describe, and which appears to have been invented by the celebrated Dr Hooke as early as the year 1656, very soon after the invention of pendulums.
In fig. 4 a tooth of the scape-wheel is just escaping from the left pallet, arid another tooth at the same time falls upon the right hand pallet at some distance from its point. As the pendulum moves on in the same direction, the tooth slides farther up the pallet, thus pro ducing a recoil, as in the crown-wheel escapement. The acting faces of the pallets should be convex, and not Hat, as they are generally made, much less concave, as they have sometimes been made, with a view of checking the motion, of the pendulum, which is more likely to injure the rate of the clock than to improve it. But when they are flat, and of course still more when they are concave, the points of the teeth always wear a hole in the pallets at the extremity of their usual swing, and the motion is obviously easier and therefore better when the pallets are made convex ; in fact they then approach more nearly to the "dead" escapement, which will be described presently. We have already alluded to the effect of some escapements in not only counteracting the circular error, or the natural increase of the time of a pendulum as the arc increases, but overbalancing it by an error of the contrary kind. The recoil escapement does so ; for it is almost invariably found that whatever may be the shape of these pallets, the clock loses as the arc of the pendulum falls off, and vice versa. It is unfortunately impossible so to arrange the pallets that the circular error may be thus exactly neutralized, because the escapement error depends, in a manner reducible to no law, upon variations in friction of the pallets themselves and of the clock train, which produce different effects ; and the result is that it is impossible to obtain very accurate time keeping from any clock of this construction.
But before we pass on to the dead escapement, it may be proper to notice an escapement of the recoiling class, which was invented for the purpose of doing without oil, by the famous Harrison, who was at first a carpenter in Lincolnshire, but afterwards obtained the first Government reward for the improvement of chronometers. We shall not however stop to describe it, since it never came into general use, and it is said that nobody but Harrison himself could make it go at all. It was also objectionable on account of its being directly affected by all variations in the force of the clock. It had the peculiarity of being very nearly silent, though the recoil was very great. Those who are curious about such things will find it described in the seventh edition of this Encyclopaedia. The recorded performance of one of these clocks, which is given in some accounts of it, is evidently fabulous.
Dead Escapements.
The escapement which has now for a century and a half been con sidered the best practical clock escapement (though there have been constant attempts to invent one free from the defects which it must be admitted to pos sess) is the dead escapement, or, as the French call it with equal expressiveness, I echappement d repos, bu- cause instead of the recoil of the tooth upon the pallet, which took place in the pre vious escapements, it falls dead upon the pallet, and reposes there until the pen dulum returns and lets it off again. It is represented in fig. 5. It will be observed that the teeth of the scape- wheel have their points set the opposite way to those of the recoil escapement in fig. 4, the wheels themselves both turning the same way ; or (as our engraver has re presented it), vice versa. The tooth B is here also represented in the act of dropping on to the right hand pallet as the tooth A scapes from the left pallet. But instead of the pallet having a con tinuous face as in the recoil escapement, it is divided iiito~two, of which BE on the right pallet, and FA on the left, are called the im pulse faces, and BD, FG, the dead faces. The dead faces are portions of circles (not necessarily of the same circle), having the axis of the pallets C for their centre; and the consequence evidently is, that as the pendulum goes on, carrying the pallet still nearer to the wheel than the position in which a tooth falls on to the corner A or B of the impulse and the dead faces, the tooth still rests on the dead faces without any recoil, until the pendulum returns and lets the tooth slide down the impulse face, giving the impulse to the pendulum as it goes.
Fig. 5.—Dead Escapement.
The great merit of this escapement is that a moderate variation in the force of the clock train produces a very slight effect in the time of the pendulum. This may be shown in a general w~ay, without resorting to mathematics, thus : Since the tooth B drops on to the corner of the pallet (or ought to do so) immediately after the tooth A has escaped, and since the impulse will begin at B when the pendulum returns to the same point at which the impulse ceased on A, it follows that the impulse received by the pendulum before and after its vertical position, is very nearly the same. low that part of the impulse which takes place before zero, or while the pendulum is descending, tends to augment the natural force of gravity on the pendulum, or to make it move faster ; but in the de scending arc the impulse on the pallets acts against the gravity of the pendulum, and prevents it from being stopped so soon ; and so the two parts of the impulse tend to neutralize each other s disturbing effects on the times of the pendulum, though they both concur in. increasing the arc, or (what is the same thing) maintaining it against the loss from friction and resistance of the air. However, on the whole, the effect of the impulse is to retard the pendulum a little, because the tooth must fall, not exactly on the corner of the pallet, but (for safety) a little above it ; and the next impulse does not bt-gin until that same corner of the pallet has come as far as the point of the tooth ; in other words, the retarding part of the impulse, or that which takes place after zero, acts rather longer than the accel erating part before zero. Again, the friction on the dead part of the pallets tends to produce the same effect on the time ; the arc of course it tends to diminish. For in the descent of the pendulum the friction acts against gravity, but in the ascent with gravity, and so shortens the time ; and there is rather less action on the dead part of the pallets in the ascent than in the descent. For these reasons the time of vibration of a pendulum driven by a dead escapement is a little greater than of the same pendulum vibrating the same arc freely ; and when you come to the next difference, the variation of time of the same pendulum with the dead escapement, under a moderate variation in the force, is very small indeed, which is not the case in the recoil escapement, for there the impulse begins at each end of the arc, and there is much more of it duiing the descent of the pendulum than during the ascent from zero to the arc at which the escape takes place and the recoil begins on the opposite tooth ; and then the recoil itself acts on the pendulum in its ascent in the same direction as gravity, and so shortens the time. And hence it is that an increase of the arc of the pendulum with a recoil escapement is always accompanied with a decrease of the time. Something more than this general reasoning is re quisite in order to compare the real value of the dead escapement with others of equal or higher pretensions, or of the several contrivances that have been suggested for remedying its defects. But we must refer to the Rudimentary Treatise on Clocks for details of the mathematical calculations by which the numerical results are obtained, and the relative value of the different kinds of escape ments determined.
It camiot be determined a priori whether cleaning and oiling a dead escapement clock will accelerate or retard it, for reasons explained in those calculations ; but it may be said conclusively that the larger the arc is for any given weight x the fall per day, the better the clock will be ; and in order to diminish the friction and the necessity for using oil as far as possible, the best clocks are made with jewels (sapphires are the best for the purpose) let into the pallets.
The pallets are generally made to embrace about one-third of the circumference of the wheel, and it is not at all desirable that they should embrace more ; for the longer they are, the longer is the run of the teeth upon them, and the greater the friction. There is a good deal of difference in the practice of clockmakcrs as to the length of the impulse, or the amount of the angle 7 + if the im pulse begins at /8 before zero and at y after zero. Sometimes you see clocks in which the seconds hand moves very slowly and rests a very short time, showing that 7 + /3 is large in proportion to 2a ; and in others the contrary. The late Mr Dent was decidedly of opinion that a short impulse was the best, probably because there is less of the force of the impulse wasted in friction then. It is not to be forgotten that the scape-wheel tooth docs not overtake the face of the pallet immediately, on account of the menu-lit of inertia of the wheel. The wheels of astronomical clocks, and indeed of all English house-clocks, are generally made too heavy, especially the scape-wheel, which, by increasing the moment of inertia, requires a larger force, and consequently has more friction. We shall see presently, from another escapement, how much of the force is really wasted in friction in the dead escapement.
But before proceeding to other escapements, it is proper to notice a very useful form of the dead escapement, which is adopted in many of the best turret clocks, called the pin-wheel escapement. Fig. 6 will sufficiently explain its action and construction. Its advantages are that it does not require so much accuracy as the other; if a pin gets broken it is easily replaced, whereas in the oth^r the wheel is ruined if the point of a tooth is injured ; a wheel of given size will work with more pins than teeth, and therefore a
