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. 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 A B, 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 E F. 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 C D must always be directed answerable to A B, 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 C D, answerable to the axis A B.

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 A B 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 F B, then must the strength of it be sufficient to attract it immediately unto itself, when it is so much nearer as E B. 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, D C, 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.

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}
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}

[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 L M, at the bottom, does represent a wooden cylinder with helical cavities cut in it, which at A B is supposed to be covered over with tin plates, and three water-wheels upon it, H I K; the lower cistern, which contains the water, being C D. 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 εὕρηκα, εὕρηκα {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 A B represents a screw covered over, C D E one helix or revolution of it, C D the ascending side, E D the descending side, the point D the middle; the horizontal line C F 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, D G, is nothing near so much, and consequently not so heavy as the other, D C; 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 εὕρηκα, εὕρηκα {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.