Henry Dircks

The antiquity of the problem of Perpetual Motion, and the countless attempts by clever and ingenious minds to accomplish its solution, and the uniform failure of such attempts is no proof at all, scientifically speaking, that Perpetual Motion is an impossibility. If there be scientific proof that Perpetual Motion is unattainable, that proof must be found elsewhere than in the number of attempts and the universality of failures, or in the number or eminence of the people who believe it to be impossible.

Dircks in his work printed in 1861, being "A History of the Search for Self-Motive Power, During the 17th 18th and 19th Centuries," says on the subject:

"The subject of Perpetual Motion opposes paradox to paradox. It is viewed both as being most simple and most difficult to find. The learned justify both its possibility and impossibility. Many mechanics believe it possible * * * Its pursuit always commences in confidence, only to end in doubt. * * *

We think a careful perusal of all that has been gathered respecting Perpetual Motion clearly establishes that much remains to be done to prove the impossibility of practically solving this knotty problem; and that a full demonstration of the difficulties that environ it is worthy of being attempted, even by the most exalted mathematicians. It is not requisite that they should descend to the level of the most ordinary minds, but leave it for others to reduce their elaborated reasonings on the subject to some generally comprehensible form. We fear the proposal partakes too much of the difficulty of proving a negative; but still, as the attempt has been made by celebrated savants, and is generally considered insufficient; and as data may have been wanting, which we conceive a collection of the chief known examples will supply; we recommend the consideration of this matter to all geometers. * * *

In a mathematical point of view, we think this subject is far from being exhausted; and, after what has been advanced, may very properly be considered as claiming grave considerations. And that, scientifically examined, it is a mark of mere shallowness and querulousness to attempt the substitution of ridicule and satire for the more difficult, but consistent course of sound, close reason and argument, such as the wonted sobriety and severity of scientific criticism accords to its investigations generally."

At the time of the publication of Dircks's work from which the above quotation is taken (1861), the doctrine of Conservation of Energy had not been announced and accepted as an established generalization of a scientific fact, and it is apparent was not understood by him. Dircks's statement "as data may have been wanting, which we conceive a collection of the chief known examples will supply," shows that he misconceived the nature of the problem of proving the impossibility of Perpetual Motion. If, however, the principle of Conservation of Energy is a true scientific fact, the impossibility of self-motive power follows as an inevitable scientific corollary, and the ignis fatuus hope of attaining Perpetual Motion which has deluded so many bright minds is forever destroyed and demolished.

A perusal of the arguments against Perpetual Motion made by thinking men with scientific minds even though long before the thorough establishment of the doctrine of transmutation and Conservation of Energy, discloses the fact that those arguments in fact depend finally on the principle now known and designated Conservation of Energy.

It is amusing to note in reading the arguments on the subject by our greatest philosophers, Newton, Gallileo, Huyghens, and Descartes, that while they lived and labored long before Conservation of Energy in its generalized form was known, or announced, they seemed to have a perception that energy could not be created; that energy must produce an effect commensurate with its own activity; that the existence of energy in one body is proof positive that some agency furnished and lost an exact equivalent of that energy. In other words, these men in reasoning on specific problems presented to them, and on the problem of Perpetual Motion in particular, appear to have appreciated and applied in their reasonings, the principle of Conservation of Energy.

Men who have worked at the problem of Perpetual Motion before the establishment of the doctrine of Conservation of Energy, and men who still work at the problem, who, through lack of opportunity have not become familiar with that doctrine, are not to be blamed or thought stupid because of that folly, but those who knowing that principle, or being in a situation to know it, must be mechanically and mathematically stupid not to realize that Perpetual Motion and Conservation of Energy are irreconcilable, and that both cannot be possibilities. In this day when the principle of Conservation of Energy is taught in the High Schools of the United States, and in every other civilized country in the world, it is not surprising that fewer people work on Perpetual Motion than formerly, and that public interest in the subject is waning, as waning it surely is.

A generation ago, however, this principle was not known and taught, and the state of the world's learning was at such a stage that many even scientific minds thought Perpetual Motion possible, and worked for its attainment.

The principle of Conservation of Energy as applied to all Perpetual Motion devices can be stated as follows: There can be no mechanical effect without an equal mechanical cause. Energy—i.e., the capacity to do work, can only be imparted by an equal amount of work done. It therefore follows axiomatically that Perpetual Motion is possible only if and when a machine be produced that runs absolutely without friction and absolutely without atmospheric resistance, or the resistance of bending of cords, or other like mechanical resistance. If there be such resistance, then the energy imparted to the machine will be diminished by that resistance, with the result that the machine can only yield the amount of energy imparted, less the energy required to overcome such resistance. That no machine can be built free of such resistance is patent to even a tyro in mechanics.

It will be interesting here, and perhaps more interesting than useful, to add some of the arguments quoted by Dircks and reproduced in his work for and against the possibility of Perpetual Motion. They have little scientific value at this time, as they were all made by men who were unfamiliar with the decisive principle of Conservation of Energy. Nevertheless, for their historical interest we offer a few:

The Possibility of Perpetual Motion Denied
Remarks of Dr. Papin on a French Contrivance

In 1665, Dr. Papin, Fellow of the Royal Society, brought before the Royal Society of London, a paper concerning a French contrivance for Perpetual Motion. The following excerpt will illustrate and explain the contrivance:

The paper printed in French, and containing contrivance for perpetual motion, being set down in such a manner that can hardly be understood but by those that are much acquainted with such descriptions, I have endeavored to explain it as follows:

Let DEF be a pair of bellows forty inches long, that may be opened by removing the part F from E; let them be exactly shut everywhere but at the aperture E; and let a pipe EG, twenty or twenty-two inches long, be soldered to the said aperture E, having its other end in a vessel G, full of mercury, and placed near the middle of the bellows.

A is an axis for the bellows to turn upon.

B, a counterpoise fastened to the lower end of the bellows.

C, a weight with a clasp to keep the bellows upright.

Now, if we suppose the bellows opened only to one-third or one-fourth, standing upright, and full of mercury, it is plain that the said mercury, being forty inches high, must fall, as in the Torricellian experiment, to the height of about twenty-seven inches, and, consequently, the bellows must open towards F, and leave a vacuity there. This vacuity must be filled with the mercury ascending from G through the pipe GE, the said pipe being but twenty-two inches long; by this means the bellows must be opened more and more, till the mercury continuing to ascend makes the upper part of the bellows so heavy that the lower part must get loose from the clasp C, and the bellows should turn quite upside down; but the vessel G being set in a convenient place, keeps them horizontal, and the part F engageth there in another clasp C; then the mercury, by its weight, runs out from the bellows into the vessel G through the pipe EG, and the bellows must shut closer and closer until the part EF comes to be so light that the counterpoise B is able to make the part F get loose from the clasp C; then the bellows come to be upright again; the mercury left in them falls again to the height of twenty-seven inches, and, consequently, all the other effects will follow as we have already seen, and the motion will continue forever. Thus much for the French author.

Upon this it is to be observed, that the bellows can never be opened by the internal pressure, unless the said pressure be stronger then the external; now, in this case, the weight of the atmosphere doth freely press up the outward part of the bellows, but it cannot come at the inward part but through the pipe GE, which, containing twenty-two perpendicular inches of mercury, does counterpoise so much of the weight of the atmosphere, so that this being supposed to be twenty-seven inches of mercury, it cannot press the inward part of the bellows but with weight equivalent to five perpendicular inches of mercury. From this we may conclude, that the pressure of the atmosphere, being weakened within the bellows more then it can be helped by the mercury contained in the same, as may easily be computed, the said bellows standing upright must rather shut then open. Thus, without losing any labor and charges in trying, people may be sure that the thing can never do.

Two "Certain" Plans for (Not) Producing Perpetual Motion

In 1834, the following article was contributed to "Mechanics' Magazine." The contributor was very frank, and presents some splendid suggestions for Perpetual Motion workers. His article is as follows:

Very few young mechanicians escape being seduced into an attempt to produce a perpetual movement, by making gravitation counteract itself. They are not contented with being told by older men, that a cause can never be made to exceed its own power; yet gravitation is expected by them to lift up on one side more weight than sinks on the other, with some percentage of friction into the bargain. Nature, however, is too true to itself to be so taken in by all or any of the multitudes of various ways the inventive genius of man has contrived, and still keeps contriving, to circumvent her immutable laws, with no other effect than to render the case so complicated as to puzzle the judgment of the inventors, which ends usually in their firm belief that they have outwitted nature instead of themselves. I acknowledge that in my youth I was one of this class, and, for the benefit of the young, I beg to present you with two certain plans for producing perpetual motion, and compelling gravity to be frolicsome, and do more work than she ought.

Let A (Fig. 1) be a cistern full of oil or water, above 4 feet deep. Let B be a wheel; freely suspended within it, on its axle, let there be four wide glass tubes, 40 inches long, cccc, having large bulbs, holding, say a pint, blown at the closed end. Fill these tubes with mercury, fix on an Indian-rubber ball or bladder, that will hold a pint, to each of them at the open end, and let them be attached round the wheel, as exhibited in the figure. As the pressure of 40 inches of mercury will exceed the atmospheric pressure, and also that of the four-foot column of water, when the Indian-rubber bottle is lowest, and the tube erect, at D, the mercury will fill it, leaving a vacuum in the glass bulb above. On the opposite side the mercury will fill the glass bulb, and the Indian-rubber bottle will be pressed flat, as will also be the case in the two horizontal tubes. Now, it is evident that the two horizontal tubes exactly balance each other; but the tube D, with its bulb swelled out, displaces a pint of water more than its opposite tube, and hence will attempt to rise with the force of about one pound; and each tube, when it arrives at the same position, must produce the same result, the wheel must have a continual power, equal to about one pound, with a radius of two feet.—Q.E.D.

Let Fig. 2 represent a light drum of wood—one-half of which is inserted into a cleft in a water-cistern A, which fits it, and from which the water is prevented from escaping by a strip of leather, which the water presses against the drum, and which thus operates as a valve, without much friction (especially if oil be substituted for water in the cistern). Now, as this drum is much lighter than water, it must ever attempt to swim, and thus, in perpetually rising, cause the drum to revolve forcibly round its axle.—Q.E.D.

I tried this last method thirty years ago, but it was so obstinate as not to move one inch at my bidding, though it obviously is proved, to demonstration, that it ought to have gone on swimmingly. I have just heard that an Italian gentleman has hit upon the same plan; so it seems that the mania is not confined to England.

The article above quoted elicited a varied correspondence on the subject of self-motive power. The editor finally made the following apt and happy remark concerning the two "Certain" plans:

We think our correspondent, S.F., has entirely misconceived the scope of the playful account, given in our last number, of two plans of perpetual motion. The object of the writer seems to have been, to impress on the minds of young mechanicians the folly of wasting their time in vain endeavors to render the effects of causes greater than the causes themselves; or, in other words, to gain power out of nothing—a process without limit or value, were it not cut short by the want of all limit to its folly; and this he could not, perhaps, have done in any way so well, as by exhibiting a couple of infallible perpetual movers that would not stir at all, though they bade as fair for it as any of their kindred.

Article by Rev. John Wilkins

Rev. John Wilkins of England, born 1614; died 1672, published a work called "Mathematical Magic," in which he discoursed scientifically and technically on efforts that had been made up to that time to attain Perpetual Motion. His work shows great scholarship, diligent search, and a thorough knowledge of mathematics and mechanics. Considering the state of scientific knowledge at the time when he lived and worked, his insight into scientific subjects is truly remarkable.

Considering the state of scientific learning in his day, his observations on the subject of Perpetual Motion show him to have possessed really a great scientific and analytical mind. Of all those who wrote or thought extensively on the subject in that century we regard what he had to say as being the most worthy of reproduction. The following excerpt from "Mathematical Magic," will give the reader an idea of his course of reasoning and conclusions on the subject of self-motive power:

CHAP. IX.—Of a Perpetual Motion—The seeming facility and real difficulty of any such contrivance—The several ways whereby it hath been attempted, particularly by Chemistry.

It is the chief inconvenience of all the automata before-mentioned, that they need a frequent repair of new strength, the causes whence their motion does proceed being subject to fail, and come to a period; and, therefore, it would be worth our enquiry to examine whether or no there may be made any such artificial contrivance, which might have the principle of moving from itself so that the present motion should constantly be the cause of that which succeeds.

This is that great secret in art which, like the Philosopher's Stone in Nature, has been the business and study of many more refined wits for divers ages together; and it may well be questioned whether either of them as yet have ever been found out; though if this have, yet like the other, it is not plainly treated of by any author.

Not but there are sundry discourses concerning this subject, but they are rather conjectures than experiments. And though many inventions in this kind may at first view bear a great show of probability, yet they will fail, being brought to trial, and will not answer in practice what they promised in speculation. Any one who has been versed in these experiments must needs acknowledge that he has been often deceived in his strongest confidence; when the imagination has contrived the whole frame of such an instrument, and conceives that the event must infallibly answer its hopes, yet then does it strangely deceive in the proof and discovers to us some defect which we did not before take notice of.

Hence it is that you shall scarce talk with any one who has never so little smattering in these arts, but he will instantly promise such a motion as being but an easy achievement, till further trial and experience has taught him the difficulty of it. There being no enquiry that does more entice with the probability and deceive with the subtilty.

I shall briefly recite the several ways whereby this has been attempted, or seems most likely to be effected, thereby to contract and facilitate the enquiries of those who are addicted to these kind of experiments; for when they know the defects of other inventions, they may the more easily avoid the same or the like in their own.

The ways whereby this has been attempted may be generally reduced to these three kinds:

• 1. By Chemical Extractions.
• 2. By Magnetical Virtues.
• 3. By the Natural Affection of Gravity.

1. The discovery of this has been attempted by chemistry. Paracelsus and his followers have bragged that by their separations and extractions they can make a little world which shall have the same perpetual motions with this microcosm, with the representation of all meteors, thunder, snow, rain, the courses of the sea in its ebbs and flows, and the like. But these miraculous promises would require as great a faith to believe them as a power to perform them; and though they often talk of such great matters:

At nusquam totos inter qui talia curant,
Apparet ullus, qui re miracula tanta
Comprobet—

yet we can never see them confirmed by any real experiment; and then, besides, every particular author in that art has such a distinct language of his own (all of them being so full of allegories and affected obscurities), that 'tis very hard for any one (unless he be thoroughly versed amongst them) to find out what they mean, much more to try it.

One of these ways (as I find it set down) is this: Mix five ounces of ? with an equal weight of ?; grind them together with ten ounces of sublimate; dissolve them in a cellar upon some marble for the space of four days, till they become like oil olive; distil this with fire of chaff, or driving fire, and it will sublime into a dry substance; and so, by repeating of these dissolvings and distillings, there will be at length produced divers small atoms, which, being put into a glass well luted and kept dry, will have a perpetual motion.

I cannot say anything from experience against this; but I think it does not seem very probable, because things that are forced up to such vigorousness and activity as these ingredients seem to be by their frequent sublimings and distillings, are not likely to be of any duration. The more any thing is stretched beyond its usual nature, the less does it last; violence and perpetuity being no companions. And then, besides, suppose it is true, yet such a motion could not well be applied to any use, which will needs take much from the delight of it.

Amongst the chemical experiments to this purpose may be reckoned up that famous motion invented by Cornelius Dreble, and made for King James; wherein was represented the constant revolutions of the sun and moon, and that without the help either of springs or weights. Marcellus Vranckhein, speaking of the means whereby it was performed, he calls it Scintillula animae magneticae mundi, seu astralis et insensibilis spiritus; being that grand secret for the discovery of which those dictators of philosophy, Democritus, Pythagoras, Plato, did travel unto the Gymnosophists and Indian Priests. The author himself, in his discourse upon it, does not at all reveal the way how it was performed. But there is one Thomas Tymme who was a familiar acquaintance of his, and did often pry into his works (as he professes himself), who affirms it to be done thus: By extracting a fiery spirit out of the mineral matter, joining the same with his proper air, which included in the axletree (of the first moving wheel), being hollow, carried the other wheels, making a continual rotation, except issue or vent be given in this hollow axletree, whereby the imprisoned spirit may get forth.

What strange things may be done by such extractions I know not, and, therefore, dare not condemn this relation as impossible; but I think it sounds rather like a chemical dream than a philosophical truth. It seems this imprisoned spirit is now set at liberty, or else is grown weary, for the instrument (as I have heard) has stood still for many years. It is here considerable that any force is weakest near the center of a wheel; and therefore, though such a spirit might of itself have an agitation, yet 'tis not easily conceivable how it should have strength enough to carry the wheels about with it. And then, the absurdity of the author's citing this, would make one mistrust his mistake. He urges it as a strong argument against Copernicus; as if, because Dreble did thus contrive in an engine the revolution of the heavens and the immovableness of the earth, therefore it must needs follow that 'tis the heavens which are moved, and not the earth. If his relation were no truer than his consequence, it had not been worth the citing.

CHAP. XIII.—Concerning several attempts of contriving a Perpetual Motion, by Magnetical Virtues.

The second way whereby the making of a perpetual motion has been attempted, is by Magnetical Virtues, which are not without some strong probabilities of proving effectual to this purpose; especially when we consider that the heavenly revolutions (being as the first pattern imitated and aimed at in these attempts) are all of them performed by the help of these qualities. This great orb of earth, and all the other planets, being but as so many magnetical globes, endowed with such various and continual motions as may be most agreeable to the purposes for which they were intended. And, therefore, most of the authors who treat concerning this invention, do agree that the likeliest way to effect it, is by these kind of qualities.

It was the opinion of Pet. Peregrinus, and there is an example pretended for it in Bettinus (apiar. 9, progym. 5, pro. 11) that a magnetical globe, or terella, being rightly placed upon its poles, would of itself have a constant rotation, like the diurnal motion of the earth. But this is commonly exploded as being against all experience.

Others think it possible so to contrive several pieces of steel and loadstone that, by their continual attraction and expulsion of one another, they may cause a perpetual revolution of a wheel. Of this opinion were Taisner, Pet. Peregrinus, and Cardan, out of Antonius de Fantis. But D. Gilbert, who was more especially versed in magnetical experiments, concludes it to be a vain and groundless fancy.

But amongst all these kinds of inventions, that is most likely, wherein a loadstone is so disposed that it shall draw unto it on a reclined plane a bullet of steel, which steel, as it ascends near to the loadstone, may be contrived to fall down through some hole in the plane, and so to return unto the place from whence at first it began to move; and, being there, the loadstone will again attract it upwards till coming to this hole, it will fall down again; and so the motion shall be perpetual, as may be more easily conceivable by this figure:

Suppose the loadstone to be represented at AB, which, though it have not strength enough to attract the bullet C directly from the ground, yet may do it by the help of the plane EF. Now, when the bullet is come to the top of this plane, its own gravity (which is supposed to exceed the strength of the loadstone) will make it fall into that hole at E; and the force it receives in this fall will carry it with such a violence unto the other end of this arch, that it will open the passage which is there made for it, and by its return will again shut it; so that the bullet (as at the first) is in the same place whence it was attracted, and, consequently, must move perpetually.

But, however, this invention may seem to be of such strong probability, yet there are sundry particulars which may prove it insufficient; for— 1. This bullet of steel must first be touched, and have its several poles, or else there can be little or no attraction of it. Suppose C in the steel to be answerable unto A in the stone, and to B; in the attraction CD must always be directed answerable to AB, and so the motion will be more difficult; by reason there can be no rotation or turning round of the bullet, but it must slide up with the line CD, answerable to the axis AB.

2. In its fall from E to G, which is motus elementaris, and proceeds from its gravity, there must needs be a rotation of it; and so 'tis odds but it happens wrong in the rise, the poles in the bullet being not in the same direction to those in the magnet; and if in this reflux it should so fall out, that D should be directed towards B, there should be rather a flight than an attraction, since those two ends do repel, and not draw one another.

3. If the loadstone AB have so much strength, that it can attract the bullet in F, when it is not turned round, but does only slide upon the plane, whereas its own gravity would rowl it downwards; then it is evident the sphere of its activity and strength would be so increased when it approaches much nearer, that it would not need the assistance of the plane, but would draw it immediately to itself without that help; and so the bullet would not fall down through the hole, but ascend to the stone, and, consequently, cease its motion: for, if the loadstone be of force enough to draw the bullet on the plane, at the distance FB, then must the strength of it be sufficient to attract it immediately unto itself, when it is so much nearer as EB. And if the gravity of the bullet be supposed so much to exceed the strength of the magnet, that it cannot draw it directly when it is so near, then will it not be able to attract the bullet up the plane, when it is so much further off.

So that none of all these magnetical experiments, which have been as yet discovered, are sufficient for the effecting of a perpetual motion, though these kind of qualities seem most conducible unto it; and perhaps, hereafter, it may be contrived from them.

CHAP. XIV.—The seeming probability of effecting a Continual Motion by Solid Weights in a Hollow Wheel or Sphere.

The third way whereby the making of a perpetual motion has been attempted is by the Natural Affection of Gravity; when the heaviness of several bodies is so contrived, that the same motion which they give in their descent, may be able to carry them up again.

But (against the possibility of any such invention) it is thus objected by Cardan:—All sub-lunary bodies have a direct motion either of ascent or descent; which, because it does not refer to some term, therefore cannot be perpetual, but must needs cease when it is arrived at the place unto which it naturally tends.

I answer, though this may prove that there is no natural motion of any particular heavy body which is perpetual, yet it does not hinder, but that it is possible from them to contrive such an artificial revolution as shall constantly be the cause of itself.

Those bodies which may be serviceable to this purpose are distinguishable into two kinds:

1. Solid and consistent; as weights of metal, or the like.

2. Fluid or sliding; as water, sand, etc.

Both these ways have been attempted by many, though with very little or no success. Other men's conjectures in this kind you may see set down by divers authors. It would be too tedious to repeat them over, or set forth their draughts.

I shall only mention two new ones, which (if I am not over-partial) seem altogether as probable as any of these kinds that have been yet invented; and, till experience had discovered their defect and insufficiency, I did certainly conclude them to be infallible.

The first of these contrivances was by solid weights being placed in some hollow wheel or sphere, unto which they should give a perpetual revolution; for, as the philosopher has largely proved, only a circular motion can properly be perpetual.

But, for the better conceiving of this invention, it is requisite that we rightly understand some principles in Trochilicks, or the art of wheel instruments; as, chiefly, the relation betwixt the parts of a wheel and those of a balance; the several proportions in the semi-diameter of a wheel being answerable to the sides in a balance, where the weight is multiplied according to its distance from the center.

Thus, suppose the center to be at A, and the diameter of the wheel, DC, to be divided into equal parts (as is here expressed), it is evident, according to the former ground, that one pound at C will equiponderate to five pound at B, because there is such a proportion betwixt their several distances from the center. And it is not material whether or no these several weights be placed horizontally; for though B do hang lower than C, yet this does not at all concern the heaviness; or though the plummet C were placed much higher than it is at E, or lower at F, yet would it still retain the same weight which it had at C; because these plummets (as in the nature of all heavy bodies), do tend downwards by a straight line; so that their several gravities are to be measured by that part of the horizontal semi-diameter, which is directly either below or above them. Thus, when the plummet C shall be moved either to G or H, it will lose one-third of its former heaviness, and be equally ponderous as if it were placed in the balance at No. 3; and if we suppose it to be situated at I or K, then the weight of it will lie wholly upon the center, and not at all conduce to the motion of the wheel on either side; so that the straight lines which pass through the divisions of the diameter may serve to measure the heaviness of any weight in its several situations.

These things thoroughly considered, it seems very possible and easy for a man to contrive the plummets of a wheel, that they may be always heavier in their fall, than in their ascent; and so, consequently, that they should give a perpetual motion to the wheel itself; since it is impossible for that to remain unmoved as long as one side in it is heavier than the other.

For the performance of this, the weights must be so ordered: 1. That in their descent they may fall from the center, and in their ascent may rise nearer to it. 2. That the fall of each plummet may begin the motion of that which should succeed it, as in the following diagram:

Where there are sixteen plummets, eight in the inward circle, and as many in the outward. (The inequality being to arise from their situation, it is therefore most convenient that the number of them be even.) The eight inward plummets are supposed to be in themselves so much heavier than the other, that in the wheel they may be of equal weight with those above them, and then the fall of these will be of sufficient force to bring down the other. For example, if the outward be each of them four ounces, then the inward must be five; because the outward is distant from the center five of those parts whereof the inward is but four. Each pair of these weights should be joined together by a little string or chain, which must be fastened about the middle, betwixt the bullet and the center of that plummet which is to fall first, and at the top of the other.

When these bullets, in their descent, are at their farthest distance from the center of the wheel, then shall they be stopped, and rest on the pins placed to that purpose; and so, in their rising, there must be other pins to keep them in a convenient posture and distance from the center, lest, approaching too near unto it, they thereby become unfit to fall when they shall come to the top of the descending side.

This may be otherwise contrived with some different circumstances, but they will all redound to the same effect. By such an engine it seems very probable that a man may produce perpetual motion; the distance of the plummets from the center increasing with weight on one side, and their being tied to one another, causing a constant succession in their falling.

But now, upon experience, I have found this to be fallacious; and the reason may sufficiently appear by a calculation of the heaviness of each plummet, according to its several situation; which may easily be done by those perpendiculars that cut the diameter (as was before explained, and is here expressed in five of the plummets on the descending side). From such a calculation it will be evident, that both the sides of this wheel will equiponderate; and so consequently, that the supposed inequality whence the motion should proceed, is but imaginary and groundless. On the descending side, the heaviness of each plummet may be measured according to these numbers (supposing the diameter of the wheel to be divided into twenty parts, and each of those sub-divided into four):

The Outward Plummets.	The Inward Plummets.
7.0}	1.0}
10.0} The sum 24.	7.2} The sum 19.
7.0}	7.2}
	3.0}

On the ascending side, the weights are to be

The Outward.	The Inward.
1.3}	4.1}
7.2}	7.0} The sum 19.
9.0} The sum 24.	5.2}
5.3}	2.1}
0.0}

The sum of which last numbers is equal with the former, and therefore both the sides of such a wheel in this situation will equiponderate.

If it be objected, that the plummet A should be contrived to pull down the other at B, and then the descending side will be heavier than the other; for answer to this, it is considerable—

1. That these bullets towards the top of the wheel, cannot descend till they come to a certain kind of inclination.

2. That any lower bullet hanging upon the other above it, to pull it down, must be conceived, as if the weight of it were in that point where its string touches the upper; at which point this bullet will be of less heaviness in respect of the wheel, than if it did rest in its own place; so that both the sides of it, in any kind of situation, may equiponderate.

CHAP. XV.—Of composing, a Perpetual Motion by Fluid Weights—Concerning Archimedes his Water Screw—The great probability of accomplishing this enquiry by the help of that, with the fallibleness of it upon experiment.

That which I shall mention as the last way, for the trial of this experiment, is by contriving it in some Water Instrument; which may seem altogether as probable and easy as any of the rest; because that element, by reason of its fluid and subtle nature (whereby, of its own accord, it searches out the lower and more narrow passages), may be most pliable to the mind of the artificer. Now, the usual means for the ascent of water is either by suckers or forces, or something equivalent thereunto; neither of which may be conveniently applied unto such a work as this, because there is required unto each of them so much or more strength, as may be answerable to the full weight of the water that is to be drawn up; and then, besides, they move for the most part by fits and snatches, so that it is not easily conceivable, how they should conduce unto such a motion, which, by reason of its perpetuity, must be regular and equal.

But, amongst all other ways to this purpose, that invention of Archimedes is incomparably the best, which is usually called Cochlea, or the Water Screw; being framed by the helical revolution of a cavity about a cylinder. We have not any discourse from the author himself concerning it, nor is it certain whether he ever writ anything to this purpose; but if he did, yet, as the injury of time hath deprived us of many other of his excellents works, so likewise of this amongst the rest.

[Near five pages are occupied in describing the use of this screw, and the form and manner of making it; then follows:]

The true inclination of the screw being found, together with the certain quantity of water which every helix does contain; it is further considerable, that the water by this instrument does ascend naturally of itself, without any violence or labor; and that the heaviness of it does lie chiefly upon the centers or axis of the cylinder, both its sides being of equal weight (said Ubaldus); so that, it should seem, though we suppose each revolution to have an equal quantity of water, yet the screw will remain with any part upwards, according as it shall be set, without turning itself either way; and, therefore, the least strength being added to either of its sides should make it descend, according to that common maxim of Archimedes—any addition will make that which equiponderates with another to tend downwards.

But now, because the weight of this instrument and the water in it does lean wholly upon the axis, hence is it (said Ubaldus) that the grating and rubbing of these axes against the sockets wherein they are placed, will cause some ineptitude and resistency to that rotation of the cylinder; which would otherwise ensue upon the addition of the least weight to any one side; but (said the same author) any power that is greater than this resistency which does arise from the axis, will serve for the turning of it round.

These things considered together, it will hence appear how a perpetual motion may seem easily contrivable. For, if there were but such a water-wheel made on this instrument, upon which the stream that is carried up may fall in its descent, it would turn the screw round, and by that means convey as much water up as is required to move it; so that the motion must needs be continual, since the same weight which in its fall does turn the wheel is, by the turning of the wheel, carried up again.

Or, if the water, falling upon one wheel, would not be forcible enough for this effect, why then there might be two or three, or more, according as the length and elevation of the instrument will admit; by which means the weight of it may be so multiplied in the fall that it shall be equivalent to twice or thrice that quantity of water which ascends; as may be more plainly discerned by the following diagram:

Where the figure LM, at the bottom, does represent a wooden cylinder with helical cavities cut in it, which at AB is supposed to be covered over with tin plates, and three water-wheels upon it, HIK; the lower cistern, which contains the water, being CD. Now, this cylinder being turned round, all the water which from the cistern ascends through it, will fall into the vessel at E, and from that vessel being conveyed upon the water-wheel H, shall consequently give a circular motion to the whole screw. Or, if this alone should be too weak for the turning of it, then the same water which falls from the wheel H, being received into the other vessel F, may from thence again descend on the wheel I, by which means the force of it will be doubled. And if this be yet unsufficient, then may the water which falls on the second wheel I, be received into the other vessel G, and from thence again descend on the third wheel at K; and so for as many other wheels as the instrument is capable of. So that, besides the greater distance of these three streams from the center or axis by which they are made so much heavier, and besides that the fall of this outward water is forcible and violent, whereas the ascent of that within is natural—besides all this, there is thrice as much water to turn the screw as is carried up by it.

But, on the other side, if all the water falling upon one wheel would be able to turn it round, then half of it would serve with two wheels, and the rest may be so disposed of in the fall as to serve unto some other useful delightful ends.

When I first thought of this invention, I could scarce forbear, with Archimedes, to cry out e????a, e????a {heurÊka, heurÊka}; it seeming so infallible a way for the effecting of a perpetual motion that nothing could be so much as probably objected against it; but, upon trial and experience, I find it altogether insufficient for any such purpose, and that for these two reasons:

1. The water that ascends will not make any considerable stream in the fall.

2. This stream, though multiplied, will not be of force enough to turn about the screw.

1. The water ascends gently, and by intermissions; but it falls continually, and with force; each of the three vessels being supposed full at the first, that so the weight of the water in them might add the greater strength and swiftness to the streams that descend from them. Now, this swiftness of motion will cause so great a difference betwixt them that one of these little streams may spend more water in the fall than a stream six times bigger in the ascent, though we should suppose both of them to be continuate; how much more, then, when as the ascending water is vented by fits and intermissions, every circumvolution voiding so much as is contained in one helix; and, in this particular, one that is not versed in these kind of experiments may be easily deceived.

But, secondly, though there were so great a disproportion, yet, notwithstanding, the force of these outward streams might well enough serve for the turning of the screw, if it were so that both its sides would equiponderate the water being in them (as Ubaldus had affirmed). But now, upon farther examination, we shall find this assertion of his to be utterly against both reason and experience. And herein does consist the chief mistake of this contrivance; for the ascending side of the screw is made, by the water contained in it, so much heavier than the descending side, that these outward streams, thus applied, will not be of force enough to make them equiponderate, much less to move the whole, as may be more easily discerned by this figure:

Where AB represents a screw covered over, CDE one helix or revolution of it, CD the ascending side, ED the descending side, the point D the middle; the horizontal line CF showing how much of the helix is filled with water, viz., of the ascending side, from C the beginning of the helix, to D the middle of it; and on the descending side, from D the middle, to the point G, where the horizontal does cut the helix. Now, it is evident that this latter part, DG, is nothing near so much, and consequently not so heavy as the other, DC; and thus is it in all the other revolutions, which, as they are either more or larger, so will the difficulty of this motion be increased. Whence it will appear that the outward streams which descend must be of so much force as to countervail all that weight whereby the ascending side in every one of these revolutions does exceed the other. And though this may be effected by making the water-wheels larger, yet then the motion will be so slow that the screw will not be able to supply the outward streams.

There is another contrivance to this purpose, mentioned by Kircher de Magnete, 1, 2, p. 4, depending upon the heat of the sun and the force of winds; but it is liable to such abundance of exceptions that it is scarce worth the mentioning, and does by no means deserve the confidence of any ingenious artist.

Thus have I briefly explained the probabilities and defects of those subtle contrivances whereby the making of a perpetual motion has been attempted. I would be loath to discourage the enquiry of any ingenious artificer by denying the possibility of effecting it with any of these mechanical helps; but yet (I conceive) if those principles which concern the slowness of the power in comparison to the greatness of the weight were rightly understood and thoroughly considered, they would make this experiment to seem, if not altogether impossible, yet much more difficult than otherwise, perhaps, it will appear. However, the inquiring after it cannot but deserve our endeavors, as being one of the most noble amongst all these mechanical subtilties. And, as it is in the fable of him who dug the vineyard for a hidden treasure, though he did not find the money, yet he thereby made the ground more fruitful, so, though we do not attain to the effecting of this particular, yet our searching after it may discover so many other excellent subtilties as shall abundantly recompense the labor of our inquiry.

And then, besides, it may be another encouragement to consider the pleasure of such speculations, which do ravish and sublime the thoughts with more clear angelical contentments. Archimedes was generally so taken up in the delight of these mathematical studies of this familiar siren (as Plutarch styles them) that he forgot both his meat and drink, and other necessities of nature; nay, that he neglected the saving of his life, when that rude soldier, in the pride and haste of victory, would not give him leisure to finish his demonstration. What a ravishment was that, when, having found out the way to measure Hiero's crown, he leaped out of the bath, and (as if he were suddenly possessed) ran naked up and down, crying e????a, e????a {Greek: heurÊka, heurÊka}! It is storied of Thales that, in his joy and gratitude for one of these mathematical inventions, he went presently to the Temple, and there offered up a solemn sacrifice; and Pythagoras, upon the like occasion, is related to have sacrificed a hundred oxen; the justice of Providence having so contrived it, that the pleasure which there is in the success of such inventions should be proportioned to the great difficulty and labor of their inquiry.

The Paradoxical Hydrostatic Balance

The following was contributed to an English scientific journal in 1831, the name of the author of the article is unknown to us, but here is what he wrote:

This hydrostatic balance, like the compound balance of Desaguliers, may be introduced to illustrate the impossibility of perpetual motion by a weight removed from the centre of a wheel.

Take the hollow-rimmed wheel AB; let it be air-tight and half filled with water. Let C be the axle; at B place a hollow ball loaded to near sinking. Such a wheel, however fine its axle may be, or however well lubricated, will not make a single revolution, though the weight B occupies that part at which every deluded perpetual-motionist is desirous it should be placed; concluding that, by such an arrangement, the production of another Orffyrean wheel must be inevitable.

Discussion by P. Gregorio Fontana

P. Gregorio Fontana was professor of higher mathematics at the Royal University of Pavia, in the Province of Lombardy, Italy. In 1786 he published what he designated "Examination of a New Argument in Favor of Perpetual Motion." In part he says:

1. A vertical wheel (Fig. 2) divided in two halves by a vertical plane which passes through its diameter FO, has the half FPO immersed in water under the level MN, and the other half wholly out of the water, being cut off in FO by a peculiar mechanism from all communication with the reservoir, the exterior half of the wheel being FQO; this turns freely round on an axle passing through the centre C. Now the wheel being specifically lighter than the water, the immersed part FPO comes with a continual rotation to the top with a force equal to the excess of the weight of a volume of water corresponding to the immersed portion, over the weight of the immersed portion; which rotation passing through the centre of gravity of the exterior part, and consequently out of the centre C, obliges the wheel to turn around C.

Such being the case, the question to be asked is whether the wheel has itself a perpetual motion, as may be judged at first sight.

2. To reply adequately, it is at first necessary to know what effect is produced on the wheel by the horizontal pressure which the water exercises on the semi-circumference FLO.

Having taken for this purpose, a part P p, and having drawn to the diameter the ordinate P. R, pr, and marked the radius PC, and from it PG perpendicular to the radius CL, which determines the quadrant OL, the distance of the lowest point O from the level of the water will be = b, the semi-diameter of the wheel = a, CR = x, and the specific gravity of the water = 1; the perpendicular pressure against the part Pp = Pp . RD, which resolved in two, one horizontal PR, the other vertical PG, gives the proportion

PG : PR :: Pp . RD : (Pp . PR . RD) / (PG).

Thence the horizontal pressure against Pp, and = (Pp . PR . RD .) / (PG), that is to say Pp . PR = Rr . PG, the given horizontal pressure is found to be = Rr . RD = (b - x) d x, and which, multiplied by RD, giving b - x, becomes the momentum of the pressure relatively to MN = (b - x)² d x, and the sum of the momenta of pressure exercised upon the indefinite arc, OP = f (b - x)² d x = -(1/3)(b - x)³ + the side. And since acting together such momenta equal x, there comes the side = (1/3)b³; and as the already-given sum of the momenta = (1/3)(b³ - (b - x)³) = b² x - bx² + (1/3)x³. Whence, taking x = 2a, the sum of all the momenta of the horizontal pressure exercised on the whole semi-circumference OLF of the wheel, will be = 2b²a - 4b a² + (8/3)a³, and dividing that sum by the whole horizontal pressure, that is to say by f(b - x)dx = (1/2)(b² - (b - x)²) = bx - (1/2)x² = 2b a - 2a², gives x = 2a, we have the formula

(2b² - 4ba + (8/3)a³) / (2ba - 2a²) = (b² - 2ba + (4/3)a²) / (b - a) = ((b - a)² + (1/3)a²) / (b - a) = b - a + ((2/3)a²) / (b - a),

which represents the distance of the level M N from the result of all the horizontal pressure against the circumference, which distance exceeds DC, and consequently the direction of the result passes from below the centre C of the wheel to a distance from the said centre, which is = ((1/3)a²)/(b - a).

If this distance be multiplied by the result of all the horizontal pressure, that is, by 2a.(b - a); there is obtained (2/3)a³ for the momentum of the force which tends to make the wheel revolve from L towards O. This being established, it is known that the force which causes the half of the wheel FLG to revolve vertically to the top (calling g the specific gravity of the wheel) is = (1 - g) FCOL, and which force passes through the center of gravity of FLO. And consequently the gravity of any circular segment divided by the half of the radius, is distant from the centre of the circle by a quantity equal to the twelfth of the cube of the chord divided by the segment; and therefore the centre of gravity of the semicircle FCOL, will be distant from the centre C by the quantity (1/12)8a³/(ECOL) = (2/3)a³/(ECOL). Consequently the momentum of this force tending to make the wheel revolve from O towards L will be = (2/3a³)/(ECOL) . (1 - g)(ECOL) = 2/3(1 - g)a³.

But moreover a certain momentum will be derived from the other half FQO of the wheel, which being out of the water, tends by its own weight downwards with a force = g . (ECOQ) = g . (ECOL), which multiplied by the distance (2/1a³)/(ECOL) of the centre of gravity of the semicircle FQO from the centre of the wheel gives as a momentum of force tending to turn the wheel from O to L the quantity 2/3ga³. Thus the whole momentum to make the wheel turn from O to L, will be 2/3(1 - g)a³, + 2/3ga³ = 2/3a³, that is to say the same that is found to turn the wheel in the opposite direction, viz., from L to O, and thence the wheel remains perfectly motionless.

3. Cor. I. If the wheel were specifically heavier than the water, one would not be able to conceive in that case any motion from L to O, as seemed probable in the former supposition. Since, then, the momentum of the force, which turns vertically downwards the portion of the wheel FCOL, and tends to make it revolve from L to O is = 2/3(g - 1)a³ to which momentum should be added a certain portion of the horizontal pressure, that is to say 2/3, and thus is obtained the whole momentum 2/3ga³, tending to cause the wheel to turn from L to O; and to which momentum precisely, is equal such of the weight of the half FCOQ as tends to give to the wheel a contrary revolution, that is, from O to L.

3. Cor. II. If the wheel in place of being a circular plane were a zone bounded by two concentric peripheries (Fig. 3), then from the sum of the horizontal pressure of the water against the exterior periphery should be taken the sum of the opposite horizontal pressure against the other interior semi-periphery of the zone. So calling a the greater radius of the zone, and ? its breadth, the sum of the first horizontal pressure is = 2a(b - a) and the sum of the second = 2(a - ?)(b - ?) - (a - ?) = 2(a - ?)(b - a). Then subtract the latter from the former and there remains 2(b - a)? for the sum of the whole pressure, which acts upon the zone (sic) of the half of the wheel immersed in the fluid in a direction tending from the outside to the interior of the wheel.

Moreover the sum of the momenta of all the horizontal pressure on the exterior circumference relatively to the level

MN is = 2ba - 4ba + 8/3a³.

And similarly the sum of the momenta of the horizontal pressure opposite, on the interior semi-circumference, relatively to the given level is = 2(b - ?)² - (a - ?) - 4(b - ?) × (a - ?)² + 8/3(a - ?)³.

Subtracting this sum from the preceding, there remains the sum of the momenta acting on the zone of the half-wheel from the exterior to the interior = 2b² a - 4ba² + 8/3a³ - 2(b - ?)² (a - ?) + 4(b - ?) (a - ?)² - 8/3(a - ?)³ - 2b² ? - 4ba ? + 4a² ? - 2a ?² + 2/3?³ = 2? (b(b - a) - ba + 2a² - a? + 1/3?²) = 2? ((b - a)(b - a) + a² - a? + 1/3?²) Then dividing this sum of the momenta by the sum of the pressure there will be 2?(((b - a)(b - a) + a² - a? + 1/3?²)/(2?(b - a))) = b + p (a(a² - a? + 1/3?²)/(b - a)) the distance of the center of the pressure from the level of the fluid, that is, to the distance of the result of all the pressure from that level. From this it is evident that the center of pressure falls under the center of the wheel, C, to the distance (a² - a? + 1/3?²)/(b - a) .

Whence multiplying this distance by the result of the pressure, or by 2?(b - a), we obtain 2?(a² - a? + 1/3?²) to express the momentum of the horizontal pressure of the water, directed to make the wheel turn from L to O.

Now the momentum with which the vertical impulse of the fluid tends to make the semicircle FCOL turn from O to L (supposing the wheel not with a simple zone, but with a circular plane) is = 2/3a³. Likewise the momentum of the impulse of the fluid to cause the internal semicircle VCIG from O to L is - 2/3(a - ?)³. Then taking this second momentum from the first, the momentum of the zone from the fluid VGI O LF to give the wheel an impulse from O to L will be = 2/3(a³ - (a - ?)³) = 2?(a² - a? + 1/3?²) which is precisely the momentum with which the horizontal pressure of the fluid to impress on the wheel an impulse in the opposite direction, that is to say from L to O. Consequently from the pressure of the fluid the wheel cannot have any motion around its center.

The weight of the wheel itself, by which the half-zone immersed in the water tends to make the wheel turn from L to O, and the half which is out of the water, to make it turn in the reverse direction, such a weight, I say, cannot induce any motion of rotation, and both halves remain in equilibrium around the center C.

Article by William Nicholson

William Nicholson was born in London in 1753; died in 1815. He was a scientist of note, and a writer of scientific subjects. In 1797 he established in London and continued publishing until 1814, a periodical entitled "Journal of Natural Philosophy, Chemistry and the Arts," known, however, throughout the civilized world as "Nicholson's Journal."

A Perpetual Motion device of Dr. Conradus Schwiers, in 1790, and the Richard Varley device, in 1797, described at page 132 et seq., ante, had attracted a great deal of attention, and were the occasion of much discussion. A consequent increased interest in the subject of self-moving mechanism was thus created.

Mr. Nicholson, whose scientific attainments were recognized by all, was asked to publish an article on the subject. His article appeared in his publication, "Nicholson's Journal," and is as follows:

On the Mechanical Projects for Affording a Perpetual Motion

In consequence of the notice taken of Mr. Varley's attempt to produce a perpetual motion, I have been requested by several correspondents to state how far the mechanical scheme for which Dr. Conrad Schwiers took out a patent in the year 1790, for the same object may be worthy of attention. I have, on that occasion, mentioned the difficulties which have prevented any clear general demonstration of the absurdity of this pursuit from being produced, though it has not been difficult to show the fallacy of the individual plans. It does not, indeed, seem easy to enunciate the scheme itself. What in universal terms is the thing proposed to be done? Is it to cause a body to act in such a manner that the reaction shall be greater than the action itself, and by that means generate force by the accumulation of the surplus? Or, can the motion communicated be greater than that lost by the agent? Since these positions are evidently contrary to the physical axioms called the laws of nature, and frictions and resistances would speedily destroy all motions of simple uniformity, it may be presumed that 's Gravesande, who thought that all the demonstrations of the absurdity of schemes for perpetual motion contained paralogism, would have stated the proposition under different terms. But without entering upon this apparently unprofitable disquisition, it may be useful, as well as entertaining, to make a few observations on the mechanical contrivances which depend on a mistaken deduction from the general theorem respecting the balance, among which that of Dr. Schwiers must be classed.

There is no doubt but numerous arrangements have been made, and still are labored at by various individuals, to produce a machine which shall possess the power of moving itself perpetually, notwithstanding the inevitable loss by friction and resistance of the air. Little, however, of these abortive exertions has been entered upon record. The plans of Bishop Wilkins, the Marquis of Worcester, and M. Orffyreus, are all which at this time occur to my recollection.

There is no doubt but the celebrated Wilkins was a man of learning and ability. His essay towards a real character and a philosophical language is sufficient to render his name immortal. Twenty years before the appearance of that work he published his "Mathematical Magic," namely, in the year 1648, containing 295 pages, small octavo, which, from the number of copies still in being, I suppose to have been a very popular treatise. It is in this work that I find, among other contrivances for the same purpose, a wheel carrying sixteen loaded arms, similar to that delineated in Fig. 4, plate 15, in which, however, for the sake of simplicity, I have drawn but six. Each lever, ABCDEF, is movable through an angle of 45 degrees, by a joint near the circumference of the wheel, and the inner end or tail of each is confined by two studs or pins, so that it must either lie in the direction of a radius, or else in the required position of obliquity. If the wheel be now supposed to move in the direction EF, it is evident that the levers ABCD, by hanging in the oblique position against the antecedent pins, will describe a less circle in their ascent than when, on the other side, they come to descend in the positions EF. Hence, it was expected that the descending weights, having the advantage of a longer lever, would always predominate. Dr. Wilkins, by referring the weights to an horizontal diameter, has shown that in his machine they will not. A popular notion of this result may also be gathered from the figure, where there are three weights on the ascending and only two on the descending side; the obliquity of position giving an advantage in point of number, equal to what the other side may possess in intensity. Or, if this contrivance were to be strictly examined, on the supposition that the levers and weights were indefinitely numerous, the question would be determined by showing that the circular arcs AK, HI, are in equilibrio with the arcs AG, GL.

The simplest method of examining any scheme of this kind with weights, consists in inquiring whether the perpendicular ascents and descents would be performed with equal masses in equal times. If so, there will be no preponderance, and, consequently, no motion. This is clearly the case with the contrivance before us.

The Marquis of Worcester, who will ever be remembered as the inventor of the steam engine, has described a perpetual motion in the fifty-sixth number of his "Century of Inventions," published in the year 1655, and since reprinted in 1767 by the Foulis's at Glasgow. His words were as follows:

"To provide and make, that all the weights of the descending side of a wheel shall be perpetually further from the center 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, two extraordinary ambassadors accompanying his Majesty, and the Duke of Richmond and Duke Hamilton, with most of the Court attending him. The wheel was fourteen feet over, and forty weights of fifty pounds apiece. Sir William Balfour, then Lieutenant of the Tower, can justify it with several others. They all saw that no sooner these great weights passed the diameter line of the lower side, but they hung a foot further from the center; nor no sooner passed the diameter line of the upper side, but they hung a foot nearer. Be pleased to judge the consequence."

Desaguliers, in his "Course of Experimental Philosophy," Vol. I, page 185, has quoted this passage, and given a sketch of a pretended self-moving wheel, similar to Fig. 5, plate 15, as resembling the contrivance mentioned by the Marquis of Worcester. The description of this last engineer agrees, however, somewhat better with the contrivance Fig. 4. It must, of course, be a mistake in terms, when he says the weight receded from the center at the lower diameter and approached towards it at the upper: the contrary being, in fact, necessary to afford any hope of success; and accordingly in the quotation it is so stated. I am, therefore, disposed to think that Fig. 5 represents the wheel of Orffyreus at Hesse Cassel, much talked of about the year 1720, and which probably was made to revolve, during the time of exhibition, by some concealed apparatus. It consists of a number of cells or partitions, distinguished by the letters of the alphabet, which are made between the interior and exterior surfaces of two concentric cylinders. The partitions being placed obliquely with respect to the radius, a cylindrical or spherical weight placed on each, it is seen from the figure, that these weights will lie against the inner surface of the larger cylinder whenever the outer end of the bottom partition of any cell is lowest; and, on the contrary, when that extremity is highest, the weight will rest on the surface of the interior cylinder. Let the wheel be made to revolve in the direction ABC; the weights in CDEFGHI being close to the external circle, and the weights KLMA B close to the inner, for the reasons last mentioned. As the cell B descends, its weight will likewise run out, at the same time that the weight in the cell I will run in in consequence of its partition being elevated. By the continuation of this process, since all the weights on the descending side pass down at a greater distance from the center, while those of the ascending side rise for a considerable part of their ascent at a less distance from the same point, it is concluded that the wheel will continue to maintain its motion. On this, however, it is to be remarked that the perpendicular ascent and descent are alike, both in measure and in time of performance; and that the familiar examination, even to those who know little of such subjects, is sufficient to show that the preponderance is not quite so palpable as at first it appears. For the weights G and F, H and E, I and D are evidently in equilibrio, because at the same horizontal distance from the center; and if the favorable supposition that the weight B has already run out be admitted, it will then remain a question whether these two exterior weights, B and C, can preponderate over the four inner weights, KLMA. The more accurate examination of this particular contrivance will lead to the following theorem: In two concentric circles, if tangents be drawn at the extreme points of a diameter of the smaller, and continued till they intersect the larger, the common center of gravity of the arc of the greater circle included between the tangents and of the half periphery of the smaller circle on the opposite side of the diameter, will be the common center of the circles. If, therefore, the balls were indefinitely numerous and small, the supposed effective parts of the wheel (Fig. 5) would be in equilibrio, as well as the parts beneath the horizontal tangent of the inner circle.

Fig. 6 represents the contrivance of Dr. Schwiers, which, in a periodical publication, in other particulars respectable, has been said to continue in motion for weeks and even months together. There is not the smallest probability that it should continue in motion for half a minute, or nearly as long as a simple wheel would retain part of its first impulse. The external circle denotes a wheel carrying a number of buckets, ABIL, etc. C represents a toothed wheel, on the same axis which drives a pinion D; and this last drives another pinion E upon the axis of a lanthorn, or wheel intended to work a chain-pump with the same number of buckets as in the larger wheel ABI. The lanthorn G is made of such a size as to receive the buckets abil with a due velocity. K represents a gutter through which a metallic ball, contained in the bucket m, may run and lodge itself in the bucket A of the wheel. Each of the buckets of the wheel, B I LM, which are below the gutter, is supplied with a metallic ball, and so likewise are the ascending buckets, abilm, of the chain-pump. As the pump supplies the wheel, it is again supplied at M, where the balls fall into its ascending buckets. Now, it is presumed that the balls in the wheel I suppose on account of their distance from the center of motion, will descend with more than sufficient force to raise those on the chain, and, consequently, that the motion will be perpetual.

The deception in this contrivance has much less seduction than in the two foregoing, because it is more easily referred to the simple lever. This, like the others, exhibits no prospect of success, when tried by the simple consideration of the quality of the ascent and descent in the whole time of the rotation of a single ball. It may also be shown from the principles of wheel-work, which are familiar to artisans, that whatever is gained by the excess of the diameter of the great wheel beyond that of the wheel C, is again lost by the excess of the lanthorn A beyond the pinion E.

The fundamental proposition of the simple lever or balance, that equal bodies at an equal distance from the fulcrum will equiponderate, but that at unequal distances the most remote will descend, has, in these and numberless other instances, led mechanical workmen and speculators to pursue this fruitless inquiry with labor and expense often ill-afforded, and with a degree of anxiety and infatuation which can hardly be conceived by those who have never suffered the pain of hope long deferred. For this reason chiefly, it has appeared desirable and useful to treat the subject in a familiar way without descending to those expressions of contempt, which ignorance, harmless to all but itself, is surely not entitled to. If such reasoners were well convinced that the power of a machine is to be estimated by the excess of motion referred to the perpendicular, without any regard to the apparent center of the machine, and that in machines very little compounded it is possible to produce effects directly contrary to the rule which is true of the simple lever, they would probably renounce many flattering projects, grounded only on the supposition of its universality. Desaguliers contrived an apparatus in which two equal weights may be placed at any distance whatever from the center of motion, and still continue in equilibrio. Fig. 3 represents this instrument. AD denotes a balance with equal arms, and EF another of the same dimensions. These move on the centers B and C, and are connected by the inflexible rods AE and DF; the motion being left free by means of joints at the corners. Across the rods AD, EF, are fixed two bars, IK, LM. Now, it is unnecessary to show that the weight G will describe exactly the same line or circular arc, when the levers are moved into the position adfe, or any other position, as it would have described in case it had been suspended at A, or K, or E; and that it is of no consequence in this respect at what part of the line AE or IK it be fixed. The same observations are true of the weight H on the other side. And accordingly it is found that these equal weights may be suspended anywhere on the lines IK and LM without altering their equilibrium.

By this contrivance it is most evidently proved to those who are totally unacquainted with the theory, that weights do not preponderate in compound engines on account of their distance from the center. Several contrivances may be made to the same effect. The following combination of wheel-work presented itself to me as one which would most probably be mistaken for a perpetual motion. (Fig. 2, plate 15.) The five circles represent the same number of wheels of equal diameter and number of teeth, acting together. The middle wheel A is fixed between two upright pillars, so that it cannot revolve. The other four wheels are pinned in a frame HI, in which they can revolve, and through which the axis of A likewise passes. From the extremity of the axis of D, and also of d, proceed the horizontal levers HK and IL, which are equal, and point in the same direction parallel to the plane of the wheels. At the extremity of these arms hang the equal weights P and p. Let it now be imagined that the end I of the frame is depressed, the wheel B will turn round by the reaction of the fixed wheel A in the same direction as HI, and it will make one revolution in the same time relative to the frame, or two with regard to absolute space, by reason of its being carried round. The action of B upon D will produce a rotation relative to the frame in the opposite direction during the same time. Instead, therefore, of two revolutions like the wheel B, this wheel D, with regard to absolute space, will not revolve at all, and in every position of the apparatus the arm IL will continue horizontal, and point the same way. For similar reasons the arm HK will retain its position. Consequently, it is seen that the descending weight will move at a great horizontal distance from the center N, while the ascending weight rises very near that center. But there will, not on this account, be a perpetual motion: for the action of the levers HK and IL upon the frame HI, by means of the toothed wheels, will, in the detail, be found precisely alike, and in the general consideration of the motions of P and p, the opposite motions in the circle EFG will be accurately the same.

It has always been considered as essential to a perpetual motion that it should be derived from some energy which is not supposed to vary in its intensity. Such are the inertia, the gravity or magnetism of bodies. For an occasional or periodical variation of intensity in any force is evidently productive of motion, which requires only to be accumulated or applied, and the apparatus for applying it cannot be considered as a machine for perpetual motion. Neither in strictness can any machine whose motion is derived from the rotation of the earth, and the consequent change of seasons and rotation of events, be so considered, because it does not generate, but only communicates. The perpetual flow of rivers; the vicissitudes of the tides; the constant, periodical and variable winds; the expansions and contractions of air, mercury, or other fluids, by daily or other changes of temperature; the differences of expansions in metals, by the same change; the rise and fall of the mercury in the barometer; the hygrometric changes in the remains of organized beings, and every other mutation which continually happens around us, may be applied to give motion to mills, clocks, and other engines, which may be contrived to endure as long as the apparatus retains its figure.

Mr. Nicholson's article, published above, shows, if nothing else had ever shown, the fact that he was endowed with a real scientific mind. It also shows what is still most interesting—that his mind anticipated and that he had a subconscious conception of the principle of Conservation of Energy.

In 1824 and 1825 there was published in London a mechanical journal called "The Artisan"; or "Mechanic's Instructor." In one of the issues the following occurred on the subject of Perpetual Motion:

Perpetual motion is a motion which is supplied and renewed from itself without the intervention of any external cause: to find a perpetual motion, or to construct a machine which shall have such a motion, is a subject which has engaged the attention of mathematicians for more than 2,000 years; though none perhaps have prosecuted it with so much zeal and hopes of ultimate success as some of the speculative philosophers of the present age.

Infinite are the schemes, designs, plans, engines, wheels, etc., to which this longed-for perpetual motion has given birth; and it would not only be endless but ridiculous to attempt to give a detail of them all, especially as none of them deserve particular mention, since they have all equally proved abortive; and it would rather partake of the nature of an affront than a compliment, to distinguish the pretenders of this discovery, as the very attempting of the thing conveys a very unfavorable idea of the mental powers of the operator.

For among all the laws of matter and motion, we know of none which seems to afford any principle or foundation for such an effect. Action and reaction are allowed to be ever equal; and a body which gives any quantity of motion to another, always loses just so much of its own; but, under the present state of things, the resistance of the air, and the friction of the parts of machines, necessarily retard every motion.

To keep the motion going on, therefore, there must either be a supply from some foreign cause, which, in a perpetual motion, is excluded.

Or, all resistance from the friction of the parts of matter must be removed; which necessarily implies a change in the nature of things.

For by the second law of motion the changes made in the motions of bodies are always proportional to the impressed moving force, and are produced in the same direction with it; no motion, then, can be communicated to any engine, greater than that of the first force impressed.

But, on our earth, all motion is performed in a resisting fluid, namely, the atmosphere, and must, therefore, of necessity, be retarded; consequently, a considerable quantity of its motion will be spent on the medium. Nor is there any engine or machine wherein all friction can be avoided; there being in nature no such thing as exact smoothness or perfect congruity; the manner of the cohesion of the parts of bodies, the small proportion which the solid matter bears to the vacuities between them, and the nature of those constituent particles not admitting it.

Friction, therefore, will also, in time, sensibly diminish the impressed or communicated force; so that a perpetual motion can never follow, unless the communicated force be so much greater than the generating force as to supply the diminution occasioned by all these causes; but the generating force cannot communicate a greater degree of motion than it had itself. Therefore, the whole affair of finding a perpetual motion comes to this, viz., to make a weight heavier than itself, or an elastic force greater than itself; or, there must be some method of gaining a force equivalent to what is lost by the artful disposition and combination of the mechanical powers: to this last point then, all endeavors are to be directed; but how, or by what means such a force can be gained, is still a mystery!

The multiplication of powers or forces avails nothing; for what is gained in power is lost in time; so that the quantity of motion still remains the same.

The whole science of mechanics cannot really make a little power equal or superior to a larger; and wherever a less power is found in equilibrio with a greater—as, for example, twenty-five pounds with one hundred—it is a kind of deception of the sense; for the equilibrium is not strictly between one hundred pounds and twenty-five pounds moving (or disposed to move) four times as fast as the one hundred pounds.

A power of ten pounds moving with ten times the velocity of one hundred pounds would have equalled the one hundred in the same manner; and the same may be said of all the possible products equal to one hundred: but there must still be one hundred pounds of power on each side, whatever way they may be taken, whether in matter or in velocity.

This is an inviolable law of nature; by which nothing is left to art, but the choice of the several combinations that may produce the same effects.

The only interest that we can take in the projects which have been tried for procuring a perpetual motion must arise from the opportunity that they afford of observing the weakness of human reason.

For a better instance of this can scarcely be supplied than to see a man spending whole years in the pursuit of an object, which a single week's application to sober philosophy would have convinced him was unattainable. But for the satisfaction of those who may not be convinced of the impossibility of attaining this grand object, we shall add a few observations on the subject of a still more practical nature than the above.

The most satisfactory confutation of the notion of the possibility of a perpetual motion is derived from the consideration of the properties of the center of gravity; it is only necessary to examine whether it will begin to descend or ascend when the machine moves, or whether it will remain at rest. If it be so placed that it must either remain at rest or ascend, it is clear, from the laws of equilibrium, that no motion derived from gravitation can take place; if it may descend, it must either continue to descend forever with a finite velocity, which is impossible, or it must first descend and then ascend with a vibratory motion, and then the case will be reducible to that of a pendulum, where it is obvious that no new motion is generated, and that the friction and resistance of the air must soon destroy the original motion.

One of the most common fallacies by which the superficial projectors of machines for obtaining a perpetual motion have been deluded, has arisen from imagining that any number of weights ascending by a certain path on one side of the center of motion, and descending on the other at a greater distance, must cause a constant preponderance on the side of the descent; and for this purpose weights have been made to slide or roll along grooves or planes, which lead them to a more remote part of the wheel, from whence they return as they ascend, as represented in the following figure: Or they have been fixed on hinges which allow them to fall over at a certain point so as to become more distant from the center; but it will appear on the inspection of such a machine that although some of the weights are more distant from the center than others, yet there is always a proportionally smaller number of them on that side on which they have the greater power; so that these circumstances precisely counterbalance each other.

We have heard it proposed to attach hollow arms to a wheel by joints or hinges at the circumference, and to fill these arms with quicksilver or small balls instead of the plan represented by the above figure; but though we have never heard of it having been tried, we are perfectly convinced that it would end as all other attempts have done; that is, in a total failure.

The Possibility of Perpetual Motion Asserted

The enthusiastic earnestness with which the subject of Perpetual Motion was formerly discussed is illustrated by the fact that the Holy Scriptures were dragged in to support arguments on the proposition.

The following is a verbatim copy of an article published in an English scientific magazine in 1829:

"Notice to Perpetual Motion Seekers."—The following is a literal copy of a communication which we have received under this head. We publish it for the benefit of all concerned: "Perpetual Motion Seekers! see Coloss., ch. ii., v. 8—'Beware lest any man spoil you, through philosophy and vain deceit, after the tradition of men, after the rudiments of the world.' Ye are making the words of God of none effect by your traditions in publishing these things to the world. How can such toys and baubles as these be perpetual? See Malachi, ch. iv., v. 1—'For behold the day cometh that shall burn as an oven; and all the proud, yea, all that do wickedly, shall be as stubble.' Here is the end of them. I, the undersigned, have to inform the public, the model for making perpetual motion is to be found in that too much neglected book of models, the Bible. I called upon the Lord, and he showed it to me. I said, 'Lord, shall I show this unto them? This was the answer to me: See Isaiah, ch. xli., v. 29—'Behold, they are all vanity; their works are nothing.' I said, 'Lord, be pleased to show me some more about it.' 'Bring forth your strong reasons, saith the King of Jacob.'—Isaiah, ch. xli., v. 21. This was the answer: See Isaiah, ch. xli., v. 14—'Fear not, thou worm Jacob. * * Behold, I will make thee a new sharp threshing instrument having teeth; thou shalt thresh the mountains, and beat them small, and shall make the hills as chaff.' See also Jeremiah, ch. vii., v. 9—'The wise men are ashamed; they are dismayed and taken,' etc. See also Jeremiah, ch. ix., v. 12—'Who is the wise man that may understand this?' If there is not a wise and learned man who can show this, there is a deaf and unlearned man that will, by the blessing of God, set it forth to you. I am that deaf and unlearned man, George Lovatt, Stafford.

"P.S.—Mr. Editor: I have told you what I was commanded to do. See Ezekiel, ch. iii., v. 4 to the end. Now, see thou forget it not; let those models which come from the Word of God have the first place.—Joshua, ch. xxiv., v. 15."

John Bernoulli's Dissertation on Perpetual Motion

John Bernoulli was born in 1667, and died in 1748. He belonged to the famous Belgian family bearing the name. His family seems to have been peculiarly prolific in men of great genius for mathematics and science. Almost any encyclopedia with any pretense for thoroughness will mention and give the sketch of the life of from five to nine members of the Bernoulli family.

John Bernoulli possessed perhaps the greatest genius of any bearing the name for pure mathematics and pure mechanics. He was a contemporary of such men as Leibnitz, Euler and Newton, a co-laborer with the two former, but never conceded the merits of Newton. He was of a peculiar disposition, of intense likes and dislikes and among his peculiarities it may be mentioned that he harbored an unreasonable hatred toward a worthy and deserving son.

In 1742 he wrote a work entitled "Dissertation on Effervescence and Fermentation." To this work he added an appendix entitled "Concerning Artificial Perpetual Motion." The appendix translated into English and as published by Dircks, is as follows:

Scarcely had I finished this dissertation, when, attentively considering the nature of precipitation and secretion, briefly explained in the last pages, there accidentally occurred to me a mode of constructing, by means of some continually flowing liquid, the much-talked of and long-desired Perpetual Artificial Motion; and this as a completion to my work, on account of the affinity of the subject, I now propose for the consideration of the learned.

No one need be told how eagerly for a length of time this same Perpetual Motion has been sought after by the most celebrated men, how ardently desired; what indeed have they not contrived? To what expense have they not gone? How many machines have they not constructed? But all in vain.

The secret desire of this Perpetual Motion still perplexes and torments many, and excites their minds to such a degree that we see the ears and minds of learned men carried away by it; yet many philosophers reject the idea, unanimously asserting that Perpetual Motion cannot be communicated and cannot be invented; which opinion is nevertheless not of any weight, seeing that they rashly judge that no one should be listened to who boasts of having found out such a thing; and their reasons (as I confess) do not suffice to convince me; for I do not hesitate to assert not only that Perpetual Motion may be discovered, but that it has now actually been discovered, as will be confessed by any one who reads these lines; and what is this labor to many? does not Nature herself (who is never said not to operate by mechanical laws) indicate Perpetual Motion to be possible? To recall but one instance, what is the constant flux and reflux of the rivers and seas but Perpetual Motion? Does it not all belong to Mechanics? Therefore, you must confess that it does not exceed the limits of mechanical laws, and is not impossible; what then hinders that following Nature in this, we should be able perfectly to imitate her? as indeed I shall so conclude, by declaring to these the possibility of Perpetual Motion and the manner of obtaining it; and lest thou come to an adverse conclusion, or regard it as a Titanic enterprise, I pray that thou mayest first well weigh the thing, or, if it so please thee, put its truth to the test of experience.

First of all the following must be premised:

1. If there are two fluids of different density, the weights of which respectively are in the ratio G to L; the altitudes of cylinders of equal weight, and having the same base, will be in the ratio L to G.

2. Therefore, if the altitude AC of one fluid contained in the vessel AD to be the altitude EF of the other fluid contained in an open tube, as L to D; the fluids so placed will remain at rest.

3. Therefore, if AC to EF be in a greater ratio than L to G, the fluid in the tube will ascend; or if the tube be not sufficiently long, the fluid will escape by the orifice E. (These are proved by Hydrostatics.)

4. It is possible to have two fluids of different gravity, which are capable of being mixed one with the other.

5. It is possible to have a filter, strainer or other separator, by means of which the lighter fluid may be separated from the heavier.

Construction

These being pre-supposed, I construct Perpetual Motion in the following manner:

Let two fluids of different gravity and capable of mixing together (which is possible by Hyp. 4) be taken in any quantities, in equal quantities, if desired; let the ratios of their gravities be first determined, which suppose as G to L, the heavier to the lighter; and being mixed, let a vessel, AD, be filled to A.

This having been done, let a tube be taken, open at both ends EF; and of such a length that AC : EF > 2 L : G + L; and the orifice F stopped, or rather filled with a filter or some substance separating the lighter fluid from the heavier (as is possible also by Hyp. 5); when the tube filled in this manner with fluid is immersed to the bottom of the vessel CD; I say that the fluid will continually ascend by the orifice of the tube F, and by the orifice E will fall into the fluid below.

Demonstration

Because the orifice of the tube F is occupied by a filter (by Constr.) which separates the lighter fluid from the heavier; it follows, that if the tube be immersed to the bottom of the vessel, the fluid lighter by itself, which is mixed with the heavier fluid, must ascend in the tube, and as it will ascend above the surface of the surrounding fluid as AC : EF = 2 L : G + L : which is (by Const.) AC : EF > 2 L : G + L, it necessarily follows (by Hyp. 3) that the lighter liquid, through the orifice E, will fall in the vessel below; there it again mixes with the heavier (by Hyp. 4); and then, penetrating the filter, ascends again into the tube, and escapes by the upper orifice. So, therefore, the flow is continued perpetually.—Q.E.D.

Corollary

Hence a reason may easily be given, why water from the depths of the ocean, ascending into the summits of the mountains, bursts from them in the form of rivers and flows again into the ocean; so does Nature offer to us the spectacle of perpetual motion.

Hence I say, they do not well explain who allege that the water ascends to these heights through the pores of the earth, as a fluid ascends in narrow tubes above the surface of the fluid surrounding; for if such were the explanation of the thing, they would never be able to demonstrate it; for the water so raised to a height from the bosom of the earth, falls again, whereas we see that the fluid in these narrow tubes, although slightly elevated above the surrounding surface, never issues from their orifices and falls into the fluid below. The following is then the more feasible explanation. It is known that water in which much salt is held in solution is heavier than fresh water; now sea-water, as is sufficiently evident from the taste, contains many saline particles; consequently it is heavier than spring or river water; so that it is credible that the earth acts like a filter through the pores of which only fresh water can pass, the saline particles being left behind, and this increases the weight of the water; the fresh water must ascend much higher on account of the immense profundity of the ocean, as it is forced to the highest peaks of the mountains by the presence of the sea-water; and thence, not being able to ascend any higher, it falls in rivers.

P. Christopher Scheiner

That an earnest belief in the possibility of Perpetual Motion has not been confined entirely to scientific tyros and enthusiastic dreamers, is sufficiently attested by the fact that a respectable number of eminent scientists, many of whom had done great service in their scientific labors, have believed in such possibility.

Among these is to be mentioned P. Christopher Scheiner, a German, born 1575, and died 1650. He was a mechanic of note; in his day made valuable additions to what was known of light and optics, invented the Pantagraph, discovered solar spots, besides benefiting mankind by many other distinguished fruits of his genius.

The subject of Perpetual Motion claimed some of his attention. He wrote in defense of its possibility. The substance of what he said, translated into English, is as follows:

Let the centre of the universe then, or of gravity, be A, and the gnomon ABC, of which the extremity A is pierced and traversed by an axis going through the centre of the world, so that it may turn and revolve freely and easily around the said centre; to the other extremity of the gnomon, C, let a phial full of water be attached.

The weight C will turn around the centre A and will first come to D, thence to E, thence to F and G; then it will return to C, having described a complete circle, CDEFG; then it will again move to D, E, F, etc., and so perpetually, since there is no reason for its stopping in any point of the circle rather than in another.

That indeed the weight C affixed to the gnomon will move from C to D, is proved by daily experience, by which it is established that a gnomon so contrived and placed erect on any flat space, will not be able to stand, but the arm BC, C preponderating, will move towards D.

It may in the second place be proved, that if, on the other hand, another arm BG be added to the gnomon, equal in weight and similar to the other, the whole GBCA will remain motionless in equilibrium; therefore the arm BG being taken away and equilibrium being destroyed, the arm BC must move in the opposite direction.

The above, from Scheiner, called forth the following from Schott, who was also an eminent mathematician:

Whether there could be a perpetual artificial motion around the centre of the earth?

We have treated this question in our Hydraulico-pneumatic Mechanics, Part 2, Class 2, Machine 13, not however universally, but only in one particular case, that of the Gnomon of Scheiner. For P. Christopher Scheiner, in "Mathematical Disquisitions," in Number XV., Corollary 4, asserts Perpetual Artificial Motion not to be repugnant to Nature, and attempts to prove it in the following manner. Let a gnomon of a certain weight ABC be suspended around A, the centre of the universe, and bound to the beam D F, which is supported by the columns DF and EG and turns at the pole D or E; or let it be fixed at the poles, but the gnomon revolving at A.

These being the conditions, I say that the gnomon ABC will revolve from C to H and towards I, thence will return to C, thence to H as before, and so on perpetually. The cause of this continual motion is the forcible suspension; for the whole gnomon preponderates in C on account of the perpendicular tangent BA; which effect becomes more marked if a globe of iron S be supposed suspended at C. As therefore the whole of this mass, as well from the supports of the balance as from the momentary diameter, hangs suspended at C, and the vertex A, on account of the firm beam DE, cannot fall from the centre of the universe; it comes to pass that all points as well of the globe S, as of the gnomon ABC, with a continual motion turn round A; but because, by the line BA in the fixed point A, they are held from falling to the centre; therefore the greatest force of that tendency is exerted in the line B, and induces it to inclination; which inclination on account of the continuous solidity of the gnomon cannot be at all abated, so that the whole impetus is exerted either at the point A about the movable beam or at the movable poles of the beam D and E; which poles being free in their sockets D and E, abandon themselves to the motion of Nature, and thus do not in any wise hinder a perpetual circular motion. What indeed is self-evident in this, reason confirms, and daily experience in statics manifests. For if a short gnomon stand either on the terrestrial superficies MN, OP, or QR; it will always fall towards the part C, or N, by the preponderating portion MKC; which is manifested in daily experiments.

Thence it is evident that if the gnomon were entire, the force which it exerts at N would pass into the line BA still hanging over the centre. And this is one argument. The other is from the contrary. For if an equal and similar gnomon were attached towards the part D, then the whole mass hanging on its centre would remain in equilibrium and there would be no motion; consequently the one half being taken away, the other would necessarily move according to the laws and experience of statics. If the shortened gnomon MBCN were bound only to the point M, the rest being left free, it would certainly revolve, and in the same case, the point C would describe almost a semicircular arc till, coming down to a perpendicular position, it would there remain.

Now as the force of the entire gnomon falls in the vertex A, there would be an entire and perpetual revolution around A. Much more would this be the case if on the centre C stood either the small curve ACLA or the larger one AKC, or finally the globe S alone, hanging from two iron rods AB and BC, or from one arc, ANC. From this, therefore, it may be demonstrated that a perpetual circular motion is possible.

In 1825, the following was contributed to and published in "Mechanics' Magazine." We are unable to give the name of the contributor, but he writes in encouragement of Perpetual Motion. The gist of his article is as follows:

We can now, however, soar above the clouds, explore the depths of the ocean, and skim over its surface. * * * And be it remembered that we owe these and many other advantages to a few persevering individuals who were, in all probability, stigmatized as chimerical visionaries by those who seem to have an unconquerable propensity to condemn everything above the level of their own understanding.

If by perpetual motion nothing more is meant than the putting in motion some of the most durable substances with which we are acquainted, in such a manner as to ensure a continuance of motion as long as those substances will resist the effects of time and friction, I do not despair of seeing it accomplished. * * * [He thinks there is] reasonable ground to hope that the time is not far distant when even this impossibility must yield to persevering ingenuity. In the present state of public opinion with regard to its practicability, it would be looked upon as an empty boast, were I to assert that the discovery is already made.

T.H. Pasley

T.H. Pasley in 1824, contributed an article to "Mechanics' Magazine," asserting the possibility of Perpetual Motion. The following excerpts give the substance of his article:

I feel no hesitation in standing up in support of this grand desideratum,—this almost forsaken friend of science,—whether the thing be practicable or not.

On the contrary, "Persevere" should be every one's advice; to do so, or discontinue, every one's own pleasure. And why should the impossibility of anything be pronounced unless it be established wherein the limits of possibility consist?

It is puerile in the extreme to be foretelling defeat when so many other objects may be gained by the highly laudable pursuit, perhaps of greater advantage to society at large than the discovery in question. * * * In a word, were the perpetual motion discovered tomorrow, it would be wise of all the governments of the world to offer a very high reward for some species of discovery that would be universally sought after, although it might never be found out. * * * The effects of industry are—enlargement of the mind, accumulation of knowledge, and rendering ourselves ignorant of the torments which idleness and dulness always engender. * * * In the next place, there are no solid grounds for the assertion that the discovery of a perpetual motion is an impossibility. In the present state of human knowledge respecting the powers of nature, it is not demonstrable one way or another. * * * The study of what relates to the perpetual motion has this great advantage, that it directs to the discovery of error as well as of truth; whereas, what are they which are called truths of science at present but vacillating human opinions, or erroneous assumptions of what we call natural causes? What are they but such as consist in mere assumption, sanctioned by time, and admitted by existing authorities in science, and of course generally acquiesced in, without previous investigation?

So far, then, from being guided in our decision respecting what is possible by the "unerring laws of nature," by "mathematical demonstration," and by "experimental proofs," we are continually misled by an erroneous faith in the nonentity, attraction.

On such an imperfect knowledge of the causes of phenomena, who should say he knows what can or what cannot be discovered?

Article From Pamphleteer

In the "Pamphleteer," published in London, the following by a correspondent whose name we cannot give was published in March of 1822:

"A few words inducing towards the discovery of Perpetual Motion, perhaps the actual discovery thereof:"

London, March, 1822.

What is meant by the term "Perpetual Motion?" Is it supposed that there is an undiscovered substance in the world, that will of itself perpetually move, with as little apparent cause as that which actuates the needle in becoming motionless in one particular position? Or, is it to be found in the combined reaction of mechanical powers?

The first idea is stamped with a degree of probability, by the mystery of the needle; yet I imagine the latter is relied on with the greater confidence of mankind, and is the pith of the following few words:

It is well known that the weight of a pendulum will almost regain the level from which it descended, losing a little space at every vibration, until it becomes motionless; if of itself it could exceed or even regain the level, doubtless it would become a perpetual motion.

To find a power that will aid the motion of the pendulum, and in conjunction renew its strength, is what is wanted to create perpetual motion.

What I shall endeavor to explain will at least induce towards the discovery of this power.

The principal parts of the machinery about to be shown are in number three:

A vibrating pendulum.

A revolving pendulum, and

A tubular lever.

A vibrating pendulum in motion describes a segment of a circle, and returns on the same segment, and at every vibration its described segment decreases.

A revolving pendulum is composed of two or more pendulums, united at their lighter extremities, there revolving on an axis, the heavier extremities being placed at equal distances in the outer circle: this, I believe, is what is termed a fly-wheel when affixed to hand-mills, etc.

The tubular lever is the chief instigator of the whole, and must contain a weight apportioned to the weights of the two pendulums.

Fix the lever on a cross axis; thus, on an axis within a circle, the circle on an axis at opposite angles, thereby is given to each extremity of the lever a revolving power of motion; attach one extremity of the lever to the outer circle of a revolving pendulum, the other extremity confine within the bar of the vibrating pendulum; thus combined, the effect to be produced when put in motion will be this:

The two pendulums will guide the motion of the lever, which then partakes of the power of a pendulum, giving fresh impulse at every vibration of the pendulum, and every half revolution of the revolving pendulum; for, as each extremity of the lever rises, the weight within falls to the opposite extremity, and gives fresh impulse to the whole: thus (if my idea is correct) will be produced motion perpetual—that is to say, perpetual so long as the materials of which it is made will hold together. I have given this short description merely by way of example, as I believe there are several ways of combining these three powers, so as to produce perpetual motion, if my idea on the subject is correct.

The lever may contain mercury or a solid orb of heavy substance; and if the tube be exhausted of air the weight will pass more freely, and certainly increase the power of the lever.

J. Welch

In 1825 the following article was published in "Mechanics' Magazine," having been contributed by J. Welch:

Those who condemn the notion altogether seem to have taken but a very confined view of the subject. What they say about mere matter is right enough; but they seem to forget that there are other active agents in nature which possess wonderful powers, that have nothing to do with either bulk, weight, or form. Such are electricity, magnetic attraction, capillary attraction, and the irregular pressure of the atmosphere. The powers of electricity are great, and, indeed, it seems to be the primum mobile that gives life and motion to the animated part of the creation. Dr. Franklin shows us how to give a circular coated plate, revolving on an axle, sufficient power to roast a chicken, merely by once changing (charging?) it. Could not a plate of this kind be made to turn a small electrical apparatus, so situated as to keep the charge in the plate always at its maximum? The whole might be kept dry by having it enclosed in a glass case.

It has often been attempted to give motion to a wheel by the power of a loadstone, but hitherto without effect; no substance in nature being found to have the power, by interposition, of cutting off its attractive property. Still I think it should be further investigated. Is a small piece of steel in the form of a wedge as strongly attracted at the smaller end as at the thicker? And would not twenty or thirty pieces of steel, of that form, placed round the circumference of a circle, the point of one towards the head of the other, cause a magnet placed in the centre, to revolve in the direction in which their points lie? I think, perhaps not; but still such experiments should be tried.

In capillary attraction we have a power that at once raises fluids above their level. It is this which carries the oil up the wick of a lamp as fast as the flame consumes it. Water and other fluids rise through cotton even quicker than oil; and he who can contrive to collect them as they arrive at the top will discover perpetual motion. Would not water run constantly through a siphon, one leg of which was made of a collection of capillary tubes, and the other in the usual way? or would the water above and below the tubes neutralize and destroy their power?

I now come to the pressure of the atmosphere, a thing easily understood. * * * Make a cast-iron barometrical tube, with a top sufficiently large to contain 2 cwt. of mercury; invert it in a basin large enough to contain 2 or 3 cwt. more, and let a piece of iron of 10 or 12 stones weight float on the mercury in this basin, so as to rise and fall along with it at every change of the weather. We have here both motion and power. The motion, indeed, will sometimes stand still, but then it can easily be regulated, and made a constant quantity in the machine to be attached. I have no doubt but clocks, etc., may be made to derive their chiming principle from a contrivance of this nature.

Article From Mechanics' Magazine

In 1831, the following article was contributed by an unknown correspondent to, and published in "Mechanics' Magazine":

"Yes; we shall conquer! All those dangers past
Will serve to enrich the future story."

The application to the subject, on my part, has been accompanied by continual experimental elucidations of the subjects considered, and comparisons of these with the axioms, theorems, and demonstrations of one of the best authorities, if I may be allowed so to call my favorite author, Emerson, whose I says are generally correct.

I disagree with Mr. B., and do trust that even a perpetual motion seeker might deserve encouragement, if it be found that such a character may exist in a person who is not so ignorant of first principles as Mr. B. supposes all are who have this bias; especially if it be found that the person's researches have been connected with subjects of a more tangible nature, relating to the improvement of the useful arts, and particularly to some modern inventions of high importance that are not perfectly correct in their construction.

In this article, Mr. B. advises those who are misspending their time in this pursuit, to consider the question in its most simple form, divested of more complicated operations, which simple form is that of a pulley accurately constructed so as to reduce the resistance to motion as much as possible. He says, "it will be found, as long as the weights are equal," there will be no motion produced, but wherever the weights are placed they will remain; and to produce vertical motion in the smallest degree, it will be necessary to add a weight to one of the former to create a preponderancy. This weight he calls the mechanical loss, and an insurmountable bar to perpetual motion, etc. We need not follow Mr. B. to his conclusion, as I think this insurmountable bar can be easily removed; and I shall be able to show that this equilibrium, for such it merely is, can be destroyed without adding to one of the weights, or absolutely taking from the other; though this may virtually be considered to be the case, inasmuch as we can at least produce an effect on the system as if the weight were reduced. Mr. B. says, under this arrangement, "wherever the weights are placed they will remain, unless an addition is made to one of them." We will therefore suppose the following diagram to represent the arrangement on a small scale, delicately constructed.

AB are the two weights connected to each other by the string passing over the pulley, and being nicely equalized in their weight, here would, of course, be an equilibrium on the principle of the lever. But take a flat piece of wood, such as a ruler, and place it obliquely in a way so as not to interfere with the pulley m in the direction d, and then bring the weight to impinge upon it in a way so as not to move the weight A m, C d, the least, or alter its position. What will be the consequence? Some would say, why, the weight A would then descend, and cause the weight B to ascend. But I should rather say, the reaction of the plane when acted on by the weight B, having destroyed the equilibrium of the forces, motion takes place. Now, if we attribute this motion to the reaction of the plane on the weight, though we will not go so far as to say motion is generated, yet if we say, by this simple arrangement the equilibrium is destroyed and motion takes place, the least we can admit is, that motion is communicated to the system, and that by the agency of part of the machine itself, the apparatus employed being considered as such. Then, why so much objection to the term self-moving machine in limited sense? But I will not dispute about words, which are but the images of things, and images may be strangely distorted by the medium through which they are received—of which distorting mediums, there is none equal to that of prejudice in favor of abstract notions—which notions perhaps, if rigidly examined, would be found to have no foundation in facts or in common sense.

Another demonstrator of the impossibility of perpetual motion, is Mr. Mackinnon (see "Mechanical Magazine," Vol. 1, Page 363). As no doubt the different attempts to produce, or communicate, continued and perpetual motion, at least, such as are often brought forward by persons unacquainted with the science of mechanics, are generally to those who are acquainted with that science, if not absolutely ridiculous, yet of a nature to excite a smile at their futility: still there are a few (perhaps a very few) who entertain an opinion that such a thing is not impracticable, and who have, from practical experience as well as study, acquired a tolerable insight into the laws of nature (so far as relate to this subject); who in their turn cannot help smiling at the weak reasoning of some other would-be philosophers, who gravely give their dictum in the case. In this class I include Mr. Mackinnon, who very gravely goes to work to prove, etc., and flatters himself he shall, if rightly understood, help to prevent much future waste of time on the subject. He then goes on to give us his definition of inertia, by which he informs us that a body in a state of rest will remain so until it is moved (wonderful!)—that it cannot move itself—that it has not that power—and that no mechanical contrivance can give it that power. (How profound!)