1911 Encyclopædia Britannica/Perpetual Motion
PERPETUAL MOTION, or Perpetuum Mobile, in its usual significance, not simply a machine which will go on moving for ever, but a machine which, once set in motion, will go on doing useful work without drawing on any external source of energy, or a machine which in every complete cycle of its operation will give forth more energy than it has absorbed. Briefly, a perpetual motion usually means a machine which will create energy.
The earlier seekers after the “perpetuum mobile” did not always appreciate the exact nature of their quest; for we find among their ideals a clock that would periodically rewind itself, and thus go without human interference as long as its machinery would last. The energy created by such a machine would simply be the work done in overcoming the friction of its parts, so that its projectors might be held merely to have been ignorant of the laws of friction and of the dynamic theory of heat. Most of the perpetual motionists, however, had more practical views, and explicitly declared the object of their inventions to be the doing of useful work, such as raising water, grinding corn, and so on. Like the exact quadrature of the circle, the transmutation of metals and other famous problems of antiquity, the perpetual motion has now become a venerable paradox. Still, like these others, it retains a great historical interest. Just as some of the most interesting branches of modern pure mathematics sprang from the problem of squaring the circle, as the researches of the alchemists developed into the science of modern chemistry, so, as the result of the vain search after the perpetual motion, there grew up the greatest of all the generalizations of physical science, the principle of the conservation of energy.
There was a time when the problem of the perpetual motion was one worthy of the attention of a philosopher. Before that analysis of the action of ordinary machines which led to the laws of dynamics, and the discussion of the dynamical interdependence of natural phenomena which accompanied the establishment of the dynamical theory of heat, there was nothing plainly unreasonable in the idea that work might be done by the mere concatenation of machinery. It had not then been proved that energy is untreatable and indestructible in the ordinary course of nature; even now that proof has only been given by induction from long observation of facts. There was a time when wise men believed that a spirit, whose maintenance would cost nothing, could by magic art be summoned from the deep to do his master's work; and it was just as reasonable to suppose that a structure of wood, brass and iron could be found to work under like conditions. The disproof is in both cases alike. No such spirit has ever existed, save in the imagination of his describer, and no such machine has ever been known to act, save in the fancy of its inventor.
The principle of the conservation of energy, which in one sense is simply denial of the possibility of a perpetual motion, rests on facts drawn from every branch of physical science; and, although its full establishment only dates from the middle of the 19th century, yet so numerous are the cases in which it has been tested, so various the deductions from it that have been proved to accord with experience, that it is now regarded as one of the best-established laws of nature. Consequently, on any one who calls it in question is thrown the burden of proving his case. If any machine were produced whose source of energy could not at once be traced, a man of science (complete freedom of investigation being supposed) would in the first place try to trace its power to some hidden source of a kind already known; or in the last resort he would seek for a source of energy of a new kind and give it a new name. Any assertion of creation of energy by means of a mere machine would have to be authenticated in many instances, and established by long investigation, before it could be received in modern science. The case is precisely as with the law of gravitation; if any apparent exception to this were observed in the case of some heavenly body, astronomers, instead of denying the law, would immediately seek to explain the occurrence by a wider application of it, say by including in their calculations the effect of some disturbing body hitherto neglected. If a man likes to indulge the notion that, after all, an exception to the law of the conservation of energy may be found, and, provided he submits his idea to the test of experiment at his own charges without annoying his neighbours, all that can be said is that he is engaged in an unpromising enterprise. The case is otherwise with the projector who comes forward with some machine which claims by the mere ingenuity of its contrivance to multiply the energy supplied to it from some of the ordinary sources of nature and sets to work to pester scientific men to examine his supposed discovery, or attempts therewith to induce the credulous to waste their money. This is by far the largest class of perpetual-motion-mongers nowadays. The interest of such cases is that attaching to the morbid anatomy of the human mind. Perhaps the most striking feature about them is the woful sameness of the symptoms of their madness. As a body perpetual-motion seekers are ambitious, lovers of the short path to wealth and fame, but wholly superficial. Their inventions are very rarely characterized even by mechanical ingenuity. Sometimes indeed the inventor has simply bewildered himself by the complexity of his device; but in most cases the machines of the perpetual motionist are of child-like simplicity, remarkable only for the extraordinary assertions of the inventor concerning them. Wealth of ideas there is none; simply assertions that such and such a machine solves the problem, although an identical contrivance has been shown to do no such thing by the brutal test of standing still in the hands of many previous inventors. Hosts of the seekers for the perpetual motion have attacked their insoluble problem with less than a schoolboy's share of the requisite knowledge; and their confidence as a rule is in proportion to their ignorance. Very often they get no further than a mere prospectus, on the strength of which they claim some imaginary reward, or offer their precious discovery for sale; sometimes they get the length of a model which wants only the last perfection (already in the inventor's brain) to solve the great problem; sometimes fraud is made to supply the motive power which their real or pretended efforts have failed to discover.
It was no doubt the barefaced fallacy of most of the plans for perpetual motion that led the majority of scientific men to conclude at a very early date that the “perpetuum mobile” was an impossibility. We find the Paris Academy of Sciences refusing, as early as 1775, to receive schemes for the perpetual motion, which they class with solutions of the duplication of the cube, the trisection of an angle and the quadrature of the circle. Stevinus and Leibnitz seem to have regarded its impossibility as axiomatic; and Newton at the beginning of his Principia states, so far as ordinary mechanics are concerned, a principle which virtually amounts to the same thing.
The famous proof of P. De la Hire simply refers to some of the more common gravitational perpetual motions. The truth is, as we have said already, that, if proof is to be given, or considered necessary, it must proceed by induction from all physical phenomena.
It would serve no useful purpose here to give an exhaustive historical account of the vagaries of mankind in pursuit of the “perpetuum mobile.” The reader may refer to Henry Dircks's Perpetuum Mobile (2 vols., 1861 and 1870), from which, for the most part, we select the following facts.
By far the most numerous class of perpetual motions is that which seeks to utilize the action of gravity upon rigid solids. We have not read of any actual proposal of the kind, but the most obvious thing to imagine in this way would be to procure some substance which intercepts gravitational attraction. If this could be had, then, by introducing a plate of it underneath a body while it was raised, we could elevate the body without doing work; then, removing the plate, we could allow the body to fall and do work; eccentrics or other imposing device being added to move the gravitation intercepter, behold a perpetual motion complete! The great difficulty is that no one has found the proper material for an intercepter.
Fig. 1 represents one of the most ancient and oftenest-repeated of gravitational perpetual motions The idea is that the balls rolling in the compartments between the felloe and the rim of the wheel will, on the whole, so comport themselves that the moment about the centre of those on the descending side exceeds the moment of those on the ascending side. Endless devices, such as curved spokes, levers with elbow-joints, eccentrics, &c, have been proposed, for effecting this impossibility. The student of dynamics at once convinces himself that no machinery can effect any such result; because if we give the wheel a complete turn, so that each ball returns to its original position, the whole work done by the ball will, at the most, equal that done on it. We know that if the laws of motion be true, in each step the kinetic energy given to the whole system of wheel and balls is equal to that taken from the potential energy of the balls less what is dissipated in the form of heat by frictional forces, or vice versa, if the wheel and balls be losing kinetic energy—save that the friction in both cases leads to dissipation. So that, whatever the system may lose, it can, after it is left to itself, never gain energy during its motion.
The two most famous perpetual motions of history, viz. the wheels of the marquis of Worcester (d. 1667) and of Councillor Orffyraeus, were probably of this type. The marquis of Worcester gives the following account of his machine in his Century of Inventions (art 56)—
“To provide and make that all the Weights of the descending side of a Wheel shall be perpetually further from the Centre than those of the mounting side, and yet equal in number and heft to 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 Embassadors accompanying His Majesty, and the Duke of Richmond, and Duke Hamilton, with most of the Court attending him. The Wheel was 14 Foot over, and 40 Weights of 50 pounds apiece. Sir William Balfore, 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 Centre, nor no sooner passed the Diameter-line of the upper side but they hung a foot nearer. Be pleased to Judge the consequence."
Orffyraeus (whose real name was Johann Ernst Elias Bessler) (1680–1745) also obtained distinguished patronage for his invention. His last wheel, for he appears to have constructed more than one, was 12 ft. in diameter and 1 ft. 2 in. broad; it consisted of a light framework of wood, covered in with oilcloth so that the interior was concealed, and was mounted on an axle which had no visible connexion with any external mover. It was examined and approved of by the landgrave of Hesse-Cassel, in whose castle at Weissenstein it is said to have gone for eight weeks in a sealed room. The most remarkable thing about this machine is that it evidently imposed upon the mathematician W. J. 'sGravesande, who wrote a letter to Newton giving an account of his examination of Orffyraeus's wheel undertaken at the request of the landgrave, wherein he professes himself dissatisfied with the proofs theretofore given of the impossibility of perpetual motion, and indicates his opinion that the invention of Orffyraeus is worthy of investigation. He himself, however, was not allowed to examine the interior of the wheel. The inventor seems to have destroyed it himself. One story is that he did so on account of difficulties with the landgrave's government as to a licence for it; another that he was annoyed at the examination by 'sGravesande, and wrote on the wall of the room contain in the fragments of his model that he had destroyed it because of the impertinent curiosity of 'sGravesande.
The overbalancing wheel perpetual motion seems to be as old as the 13th century. Dircks quotes an account of an invention by Wilars de Honecort, an architect whose sketchbook is still preserved in the Écoles des Chartes at Paris. De Honecort says, “Many a time have skilful workmen tried to contrive a wheel that shall turn of itself; here is a way to do it by means of an uneven number of mallets, or by quicksilver.” He thereupon gives a rude sketch of a wheel with mallets jointed to its circumference. It would appear from some of the manuscripts of Leonardo da Vinci that he had worked with similar notions.
Another scheme of the perpetual motionist is a water-wheel which shall feed its own mill-stream. This notion is probably as old as the first miller who experienced the difficulty of a dry season. One form is figured in the Mathematical Magic (1648) of Bishop Wilkins (1614–1672); the essential part of it is the water screw of Archimedes, which appears in many of the earlier machines of this class. Some of the later ones dispense with even the subtlety of the Water-screw, and boldly represent a water-wheel pumping the water upon its own buckets.
Perpetual motions founded on the hydro statical paradox are not uncommon; Denis Papin exposes one of these in the Philosophical Transactions for 1685. The most naive of these devices is that illustrated in fig. 2, the idea of which is that the larger quantity of water in the wider part of the vessel weighing more will overbalance the smaller quantity in the narrower part, so that the water will run over at C, and so on continually.
Capillary attraction has also been a favourite field for the vain quest; for, if by capillary action fluids can be made to disobey the law of never rising above their own level, what so easy as thus to produce a continual ascent and overflow, and thus perpetual motion? Various schemes of this kind, involving an endless band which should raise more water by its capillary action on one side than on the other, have been proposed. The most celebrated is that of Sir William Congreve (1772–1828). EFG (fig. 3) is an inclined plane over pulleys; at the top and bottom travels an endless band of sponge, abcd, and over this again an endless band of heavy weights jointed together. The whole stands over the surface of still water. The capillary action raises the water in ab, whereas the same thing cannot happen in the part ad, since the weights squeeze the water out. Hence, inch for inch, ab is heavier than ad; but we know that if ab were only just as heavy inch for inch as ad there would be equilibrium, if the heavy chain be also uniform; therefore the extra weight of ab will cause the chain to move round in the direction of the arrow, and this will go on continually.
The more recondite vehicles of energy, such as electricity and magnetism, are more seldom drawn upon by perpetual-motion inventors than might perhaps be expected. William Gilbert, in his treatise De Magnete, alludes to some of them, and Bishop Wilkins mentions among others a machine “wherein a loadstone is so disposed
that it shall draw unto it on a reclined plane a bullet of steel, which, still, as it ascends near to the load stone, may be contrived to fall through some hole in the plane and so to return unto the place whence at first it began to move, and being there, the loadstone will again attract it upwards, till, coming to this hole, it will fall down again, and so the motion shall be perpetual.” The fact that screens do exist whereby electrical and magnetic action can be cut off would seem to open a door for the perpetual-motion seeker. Unfortunately the bringing up and removing of these screens involves in all cases just that gain or loss of work which is demanded by the law of the conservation of energy. A shoemaker of Linlithgow called Spence pretended that he had found a black substance which intercepted magnetic attraction and repulsion, and he produced two machines which were moved, as he asserted, by the agency of permanent magnets, thanks to the black substance. The fraud was speedily exposed, but it is worthy of remark that Sir David Brewster thought the thing worth mentioning in a letter to the Annales de chimie (1818), wherein he states “that Mr Playfair and Captain Kater have inspected both of these machines and are satisfied that they resolve the problem of perpetual motion.”
The present writer once was sent an elaborate drawing of a locomotive engine which was to be worked by the agency of permanent magnets. He forgets the details, but it was not so simple as the plan represented in fig. 4, where M and N are permanent magnets, whose attraction is “screened” by the wooden blocks A and B from the upper left and lower right quadrants of the soft iron wheel W, which consequently is attracted round in the same direction by both M and N, and thus goes on for ever.
One more page from this chapter of the book of human folly; the author is the famous Jean Bernoulli the elder. We translate his Latin, as far as possible, into modern phraseology. In the first place we must premise the following (see fig. 5). (1) If there be two fluids of different densities whose densities are in the ratio of G to L, the height of equiponderating cylinders on equal bases will be in the inverse ratio of L to G. (2) Accordingly, if the height AC of one fluid, contained in the vase AD, be in this ratio to the height EF of the other liquid, which is in a tube open at both ends, the liquids so placed will remain at rest. (3) Wherefore, if AC be to EF in a greater ratio than L to G, the liquid in the tube will ascend; or if the tube be not sufficiently long the liquid will overflow at the orifice E (this follows from hydrostatic principles). (4) it is possible to have two liquids of different density that will mix. (5) It is possible to have a filter, colander, or other separator, by means of which the lighter liquid mixed with the heavier may be separated again therefrom.
Construction.—These things being presupposed (says Bernoulli), I thus construct a perpetual motion. Let there be taken in any (if you please, in equal) quantities two liquids of different densities mixed together (which may be had by hyp. 4), and let the ratio of their densities be first determined, and be the heavier to the lighter as G to L, then with the mixture let the vase AD be filled up A. This done let the tube EF, open at both ends, be taken of such a length that AC : EF > 2L : G + L; let the lower orifice F of this tube be stopped, or rather covered with the filter or other material separating the lighter liquid from the heavier (which may also be had by hyp. 5); now let the tube thus prepared be immersed to the bottom of the vessel CD; I say that the liquid will continually ascend through the orifice F of the tube and overflow by the orifice E upon the liquid below.
Demonstration.—Because the orifice F of the tube is covered by the filter (by constr.) which separates the lighter liquid from the heavier, it follows that, if the tube be immersed to the bottom of the vessel, the lighter liquid alone which is mixed with the heavier ought to rise through the filter into the tube, and that, too, higher than the surface of the surrounding liquid (by hyp. 2), so that AC.EF = 2L : G+L; but since by constr. AC : EF > 2L ⋅ G+L it necessarily follows (by hyp. 3) that the lighter liquid will flow over by the orifice E into the vessel below, and there will meet the heavier and be again mixed with it; and it will then penetrate the filter, again ascend the tube, and be a second time driven through the upper orifice. Thus, therefore, will the flow be continued for ever.—Q E D.
Bernoulli then proceeds to apply this theory to explain the perpetual rise of water to the mountains, and its flow in rivers to the sea, which others had falsely attributed to capillary action—his idea being that it was an effect of the different densities of salt and fresh water.
One really is at a loss with Bernoulli's wonderful theory, whether to admire most the conscientious statement of the hypothesis, the prim logic of the demonstration, so carefully cut according to the pattern of the ancients, or the weighty superstructure built on so frail a foundation. Most of our perpetual motions were clearly the result of too little learning; surely this one was the product of too much.
- We may here notice, so far as more recent times are concerned, the claim of an American enthusiast, who, having worked a Hampson plant for liquefying air, stated that 3 lb of liquid air sufficed to liquefy ten, and of these ten seven could be employed as a source of motive power, whilst the remaining three could be utilized in the production of another 10 lb of the liquid gas. There was thus available an inexhaustible supply of energy! The absurdity of the proposition is obvious to any one acquainted with the laws of thermodynamics. Of more interest is the radium clock devised by the Hon R J Strutt. This consists of a vacuum vessel from the top of which depends a short tube containing a fragment of a radioactive substance. At the lower end of this tube there are two gold leaves as in an electroscope. Fused into the sides of the vacuum vessel at points where the extended gold leaves touch the glass are two platinum wires, the outer ends of which are earthed. The “clock” acts as follows. The radio-active substance emits a preponderating number of positively electrified particles, so that the leaves become charged and hence extended. On contact with the wires fused into the vessel, this charge is conducted away and the leaves fall together. The process is then repeated, and will continue until all the energy of the radium has been dissipated. This period is extremely long, for 1000 years must elapse before even half the radium has disappeared—[Ed]