners of it; at the same time it must not be too large, as it would necessitate a longer horn on the fork than is necessary.

Fig. 24 shows the slot _n_ of the fork standing at the bank. The ruby pin _o_ touches it, but has not as yet acted on it; _s s_ ill.u.s.trates a single roller, while S2 ill.u.s.trates the safety roller for a double roller escapement. In order to find the dimensions of the crescent in the single roller we must proceed as follows: WA is in the center of the fork when it rests against the bank, and is, therefore, one of the sides of the fork angle, and is drawn from the pallet center; V A W is an angle of 1, which equals the freedom between the guard point and the roller; _g g_ represents the path of the guard pin _u_ for the single roller, and is drawn at the intersection of VA with the roller A' A2 is a line drawn from the balance center through that of the ruby pin, and therefore also pa.s.ses through the center of the crescent. By planting a compa.s.s on this line, where it cuts the periphery of the roller, and locating the point of intersection of VA with the roller, will give us one-half the crescent, the remaining half being transferred to the opposite side of the line A' A2. We will notice that the guard point has entered the crescent 1 before the fork begins to move.

The angle of opening for the crescent in the double roller escapement is greater than in the single, because it is placed closer to the balance center, and the guard point or dart further from the pallet center, causing a greater intersection; also the velocity of the guard point has increased, while that of the safety roller has decreased. Fig. 24, at _ff_, shows the path of the dart _h_, which also has 1 freedom between bank and roller. From the balance center we draw A' _d_ touching the center or point of the dart; from this point we construct at 5 angle _b_ A' _d_. This is to ensure sufficient freedom for the dart when entering the crescent. We plant a compa.s.s on the point of intersection of A' A2 with the safety roller, S2, and locating the point where A'_b_ intersects it, have found one-half the opening for the crescent, the remaining half being constructed on the opposite side of the line A' A2.

_The Horn_ on the fork belongs to the safety action: more horn is required with the double than with the single roller, on account of the greater angle of opening for the crescent.

The horn should be of such a length that when the crescent has pa.s.sed the guard point, the end of the horn should point to at least the center of the ruby pin.

The dotted circle, _s s_, Fig. 25, represents a single roller. It will be noticed that the corner of the crescent has pa.s.sed the guard pin _u_ by a considerable angle, and although this is so, in case of an accident the _acting edge_ of the fork would come in contact with the ruby pin; this proves that a well made single roller escapement really requires but little horn, only enough to ensure the safe entry of the ruby pin in case the guard point at that moment be thrown against the roller. We will now examine the question from the standpoint of the double roller; S2, Fig. 25, is the safety roller; the corner of the crescent has safely pa.s.sed the dart _h_; the centers of the ruby pin _o_ and of the crescent being on the line A' A2, we plant the compa.s.s on the pallet center and the center of the face of the ruby pin and draw _k k_, which will be the path described by the horn. The end of the horn is therefore planted upon it from 1 to 1 from the ruby pin; this freedom at the end of the horn is therefore from to more than we allow for the guard point; it depends upon the size of the escapement and locking angles which we would choose. It must in any case be less than the lock on the pallets, so that the fork will be drawn back against the bank in case the horn be thrown against the ruby pin.

When treating on the width of the ruby pin, we mentioned the Savage pin roller escapement, which we ill.u.s.trate in Figs. 26 and 27. This ingenious arrangement was designed with the view of combining the advantages of both wide and narrow pins and at the same time without any of their disadvantages.

In Fig. 26 we show the unlocking pins _u_ beginning their action on the line of centers--the best possible point--in unlocking the escapement.

These pins were made of gold in all which we examined, although it is recorded that wide ruby pins and ruby rollers have been used in this escapement, which would be preferable.

The functions of the two pins in the roller are simply to unlock the escapement; the impulse is not transmitted to them as is the case in the ordinary fork and roller action. In this action the guard pin _i_ also acts as the impulse pin. We will notice that the pa.s.sing hollow in this roller is a rectangular slot the same as in the ordinary fork. When the escapement is being unlocked the guard pin _i_ enters the hollow and when the escape tooth comes into contact with the lifting plane of the pallet the pin _i_, Fig. 27, transmits the impulse to the roller.

[Ill.u.s.tration: Fig. 26.]

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

The impulse is transmitted closer to the line of centers than could be done with any ruby pin. If the pin _i_ were wider the impulse would be transmitted still closer to the line of centers, but the intersection of it with the roller would be less. It is very delicate as it is, therefore from a practical standpoint it ought to be made thin but consistent with solidity. If the pin is anyway large, it should be flattened on the sides, otherwise the friction would be similar to that of the round ruby pin. It would also be preferable (on account of the pin _i_ being very easily bent) to make the impulse piece narrow but of such a length that it could be screwed to the fork, the same as the dart in the double roller. The impulse radius is also the radius of the roller, because the impulse is transmitted to the roller itself; for this reason the latter is smaller in this action than in the ordinary one having the same angles; also a shorter lever is in contact with a longer one in the unlocking than in ordinary action of the same angles; but for all this the pins _u u_ should be pitched close to the edge of the roller, as the angular connection of the balance with the escapement would be increased during the unlocking action. This escapement being very delicate requires a 12 pallet angle and a proportion between impulse and pallet angles of not less than 3 to 1, which would mean an impulse angle of 36; this, together with the first rate workmanship required are two of the reasons why this action is not often met with.

George Savage, of London, England, invented this action. He was a watchmaker who, in the early part of this century, did much to perfect the lever escapement by good work and nice proportion, besides inventing the two pin variety. He spent the early part of his life in Clerkenwell, but in his old days emigrated to Canada, and founded a flourishing retail business in Montreal, where he died. Some of George Savage's descendants are still engaged at the trade in Canada at the present day.

The correct delineation of the lever escapement is a very important matter. We ill.u.s.trate one which is so delineated that it can be practically produced. We have not noticed a draft of the lever escapement, especially with equidistant pallets and club teeth, which would act correctly in a watch.

We have been aggressive in our work and have sometimes found theories propounded and elongated which of themselves were not right; this may have something to do with it, that we so often hear workmen say, "Theory is no use, because if you work according to it your machine will not run." We say, "No, sir, if your theory is not right in itself, then your work will certainly not be correct; but if your theory be correct then your work _must_ be correct. Why? it simply cannot be otherwise." We will give it another name; let us say, apply sense, reason, thought, experience and study to your work, and what have you done? You have simply applied theory.

A theorem is a proposition to be proved, not being able to prove it, we must simply change it according as our experience dictates, this is precisely what we have done with the escapement after having followed the deductions of recognized authorities with the result that we can now ill.u.s.trate an escapement which has been thoroughly subjected to an impartial a.n.a.lysis in every respect, and which is theoretically and practically correct.

We will not only give instructions for drafting the escapement now under consideration, but will also make explanations how to draft it in different positions, also in circular pallet and single roller. We are convinced that by so doing we will do a service to many, we also wish to avoid what we may call "the stereotyped" process, that is, one which may be acquired by heart, but introduce any changes and perplexity is the result. It is really not a difficult matter to draft escapements in different positions, as an example will show.

Before making a draft we must know exactly what we wish to produce. It is well in drafting escapements to make them as large as possible, say thirty to forty times larger than in the watch, in the present case the size is immaterial, but we must have specifications for the proportions of the angles. Our draft is to be the most difficult subject in lever escapements; it is to be represented just as if it were working in a watch; it is to represent a good and reliable action in every respect, one which can be applied without special difficulty to a good watch, and is to be "up to date" in every particular and to contain the majority of the best points and conclusions reached in our a.n.a.lysis.

_Specifications for Lever Escapement_: The pallets are to be equidistant; the wheel teeth of the "club" form; there are to be two rollers; wheel, pallet, and balance centers are to be in straight line.

The lock is to be 1, the run , making a total lock of 1; the movement of pallets from drop to drop is to be 10, while the fork is to move through 10 from bank to bank; the lift on the wheel teeth is to be 3, while the remainder is to be the lift on the pallets as follows: 10 - (1 + 3) = 5 for lift of pallets.

The wheel is to have 15 teeth, with pallets spanning 3 teeth or 2 s.p.a.ces, making the angle from lock to lock = 360 15 2 = 60, the interval from tooth to tooth is 360 15 = 24; divided by 2 pallets = 24 2 = 12 for width of tooth, pallet and drop; drop is to be 1, the tooth is to be the width of the pallet, making a tooth of a width of 4 and a pallet of 6.

The draw is to be 12 on each pallet, while the locking faces of the teeth are to incline 24. The acting length of fork is to be equal to the distance of centers of scape wheel and pallets; the impulse angle is to be 28; freedom from dart and safety, roller is to be 1, and for dart and corner of crescent 5; freedom for ruby pin and acting edge of fork is to be 1; width of slot is to be the total motion, or 10 2 = 5?; shake of ruby pin in slot = , leaving 5? - = 4? for width of ruby pin.