We will warn our readers in advance, that if they make such a testing device they will be astonished at the inaccuracy which they will find in the escapements of so-called fine watches. The lock, in many instances, instead of being one and a half degrees, will oftener be found to be from two to four degrees, and the impulse derived from the escape wheel, as ill.u.s.trated at Fig. 76, will often fall below eight degrees. Such watches will have a poor motion and tick loud enough to keep a policeman awake. Trials with actual watches, with such a device as we have just described, in conjunction with a careful study of the acting parts, especially if aided by a large model, such as we have described, will soon bring the student to a degree of skill unknown to the old-style workman, who, if a poor escapement bothered him, would bend back the banking pins or widen the slot in the fork.

We hold that educating our repair workmen up to a high knowledge of what is required to const.i.tute a high-grade escapement, will have a beneficial effect on manufacturers. When we wish to apply our device to the measurement of the escapement of three-quarter-plate watches, we will require another index hand, with the grasping end bent downward, as shown at Fig. 77. The idea with this form of index hand is, the bent-down jaws _B'_, Fig. 77, grasp the fork as close to the pallet staff as possible, making an allowance for the acting center by so placing the index arc that the hand _A_ will read correctly on the index _D_. Suppose, for instance, we place the jaws _B'_ inside the pallet staff, we then place the index arc so the hand reads to the arc indicated by the dotted arc _m_, Fig. 78, and if set outside of the pallet staff, read by the arc _o_.

[Ill.u.s.tration: Fig. 78]

HOW A BALANCE CONTROLS THE TIMEKEEPING OF A WATCH.

We think a majority of the fine lever escapements made abroad in this day have what is termed double-roller safety action. The chief gains to be derived from this form of safety action are: (1) Reducing the arc of fork and roller action; (2) reducing the friction of the guard point to a minimum. While it is entirely practicable to use a table roller for holding the jewel pin with a double-roller action, still a departure from that form is desirable, both for looks and because as much of the aggregate weight of a balance should be kept as far from the axis of rotation as possible.

We might as well consider here as elsewhere, the relation the balance bears to the train as a controlling power. Strictly speaking, _the balance and hairspring are the time measurers_, the train serving only two purposes: (_a_) To keep the balance in motion; (_b_) to cla.s.sify and record the number of vibrations of the balance. Hence, it is of paramount importance that the vibrations of the balance should be as untrammeled as possible; this is why we urge reducing the arc of connection between the balance and fork to one as brief as is consistent with sound results. With a double-roller safety action we can easily reduce the fork action to eight degrees and the roller action to twenty-four degrees.

Inasmuch as satisfactory results in adjustment depend very much on the perfection of construction, we shall now dwell to some extent on the necessity of the several parts being made on correct principles. For instance, by reducing the arc of engagement between the fork and roller, we lessen the duration of any disturbing influence of escapement action.

To resume the explanation of why it is desirable to make the staff and all parts near the axis of the balance as light as possible, we would say it is the moving portion of the balance which controls the regularity of the intervals of vibration. To ill.u.s.trate, suppose we have a balance only 3/8" in diameter, but of the same weight as one in an ordinary eighteen-size movement. We can readily see that such a balance would require but a very light hairspring to cause it to give the usual 18,000 vibrations to the hour. We can also understand, after a little thought, that such a balance would exert as much breaking force on its pivots as a balance of the same weight, but " in diameter acting against a very much stronger hairspring. There is another factor in the balance problem which deserves our attention, which factor is atmospheric resistance. This increases rapidly in proportion to the velocity.

HOW BAROMETRIC PRESSURE AFFECTS A WATCH.

The most careful investigators in horological mechanics have decided that a balance much above 75/100" in diameter, making 18,000 vibrations per hour, is not desirable, because of the varying atmospheric disturbances as indicated by barometric pressure. A balance with all of its weight as near the periphery as is consistent with strength, is what is to be desired for best results. It is the moving matter composing the balance, pitted against the elastic force of the hairspring, which we have to depend upon for the regularity of the timekeeping of a watch, and if we can take two grains' weight of matter from our roller table and place them in the rim or screws of the balance, so as to act to better advantage against the hairspring, we have disposed of these two grains so as to increase the efficiency of the controlling power and not increase the stress on the pivots.

[Ill.u.s.tration: Fig. 79]

We have deduced from the facts set forth, two axioms: (_a_) That we should keep the weight of our balance as much in the periphery as possible, consistent with due strength; (_b_) avoid excessive size from the disturbing effect of the air. We show at _A_, Fig. 79, the shape of the piece which carries the jewel pin. As shown, it consists of three parts: (1) The socket _A_, which receives the jewel pin _a_; (2) the part _A''_ and hole _b_, which goes on the balance staff; (3) the counterpoise _A'''_, which makes up for the weight of the jewel socket _A_, neck _A'_ and jewel pin. This counterpoise also makes up for the pa.s.sing hollow _C_ in the guard roller _B_, Fig. 80. As the piece _A_ is always in the same relation to the roller _B_, the poise of the balance must always remain the same, no matter how the roller action is placed on the staff. We once saw a double roller of nearly the shape shown at Fig. 79, which had a small gold screw placed at _d_, evidently for the purpose of poising the double rollers; but, to our thinking, it was a sort of hairsplitting hardly worth the extra trouble. Rollers for very fine watches should be poised on the staff before the balance is placed upon it.

[Ill.u.s.tration: Fig. 80]

We shall next give detailed instructions for drawing such a double roller as will be adapted for the large model previously described, which, as the reader will remember, was for ten degrees of roller action. We will also point out the necessary changes required to make it adapted for eight degrees of fork action. We would beg to urge again the advantages to be derived from constructing such a model, even for workmen who have had a long experience in escapements, our word for it they will discover a great many new wrinkles they never dreamed of previously.

It is important that every practical watchmaker should thoroughly master the theory of the lever escapement and be able to comprehend and understand at sight the faults and errors in such escapements, which, in the every-day practice of his profession, come to his notice. In no place is such knowledge more required than in fork and roller action. We are led to say the above chiefly for the benefit of a cla.s.s of workmen who think there is a certain set of rules which, if they could be obtained, would enable them to set to rights any and all escapements. It is well to understand that no such system exists and that, practically, we must make one error balance another; and it is the "know how" to make such faults and errors counteract each other that enables one workman to earn more for himself or his employer in two days than another workman, who can file and drill as well as he can, will earn in a week.

PROPORTIONS OF THE DOUBLE-ROLLER ESCAPEMENT.

The proportion in size between the two rollers in a double-roller escapement is an open question, or, at least, makers seldom agree on it.

Grossmann shows, in his work on the lever escapement, two sizes: (1) Half the diameter of the acting roller; (2) two-thirds of the size of the acting roller. The chief fault urged against a smaller safety roller is, that it necessitates longer horns to the fork to carry out the safety action. Longer horns mean more metal in the lever, and it is the conceded policy of all recent makers to have the fork and pallets as light as possible. Another fault pertaining to long horns is, when the horn does have to act as safety action, a greater friction ensues.

In all soundly-constructed lever escapements the safety action is only called into use in exceptional cases, and if the watch was lying still would theoretically never be required. Where fork and pallets are poised on their arbor, pocket motion (except torsional) should but very little affect the fork and pallet action of a watch, and torsional motion is something seldom brought to act on a watch to an extent to make it worthy of much consideration. In the double-roller action which we shall consider, we shall adopt three-fifths of the pitch diameter of the jewel-pin action as the proper size. Not but what the proportions given by Grossmann will do good service; but we adopt the proportions named because it enables us to use a light fork, and still the friction of the guard point on the roller is but little more than where a guard roller of half the diameter of the acting roller is employed.

The fork action we shall consider at present is ten degrees, but subsequently we shall consider a double-roller action in which the fork and pallet action is reduced to eight degrees. We shall conceive the play between the guard point and the safety roller as one degree, which will leave half a degree of lock remaining in action on the engaged pallet.

THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED.

In the drawing at Fig. 81 we show a diagram of the action of the double-roller escapement. The small circle at _A_ represents the center of the pallet staff, and the one at _B_ the center of the balance staff.

The radial lines _A d_ and _A d'_ represent the arc of angular motion of fork action. The circle _b b_ represents the pitch circle of the jewel pin, and the circle at _c c_ the periphery of the guard or safety roller. The points established on the circle _c c_ by intersection of the radial lines _A d_ and _A d'_ we will denominate the points _h_ and _h'_. It is at these points the end of the guard point of the fork will terminate. In construction, or in delineating for construction, we show the guard enough short of the points _h h'_ to allow the fork an angular motion of one degree, from _A_ as a center, before said point would come in contact with the safety roller.

[Ill.u.s.tration: Fig. 81]

We draw through the points _h h'_, from _B_ as a center, the radial lines _B g_ and _B g'_. We measure this angle by sweeping the short arc _i_ with any of the radii we have used for arc measurement in former delineations, and find it to be a trifle over sixty degrees. To give ourselves a practical object lesson, let us imagine that a real guard point rests on the circle _c_ at _h_. Suppose we make a notch in the guard roller represented by the circle _c_, to admit such imaginary guard point, and then commence to revolve the circle _c_ in the direction of the arrow _j_, letting the guard point rest constantly in such notch. When the notch _n_ in _c_ has been carried through thirty degrees of arc, counting from _B_ as a center, the guard point, as relates to _A_ as a center, would only have pa.s.sed through an arc of five degrees. We show such a guard point and notch at _o n_. In fact, if a jewel pin was set to engage the fork on the pitch circle _b a_, the escapement would lock. To obviate such lock we widen the notch _n_ to the extent indicated by the dotted lines _n'_, allowing the guard point to fall back, so to speak, into the notch _n_, which really represents the pa.s.sing hollow. It is not to be understood that the extended notch at _n_ is correctly drawn as regards position, because when the guard point was on the line _A f_ the point _o_ would be in the center of the extended notch, or pa.s.sing hollow. We shall next give the details of drawing the double roller, but before doing so we deemed it important to explain the action of such guard points more fully than has been done heretofore.

HOW TO DESIGN A DOUBLE-ROLLER ESCAPEMENT.

We have already given very desirable forms for the parts of a double-roller escapement, consequently we shall now deal chiefly with acting principles as regards the rollers, but will give, at Fig. 82, a very well proportioned and practical form of fork. The pitch circle of the jewel pin is indicated by the dotted circle _a_, and the jewel pin of the usual cylindrical form, with two-fifths cut away. The safety roller is three-fifths of the diameter of the pitch diameter of the jewel-pin action, as indicated by the dotted circle _a_.

The safety roller is shown in full outline at _B'_, and the pa.s.sing hollow at _E_. It will be seen that the arc of intersection embraced between the radial lines _B c_ and _B d_ is about sixty-one and a half degrees for the roller, but the angular extent of the pa.s.sing hollow is only a little over thirty-two degrees. The pa.s.sing hollow _E_ is located and defined by drawing the radial line _B c_ from the center _B_ through the intersection of radial line _A i_ with the dotted arc _b_, which represents the pitch circle of the safety roller. We will name this intersection the point _l_. Now the end of the guard point _C_ terminates at the point _l_, and the pa.s.sing hollow _E_ extends on _b_ sixteen degrees on each side of the radial line _B c_.

[Ill.u.s.tration: Fig. 82]

The roller action is supposed to continue through thirty degrees of angular motion of the balance staff, and is embraced on the circle _a_ between the radial line _B k_ and _B o_. To delineate the inner face of the horn _p_ of the fork _F_ we draw the short arc _g_, from _A_ as a center, and on said arc locate at two degrees from the center at _B_ the point _f_. We will designate the upper angle of the outer face of the jewel pin _D_ as the point _s_ and, from _A_ as a center, sweep through this point _s_ the short arc _n n_. Parallel with the line _A i_ and at the distance of half the diameter of the jewel pin _D_, we draw the short lines _t t'_, which define the inner faces of the fork.

The intersection of the short line _t_ with the arc _n_ we will designate the point _r_. With our dividers set to embrace the s.p.a.ce between the point _r_ and the point _f_, we sweep the arc which defines the inner face of the p.r.o.ng of the fork. The s.p.a.ce we just made use of is practically the same as the radius of the circle _a_, and consequently of the same curvature. Practically, the length of the guard point _C'_ is made as long as will, with certainty, clear the safety roller _B_ in all positions. While we set the point _f_ at two degrees from the center _B_, still, in a well-constructed escapement, one and a half degrees should be sufficient, but the extra half degree will do no harm. If the roller _B'_ is accurately made and the guard point _C'_ properly fitted, the fork will not have half a degree of play.

The reader will remember that in the escapement model we described we cut down the drop to one degree, being less by half a degree than advised by Grossmann and Saunier. We also advised only one degree of lock. In the perfected lever escapement, which we shall describe and give working drawings for the construction of, we shall describe a detached lever escapement with only eight degrees fork and pallet action, with only three-fourths of a degree drop and three-fourths of a degree lock, which we can a.s.sure our readers is easily within the limits of practical construction by modern machinery.

HOW THE GUARD POINT IS MADE.

[Ill.u.s.tration: Fig. 83]

The guard point _C'_, as shown at Fig. 82, is of extremely simple construction. Back of the slot of the fork, which is three-fifths of the diameter of the jewel pin in depth, is made a square hole, as shown at _u_, and the back end of the guard point _C_ is fitted to this hole so that it is rigid in position. This manner of fastening the guard point is equally efficient as that of attaching it with a screw, and much lighter--a matter of the highest importance in escapement construction, as we have already urged. About the best material for such guard points is either aluminum or phosphor bronze, as such material is lighter than gold and very rigid and strong. At Fig. 83 we show a side view of the essential parts depicted in Fig. 82, as if seen in the direction of the arrow _v_, but we have added the piece which holds the jewel pin _D_. A careful study of the cut shown at Fig. 82 will soon give the horological student an excellent idea of the double-roller action.

We will now take up and consider at length why Saunier draws his entrance pallet with fifteen degrees draw and his exit pallet with only twelve degrees draw. To make ourselves more conversant with Saunier's method of delineating the lever escapement, we reproduce the essential features of his drawing, Fig. 1, plate VIII, of his "Modern Horology,"

in which he makes the draw of the locking face of the entrance pallet fifteen degrees and his exit pallet twelve degrees. In the cut shown at Fig. 84 we use the same letters of reference as he employs. We do not quote his description or directions for delineation because he refers to so much matter which he has previously given in the book just referred to. Besides we cannot entirely endorse his methods of delineations for many reasons, one of which appears in the drawing at Fig. 84.

[Ill.u.s.tration: Fig. 84]

MORE ABOUT TANGENTIAL LOCKINGS.

Most writers endorse the idea of tangential lockings, and Saunier speaks of the escapement as shown at Fig. 84 as having such tangential lockings, which is not the case. He defines the position of the pallet staff from the circle _t_, which represents the extreme length of the teeth; drawing the radial lines _A D_ and _A E_ to embrace an arc of sixty degrees, and establishing the center of his pallet staff _C_ at the intersection of the lines _D C_ and _E C_, which are drawn at right angles to the radial lines _A D_ and _A E_, and tangential to the circle _t_.

Here is an error; the lines defining the center of the pallet staff should have been drawn tangent to the circle _s_, which represents the locking angle of the teeth. This would have placed the center of the pallet staff farther in, or closer to the wheel. Any person can see at a glance that the pallets as delineated are not tangential in a true sense.

[Ill.u.s.tration: Fig. 85]

We have previously considered engaging friction and also repeatedly have spoken of tangential lockings, but will repeat the idea of tangential lockings at Fig. 85. A tangential locking is neutral, or nearly so, as regards engaging friction. For ill.u.s.tration we refer to Fig. 85, where _A_ represents the center of an escape wheel. We draw the radial lines _A y_ and _A z_ so that they embrace sixty degrees of the arcs _s_ or _t_, which correspond to similar circles in Fig. 84, and represent the extreme extent of the teeth and likewise the locking angle of such teeth. In fact, with the club-tooth escapement all that part of a tooth which extends beyond the line _s_ should be considered the same as the addendum in gear wheels. Consequently, a tangential locking made to coincide with the center of the impulse plane, as recommended by Saunier, would require the pallet staff to be located at _C'_ instead of _C_, as he draws it. If the angle _k'_ of the tooth _k_ in Fig. 84 was extended outward from the center _A_ so it would engage or rest on the locking face of the entrance pallet as shown at Fig. 84, then the draw of the locking angle would not be quite fifteen degrees; but it is evident no lock can take place until the angle _a_ of the entrance pallet has pa.s.sed inside the circle _s_. We would say here that we have added the letters _s_ and _t_ to the original drawings, as we have frequently to refer to these circles, and without letters had no means of designation. Before the locking angle _k'_ of the tooth can engage the pallet, as shown in Fig. 84, the pallet must turn on the center _C_ through an angular movement of at least four degrees. We show the situation in the diagram at Fig. 86, using the same letters of reference for similar parts as in Fig. 84.

[Ill.u.s.tration: Fig. 86]

As drawn in Fig. 84 the angle of draft _G a I_ is equal to fifteen degrees, but when brought in a position to act as shown at _G a' I'_, Fig. 86, the draw is less even than twelve degrees. The angle _C a I_ remains constant, as shown at _C a' I'_, but the relation to the radial _A G_ changes when the pallet moves through the angle _w C w'_, as it must when locked. A tangential locking in the true sense of the meaning of the phrase is a locking set so that a pallet with its face coinciding with a radial line like _A G_ would be neutral, and the thrust of the tooth would be tangent to the circle described by the locking angle of the tooth. Thus the center _C_, Fig. 86, is placed on the line _w'_ which is tangent to the circle _s_; said line _w'_ also being at right angles to the radial line _A G_.

The facts are, the problems relating to the club-tooth lever escapement are very intricate and require very careful a.n.a.lysis, and without such care the horological student can very readily be misled. Faulty drawings, when studying such problems, lead to no end of errors, and practical men who make imperfect drawings lead to the popular phrase, "Oh, such a matter may be all right in theory, but will not work in practice." We should always bear in mind that _theory, if right, must lead practice_.

CORRECT DRAWING REQUIRED.

If we delineate our entrance pallet to have a draw of twelve degrees when in actual contact with the tooth, and then construct in exact conformity with such drawings, we will find our lever to "hug the banks"