The Wheel of Orffyreus 2

The second and last part of a chapter from this fascinating forgotten work Oddities: A Book of Unexplained Facts (Allan, London 1928) by R.T. Gould. Gould was a polymath who appears to have tolerated fools and cranks gladly...however Johann Bessler was no fool (although he may have been insane) and no less a figure than the philosopher Leibniz and  and the scientist and Newtonian Willem Jacob 's Gravesande thought he had the secret of perpetual motion. Gould gets to the heart of the matter -as always with footnotes blazing...

Was Orffyreus honestly deceived when he wrote down such an incorrect description (for so we must regard it)† of his own mechanism? The thing is unlikely–but it is possible, as a later case has sufficiently shown.

 † The supposition that the wheel was kept going by external power does not, of course, exclude the possibility that it also contained "overbalancing" mechanism. If well made, this would waste very little power, though it could not generate any: and it would certainly impress an amateur mechanic like the Landgrave–the only man who ever saw it.

 Towards the end of the last War, public attention in the United States became focused, for a short time, upon an inventor bearing the perfectly incredible name of Giragossian. He appears to have been an honest but misguided man.
He had evolved a project for obtaining what he called "free power", and which proved, in reality, to be a "perpetual motion" fallacy of an interesting kind. It attracted more attention than most, partly because of its novelty and partly because its inventor considered it to be of such far-reaching importance that it could scarcely be secured from piracy by an ordinary patent. An attempt was therefore made to attain this end by means of a special Act of Congress.

 It may be noted that the U.S. Patent Office does not follow the precedent set by the French Académie des Sciences in 1775 when that body passed its celebrated resolution declaring, inter alia, that it would not consider, in future, "any machine announced as showing perpetual motion". But it sometimes has recourse to its legal right of requiring the patentee of such a machine to deposit a working model of his invention. Its Museum, I believe, has not yet acquired a model of this kind.

 A committee appointed to examine the Giragossian machine had little difficulty in classifying it. Broadly speaking, its operation was as follows:

 A very large and heavy flywheel was set in motion, and gradually accelerated, by means of a very small electric motor of (say) one-quarter horse-power. The process of "speeding-up" the flywheel may have taken a fortnight. The motor was then disconnected, and the flywheel brought to rest by the application of a brake. A horse-power test made during the stopping process indicated that the flywheel was then developing several hundred horse-power. It was pointed out that the original source of this power was a one-quarter horse-power motor; and it was claimed that, since the accepted horse-power formula takes account of time, there could be no doubt that "free power" had been generated to the amount of the difference between the horse-power required to spin the wheel and that needed to stop it.

 A simple analogy will prove the fallacy of this reasoning. If the electric motor had been made to pump water into a reservoir for the same length of time, and the whole contents of the reservoir then run through a suitable turbine in the time taken to stop the flywheel, the horse-power developed by the turbine would probably have been much the same as that exerted at the brake around the flywheel. The parallel would have been complete; and the fact would have become obvious that, neglecting the inevitable losses by friction, etc., the power stored by the motor was equal to that given out by the turbine, the only difference being that the power was given out much faster than it had been stored. In the same way a man earning two hundred a year might, say, save half of this for two years and then dissolve the proceeds in the course of a very pleasant week in Paris, or even nearer home. During that hectic period he would certainly be spending at the rate of something over ten thousand a year; but if he had any lucid intervals he would surely not delude himself into thinking that he had permanently raised his salary to that figure.

 All that Mr. Giragossian had really done was to evolve a form of leverage depending on time instead of space. Yet I have no doubt that he believed (and, for all I know, still believes) that his machine was capable of creating power.

In view of this case, it is not to be denied that Orffyreus may have been misled as to the action of his machine. It worked–so, in its way, did Giragossian's. Its results may have been equally fallacious. But the puzzle of its actual mechanism remains unsolved.

In one minor point Orffyreus certainly showed great ingenuity. That is, the arrangement of pendulums by which he controlled his machine.

Incidentally, nearly all of the writers who have attempted to describe his wheel have omitted all mention of these pendulums–although the latter explain several obscure points in connection with the whole story.

Judging by the engraving in his book (Plate III) they were connected by links to two opposed cranks on the axle of the wheel, their effects being thus balanced, so that they did not, in any position, oppose the rotation of the wheel, even when it was being started from rest. They appear to have been about 11 feet long, and would therefore have had a period, if they were simple pendulums, of some 1.8 seconds, corresponding to a wheelspeed of roughly thirty-three revolutions per minute. But, as shown, they were not simple pendulums by any means, since they had three "bobs", two being at their upper ends. In consequence, their period would have been lengthened, and might easily have coincided with a wheel-speed of twenty-six turns a minute, which was that observed by's Gravesande and Fischer. It would have been difficult to use an escapement to control the wheel, and these pendulums probably formed a very efficient substitute–although a fan, one thinks, would probably have been better.

It will be noticed that I'am assuming that the wheel possessed inherent power of rotation sufficient to require some form of control. I regard this as strongly suggested by the evidence–although I can offer no indication of its real source.

It is certain that power cannot be generated by any form of "overbalancing wheel". It is almost certain that it cannot be generated by any mechanical means whatsoever. I qualify this second statement, because of what was once written on the point by a man well equipped to judge.

Sir George Airy was one of the most outstanding scientific figures of the past century. He was, to begin with, a Senior Wrangler and Smith's Prizeman–and, contrary to the prevailing impression, these distinctions did not handicap him in after-life. He was subsequently Director of the Cambridge Observatory for eight years, and Astronomer Royal for forty-six. He was a first-class mathematician and a clear-headed thinker, with a pronounced bent for original investigation.

In 1830 he published, in the Cambridge Philosophical Transactions, a paper with the somewhat surprising title "On Certain Conditions under which a Perpetual Motion is Possible". It is very short–and, by omitting most of the mathematics, can be condensed still further. It opens as follows:

"It is well known that Perpetual Motion is not possible with any laws of force with which we are acquainted. The impossibility depends on the integrability per se of the expression Xdx +Ydy +Zdz: and as in all the forces of which we have an accurate knowledge this expression is a complete differential, it follows that perpetual motion is incompatible with these forces."

(I may point out that the second sentence above is a statement, in mathematical language, of the fact that the. hypothesis of the Conservation of Energy holds for any three-dimensional field of force–i.e, for our space as we know it.)

"But it is here supposed that, the law of the force being given, the magnitude of the force acting at any instant depends on the position, at that instant, of the body on which it acts. If, however, the magnitude of the force should depend not on the position of the body at the instant of the force's action, but on its position at some time preceding that action, the theorem that we have stated would no longer be true. It might happen that, every time that the body returned to the same position, its velocity would be less than at the preceding time: in this case the body's motion would ultimately be destroyed. On the contrary it might happen that the body's velocity in any position would be more rapid every time than at the time previous. In this case the velocity would go on perpetually increasing: or the velocity might be made uniform if the machine were retarded by some constantly acting resistance: or in other words, the machine might move with uniform velocity, and might at the same time do work, which is commonly understood to be the meaning of the term perpetual motion. If the machine had no work to do, the increasing friction, etc., would operate as an increasing work, and the velocity would be accelerated till the acceleration caused by the forces was equal to the retardation caused by the friction; after which it would remain unaltered.

"For this idea I am indebted to the admirable account of the organs of voice given by Mr. Willis. The phenomenon to be explained was this.

"When two plates are inclined at an angle greater than a certain angle, it is found that the effect of a current of air passing between them is to give a tendency to open wider. When they are inclined at any angle smaller than that certain angle, the effect of the current is to make them collapse. If, then, the plates be supposed to vibrate through the position corresponding to that angle, the tendency of the forces is at all times to bring them to that position. Each plate is in the state of a vibrating pendulum: and whatever be the law of force which acts upon it, it is certain that if the force be the same when the plate is in the same position, this force will have no tendency to increase the velocity. The retardation arising from friction, etc., will, therefore, soon destroy the motion.

"But it is found, in fact, that the motion is not destroyed. What, then, is the accelerating force which keeps up the motion?

"Mr. Willis explains this by supposing that time is necessary for the air to assume the state and exert the force corresponding to any position of the plate: which is nearly the same as saying that the force depends on the position of the plate at some previous time. In this paper, which is intended to investigate the mathematical consequences of an assumed law, I shall not discuss the identity of these suppositions: I shall only remark that the general explanation appears to be correct, and that it clears up several points which have always appeared to be in great obscurity."

And this he proceeds to do, mathematically, with a profusion of symbols a little alarming to the casual reader. He concludes by modestly remarking:

"My object is gained if I have called the attention of the Society to a law hitherto (I believe) unnoticed, but not unfruitful in practical applications." 

Like many another paper read before a "learned Society", this of Airy's was printed–and forgotten. For his own sake for the sake of his peace of mind and reputation–this was probably as well. If it had become widely known, it would at once have been seized upon by the perpetual-motion cranks–who, as is their cheerful custom, would probably have paraded the authority while deriding the author. I can find no record of Airy having altered his views on the subject; but he did not recur to it in any of his later writings.

There are one or two phrases in his paper curiously reminiscent of those used by Orffyreus . . . and I return to that singular man. Was he charlatan, or monomaniac–or both? Did he deliberately carry out, through many years, a campaign of imposture which gained him no money, no repose, no reputation–nothing but enmity and obloquy? He may have done so. There are some perverted minds that will endure much to gain even an evil reputation. Many an old crone in a country village has found solace for her declining years in hugging the thought that her neighbours, while openly deriding her, secretly dread her powers of witchcraft–many such have deliberately encouraged this impression. Orffyreus may have done the same.

Or was he only a harmless crank, pursuing a mechanical ignis fatuus with an intensity which produced, or was itself produced by, monomania? Did he fall at odds with the world because he thought its concerns trivial by comparison with his own–a feeling heartily reciprocated? If his labours were systematic and prolonged–if he consecrated his life to the attainment of a single object–did he, really, win some reward? And was that reward the secret of a genuine discovery which perished with him, or only that of a most marvellous deception? Did he deceive others, or only himself–or neither?

Still offering an unsolved problem, he passes from our sight, an exasperating and yet pathetic figure–morose, self-centred, childishly passionate, vacillating and yet tenacious, his own worst enemy, forgetting the duties of ordinary human intercourse in his passion for mechanism and wrecking his life as the result. Non deficit alter.