The lectures appear to have been illustrated by a plate having two figures of a simple apparatus used to demonstrate the action of a spring and two unequal weights; also an inflexible ruler suspended between two unequal balls—with both he experimented before his auditors; but the engraving is wanting in the edition now used. In conclusion, he observes:
You see, gentlemen, I am purposely provided here with a very simple and clumsy apparatus. The perpetual motion does not need the assistance of friction wheels, or depend on the niggling nicety of tooth and pinion. If the practical part of my discovery be not superior to the manual dexterity of a village carpenter or country smith, I am satisfied. There will be no great discernment required to comprehend the design they are to put in execution. You will permit me, however, at present, to defer what I have farther to offer on the subject to another opportunity.
In 1770 Dr. Kenrick published a quarto-pamphlet concerning the Orffyrean Wheel, and in the pamphlet appears the following regarding a letter from Prof. Gravesande to Sir Isaac Newton, and a letter from Baron Fischer to Dr. Desaguliers:
A Letter from Professor 's Gravesande to Sir Isaac Newton, Concerning Orffyreus's Wheel
Sir: Doctor Desaguliers has doubtless shown you the letter that Baron Fischer wrote to him some time ago about the wheel of Orffyreus; which the inventor affirms to be a perpetual motion. The landgrave, who is a lover of the sciences and fine arts, and neglects no opportunity to encourage the several discoveries and improvements that are presented him, was desirous of having this machine made known to the world, for the sake of public utility. To this end he engaged me to examine it; wishing that, if it should be found to answer the pretensions of the inventor, it might be made known to persons of greater abilities, who might deduce from it those services which are naturally to be expected from so singular an invention. You will not be displeased, I presume, with a circumstantial account of this examination; I transmit you, therefore, a detail of the most particular circumstances observable on an exterior view of a machine, concerning which the sentiments of most people are greatly divided, while almost all the mathematicians are against it. The majority maintain the impossibility of a perpetual motion, and hence it is that so little attention has been paid to Orffyreus and his invention.
For my part, however, though I confess my abilities inferior to those of many who have given their demonstrations of this impossibility; yet I will communicate to you the real sentiments with which I entered on the examination of this machine. It is now more than seven years since I conceived I discovered the paralogism of those demonstrations, in that, though true in themselves, they were not applicable to all possible machines; and have ever since remained perfectly persuaded it might be demonstrated that a perpetual motion involved no contradiction; it appearing to me that Leibnitz was wrong in laying down the impossibility of the perpetual motion as an axiom. Notwithstanding this persuasion, however, I was far from believing Orffyreus capable of making such a discovery, looking upon it as an invention not to be made (if ever) till after many other previous discoveries. But since I have examined the machine, it is impossible for me to express my surprise.
The inventor has a turn for mechanics, but is far from being a profound mathematician, and yet his machine has something in it prodigiously astonishing, even though it should be an imposition. The following is a description of the external parts of the machine, the inside of which the inventor will not permit to be seen, lest any one should rob him of his secret. It is a hollow wheel, or kind of drum, about fourteen inches thick and twelve feet diameter; being very light, as it consists of several crosspieces of wood framed together; the whole of which is covered over with canvas, to prevent the inside from being seen. Through the center of this wheel or drum runs an axis of about six inches diameter, terminated at both ends by iron axes of about three-quarters of an inch diameter upon which the machine turns. I have examined these axes and am firmly persuaded that nothing from without the wheel in the least contributes to its motion. When I turned it but gently, it always stood still as soon as I took away my hand; but when I gave it any tolerable degree of velocity, I was always obliged to stop it again by force; for when I let it go, it acquired in two or three turns its greatest velocity, after which it revolved for twenty-five or twenty-six times in a minute. This motion it preserved some time ago for two months, in an apartment of the castle: the door and windows of which were locked and sealed so that there was no possibility of fraud. At the expiration of that term indeed his serene highness ordered the apartment to be opened, and the machine to be stopped, lest, as it was only a model, the parts might suffer by so much agitation. The landgrave being himself present on my examination of this machine, I took the liberty to ask him, as he had seen the inside of it, whether after being in motion for a certain time no alteration was made in the component parts; or whether none of those parts might be suspected of concealing some fraud: on which his serene highness assured me to the contrary, and that the machine was very simple.
You see, sir, I have not had any absolute demonstration, that the principle of motion which is certainly within the wheel, is really a principle of perpetual motion; but at the same time it cannot be denied me that I have received very good reasons to think so, which is a strong presumption in favor of the inventor. The landgrave hath made Orffyreus a very handsome present, to be let into the secret of the machine, under an engagement nevertheless not to discover, or to make any use of it before the inventor may procure a sufficient reward for making his discovery public.
I am very sensible, sir, that it is in England only the arts and sciences are so generally cultivated as to afford any prospect of the inventor's acquiring a reward adequate to this discovery. He requires nothing more than the assurance of having it paid him in case his machine is found to be really a perpetual motion; and as he desires nothing more than this assurance till the construction of the machine be displayed and fairly examined before such assurance be given him. Now, sir, as it would conduce to public utility as well as to the advancement of science, to discover the reality or the fraud of this invention, I conceive the relation of the above circumstances could not fail of being acceptable. I am, etc.
In the same book appear the following animadversions by Prof. Allaman, on the neglect of Orffyreus's invention:
We see that the testimony of M. 's Gravesande was as advantageous as possible to Orffyreus, not having seen the interior of the machine, he could form no other judgment; however, that extraordinary man was not contented, for in consequence of the examination Orffyreus broke the machine into pieces. By the accounts of M. 's Gravesande, Baron Fischer and the testimony of the Landgrave it appears clear that the wheel was not moved by any exterior agent. Orffyreus is, however, accused of being an impostor, of having imposed on the good faith of the prince, deceived M. 's Gravesande and all those who examined his machine. His own servant deposed against him and said that she was made to turn the wheel, and thus he has fallen into contempt; and everyone who protected him, is ashamed of him. M. de Crousaz, who was at that time at the court of Cassel, writes a letter to M. 's Gravesande dated February 3, 1729, in these terms:—'First, Orffyreus is a fool; Second, It is impossible that a fool can have discovered what such a number of clever people have searched for without success; Third, I do not believe in impossibilities; Fourth, One can easily imagine that persons keep a secret from which they are to receive benefit, but this fellow, hoping only to receive reputation, allows it to be tarnished by an accusation which he has in his power to disprove, if false; Fifth, The servant who ran away from his house, for fear of being strangled, has in her possession, in writing, the terrible oath that Orffyreus made her swear; Sixth, He only had to have asked, in order to have had this girl imprisoned, until he had time to finish his machine; Seventh, They publish that the machine is going to be exhibited, when suddenly those who advertise it become silent; Eighth, It is true there is a machine at his house, to which they give the name of perpetual motion, but that cannot be removed; it is much smaller, and differs from the first, inasmuch as it only turns one way.
This is what makes Orffyreus and his machine to be suspected; can it be that M. 's Gravesande was so mistaken as to be his dupe? Let us read what he himself says in answer to M. Crousaz, which I have found among my papers, without date:—"I have deferred replying to you until I had found a paper which I wrote the day after I examined Orffyreus' machine, for although I remember well all that passed, I believe that a paper, written the day after the examination, and communicated to my Lord and all those who were with him, must have more weight.
"This is what I heard; they say that a servant under oath, turned Orffyreus' machine, being placed in an adjoining room.
"I know well that Orffyreus is a fool, but I ignore that he is an impostor; I have never decided whether his machine is an imposture or not, but this I know as certainly as anything in the world, that if the servant says the above, she tells a great falsehood.
"My Lord the Landgrave in the presence of the Baron Fischer, Architect of the Emperor, and other persons at my request, showed the supports of the machine; we saw the axles uncovered; I examined the plates or brasses on which the axles rested and in that examination there did not appear the slightest trace of communication with the adjoining room. I remember very distinctly the whole of the circumstances of that examination, which put Orffyreus in such a rage with me, that the day after he broke his machine in pieces, and wrote on the wall that, it was the impertinent curiosity of Professor 's Gravesande which was the cause. I read this myself the following year, and the result of the examination is clearly explained in the paper of which I spoke to you.
"They told me several circumstances on the testimony of the servant, but I pay little attention to what a servant can say about machines, perhaps in turning her master's roast-jack she thought she saw a perpetual motion. If you know anything concerning this matter I shall feel much pleasure if you would communicate it."
It is difficult to determine what to believe about this machine. It seems to me, however, that on examining minutely the for and against Orffyreus we can come to these conclusions: 1. That Orffyreus was evidently mad, as M. 's Gravesande and M. de Crousaz both affirm; his machinery broken at different times without either reason or necessity prove this. But his was a sort of madness we do not often see: a folly fixed only on certain objects, and merits more the name of fantasticalness or whimsicalness; this kind of folly is often accompanied by much genius, and when persons of this disposition apply themselves solely to one subject, as it appears he did, it is not surprising to find them making discoveries which had escaped the sagacity of wiser people. Thus I do not wish to agree with M. de Crousaz, that it is incredible that a madman, such as Orffyreus should have found out something that learned men have searched for unsuccessfully. Added to this he is mistaken in saying that Orffyreus could hope for no other reward for his secrets than mere reputation: for he expected a considerable profit seeing that he demanded for it 200,000 florins. 2. No exterior agent moved the machine; if it were a servant that moved it, would it not have been apparent to eyes so searching as those that made the examination, or to the Landgrave, who had seen the interior of the machine? Besides how can any one imagine that a wheel of so great a volume could have been moved by such a cause, a cause which would act simply on the axle in crossing the supports, and which must have been so small as to have escaped the most rigorous examination? 3. If the servant has not been paid to depose against Orffyreus, what does her testimony prove? Only that her master made her believe that by turning a little wheel, she moved the whole machine, and we can fancy a singular character, such as he was might have done this to prevent the curiosity of those who sought to penetrate his secret; M. 's Gravesande's opinion of this strange character is such that he doubts not his whimsicalness prevented him from making a new machine. 4. It must be confessed that this wheel was a very remarkable mechanical phenomenon, and this is all we can say, not knowing more than the preceding details; it were too much temerity to say that this invention was a perpetual motion, as much as it would be wrong to call it an imposture, seeing that no exterior agent was employed.
Dr. Kenrick proceeds to state that:—The celebrated John Bernoulli, speaking of the above demonstration, in a letter to the author, remarks that it is very just; the principle assumed necessarily involving an augmentation of force, viz., a perpetual motion. But this, continues he, is no more than Leibnitz had long before demonstrated in his dispute with Papin and others.
Having thus occupied twenty-three pages in fencing himself with a screen against the ridicule he appears to have so much dreaded, and reasonably anticipated from the many authors he had himself similarly treated in the "London Review," we are informed that,—An accidental conversation, many years ago, on the spot where Orffyreus exhibited his machine, awakened the author's curiosity and directed his attention to an object which he has ever since occasionally pursued. The experiments he has made, even so long since as the year 1761, convinced him so far of the reality of Orffyreus' discovery, that he applied for letters-patent to secure an exclusive right to the construction of a similar machine; which he had contrived and denominated A Rotator. Before his patent, however, was expedited, he reflected that, though the model he had constructed might serve to remove the prejudices of the public, it was not so well calculated as it might be, to answer the practical purposes of so important a discovery. To the improvement of the Rotator, therefore, has he long since dedicated all the time and attention he could possibly spare from his other, more immediately necessary, pursuits.
Nothing can be more flimsy than the statement here made, and the next sentence would seem to explain the true state of the case. He proceeds: "Not that he believes he has contrived quite so many different machines as Orffyreus did, though he has been almost as many years engaged in the like undertaking; he has, nevertheless, both contrived and constructed a considerable number, many of them useless as costly, except indeed as they served to assist him in completing his invention."
His invention, however, was not complete; the very model of it was unsatisfactory. Like Orffyreus, he had spent nearly twenty years, making numerous, and some costly, machines. He no doubt had his own misgivings, and wished to reimburse himself for the great outlay he must have incurred during that long period, before the bubble finally burst! However, poor man, he died nine years after publishing this elaborate advertising prospectus, which concludes: "Such bodies corporate, private companies or individuals, as are interested in the construction or use of considerable mechanical engines, or are disposed to encourage the present discovery, may receive any further information they require, on applying to the inventor, William Kenrick, Charles street, St. James's Square, March 1, 1770."
In 1803, Dr. Charles Hutton, LL.D., and F. R. S., contributed in a brief work entitled, "Recreations in Mathematics and Natural Philosophy," gave the following notice to the Orffyrean Wheel:
The perpetual motion has been the quicksand of mechanicians, as the quadrature of the circle, the trisection of an angle, etc., have been that of geometricians: and as those who pretend to have discovered the solution of the latter problems are in general persons scarcely acquainted with the principles of geometry, those who search for, or imagine they have found, the perpetual motion, are always men to whom the most certain and invariable truths of mechanics are unknown.
It may be demonstrated, indeed, to all those capable of reasoning in a sound manner on those sciences, that a perpetual motion is impossible: for, to be possible, it is necessary that the effect should become alternately the cause, and the cause the effect. It would be necessary, for example, that a weight raised to a certain height by another weight, should in its turn raise the second weight to the height from which it descended. But, according to the laws of motion, all that a descending weight could do, in the most perfect machine which the mind can conceive, is to raise another in the same time to a height reciprocally proportional to its mass. But it is impossible to construct a machine in which there shall be neither friction nor the resistance of some medium to be overcome; consequently at each alternation of ascent and descent, some quantity of motion, however small, will always be lost: each time, therefore, the weight to be raised will ascend to a less height; and the motion will gradually slacken, and at length cease entirely.
A moving principle has been sought for, but without success, in the magnet, in the gravity of the atmosphere, and in the elasticity of bodies. If a magnet be disposed in such a manner as to facilitate the ascension of a weight, it will afterwards oppose its descent. Springs, after being unbent, require to be bent by a new force equal to that which they exercise; and the gravity of the atmosphere, after forcing one side of the machine to the lowest point, must be itself raised again, like any other weight, in order to continue its action.
We shall, however, give an account of various attempts to obtain a perpetual motion, because they may serve to show how much some persons have suffered themselves to be deceived on this subject.
Fig. 52, plate 12, represents a large wheel, the circumference of which is furnished, at equal distances, with levers, each bearing at its extremity a weight, and movable on a hinge, so that in one direction they can rest upon the circumference, while on the opposite side, being carried away by the weight at the extremity, they are obliged to arrange themselves in the direction of the radius continued. This being supposed, it is evident that when the wheel turns in the direction a b c, the weights A B and C will recede from the centre; consequently, as they act with more force, they will carry the wheel towards that side; and as a new lever will be thrown out, in proportion as the wheel revolves, it thence follows, say they, that the wheel will continue to move in the same direction. But, notwithstanding the specious appearance of this reasoning, experience has proved that the machine will not go; and it may indeed be demonstrated that there is a certain position in which the centre of gravity of all these weights is in the vertical plane passing through the point of suspension, and that therefore it must stop.
The case is the same with the following machine, which it would appear ought to move also incessantly. In a cylindric drum, in perfect equilibrium on its axis, are formed channels as seen in Fig. 53, which contain balls of lead, or a certain quantity of quicksilver. In consequence of this disposition, the balls or quicksilver must, on the one side, ascend by approaching the centre; and on the other must roll towards the circumference. The machine then ought to turn incessantly towards that side.
A third machine of this kind is represented in Fig. 54. It consists of a kind of wheel formed of six or eight arms, proceeding from a centre, where the axis of motion is placed. Each of these arms is furnished with a receptacle in the form of a pair of bellows, but those on the opposite arms stand in contrary directions, as seen in the figure. The movable top of each receptacle has affixed to it a weight, which shuts it in one situation and opens it in the other. In the last place, the bellows of the opposite arms have a communication by means of a canal, and one of them is filled with quicksilver.
These things being supposed, it is visible, that the bellows on the one side must open, and those on the other must shut; consequently the mercury will pass from the latter into the former, while the contrary will be the case on the opposite side.
It might be difficult to point out the deficiency of this reasoning; but those acquainted with the true principles of mechanics will not hesitate to bet a hundred to one that the machine, when constructed, will not answer the intended purpose.
The description of a pretended perpetual motion, in which bellows, to be alternately filled with and emptied of quicksilver, were employed, may be seen in the "Journal des Savans" for 1685. It was refuted by Bernouilli and some others, and it gave rise to a long dispute. The best method which the inventor could have employed to defend his invention would have been to construct it, and show it in motion; but this was never done.
We shall here add another curious anecdote on this subject. One Orffyreus announced, at Leipsic, in the year 1717, a perpetual motion, consisting of a wheel which would continually revolve. This machine was constructed for the Landgrave of Hesse Cassel, who caused it to be shut up in a place of safety, and the door to be sealed with his own seal. At the end of forty days, the door was opened, and the machine was found in motion. This, however, affords no proof in favor of a perpetual motion; for as clocks can be made to go a year without being wound up, Orffyreus's wheel might easily go forty days, and even more.
The result of this pretended discovery is not known. We are informed that an Englishman offered 80,000 crowns for this machine; but Orffyreus refused to sell it at that price: in this he certainly acted wrong, as there is reason to think he obtained by his invention, neither money, nor even the honor of having discovered the perpetual motion.
The Academy of Painting at Paris possessed a clock which had no need of being wound up, and which might be considered as a perpetual motion, though it was not so. But this requires some explanation. The ingenious author of this clock employed the variations in the state of the atmosphere for winding up his moving weight. Various artifices might be devised for this purpose; but this is no more a perpetual motion than if the flux and reflux of the sea were employed to keep the machine continually going; for this principle of motion is exterior to the machine, and forms no part of it.
But enough has been said on this chimera of mechanics. We sincerely hope that none of our readers will ever lose themselves in the ridiculous and unfortunate labyrinth of such a research.
To conclude, it is false that any reward has been promised by the European Powers to the person who shall discover the perpetual motion; and the case is the same in regard to the quadrature of the circle. It is this idea, no doubt, that excites so many to attempt the solution of these problems; and it is proper they should be undeceived.
The foregoing, we believe, are sufficient to disclose the gist of all that is known, and all that has been said concerning the claimed inventions of the distinguished Marquis and the distinguished Councillor. It is manifest from reading the above that Dircks himself, as well as nearly all the other eminent persons quoted above, felt an extreme delicacy in stating their honest belief concerning the claims of the distinguished inventors. That delicacy arose from their deference to the rank and prominence of the Marquis and the Councillor. The author of this book is not thus encumbered, and has no such regard for family or official rank, and feels at liberty to say exactly what he thinks.