and unlocking is as little as possible, for the pressure on the locking teeth is less than half of that of the impulse pins.
In practice the pallet P is a separate bit of steel, screwed on, and therefore adjustable. The locking teeth are about 6 inches long from the centre, and the impulse pin-edges ¼ in. from the centre, which is 7 in. below the top of the pendulum and crutch, so that the impulse begins 1 before zero and ends 1 after, corresponding each to 36 turn of the scape-wheel. If r is the distance of the pins from the centre and p the length of the crutch down to the centre, rsin. 36must= p sin. 1, if you want an impulse of 1 on each side of; which makes p = 33 7r. BB are eccentric beat pins for adjusting the beat to whatever 1 position of the pendulum you please, i.e., you can make it less than 1 before or after zero as you please. In some respects it would be better to have no crutch, but it would be very difficult to make the adjustments. This escapement should evidently be at the bottom of the clock-frame instead of the top, as in the gravity escapements which will be described presently. The back part of the scapewheel is carried by a long cock or bridge within which the crutch also moves.
Remontoire or Gravity Escapements.
A remontoire escapement is one in which the pendulum does not receive its impulse from the scape-wheel, but from some small weight or spring which is lifted or wound up by the scape-wheel at every beat, and the pendulum has nothing to do with the scapewheel except unlocking it. When this impulse is received from a weight the escapement is also called a gravity escapement; and in asmuch as all the remontoire clock escapements that are worth notice have been gravity escapements, we may use that term for them at once. The importance of getting the impulse given to the pendulum in this way was recognized long before all the properties of the dead escapement, as above investigated, were known. For it was soon discovered that, however superior to the old recoil escapement, it was far from perfect, and that its success depended on reducing the friction of the train and the pallets as far as possible, which involves the necessity of high-numbered pinions and wheels, small pivots, jewelled pallets, and a generally expensive style of workmanship. Accordingly the invention of an escapement which will give a constant impulse to the pendulum, and be nearly free from friction, has been for a century the great problem of clockmaking. We can do no more than shortly notice a very few of the attempts which have been made to solve it. The most simple form of gravity escapement, and the one which will serve the best for investigating their mathematical properties (though it fails in some essential mechanical conditions), is that invented by Mudge. The tooth A of the scape-wheel in fig. 10 is resting against the stop or detant a at the end of the pallet OA, from the axis or arbor of which descends the half fork CP to touch the pendulum. From the other pallet CB descends the other half fork CO. The two arbors are set as near the point of suspension, or top of the pendulum spring, as possible. The pendulum,,,, A as here represented, must be moving to the right, and just leaving contact with the left pallet in. going to take up the right one; as soon as it has raised that 3t a little it will evidently unlock the wheel and let it turn, and then the tooth B will raise the left pallet until it is caught by the .top b on that pallet and then it will stay until the pendulum reurns and releases it by raising that pallet still higher! Each pallet!vW? tT" J h? IT lulum to a lo Point than that where it is taken up, and the difference between them is supplied by B lifting of each pallet by the clock, which does not act on the pendulum at all; so that the pendulum is independent of all varia tions of force and friction in the train.
Fig. 10.—Mudge's Gravity Escapement.
Again referring to the Rudimentary Treatise on Clocks for the mathematical investigation of the errors of this class of escapements, or to a paper by the late J. M Bloxam, in the R. A. S. M^unrs of Io3, we may say it is proved that though the time of a crravitv escapement pendulum differs from that of a free r.endulum more than from that of a dead escapement, yet the variations of that hflerence (which are the real variations of the dock) may be made much less than m any kind of dead escapement.
The difficulty which long prevented the success of gravity escapements was their liability to what is called (ripping. .Referring again to fig. 10, it will be seen at once that if the scape-wheel should happen to move too fast when it is released, the left pallet will not be raised gradually by the tooth B, but be thrown up with a jerk, perhaps so high that the tooth slips past the hook; and then not only will that tooth slip, but several more, and at last when the wheel is stopped it will be running fast, and the points of some of the teeth will probably be bent or broken by catching against the pallets. And even if the pallet is not raised high enough for the tooth to get past or completely trip, it may still be raised so high that the point of the tooth does not rest on the hook exactly where the slope of the pallet ends, but lower v and the friction between them is quite enough to keep the pallet there; and consequently the pendulum does not begin to lift it at the proper angle 7, but at some larger angle; and as the pallet always descends with the pendulum to the same point, the duration of the impulse is increased, and the pendulum made to swing farther. Sir E. Beckett called this approximate tripping, and though not so injurious to the clock as actual tripping, it is obviously fatal to its accurate performance, though it appears never to have been noticed before he pointed it out in 1851. Various contrivances have been resorted to for preventing tripping. But on account of the delicacy required in all of them, and other objections, none of them ever came into use until the invention of the three-legged and four-legged escapements to be mentioned presently. The only one which approached near enough to satisfying all the requisite conditions to be worth description is Mr Bloxam's, and we accordingly give a sketch of it in fig. 11, which is copied (with a little alteration for distinctness) from his own description of it, communicated in 1853 to the Astronomical. Society, some years after he had had it in action in a clock of his own. This drawing will enable any one conversant with these matters to understand its action. He made the pallet arbors cranked, to embrace the pendulum-spring, so that thencentres of motion might coincide with that of the pendulum as nearly as possible, perhaps an unnecessary refinement; at least the three-legged and four-legged gravity escapements answer very well with the pallet arbors set A on each side of the top of the spring. The size of the wheel determines the length of the pallets, as they must be at such an angle to each other that the radii of the wheel when in contact with each stop may be at right angles to the pallet arm; and therefore, for a wheel of this size, the depth of locking can only be very small. The pinion in Mr Bloxam's clock only raises the pallet through 40 at each beat; i.e., the angle which we called 7 is only 20; and probably, if it were increased to anything like -r-, the escapement would trip immediately. The two broad pins marked E, F. are the fork-pins. The clock which Mr Bloxam had went very well; but it had an extremely fine train, with pinions of 18; and nobody else appears to have been able to make one to answer. In short Bloxam's was not a practical solution of the gravity escapement problem, any more than those of Captain Kater, or Hardy, or various other inventors. A few clocks of Hardy's alone still exist.
Fig. 11.—Bloxam's Gravity Escapement.
The only gravity escapement or escapements that really have come into common use are the "four-legged" and the "double threelegged" escapements of Sir E. Beckett. They passed through various phases before settling into the present form, ot which it is unnecessary to say more now than that the first was the single three-legs described in the last edition of this Encyclopaedia, which was suggested by his three-legged dead escapement. A five-legged one was also tried; but though it had some slight advantages they are quite overbalanced by disadvantages, and it requires much more delicacy of construction than either the double three-legs or the four-legs which we shall now describe, remarking that the latter is the best for "regulators," and the formei in large clocks. Fig. 12 is a back view of the escapement part of an astronomical clock with the four-legged wheel; seen from the front the wheel would turn the other way. The long locking teeth are made about 2 inches loi.g from the centre, and the lifting pins, of which there are four pointing forwards and the other four intermediate pointing back wards, are at not more than one-30th of the distance between the
