Perpetual Motion

by Percy Verance; Henry Dircks

Energy

Energy is the capacity to do work, and the energy of a moving body is the amount of work it will do, i. e., the distance it will move against a resistance by virtue of its tendency to move, before being brought to a state of rest.

Now note, and note carefully, that the amount of energy is proportional to the mass, and to the square of the velocity.

Note this carefully: Any body in motion has both momentum and energy. Its momentum is proportional to its velocity; its energy to the square of its velocity. If the velocity be doubled, the momentum will be doubled, but its energy quadrupled. If the velocity be trebled, its momentum will be trebled, but its energy increased nine-fold.

It is important that the student get clearly what is meant by saying that Energy is the capacity to do work, and is proportional to the square of the velocity.

The capacity to do work means the capacity to move against resistance, i. e., to overcome resistance. The word "work" being used in a purely mechanical sense and in that sense it is used whether the result accomplished is destructive or beneficial.

A revolving fly wheel will run machinery for some time after the application of force has ceased. This is doing work, and represents energy.

A bullet fired from a gun will accomplish destruction before having its motion arrested. This is work—energy.

If a boy throw a ball into a snow bank, its motion will sink it into the snow, but not far, the resistance of the snow will soon bring the ball to rest. The ball overcomes resistance in passing through the snow until it is brought to rest, and thus it does the work of forcing itself through the snow, and possesses the energy necessary to do that work.

The overcoming of the resistance of the air by a moving body is work. A steamboat will move for some time in water after the steam has been turned off. The overcoming of the resistance of the water is work, and by virtue of the motion of the boat when the steam was turned off it possessed the energy to do the work of forcing itself for some time through the resistance of the water.

The Perpetual Motion worker in each case had reasoned himself into this conclusion: That the same energy will impart the same acceleration of velocity, regardless of the velocity at the beginning of the application of energy. That the same amount of energy or work necessary to impart to a body a velocity of ten feet per second will increase that velocity to twenty feet per second, or from twenty feet per second to thirty feet per second. In other words, that the same amount of energy, and only the same amount of energy is required for a given increase in velocity without regard to the initial velocity. This appears plausible, and almost self-evident. We believe the great majority of people, other than mechanical engineers would, upon presentation of the theory accept it as axiomatic, and as a matter of course. The fallacy becomes manifest only from a critical and technical examination of the Laws of Momentum and Energy.

The Perpetual Motion worker had learned from his text-books that if the velocity be doubled, the energy would be multiplied by four. His idea was to so arrange his mechanism that he would apply the amount of energy to move a fly wheel free to revolve, from a position of rest to a revolving velocity of ten revolutions per second. Then apply again the same amount of energy, and accelerate that velocity from ten revolutions per second to twenty revolutions per second. Thus, the energy at the end of the second second would be four times what it was at the end of the first second. But to make it so, only double the amount of energy had been applied that had been expended at the end of the first second. Thus, he reasoned, his machine was by virtue of its structure, accumulating energy, and this energy could be used one-half to continue the motion of his machine, and the other half to run other machinery, or for any other purpose for which energy might be desired.

Wherein lies the fallacy of this supposition?

We will now endeavor to explain. And for the young student to get the explanation fully, it will be necessary for him to pay the closest attention to what we here state.

A force, for instance the pressure of the finger or the hand, equal to one pound against a body free to move, will, we will say, move that body in one second of time through a space of ten feet, and at the end of that second the body will have a velocity of twenty feet. It is manifest that at the end of the second the velocity will be twenty feet per second for its initial velocity is zero, and its average velocity ten feet per second, the acceleration being, of course, presumed uniform.

Now, it is not true as the Perpetual Motion worker had assumed that the same energy—i. e., the same work that is required to increase the velocity from zero to ten feet per second will increase the velocity from ten feet per second to twenty feet per second, and in that assumption lay the fallacy of our friends who were thus seeking Perpetual Motion.

The greater the velocity, the more energy is required to impart a given acceleration. To increase the velocity from ten feet per second to twenty feet per second, the applied force must continue through one second of time, and more energy is required to follow a rapidly moving body, and continue to apply to it a given force for one second than would be required to follow and maintain the application of the same force to a body moving more slowly—the distance traveled is greater in one case than in the other.

It must be plain that if the moving body have a velocity at the end of the first second of twenty feet per second, it will, at the end of the second second, with the same pressure (force) continued against the same resistance, have a velocity of forty feet per second, and at the end of three seconds have a velocity of sixty feet, and at the end of four seconds a velocity of eighty feet, and so on.

Now, at the beginning of the second second it had a velocity of twenty feet, and at the end of that second a velocity of forty feet. It therefore, traveled through that second with an average velocity of thirty feet and, of course, during the second second traveled exactly thirty feet. It traveled ten feet the first second, and if it traveled thirty feet the second, then in the two seconds it traveled forty feet—four times as far as it traveled the first second. At the beginning of the third second it had a velocity of forty feet, and at the end of the third second a velocity of sixty feet. The average velocity then for the third second would be one-half the sum of forty feet and plus sixty feet—that is to say, it would be fifty feet, and that would be the distance traveled during the third second. The first second it traveled ten feet, the second second thirty feet, and the third second fifty feet, making a total in three seconds of ninety feet—that is to say, in three seconds it traveled nine times as far as in one second.

It will be noticed from the above that the velocity is proportional to the number of seconds, but that the distance traveled is proportional to the square of the number of seconds, and also proportional to the square of the velocity.

Momentum is mass multiplied by velocity; energy is measured by the distance through which a body will move against a given resistance.

Should you prop up one wheel of a carriage and revolve the wheel, then with the pressure of the finger or the thumb on the hub as a brake, stop it, it will be found that (omitting the effect of atmospheric resistance), the wheel will make four times as many revolutions before stopping with a doubled velocity; nine times as many with a trebled velocity.

Falling bodies afford the most perfect illustration of the principle of Momentum and Energy, and are so commonly used to illustrate those principles that many students get the idea that the application of those principles is confined to falling bodies, and do not realize that they extend generally through the field of mechanics.

A falling body is, of course, acted upon by gravity with uniform force equal to the weight of the falling body, and that force continues to follow the falling body and to be applied uniformly and equally, however slowly, or rapidly the body may be falling. And, omitting atmospheric resistance, the body is absolutely free to move except for its natural tendency to remain at rest, or at uniform velocity. It is well known that a body falls (almost exactly) sixteen feet in one second, and at the end of one second has a velocity of thirty-two. During the second second it falls through a distance of forty-eight feet, and during the third second a distance of eighty feet. In two seconds it falls sixty-four feet, and in three seconds one hundred twenty-eight feet, and so on. Thus, it will be observed that the velocity is proportional to the time during which it has fallen, but that the distance fallen in any number of seconds is proportional to the square of the time.

This, indeed, is a property of numbers, and results from mathematical law. If the reader will form a series of numbers, setting down any number for the first term of the series, adding to it its double for the second term, and adding to the second term double the first term for the third, and adding double the first term to the third term for the fourth, and so on—in other words, form any increasing arithmetical series with double the first term for the common difference, he will discover that the sum of all the terms is equal to the first term multiplied by the square of the number of terms. Thus:

1st Term	2nd Term	3rd Term	4th Term	5th Term
5	15	25	35	45

In the above series the sum of the first two terms is 20, which is 4 times the first term. The sum of the first three terms, i. e., 5 + 15 + 25 = 45-nine times the first term. The sum of the first four terms, i. e., 5 + 15 + 25 + 35 = 80, sixteen times the first term, and so on.

It will thus be seen that Momentum and Energy are entirely different, although co-related; that momentum relates to velocity, which includes the element of time, whereas energy relates to the amount of work done, and may be represented by a force operating against a certain resistance, through a certain distance, entirely irrespective of time. The energy is the same with the same force operating against the same resistance, through the same distance whether the time consumed be great or small. It takes as much energy in the aggregate to wind up a bucket from the bottom of the well if done slowly as if done quickly.

It would seem hardly necessary to do so, and yet it is worth while remarking that the amount of energy necessary to impart a given motion is exactly the amount of Energy that will be required to arrest that motion, and represents the amount of Energy possessed by the moving body by virtue of its motion. Work done, i. e., Energy applied in giving motion is there in that motion, ready to be returned in exactly an equal quantity—no more—no less.

In all the considerations in this chapter no notice is taken of loss by friction or atmospheric resistance. We are considering pure mechanics and the laws governing them only. In actual mechanical devices it is always necessary to make allowance for atmospheric, frictional and other unavoidable resistances.

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[CHAPTER X]
The Alleged Inventions of Edward Sommerset, Sixth Earl and Second Marquis of Worcester, and of Jean Ernest Eli-Bessler (Councillor) Orffyreus

More interest has been taken, and more has been said and written concerning the claimed inventions of the men forming the subject of this chapter than of all other Perpetual Motion devices known to history. The reason is not difficult to explain. It was the rank and eminence of the inventors and of others whom they induced to take an interest in their inventions, and to proclaim them to the world. Intrinsically, neither their claims nor their devices are entitled to any more notice than are those of the humblest mechanic that ever labored to attain Perpetual Motion. However, so much has been said and written concerning them that they have an historical value and interest. Then, too, the interest taken in their inventions brought forth some splendid discussions which necessarily involve in a general way, at least, the entire question of Self-Motive Power. The historical interest attaching to their inventions and the discussions concerning them, entitles them to more than a passing notice in this book.

They were not co-laborers; they were not even compatriots, nor contemporaries. Worcester was an Englishman and Orffyreus a Frenchman, though most of his labors were in what is now Germany. The former died thirteen years before the latter was born.

Edward Sommerset, of England, Sixth Earl and Second Marquis of Worcester, was born in the year 1601, and died in 1667. He was famous not only for his noble birth and family rank, but for personal attainments. He was the author of a work entitled "Century of Names and Scantlings of Such Inventions as at Present I Can Call to Mind Have Tried and Perfected" (1663), which has often been reprinted, and is usually referred to simply as "Century Inventions." He was very prominent in public life; was greatly interested in mechanical experiments, and made valuable suggestions, inventions and improvements in connection with the use of steam as a motive power.

Henry Dircks, who is so frequently mentioned in this book, wrote a book which was published in 1865, entitled "Life, Times and Scientific Labors of the Second Marquis of Worcester." The Marquis appears to have been all his life greatly interested in science, mechanics and mathematical contrivances. His first wife died in 1635, and it seems probable that thenceforth he became and remained more than ever devoted to mechanics, and sometime after that period announced a successful Perpetual Motion machine, the gist of all known information concerning which appears from the articles and discussions hereinafter set forth in this chapter.

Jean-Ernest Eli-Bessler (Councillor) Orffyreus was born in 1680, near Zittan, Alsace, France. He was a man of great ability and attained an eminent place in public life. The title "Councillor," he acquired by having been selected Councillor to the Prince of Hesse Castle. The best information concerning him indicates that he was of very erratic temperament, given to fits of melancholy and extreme anger. In early life he was a student of theology and medicine, but his penchant was really for mechanics. He claimed that in his search for whatever might prove curious and valuable he had discovered Perpetual Motion, and that between the years 1712 and 1719 he had made two successfully working machines on his system. The following discussions disclose all that is known of the claimed inventions of these two distinguished Perpetual Motion workers.

The alleged inventions of the Marquis of Worcester is stated by him in the 56th article of his book entitled "Century of Names and Scantlings of Such Inventions as at Present I Can Call to Mind to Have Tried and Perfected," and translated from the ancient English style in which his book is written into modern style of English, reads as follows:

The inventor offers the accompanying sketch, with description of an Hydraulic Mover, for communicating power to machinery, and recently invented by him:—

"To provide and make that all the weights of the descending side of a wheel, shall be perpetually farther 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 of Hamilton, with most of the Court attending him. The wheel was fourteen foot over, and had forty weights of fifty pounds apiece. Sir William Balfore, 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 farther from the center; nor no sooner passed the diameter line of the upper side, but they hung a foot nearer. Be pleased to judge of the consequence."

In October of 1719, Orffyreus published a small book, or pamphlet, both in German and Latin, entitled "Perpetual Motion Triumphant, by Orffyreus." The book commences:

It is a notorious fact that Perpetual Motion has not only been sought after by ingenious mathematicians and artists with more or less expense, but many have arisen here and there pretending that they have made the discovery. Nevertheless, it appears that to carry out this most subtle mechanical idea, namely, to make a dead material not only move itself, but lift weights and perform work, even the most profound mathematicians and the most learned people have continually fallen into error. It is no less notorious that those who have so sought, not only refuse their consent, but have set their seal on the discovery as an unsolvable problem.

On a subsequent page he proceeds thus:

When I, at last, an unworthy man, was made an instrument in God's hands to solve this long-looked-for and valuable secret, and to give a representation, proposition and instruction on this rare invention; also to publish and propound it to all the world, no longer do I doubt, nay I presume, that as the discoverer I possess it, after many years of scrupulous doubts, much calumny and exasperation from all my enemies.

He speaks of his opponents under four divisions: First, the scientific world; second, persons in high authority; third, the public in general; and fourth, the press;—observing—

Now my wish was to convince the world that this illiberal, rude and inhuman treatment was false, yet God's providence has brought to my help, protection and succour the mighty Prince Lord Charles, Landgrave of Hesse.

On a subsequent page he indulges in the following sycophantic adulation of the Prince of Hesse Castle, and suggestion of the description of his claimed device:

It has not only pleased this mighty Prince to protect me against my numerous enemies, but also to give me house-room in his princely Castle of Weissenstein, near Cassel; to name me one of his most honored servants, and restore me in a measure all the honor and means that I had lost in my native country; wishing no doubt to give to Hessin Cassel the high honor which belonged to Saxony by right. In gratitude for all these gracious acts, I consented to give another example of my Perpetuum Mobile machine. I put all in fresh order, and began work in all possible haste, doing everything in the manner of those I had already made and destroyed, with only a few changes in the dimensions of the so-named turning-wheel. For as a grindstone may be called a wheel, so may the principal part of my machine be named. The outward part of this wheel is drawn over or covered with waxed linen in the form of a drum. This cylindrical basis was 12 Rhenish feet in diameter, the thickness from 15 to 18 inches, the middle axle 6 feet long and 8 inches in thickness. It is supported in its movement on two pointed steel balance-pegs, each 1 inch thick; and the wheel is vertically suspended. The movement is modified by two pendulums, as shown in the engraving at the end of this book. The inward structure of the wheel is of a nature according to the laws of mechanical perpetual motion, so arranged that by disposed weights once in rotation they gain force from their own swinging, and must continue their movement as long as their structure does not lose its position and arrangement. Unlike all other automata, such as clocks or springs or other hanging weights which require winding up or whose duration depends on the chain which attaches them, on the contrary, these weights are the essential parts and constitute perpetuum mobile itself; as from them is received the universal movement which they must exercise so long as they remain out of the center of gravity; and when they come to be placed together, and so arranged one against another that they can never obtain equilibrium, or the punctum quietus which they unceasingly seek in their wonderous speedy flight, one or other of them must apply its weight vertically to the axis, which in its turn will also move.

The author and inventor then suggests the following uses of his machine: "raising weights, raising stampers, water," etc. He criticises all critics of his scheme and denounces them as cunning rogues, and fools who are contemptibly endeavoring to overthrow an incontestable fact. He makes a quadrupled dedication of his device:

• 1. To God,
• 2. To the Public in General,
• 3. To Men of Learning,
• 4. To Himself as Discoverer,

and he very modestly suggests a method by which he could be approached on the subject of selling the secret of his machine for one hundred thousand rix-thalers, and points out the great importance to the public of such an acquisition. The book contains a cut of his device with the following very brief explanation:

Number 1 shows the entire size of the wheel; 2, a cord wound round the principal axle; 3, the wheel or pulley to guide the cord; 4, the cord passed through a window and over 5, another pulley; 6, the box of stones raised or lowered; 7, the lock to prevent motion; 8, the pendulum with three weights; 9, a winch-handle acting on the pendulum; and 10, shows above and below transparent, so that the machine stands clear and can be moved about.

In 1720 the following article was contributed to and published in the "Gentleman's Magazine," concerning the Orffyrean Wheel:

Mr. Urban: Being an admirer of improvements in mechanics and desirous of seeing the perpetual motion discovered, I was much pleased on reading, some time ago, an account of the automaton constructed by Orffyreus in two letters, one from Professor 's Gravesande to Sir Isaac Newton, the other from Baron Fischer to Dr. Desaguliers, with the testimonial of the Landgrave of Hesse-Cassel (who had seen the inside of it) in favor of its construction. To which are added some remarks by William Kenrick, the writer of the pamphlet, who takes that opportunity to propose a subscription for a similar machine, which he says he has contrived and denominated a Rotator.

It is much to be lamented that the learned did not examine more strictly into the merit of Orffyreus's wheel; but, on the contrary, being prepossessed with a notion of the impracticability of the perpetual motion, suffered it to be neglected, and at last destroyed by the hands of a disappointed mechanic, who, with unwearied application and steady perseverance, had brought it to perfection. I wish we may not again let slip an opportunity of becoming acquainted with an invention, which, when made public, will reflect honor on the inventor, and be of the utmost utility to the world. Such, I would hope, is the rotator mentioned by W. Kenrick; for, unless his discovery were real, I cannot think that he would have taken the liberty to express himself as he does in p. 26, etc., "The inventor flatters himself that, if the contents of the foregoing pages are seriously attended to, and it be farther considered, that not a penny of the proposed premium is required, till the subscribers are fully satisfied of the reality and utility of the invention, his proposal will not be treated with so mortifying a neglect as that of Orffyreus." Again he says, "If it does not supply the place of a first mover, at the expense only of the construction and repair of a simple wheel subject to very little friction, and that in all such engines and machines, even from the slightest piece of clockwork to the waterworks of Marli or London-bridge, he expects nothing for his discovery, but to stand exposed to the contempt that will be justly thrown on him for having so miserably misspent his time, and frivolously engaged the attention of the public."

Now, I think that W. Kenrick's proposals are very fair; and should be glad to be informed, whether any attention has been paid to them, and whether Sir Isaac Newton took any notice of the letter addressed to him by Professor Gravesande. I shall consider it as a favor if any correspondent will oblige me with an answer to these particulars.

A Constant Reader.

In 1721 Rev. Dr. J. T. Desaguliers, LL.D., F.R.S., contributed to an English periodical entitled "Philosophical Transactions," the following article concerning the device of the Marquis of Worcester, and the Orffyrean Wheel:

REMARKS ON SOME ATTEMPTS MADE TOWARDS A PERPETUAL MOTION; BY THE REVEREND DR. DESAGULIERS, F.R.S.

The wheel at Hesse-Cassel, made by Monsieur Orffyreus, and by him called a perpetual motion, has, of late, been so much talked of on account of its wonderful phenomena, that a great many people have believed it to be actually a self-moving engine; and accordingly have attempted to imitate it as such. Now, as a great deal of time and money is spent in those endeavours, I was willing (for the sake of those that try experiments with that view) to show that the principle which most of them go upon is false, and can by no means produce a perpetual motion.

They take it for granted that if a weight descending in a wheel at a determined distance from the center, does, in its ascent, approach nearer to it; such a weight in its descent will always preponderate and cause a weight equal to it to rise, provided it comes nearer the center in its rise; and accordingly as itself, rises, will be overbalanced by another weight equal to it; and, therefore, they endeavour by various contrivances to produce that effect as if the consequence of it would be a perpetual motion.

But I shall show that they mistake one particular case of a general theorem, or rather a corollary of it, for the theorem itself. The theorem is as follows:

Theor.—If one weight in its descent does, by means of any contrivance, cause another weight to ascend with a less momentum or quantity of motion than itself, it will preponderate and raise the other weight.

Cor. 1.—Therefore, if the weights be equal, the descending weight must have more velocity than the ascending weight, because the momentum is made up of the weight multiplied into the quantity of matter.

Cor. 2.—Therefore, if a leaver or balance have equal weights fastened or hanging at its ends, and the brachia be ever so little unequal that weight will preponderate which is farthest from the center.

Scholium.—This second corollary causes the mistake; because those who think the velocity of the weight is the line it describes, expect that that weight shall be overpoised, which describes the shortest line, and, therefore, contrive machines to cause the ascending weight to describe a shorter line than the descending weight. As for example, in the circle A D B a (Fig. 3) the weights A and B being supposed equal, they imagine that if (by any contrivance whatever) whilst the weight A describes the arc A a, the weight B is carried in any arc, as B b, so as to come nearer the center in its rising than if it went up the arc B D; the said weight shall be overpoised, and consequently, by a number of such weights a perpetual motion will be produced.

This is attempted by several contrivances, which all depend upon this false principle; but I shall only mention one which is represented by Fig. 4, where a wheel having two parallel circumferences, has the space between them divided into cells, which being curved, will (when the wheel goes round) cause weights placed loose in the said cells to descend on the side A at the outer circumference of the wheel, and on the side D to ascend in the line B b b b, which comes nearer the center and touches the inner circumference of the wheel. In a machine of this kind the weights will indeed move in such a manner if the wheel be turned round, but will never be the cause of the wheel's going round. Such a machine is mentioned by the Marquis of Worcester in his "Century of Inventions," in the following words, No. 56:

"To provide and make that all the weights of the descending side of a wheel shall be perpetually farther 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 of Hamilton, with most of the court attending him. The wheel was fourteen foot over and had forty weights of fifty pounds a piece. Sir William Balfore, 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 farther from the center; nor no sooner passed the diameter line of the upper side, but they hung a foot nearer. Be pleased to judge of the consequence."

Now the consequence of this and such like machines, is nothing less than a perpetual motion; and the fallacy is this: The velocity of any weight is not the line which it describes in general, but the height that it rises up to or falls from, with respect to its distance from the center of the earth. So that when the weight (Fig. 3) describes the arc A a, its velocity is the line A C, which shows the perpendicular descent (or measures how much it is come nearer to the center of the earth), and likewise the line B C denotes the velocity of the weight B, or the height that it rises to when it ascends in any of the arcs B b, instead of the arc B D: so that in this case whether the weight B in its ascent be brought nearer the center or not, it loses no velocity which it ought to do in order to be raised up by the weight A. Nay, the weight in rising nearer the center of a wheel may not only lose of its velocity, but be made to gain velocity in proportion to the velocity of its counterpoising weights that descend in the circumference of the opposite side of the wheel; for if we consider two radii of the wheel, one of which is horizontal, and the other (fastened to and moving with it) inclined under the horizon in an angle of 60 degrees (Fig. 5) and by the descent of the end B of the radius B C, the radius C D by its motion causes the weight at D to rise up the line p P, which is in a plane that stops the said weight from rising in the curve D A, that weight will gain velocity, and in the beginning of its rise it will have twice the velocity of the weight at B; and consequently, instead of being raised, will overpoise, if it be equal to the last mentioned weight. And this velocity will be so much the greater in proportion as the angle A C D is greater, or as the plane P p (along which the weight D must rise) is nearer to the center. Indeed, if the weight at B (Fig. 3) could, by any means, be lifted up to β, and move in the arc β b, the end would be answered; because then the velocity would be diminished and become β C.

Experiment (Fig. 5).—Take the leaver B C D, whose brachia are equal in length, bent in an angle of 120 degrees at C and moveable about that point as its center: in this case a weight of two pounds hanging at the end of B of the horizontal part of the leaver will keep in equilibrio a weight of four pounds hanging at the end D. But if a weight of one pound be laid upon the end D of the leaver, so that in the motion of D along the arc p A, this weight is made to rise up against the plane P p (which divides in half the line A C equal to C B) the said weight will keep in equilibrio two pounds at B, as having twice the velocity of it when the leaver begins to move. This will be evident, if you let the weight 4 hang at D, whilst the weight 1 lies above it: for if then you move the leaver the weight 1 will rise four times as fast as the weight 4.

"To provide and make that all the weights of the descending side of a wheel shall be perpetually farther 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 of Hamilton, with most of the court attending him. The wheel was fourteen foot over and had forty weights of fifty pounds a piece. Sir William Balfore, 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 farther from the center; nor no sooner passed the diameter line of the upper side, but they hung a foot nearer. Be pleased to judge of the consequence."

In 1770 Dr. William Kenrick published "A Lecture on the Perpetual Motion." In it he has the following to say concerning the alleged inventions of the Marquis of Worcester, and Councillor Orffyreus, and Perpetual Motion in general. The following excerpts of and comments on the lecture are taken verbatim from Dircks:

The mere exhibition of a self-moving machine without a display of its mechanism, or the principles on which its motion is begun and continued, could produce no conviction. The fate of Orffyreus and his machine is a proof of this. Scarce fifty years ago that whimsical mechanician exhibited a perpetual motion at Hesse Cassel, the constancy of whose operation was experienced for many weeks under the most exact caution of the Landgrave of that Principality, whose testimony of such operation, as well as in favor of its construction (to the secret of which he was admitted), was given in the most explicit and determinate form. And yet, because Orffyreus could not display the mechanism without the previous assurance of a premium of 200,000 florins (near twenty thousand pounds), or because he would not or could not discover the principles on which it acted, his pretensions were neglected, his machine was destroyed by his own hands, and his life made a sacrifice to the chagrin attending his disappointment. Twenty years had he racked his brains for invention, and expended a patrimonial competence with parsimony in prosecuting his design. And when success inspired the hope of reward, he found his ingenuity suspected of imposture, and his industry rewarded with contempt.

Whether any of his successors in the same pursuit will meet with a better fate is at length to be determined. One species of our predecessor's merit, however, I (adds Dr. Kenrick) presume myself at least entitled to, that of perseverance; it being now fifteen years since I first engaged in this undertaking, which I have since pursued with almost unremitted assiduity, and that not only at a considerable waste of time and expense, but under the constant mortification of hearing it equally ridiculed by those who do know, and by those who do not know, anything of the matter.

It is, indeed, generally supposed, and as confidently affirmed, that the mathematicians have published demonstrations of the impossibility of a perpetual motion. But I can safely take upon me to affirm that no such demonstration was ever published by any. Within these twelve years past the mathematicians who deny the possibility of a perpetual motion have been repeatedly and publicly called upon, both in the foreign and English prints, to produce a single instance of these demonstrations. They have not done it. They might have produced, indeed, the demonstrations of Huygens, De la Hire, and others to prove, as Desaguliers very properly expresses it the fallacy of the schemes of most of the pretenders to the perpetual motion. They proved nothing more; and this was so far unnecessary in that the fallacy evidently appeared in the discovery of the principle on which they were founded.

This was done in the last century by the celebrated Marquis of Worcester, in the presence of the King and his Court, at the Tower, by the exhibition of a wheel so contrived that in revolving on its axis it carried up several weights nearer its center on one side than they descended on the other. The scheme was plausible and to appearance practicable; but, though the wheel was polite enough to turn about while his Majesty was present, it could not be prevailed upon to be so complaisant in his absence. The mathematicians avenged themselves of the short triumph of the mistaken Marquis, but were equally mistaken themselves in thinking they had routed the problem or that in hunting down the jackal they had destroyed the lion. The perpetual motion survived; it had still its advocates; Professor Gravesande and John Bernouille maintained its practicability, the former giving his testimony in favor of Orffyreus's machine, after a long and scrutinous examination. It is not twelve years since this testimony was republished by Dr. Allaman, the present Professor of Natural Philosophy at Leyden, whose own opinion, given at the same time, is also greatly in favor of the discovery. It is even some years later that a dissertation still more in its favor, written, if I am not mistaken, by the celebrated De Gorter of Petersburg, appeared in the "Philosophical Transactions" of Haarlem. My end is not to amuse or persuade, but, with due deference, to inform and convince. To remove every cause of objection, I must beg leave to expatiate somewhat at large on the theory of this discovery. It is with the more propriety I presume on this method, as the discovery to which I pretend has not been (as frequently happens) the effect of mechanical accident, but the premeditated result of mathematical reasoning and physical experiment. I shall proceed to elucidate the principal arguments a priori, that prove the practicability of a perpetual motion to be the necessary consequence of the known and established laws of nature.

Having proceeded thus far, he opens his lecture at page 7 with the introduction; and first "On the Nature of Motion in General," which, in fourteen pages, being more metaphysical than mechanical, affords no extractable matter for our present object. Part I is "On the Cause and Effect of Motion." This elementary part is needlessly labored and elaborated through 27 pages. In the course of his remarks he states:

The discovery of a perpetual motion, says De la Hire, would be to discover a body at once heavier and lighter than itself. But this is not a fair state of the question. It is not necessary that all the parts of a perpetually-moving machine should be attached to, and inseparable from each other; which they must be, to constitute one gravitating body of a determinate weight.

He proceeds to consider the nature of the circulation of the blood, pneumatic pressure, the steel-yard, real and relative weight, and spiral action. Again, we have Hobbes, Locke, and Stewart, in the same sentence with such language as—"I could almost as readily impute ingenuity to vegetables and fossils—to the sensitive plant and the loadstone—as mediation to muscles, or cogitabundity to cockles, periwinkles and rock oysters!" In conclusions he says:

I have endeavoured to make it appear that motion is the mechanical effect of the physical action of the primary elements; that the direction of motion only comes within the province of animal intellect; that the vital system is supported by mere mechanic motion, kept up by the elasticity of the solids and the gravity of the fluids composing the animal body; that by the same means a more simple inanimate system or machine may be framed which may have the same property of continued action (or, as it is called, self-motion). And this is all that is, or can be, expected of a perpetual motion; the momentum of which may be increased to any degree, according to the weight of the bodies employed and the work required to be done.

The second part of this lecture commences with a Proem of thirteen pages:

I am induced (he says) to trespass farther by extending in like manner the subsequent divisions of it; making the second and third parts of my printed syllabus the topics of the present reading, and reserving the last part, with the concluding experiment, to the third and final lecture.

I pretend merely to the investigation of the general principles of mechanics, and even to illustrate these so far only as I conceive they relate to the immediate object of my lecture, the discovery of an artificial perpetual motion; leaving the application of such principles, in the solution of particular phenomena, or the construction of particular machines, to such as make the different arts and sciences their peculiar study.

He very prudently ends, observing:

But I beg pardon, gentlemen, for the length of this digressive introduction, and shall proceed to the more immediate subject of my lecture.

Section 1 of this lecture is "On the Composition and Combination of Motion." After discussing, in his own peculiar style, mechanical principles of motion, he adds:

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

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

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

The lectures appear to have been illustrated by a plate having two figures of a simple apparatus used to demonstrate the action of a spring and two unequal weights; also an inflexible ruler suspended between two unequal balls—with both he experimented before his auditors; but the engraving is wanting in the edition now used. In conclusion, he observes:

You see, gentlemen, I am purposely provided here with a very simple and clumsy apparatus. The perpetual motion does not need the assistance of friction wheels, or depend on the niggling nicety of tooth and pinion. If the practical part of my discovery be not superior to the manual dexterity of a village carpenter or country smith, I am satisfied. There will be no great discernment required to comprehend the design they are to put in execution. You will permit me, however, at present, to defer what I have farther to offer on the subject to another opportunity.

In 1770 Dr. Kenrick published a quarto-pamphlet concerning the Orffyrean Wheel, and in the pamphlet appears the following regarding a letter from Prof. Gravesande to Sir Isaac Newton, and a letter from Baron Fischer to Dr. Desaguliers:

A Letter from Professor 's Gravesande to Sir Isaac Newton, Concerning Orffyreus's Wheel

Sir: Doctor Desaguliers has doubtless shown you the letter that Baron Fischer wrote to him some time ago about the wheel of Orffyreus; which the inventor affirms to be a perpetual motion. The landgrave, who is a lover of the sciences and fine arts, and neglects no opportunity to encourage the several discoveries and improvements that are presented him, was desirous of having this machine made known to the world, for the sake of public utility. To this end he engaged me to examine it; wishing that, if it should be found to answer the pretensions of the inventor, it might be made known to persons of greater abilities, who might deduce from it those services which are naturally to be expected from so singular an invention. You will not be displeased, I presume, with a circumstantial account of this examination; I transmit you, therefore, a detail of the most particular circumstances observable on an exterior view of a machine, concerning which the sentiments of most people are greatly divided, while almost all the mathematicians are against it. The majority maintain the impossibility of a perpetual motion, and hence it is that so little attention has been paid to Orffyreus and his invention.

For my part, however, though I confess my abilities inferior to those of many who have given their demonstrations of this impossibility; yet I will communicate to you the real sentiments with which I entered on the examination of this machine. It is now more than seven years since I conceived I discovered the paralogism of those demonstrations, in that, though true in themselves, they were not applicable to all possible machines; and have ever since remained perfectly persuaded it might be demonstrated that a perpetual motion involved no contradiction; it appearing to me that Leibnitz was wrong in laying down the impossibility of the perpetual motion as an axiom. Notwithstanding this persuasion, however, I was far from believing Orffyreus capable of making such a discovery, looking upon it as an invention not to be made (if ever) till after many other previous discoveries. But since I have examined the machine, it is impossible for me to express my surprise.

The inventor has a turn for mechanics, but is far from being a profound mathematician, and yet his machine has something in it prodigiously astonishing, even though it should be an imposition. The following is a description of the external parts of the machine, the inside of which the inventor will not permit to be seen, lest any one should rob him of his secret. It is a hollow wheel, or kind of drum, about fourteen inches thick and twelve feet diameter; being very light, as it consists of several crosspieces of wood framed together; the whole of which is covered over with canvas, to prevent the inside from being seen. Through the center of this wheel or drum runs an axis of about six inches diameter, terminated at both ends by iron axes of about three-quarters of an inch diameter upon which the machine turns. I have examined these axes and am firmly persuaded that nothing from without the wheel in the least contributes to its motion. When I turned it but gently, it always stood still as soon as I took away my hand; but when I gave it any tolerable degree of velocity, I was always obliged to stop it again by force; for when I let it go, it acquired in two or three turns its greatest velocity, after which it revolved for twenty-five or twenty-six times in a minute. This motion it preserved some time ago for two months, in an apartment of the castle: the door and windows of which were locked and sealed so that there was no possibility of fraud. At the expiration of that term indeed his serene highness ordered the apartment to be opened, and the machine to be stopped, lest, as it was only a model, the parts might suffer by so much agitation. The landgrave being himself present on my examination of this machine, I took the liberty to ask him, as he had seen the inside of it, whether after being in motion for a certain time no alteration was made in the component parts; or whether none of those parts might be suspected of concealing some fraud: on which his serene highness assured me to the contrary, and that the machine was very simple.

You see, sir, I have not had any absolute demonstration, that the principle of motion which is certainly within the wheel, is really a principle of perpetual motion; but at the same time it cannot be denied me that I have received very good reasons to think so, which is a strong presumption in favor of the inventor. The landgrave hath made Orffyreus a very handsome present, to be let into the secret of the machine, under an engagement nevertheless not to discover, or to make any use of it before the inventor may procure a sufficient reward for making his discovery public.

I am very sensible, sir, that it is in England only the arts and sciences are so generally cultivated as to afford any prospect of the inventor's acquiring a reward adequate to this discovery. He requires nothing more than the assurance of having it paid him in case his machine is found to be really a perpetual motion; and as he desires nothing more than this assurance till the construction of the machine be displayed and fairly examined before such assurance be given him. Now, sir, as it would conduce to public utility as well as to the advancement of science, to discover the reality or the fraud of this invention, I conceive the relation of the above circumstances could not fail of being acceptable. I am, etc.

In the same book appear the following animadversions by Prof. Allaman, on the neglect of Orffyreus's invention:

We see that the testimony of M. 's Gravesande was as advantageous as possible to Orffyreus, not having seen the interior of the machine, he could form no other judgment; however, that extraordinary man was not contented, for in consequence of the examination Orffyreus broke the machine into pieces. By the accounts of M. 's Gravesande, Baron Fischer and the testimony of the Landgrave it appears clear that the wheel was not moved by any exterior agent. Orffyreus is, however, accused of being an impostor, of having imposed on the good faith of the prince, deceived M. 's Gravesande and all those who examined his machine. His own servant deposed against him and said that she was made to turn the wheel, and thus he has fallen into contempt; and everyone who protected him, is ashamed of him. M. de Crousaz, who was at that time at the court of Cassel, writes a letter to M. 's Gravesande dated February 3, 1729, in these terms:—'First, Orffyreus is a fool; Second, It is impossible that a fool can have discovered what such a number of clever people have searched for without success; Third, I do not believe in impossibilities; Fourth, One can easily imagine that persons keep a secret from which they are to receive benefit, but this fellow, hoping only to receive reputation, allows it to be tarnished by an accusation which he has in his power to disprove, if false; Fifth, The servant who ran away from his house, for fear of being strangled, has in her possession, in writing, the terrible oath that Orffyreus made her swear; Sixth, He only had to have asked, in order to have had this girl imprisoned, until he had time to finish his machine; Seventh, They publish that the machine is going to be exhibited, when suddenly those who advertise it become silent; Eighth, It is true there is a machine at his house, to which they give the name of perpetual motion, but that cannot be removed; it is much smaller, and differs from the first, inasmuch as it only turns one way.

This is what makes Orffyreus and his machine to be suspected; can it be that M. 's Gravesande was so mistaken as to be his dupe? Let us read what he himself says in answer to M. Crousaz, which I have found among my papers, without date:—"I have deferred replying to you until I had found a paper which I wrote the day after I examined Orffyreus' machine, for although I remember well all that passed, I believe that a paper, written the day after the examination, and communicated to my Lord and all those who were with him, must have more weight.

"This is what I heard; they say that a servant under oath, turned Orffyreus' machine, being placed in an adjoining room.

"I know well that Orffyreus is a fool, but I ignore that he is an impostor; I have never decided whether his machine is an imposture or not, but this I know as certainly as anything in the world, that if the servant says the above, she tells a great falsehood.

"My Lord the Landgrave in the presence of the Baron Fischer, Architect of the Emperor, and other persons at my request, showed the supports of the machine; we saw the axles uncovered; I examined the plates or brasses on which the axles rested and in that examination there did not appear the slightest trace of communication with the adjoining room. I remember very distinctly the whole of the circumstances of that examination, which put Orffyreus in such a rage with me, that the day after he broke his machine in pieces, and wrote on the wall that, it was the impertinent curiosity of Professor 's Gravesande which was the cause. I read this myself the following year, and the result of the examination is clearly explained in the paper of which I spoke to you.

"They told me several circumstances on the testimony of the servant, but I pay little attention to what a servant can say about machines, perhaps in turning her master's roast-jack she thought she saw a perpetual motion. If you know anything concerning this matter I shall feel much pleasure if you would communicate it."

It is difficult to determine what to believe about this machine. It seems to me, however, that on examining minutely the for and against Orffyreus we can come to these conclusions: 1. That Orffyreus was evidently mad, as M. 's Gravesande and M. de Crousaz both affirm; his machinery broken at different times without either reason or necessity prove this. But his was a sort of madness we do not often see: a folly fixed only on certain objects, and merits more the name of fantasticalness or whimsicalness; this kind of folly is often accompanied by much genius, and when persons of this disposition apply themselves solely to one subject, as it appears he did, it is not surprising to find them making discoveries which had escaped the sagacity of wiser people. Thus I do not wish to agree with M. de Crousaz, that it is incredible that a madman, such as Orffyreus should have found out something that learned men have searched for unsuccessfully. Added to this he is mistaken in saying that Orffyreus could hope for no other reward for his secrets than mere reputation: for he expected a considerable profit seeing that he demanded for it 200,000 florins. 2. No exterior agent moved the machine; if it were a servant that moved it, would it not have been apparent to eyes so searching as those that made the examination, or to the Landgrave, who had seen the interior of the machine? Besides how can any one imagine that a wheel of so great a volume could have been moved by such a cause, a cause which would act simply on the axle in crossing the supports, and which must have been so small as to have escaped the most rigorous examination? 3. If the servant has not been paid to depose against Orffyreus, what does her testimony prove? Only that her master made her believe that by turning a little wheel, she moved the whole machine, and we can fancy a singular character, such as he was might have done this to prevent the curiosity of those who sought to penetrate his secret; M. 's Gravesande's opinion of this strange character is such that he doubts not his whimsicalness prevented him from making a new machine. 4. It must be confessed that this wheel was a very remarkable mechanical phenomenon, and this is all we can say, not knowing more than the preceding details; it were too much temerity to say that this invention was a perpetual motion, as much as it would be wrong to call it an imposture, seeing that no exterior agent was employed.

Dr. Kenrick proceeds to state that:—The celebrated John Bernoulli, speaking of the above demonstration, in a letter to the author, remarks that it is very just; the principle assumed necessarily involving an augmentation of force, viz., a perpetual motion. But this, continues he, is no more than Leibnitz had long before demonstrated in his dispute with Papin and others.

Having thus occupied twenty-three pages in fencing himself with a screen against the ridicule he appears to have so much dreaded, and reasonably anticipated from the many authors he had himself similarly treated in the "London Review," we are informed that,—An accidental conversation, many years ago, on the spot where Orffyreus exhibited his machine, awakened the author's curiosity and directed his attention to an object which he has ever since occasionally pursued. The experiments he has made, even so long since as the year 1761, convinced him so far of the reality of Orffyreus' discovery, that he applied for letters-patent to secure an exclusive right to the construction of a similar machine; which he had contrived and denominated A Rotator. Before his patent, however, was expedited, he reflected that, though the model he had constructed might serve to remove the prejudices of the public, it was not so well calculated as it might be, to answer the practical purposes of so important a discovery. To the improvement of the Rotator, therefore, has he long since dedicated all the time and attention he could possibly spare from his other, more immediately necessary, pursuits.

Nothing can be more flimsy than the statement here made, and the next sentence would seem to explain the true state of the case. He proceeds: "Not that he believes he has contrived quite so many different machines as Orffyreus did, though he has been almost as many years engaged in the like undertaking; he has, nevertheless, both contrived and constructed a considerable number, many of them useless as costly, except indeed as they served to assist him in completing his invention."

His invention, however, was not complete; the very model of it was unsatisfactory. Like Orffyreus, he had spent nearly twenty years, making numerous, and some costly, machines. He no doubt had his own misgivings, and wished to reimburse himself for the great outlay he must have incurred during that long period, before the bubble finally burst! However, poor man, he died nine years after publishing this elaborate advertising prospectus, which concludes: "Such bodies corporate, private companies or individuals, as are interested in the construction or use of considerable mechanical engines, or are disposed to encourage the present discovery, may receive any further information they require, on applying to the inventor, William Kenrick, Charles street, St. James's Square, March 1, 1770."

In 1803, Dr. Charles Hutton, LL.D., and F. R. S., contributed in a brief work entitled, "Recreations in Mathematics and Natural Philosophy," gave the following notice to the Orffyrean Wheel:

The perpetual motion has been the quicksand of mechanicians, as the quadrature of the circle, the trisection of an angle, etc., have been that of geometricians: and as those who pretend to have discovered the solution of the latter problems are in general persons scarcely acquainted with the principles of geometry, those who search for, or imagine they have found, the perpetual motion, are always men to whom the most certain and invariable truths of mechanics are unknown.

It may be demonstrated, indeed, to all those capable of reasoning in a sound manner on those sciences, that a perpetual motion is impossible: for, to be possible, it is necessary that the effect should become alternately the cause, and the cause the effect. It would be necessary, for example, that a weight raised to a certain height by another weight, should in its turn raise the second weight to the height from which it descended. But, according to the laws of motion, all that a descending weight could do, in the most perfect machine which the mind can conceive, is to raise another in the same time to a height reciprocally proportional to its mass. But it is impossible to construct a machine in which there shall be neither friction nor the resistance of some medium to be overcome; consequently at each alternation of ascent and descent, some quantity of motion, however small, will always be lost: each time, therefore, the weight to be raised will ascend to a less height; and the motion will gradually slacken, and at length cease entirely.

A moving principle has been sought for, but without success, in the magnet, in the gravity of the atmosphere, and in the elasticity of bodies. If a magnet be disposed in such a manner as to facilitate the ascension of a weight, it will afterwards oppose its descent. Springs, after being unbent, require to be bent by a new force equal to that which they exercise; and the gravity of the atmosphere, after forcing one side of the machine to the lowest point, must be itself raised again, like any other weight, in order to continue its action.

We shall, however, give an account of various attempts to obtain a perpetual motion, because they may serve to show how much some persons have suffered themselves to be deceived on this subject.

Fig. 52, plate 12, represents a large wheel, the circumference of which is furnished, at equal distances, with levers, each bearing at its extremity a weight, and movable on a hinge, so that in one direction they can rest upon the circumference, while on the opposite side, being carried away by the weight at the extremity, they are obliged to arrange themselves in the direction of the radius continued. This being supposed, it is evident that when the wheel turns in the direction a b c, the weights A B and C will recede from the centre; consequently, as they act with more force, they will carry the wheel towards that side; and as a new lever will be thrown out, in proportion as the wheel revolves, it thence follows, say they, that the wheel will continue to move in the same direction. But, notwithstanding the specious appearance of this reasoning, experience has proved that the machine will not go; and it may indeed be demonstrated that there is a certain position in which the centre of gravity of all these weights is in the vertical plane passing through the point of suspension, and that therefore it must stop.

The case is the same with the following machine, which it would appear ought to move also incessantly. In a cylindric drum, in perfect equilibrium on its axis, are formed channels as seen in Fig. 53, which contain balls of lead, or a certain quantity of quicksilver. In consequence of this disposition, the balls or quicksilver must, on the one side, ascend by approaching the centre; and on the other must roll towards the circumference. The machine then ought to turn incessantly towards that side.

A third machine of this kind is represented in Fig. 54. It consists of a kind of wheel formed of six or eight arms, proceeding from a centre, where the axis of motion is placed. Each of these arms is furnished with a receptacle in the form of a pair of bellows, but those on the opposite arms stand in contrary directions, as seen in the figure. The movable top of each receptacle has affixed to it a weight, which shuts it in one situation and opens it in the other. In the last place, the bellows of the opposite arms have a communication by means of a canal, and one of them is filled with quicksilver.

These things being supposed, it is visible, that the bellows on the one side must open, and those on the other must shut; consequently the mercury will pass from the latter into the former, while the contrary will be the case on the opposite side.

It might be difficult to point out the deficiency of this reasoning; but those acquainted with the true principles of mechanics will not hesitate to bet a hundred to one that the machine, when constructed, will not answer the intended purpose.

The description of a pretended perpetual motion, in which bellows, to be alternately filled with and emptied of quicksilver, were employed, may be seen in the "Journal des Savans" for 1685. It was refuted by Bernouilli and some others, and it gave rise to a long dispute. The best method which the inventor could have employed to defend his invention would have been to construct it, and show it in motion; but this was never done.

We shall here add another curious anecdote on this subject. One Orffyreus announced, at Leipsic, in the year 1717, a perpetual motion, consisting of a wheel which would continually revolve. This machine was constructed for the Landgrave of Hesse Cassel, who caused it to be shut up in a place of safety, and the door to be sealed with his own seal. At the end of forty days, the door was opened, and the machine was found in motion. This, however, affords no proof in favor of a perpetual motion; for as clocks can be made to go a year without being wound up, Orffyreus's wheel might easily go forty days, and even more.

The result of this pretended discovery is not known. We are informed that an Englishman offered 80,000 crowns for this machine; but Orffyreus refused to sell it at that price: in this he certainly acted wrong, as there is reason to think he obtained by his invention, neither money, nor even the honor of having discovered the perpetual motion.

The Academy of Painting at Paris possessed a clock which had no need of being wound up, and which might be considered as a perpetual motion, though it was not so. But this requires some explanation. The ingenious author of this clock employed the variations in the state of the atmosphere for winding up his moving weight. Various artifices might be devised for this purpose; but this is no more a perpetual motion than if the flux and reflux of the sea were employed to keep the machine continually going; for this principle of motion is exterior to the machine, and forms no part of it.

But enough has been said on this chimera of mechanics. We sincerely hope that none of our readers will ever lose themselves in the ridiculous and unfortunate labyrinth of such a research.

To conclude, it is false that any reward has been promised by the European Powers to the person who shall discover the perpetual motion; and the case is the same in regard to the quadrature of the circle. It is this idea, no doubt, that excites so many to attempt the solution of these problems; and it is proper they should be undeceived.

The foregoing, we believe, are sufficient to disclose the gist of all that is known, and all that has been said concerning the claimed inventions of the distinguished Marquis and the distinguished Councillor. It is manifest from reading the above that Dircks himself, as well as nearly all the other eminent persons quoted above, felt an extreme delicacy in stating their honest belief concerning the claims of the distinguished inventors. That delicacy arose from their deference to the rank and prominence of the Marquis and the Councillor. The author of this book is not thus encumbered, and has no such regard for family or official rank, and feels at liberty to say exactly what he thinks.

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

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

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

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[CHAPTER XI]
Conservation of Energy—A Discussion of the Relation of the Doctrine of Conservation of Energy, and the Possibility of Perpetual Motion

Conservation of Energy is a doctrine to the effect that energy, like matter, is indestructible, and, except by the infinite, can neither be created nor destroyed; that the sum total of all Energy in the world remains constant; that it may manifest itself in different forms, as heat, magnetism, electricity, mechanical motion, vaporization, but that the sum total remains the same.

Nothing could be more satisfactorily proved than this doctrine, and, yet, like Newton's theory of universal gravitation the proof does not amount to a mathematical demonstration. Mathematics demonstrates the conformity of the doctrine of universal gravitation, and of Conservation of Energy with all known natural processes and observed phenomena; but mathematics does not otherwise prove the Universality of Gravitation nor Conservation of Energy.

Writing on this subject of proof, with reference to gravitation, the late and eminent Simon Newcomb says:

"It may be inquired, is the induction which supposes gravitation universal so complete as to be entirely beyond doubt? We reply that within the solar system it certainly is. The laws of motion as established by observation and experiment at the surface of the earth must be considered as mathematically certain. Now, it is an observed fact that the planets in their motion deviate from straight lines in a certain way. By the first law of motion, such deviation can be produced only by a force; and the direction and intensity of this force admit of being calculated once that the motion is determined. When thus calculated, it is found to be exactly represented by one great force constantly directed toward the sun, and smaller subsidiary forces directed toward the several planets. Therefore, no fact in nature is more firmly established than is that of universal gravitation, as laid down by Newton, at least within the solar system."

It will thus be observed that the theory of Universal Gravitation is not by scientific men claimed to have been mathematically demonstrated, but its proof is regarded as resting upon its conformity with known natural phenomena. The same thing is true of Conservation of Energy. Scientists and mathematicians do not claim proof of this doctrine other than by its universal coincidence with all natural manifestations, and, yet its proof rests upon such a solid structure of coincidence and conformity with all known things in nature, that now all scientific research begins with its assumption, and with the exclusion of the possibility of Perpetual Motion.

It is not within the purview of this work to give a history of the origin and establishment in science of the doctrine. While, as heretofore noted in this book, a number of scientists of the past few centuries are shown by their reflections to have had a measure of appreciation of its ultimate effect, and to have applied that effect in their scientific researches, there is no evidence that they ever dreamed of its establishment as a basic fact of science. The real establishment and acceptance of the doctrine dates not much over a half century back. Since that time many scientists have in their researches and writings contributed to its evolution and formation. The experiments of Joule, of England, and the generalizations of Helmholtz, of Germany, are entitled to special mention.

Scientists are naturally and necessarily conservative. So many startling pseudo-scientific facts are announced, that every startling scientific theory, before it is accepted, is submitted to the most careful and crucial tests. No modern scientist will announce a scientific fact as having been demonstrated until the demonstration is complete and fortified with repeated tests of mathematical rigidity, and as long as there remains a phenomenon that does not conform to the supposed theory, acceptance and promulgation will be withheld. It is, therefore, not surprising that the doctrine of Conservation of Energy has been thoroughly intrenched as an established indisputable and accepted fact of science, less than a single generation.

The student of natural science should be warned against the common error of supposing that the discovery of a scientific fact or theory, means demolition of the old theories. The rule is the other way. New theories are additional information to the world, and usually conform to, and are built upon what was known before. Conservation of Energy was generalized from previously known facts conformed to them and reflexively elucidated them, and left them standing clearer than before.

The proof that Conservation of Energy conforms to all other known phenomena of nature has been aided, and hastened by the refinement of scientific instruments by which forms of energy such as heat, electricity, and magnetism can be more delicately measured and determined than ever before, and if instruments for measuring and determining the amount of energy in its various forms were as crude as they were even a single century ago, it is probable Conservation of Energy would still be the undiscovered foundation of all natural phenomena.

Let us now consider a few well-known facts which it has been determined positively by the most delicate instruments, prove and illustrate the doctrine of Conservation of Energy.

Resistance to motion, or which is the same thing, motion against resistance, is always accompanied by heat. This developed heat is not always readily perceptible to our sense of touch. A stone, ball or other object thrown through the air has its motion gradually arrested by the air. Heat is developed, but the heat is distributed through so much air and the object thrown is heated so little that this development of heat was not known until scientifically discovered. Where the resistance is friction, the development of heat is quite perceptible, and has always been well known. Suppose a coin be rubbed on a cloth or blotter. Heat is developed both in the coin and the blotter—the more vigorous the rubbing—i. e., the more energy expended, the greater the heat. Science has determined that the developed heat is exactly proportional to the expended energy. Every machinist knows that in turning a tap on a bolt where the threads are rusty so that it turns only with the application of great force, a considerable amount of heat is readily developed. The heat developed is proportional to the energy expended in turning the tap.

A wheel revolving on a spindle will develop heat exactly proportional to the resistance the spindle offers to the wheel turning upon it. Thus, we often see smoke and a blaze rising from the spindles of the car wheels where oil is lacking, and they turn with difficulty.

Every farmer knows that if a buggy wheel turns with difficulty for want of lubrication, or for any other reason, the spindle will heat, expand and lock the wheel, so that it will often either grind out the boxing or slide on the ground. Whereas, if the parts be kept lubricated so that less energy is required to turn the wheel on the spindle, there is no perceptible heat developed, but in all cases heat is developed to some extent, and the heat developed is exactly proportional to the energy necessary to force the revolution.

With heat we can boil water and make steam under a pressure, and with the steam under a pressure we can run an engine, and with the engine make heat by friction, or make electric current that can produce heat. Carry this proposition back to the fuel box, and knowing the amount of heat developed by the burning of a certain quantity of fuel, it is found that, counting the heat that rises in the air through the smoke stack, the heat that is radiated from the boiler, the heat that is carried away in warmed ashes, the heat that exists in the steam after it is exhausted from the cylinder, and all other heat expended whether utilized in driving the machinery or going to waste, the sum total is in every case equal to the heat developed by the fuel box combustion. The most striking thing about all this is that when the steam goes into the cylinder where it is cooled as it expands and drives the pistons, the heat thus lost by the expanding steam is the exact equivalent of the mechanical energy realized against the piston head. Not all of the energy that is realized at the piston head is delivered to the driving shaft. Some of it is lost in the friction of the piston rings wearing against the cylinder lining; some, of course, is lost in friction at the journals connecting with the driving shaft. It is usual in counting engine efficiency to count the amount of energy delivered to the belt, or to the driving shaft, and because of the frictional resistance of the pistons working in the cylinder, there is always found a little discrepancy between the energy represented by the cooling of the steam in the cylinder and the energy delivered to the belt, or the driving shaft.

It is quite surprising how much energy a small amount of heat represents if it could all be converted into the obvious forms of energy. Owing to the great waste suffered in all modern machinery, heat represents much more energy than is ordinarily supposed, in the absence of exact knowledge. One would hardly think it possible that the amount of heat that will raise the temperature of one pound (almost exactly one pint) of water, one single degree (Fahrenheit) is the equivalent of energy required to elevate one pound seven hundred seventy-eight feet high against the force of gravity. Yet, such is the case. This was one of the demonstrations of the immortal Joule. It was he who enabled us to cross the bridge with calculations from mechanical force and motion to heat. He stated the equivalent to be seven hundred seventy-two feet, but more delicate instruments than could be had in his day have shown a slight discrepancy in his calculations, and it is now known to be almost exactly seven hundred seventy-eight feet. Thus, if the Falls of Niagara be considered as being one hundred sixty feet high, the energy developed by the descent is only the equivalent of the heat necessary to raise the temperature of the water about one-fifth of one degree. A modern railroad locomotive does well to realize to the driving rod two per cent of the total energy developed in the fuel box. An ordinary thrasher engine realizes no more than one per cent. The very best steam engines known in large stationary plants do not realize as much as fifteen per cent.

The amount of heat necessary to raise the temperature of one pound of water one degree is taken as a standard for heat measurement, and is known as a British Thermal Unit—nearly always in scientific works abbreviated to B. T. U. The common standard of energy is the amount of energy or work necessary to elevate one pound one foot against the force of gravity. This in scientific works is usually referred to as the foot-pound.

From what is said above it is manifest that one B. T. U. is the equivalent of seven hundred seventy-eight foot-pounds, and vice versa.

The amount of energy must not be confused with the rate of expending energy, or doing work. The horse-power is the common measurement of the rate of delivery of energy or of doing work and is equivalent to 33,000 foot-pounds per minute. It is what one horse can do, and continue doing several hours with reasonable ease. For a short time a horse can exert several horse-power.

Remember, and remember always that heat and electricity are just as much forms of energy as the motion of concrete objects.

We have introduced the above statement of equivalents for the purpose of enabling us to present a few fundamental facts more clearly than could otherwise be done.

Everyone knows that if paddles be revolved rapidly in a vessel containing a liquid, such as a churn, or the like, the liquid will offer considerable resistance to their motion, the amount of resistance depending upon the nature of the liquid, and the rapidity of the motion.

Our scientific instruments have determined the fact to be that the B. T. U. developed in the liquid and on the paddles is the exact equivalent to the foot-pounds of energy required to drive the paddles, i. e., the number of B. T. U. is 778 times the number of foot-pounds.

An engine is run with steam—the engine drives an electric generator. Electricity is developed. This electricity is conducted over a wire to a motor. It is always found that not as much energy can be derived from the motor as is supplied from the generator to the wire. Where is the loss?

It is found that the loss is in the resistance of the wire to the current, and that the wire is warmed—possibly not sufficient to be perceptible to the ordinary sense of touch, and, yet, it is warmed to some extent, and the B. T. U., developed in, and radiated away by the wire, amounts precisely and exactly to the difference in foot-pounds between the energy supplied to the wire at one end of the wire, and the energy supplied by the wire at its other end.

Capillary Attraction is one form of motion by which liquids are elevated and carried considerable distance. The moisture is taken from the earth and carried up the trunks of trees, and out through their limbs to their leaves. This cannot be done without force and energy, but where is the heat? It has been determined and proven that there is an expenditure of heat in doing that work, and that the expenditure of heat is precisely equivalent to the work done. It is hardly believable that there is a loss of heat by coal oil or water, or other liquid performing the work of ascending the wick, and yet, science has determined that that work is only done at the expense of that other form of energy—heat.

If an object falls a distance of twenty feet, and it strikes one end of a lever having two arms of equal length, and at the other end of the lever there be a ball of equal weight, the other ball will be thrown upward twenty feet, less an allowance for the resistance of the air in the descent and ascent, and for the frictional resistance of the motion of the lever. It would throw a ball of twice the weight half the height by adjusting the levers properly. Or, it would throw a ball of one-third the weight three times as high, and so on.

A ball rolling down an inclined plane is found to have a velocity, and consequently a striking force, and an energy equal to that acquired in falling the vertical distance of its descent, due allowance being made for the resistance offered to its rolling motion. It makes no difference whether the incline be great or small, the velocity, the energy are the same as though it had fallen perpendicularly through the same vertical distance.

Instances and illustrations can be multiplied indefinitely. Millions of tests have been made by scientific men, and the basic fact of Conservation of Energy is found true everywhere. That fact is that energy cannot be created. So much as is given is returned in some other form, or else in the form of heat, but in some form, precisely the equivalent is always found to exist.

One of the most beautiful experiments is with the pendulum. Imagine a nail or peg driven into a wall and projecting out—say six inches from the wall. Hang a pendulum four feet long—let the pendulum swing parallel to the wall in the annexed figure. Let "A" represent the point from which the pendulum is suspended. Draw the pendulum back to C, and release it. Its lowest descent in the swing will be at B. It will swing to D, and a line connecting D & C is exactly horizontal, showing that the energy represented by the motion of the pendulum at B was sufficient to elevate it to the point D. Now, on a line on the wall downward from where the nail or peg is driven into the wall, let there be made holes into which a nail or peg can be inserted, and suppose a peg be driven at the point F. If now pendulum be released at C, it will be found that when the cord strikes F the pendulum will swing to the point J, which is on the horizontal line D C. It makes no difference where the interrupting peg or nail be placed, the pendulum will rise to the same horizontal from which it was released. It is said that this was one of Gallileo's experiments. If so, it is another example of the masterly force and originality of his genius, and shows that he subconsciously had some appreciation of the basic facts of the now accepted doctrine of Conservation of Energy.

We believe it is useless to multiply instances further, to illustrate the doctrine of Conservation of Energy, and show the character of proof upon which it rests. There is no fact in nature, but what in the hands of modern science appears to conform to this doctrine. A few years ago when radio-active properties were first discovered it was thought that it was an exception, but even that has been found to conform to this wonderful generalized doctrine.

If the doctrine of Conservation of Energy be true about which there seems to be no doubt, then all hopes of ever attaining Perpetual Motion must cease, for the idea of Perpetual Motion is predicated and has its foundation upon the creation of energy. The mechanism must give more energy than is imparted to it. It must make energy, and this in the light of the generalized truth of Conservation of Energy is an impossibility. We might as well talk about making substance, and the creation of substance, or the creation of energy either one is not an attribute of man. It is an attribute to be accredited only to the infinite, and can not be conceived as an attribute of the finite.

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[CHAPTER XII]
Will Perpetual Motion Ever Be Accomplished?

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 D E F 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 E G, 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 G E, 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 E G, and the bellows must shut closer and closer until the part E F 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 G E, 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.