CHAPTER I

DEVICES BY MEANS OF WHEELS AND WEIGHTS

Wilars de Honecort

While attempts at Perpetual Motion are as old as the human race, not many of the more ancient devices have been preserved, either by engraving or by explanation.

Among the very earliest of these attempts of which we have detailed information is the device of Wilars de Honecort. He was an architect, and lived in the thirteenth century. The information is preserved in "A Sketch Book" by him which was deposited and remains in the Ecole des Chartes at Paris. About the middle of the nineteenth century comments were published in France on this ancient device. Some of these were translated into English. The following account is an extract from a translation made by Professor Willis, of Cambridge.

"_Many a time have skilful workmen tried to contrive a wheel that shall turn of itself: here is a way to make such a one, by means of an uneven number of mallets, or by quicksilver._"

Wilars de Honecort presents to us a device for a perpetual motion; it is not clear whether he intends to claim the contrivance of it, or whether he had met with it in the course of his travels. It differs very little from a well-known contrivance for this purpose which has been so often published, and its fallacy so fully explained in popular books, that it is unnecessary to dwell at length upon the mechanical principles which it involves. It is extremely curious in this place, because it shows the great antiquity of the problem, the solution of which has wasted the time, the brains, and the means of many an unhappy artisan or philosopher.

In the drawing we have now before us, the two upright posts, which are framed together and skilfully braced so as to ensure their steadiness, support between them a long horizontal axle, to the center of which is fixed a wheel with four spokes. The absence of perspective in this drawing makes the wheel appear as if it were parallel to the frame, instead of being, as it is, at right angles to it.

Seven mallets, or arms, each loaded with a heavy weight at the end, are jointed at equal distances to the circumference of the wheel, so that those which happen to have their joints below the diameter of the wheel will hang freely down, but if the wheel be turned round by hand or otherwise, the weights of those which are on the ascending side will, in succession, rest on its circumference, and will, in that position, be carried over the highest part of the wheel and downwards on the descending side, until the arms that bear them are brought into a vertical position and a little beyond it, and then the weight will fall suddenly over and rest on the opposite position on the circumference of the wheel, until its further descent enables it to dangle freely as before. The effect of this mechanism upon the position of the weights is not truly represented, for the upper mallet has fallen over too soon. In the modern form of this contrivance a pin, or stop, is introduced, by which the mallet, when it falls over, is compelled to rest so that its arm shall point to the center of the wheel, and thus the descending weight be held at a greater distance from the center than when ascending. It is extremely probable that this difference is a mere error of the artist, for the drawing has the appearance of having been made from a model of the wheel at rest; a condition in which, of course, it would always be found, unless moved by some external force. The inventor seems to have thought that the action above described would always place four weights on the descending side, and leave but three on the ascending side, each weight as it rises to the top being intended to leap suddenly over to the descending side, in the manner just explained; or perhaps, as M. Lassus suggests, the contriver imagined that the blows given to the wheel in succession by the falling mallets would help it forward. It is surprising that although the slightest model would show the failure of devices of this class to persons incapable of mathematical reasoning, yet such machines have been seriously proposed in books, and are continually recontrived by ingenious workmen. The allusion to quicksilver in the manuscript shows that Wilars was acquainted with the well-known contrivance described in the books already referred to, in which portions of that metal inclosed in channels are used instead of the falling weights.

A Repetition of Wilars de Honecort's Plan

This device was brought forth in 1831 in England, and illustrates what we say in the Introductory Essay to the effect of inventors working on the same plan in different parts of the earth and centuries apart.

We are unable to give the inventor's name. He was a correspondent to Mechanics' Magazine, and the description furnished by the inventor as published in Mechanics' Magazine, is as follows:

Description.--A A A is a ring of thin wood; B B B, several spokes, movable round the fixed points C C C, and only allowed to move one way by the construction of the openings D D D; E E E, heavy weights fixed to the ends of the spokes.

From the position in which the wheel is at present, it is evident that the weights on the right-hand side (1 and 2) acting at a greater distance from the center than those (4 and 5) on the other side, will cause that side to descend until the spoke 1 reaches the position 3, when it will exert no moving influence, but by which time the weight 8 will have fallen into the position 1, when a similar effect will take place, and so on with the rest.

Leonardo da Vinci

It is with a mingled feeling of sorrow and exaltation that we note the Perpetual Motion labors of the great Leonardo da Vinci. Of all of the men who ever gave the subject more than a passing notice he is the most famous.

Leonardo da Vinci was an Italian, born in 1452, and died in 1519. He was the illegitimate son of Florentine, lawyer. His mother has been variously described as a peasant, and as of gentle birth. Little about her is known. The father belonged to a family of lawyers, and never repudiated the son, but took him, educated him, and cared for him. It is well for the world that he did, for Leonardo da Vinci has perhaps contributed more to art and learning in the world than any other single individual that ever lived. He was a painter, a sculptor, an architect, a musician, a mechanician, engineer and natural philosopher. Each subject in art or science that he touched he not only mastered, but improved and embellished. He painted the original of the well-known picture of the Christ and His twelve Apostles, known as the "Last Supper," or the "Last Supper of Our Lord." This, and Mona Lisa, are perhaps the paintings by which he is known to the greatest number of people, and are considered by many connoisseurs the highest perfection in art ever attained by mortal man.

But, as painter and sculptor, he is to be regarded as among the greatest, if not the very greatest that ever lived. In art he ranks beside, if not ahead of Michelangelo and Raffael, and yet they are known only as artists, while he was preeminent in both art and science. The work he did in natural science was entirely original and emanated from an inherent initiative and originality, and as a scientist, he is entitled to rank below only Newton, Gallileo and Copernicus, and very few others. In all the history of the world he is the only man of whom it can be said that he attained the apex of eminence in both art and science.

The information concerning Leonardo da Vinci's devices for obtaining Perpetual Motion is extremely meager. There does not seem to be extant any detailed explanation of just how he expected his different designs to work.

All that is known concerning his efforts is sufficiently illustrated by the following cuts and language from Dircks:

Fig. 1 may be taken as a scheme belonging to the fifteenth century. It seems to be placed at the head as a simple or elementary design for future improvement. It is a chambered drum wheel, containing balls or weights, which, being always farthest from the center on one side, as compared to the other, are expected to keep the wheel constantly rotating.

Fig. 2. Failing in this scheme, the inventor next offers one with weighted levers, which are to fall outwards on one side, but to fall inwards on the opposite side, the weight at the same time sliding up the lever when vertical at the bottom, so as to be nearer the center throughout on the ascending side. But how the weight is to be made to ascend _at the bottom_ remains to be shown.

Fig. 3. The difficulty of elevating the weight would appear to have suggested its immersion in a trough of water, as here shown. The weights seem to be attached to some contrivance to float them _upwards_; but we are perplexed, and so no doubt was da Vinci, how to sink them, or being sunk, how to render them again buoyant by any self-motive process.

Fig. 4. It would appear as though the difficulties observable in Fig. 3 were attempted to be met here, in a plan which evidently combines several views of the case, yet without removing the main difficulty; for although the weight at the end of the long arm may be quite capable of sinking in the liquid, we still inquire, How is it ever to be raised again?

Fig. 5 seems to be an incomplete sketch, and a mere variation on the preceding designs, with the addition either of machinery below to be worked by it, or to give it motion. Possibly it was proposed to have a magnet at the bottom of the vessel.

Fig. 6 appears to be two designs in one sketch. On one side we have long single levers, with a single weight at their ends, and a weight between each at the periphery; on the other end, double or forked levers and double weights. Its mixed character renders it probable that it was merely some preliminary sketch.

The great value of the present exhibition of these early contrivances of misdirected mechanical ingenuity consists in the convincing evidence which they afford, that all young inventors who occupy themselves in the search for self-motive machines, do little more than reproduce the blunders of a past age. After a lapse of five centuries modern inventors often become patentees of contrivances which are only more complicated than the assumed-to-be overweight wheel of Wilars de Honecort, or the six similar ones of Leonardo da Vinci. But such has hitherto been the ignorance of mechanics on this subject, that Fig. 1 of the annexed diagrams has frequently been adduced by writers on the subject, as the veritable wheel invented by the Marquis of Worcester, in the seventeenth century!

A. Capra's Device

In 1678, A Capra, of Italy, revived the ancient, but still favorite scheme that dates back to the 13th century. (See page 22 ante.) He illustrates his idea with the following figure and the following comment:

On the wheel A (of the facsimile engraving opposite), which must be hung well equipoised between two uprights, are appended counter-weights, eighteen in number, all precisely at the same distance from each other, and all exactly of the same weight. The counter-weights are provided with a small ring by which they are hung.

Whilst the counter-weights B are farther from the center C of the wheel, they weigh more than the counter-weights I, because these are low and nearer to the center C of the wheel, so that the counter-weights B descend and the weight I drops; and whilst the weight B is alternately descending and the weight I ascending, the wheel will revolve continually. But it must be understood that it is necessary to make the wheel perfectly true in equilibrium, so that it do not weigh more on one side than on the other on account of the counter-weights.

The Device of Dixon Vallance. England, 1825

This inventor was certain he had overtaken and captured the ever-illusive Perpetual Motion. He gives a description of his happiness and his machine in the following effusively joyous language:

The annexed drawing shows how I have at length taken this enticing jilt (perpetual motion), though after a long and weary chase--

Through pleasant and delightful fields, Through barren tracts and lonely wilds; 'Mongst quagmires, mosses, muirs and marshes, Where deil or spunkie never scarce is! By chance I happened on her den, And took her when she didna ken.

W W W W represents a wheel with twelve hollow spokes, in each of which there is a rolling weight or ball. C C C C is a chain passing over two pulleys P P. There is an opening round the wheel from the nave to the circumference, so as to allow the chain to pass freely and to meet the weights. The weights are met by the chain as the wheel revolves, and are raised from the circumference till they are at last brought close to the nave, where they remain till, by the revolution of the wheel, they are allowed to roll out to the circumference. By this arrangement the weights are, on one side of the wheel, always at the circumference, so that that side is more powerful than the other, which causes the wheel continually to revolve. F F F F is the frame of the machine; M M M M the mortices for joining the two sides of the frame by cross rails. The arrows point out the direction in which the wheel turns.--I am, yours, &c., Dixon Vallance. Liberton, Lanarkshire, Nov. 10, 1825.

Furman's Device

Strange as it may seem, the patent office of the U. S. government as late as 1884 and 1886, received and filed, seriously considered and granted Letters Patent on Perpetual Motion Devices as appears from the description of Furman's Device following, and from Schirrmeister's "Mechanical Movement," and Enbom & Anderson's "Improvement in Pumps," appearing on pages 38 and 76 respectively, supra.

These were not denominated Perpetual Motion Devices by the inventors, but the specifications show them to be simply that and nothing more.

July 15, 1884, George H. Furman, of Rochester, Ohio, U. S. A., was granted U. S. Patent No. 301979, on

"A New and Improved Motor."

The essentials are sufficiently shown by the following excerpt from the specifications and the following figure. We have omitted Figure 2, mentioned in the specifications:

UNITED STATES PATENT OFFICE.

George H. Furman, of Rochester, Ohio.

MOTOR.

Specification forming part of Letters Patent No. 301979, dated July 15, 1884. Application filed March 6, 1884. (No model.)

The action of the motor is as follows: A suitable quantity of the small weights _d_ being placed in the outer drum, F, through the door _f_, the machine being at rest, they will accumulate at the lower part of the drum F in the pockets _c´ c´_. Now, to run the machine a person will apply his hands to the rim H and revolve the outer drum, F, in the direction of the arrow shown in Fig. 1. This movement of the outer drum will cause the weights _d_ to be carried in the pockets _c´ c´_ to the upper side of the drum, at which point they will roll from the pockets _c´ c´_ into the pockets _b b_ of the inner drum, G, where their weight will cause the drum G and shaft E to revolve. _As the pockets_ b _of the inner drum pass below the shaft E they empty the weights into the troughs_ c´ _of the outer wheel, F, to be again carried above the shaft and dropped into the pockets_ b, _so that the inner wheel, G, and shaft E will be revolved continuously._

Schirrmeisters Mechanical Movement

July 6, 1886, Charles Schirrmeister, of Brooklyn, Kings County, State of New York, U. S. A., obtained Letters Patent No. 345077, on a new and useful

"Mechanical Movement."

The essentials of the patented device appear from the following excerpts from the specifications, and the following figures accompanying the specifications. (Figs. 2, 3 and 4 we do not show.)

The object of my invention is to furnish a cheap and simple _means for imparting mechanical power_; and I accomplish this by means of a series of radial arms placed at right angles to and projecting from the axis of motion where power is first applied, and so arranged that each arm is in a different vertical plane, said arms being weighted at each end with a ball of metal. Some of these arms are also made hollow and inclose sliding or rolling weights, which move back and forth as the axis revolves, and the motion is still further re-enforced by a series of springs which are attached to the axis by a lever and eccentric.

Taking the simplest form of my device, I illustrate the same by the accompanying drawings, in which--

Figure 1 is a side elevation of the entire apparatus. Fig. 2 is a sectional view showing the hollow arm with a rolling weight. Fig. 3 is an end view showing the operation of a re-enforcing spiral spring. Fig. 4 is a detailed view showing still further the method of re-enforcing motion by springs. Fig. 5 is a view of the driving-pulley with its hollow arms.

Similar letters refer to similar parts in the several views.

A is the axis to which the power first imparting motion is applied.

N are the bearings supporting the same.

B is the driving-pulley attached to said axis, and from which motion is imparted by means of the driving belt _b_ to any point desired.

C are the hollow arms of the driving-pulley B.

D are the solid arms radiating from the axis A.

E are the hollow arms radiating from the axis A.

F are the solid balls or weights secured to the ends of the arms D and E.

_a_ are the sliding or rolling weights, which are inclosed within the hollow arms C and E.

_c_ are the slots cut into the hollow arms E, to relieve the air-pressure formed by the backward and forward motion of the weights _a_.

G are springs so arranged as to expend their force upon the axis A by means of the connecting rods H, both attached to the springs and one attached to the axis A by means of the eccentric I and the other to the wheel J at one end of the axis.

K is a balanced lever, upon which the springs G may rest, said lever being supported at each end upon the springs L.

M is a crank attached to one end of the axis A, and serves to show the place and manner in which the power may be applied.

The manner of constructing and operating my invention is as follows: The entire apparatus is made of steel or iron, and the shaft, bearings, arms, springs and connecting-rods are of ordinary form. The main or driving pulley is cast with four hollow arms, in which round weights are inclosed, which move back and forth within the arms when the wheel is set in motion. The solid arms, as well as the hollow arms, which are used in addition to those forming a part of the driving-pulley, are arranged by means of set-screws a suitable distance apart upon the axis and in different perpendicular planes, so as to give steadiness in motion. A thread is cut upon each end of these arms, and the fixed weights are then screwed on. When the shaft or axis revolves, the weights which move toward the ends of the arms above the center accelerate the motion, and the momentum of the machine aids in overcoming the resistance caused by the weights, which are below the center. At the same time the revolution of the eccentric and crank-pin upon the axis depresses the connecting-rods, which in turn depress the springs, which, being released as soon as the eccentric and crank-pin have reached their lowest point, contribute a lifting power to overcome the resistance above mentioned. As shown in the drawings, these springs joined to the connecting-rods may be supported and assisted by other springs.

The power is applied by hand, operating upon a crank at the end of the axis, or may be imparted by steam, hot air, electricity, or in any other known method, and is conducted to any desired point by means of the belt _b_.

Having fully described my invention, what I claim as new, and desire to secure by Letters Patent, is:

1. The combination, in apparatus for increasing mechanical power, of an axis, as A, supported upon bearings N, with a driving-pulley, as B, having hollow arms, as C, with movable weights, as _a_, and radial arms, both solid and hollow, the latter having movable weights, together with fixed weights attached to the end of each arm, all substantially as and for the purpose described.

Ferguson's Device

James Ferguson was an eminent Scotch mechanician and astronomer. He was born in 1710, and died in 1776. He was reared in very humble circumstances, and is known as the Peasant Boy Philosopher. A most interesting story of his life was written by Henry Mayhew, and published in England in 1857, entitled "The Story of the Peasant Boy Philosopher."

He prepared astronomical tables of great value and lectured on astronomical and mechanical subjects. His lectures were edited by a no less eminent man than Sir David Brewster.

While Perpetual Motion seemed to have received considerable time and attention from him, and while his writings show that he examined a great many mechanical devices, he seems all the time to have entertained serious doubt of the possibility of a machine having self-motive power. However, in 1770, he devised a machine for the purpose of producing Perpetual Motion. It does not appear that he ever offered the machine to the public, or sought publicity for it. A description of it is to be found in his Common Place Book in the University Library, Edinburg. The description there furnished is as follows:

The axle at A is placed horizontally, and the spokes B, C, D, etc., turn in a vertical position. They are jointed at _s_, _t_, _u_, etc., as a common sector is, and to each of them is fixed a frame as R, S, T, etc., in which the weights 7, 8, 9, 1, 2, etc., have liberty to move. When any spoke as D is in a horizontal position, the weight I in it falls down and pulls the part _b_ of the then vertical spoke B straight out, by means of a cord going over the pulleys K and k to the weight I. The spoke C _c_ was pulled straight out before, when it was vertical, by means of the weight 2, belonging to the spoke E _e_ which is in the horizontal position D _d_; and so of all the others on the right hand. But when these spokes come about to the left hand, their weights 4, 5, 6 fall back, and cease pulling the parts _f_, _g_, _h_, _i_; so that the spokes then bend at their joints X, _y, z_, and the balls at their ends come nearer the center A, all on the left side. Now, as the balls or weights at the right hand side are farther from the center A than they are on the left, it might be supposed that this machine would turn round perpetually. I have shown it to many who have declared it would; and yet for all that, whoever makes it, will find it to be only a mere balance. I leave them to find out the reason.

B. Belidor's Device

This device was incubated in the brain of an American. His name is unknown. We have denominated it "B. Belidor's Device," not because B. Belidor was the inventor, but because the account of the invention was furnished by him. This device seems to the author to have possessed originality, though, of course, it failed to work for reasons clearly apparent.

An account of it was given in the Journal of Franklin's Institute, Philadelphia, in 1828. The article contributed by B. Belidor is as follows:

Even the pursuit after perpetual motion, hopeless as it is, may not be considered entirely vain, in occasionally leading to useful modifications of machinery. As an instance of this, I here submit to you a plan suggested by an ingenious friend of mine, several years ago, as in the diagrams annexed, Fig. 1, a perpendicular, and Fig. 2 a horizontal view.

A A, two vertical wheels, placed diagonally, and revolving on the axes X X. The levers B B and C C are hinged at the peripheries of the wheels. By rotation the arms B B are projected from the center of motion, while the arms C C are drawn in.

It is plain that a series of arms as shown in Fig. 2, will produce an eccentric motion, causing the weights at their ends apparently to preponderate on the side B.--BELIDOR.

Desagulier's Proposition on the Balance

This so-called problem is of doubtful classification. The author of the problem did not claim that the discovery of the problem discloses any means for attaining Perpetual Motion, and, yet, it is apparent that if the author of the problem was correct in his solution of it, Perpetual Motion was thereby already within his grasp. The difficulty about it all is that while the problem is quite interesting, the author's solution shows that he was not familiar with even fundamental mechanics. The name of the author was J. T. Desagulier, LL.D., F. R. S. He was a minister of the gospel, but evidently gave considerable attention to mechanical questions. He is mentioned in chapter X of this work.

Rev. Desagulier presented two problems of the balance. One he calls "A Proposition on the Balance, not taken notice of by Mechanical Writers, explained and confirmed by an Experiment." The article under this heading is as follows:

In the last papers I published in "Philosophical Transaction" against this perpetual motion, described in No. 177, I intreated the author to permit me to say nothing as to what alterations he might make in his engine, resolving to leave it to others to show him that upon that principle all he can do signifies nothing. But I find since, in the "Nouvelles de la Republique" for December last, that he still persists to urge some new contrivances, which being added, he conceives his engine must succeed. To this I answer, that I undertook only to shew that his first device would faile, which yet I should scarce have done if I had thought a dispute of this nature could have lasted so long. To come, therefore, to the point where he saith that this engine may well succeed without alteration, because he hath tryed with liquors put into bellows immersed in water; I again say that I grant him the truth of the experiments, but deny the consequences he would draw from them. I have already given the reasons of my dissent, which this gentleman is not pleased to understand. But to end all controversies, he may please to consult Mr. Perrault, De la Hire, or any other at Paris well known to be skilled in hydraulicks, and I doubt not but he will find them of the same opinion with Mr. Boyle, Mr. Hook, and other knowing persons here, who all agree that our author is in this matter under a mistake.

A Proposition on the Balance, not taken notice of by Mechanical Writers, explained and confirmed by an Experiment.

A B is a balance, on which is supposed to hang at one end, B, the scale E, with a man in it, who is counterpoised by the weight W hanging at A, the other end of the balance. I say, that if such a man, with a cane or any rigid straight body, pushes upwards against the beam anywhere between the points C and B (provided he does not push directly against B), he will thereby make himself heavier, or overpoise the weight W, though the stop G G hinders the scale E from being thrust outwards from C towards G G. I say likewise, that if the scale and man should hang from D, the man, by pushing upwards against B, or anywhere between B and D (provided he does not push directly against D), will make himself lighter, or be overpoised by the weight W, which before did only counterpoise the weight of his body and the scale.

If the common center of gravity of the scale E, and the man supposed to stand in it, be at _k_, and the man, by thrusting against any part of the beam, cause the scale to move outwards so as to carry the said common center of gravity to _k_ _x_, then, instead of B E, L _l_ will become the line of direction of the compound weight, whose action will be increased in the ratio of L C to B C. This is what has been explained by several writers of mechanics; but no one, that I know of, has considered the case when the scale is kept from flying out, as here by the post G G, which keeps it in its place, as if the strings of the scale were become inflexible. Now, to explain this case, let us suppose the length B D of half of the brachium B C to be equal to 3 feet, the line B E to 4 feet, the line E D of 5 feet to be the direction in which the man pushes, D F and F E to be respectively equal and parallel to B E and B D, and the whole or absolute force with which the man pushes equal to (or able to rise) 10 stone. Let the oblique force E D (= 10 stone) be resolved into the two E F and E B (or its equal F D) whose directions are at right angles to each other, and whose respective quantities (or intensities) are as 6 and 8, because E F and B E are in that proportion to each other and to E D. Now, since E F is parallel to B D C A, the beam, it does no way affect the beam to move it upwards; and therefore there is only the force represented by F D, or 8 stone, to push the beam upwards at D. For the same reason, and because action and reaction are equal, the scale will be pushed down at E with the force of 8 stone also. Now, since the force at E pulls the beam perpendicularly downwards from the point B, distant from C the whole length of the brachium B C, its action downwards will not be diminished, but may be expressed by 8 × BC; whereas the action upwards against D will be half lost, by reason of the diminished distance from the center, and is only to be expressed by 8 × B C/2; and when the action upwards to raise the beam is subtracted from the action downwards to depress it, there will still remain 4 stone to push down the scale; because 8 × B C - 8 × B C/2 = 4BC. Consequently, a weight of 4 stone must be added at the end A to restore the æquilibrium. Therefore a man, &c., pushing upwards under the beam between B and D, becomes heavier. Q. E. D.

On the contrary, if the scale should hang at F, from the point D, only 3 feet from the center of motion C, and a post G G hinders the scale from being pushed inwards towards C, then, if a man in this scale F pushes obliquely against B with the oblique force above mentioned, the whole force, for the reasons before given (in resolving the oblique force into two others acting in lines perpendicular to each other) will be reduced to 8 stone, which pushes the beam directly upwards at B, while the same force of 8 stone draws it directly down at D towards F. But as C D is only equal to half of C B, the force at D, compared with that at B, loses half its action, and therefore can only take off the force of 4 stone from the push upwards at B; and consequently the weight W at A will preponderate, unless an additional weight of 4 stone be hanged at B. Therefore, a man, &c., pushing upwards under the beam between B and D, becomes lighter.

The other problem presented by Rev. Desagulier is denominated by him "An Experiment explaining a Mechanical Paradox, that two bodies of equal weight suspended on a certain sort of balance do not lose their equilibrium by being removed, one farther from, the other nearer to, the center."

The article concerning this problem is as follows:

If the two weights P W hangs at the ends of the balance A B, whose center of motion is C, those weights will act against each other (because their directions are contrary) with forces made up of the quantity of matter in each multiplied by its velocity; that is, by the velocity which the motion of the balance turning about C will give to the body suspended. Now, the velocity of a heavy body is its perpendicular ascent or descent, as will appear by moving the balance into the position _a b_, which shews the velocity of P to be the perpendicular line _e a_, and the velocity of B will be the perpendicular line _b g_; for if the weights P and W are equal, and also the lines _e a_ and _b g_, their momenta, made up of _e a_ multiplied into W, and _b g_ multiplied into P, will be equal, as will appear by their destroying one another in making an equilibrium. But if the body W was removed to M, and suspended at the point D, then, its velocity being only _f d_, it would be overbalanced by the body P, because _f d_ multiplied into M would produce a less momentum than P multiplied into _b g_.

As the arcs A _a_, B _b_, and D _d_, described by the ends of the balance or points of suspension, are proportionable to their sines _e a_, _g b_, and _d f_, as also the radii or distances C A, C B, and C D; in the case of this common sort of balance, the arcs described by the weights, or their points of suspension, or the distances from the center, may be taken for velocities of the weights hanging at A, B, or D, and, therefore, the acting force of the weights will be reciprocally as their distances from the center.

Scholium.--The distances from the center are taken here for the velocities of the bodies, only because they are proportionable to the lines _e a_, _b g_, and _f d_, which are the true velocities; for there are a great many cases wherein the velocities are neither proportionable to the distances from the center of motion of a machine, nor to the arcs described by the weights or their points of suspension. Therefore, it is not a general rule that weights act in proportion to their distances from the center of motion; but a corollary of the general rule that weights act in proportion to their velocities, which is only true in some cases. Therefore, we must not take this case as a principle, which most workmen do, and all those people who make attempts to find the perpetual motion, as I have more amply shewn in the Phil. Trans., No. 369.

But to make this evident even in the balance, we need only take notice of the following experiment:--A C B E K D is a balance in the form of a parallelogram passing through a slit in the upright piece N O standing on the pedestal M, so as to be moveable upon the center pins C and K. To the upright pieces A D and B E of this balance are fixed at right angles the horizontal pieces F G and H I. That the equal weights P W must keep each other in æquilibrio, is evident; but it does not at first appear so plainly, that if W be removed to V, being suspended at 6, yet it shall still keep P in æquilibrio, though the experiment shews it. Nay, if W be successively moved to any of the points 1, 2, 3, E, 4, 5, or 6, the æquilibrium will be continued; or if, W hanging at any of those points, P be successively moved to D, or any of the points of suspension on the cross-piece F G, P will at any of those places make an æquilibrium with W. Now, when the weights are at P and V, if the least weight that is capable to overcome the friction at the points of suspension C and K be added to V, as u, the weight V will overpower, and that as much at V as if it was at W.

From what we have said above, the reason of this experiment will be very plain.

As the lines A C and K D, C B and K E, always continue of the same length in any position of the machine, the pieces A D and B E will always continue parallel to one another, and perpendicular to the horizon. However, the whole machine turns upon the points C and K, as appears by bringing the balance to any other position, as _a b e d_; and therefore, as the weights applied to any part of the pieces F G and H I can only bring down the pieces A D and B E perpendicularly, in the same manner as if they were applied to the hooks D and E, or to X and Y, the centers of gravity of A D and B E, the force of the weights (if their quantity of matter is equal) will be equal, because their velocities will be their perpendicular ascent or descent, which will always be as the equal lines 4 _l_ and 4 L, whatever part of the pieces F G and H I the weights are applied to. But if to the weight at V be added the little weight _u_, those two weights will overpower, because in this case the momentum is made up of the sum of V and _u_ multiplied by the common velocity 4 L.

Hence follows, that it is not the distance C 6 multiplied into the weight V which makes its momentum, but its perpendicular velocity L 4 multiplied into its mass. Q. E. D.

This is still further evident by taking out the pin at K; for then the weight P will overbalance the other weight at V, because then their perpendicular ascent and descent will not be equal.

The Rev. Dr. Desagulier was evidently a man of scientific turn and capacity. It is unusual to find ministers deeply interested in scientific matters, and yet, he seems to have been. The net result of his experiments can be succinctly stated as follows:

In the first problem there is _no change in the distance of the center of gravity from the support_, and, therefore, there could be no disturbance of the equilibrium.

In the second problem there _is a change in the distance in the center of gravity from the support_, and there must have been a disturbance of the equilibrium.

John Haywood's Device

In 1790, John Haywood, of Long Acre, Middlesex, draftsman and mechanic, obtained British patent on:

"A machine for working mills and engines without the aid of fire, water, or wind, or in aid of all or any of those or any other powers."

The specification describes the device as follows:

"The machine acts on a rotative principle, or, in other words, has a revolving circular or circulating motion round an axis, center, or centers. It may be made or constructed of any materials or matter whatsoever, so it be of sufficient strength to sustain the power of action when applied to any mill, engine, or machine to which action or motion can or may be communicated by a wheel. The size or dimensions of this machine are by no means confined, but may be varied or altered as circumstances may require.

"References to the drawings of the machine hereunto annexed:--Fig. 1 is the section of the machine. A, A, B, a cranked or double center, fixed to the stand or frame D by the bolts E. C, C, the wheel which turns or revolves round that part of the cranked center mark A. F, levers which turn or revolve round the cranked center B. G, G, rollers or weights which revolve in the circular guides or grooves by means of the leavers F. H, H, circular grooves or guides which are affixed to the inner sides of the wheel. N. B.--the distance from A to B is the radius in all cases to determine the space between the center of the guide or groove H and the center of the roller or weight G. The distance of the two concentric circles which form the guides or grooves H must be equal to the diameter of the roller or weight G. I, I, springs which stop the rollers or weights G from returning when at the horizontal diameter of the wheel. K, weights, which may be increased or diminished at pleasure. L, ledges which connect the sides of the wheel together. N. B.--By fixing cogs or teeth on the rim of the wheel, so as to connect it with any mill, machine, or engine to which motion can be given by a wheel, the power of this machine may be communicated."

Explanation of the Failure of the Preceding Wheels and Weights Devices

It must not be presumed that the preceding devices shown in this chapter constitute any considerable part of the Wheels and Weights Devices that have been constructed through the hope of attaining Perpetual Motion. Of all the means whereby Perpetual Motion has been sought wheels and weights have been by far the most prolific. There is scarcely a village or a rural community in the civilized world that cannot point out its Perpetual Motion worker, and he generally starts with wheels and weights, though often, after long labor and final failure with wheels and weights, he still exploits other attractive fields of hopeless endeavor. Of the devices of that kind, accounts of which have appeared in scientific journals, or application for patents upon which have been made, and, indeed, patents often granted, it would be possible to write a book of thousands of pages, but to do so would be to no purpose.

It is believed by the author that the preceding devices are sufficient to illustrate, and show the controlling features of all the various mechanical contrivances for the utilization of wheels and weights as a means of Self-Motive Power. Countless others could be shown of more or less complicated mechanism, but an examination would disclose the fact that each gets back to some combination of parts well illustrated in the preceding. Also, in endeavoring to express why all wheels and weights devices have failed to work, each essential point of weakness is disclosed in the preceding. Now, why have they failed to work, and wherein are they inherently wrong and unscientific?

A cursory examination of the preceding devices shows that each depends ultimately on the supposition:

1. That a descending weight elevates an equal weight through a distance equal to the descent, and at the same time overcomes the frictional resistance of mechanism, both ascent and descent being measured on perpendicular lines, or

2. That weights affixed to an axis and caused to have a longer leverage on the descending side than on the ascending side, and consequently the downward pull on the long lever side is supposed to be greater than the downward pull or resistance on the short lever side of the axis.

If the fallacy of these supposed principles is explained and fully understood, it disposes, and disposes effectually, of the possibility of obtaining Perpetual Motion by means of wheels, weights and the force of gravity.

It should be remembered that a wheel is a lever, or rather it is a continuous series of levers--nothing more--nothing less.

We first refer to the figure shown in A. Capra's device, page 33 ante. The left side of this wheel is, of course, supposed to be the descending side on which the weights are farthest from the center of the wheel. It is apparent that only five weights are having any leverage advantage whatever, while a much greater number are being made to ascend. The advantage which a few of the weights have by virtue of the leverage pulling downward is always exactly counterbalanced by an _increased number_ of weights being drawn upward. It should be borne in mind that the direction of the force of gravity is toward the center of the earth, and not in the direction of the motion of the wheel, except at the extreme left side of the wheel.

Again, consider the figure appearing on page 63. It is manifest that the weights on the right hand are further out, and have a leverage advantage of the weights on the left hand side, but it is also manifest that there is, and always must be, a greater _number_ of weights on the left hand side. The _greater leverage_ of the weights on one side is exactly balanced by the greater number of weights on the other side.

For a further illustration, take the figure shown on sheet 65, ante. The weight "1" has a distinct advantage over weight "5." Weight "2" has a distinct advantage over weight "6." But here we have only three weights: 1, 2 and 8, tending to pull the wheel from left to right, whereas there are five weights, 3, 4, 5, 6 and 7, tending to prevent its going to the right.

In other words, if weights 1, 2 and 8 were removed, it is clear that the wheel would turn back to the left by reason of the action of the weights 3, 4, 5, 6 and 7. Here again the _leverage advantage_ which weights have descending is counterbalanced by the _increased number of weights_ on the opposite side acted on by the force of gravity, tending to prevent the descent of those having the greater leverage.

All the simpler devices failed, of course, to work. The more complicated devices are simply efforts to overcome the elementary principles that prevented the simpler devices from working. Among these that of Dixon Vallance (see page 34, ante), is best adapted to illustrate the folly and the fallacy of these various devices to overcome elementary principles.

We here refer to the figure appearing on page 35, ante, shown in connection with Dixon Vallance's Device. The obvious purpose was to keep all the weights close to the hub, except those depended upon to produce continuous motion by their greater leverage.

To the untrained and untechnical person it would perhaps not be manifest at first just why the Vallance machine failed to work. Here is its failure: Weight "c" must be raised toward the hub of the wheel. To raise that weight requires the application of force. That force must be supplied. The belt "cc" would work more freely if it were not elevating a weight, and the force required from "w" to turn the wheel so as to elevate the weight at "c" is counterbalanced by the resistance the weight "c" offers to being raised, and consequently to the motion of the belt and in turn to the progress of the wheel.

It should always be remembered that, omitting friction, the energy exerted by a descending body is the _perpendicular distance_ of its descent multiplied by its weight. For, notwithstanding what its course may be from an elevated point to a lower point the energy accumulated in the descent is still the product of the perpendicular distance and the mass, or weight.

In all of these devices it is apparent that every weight is brought back by some force from the lowest point it reaches to the same elevation from which it started to descend. It is axiomatic, therefore, that the perpendicular ascent is equal to the perpendicular descent. The ascending weight and the descending weight are, of course, the same. Therefore, the product of the weight and the perpendicular distance of _ascent_ is exactly equal to the product of the weight and the perpendicular distance of _descent_. Hence, there is an exact balancing of energies, and no motion results. Any motion imparted by wind, water or steam will, if the moving force be withdrawn, soon be overcome by unavoidable friction, and a state of rest follows. There can be no doubt that any attempt to attain Self-Motive Power by means of wheels, weights, levers, and the force of gravity must result in failure. The thing itself is physically impossible.

In addition to what is above stated, read carefully Chapter XI, on Conservation of Energy; also read Chapter XIV, entitled "The Seeming Probability of Effecting a Continual Motion by Solid Weights in a Hollow Wheel or Sphere" at page 290 of this book.