Chapter XII: Section 1: of this lecture is "On the Composition and Combination of

Motion." After discussing, in his own peculiar style, mechanical principles of motion, he adds:

It would require a volume, and that not a small one, to
illustrate these subjects and support them by the necessary
demonstrations and experiments. Should Providence give me life
and health, therefore, they (his auditors) shall have it. Indeed,
I have already spent some years in preparing such a volume for
the press.

He is very prolix on gravity and motion, then commences Section 2 "On the Communication and Dissipation of Motion." Five pages are occupied in discussing motion, in popular language, in the course of which he remarks:

And as to the imperfectly elastic bodies, their power of
retaining or communicating motion depends entirely on their
_vis inertiae_ and weight; nor can they on any occasion
whatever communicate a greater momentum to another body than
they themselves possess. It is sufficient for the purpose of a
perpetual motion that they can do this. And, indeed, here all the
difficulty lies, viz., in the means of communicating the momentum
or moving force of a heavy body to a light one. Now, the most
virulent opponents to the practicability of perpetual motion
have never pretended to demonstrate the impracticability of this
communication. The _quomodo_, or means of effecting it, being
the point in dispute. It is to this discovery that I pretend; and
to show that my pretensions are well grounded, have taken the
liberty to invite you to this lecture.

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.

No one now actually believes that either the Marquis or the Councillor ever made a wheel or machine that actually furnished its own motive-power. Those who believe in the impossibility of Perpetual Motion, of course, do not admit the possibility of such a thing. Those who may still believe in the possibility of Perpetual Motion devices admit, as they must, that had either of these discoveries actually been made it would have supplanted steam, electricity, wind, water and all other forms of power for driving machinery, and, indeed, for furnishing heat. And, yet, the above articles and comments show that the contemporaries of the Marquis and the Councillor, and subsequent writers on their claims sought to find excuses and explanations consistent with their good faith and their claims. We do not accuse either one of them of vicious falsehood, but the truth is that when the Marquis of Worcester wrote that "all the weights of the descending side of a wheel shall be perpetually farther from the centre than those of the mounting side, and yet equal in number and heft to the one side as the other. A most incredible thing, if not seen; but tried before the late King (of blessed memory) in the Tower by my directions," etc., he meant, if he meant anything, to convey the idea that he had constructed such a machine, and had exhibited it before King Charles I, and when Orffyreus wrote "The inward structure of the wheel is of a nature according to the laws of mechanical perpetual motion, so arranged that by disposed weights once in rotation they gain force from their own swinging and must continue their movement as long as their structure does not lose its position and arrangement," he meant, as clearly appears from the entire context of what he wrote, to convey the idea that he had constructed a wheel capable of moving perpetually by virtue of the arrangement of its own parts until it should wear out. Neither one spoke the truth. Each knew that he had done no such thing as he claimed to have done. He probably thought the solution so near at hand that he could safely announce it to the world, and when called upon for a demonstration could produce the finished working article.

The author of this book has known many Perpetual Motion workers so confident and so enthusiastic that unhampered with extreme discretion, they announced that they were near enough to the solution of this ages-old puzzle that they were certain of success. A little less discretion, with the slightest disregard or even carelessness about the absolute truth could have easily led them to announce that they had such a working machine. The author has indeed known a few such announcements. It is therefore, not surprising that in the history of Perpetual Motion labors, instances can be found where the tireless, but enthusiastic worker being full of confidence, and not secretive, and with the least bit of human carelessness about the truth have announced the actual discovery and successful operation of the machine. We will undertake to say that there have been thousands of just such instances during the last three or four centuries, probably tens of thousands. It is probable that such an instance could be found in every township in the United States. It is not, therefore, surprising that two instances can be found in persons of sufficient personal eminence to give credence and weight to their stories. Such we conceive the facts with reference to the Marquis and the Councillor. Each thought what he told when telling it to be a harmless stretch of the truth, and felt sure that he could protect himself by a very little added perfection to his device. How many many Perpetual Motion devices have been perfect and ready for successful operation except for "one little thing," which the inventor felt sure of finding.

The Marquis and Councillor by their little indiscretion, and their puerile carelessness about the truth, each made himself neither famous, nor infamous, but ridiculous in history.