Perpetual Motion

by Percy Verance; Henry Dircks

Article by William Nicholson

William Nicholson was born in London in 1753; died in 1815. He was a scientist of note, and a writer of scientific subjects. In 1797 he established in London and continued publishing until 1814, a periodical entitled "Journal of Natural Philosophy, Chemistry and the Arts," known, however, throughout the civilized world as "Nicholson's Journal."

A Perpetual Motion device of Dr. Conradus Schwiers, in 1790, and the Richard Varley device, in 1797, described at page 132 et seq., ante, had attracted a great deal of attention, and were the occasion of much discussion. A consequent increased interest in the subject of self-moving mechanism was thus created.

Mr. Nicholson, whose scientific attainments were recognized by all, was asked to publish an article on the subject. His article appeared in his publication, "Nicholson's Journal," and is as follows:

On the Mechanical Projects for Affording a Perpetual Motion

In consequence of the notice taken of Mr. Varley's attempt to produce a perpetual motion, I have been requested by several correspondents to state how far the mechanical scheme for which Dr. Conrad Schwiers took out a patent in the year 1790, for the same object may be worthy of attention. I have, on that occasion, mentioned the difficulties which have prevented any clear general demonstration of the absurdity of this pursuit from being produced, though it has not been difficult to show the fallacy of the individual plans. It does not, indeed, seem easy to enunciate the scheme itself. What in universal terms is the thing proposed to be done? Is it to cause a body to act in such a manner that the reaction shall be greater than the action itself, and by that means generate force by the accumulation of the surplus? Or, can the motion communicated be greater than that lost by the agent? Since these positions are evidently contrary to the physical axioms called the laws of nature, and frictions and resistances would speedily destroy all motions of simple uniformity, it may be presumed that 's Gravesande, who thought that all the demonstrations of the absurdity of schemes for perpetual motion contained paralogism, would have stated the proposition under different terms. But without entering upon this apparently unprofitable disquisition, it may be useful, as well as entertaining, to make a few observations on the mechanical contrivances which depend on a mistaken deduction from the general theorem respecting the balance, among which that of Dr. Schwiers must be classed.

There is no doubt but numerous arrangements have been made, and still are labored at by various individuals, to produce a machine which shall possess the power of moving itself perpetually, notwithstanding the inevitable loss by friction and resistance of the air. Little, however, of these abortive exertions has been entered upon record. The plans of Bishop Wilkins, the Marquis of Worcester, and M. Orffyreus, are all which at this time occur to my recollection.

There is no doubt but the celebrated Wilkins was a man of learning and ability. His essay towards a real character and a philosophical language is sufficient to render his name immortal. Twenty years before the appearance of that work he published his "Mathematical Magic," namely, in the year 1648, containing 295 pages, small octavo, which, from the number of copies still in being, I suppose to have been a very popular treatise. It is in this work that I find, among other contrivances for the same purpose, a wheel carrying sixteen loaded arms, similar to that delineated in Fig. 4, plate 15, in which, however, for the sake of simplicity, I have drawn but six. Each lever, A B C D E F, is movable through an angle of 45 degrees, by a joint near the circumference of the wheel, and the inner end or tail of each is confined by two studs or pins, so that it must either lie in the direction of a radius, or else in the required position of obliquity. If the wheel be now supposed to move in the direction E F, it is evident that the levers A B C D, by hanging in the oblique position against the antecedent pins, will describe a less circle in their ascent than when, on the other side, they come to descend in the positions E F. Hence, it was expected that the descending weights, having the advantage of a longer lever, would always predominate. Dr. Wilkins, by referring the weights to an horizontal diameter, has shown that in his machine they will not. A popular notion of this result may also be gathered from the figure, where there are three weights on the ascending and only two on the descending side; the obliquity of position giving an advantage in point of number, equal to what the other side may possess in intensity. Or, if this contrivance were to be strictly examined, on the supposition that the levers and weights were indefinitely numerous, the question would be determined by showing that the circular arcs A K, H I, are in equilibrio with the arcs A G, G L.

The simplest method of examining any scheme of this kind with weights, consists in inquiring whether the perpendicular ascents and descents would be performed with equal masses in equal times. If so, there will be no preponderance, and, consequently, no motion. This is clearly the case with the contrivance before us.

The Marquis of Worcester, who will ever be remembered as the inventor of the steam engine, has described a perpetual motion in the fifty-sixth number of his "Century of Inventions," published in the year 1655, and since reprinted in 1767 by the Foulis's at Glasgow. His words were as follows:

"To provide and make, that all the weights of the descending side of a wheel shall be perpetually further from the center than those of the mounting side, and yet equal in number and heft to the one side as the other. A most incredible thing if not seen, but tried before the late King (of blessed memory) in the Tower by my directions, two extraordinary ambassadors accompanying his Majesty, and the Duke of Richmond and Duke Hamilton, with most of the Court attending him. The wheel was fourteen feet over, and forty weights of fifty pounds apiece. Sir William Balfour, then Lieutenant of the Tower, can justify it with several others. They all saw that no sooner these great weights passed the diameter line of the lower side, but they hung a foot further from the center; nor no sooner passed the diameter line of the upper side, but they hung a foot nearer. Be pleased to judge the consequence."

Desaguliers, in his "Course of Experimental Philosophy," Vol. I, page 185, has quoted this passage, and given a sketch of a pretended self-moving wheel, similar to Fig. 5, plate 15, as resembling the contrivance mentioned by the Marquis of Worcester. The description of this last engineer agrees, however, somewhat better with the contrivance Fig. 4. It must, of course, be a mistake in terms, when he says the weight receded from the center at the lower diameter and approached towards it at the upper: the contrary being, in fact, necessary to afford any hope of success; and accordingly in the quotation it is so stated. I am, therefore, disposed to think that Fig. 5 represents the wheel of Orffyreus at Hesse Cassel, much talked of about the year 1720, and which probably was made to revolve, during the time of exhibition, by some concealed apparatus. It consists of a number of cells or partitions, distinguished by the letters of the alphabet, which are made between the interior and exterior surfaces of two concentric cylinders. The partitions being placed obliquely with respect to the radius, a cylindrical or spherical weight placed on each, it is seen from the figure, that these weights will lie against the inner surface of the larger cylinder whenever the outer end of the bottom partition of any cell is lowest; and, on the contrary, when that extremity is highest, the weight will rest on the surface of the interior cylinder. Let the wheel be made to revolve in the direction A B C; the weights in C D E F G H I being close to the external circle, and the weights K L M A B close to the inner, for the reasons last mentioned. As the cell B descends, its weight will likewise run out, at the same time that the weight in the cell I will run in in consequence of its partition being elevated. By the continuation of this process, since all the weights on the descending side pass down at a greater distance from the center, while those of the ascending side rise for a considerable part of their ascent at a less distance from the same point, it is concluded that the wheel will continue to maintain its motion. On this, however, it is to be remarked that the perpendicular ascent and descent are alike, both in measure and in time of performance; and that the familiar examination, even to those who know little of such subjects, is sufficient to show that the preponderance is not quite so palpable as at first it appears. For the weights G and F, H and E, I and D are evidently in equilibrio, because at the same horizontal distance from the center; and if the favorable supposition that the weight B has already run out be admitted, it will then remain a question whether these two exterior weights, B and C, can preponderate over the four inner weights, K L M A. The more accurate examination of this particular contrivance will lead to the following theorem: In two concentric circles, if tangents be drawn at the extreme points of a diameter of the smaller, and continued till they intersect the larger, the common center of gravity of the arc of the greater circle included between the tangents and of the half periphery of the smaller circle on the opposite side of the diameter, will be the common center of the circles. If, therefore, the balls were indefinitely numerous and small, the supposed effective parts of the wheel (Fig. 5) would be in equilibrio, as well as the parts beneath the horizontal tangent of the inner circle.

Fig. 6 represents the contrivance of Dr. Schwiers, which, in a periodical publication, in other particulars respectable, has been said to continue in motion for weeks and even months together. There is not the smallest probability that it should continue in motion for half a minute, or nearly as long as a simple wheel would retain part of its first impulse. The external circle denotes a wheel carrying a number of buckets, A B I L, etc. C represents a toothed wheel, on the same axis which drives a pinion D; and this last drives another pinion E upon the axis of a lanthorn, or wheel intended to work a chain-pump with the same number of buckets as in the larger wheel A B I. The lanthorn G is made of such a size as to receive the buckets a b i l with a due velocity. K represents a gutter through which a metallic ball, contained in the bucket m, may run and lodge itself in the bucket A of the wheel. Each of the buckets of the wheel, B I L M, which are below the gutter, is supplied with a metallic ball, and so likewise are the ascending buckets, a b i l m, of the chain-pump. As the pump supplies the wheel, it is again supplied at M, where the balls fall into its ascending buckets. Now, it is presumed that the balls in the wheel I suppose on account of their distance from the center of motion, will descend with more than sufficient force to raise those on the chain, and, consequently, that the motion will be perpetual.

The deception in this contrivance has much less seduction than in the two foregoing, because it is more easily referred to the simple lever. This, like the others, exhibits no prospect of success, when tried by the simple consideration of the quality of the ascent and descent in the whole time of the rotation of a single ball. It may also be shown from the principles of wheel-work, which are familiar to artisans, that whatever is gained by the excess of the diameter of the great wheel beyond that of the wheel C, is again lost by the excess of the lanthorn A beyond the pinion E.

The fundamental proposition of the simple lever or balance, that equal bodies at an equal distance from the fulcrum will equiponderate, but that at unequal distances the most remote will descend, has, in these and numberless other instances, led mechanical workmen and speculators to pursue this fruitless inquiry with labor and expense often ill-afforded, and with a degree of anxiety and infatuation which can hardly be conceived by those who have never suffered the pain of hope long deferred. For this reason chiefly, it has appeared desirable and useful to treat the subject in a familiar way without descending to those expressions of contempt, which ignorance, harmless to all but itself, is surely not entitled to. If such reasoners were well convinced that the power of a machine is to be estimated by the excess of motion referred to the perpendicular, without any regard to the apparent center of the machine, and that in machines very little compounded it is possible to produce effects directly contrary to the rule which is true of the simple lever, they would probably renounce many flattering projects, grounded only on the supposition of its universality. Desaguliers contrived an apparatus in which two equal weights may be placed at any distance whatever from the center of motion, and still continue in equilibrio. Fig. 3 represents this instrument. A D denotes a balance with equal arms, and E F another of the same dimensions. These move on the centers B and C, and are connected by the inflexible rods A E and D F; the motion being left free by means of joints at the corners. Across the rods A D, E F, are fixed two bars, I K, L M. Now, it is unnecessary to show that the weight G will describe exactly the same line or circular arc, when the levers are moved into the position a d f e, or any other position, as it would have described in case it had been suspended at A, or K, or E; and that it is of no consequence in this respect at what part of the line A E or I K it be fixed. The same observations are true of the weight H on the other side. And accordingly it is found that these equal weights may be suspended anywhere on the lines I K and L M without altering their equilibrium.

By this contrivance it is most evidently proved to those who are totally unacquainted with the theory, that weights do not preponderate in compound engines on account of their distance from the center. Several contrivances may be made to the same effect. The following combination of wheel-work presented itself to me as one which would most probably be mistaken for a perpetual motion. (Fig. 2, plate 15.) The five circles represent the same number of wheels of equal diameter and number of teeth, acting together. The middle wheel A is fixed between two upright pillars, so that it cannot revolve. The other four wheels are pinned in a frame H I, in which they can revolve, and through which the axis of A likewise passes. From the extremity of the axis of D, and also of d, proceed the horizontal levers H K and I L, which are equal, and point in the same direction parallel to the plane of the wheels. At the extremity of these arms hang the equal weights P and p. Let it now be imagined that the end I of the frame is depressed, the wheel B will turn round by the reaction of the fixed wheel A in the same direction as H I, and it will make one revolution in the same time relative to the frame, or two with regard to absolute space, by reason of its being carried round. The action of B upon D will produce a rotation relative to the frame in the opposite direction during the same time. Instead, therefore, of two revolutions like the wheel B, this wheel D, with regard to absolute space, will not revolve at all, and in every position of the apparatus the arm I L will continue horizontal, and point the same way. For similar reasons the arm H K will retain its position. Consequently, it is seen that the descending weight will move at a great horizontal distance from the center N, while the ascending weight rises very near that center. But there will, not on this account, be a perpetual motion: for the action of the levers H K and I L upon the frame H I, by means of the toothed wheels, will, in the detail, be found precisely alike, and in the general consideration of the motions of P and p, the opposite motions in the circle E F G will be accurately the same.

It has always been considered as essential to a perpetual motion that it should be derived from some energy which is not supposed to vary in its intensity. Such are the inertia, the gravity or magnetism of bodies. For an occasional or periodical variation of intensity in any force is evidently productive of motion, which requires only to be accumulated or applied, and the apparatus for applying it cannot be considered as a machine for perpetual motion. Neither in strictness can any machine whose motion is derived from the rotation of the earth, and the consequent change of seasons and rotation of events, be so considered, because it does not generate, but only communicates. The perpetual flow of rivers; the vicissitudes of the tides; the constant, periodical and variable winds; the expansions and contractions of air, mercury, or other fluids, by daily or other changes of temperature; the differences of expansions in metals, by the same change; the rise and fall of the mercury in the barometer; the hygrometric changes in the remains of organized beings, and every other mutation which continually happens around us, may be applied to give motion to mills, clocks, and other engines, which may be contrived to endure as long as the apparatus retains its figure.

Mr. Nicholson's article, published above, shows, if nothing else had ever shown, the fact that he was endowed with a real scientific mind. It also shows what is still most interesting—that his mind anticipated and that he had a subconscious conception of the principle of Conservation of Energy.

In 1824 and 1825 there was published in London a mechanical journal called "The Artisan"; or "Mechanic's Instructor." In one of the issues the following occurred on the subject of Perpetual Motion:

Perpetual motion is a motion which is supplied and renewed from itself without the intervention of any external cause: to find a perpetual motion, or to construct a machine which shall have such a motion, is a subject which has engaged the attention of mathematicians for more than 2,000 years; though none perhaps have prosecuted it with so much zeal and hopes of ultimate success as some of the speculative philosophers of the present age.

Infinite are the schemes, designs, plans, engines, wheels, etc., to which this longed-for perpetual motion has given birth; and it would not only be endless but ridiculous to attempt to give a detail of them all, especially as none of them deserve particular mention, since they have all equally proved abortive; and it would rather partake of the nature of an affront than a compliment, to distinguish the pretenders of this discovery, as the very attempting of the thing conveys a very unfavorable idea of the mental powers of the operator.

For among all the laws of matter and motion, we know of none which seems to afford any principle or foundation for such an effect. Action and reaction are allowed to be ever equal; and a body which gives any quantity of motion to another, always loses just so much of its own; but, under the present state of things, the resistance of the air, and the friction of the parts of machines, necessarily retard every motion.

To keep the motion going on, therefore, there must either be a supply from some foreign cause, which, in a perpetual motion, is excluded.

Or, all resistance from the friction of the parts of matter must be removed; which necessarily implies a change in the nature of things.

For by the second law of motion the changes made in the motions of bodies are always proportional to the impressed moving force, and are produced in the same direction with it; no motion, then, can be communicated to any engine, greater than that of the first force impressed.

But, on our earth, all motion is performed in a resisting fluid, namely, the atmosphere, and must, therefore, of necessity, be retarded; consequently, a considerable quantity of its motion will be spent on the medium. Nor is there any engine or machine wherein all friction can be avoided; there being in nature no such thing as exact smoothness or perfect congruity; the manner of the cohesion of the parts of bodies, the small proportion which the solid matter bears to the vacuities between them, and the nature of those constituent particles not admitting it.

Friction, therefore, will also, in time, sensibly diminish the impressed or communicated force; so that a perpetual motion can never follow, unless the communicated force be so much greater than the generating force as to supply the diminution occasioned by all these causes; but the generating force cannot communicate a greater degree of motion than it had itself. Therefore, the whole affair of finding a perpetual motion comes to this, viz., to make a weight heavier than itself, or an elastic force greater than itself; or, there must be some method of gaining a force equivalent to what is lost by the artful disposition and combination of the mechanical powers: to this last point then, all endeavors are to be directed; but how, or by what means such a force can be gained, is still a mystery!

The multiplication of powers or forces avails nothing; for what is gained in power is lost in time; so that the quantity of motion still remains the same.

The whole science of mechanics cannot really make a little power equal or superior to a larger; and wherever a less power is found in equilibrio with a greater—as, for example, twenty-five pounds with one hundred—it is a kind of deception of the sense; for the equilibrium is not strictly between one hundred pounds and twenty-five pounds moving (or disposed to move) four times as fast as the one hundred pounds.

A power of ten pounds moving with ten times the velocity of one hundred pounds would have equalled the one hundred in the same manner; and the same may be said of all the possible products equal to one hundred: but there must still be one hundred pounds of power on each side, whatever way they may be taken, whether in matter or in velocity.

This is an inviolable law of nature; by which nothing is left to art, but the choice of the several combinations that may produce the same effects.

The only interest that we can take in the projects which have been tried for procuring a perpetual motion must arise from the opportunity that they afford of observing the weakness of human reason.

For a better instance of this can scarcely be supplied than to see a man spending whole years in the pursuit of an object, which a single week's application to sober philosophy would have convinced him was unattainable.

But for the satisfaction of those who may not be convinced of the impossibility of attaining this grand object, we shall add a few observations on the subject of a still more practical nature than the above.

The most satisfactory confutation of the notion of the possibility of a perpetual motion is derived from the consideration of the properties of the center of gravity; it is only necessary to examine whether it will begin to descend or ascend when the machine moves, or whether it will remain at rest. If it be so placed that it must either remain at rest or ascend, it is clear, from the laws of equilibrium, that no motion derived from gravitation can take place; if it may descend, it must either continue to descend forever with a finite velocity, which is impossible, or it must first descend and then ascend with a vibratory motion, and then the case will be reducible to that of a pendulum, where it is obvious that no new motion is generated, and that the friction and resistance of the air must soon destroy the original motion.

One of the most common fallacies by which the superficial projectors of machines for obtaining a perpetual motion have been deluded, has arisen from imagining that any number of weights ascending by a certain path on one side of the center of motion, and descending on the other at a greater distance, must cause a constant preponderance on the side of the descent; and for this purpose weights have been made to slide or roll along grooves or planes, which lead them to a more remote part of the wheel, from whence they return as they ascend, as represented in the following figure: Or they have been fixed on hinges which allow them to fall over at a certain point so as to become more distant from the center; but it will appear on the inspection of such a machine that although some of the weights are more distant from the center than others, yet there is always a proportionally smaller number of them on that side on which they have the greater power; so that these circumstances precisely counterbalance each other.

We have heard it proposed to attach hollow arms to a wheel by joints or hinges at the circumference, and to fill these arms with quicksilver or small balls instead of the plan represented by the above figure; but though we have never heard of it having been tried, we are perfectly convinced that it would end as all other attempts have done; that is, in a total failure.