Part 2
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.”