Chapter I: Preface (1)

It has been my lot, during a long and eventful passage through life, to have my attention forcibly drawn to a multitude of Mechanical Subjects; the present review of which permits me to hope, that in making them publicly known, I should render an important service to the Arts and to Society. But the manner of doing this has been so long a question with me, that I have sometimes feared my ability would be extinct before I could do it at all. The reasons, however, that urge me to make the attempt acquire strength with the lapse of time: and whenever my declining health bespeaks the approach of that “night in which no man can work,” I feel deep regret, that this tribute should not have been thrown into the treasury of human knowledge while yet, by the favour of a good Providence, the means of doing it were more fully at my disposal.

I have determined therefore to publish these Inventions. Not because they have been matured into a regular System of Mechanical truth; but because they consist of _many_ distinct objects of immediate application:--coupled with _some_ ideas of a more comprehensive nature, that may probably extend the usefulness of this admirable study, in the hands of Artists yet unborn.

The form, or rather the title of this work, has but one example, that of the illustrious Marquis of Worcester; whose name may, perhaps, prolong the remembrance of mine: an event the rightful anticipation of which, I confess, would give me pleasure. Not that I either covet or regard what is commonly called popular applause: but the approbation of the wise and good I do regard, and aspire to obtain; since that alone seems to fulfil the adage--“Vox populi vox dei.”

On the subject of our respective Inventions, my views are somewhat different from those of the Noble Marquis; whose description of his labours, as the custom then was, seems chiefly calculated to excite the desire of knowing them better: whereas my wish is to infuse, at once, the knowledge of my subjects into every head capable of receiving it.

This Work then, treats less of Theory than Practice. What are called Principles in Mechanics, are, and must be, founded on numerous suppositions; to present which to “the mind’s eye” requires often a _forest_ of signs, which some readers _will_ not, and others _can_ not penetrate; so that, for many, Theory might as well not exist. This evil is increased when, as it sometimes happens, these suppositions are laid so far from reality, as to leave the result, though correctly deduced, further from the truth than the point to which a sound understanding unassisted by science, would have carried it. To this extreme discrepance of views between theoretical and practical men, may be ascribed their well-known antipathy to each other--in indulging which, they are alike to blame! since no theory inconsistent with fact can be complete; nor any fact be adduced, that a perfect theory will not account for and confirm.

Happily these discussions do not affect my present purpose. For although I shall offer nothing contrary to sound theory, I do not consider that as my subject; but make it my business to present rational methods of producing useful effects.--In other words to describe these Inventions as connected with immediate Practice. And if, hereafter, it should become desirable to resume the discussion of any _principle_ relating to these subjects, I shall cheerfully enter upon it; but hasten, mean while, to do what seems more important--to place the subjects themselves beyond the danger of being wholly lost, whatever may befall me in the course of those events which are still among the secrets of Heaven.

In the pursuit of knowledge, in general, it is often desirable to trace it from its _upper_ source; and to know all the circumstances that have attended its progress, down to the very moment when it falls under our observation. Nor is it a matter of indifference to examine the minutest form which talent assumed, in the young mind whose subsequent efforts have engaged our attention, or gratified us with more varied and solid productions. In this view I have presumed to think myself justified in commencing this Work, by a succinct reference to those feeble efforts which marked my first steps in this career. Young I then was, and my musings puerile indeed! But they were original: they were the links of a chain which time has not yet snapt asunder--and of which my honoured Father saw the connection with my subsequent labours, long before I thought, myself, of any thing but working for the purposes of amusement; or, in the childish phraseology, of “playing at work.”

Should any reader then enquire what were my first avocations? the answer would be, I was (in imagination) a Millwright, whose Water-wheels were composed of Matches. Or a Woodman, converting my chairs into _Faggots_, and presenting them exultingly to my Parents: (who doubtless caressed the workman more cordially than they approved the work.) Or I was a Stone-digger, presuming to direct my friend the Quarry-man, _where_ to bore his Rocks for blasting. Or a Coach-maker, building Phætons with _vaneer_ stripped from the furniture, and hanging them on springs of Whalebone, borrowed from the hoops of my Grandmother. At another time, I was a Ship Builder, constructing Boats, the sails of which were set to a side-wind by the vane at the mast head; so as to impel the vessel in a given direction, _across a given Puddle_, without a steersman. (See Plate 2. Fig. 3.) In fine, I was a Joiner, making, with one tool, a plane of most diminutive size, the [relative] perfection of which obtained me from my Father’s Carpenter a profusion of tools, and dubbed me an artist, wherever his influence extended. By means like these I became a tolerable workman in all the mechanical branches, long before the age at which boys are apprenticed to any: not knowing till afterwards, that my good and provident Parent had engaged all his tradesmen to let me work at their respective trades, whenever the more regular engagements of school permitted.

Before I open the list of my intended descriptions, I would crave permission to exhibit _two_ more of the productions of my earliest thought--namely, an Instrument for taking Rats, and a Mouse Trap: subjects with which, fifty years ago, I was vastly taken; but for the appearance of which, here, I would apologize in form, did I not hope the considerations above adduced would justify this short digression. If more apology were needful.... Emerson himself describes a Rat-trap: and moreover, defies criticism, in a strain I should be _sorry_ to imitate! my chief desire being to instruct at all events, and to please if I can: without, however, daring to attempt the elegant PROBLEM, stated and resolved in the same words--“Omne tulit punctum, qui miscuit utile dulci.”

The town of Cirencester (my native place) is intersected by several branches of the river Churn, whose waters are pure and transparent, and whose banks, formerly, were much perforated by the industry of the Rats that had made them their residence. These holes had generally two openings; one at or near the surface of the ground, and the other near the bottom of the river: so that the rats could range the fields from the former, and dive into the water from the latter--where they were often seen gliding along the bottom, either up or down the stream. The Instrument for taking them in these circumstances, was no other than my Father’s Walking-stick, (represented at A. Fig. 1. Plate 2.) connected with the curve B by the joint C; the curve having a string fastened to it, which, passing through the body of the stick, rose to the hand at D, for the purpose of closing the fork at the proper moment. The Machine, thus constructed, was put over the rat’s back while in the act of diving; and by pulling the string C D, he was sufficiently pinched to be drawn out of the water, where a Dog stood ready to dispatch him.

On the Mouse-trap (Fig. 2. and 4.) more thought was bestowed. It appeared adviseable (I remember) to lay the deceptive plan rather deep: and to lull the little animal into a false security till the snare had taken full effect; and even then to hide from her some of its horrors till she was far enough from this vestibule of misery, _not_ to deposit there any of those tokens of distress that might deter other mice from following her example. The trap then, consisted of a _long_ passage, formed spirally round the surface of a Cone, like the figures we have of the Tower of Babel. This passage is uncovered in Fig. 4 to shew the entrance E, and the subsequent gates F G H, &c. which like the valves of a pump, gave easy entrance to the victim, but forbade her return. At the length of a mouse from the outer gate E, was placed the first bait N, say a small rind of cheese, well toasted to allure, but nailed down to prevent its removal. Its position was further indicated by a train of meal reaching from it to the outer gate E; which latter was nicely hung on pivots inclined a little to the perpendicular, so as to open with ease but never fail to close itself again. It had besides an horizontal plate O, fixed to its bottom on the inside, so that if the mouse attempted to open it that way, she trode on this plate and destroyed the result of her own efforts.

When, therefore, the little wretch had passed this barrier, she was in reality taken: but unconscious yet of danger, she nibbled the first bait with pleasure, and then skipped forward in search of more substantial food: but to obtain this she must pass more of these faithless gates, F G H, &c. which with progressive effort she opened, and at length found the inner compartments replete with good things, on which she fed to satiety, and then only began to think of her situation. Nor yet, with _much_ alarm: for at the end of this labyrinth, so easy of access, she hoped to find an easy exit. But alas, these hopes were illusive. Instead of light, she found the _dark_ gallery O; the least evil of which was to be too narrow for two mice abreast, since it overhung a tremendous cavern, Q, that entirely occupied the Cone below, and was filled with water deep enough to drown her, were she to fall, or be jostled into it. And one of these disasters she could hardly escape! for other mice would not fail to be beguiled into this cruel Bastille; to reach the same spot; and finally, to plunge her into this watery grave.

Having endeavoured to recollect the substance of these youthful attempts to unite cause and effect, or to fulfil a given purpose by preconcerted means, I now turn to things of greater importance, and more worthy to be the theme of my readers’ attention. The subjects to be presented will observe a miscellaneous order; since they have not only originated at different periods, but offer likewise different degrees of interest--to _equalize_ which throughout the Work, appears a desirable attempt. As to the _manner_ of treating each subject, it will be, generally, to describe the Machines by a reference to the Figures; and then to add some remarks on their date, construction, properties, and uses.

PART FIRST.
A NEW CENTURY OF
Inventions.

A
DYNAMOMETER;
OR,
_Machine for measuring Power and resistance while in Motion_.

Dynamics being a science that relates to bodies in motion--comprehending not their weight only, or their velocities only, but the product of the one by the other; so the Dynamometer is a mean of measuring both these circumstances together, and thus of making known the _momentum_ of a power or resistance in motion. As this Machine has a connection more or less intimate with almost every other, it seems entitled to the first place in this collection. Its description follows:

In Plate 3, Fig. 1 and 3, M M, represent two cheeks, standing parallel to each other, and forming a cage or frame by means of the cross bars E and the nuts F G. A P, Fig. 2, is the principal axis of the Dynamometer, fixed to the wheel R N of which it is the centre of motion. It has a square end A, formed to receive the wheels and other supplemental parts, to be mentioned below. After the square A, comes a bearing E, to fit the steps in the frame; and beyond the wheel R N is a cylindrical part O, fitted to the hollow axis T of the wheel or frame I K, (Fig. 4); and in fine the form P of this shaft fits and turns in the _cannon_ of the axis B H, of the wheel C D; so as, when put together and connected with the frame I K, to assume the form C R F G of the third figure. L P, Fig. 3 and 4, are two intermediate wheels (thus placed to balance each other on the common centre T) whose axes turn on proper steps in the frame I K; and which by their teeth connect the motion of this frame with that of _both_ the wheels R N, and C D.

Such are the parts of the Dynamometer properly so called; and they are shewn as in their places in Plate 1, where the parts above described, as far as visible, are marked with the same letters. Moreover, this figure shews a scale-bason P, to receive the weights used to measure equable powers, as will be seen hereafter.

Plate 4 contains some of the auxiliary parts of this Machine. But before we proceed to describe them, it may be proper to observe that the _measuring power_, by the action of which at K, (Plate 1) the energy of the _force_ is transmitted to the _resistance_, must, to meet every case, be susceptible of change, according as the resistance or force to be measured is uniform or convulsive. For example, in a mill grinding corn, driven by a fall of water, the whole process is sensibly uniform, and a weight at P is the proper measurer. But if it were desired to measure the effect of a pump driven by water, or of a tilt hammer worked by a Steam Engine, then the measuring power at P must be a spring: for in these cases the _vis inertiæ_ of a weight would add to its force of gravity when suddenly raised, or detract from it when the resistance should suddenly give way. Whenever therefore, the force and resistance are both _equable_, a weight will best measure them; and when _either_ is convulsive, a spring: but a spring so equalized as to offer the same resistance at every degree of tension it may have to sustain.

In the 6th. and 7th. Figures, (Plate 4) these demands are fulfilled. The first represents a barrel-spring, similar to that of a watch, but _surrounded_ by a fusee, the increasing radii of which compensate for the increased tension of the spring in the barrel G; so that the action of the system on the chain is always the same.

The 7th. Figure exhibits a spring adapted to heavier purposes. It is a cylinder nicely bored and hermetically closed at bottom; in which works a Piston P plunged in oil, which when forcibly drawn up forms a vacuum in the cylinder, into which the atmosphere endeavouring to enter, acts like a spring on the Piston; and preserves the same stress whatever be the height of this Piston in the cylinder.

This then, is also an _equalized Spring_, such as these experiments require; but it is _not_ my invention. I first saw a vacuum used, as a spring, by my noble Patron, the late Earl Stanhope: to whose mechanical attainments, I owe this tribute of applause on the present occasion.

In the three Figures of this Plate, 8, 9, 10, are shewn two of the means I use for creating those factitious resistances that are sometimes wanted in the process of measuring power. In Fig. 8, E H F, is a gripe or brake, such as millers use to stop their wind-mills with; fixed under L, it surrounds the wheel E H, and is then fastened to the end F of the lever K L. The brake is thus pressed with greater or less force against the wheel, as the weight I is placed more or less distant from the fulcrum L of the lever. By these means a resistance of the equable kind is produced, capable of being adapted to _any_ power it may be wished to measure; which makes this Dynamometer a real _tribometer_ or measurer of friction.

The second kind of resistance brought forward in this Plate, is a Pendulum P (Fig. 9 and 10,) set a vibrating by a pallet-wheel A B, connected with the axis of resistance; and working in the pallets N. It appears besides, in the Figure, that the times of vibration can be changed by the mechanism T N R, which raises or lowers the ball P. This then, is another resistance, such as we sometimes want: but it is also a mean of finding the quantity of resistance that a vibrating body opposes to motion, when oscillating in times _not_ those due to its length as a pendulum. In other words it is a mean of measuring _vis inertiæ_ itself--which an _astounding_ modern writer declares does not exist!

I hasten to give a description of certain other parts relating to the measuring system: and some methods of connecting with the Dynamometer the several kinds of forces it may be desirable to examine.

In Plate 5, Fig. 12, A X represents a Crank or Handle with a variable radius, the intent of which is to adapt a man’s strength to the velocity and intensity of any resistance he may have to overcome. The manner is this: B is a Screw pressing on the quadrant, and fixing the arm C X to any required angle with the part A C: thus determining the virtual radius of the handle.

Fig. 14, shews a method of applying to the Machine the force of a man pumping: for the catch N permits the handle O to rise alone, but carries round the wheel R, at every downward stroke, while the fixed catch C secures all the forward motion thus given. The same Figure shews, at B, the force of a man in the act of _rowing_: for the catch M permits the lever V M to recede when the man _fetches_ his stroke, and carries the wheel round when he _takes_ it. An operation, by the bye, which I think the best mode of employing human strength, if every possible advantage is taken of the method.

The 13th. Figure shews the last method I shall now offer of adapting power to the Dynamometer. T S represents the Piston of a Steam Engine, the rod of which is formed of _two_ bars, including between them the chains F G and F D, the first of which is single, merely to carry back the acting wheel; and the last double, to draw round the ratchet wheel E, by the catch O, at every stroke of the Piston.

I must obviate here an objection that may strike some readers. This Piston T S, acts only one way, like that of an atmospheric engine, a thing now quite out of date! I answer that this figure is chiefly intended to give the _idea_; and shew a rotatory Steam Engine that _might_ act without a fly. I will add, that it is my intention some day to bring forward a method of using these suspended actions, better than by a mere ratchet wheel: and especially without incurring danger from the length of the ratchet teeth, or the blow they suffer at the beginning of the strokes. But of this more hereafter.

A short description will suffice for the mechanism of the 18th. figure (Plate 6), which is intended to convert the alternate pressure of a man’s feet into rotatory motion, and then to measure his _power_. To do this two catches A B, take into the teeth of the same wheel M, and each catch carries an arm, P, embracing somewhat stiffly the boss of the wheel. The treadles have a common centre at E, and are fastened to the same rope going over a pulley, F, so as for the depression of the one to raise the other. Again, the pulling bars C D, are connected with the treadles, and from the form of the catches, it is evident (since the levers move with some stiffness), that the first effect of an ascending motion will be to draw the rising catch out of the teeth, and keep it out until arrived at its greatest height; when the very beginning of its descending motion will bring the catch into the teeth again, and thus carry round the wheel at every downward movement of the treadle;--a method this of making a ratchet work without rattling upon the wheel.

The mechanism shewn in figure 19, is intended to produce another of our factitious resistances; and it serves likewise to make experiments on the resistance of the air. It is a fly, meeting with an _equable_ resistance as does the fly in the striking train of a clock. The wheel W, is put on the axis of resistance of the Dynamometer; and its teeth geer in those of the vertical shaft L H. This latter is perforated from above, and has an open mortice all along its body, which a small bar penetrates, meeting at bottom the ring H, to which it is fastened by a pin going through the mortice. Again, this ring H, is moved, downward, by the rollers of the sliding bracket P, which has its motion from the wheel and rack G: and finally, the leaves I K slide in the horizontal frame; and when the machine turns _would_ obey the centrifugal force and fly outward; but are withheld by the cords N O, which passing over the pulleys N O, and under those L M, are then fixed to the frame above L. When, now, this Machine is used, and the fly made to revolve swiftly, the leaves I K, oppose a certain resistance to the rotatory motion; and if _this_ be too feeble, the key G must be turned backward, which will permit the ring H to rise, and the wings I K to recede from the centre. But if this resistance is already too strong, the key G must be turned forward, and the wings brought nearer: between which extremes, a point will easily be found where the resistance of the air will _expend_ just power enough to balance that brought into the Dynamometer through the _power-axis_; and thus to keep the measuring weight in the position required for any given experiment.

There remains only one part to be described as belonging to this Machine. It is represented in Plate 5, fig. 15, and is a graduated bar, made to fit in the holes K, of the measuring cylinder I K Plate 1: and to carry one of the arcs A A, which thus serves to extend, virtually, the radius of that cylinder to any required dimension.

It is now time to shew something of the manner of using this Dynamometer in the measurement of forces. Let the object then be to measure the power expended by a Horse in drawing a Carriage.

To do this, we fix a Drum (see fig. 16,) of equal radius with the measuring cylinder, on the power axis A; and a similar Drum to the resisting axis H. After firmly fixing the Machine, we place the Carriage at a distance behind it in the plane of the Drum H; and carry a rope from that Drum to the Carriage: on the other hand, we fill the first Drum A, with a coil of rope, to which the Horse is harnessed; and while he travels in the plane of the Drum A, the scale P (Plate 1,) is loaded with weights, until the Carriage follows the horse’s motion without any (or with little) agitation to the scale P: at which moment the _power_ employed _is equal to one half the weight at P, multiplied by the space gone through both by the Horse and the Carriage_.

If it were now desired to find the power of a man turning a crank or handle, we should take that given in the figure 12, and fix it to the power-axis A. We should also take the fly-system shewn in fig. 19, and place it on the axis-of-resistance H. Then causing the man to turn the Machine, we should put _twice_ as much weight into the scale P, as his strength was thought able to bear. Then if he thought the work too heavy, we should draw inward the leaves of the fly, and take away part of the weight P, until the man were satisfied he could work with convenience: and when, as before, the weight P should overcome the resistance of the fly I K, without either rising or falling, (sensibly) then the _power_ expended would be _one half of the weight P, multiplied by the space described by the man’s hand in the act of turning the handle_.

It may occur to some of my readers that in these experiments the whole effect is not actually _measured_: since the space described by the horse or the man’s hand, must be determined after the experiment. I answer that these quantities, necessarily _variable_, must bear an inverse proportion to the weight P: and in all cases, this weight multiplied by that space, must give the _power_ or momentum required. Besides, it is most easy to add a piece of mechanism that shall count the number of turns, and express them _in space_, by the inspection of a graduated scale. Nor need we stop here. The duration, in time, of any experiment, may also be recorded by the Machine itself. These are things so naturally connected with the subject, that I cannot feel it necessary, with so much before me, to attempt exhausting them. But _this_ I engage to do: if any serious difficulty should actually stop any reader in this career of investigation, I will obviate such difficulty at some convenient future period. And mean while those persons who have aptitude for such subjects, will find in this Machine, ample scope for extending their enquiries; and comparing many mechanical realities with the deductions of Theory, thus amending and conciliating the conclusions both of Theory and Practice.

I have said above, that the weight or spring acting on the measuring cylinder at K, _must_ be equalized: but in reference to _some_ applications of this Machine to real use, I would modify that precept a little. I should, indeed, always like the principal action to be of a constant nature: with a supplementary part of less intensity, prepared to add something to the former; and this, for the purpose of meeting spontaneously the case of any unexpected addition of the moving power. Thus in Plate 1, if P be a weight _nearly_ adapted to a given resistance, I would (to prevent accident, from its being overraised by any sudden jerk of the power,) hang one or more heavy chains under the scale, which drawn from the ground to a certain length, would add a known quantity to the measuring power; and transmit with a certain softness to the work, the unequal action of the _mover_.

One word on the _friction_ of this Machine. All friction must of course be avoided as much as possible; but as it will be nearly the same in every class of experiments, it is not of great importance. The same may be said of the _vis inertiæ_ of the parts, _in convulsive motions_. The parts would, of course, be made as light as a proper strength would permit. My mechanical readers will easily supply these small items of foresight; to anticipate the whole of which would make this Work interminable.

OF A NEW KIND OF
BARREL SPRING,
_To lengthen the going of Clocks, Jacks, &c._

Although this invention does not properly constitute a _new Spring_, yet it produces effects both new and important. It protracts almost indefinitely the action of a barrel Spring, and thus reduces considerably the number of wheels in a clock or other spring-driven machine. This effect is produced by _setting the two ends of the spring at variance_; or making them _act one against another_: for as these opposite tendencies can be made nearly equal, one end of the spring will be wound up _almost_ as much as the other end runs down: thus prolonging the effect in any desired proportion. It will be making 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, on which de la Hire says absolutely _nothing_. Is this then inadvertency? or is it uncandid nationality? I hope, the former.

A further remark on the utility of this System as a first motion, may be of use in this place. It respects the _geering_ of the fixed and moveable wheels A B, and F, on the _perfection_ of which depends the truth of the statement, that the stud, a, describes a diameter of the large wheel. Now, perfection is too much to be expected from common teeth when of the necessary strength; so that my Patent Geering is an indispensable complement to this Invention: as by its use, the principle is made practically true; this line becoming really straight, and this motion, under proper circumstances, being unattended with noise or commotion. In a word, I cannot move a step in this mechanical field, without meeting with instances where the new System shews its superiority to the old: whence it becomes a duty for me to commence the consideration of this subject in the very next _part_ of this publication.

OF
A SYSTEM OF CONCENTRIC PULLEYS,
_Already known as White’s Patent Pulleys_.

These Pulleys have been frequently described since I first entered my _specification at the Patent Office_. The Authors of the Encyclopedia Britannica; the Rev. Mr. Joyce, in his juvenile philosophy; and Dr. Gregory in his mechanics, have all adverted to them. In the latter work, I find the following quotation from my own description, thus introduced:

A very considerable improvement in the construction of pulleys has been made by Mr. James White, who obtained a Patent for his Invention, of which _he_ gives the following description: “Fig. 4, Plate 7, _of this work_, shews the Machine, consisting of two pullies, Q and R; the former fixed, the other moveable. Each of these has six concentric grooves, capable of having a line put round them, and thus of acting like as many different pulleys having diameters equal to those of the grooves. Supposing then, each groove to be a distinct pulley, and that all these diameters were equal, it is evident, that if the weight 144 were to be raised by pulling at S, till the pulleys touched each other, the first pulley must receive the length of line as many times as there are parts of the line hanging between it and the lower pulley. In the present case there are 12 lines, b, d, f, &c. hanging between the two pulleys, formed by its revolution about the six upper and six lower grooves. Hence as much line must pass over the uppermost pulley as is equal to 12 times the distance of the two. But, from an inspection of the figure, it is plain that the second pulley R S, cannot receive the full quantity of line by as much as is equal to the distance betwixt it and the first. In like manner, the third pulley receives less than the first, by as much as is equal to the distance between the first and the third; and so on to the last which receives only 1/12 of the whole: for this receives it’s share of line n, from a _fixed_ point in the upper frame which gives it nothing: while all the others in the same frame receive the line partly by moving to meet it, and partly by the line coming to meet them.”

“Supposing now these pulleys to be equal in size, and to move freely as the line determines them, it appears from the nature of the system, that the number of their revolutions, and consequently their velocities, must be in proportion to the number of suspending parts, that are between the fixed point above-mentioned, (n) and each pulley respectively. Thus the outermost pulley would go twelve times round in the time that the pulley under which the part n of the line passes, (if equal to it) would revolve only once; and the intermediate times and velocities would be a series of arithmetical proportionals of which, if the first term were l, the last would always be equal to the whole number of terms. Since then, the revolutions of equal and distinct pulleys are measured by their velocities, and that it is possible to find _any_ proportion of velocity on a single body running on a centre, viz. by finding proportional distances from that centre; it follows, that if the diameters of certain grooves in the same body be exactly adapted to the above series, (the line itself being supposed inelastic and of no magnitude) the necessity of using several pulleys in each frame will be obviated, and with that some of the inconveniences to which the use of the common pulley is liable.”

“In the figure referred to the coils of rope, by which the weight is supported, are represented by the lines a, b, c, &c. a is the line of traction commonly called the fall, which passes over and under the proper grooves, until it is fastened to the upper frame just above n. In practice, however, the grooves are not arithmetical proportionals; nor can they be so, for the diameter of the rope employed must be deducted from each term, without which, the small grooves to which the said diameter bears a greater proportion than to the larger ones, will tend to rise and fall faster than the latter, and thus introduce worse defects than those which they were intended to obviate.”

“The principal advantage of this kind of pulley is, that it destroys lateral friction, and that kind of shaking motion which are so inconvenient in the common pulley; and lest, says Mr. White, (I quote Dr. Gregory) this circumstance (of a long pin) should give the idea of weakness, I would observe, that to have pins for pulleys to run upon, is not the only, nor perhaps the best method: but that I sometimes use centres fixed in the pulleys, and revolving on a short bearing in the side of the frame, by which strength is increased, and friction much diminished: for to the last moment of duration, the motion of the pulley is circular, and this very circumstance is the cause of it’s not wearing out in the centre as soon as it would, assisted by the ever increasing irregularities of a gullied bearing.--These pullies when well executed, apply to Jacks and other Machines of that nature with great advantage: both as to the time of their going and their own durability: and it is possible to produce a System of pulleys of this kind, composed of six or eight parts only, and adapted to the pocket, which by means of a skain of sewing silk, would raise more than a hundred weight.”

There are several real and solid advantages attending the use of this pulley; some of which are only hinted at in this description. I have thought, therefore, it might be useful to introduce here an account of some trials which the System underwent a few years ago at Portsmouth,--at the request of an Officer of the Navy, who had _re-invented_ it with some ingenious additions to my ideas. Not being at present in correspondence with that Gentleman, I hardly think myself at liberty to mention his name; but fully so to give an extract from the report which followed these experiments--in which the superiority of the System _in respect of power_, is made evident, although some less favourable circumstances prevented its adoption on that occasion.

“With a view to comparison, it was settled with Lieutenant S. that his blocks should be made to correspond with the treble and double 16 inch blocks of a 24 gun ship, which carry a 4-1/2 inch rope. The sheeves in the new blocks are fixed upon the pin, revolving therewith, and are of different diameters proportioned to the velocity of the parts of the rope that pass over them; they are also reeved with a double rope so that there are two grooves of each size, the diameter of the smallest groove in this tackle being 2-8/12, and of the largest 15 inches. The diameter of the sheeves of the common blocks would have been (as usually made) 9-1/8 to the bottom of the grooves, but were reduced at the request of Lieutenant S. in the treble block to 8-1/8, and in the double block to 8-7/8, in order that the sum of the diameters of the sheeves in each tackle should be the same. The Lieutenant intending in the first instance, to have used a roller under the pin, for the purpose of diminishing friction, but afterwards laying aside this idea on account of it’s complication, was the reason that he had not made his sheeves in the same proportion with the common blocks: the weight and length of the respective blocks are as follows:

Weight. Length.

Lieutenant S.’s treble blocks 131lbs. 24 Inches.
Common ditto 78 „ 16 „
Lieutenant S.’s double block 73 „ 21 „
Common ditto 60 „ 16 „
Lieutenant S.’s single block 22 „ 17 „
Common ditto 34 „ 16 „

“Lieutenant S.’s blocks were reeved with a 2-1/2 inch double rope, and the common block with a 4-1/2 inch single rope, and both tackles suspended from a beam, and their respective falls let over the single blocks, so as to keep the weight applied as a power, just clear of the weight to be lifted, thus forming a power of six to one; the following experiments were made:

Weight very Power required Power required
slowly lifted. with Lieutenant S.’s blocks. with the common blocks.
℔s. ℔s. ℔s.
336 88 124
672 169 252
1344 312 448
2688 588 808
5376 1101 1344.

“After reeving the common blocks with a 3-1/2 inch rope in lieu of a 4-1/2 inch rope, it was as follows: 5376 1101 1232.

“It must be observed, that the double 2-1/2 inch rope in Lieutenant S.’s blocks, is not of equal strength with the single 4-1/2 inch rope first used in the common blocks; and that his blocks had an undue advantage in the first experiment over the common blocks, in respect to the pliability of the rope. The rope should therefore, be taken larger in the one or smaller in the other case, on this account: The common blocks were reeved in the last experiment, with a 3-1/2 inch rope, which is as near as may be of the same strength as the double 2-1/2 inch rope.

“In these experiments it was observable, that the tar was much more squeezed out of the parts of the rope that passed over the smallest sheeves in Lieutenant S.’s blocks, than out of those passing over the larger sheeves, or out of those passing over the sheeves of the common blocks; by which, as well as by the nature of the thing, we judge that with blocks requiring such small sheeves, the ropes would be more crippled and broken than by the common blocks, especially if any constant strain or weight in motion, as on ship board, should be held by them. In regard to our opinion of the merits of the blocks proposed by Lieutenant S. compared with common blocks, we beg leave to submit, that the mechanical principle of them is very inviting, and it is not to be wondered that an ingenious person should pursue the idea; yet _allowing there would be a saving of power_, which is attained in so great a degree with the common blocks, but considering the greater complication, weight, and expence of these blocks, and their greater disposition to cripple the ropes, we do not perceive any application of them on ship board, for which we could recommend them in preference to common blocks; neither do we perceive any purposes on shore, for the services of the dock yards in which to recommend their application in preference to the other powers in use.”

To this account of the result of these experiments, I beg leave to add what seems to be a great improvement of this System: namely, a method by which the diameters of the larger pulleys are considerably lessened; and thus the principal, if not the only objection, obviated. It has been before observed, that the larger pulleys, as Q R, are the ultimate terms of an arithmetical progression, beginning at unity; and that consequently they cannot be very small, even though the first terms should be so. If a first pulley were only one inch in diameter, the _twelfth_ pulley would be twelve inches,--where we see a large and inconvenient difference. But this evil I now obviate, by placing at the beginning of the series, one or more _loose pulleys_, over which to _reeve_ the cord, before the concentric or fixed grooves begin; thus lowering the _ratio_ of the progression, and keeping the larger pulleys within bounds. For example, the smallest fixed pulley (supposed as before, to be one inch in diameter) I now make the _second_ of the series instead of the first: and therefore, the second _fixed pulley_ is to the first as 3 to 2, instead of being as 2 to 1; for the same reason, the third fixed pulley is to the second as 4 to 3; and in a system of 12 pulleys, (with one loose one) the respective terms will be as follows:

Terms 1----2----3----4----5----6----7----8----9---10---11---12
loose;2/2; 3/2; 4/2; 5/2; 6/2; 7/2; 8/2; 9/2;10/2;11/2;12/2

or 6 inches for the largest pulley, instead of 12 inches given by the last progression.

So likewise, if we take _two_ loose pulleys, (which will not add much to the complication of the Machine) and make the third term 1 inch, the fourth will become 4/3, shewing the _ratio_ of the progression to be 1/3, so that the series of 12 terms will stand thus:

Terms, 1-----2----3---4----5----6----7----8----9---10---11---12
loose;loose; 1; 4/3; 5/3; 6/3; 7/3; 8/3; 9/3;10/3;11/3;12/3; or,

four inches for the largest groove in the concentric part of the System.

Now we saw before, that the first and last pulley were in diameter to each other, as 1 to 12; whereas, here, with only two loose pulleys, these extremes are but as 1 to 4: dimensions much more convenient and manageable. The 5th. figure of the Plate 7, is intended to shew graphically, the effect of this modification of the principle. In that figure, if the line a, be the diameter of the _first_ pulley, that of the sixth pulley will be shewn by the line b c; but if the same line a be made the _second_ pulley, the diameter of the sixth will be shewn by the line e d; only 2/3 of the former. And in fine, if the same a, be the third pulley, the sixth will have it’s diameter reduced to the line f g, only one half of what it was in the first case. In a word, the more loose pulleys are put before the fixed ones begin, the nearer to cylindrical will the general form become; and the more conveniently may pulleys be used for general purposes. I might even assert, that if _one_, or at most two loose pulleys had been used in the above-mentioned experiments, the result would have been as favourable to the System, with respect to the _weight of the tackle and stress on the ropes_, as it was in respect of _power_; where it’s advantages were important and undeniable.

OF
A POWER-WHEEL,
_Turned by heated Air, Gas, &c._