known the principle, to describe the first motion of a clock founded upon it.
In Plate 7, fig. 1, A is the spring barrel, to which is fixed a wheel, B, of 96 teeth, working in C, a pinion of 17. E is another wheel of 92 teeth, working in F, a pinion of 22: both pinions being fixed on the same arbor, I G. The smaller wheel E, turns on a round part of the axis H D; and is connected with its motion in the backward direction only, by a ratchet wheel R, fixed on a square part of the same arbor. As usual, this latter has a cylindrical boss within the barrel A, to which the inner end of the spring is hooked; as its outer end is, to the rim of the barrel; and thus does the wheel B (when the clock is wound up) tend to turn forward as shewn by the arrow B; while the wheel E, tends to turn backward in the direction of E, the second arrow. But these opposite tendencies are not equal; because the wheel B is larger, and acts disadvantageously on C, the smallest pinion; while the wheel E is smaller, and acts to advantage on the larger pinion F: so that there is a decided tendency in the whole to turn backward. Now, to find precisely what is the effect of that tendency, we observe that when the barrel and the larger wheel B, have made one revolution round the common axis H D, the pinions C and F will both have made 96⁄17 of a revolution (being the quotient of the division of the wheel B by the pinion C:) and since the larger pinion of 22 teeth, works in the smaller wheel of 92 teeth; this latter wheel in the same time will have made 96⁄17 of 22⁄92 of a revolution, or 1,350 of a turn very nearly. The difference then between this quantity and unity, namely the decimal 0,350, is what the spring has really gone down during one turn of the barrel. And as the whole number of coils in the spring are 10, the number of turns of the barrel to uncoil it entirely, will be 10⁄0,350 or 10000⁄350 equal to 28,57 nearly: instead of ten revolutions which it would have been on the common principle.
It is almost superfluous to add that this prolongation of the time might have been greater, had I not been confined to the above numbers, for want of others more nearly alike, and having a common difference, on my engine.
An important remark here presents itself, viz. that the best properties of this invention are unattainable by the use of the common geering—the friction of whose teeth would have absorbed the small rotatory tendency thus retained; and in which system, also the working diameters of the wheels could not have been defined with sufficient exactitude. This then, is one of the cases in which (as I have observed in a former work) my late Patent System of Geering has “given rise to machines that could not have existed without it,”—which it does by possessing exclusively the property of realizing (sensibly) the whole calculated effect; and working without commotion or assignable friction. It may please some of my readers to be informed that this System, and the means of executing it in every dimension, will hold a prominent place in some future page of this essay.
Referring again to the figure 1, the teeth X X, Y Y, are there placed to give a first idea of this principle: and they are unaccompanied by others, to avoid the confusion of lines that would have arisen from attempting to shew all the teeth, in their due position, on so small a scale. These things will claim all our attention when the System itself comes under examination.
The above representation of this Machine may leave a technical difficulty on the minds of clock makers relative to the winding up of this spring; which, in the present state of things, will suspend, for the time, it’s action on the pendulum: for in order to effect it, (in a reasonable number of turns) the introduction of the key must, by a proper check-piece, be made to stop the wheel B, and leave it again at liberty when the key is taken out: in which case ten turns of the key will effect the winding, although the Machine should be calculated to give out forty turns in the uncoiling of the spring. But if the wheels B and E had changed places; that is, if E had been fixed to the barrel A, and B been connected with the ratchet wheel R, then the act of winding up would have taken place in the opposite direction; or in that which tends to keep up the motion of the pendulum, in which case, however, the machinery of the clock must have borne the whole stress of the spring during the act of winding, instead of the small portion it sustains when the two ends counteract each other.
But I anticipate another objection to this method of employing a barrel spring: which is the inequality of stress, when the spring is much or little wound. The answer is, that many clocks and watches are made to go well without fusees; either by modifying the thickness of the springs, or employing only a few of the middle coils. My Invention may, perhaps, help to nurse this System to perfection: if not, its influence will be the more confined, but in no wise destroyed.
OF
A PARALLEL MOTION,
Being a combination of the Crank with the Epicycloid.
A B, Plate 7, fig. 2 and 3, is a ring or wheel fixed to the frame C D; and having all round it’s inside, teeth directed to the centre. F is a wheel of half the diameter, and exactly half the number of teeth of the wheel A B. It turns on a Crank-arm, E F, whose radius is equal to one quarter of the diameter of the fixed wheel A B—in the centre of which the axis of this Crank finds it’s due position. The latter, therefore, so conveys the wheel F round the inside of the fixed wheel A B, that the teeth of both are constantly geering to a proper depth: and a stud being fixed on the face of the wheel F, opposite the middle of any tooth, a, directly over the centre of the Crank E, this stud describes the perpendicular diameter of the large wheel: and will either receive motion from the rod R of a Steam Engine Piston, so as to give the fly I K, a rotatory motion; or communicate to a Pump-piston a reciprocating motion, drawn from the rotatory one of the fly, when that is the effect desired to be produced.
This Invention will be remembered, as having procured me a remunerating Medal from the late Napoleon Bonaparte, then first Consul of the French Republic. That period, however, (1801) was not the real date of this production, although then first made public. I have proof, on the contrary, of its existence with me several years before; and it is generally ascribed to me by the publicists. I might quote in particular Doctor Gregory: who likewise mentions its having been executed by Messrs. Murray and Wood, of Leeds, subsequently to it’s exhibition at Paris. The Doctor commits, however, a small error in calling me an Anglo-American; but this is accounted for by my then living in a country where to be an Englishman was itself a crime! and where some kind friends, wishing to hide me from the relentless decrees of the day, felt justified in using this sort of pious fraud in my favour: a resource from which, though I did not authorize it, I reaped no small advantage; and still think of with gratitude, though not with unmixed approbation.
I think it a duty more imperious than agreeable, to expostulate a little with Messrs. Lanz & Betancourt, on their apparent partiality in giving an account of this Machine. In their work on the construction of machines, art. 97, page 37, they make M. de la Hire the inventor of it, by the terms in which they introduce his treatise on Epicycloids: and they leave me the thread-bare merit of having “presented a model of this movement at the last exposition but one,” &c. Now, although I do not attach great importance to this kind of misrepresentation, I cannot but observe, that neither my Machine or their description of it can be called a Theorem! nor especially a theorem relating solely to the Epicycloid, as M. de la Hire’s was. These Gentlemen knew that he insisted principally on the application of this curve to the teeth of wheels, with which my Invention has nothing to do. On the contrary, my Machine is a combination of two curves at least,