Let us now make a similar comparative trial with the dead beat 'scapement. An additional motive force being put to it, we find that the arc of vibration is considerably in creased, and the clock, in consequence of this, goes very slow. There are two causes which produce this ; the one is, the greater pressure by the swing wheel teeth on the circular part of the pallets during the time of rest ; the other is, the increase of the arc of vibration. It was ob served in the case of recoil, that an additional motive force made the clock go fast ; and the same cause is found to make the clock having the dead beat go slow. As the causes are the same, and yet produce effects diametrically opposite, does not this evidently point out what is necessa ry to be done The pallets should be so formed, as to have very little of a recoil, and as little of the dead beat ; and here any variation in the motive force, or in the arc of vibration, will produce no sensible deviation from its set tled rate of time-keeping. We have been informed, that a clock was given by Mr Thomas Grignion to the Society for the encouragement of Arts, Manufactures, Sec. cc which had a dead beat 'scapement, so constructed, or drawn off, that any diminution or addition of motive force would not alter the time-keeping of the clock." All the 'scapements of this kind which have been hitherto made, were common ly drawn off nearly in the same way as Mr Grignion's, that is,the distance between the centre of the pallets, and the cen tre of the swing wheel, is equal to one diameter of the wheel; and the line joining the centre of the pallets, and the acting part of them, is a tangent to the wheel, taking in ten teeth, and 'scaping on the eleventh. This is nearly the same as represented in Plate II. of Mr Cuming's book. The only difference is, that Mr Grignion's circle of rest is the same on each pallet. But whether it possesses the properties which have been ascribed to it, shall be left to the determi nation of those who may chose to try this experiment with it.
Clockmakers in general have an idea, that, in a 'scape ment, the pallets ought to take in seven, nine, or eleven teeth, thinking that an even number would not answer. This opinion seems to have arisen front the old crown wheel having always an odd number of teeth, because an even number could not have been so fit for it.
Thet;e seem to be no rules (as some have imagined) ne cessarily prescribed by either the recoiling or the dead beat 'scapement, for any particular distance, which the centre of the pallets ought to have from that of the swing wheel. The nearer that the centres of the swing wheel and pallets are, she less will be the number of teeth taken in by the pallets, when a tangent for them is drawn to the wheel. It is very obvious, that when the arms of the pallets are long, the greater will be the influence of the motive force on the vi brations of the pendulum, and vice versa, when the pallets are short, the angle of the 'scapement will naturally be greater than may be required, but this can be easily lessen ed by making the flanches so as to give any angle required.
When this angle is not quite half a degree on each side, a very small motive force will keep a pretty heavy pendulum in motion. We have known a very good clockmaker, who thought that the flanch of the pallets was an arbitrary or fixed point, which could be made only in one way, and it was some little while before he could be convinced of the contrary. The flanches may be made so long as to act something like detents, so as to stop the wheel altogether by the teeth, (see Fig. 5.) or they may be made so short as to allow the wheel teeth to pass them altogether, without giv ing any impulse at all to them. It is true, that there would be no 'scapement here ; only it shows that the flanch of the pallets may be made to give any angle of 'scapement, from a few minutes to two or three degrees. Whatever the an gle of the flanches may be taken at, all that is requsite is, to make the wheel 'scape so, that the tooth, when it chops on the pallet, shall fall just beyond the corner of the flanch, on the circular or recoiling part of the pallet.
Harrison's clock pallets (which are sometimes made to act by means of very delicate springs, and sometimes by their own gravity), have a very considerable recoil, which was a most ingenious contrivance, to do away the necessity of having oil put to them. The construction of them seems to be but little known ; and they have very rarely been adopted in practice. Indeed, it is a 'scapement of such a nature, that very few would be competent to exe cute it properly. The circumstances which led to the in vention of them, were mentioned by Mr Harrison himself to the late Professor Robison. Having been sent for to look at a turret clock which had stopt, he went to it, though it was at a considerable distance from his home, and found that the pallets were very much in want of oil, which he then applied to them. On his returning, and ruminating by the way on the indifferent sort of treatment which he thought he had met with, after having come so far, he set himself to work, to contrive such a 'scapement, as should not give to others that trouble to which he had been put in consequence of this turret clock. Hence the origin of his pallets. A drawing and description of them will be given in a future part of this article.
The justly celebrated Mr Mudge, in a small tract, pub lished in June 1763, relative to the best means of improv ing marine time-keepers, suggested, as a great advantage, that of making the moving power bend up, at every vibra tion of the balance, a small spring, whose returning force should be exerted in maintaining the motion of the balance, (see Plate CCC. Fig. 9.) The first essay of this most in genious contrivance was a small pocket watch, executed by himself, nearly about this period ; and this is the same' principle which, some years afterwards, he adopted and practised in those time-keepers which he made.