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Source: September 1871 The Galaxy
THERE is probably not a single important city in the United States where some active brain is not busily poring, and some dexterous pair of hands industriously framing, in the pursuit of an absolute and perfectly demonstrable impossibility — Perpetual Motion.

The writer of this paper was a short time ago speaking of what he supposed to be the discontinuance of this sort of research in the United States, when an uncommonly intelligent lady in the company surprised him by asserting that on the contrary some body was working it a perpetual motion machine in every large town in the country. When questioned
as to her authority she effectually quieted any notion to doubt her by a statement which could not be disputed, startling as it was.

"I know it," she said, “of my own knowledge. My own father was working at the subject almost all his life. And I know perfectly well that he was all the time receiving letters about it from all over the United States, because I saw them; a great many of them from people who were in need of only fifty dollars — or two hundred and fifty dollars — more, in order to be sure and make the machine work."

Four years less than one hundred years ago, the Academie Royale des Sciences at Paris passed a resolution that they would no longer entertain communications about discoveries of perpetual motion. They included in the same prohibition the duplication of the cube, the trisection of the angle, and the quadrature of the circle." And they gave the reasons for this decision at some length; all, however, amounting to the observation of the fellow in the story—" That little thing can't be did."
For centuries before that time, however, perpetual motion had been perpetually moving in the inventive and scientific intellect of the period. It will be remembered that those were also the days of alchemy, and that the transmutation of metals, the philosopher's stone, and the elixir vitae were believed in and sought after by the really scientific men of those times. Nobody nowadays is prosecuting those mystic wild-goose chases, though Sir Humphry Davy—a man of thoroughly and preeminently modern, progressive, sensible, and well-balanced mind, if ever there was one—believed that it may ultimately be found that metals are transmutable.
It is not, however, always the ease that the foolishest phantoms disappear first. Witchcraft is at this day extensively believed in. Ten years ago an English mob murdered a helpless old woman for being a witch, just as that famous scoundrel Matthew Hopkins the Witchfinder - General and his assistant scamps might have clone two hundred years before; and dozens of " astrologers" are to-day swindling foolish servant girls and other silly persons in this very city of New York, by the aid of " respectable " editors who advertise and assist notorious cheats for money.
Perpetual motion is not dead either. It seems a curious fact enough, though the explanation is simple. Like the other insoluble problems which the French Academy associated with it, it is exactly suited to constitutional wonderers and to half-learned mechanicians. And as general information becomes more diffused throughout the community, the previous great number of persons totally ignorant is succeeded by a great number of persons half-learned, who will continue until the time when high average education shall provide against such delusions by instilling sound general principles into the popular mind.
Indeed — as follows, however, from what was just stated about the more rapid spread of mental activity than of sound principle to control it — more work has been wasted over perpetual motion during this century than during any other part of the seven centuries or thereabouts which include the whole known history of the subject. Patents have been granted for machines for the pur¬pose ever since the reign of Charles II; but a hundred and nine were taken out in France and England alone during the ten years ending with 1870.
A perpetual motion is a machine to be moved by a power furnished by the machine itself, and not from any source outside of it. A clock, or a mill, for instance, so adjusted as to move incessantly by the rise and fall of the tide, is not a perpetual motion; nor a machine that runs by the power of terrestrial or other magnetism, or of the wind, or of variations in the weight of the atmosphere, or by electricity coming from outside of the machine, or by the force of heat coming from the sun. It is said that Napoleon I. used to carry a watch which contained a lever so hung and balanced that the usual motion of his person in walking and riding caused it to play up and down, the short arm of the lever working a cog-wheel which kept winding up the watch. If we sup-pose the train so adjusted that two hours' walking would wind the watch enough to keep it going twenty-four hours, and if we further suppose that great and busy sovereign to be always in motion at least two hours a day, his watch would never stop until he died. If lie were ill, he could send a chamberlain out to trot the watch, like a nurse with a child. But that watch was not a perpetual motion, nor are the mills anchored on floats and worked by the current in the Rhine opposite Mayence, although they would continue turning until either the river or the wheel-work should give out.
But if, for instance, there were a wheel which would of itself always keep more weight at one side than at the other, that wheel would make itself turn forever, if the materials lasted. That would be a perpetual motion; and in-deed, such a wheel has been the form of the machines invented for the purpose much oftener than any other model. Such was the form of the earliest known machine for the purpose, that invented, or at least described, by Willard de Honecort, a Flemish architect who flourished somewhere from about A.D.1230 to 1260. A quarto sketch-book of his is still preserved in the Imperial Library at Paris, and has been a good deal edited and commentated by various learned men. An English translation, with additions and alterations, of a French hook on it, was published in London, with facsimiles of all the drawings, and very interesting they are.

Most of them are architectural—parts of churches, or details of window, door, pillar, and other ornaments; a number of rather knock-kneed saints, with the ghastly phiz and long, dried-up, splay feet which seem to have been signs of grace in those days; a lion, an architectural - looking image enough, drawn so as to resemble the Nineveh lions, but which Master Wilars certifies us was drawn from a live lion; and a porcupine (pore-epic, whence "porcupig" in the old ballad of "Moor of Moor Hall and the Dragon of Wantley") ; and so on. The perpetual motion which he represents is drawn as in the accompanying engraving, though in the original much larger, filling a good-sized quarto page; and, as on most of the sketches, there is a memorandum in old Flemish French, as follows: " Many a time have skillful workmen tried to contrive a wheel that shall turn of itself. Here is a way to make such a one, by an uneven number of mallets, or by quicksilver."

Leonardo da Vinci, the great Italian painter, engineer, architect, and musician (born 1452, died 1519), also speculated on the subject, and several designs of machines are in an autograph memorandum book of his now in the British Museum. They are all modifications of the wheel idea.
Orffyreus signatureOrffyreus signature
Another wheel, well known in the annals of Perpetual Motion, was that of Orffyreus. This gentleman's real name was Trans Ernst Elias Kessler, and the way in which he modified it to the big-sounding Latinized word is worth noting, as an instance of the sort of thing then considered scientific, and to show what sort of a mind he had. Herr Kessler, then, wrote an alphabet in two lines, thus :
a b c d e f g h i k l m
n o p q r s t u w x y z
(I and j were then the same, as were u and v.) Next, he took the successive letters opposite those of his real name. That is, B being the first letter of his name, he wrote instead' ‘O, which is opposite it in the other row; instead of e, he wrote next r; for ss, ff; for l, y; for e again, r; for r, e. This gave hint Orfyre, which he Latinized by sticking " us " on its tail, and so obtained his fine new name Orffyreus, the given names becoming Johannes Ernestus Elias. There is a kind of obscure classical reminiscence about Orffyreus, as if it were Orphie; and we know that things Orphie are very wonderful, whether they be of the Thracian or Trimontane kind, so that it is a sufficiently reverend appellation itself. As signed by its owner it becomes really not only Orphie, but awful, and looks as if it were a perpetual motion itself in full wiggle. It is this : J. E. E. Orffyres; for he seems to have omitted the u.
Orffyreus succeeded in convincing the Landgrave of Hesse-Cassel at least that his labors were worth attention ; for that prince accommodated him in castle of Weissenstein, where in the year 1717–'18 Orffyreus made a who said to have been shaped like a cheese, twelve feet across and two and a half feet thick. It was hung on an axle six feet long and eight inches thick, was supported in a solid oaken frame, and on each side of the wheel were two pendulums, said to regulate the movement. Orffyreus had made three other smaller wheels before, by the way : one at Gera, one at Draschwitz, and one Merseburg. The Weissenstein wheel, having been set a-going, is said to have been shut within its room by the Landgrave and left sealed up for eight weeks when, the door being opened, it was found still in motion, " which," says account, “satisfied him of the truth of perpetual motion." What it did prove — if it had been going eight weeks — was that it had been going eight weeks.
Any smart clockmaker could make a machine that would do as much, or times as much. Indeed, the sequel pretty much proved, so far as circumstantial evidence could do it, that the wheel was a clockwork humbug. Professor 'sGravesande, an eminent Dutch mathematician and physicist, inspected the Weissenstein wheel with keen, intelligent, scientific eyes. He was not permitted to see the inside, lest the secret should be discovered. He appears have discreetly held his tongue, and he wrote down his observations next day for record. They were to the effect that he did not know whether the machine was an imposture or not, as he had not examined the interior—which was nothing very wonderful by way of a conclusion, surely. He added further what was favorable to Orffyreus as far as it went, viz. : that there was not slightest trace of any communication with the adjoining room, where, it been charged, a servant girl was secretly employed to supply motive power a crank. However, Master Orffyreus was greatly discomposed and enraged by the cool inspection of 'sGravesande, which, writes the Professor "put Orffyreus in such a rage with me that the next day he broke his machine in pieces, and wrote on the wall that it was the impertinent curiosity of Professor 'sGravesande which was the cause." If my one circumstance could pro that the machine was a deception, this was it. Orffyreus died in November; 1745, after having lived seemingly in a sufficiently respectable way, as a mechanician and minor official. Whatever secret he had, died with him.
From the time of Wilars de Honecort — and indeed from before that time for he says expressly that many had tried the experiment before him — down the present day, seekers after the perpetual motion have been numerous, and many of them reckoned intelligent and respectable. For instance, among seventy four of those who were patentees of perpetual motions in England down to 1860, whose names are given in Mr. Dircks's book on the subject, were a prince, two counts, a knight of the Tower and Sword, a general, a groom of the privy chamber, a doctor of divinity, two doctors of medicine, a surgeon, ten engineers, three civil engineers, five machinists, etc. And among the receivers of eighty-six English and twenty-three French patents taken out for perpetual motions between 1860 and 1869, were a colonial bishop, a professor of philosophy, one of languages, two barons, a Knight Templar, a doctor of medicine, two civil engineers, several mechanical engineers, etc. Of eminent scientific and other persons who have believed in the possibility of a perpetual motion, may be named, besides Leonardo da Vinci and many more of his and earlier times, Arkwright, the celebrated English inventor (in his, younger days), Newton, 'sGravesande, Bernouilli, and other philosophers, who thought it might be possible. Even Sir David Brewster, so late as 1818, appears to have been deluded by the pretended invention of a Scotch cobbler; named Spence; for he wrote a letter to the French "Annales de Chimie" for 1818, pp. 219, 220, in which he says: " I am almost afraid to inform you that at this moment in Edinburgh may be seen a machine made by a shoemaker at Linlithgow, which realizes the perpetual motion. . . . Mr. Playfair and .Captain Kater have inspected both these machines, and are satisfied that they resolve the problem of perpetual motion." Even the Astronomer Royal of England, George Biddell Airy, in a paper to be found in the " Transactions of the Cambridge Philosophical Society," vol. 3, for 1830, p. 360, says that a perpetual motion is possible " under certain conditions. " To find these, however, he says it is necessary to solve the following equation:

Which, ingenuously admits the Astronomer Royal, “I am unable to solve rigorously." He adds, however, a number of other similar abracadabras, some big¬ger and some less than the above. But it would take a great many acres of x+y make a machine go; and if such a learned man as Professor Airy could not even "solve rigorously " the equation of his discovery, it is not probable he could execute the still harder task of making a perpetual motion according to it that would go.

The great majority of men of science as well as of men of sense, however, have been unbelievers in a perpetual motion, and scores of them have demon¬strated its absurdity, some with grave arguments and some with sarcastic comments. Among these may be mentioned Desaguliers, Maupertuis, Leibnitz, Descartes, Dr. Thomas Young, Arnott, Borelli, De La Hire, Maclaurin, Carnot, Bonnycastle, Arago, Dr. O. Gregory, Dr. Whewell, Professor De Morgan, and President Day of Yale College, who disproved the notion in a paper of some length, published in the " American Journal of Science and Arts " for November, 1850, p. 174.
As for De Morgan, always a pointed writer, he slashes at the subject as follows (in "Notes and Queries," 2d series, vol. 3, 1877, p. 273):
“The purse of Fortunatus, which could always drop a penny out, though never a penny was put in, is a problem of the same kind. He who can construct this purse may construct a perpetual motion, in this way: Let him hang the purse upside down, and with the stream of pence which will flow out let him buy a strong steam engine and pay for keeping it at work day and night. Have a new steam engine ready to be set in motion by the old one at its last gasp, and so on to all eternity.”
After mentioning a stock company for a perpetual motion, of which he himself had been made a director without his knowledge, but which the smashed when he found it out by a newspaper article, the Professor ends by disrespect-fully saying:
“Certainly had the scheme been proposed to me I should have declined to join until I had derived assurance from seeing the donkey who originated it turned into a head-over-heels perpetual motion by tying a heavy weight to his tail and an exhausted receiver to his nose. ,. (See Fig. 1 at head of this article.)”

A considerable number of so-called perpetual motion machines have been deliberate impositions, exhibited for pay, or perhaps for mere mischief, or to refute the pretensions of some impostor. Titus one Gartner, a contemporary of our friend Orffyreus, tormented that sage a good deal in print, and finally set to work and made a perpetual motion of his own for King Augustus of Saxony. It appeared to be a wheel on the plan already mentioned as the oldest and most common, with weights falling over to one side. This wheel stood on a pedestal, and ran not merely for eight weeks, like that of Orffyreus, but for some months, at the end of which time some well-made clockwork was found in pedestal.

A number of wheel machines were exhibited in different places in America and Great Britain from 1813 to 1825, of which Redheffer's is a sufficient specimen. It is of this that the anecdote of Robert Fulton is told. Fulton, as the story goes, went to see the so-called “perpetual motion," having a friend with him. After sitting and listening and looking intently for a few minutes, Fulton's sensitively accurate ear and eye told him that the movements of the machinery showed the recurring alternation of comparative speed and slowness, which always comes from a crank turned by hand. In spite of the opposition of the enraged exhibitor, Fulton and his friend seized the machine, jerked away the table it stood on, found that a cord led through one leg and away under floor, and following the track out into the back yard, there they found the "motion," which was old if not perpetual, being a venerable, white-bearded beggar seated on a stool, munching a crust, and grinding away at a crank.

Spence's, however, which, as has been mentioned, deceived Sir David Brewster, was not a wheel machine, but a magnetic one, arranged as in figure 3:

Here the pendulum E F, hung at G, has a piece of soft iron E at its top. A B is a “black substance” (being the gist of Spence’s invention), so arranged that the upright ends of it can alternately be interposed between E and each of the magnets C and D. The machine, Spence claimed, worked thus: On moving the pendulum bob to F, a light lever-train withdrew A from between E and C, and was so arranged as to trip and interfere again just as E came very near C. This interference shut off the magnetic attraction, while the simultaneous dropping of B let in that of D, and E of course flew back, until, B interposing, C could once more draw upon E, and so on without end. But in the first place, this is not a true perpetual motion, for the magnetic force is nothing inherent in the machinery, any more than the weight of the atmosphere is inherent in the materials of a barometer. In the second place, the “black substance” did not shut off the magnetism, as was shown by an Edinburgh scientific man, Mr. Deuchar, who tried it with magnets of his own, and proved that it did not interfere at all. And in the third place, it was shortly shown that the pendulum was moved by machinery hidden in the base of the stand. The same was the case with another form of the machine, where a horizontal magnetic needle was made to revolve on an upright pivot between two horse-shoe magnets.

The powers that have been relied upon to furnish perpetual motion, either singly or in combinations, have been; gravity, magnetism, electricity, capillary attraction, and the intermixture of fluids. The great majority has been gravitation machines of various kinds, and the weight has been varied in materials, and in mode of application, in numerous ingenious ways. Water, mercury, and sand have been used. The lever, balls rolling on an inclined plane, the wheel and axle, Barker's mill, the Archimedean screw, the pump, the syphon, the hydrostatic bellows, the hydraulic ram, the ascensive power of floats in water, mill-wheels, a double cone trundling on parallel bars, have been tried, Sometimes a wheel turned by water was to work a pump that was to carry the water up again above the wheel. Sometimes the wheel was to work an Archimedean screw instead of the pump. Or a wheel was to be turned by balls which were to roll off it at bottom, to trundle down an inclined plane and burst in through a valve at the foot of a tube of water, where they were to rise by specific levity and pop over at the top upon the wheel again. Sometimes a large wheel was to carry weights down, while a small one geared to it was to receive them and carry them up on an endless chain.

One ancient philosopher, ignorant of the "hydrostatic paradox," contrived a simple device represented in fig. 4, by which the greater weight of the water in the broad cup was s to drive it up through the hollow horn and empty it into itself again. Another, the Abbe de la Roque (see Journal des Scavans, 1686, page 99), in 1686, would vary this idea by forming the bowl of wax and the horn of iron. In the iron part, he reasoned, the liquid would he more condensed than in the wax part, and `therefore it would drop out of the former into the latter, and so continue. Still another of these ignoramus devices was that of a syphon, to be small where it drew in the water, and big on the further side, so as to pull the water over by this excess of weight; the endless discharge thus maintained to be used in turning a mill-wheel before it ran back to the small end of the syphon again.
There was a combination of gravity and capillary attraction, by means of a wheel or cylinder, over which several endless cloths, like what are called "roller towels," were to be hung, reaching down into water. The water was to creep up into one side by capillary attraction, and to be prevented by a tight band from doing so on the other, and the increase of weight on the wet side was expected to drag the cloths through this band. If this were only practicable, how evident it is that the wet cloths in the wash-tub could be made to run themselves through the patent wringer! Sir William Congreve, the inventor the Congreve rockets, substituted sponges for cloths, but with no better success.

An old fellow in New-York—Judge somebody or other—a few years ago had a device for a perpetual motion, which consisted of a strong box, into which water was to be pumped through a small bore as in the usual hydraulic presses. But there was this additional advantage, that a fan within the strong box as to he constantly kept partly relieved on one side from the pressure, so that would turn; and its axle, projecting through one side of the box, was to be geared to the pump-handle. The writer of the present paper can testify to the substantial correctness of this plan so far ; he heard further, but does not know, although he thinks it entirely probable, that the old fellow had obtained testimonials to the practicability of his device from a certain reputable Professor, and here is the " nub " of the whole — had, thus fortified, not pumped water with machine, but pumped a number of thousands of dollars out of the pocket a credulous old gentleman who expected to become worth tens of millions superseding steam and water power.
One very simple plan consisted of a see-saw trough to be kept going by a cannon-ball running backwards and forwards in it. Another almost as simple has an endless pipe, say a long oval, to stand erect; one side filled with water and the other with air. Balls heavier than air but lighter than water were to fall down the air side, pop through a valve (the water being so kind as to stay its own side), and so up through the water and over again.

Machines to work by the alternation of ascending and descending planes have been quite frequent. The most elaborate of these consisted —or was to consist— of two large cones, rolling base to base on the same axle. Between them, carried by the axle, not turning with it, was a cheese-shaped box, in lower half of which was room for freight and passengers; and the whole was to trundle on two rails, first down a slant and then up another, or first up one and then down another; for really the two arrangements are equally practicable.
An old form of machine was where a loadstone perched on a post was to draw an iron ball up an inclined plane, until when almost there it should fall through a hole into a trough which should carry it back to the foot of the plane. Perhaps as witless a scheme as any was one where a wheel was to be hauled round and round by permanent magnets set near it, acting on iron in the rim of the wheel; as if a magnet would draw a piece of iron at right angles to the line of attraction!

Some machines have been very elaborate, especially some from among the one hundred and seventy perpetual motion patents, or thereabouts, which have been taken out during the enlightened nineteenth century. Two citizens of Liverpool, James Smith and Sidney Arthur Chease, from 1838 to 1865 took out patents in England for four different enormous engines, to be run as perpetual motions by air and water. It is unnecessary to reproduce any of the drawings of these machines, which contain as many parts and as much work as an elaborate, steam engine. They spent, however, about $50,000 in their undertaking, and of course, almost succeeded. It seems altogether probable that this Mr. Chease is the same old green cheese that fools believe in as the material of the moon.

A single specimen of the more complicated style of wheel perpetual motions is enough to show how recent projectors have tried in vain to make Nature tell a lie by a circumlocution.
Mr. Adderley Sleigh's machine, as can be seen by inspection, is only another variation of the same idea as that of Wilars de Honecort, seven centuries old and more covered with more numerous details of mechanism. It was patented in 1865 by "Adderley Sleigh, Knight of the most noble and ancient Order of the Tower and Sword, and formerly of the English naval and military services." Two other gentlemen of the name of Sleigh, one also a retired army officer, and the other his father, a doctor of medicine, also patented devices for the same purpose within a few years of the same time; so that perpetual motion runs in the Sleigh family, if it does not run their machines.
Mr. Dircks, from whose two interesting though singularly ill-arranged volumes on the subject most of the information and cuts in this paper were obtained, ends his work with a vigorous blast against modern perpetual motionists, summing up thus:
"From the infant machines projected in the thirteenth century to the last hydraulic, pneumatic, weighted, and lever-worked pretensions patented as motions, no motion whatever has resulted from the one or the other to the present day. Not a solitary discovery is on record, not one absolutely ingenious scheme projected, or one simple self-motive model accomplished. Under such circumstances what shall we say of the modern mechanic who shall hereafter presume to add his dreary dreams to the lifeless lumber of the last seven centuries? No language can be too severe in denouncing the continuance of research in this insane undertaking; nor any criticism too sarcastic in exposing the foolish results pompously published by a class of blind, deaf, and doggedly stupid projectors," etc. This alliterative and angry allocution is doubtless dictated by cool kindness; yet the denunciatory Dircks should perhaps have popped less pepper into his peroration.
Various odd ideas, phrases, and occurrences are connected with the history of perpetual motion, as with that of every eccentric pursuit. Thus, a favorite co-delusion of English inventors was, that there was a standing offer of £10,000 to the discoverer of the P. Ms. A funny though natural part of the expecta¬tions of the P. Ns. has frequently been, that the machine once started would go on more and more rapidly (as indeed it would do if it would start in a power-brewing career at all), so as to require ample precautions for controlling stopping the motion. One man equipped himself with a table cloth, with which he proposed to smother his machine when its force began to be too "fast and furious." He found, however, that all he had to do with the table cloth was to fold it up and lay it away.

Mr. Dircks tells the following: " About fifty years ago a carpenter at Nether Stowey, Somersetshire, of about seventy years of age, hurl spent much time and the hard earnings of his life on a wheel machine twenty feet in diameter, the result of a dream, to be operated by counterweights, and which, along with mills for grinding corn, etc., he set up in a barn. Observing one day that a neighbor was about erecting a building in an adjoining field, he tendered his advice to him to go to work with some caution, at the same time apprising hint of the wonderful perpetual motion he was about starting to work in the barn, but which he had taken the precaution so to secure by means of a strong prop, which was to be struck away when all was ready, as well as brakes, that he trusted no serious accident would happen, which must ensue if it broke loose from its moorings. His neighbor, being thus interested, was in attendance to see its operations, undertaking at the same time to put on one of the brakes placed in his charge, so as to prevent as far as possible the disasters that a heavily-weighted runaway engine might too probably inflict. But props, ropes, and brakes were all rendered superfluous on the grand day of exhibition, for not a sound was heard nor was the slightest motion visible."

Many have been the like disappointments; though the majority of inventors have witnessed their disappointment, as they meant to see their triumph, alone. One of those who have been so confident as to summon witnesses got a cruel punch in the midst of his grief; for as the wonderful invention stood motionless before them, the unfeeling friend with an infamous caricature of sympathy said, “Well, it is a perpetual motion still!”

As extravagant a scheme as any of them all was probably that of "Predaval's Patent Motive Power Company," whose prospectus was issued in 1833, and which may have been that in which Professor De Morgan found himself a director. This prospectus proposed a capital of £1,500,000, that is, about seven and a half million dollars, on which there was to be an annual profit of ten million dollars, very handsome thing indeed. This profit was to accrue from the licenses issued for the use of the patent motive powers, in place of steam engines and such like obsolete trash; it being computed that there were twenty thousand steam engines in England, together of one million horse power, and that two pounds a year per horse power would readily be paid for the privilege of using the new substitute. No license was ever issued.
It remains to speak of the disproofs of a perpetual motion. These have been numerous and various. Some proceed by algebraic formulas, with x and y and other remote letters of the alphabet in them. Some argue from the comparative nature of cause and effect; others begin with the centre of gravity; others again explain that machines cannot generate power.
All these are valid methods. All that need be said in this place, however, will apply to rising and falling weights and the comparison of them, and will, it is believed, be found a clear statement of the case for all perpetual 'notions depending on gravitation. What has been sought in arranging it is to make the point clear, not to scientific men or trained mechanics, but to anybody of common sense and a fair common-school education?

To begin with, perpetual motion is only a perpetual notion. Practically the machines for it don't work; theoretically they can't.

The simplest form of the job undertaken by the perpetual motionists would be to place a weight on the ground and try to have it lift itself up. The same idea is sometimes imaginatively presented in the phrase "hoisting one's self up by the straps of one's boots." The weight will not lift itself up.
If now this single weight, instead of being left motionless, be either used as a pendulum or set rolling backward and forward on two inclined planes or curves (i.e., as it were, back and forth across a valley), or constantly forward over a series of ascents and descents, the distance from the performance of the task seems less, but it is really just as great; it is in either ease the vast breadth of impossibility. For instance, it will quickly appear, if we consider the case, that what is really required is that the pendulum-bob or the ball shall go up at the further side of its swing or curve higher than it went down on this side—which is, it may almost be said, a self-evident impossibility. Thus take the pendulum: suppose it weighs ten pounds, and swings downward swiftly enough to give it at the lowest point a total force (or momentum) of fifteen pounds, If it spends all this in going up on the further side, it will stop there and come back, so as to have fifteen pounds force again at the lowest point, and so on. But it does not. Part of the force is spent in overcoming atmospheric resist¬ance; not so much as if the pendulum swung in tar, because air is thinner fluid than tar, but still some, because air is a fluid, though a thin one. Another minute part of the force is spent in overcoming the tendency of the pivot ar-rangement to bring that which rests on it to rest; for even in the sharpest and hardest knife edge there is such a tendency. Therefore the pendulum will gradually come to rest if left to itself. If other work, such as moving a wheel, etc., is required of it besides, it will stop the sooner. The same reasoning applies to the rolling ball, except as to the point of suspension; but instead of this, the ball will be impeded in a like minute degree by the irregularities of its own surface and of the surface it rolls on. This and the resistance of the atmosphere will instantly begin to bring the ball to rest, and after a time will do so. And if work is required of the ball, it will stop the sooner. So that, as was said, perpetual motion requires, in the case of a pendulum or rolling ball, that it should go up with more force than it had in going down. Of course, if it could do this it could keep itself going, and spare a little power at every swing toward turning a wheel, or doing any other work. Indeed, it could spare a good deal just as well; for if it could have any more power at all in going up than it gathered in going down, it could have any quantity.
Now go a step further and consider the wheel question. First, a bar balanced on a transverse axle—such for instance as two opposite horizontal spokes of a wheel left alone in the hub—and with equal weights at the ends, will stay in whatever position it is turned to. If set whirling, it will instantly begin to go slower from the resistance of the air and the friction of the axle, and in time will stop. It cannot gain force, because it takes exactly the same quantity of power to carry one weight up as the other weight exerts in going down; and further than this, it also loses by the constant resistance of air and friction, as just stated. If these were removed, it would keep whirling; but if any work ' Were required of it, that would stop it in time, as the other resistance would.
This supposed balanced bar with two weights is really the whole story of the wheel perpetual motions, and indeed of all the gravity perpetual motions; it perfectly exemplifies the law under which they all stand still with such uni¬form obedience. For a place of the deadest and utterest stillness, indeed, a collection of perpetual motions would be the most motionless and the deadest of all. The law in question is this, as stated just above: To lift a weight any distance requires exactly the power (or momentum or force) accumulated by the same weight in dropping that same distance.
Thus in the case of the balanced bar with weighted ends, suppose the bar is three feet long and the weights are a force when moving of one hundred pounds each. Now the descending one must more than raise its ascending;. equal in order to keep up its speed and prevent stopping at last, since it must
First. Lift the other ball ;
Second. Overcome axle friction ;
Third. Overcome air friction.

If it does not do this, it must after a while stop. Even if it could do this, it could not do a particle of work without being sooner or later stopped. But if it could do the three tasks, and no matter how little more, then it could lay up an infinite store of force ready to use, as was said of the pendulum. Now to consider the modification of our balanced bar, which has been used in so very many different forms for an ever-turning wheel:
First. It is sufficient to consider two opposite spokes or radii, instead of a whole wheel; for the wheel is only made up of a certain number of such couples. If a wheel of a hundred spokes will turn in consequence of mechanism at the end of each couple of spokes, then exactly the same can be done with any single couple of opposite spokes. Indeed, so far as perpetual motion is concerned, one spoke without any opposite one is as good as a million. Let it hang straight down from its hub, as it would naturally do, with its weight at the end; it is just as likely to send itself round and round perpetually as if its opposite were added. It is only the pendulum in fact; and the pendulum is only a modification of the lump of stone lying on the floor.
But let us allow our perpetual motionist not merely the weight, not merely; the pendulum, not merely the balanced pair of spokes. Allow also the whole additional mechanism which, in one or another modification, contains the whole of the gravitation schemes for perpetual motion. This is the carrying of descending weight to a further distance from the axle of the wheel than its distance while it ascends.
This, it will be observed, amounts to a lengthening of one of the spokes or,
halves of the balanced bar, so as to outweigh the other half and lift it over to
the point where it may lengthen in its turn, while the first shortens, and so on.
This has been most commonly accomplished by a joint with a stop, permitting
the extensible part of the spoke or radius to fall out into the same line with the ,
inner part, but no further ; while of course it would permit the weight to hang
down during the ascent on the opposite side of the wheel. Sometimes the lengthening has been by an arrangement of levers or springs; or by "lazy tongs," i. e., crossed diagonals hinged to each other so as to be, extensible; or by one or more eccentrics, with a double wheel or sub-wheels, or combinations of levers or springs, or wheel gearing, or some of them together. The object, however, was always one and the same—to keep the descending weight further from the centre than the ascending counterweight.

Like the accompanying diagram (fig. 7) A is the centre of the perpetual motion wheel B F D H ; A B and A D are the two fixed spokes, jointed at B and D, so that when the position A B is m. reached, B C falls into the line of A B, but no further ; and so that when the spoke thus extended has passed the position A F G, the outer half may hang as at I) E and proceed through A H J, until it returns and falls out again at A B C.
During all the upper portion of the turning of the wheel, the line A J is the radius of the circle that the weight on the shortened spoke describes. Accordingly, the line K L, or M G, which is of the same length as K L, is the whole perpendicular height through which each weight must astend on one side and descend on the other.
Now the force acquired by any given weight C in falling through K L (or M G) is exactly equal to that expended in raising C, or its equal E, through L K (or G M).
Moreover, the fact that this weight moves sideways more or less in either direction, neither increases nor diminishes the result of its perpendicular movement; since the sideways motion does nothing either to prevent the weight form being pulled in a straight line toward the centre of the earth, or to add to this pull. It is absolute approach on the direct line toward the centre of the earth (viz., in this instance the distance K L), and nothing else, which shows the total momentum of the descending weight, and of course the total expenditure to carry up the ascending one. There are equal. Therefore, this jointspoked wheel will gradually stop just like a common wheel, in consequence of axle friction and air friction. Moreover, the place where it will come to rest can be accurately determined, and can be pretty nearly judged of. See diagram, fig. 8. It will be with the long arm A B C just half-way down toward A G, t which will bring the weight C just as far to the right of the perpendicular to G as the weight E will be to the left of it. Thus placed, the long arm and the short arm will become equivalent to equal arms. See fig. 8, in which the letters denote the same parts as in the last figure except Z. Here an imaginary balance is hung across m, and dotted lines which may indicate suspension cords suspend the two weights C and E.

The geometrical proof of this balance is easy; it is thus: Take a square, say fig. 9, A B C D, and quarter it by two diagonals. The square is thus bisected into two right-angled triangles, each of which is bisected into two others. The hypothenuse of either small triangle, say A B, is one of the shorter sides of the larger triangle A B D. Now in figure 8, it is evident on inspection, and by the construction of the wheel, that the triangle A D E equals A B Z, or B Z C, and that they are all right-angled triangles. Accordingly, A E, the hypothenuse of the triangle A D E, must equal A Z, a short side of the triangle A Z C, which is double of A D E, which was the thing to be shown. That is, if a perpetual motion wheel have two spokes jointed in the middle so that the outer half of each may fall out to a horizontal right line with the inner half while descending on one side of the wheel, and may hang while ascending on the other side, until the inner half of the spoke is horizontal, and shall thence lift at right angles to that inner half until it passes over and falls out to a horizontal again, and if such wheel be set going
First. It will not keep on going forever, but will stop, because whatever force is gained by the descent of a weight on one side has to be lost by carrying up the same weight through an equal ascent on the other; and the axle friction and air friction are therefore left unchecked to gradually stop the wheel.
Second. The wheel will stop at its natural place of balance, where one weight is just as far to one side of the centre of the wheel as the other to the other; and in the wheel here described that position will be with the descending arm 45 deg. below a horizontal line, and the ascending one as much above it.
Now, these principles apply to any number of couples of spokes.
And to a wheel with an odd number of spokes; for the total of all the weights will act all together exactly like one couple whose place and size can be mathematically determined.
And to any other proportion in the jointed parts of the spokes; for such other proportion would merely vary the details of the diagram already given.
And to any other plan of pushing the weight at the rim of a wheel further out on the descending than on the ascending side.
And, lastly, to any plan for making a weight (as of sand, mercury, balls, etc.) weigh more as it goes down than as it goes up.
In conclusion: It is useless, for many people, to take so many pains to prove that a thing cannot be heavier than itself. Most persons are satisfied of it already; and inveterate perpetual motionists become, there is no doubt, men-tally affected by their pursuit, so as to be unable to comprehend reasonings against it. But there are others working at it who are not too far gone to be cured. Besides, it is well to know how to specifically refute a delusion, even if you don't believe it; and it is believed that the demonstration above given is a clear and practical one, handy enough, for instance, to be used by any intelligent journeyman carpenter. And it is not the best way to answer a mistaken belief with jeers. It is kinder and more effective to show that there is a mistake, and what it is.
written by F.B.Perkins 1871