A LECTURE ON THE PERPETUAL MOTION.
Haud facilè inventum perpetuum-mobile purum artificiale; haudquaquam quod fieri non potest:
BERNOULLI.
Comme il est très-possible qu'un corps monte plus vîte qu'il n'est descendu; c'est sur quoi je fonde ma preuve de la possibilité du Mouvement Perpetuel.
'sGRAVESANDE.
PART THE FIRST.
LONDON: Printed for the AUTHOR. Sold by T. EVANS, Bookseller, PATER-NOSTER-ROW.
MDCCLXXI.
ADDRESS TO THE PROFESSED PHILOSOPHICAL CRITICKS.
GENTLEMEN,
I Should have taken earlier notice of the honour done me in your periodical lucubrations, had I been less indifferent to literary attacks, or could any body give a better reason than myself for disregarding the censure of anonymous reviewers. Yet, finding it a very general opinion that men only affect to despise, and turn their backs on, the shafts they cannot repell, I am induced, against my inclination, and much against the dictates of my pride, to expostulate with you a moment on the inconsistency and injustice of your remarks on my account of the automaton, or self-moving wheel, of Orffyreus.
I was in hopes the very respectable authorities and explicit evidence, on which I rested the veracity of the fact, would have had more weight with men so confessedly open to conviction as yourselves: all it seems to have had on you, being to induce you to scoop out the marrow of my pamphlet for the entertainment of your readers, and to leave the bare bone to be picked by my bookseller.—But of this I do not complain. The republic of letters is ever in a state of civil warfare; in which every man, being an enemy to his neighbour, takes the spoil of his goods for lawful plunder. Indeed, were it otherwise, and the genus irritabile vatum more peaceable creatures, it would be still much the same with you. Being pirates by profession and the public indulgence winking at your occupation as warrantable, you would doubtless think, with the highwayman in the play, there is no harm in labouring in your vocation.—What I do complain of, is, that having thus rendered my publication useless to me, my publisher and the public, you should proceed to treat me as if I were an ignorant visionary, capable of weakly deceiving myself, or a designing impostor capable of wilfully deceiving others.
You are, some of you indeed, pleased to pay me the compliment of saying, you have the highest opinion of my abilities as a writer. But is not this strangely inconsistent? Can you have an high opinion of the abilities of a writer, capable of imposing on himself, in one and the same pursuit, for fifteen years together? A castle-builder? A mistaken projector?—Of what sort of stuff, for heaven's sake, do you, wise critics, take good writers to be made? There was a time when you, or your predecessors, professed as high an opinion of my abilities as a metaphysician. Have I betrayed any want of metaphysical capacity since? Or is it because I have occasionally misemployed myself in tagging rhimes, translating novels, scribbling comedies, or, for want of a sufficient independency in toiling like yourselves, invitâ Minervâ for worse than Egyptian task-masters: is it from all this you infer I can know nothing of the subject, to the knowledge of which I was in a manner bred, and which I have made the constant study of my life? Really, Gentlemen, if you thus lightly pronounce and retract your opinion of writers and writings, the public will soon learn to have no higher opinion of you than is entertained by those who are already in your secret. So much for your consistency.
I charge you with injustice in so rashly giving your sanction, however insignificant it may prove, to the powerful prejudice which so generally prevails against the practicability of a discovery of confessed and universal utility. For, give me leave to tell you, how just soever may be your pretensions to science in general, you have by no means taken the pains to qualify yourselves to be competent judges of the perpetual motion in particular. If, then, it be deemed an instance of injustice and cruelty to attempt, through prejudice to blast the hopes of industrious ingenuity, employed in the production of a puerile play or frivolous farce; the composition of which, whatever drudgery it may prove to men of confined talents, cannot be the labour of any length of time to a writer of abilities: yet if this, I say, be thought cruel and unjust, how much more unjust and cruel must it be deemed to endeavour to fortify prepossession against the painful application, profound study and patient perseverance, exerted in the prosecution of a series of expensive experiments, as I have said, for near fifteen years together; and those in the very prime and pleasurable part of life?
When the object of such a pursuit also is considered as useful to the public, it is not only injurious to the individual who hath thus devoted his youth, his health and even his means of subsistence to their service; but to a whole community, that might expect to profit by his having made so laborious and, it is presumed, laudable a sacrifice. For the sake of the public, for your own sake, then, Gentlemen, let me pre
ail on you to look a little farther into this matter before you proceed to confirm your dictatorial decisions on a subject, which you have so very, very, superficially considered. Reflect that, whatever may be your disposition towards me, it will be prudential with regard to yourselves, to promote, as far as lies in your power, a candid and impartial discussion of my pretensions; since, if I should make them good, you will thence avoid the mortification of becoming hereafter the objects of ridicule; and if I should not, you will have the triumph of seeing me the more compleatly ridiculous. In the mean time there is no danger of the world's being imposed on; it is too well armed by its own prejudices to need any caution from you, even if the private emolument I propose to myself did not depend, as it entirely does, on the advantages of which my discovery may prove to the public.
I am,
GENTLEMEN,
Your humble Servant, W. KENRICK.
Jan.
24, 1771.
*⁎* Such readers of the following Lecture, as have not been auditors and may be desirous of seeing the experiments exhibited in its recital; will, on sending their address to the author, or the publisher, be furnished
gratis
with tickets of admission for that purpose.
The plates will be delivered with the third and last part of the Lecture.
APOLOGY.
IT was my original design, Gentlemen, to have given you the trouble of but one attendance on this lecture: but the doubts and objections, that have been started since the publication of my Syllabus, have reduced me to the necessity of letting them go unresolved, or of enlarging my discourse, if not beyond the bounds of your patience, beyond the abilities of an indifferent speaker, ill qualified as unaccustomed to recite in publick.
To give the greater satisfaction, therefore, on a subject so much neglected, and of course so little understood, I shall enter into a more minute discussion of it than I at first intended, but which, I find by repeated intimations from those to whose judgment I pay a particular deference, the curiosity of my auditors may require.
The mere exhibition of what is called 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; would gratify no curiosity.
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 favour of its construction, (to the secret of which he was admitted) was given in the most explicit and determinate form.
And yet, because Orffyreus would not display the mechanism of his machine, 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; worn his hands with labour, 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. He died mad: a terrible example to all future projectors and particularly to pretenders to the perpetual motion!
Happy indeed is it for society (though often peculiarly unhappy for themselves) that projectors never take warning.
One would hence be apt to think that, as they say of poets, they are born such and are impelled by a fatal necessity to encounter poverty, contempt and even death itself, to attain the object of their pursuit. It is otherwise difficult to account for such amazing perseverance as that of Orffyreus in spite of innumerable disappointments, contradictions and railleries. To stand the butt of ridicule for twenty years together, argues a degree of fortitude or obstinacy, call it which you will, almost incredible: yet such was the fact and such was the ill fate of Orffyreus.
Whether any of his successors in the same pursuit will meet with a better, on the like presumption, is at length to be determined. One species of our predecessor's merit, however, I presume myself at least entitled to, that of perseverance; it being now near fifteen years since I first engaged in this undertaking: which I have since pursued with almost unremitted affiduity, and that not only at a considerable waste of time and expence, but under the constant mortification of hearing it equally ridiculed, by those who do know, and by those who do not know, any thing of the matter.
One conclusion, however, was very naturally to be hence inferred; that, either a man must be invincibly stupid, not to have in all that time discovered his error, or that such error must lie much deeper than to be so universally obvious, as is pretended.
The truth is, that the public in general, and even men of science, conceiving the subject unworthy attention, have not sufficiently considered the nature of it, to determine with certainty any thing about it. I could give a very pleasant relation of the strange misconceptions I have met with, on this head in persons of the first rank and reputation in the world of science. But as I know they were rather the effect of prepossession than incapacity, their future conviction will be a sufficient reprehension of their past prejudice.
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 publickly called upon, both in the foreign and English prints, to produce a single instance of these demonstrations. They have not done it. They could not do 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. But this was all. They proved nothing more; and this was so far unnecessary, in that the fallacy evidently appeared on 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 centre 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 court, however, was amused and persuaded: the Marquis was looked upon as a very extraordinary man (as he certainly was,) though, out of his celebrated century of inventions, I think much the greater part died with him. 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 'sGravesande and John Bernoulli maintained its practicability; the former giving his testimony in favour 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 favour of the discovery. It is even some years later that a dissertation, still more in its favour, written, if I am not mistaken, by the celebrated de Gorter of Petersberg, appeared in the philosophical transactions of Haarlem.
But to what purpose you will probably say, Gentlemen, is a reference to authorities in a matter, that seems so easily decided?
To very little purpose indeed, unless to shew that even the prejudices against this discovery are not quite so general among men of science, as among men of no science is generally imagined.
But you will say, perhaps, if the perpetual motion be practicable and the mode of rendering it so discovered, the simple exhibition of the machine in motion, would at once remove doubt and enforce universal conviction, without farther trouble of explanation.
Not so, Gentlemen. I have already observed that this was far from being the case with Orffyreus. It is true the mechanism of his machine was totally concealed; but, had it been otherwise; unless, with the display of its construction, he had at the same time illustrated its principles of action, and thence demonstrated the certainty of its continuing the motion, impressed on it; such an exhibition would have served only to amuse the ignorant, and persuade the credulous.
Thus, should I content myself with the mere exhibition of the experiment I propose (demonstrative as it will be to those who are previously acquainted with the principles on which it is made) it might convey no conviction to others. For, unless I could comprize the space of a twelve month, within an hour, how could the mere motion of a machine for that hour prove its capacity of moving, in like manner, a whole year? Or how should a model, merely raising a pound weight, prove a larger engine capable of raising up an hundred, or a ton? And yet, if it would not, the discovery must be nugatory; and might, however plausible, be after all illusive.
But I can have no interest in persuading the public into a futile belief of having discovered what, being of no use to the world, can be of no advantage to me. My end is not to amuse or persuade; but, with due deference, to inform and convince.
To remove every cause of objection, therefore, I must beg leave to trespass on your patience, by expatiating somewhat more at large on the theory of this discovery, than would on a less neglected topic be altogether pertinent to a practical discourse.
It is, however, 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.
In conformity to this mode of investigation, I shall not take up your time merely in con
uting a number of contradictory pleas, deduced a posteriori from equivocal facts; but 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. Were this impracticability indeed read, as it is supposed, I shall shew that neither could you, Gentlemen, have done me the pleasure of attending this lecture; nor should I have had the honour of reciting it.
INTRODUCTION.
On the Nature of Motion in general.
MANY and various have been the opinions of philosophers, respecting the Nature of Motion. It has been urged, indeed, of late, by some eminent writers, that all attempts to define it, are vain and futile; it being utterly impossible to define a simple idea.
With submission however to great authorities, I must take upon me to observe that, the idea of motion, as suggested by physical experiment, is very far from being a simple idea. It is a complex notion, composed of several ideas, viz. that of the resistance of the moving object, of the medium through which it moves, and of the time it takes up in moving. For we can form no compleat conception of motion abstracted from either of these.
To give a clear definition, therefore, or explain the nature and cause of motion in general, it is necessary to illustrate the simple ideas, of which that of motion is compounded.
Metaphysicians indeed have usually defined motion to be change of place, or a passage from one place to another.
This was Epicurus's definition.—That of Aristotle,
actus entis in potentia quatenus in potentia,
is condemned by Mr. Locke as absolute jargon.—Leibnitz censures, as imperfect, that of Sturmeus,
Successiva rei motae in diversis locis existentia
; and substitutes another equally defective, in calling it
continua loci mutatie.
In all these cases however it is plain the philosophers were endeavouring to give the definition of an abstract idea and not a palpable phaenomenon.
But change of place, or the mere transition of any thing from one place to another, as that of thought, for instance, by the imagination, is not motion.
Some philosophers, indeed, and Mr. Colden in particular, have spoken of the motion of things, destitute of the power of resistance: but such motion must be merely ideal. If the moving object have not some essential resistance, independant of its motion, its change of place would be impalpable as that of thought; or rather it could not change its place at all. Place is peculiar to resisting objects and such only are the objects of physical science. I now feel by its resistance, that something exists between my fingers. That resistance is now gone, and there is nothing in its former place.
Again, mere change of place may be instantaneous. I can as soon transport myself in imagination to York-Minster, as to St. Paul's Cathedral; to St. Peter's at Rome, as to Notre Dame at Paris: but the difference of time would be very considerable, in the removal of the swiftest animal to those different places.
In constituting actual motion, it is necessary that the moving object should possess some kind of force, or impulse; in consequence of which it resists every other object of the like nature, in the line of its direction; and that not merely in proportion to its velocity; but in a ratio compounded of that velocity and the quantity of such resistance. A small body in motion will not resist an opposing obstacle so much as a great one of the same kind, moving with the same velocity.
Every moving object must therefore be a resisting substance. But what is this substance? And what the cause of its resistance? Here, Gentlemen, I must beg leave to draw the line of definition.
It is admitted, that we cannot define a simple idea; and such is that of physical substance, immediately suggested to us by the sensation arising from the resistance of palpable objects.
To investigate the primary cause of this resistance, I shall not attempt. It is sufficient, for the present purpose, that we have the evidence of our senses that such objects exist. It had been well if natural philosophers had been always content to found their systems on such evidence. We should then never have heard of solid particles of matter, a perfect vacuum, or the motion of inactive elements by immediate impulse; none of which are deducible from the senses; and natural philosophy is confined to the investigation of things whose existence is to be rationally inferred from the evidence of sense.
A philosopher indeed has lately started up, who, affecting to be shocked at the absurdities of the ideal system of Locke and Hume, has undertaken to reform it on the principles of common sense; in consequence of which he affirms, that our notions of the qualities of bodies are none of them acquired by the senses: but that we are led to conceive them (he cannot tell how) by our nature and constitution.
See Reid on the human mind, Chap. vi. Sect. 21.
By our nature and constitution to be sure we are; for these consist of the union and operation of the senses. Indeed this same philosopher refines so far as to suppose we might have been so made, as to taste with our fingers, to smell with our ears, and to hear with our noses.—Risum teneatis! What a pity he did not add too, understand with our elbows! This he might certainly as well have done as have asserted, that the judgment sometimes precedes simple apprehension, as if the truth of a proposition might be known, before the terms of it are understood. But if this be common sense, it is common sense to say a man may see without eyes, hear without ears, and judge without understanding.
This method of reasoning is so far from improving philosophy on the principles of common sense, that it brings it back again to its ancient and exploded state of occult qualities and innate ideas.
I shall proceed, therefore, on the well-known and established principles of experimental philosophy; concluding, that all our ideas of the properties of bodies are derived from the senses, and that such evidence is sufficient proof of their existence.
Now there never was, nor ever can be, a single experiment made, from which we may justly infer, that inactive elements of any absolute dimensions, or, as they are commonly called, extended, inert, impenetrable particles of matter, exist in nature.
That resisting objects exist, we feel, and know. But that their resistance is the effect of the absolute impenetrability of their constituent parts, we neither can feel, nor know. The penetrability of palpable objects (and such only I repeat again, can come under the scrutiny of physical experiment) is merely relative.
By experience we learn that some bodies are comparatively more soft or hard, penetrable or impenetrable, compressible or incompressible than others: but, when we shall have found the hardest and most compact body in nature, we shall only have found a body that is impenetrable to others less penetrable. We have no means to make trial of its own absolute impenetrability; for, even the substance of soft clay is as impenetrable to soft clay, as that of iron to iron. And the body which appears hard and impenetrable as iron to the gentle pressure of a soft hand, would appear soft and penetrable to the forcible impulse of a hand as hard as iron.
When Sir Isaac Newton therefore, inferred from the extension, hardness and weight of palpable bodies, that the primary homogeneous elements of which all bodies are constituted must be extended, solid and heavy too, he reasoned illogically; as well as took that for granted which he should have proved. We find, says he, that several bodies are hard; and argue that the hardness of the whole only arises from the hardness of the parts: whence we infer that the particles, not only of perceptible bodies, but of all others, are hard likewise.
With all becoming deference, however, to the opinion of this great philosopher, it was but a weak way of arguing. Might not one say with equal propriety, squeezing a soft piece of spunge or other similar substance in one's hand, that we find several bodies soft and elastic, and therefore their primary particles, as well as those of all others, are soft and elastic too? Such argument is, indeed, altogether inconclusive. Palpable bodies are all compounds; and their various properties the effects of the combination of their parts, or the specific modification of the whole.
Were it otherwise, compounds would be mere aggregates of simples: nor could there be any specific difference between them. The truth is, as already observed, that all the terms by which we express the properties of palpable objects, are relative to the organs by which we perceive them. Nothing is absolutely solid or impenetrable; but all things are big or little, hard or soft, light or heavy, as they bear a comparison with each other, and stand related to the organs of sense: which form the common standard, by which we judge of their respective properties.
The misfortune is, that the conclusion we deduce from experiment, is frequently a mistaken one. It is not thence really and logically deducible.
There is nothing in which people in general are more mistaken than in the evidence of a single sense. Even ocular demonstration, generally supposed the most convincing of all others, is of all others the most delusive.
Almost every one imagines himself capable of seeing what no body can possibly see. Had we no other evidence, than that of sight, it would be impossible for us to distinguish between a superficies and a solid; between things near and afar off.
Length and breadth are objects of sight; thickness not. We see only surfaces, and by the arts of perspective might be constantly deluded. It is the same with the other senses. Thus when I feel a resisting substance; by the immediate touch, I perceive nothing but the sensation of that resistance, and can truly infer nothing from it, but the existence of a property, or power, of resistance in the perceptible object. Here therefore we should stop.
But our philosophers proceed to infer that this object must be an extended solid substance. It must have dimensions, say they, length, breadth and thickness. And yet by the simple and immediate touch I perceive neither. By moving my hand, indeed, along its edges and over its surfaces, I gather by reflection, the idea of its extension.
From the comparative evidence also of my other senses, I find that most bodies, palpable to the touch, have the appearance of solidity: they exhibit a determinate form and figure. But I observe, that this apparent solidity is in many bodies adventitious and circumstantial; dependent on the qualities of the medium, in which they exist.
Bodies of slight tenacity appear, in cold countries, in the solid form of wax, butter, tallow and the like; and assume in warm climates the fluid appearance of oil. Water, a perpetual fluid under the equator, is solid ice in Nova Zembla. Even quicksilver will become solid, in a medium of artificial cold, as has been experienced at Petersburg.
On the other hand, so tough and heavy a body as lead, dissolves in a medium moderately warm, and even steel itself becomes fluid, in the highly rarified medium of an heated furnace.
A reflection on these circumstances, hath induced some philosophers to question whether fluidity or solidity be, properly speaking, the natural state of bodies. And this, however ridiculed by some, would have been a question worthy of philosophers, if the terms, natural state, had borne a more explicit and determinate meaning.
But, be this as it may, when I see thus the same body at one time and place, and under some circumstances, a solid, and, at another time, or in another place, and under other circumstances, a fluid; what reason have I to conclude solidity essentially connected with resistance? Certainly none. At the same time, however I find, that under all circumstances, in all times and places, the resistance of the body remains. Though varied in its mode of appearance, its quantity is still the same. Inclose it in any containing vessel and it will equally resist compression in a fluid as a solid state, it will move, or resist any moving body, with the same force as a solid of the same dimensions and density. The simple resistance of body, therefore, is an essential quality inherent in every moving object or physical substance.
It is also the only essential quality we can assign it: all that we can philosophically affirm of the primary elements, being that they are moveable powers of resistance.
Some of you, Gentlemen, will perhaps find it difficult to form the idea of a power abstracted from some substratum, or extended substance, in which that power subsists. But I can assure you that inability is more owing to your being so accustomed to the notions of void space, and impenetrable matter, than to any incapacity of conception. Mr. Locke says, it is as easy to form an idea of power in the abstract as of substance; and indeed I should think it is full as difficult to conceive the essence of an inactive, impenetrable substance of absolute dimensions, incapable of compression and dilatation, as that of an active elastic substance of relative dimensions capable of both. We do not presume in general to impute dimensions to the great first cause, and yet we cannot dispute his existence or omnipotence. It is indeed to be observed that physical principles are not founded so much on the perspicuity of our ideas, as on the certainty of our sensations. They are more immediately deduced from the conceptions, however obscure, of what we perceive, and thence conclude, really to exist, than on abstract notions of nonentities or things of meer ideal existence. We know that things exist only by their properties. We define their essence only by these properties; nor are we permitted, in natural philosophy, to indulge the imagination, in forming conceptions of chimerical substrata, to which those properties belong.
We feel and know that moveable resisting powers exist; but whether the action or exertion of those powers be confined to certain determinate limits, within which their intensity is fixed and absolute, as in impenetrable matter, or whether they are capable of occupying a greater or less quantity of space, with an intensity proportionable to their dimensions, as in elastic substances, are questions we shall be better able to determine, from considering the other component parts of motion.
To come to that of the place, or the space in which the moving object exists. This is generally conceived to be mere vacuity, a physical nonentity; rather a privation, or negation, of existence than any thing really existing.
But however justly we may reason on negative terms, in algebra and other branches of metaphysics, we cannot admit negative principles in physics. Qualities, however occult in their essence, must be positive in their existence. We cannot explain or account for animal perception; but that we do perceive, cannot be disputed. At least those who doubt that they see, hear and feel, may be not uncharitably supposed to doubt every thing else. And it would be in vain to attempt their conviction.
Extension indeed, is not to be immediately inferred from the simple touch; but it is from the fight. The length and breadth of any body, and the distance between any two bodies, is as visible to the eye, as the surfaces of those bodies themselves, or as their resistance is palpable to the touch. Space therefore hath as real an existence as physical power, or resisting substance itself.
It may be objected that, if the magnitude of the resisting substance be merely relative, it would be reducible by a sufficient force ad infinitum, and the whole universe be compressible into a mathematical point; in which case the extension of bodies, as well as their distance, would be annihilated, and of course no space remain.
That the annihilation of physical power, or resisting substance, would annihilate physical space, I readily admit: Nay that the accumulation of all such powers or substances into one individual power or substance would annihilate motion. But, so long as they remain divided, so long as two substances coexist, though each separately were confined to a mathematical point, and the addition or multiplication of cyphers in arithmetic amount to nothing, yet there must of necessity be some real extension, or positive distance, however small, between them. They would otherwise not be two substances; not two mathematical points; but one.
If it were possible for two bodies to come into actual contact, without becoming really one, their two adjoining surfaces would constitute but one point or ideal plane of separation.
Number and identity depend either on locality or succession. It is impossible for two objects of the same nature to exist in the same place, at the same time. They must be either distinguished by some positive distance of place, if they exist at the same time, or by some positive distance of time if they exist in the same place.
Hence it is plain that, were the potential elements of resisting substance even mere mathematical points, the coexistence of a prodigious number of them must necessarily describe a vast extent of space, even though the distance between each should be ever so little.
And hence we see also that duration, the other component part of motion, hath as real an existence, as either extension or resistance. Indeed the transition of body from place to place, is frequently as obvious to sense, as either the bodies themselves, or the distance between them.
We are here also to observe that the limits of bodies form no part of their extension or place. Extended objects may be separated by dimensionless points; but dimensionless points cannot be separated, but by some real distance, or something really extended. If the wall or partition were taken away, that separates this room and the next adjoining, we should either call it one room, or should allow that the two rooms were divided only by their distance of place. But there would be no distance between the east side of one and the west of the other. The west side of the one might nevertheless be at a considerable distance from the west side of the other; as the east side of the one would be at the same distance from the east side of the other. There would be also two points in the middle of each equally distant, which would determine the locality of the two rooms, or the distance of their respective places.
Thus the place of a dimensionless point, is in that point; but the place of an extended substance, is in the centre of its dimensions.
We are come then to this dilemma; either the resisting elements themselves must be compressible only to a certain degree; that is into certain dimensions, within which they cannot be reduced; or the distance between them, if reducible to dimensionless points, must be absolutely positive; a conclusion that, involving an impenetrable fluid, is equally repugnant to motion, with that of impenetrable matter existing in vacuo.
From the very phaenomenon of motion itself, therefore, we are reduced to the necessity of concluding; that the elements among which it is originally generated, are elastic substances of a determinate power, limited as to their degree of compressibility, and doubtless also, as finite created beings, to that of their dilatation: within the bounds of which however, the intensity of their resistance or elastic force is, like that of all other elastic bodies, proportional to to their density, or the dimensions they describe.
As a Corollary of this proposition it will follow that space is a plenum; not of one solid impenetrable matter, but of innumerable elastic substances, mutually resisting each other; and constituting by their coexistence, an elastic fluid medium; similar, if not exactly the same, with the subtile aether hinted at by Sir Isaac Newton, and whose existence is so fully confirmed by the electrical experiments of Dr. Hoadley and Mr. Wilson.
Not that there would he no interstices between the elements. This appears necessary as each element would assume a spherical form, and touch the contiguous elements only in a few points.
It will follow also, from the known properties of elastic fluids, that no change of place could be effected in such a medium, but in time, as we see all motion is. And that motion, once generated in such a medium, might be propagated and continued ad perpetuum.
On the other hand, were the moving elements absolutely solid, inactive and heavy, existing in vacuo; they could neither be put in actual motion, nor, if possible to be put in motion, could that motion be long continued.
Sir Isaac Newton himself, indeed, gives up the point with respect to the gravity of the primary elements; which, he admits, may be the effect of some mechanical impulse: abiding only by the solidity, and vis inertiae of those elements, or their perfect indifference to motion and rest. It was the admission of these solid, impenetrable particles of matter into his system, which reduced him to the necessity of admitting also of a vacuum. Without this, it would have been impossible for his elements to undergo that change of place, and in that manner, which all bodies evidently do.
With regard to their actual motion indeed, he did not pretend to account for it, otherwise than by an occult and instantaneous impulse, arbitrarily exerted or impressed on them by the will of the creator. But I shall shew, that this could not be the case, consistently with the known and established laws of nature.
In the generation of motion among palpable bodies, existing in a resisting medium, the bodies at rest are always moved with a velocity proportionable partly to the velocity and quantity of the body putting them in motion, and partly to the density of the medium in which they move: Being compounds, their velocity is generated between the component parts of each; for it is to be observed, that the parts of the one body do not all directly strike against, or impell, all those of the other. There are but a few of those parts that come immediately in contact, the rest are successively impelled and repelled by each other till the whole be gradually affected, the compound itself not actually changing its place, till all its component parts are equally impelled. And this is the reason, as I shall more fully explain hereafter, why bodies can in no case communicate more motion than they possess, and that even this must be equally distributed in the conflict among their component parts, before the whole body be put in motion.
The case however would be different in the original motion supposed to be given to a simple uncompounded element, equally indifferent to motion and rest, existing in a perfect vacuum. For this, being solicited by a determinate impulse on one side, and there being no resistance to that impulse in the element itself, nor from the medium on the other, it could not be disposed to take up any time in passing from one place to another; but might, for any thing that appears to the contrary, move a million of miles in any given time as well as a single foot.
For, be the impulse great or small, being instantaneous and the element itself perfectly indifferent to motion and rest: and, there being no resistance in the medium, no proportionable velocity could possibly be generated. Nullity has the same want of proportion to one as to one million!
Lord Kaims whose acknowledged abilities were exerted some years ago in the illustration of this subject, supposes indeed, that the generation and communication of motion is in all cases instantaneous. In analyzing the operation however, he is obliged to divide it into three successive steps. But it is a contradiction in terms to suppose any action to be at once instantaneous and gradual.
This supposition is also founded on the misconception of the absolute solidity of bodies, and an inattention to the cause and mechanism of cohesion; which I mean to explain.
Admitting however, that motion were not the mechanical effect of a physical cause; but immediately given to such inactive elements by the fiat of the creator, the consequence, as Sir Isaac Newton himself admits, is obvious; their motion would, by their mutual collisions, be soon utterly destroyed.
The evident necessity of renewing it therefore, in order to keep up the system, induced him to hint at the existence of some active principle in that of a subtile aether, or elastic fluid, agreeably to the system I have adopted.
Later philosophers have devised various other expedients. Mac Laurin supposes there may be different kinds of moveable elements or matter possessed of different degrees of inactivity.
Dr. Knight conceives the whole system of nature to be kept up by the mutual exertions of two active principles, subsisting in his elements of attraction and repulsion.
Mr. Colden, in his treatise on the principles of action in matter, supposes that there are at least three kinds essentially different, a resisting matter, a moving matter, and an elastic matter, neither resisting nor moving.
Lord Kaims conceives that all matter is endowed with three powers or pro perties; first, that of continuing itself in motion; secondly, that of resisting a change from rest to motion; and thirdly, that of gravitation; or, as he expresses it, a power to unite itself with every other piece of matter.
On the other hand Dr. Stewart professor of natural philosophy at Edinburgh, rejects any supposed activity in matter, or the moving object, conceiving it impossible to solve the phaenomena of nature, on mechanical principles alone. The mutual repulsion and attraction which subsists between palpable solids and between the fluids in which such solids swim (for so he terms it) he regards as the continual effects of thought and design in the first immaterial cause.
I leave metaphysicians to treat of the immediate effects of immaterial causes. That the actions and reactions of the primary physical causes; in consequence of which palpable bodies are generated and moved, and their situation and direction determined; that these I say, are the constant effects of an immaterial cause is most certain. But that the effects of this action or the modes of its exertion are not to be mechanically investigated, I do presume to deny.
To attempt indeed to give a reason why a power of resistance universally prevails in all bodies. To give a reason for the formation of bodies specifically different. To say why the same homogeneous resisting substance should successively enter into the composition of such different bodies; why the same moving object is now the apparently inert and insensible stratum of a fossile, now the moving and sensitive fibre of a vegetable, and now the active and sensible nerve of an animal. To say why the marrow that forms the brain of a goose may in a short time form the brain of a philosopher: all this, I say, must be imputed to the inscrutinable direction of a superior metaphysical agent: to that omniscient and omnipotent cause by whom we live, move, and have our being.
But to be assured that a resisting substance exists; that such an universal principle or power of reaction really prevails; and to determine the constant and regular method in which the various revolutions, as well of the particular systems of bodies, as the general system of nature, are mechanically performed; this is within our reach. Demonstration and experiment, indeed, are confined within the narrow limits of sense. Men of powerful organs and acute discernment may penetrate something farther into the secrets of nature than others. Lyonet hath dissected the caterpillar with nearly as much accuracy, as Albinus hath anatomized the human body. With the artificial assistance of telescopes and microscopes, we can proceed still a little farther. We can trace the motion of stars and planets otherwise invisible; discover the almost invisible animalculae preying on the scarce-visible insect, and perceive how easy it is with a steady hand and a sharp instrument to divide corpuscles and to split hairs. These acquirements however are of little advantage. While perceptible magnitude is relative, numberless will be the systems of mechanical motion which we cannot explore. It will ever be impossible for us, for instance, to trace particularly the minuter parts of the mechanism of animals.
But though the complication of a multiplicity of moving objects in any system, may perplex and baffle our capacity of investigation, it does not therefore render their operation the less mechanical.
We may argue, therefore, as justly from analogy, as from actual experiment; if the premises on which the argument be founded are themselves founded on experience.
I have shewn that, by a parity of reasoning, we may as justly conclude the elements of bodies to be soft and elastic as hard and impenetrable. I have just now mentioned the several shifts to which, in the latter case, philosophers are reduced to account for natural phaenomena, either by the adoption of a variety of imaginary principles, or that unphilosophical expedient of having immediate recourse on every difficulty to the fiat of the creator.
If then, by admitting only this position, that the primary elements of bodies are elastic substances, originally disposed by the will of the creator, in such local relations to each other, or are partially impelled in such different directions as to occasion the particular inequalities of resistance, necessary to produce the various motions intended; if from this simple position may be mathematically and mechanically deduced, not only the origin of motion, but the necessity of its known and established laws: if, not only the general laws of nature, but its principal phenomena, are hence to be inferred and explained; it is presumed the attempt to prove this practicable will be as acceptable to the philosophical world in general, as it is necessary to prepare my auditors for being convinced of the practicability of the perpetual motion in particular.
PART I.
On the Cause and Effects of Motion.
PRESUMING, on what has been said, Gentlemen, that I have given some satisfactory idea of the nature and cause of motion in general; and taking it for granted that the simplest moving object is an elastic substance, whose dimensions are determined by the resistance of the like objects surrounding it; and not an impenetrable substance of a determinate form and absolute dimensions. I shall proceed to shew that motion is the natural and necessary consequence of any inequality, by whatever means introduced, in the reciprocal resistance of such primary elements.
It may be previously necessary, however, to dwell a little on the mode of action of such elements.
Elasticity is supposed to be the effect of the modification of the parts of elastic substances. That of compound bodies indeed is so, but elasticity in the simple elements is the primary cause, not a secondary effect, of motion.
And here we are led to make the necessary distinction between motion and action. Action is properly a physical term, motion a mechanical one.
We do indeed use the word action in mechanics, when we speak of the application of mechanic powers; but the distinction between action and motion even here is evident, the motion of the parts of a machine about their common centre of gravity may be called its action. The change of place of the whole machine is its motion. The action even of a simple lever, is its turning on its fulcrum or point of rest. Its motion would be the change of that fulcrum for another.
In circular motions, it is true, we commonly say, that a thing turns, or moves round its axis; but if the centre of gravity continue in the centre of motion, the place of the whole is not changed. It may be said to act, if you will, but it cannot properly be said to move.
Every simple motion must be recti-linear. Whatever moves must move in some one particular direction. It cannot move two ways at once. And though its direction may be changed every moment as in apparently circular motions, effected by the resistance of surrounding obstacles, every apparent circle is only a polygon of an imperceptible number of sides: these sides themselves being described merely by motion, as I shall hereafter explain.
Mathematicians may amuse themselves with squaring the circle, and illustrating the doctrine of infinites by the ratios subsisting between strait lines and circles. There is no such thing as a circle in physicks. Infinite ratios may exist in idea, but infinite quantities do not exist in nature.
And, though we might reason as truly about infinites as finites in geometry, we must exclude the former from natural philosophy.
We may endeavour to imagine an infinity of space and an eternity of duration, but we can perceive, and thence have a physical idea of, nothing but what is limited both as to place and time. Agreeably to this, it is very justly observed, by a late ingenious writer on the doctrine of fluctions, that quantities themselves are not properly the objects of arithmetic or geometry; but only the ratios of quantities.
Mr. Colden. See Enquiry into the principles of action in matter.
Even the recti-linear extension of bodies, as I just now hinted, is a fluction. It is the mechanical effect of motion. The primary elements, though their resistance be local, do not exert that resistance in any one particular direction. Their dimensions are not limited by right lines. If it were, they could not preserve their essential properties of number and identity, on which their very existence as elements depends. They might, like the solid substance of the Newtonians, be divisible ad infinitum; without losing any essential property imputed to them.
A right line may be divided into any number of parts, each of those parts would be as compleat and perfect a right line as the whole. But physical elements cannot be divided, without being destroyed, or divested of their resistance; the quality essential to their existence. Thus the division of an elastic element would destroy its elasticity. But division and destruction are two things. Compounds may be cut to pieces and destroyed; but the wisdom of Solomon could not divide one child between two mothers.
You will perhaps wonder, Gentlemen, by what line the extension of such elements can be described; if no such thing as a circle exists and right lines are the mere mechanical effect of motion.
It may be described by a line, which is neither circular nor recti-linear; one that cannot be divided into lines of the same kind, or divided at all without losing its essential property, by such division. This is the spiral, a form which renders every body in nature capable of supporting it, elastic.
I say capable of supporting it, because Mr. Colden says, it is to him inconceiveable why a spiral shape, or any shape or arrangement of the parts of any thing, should give it any power which it had not before.
A spiral of lead, continues he, is as little elastic as a strait line of lead.—True it is nearly so, but why? Because lead is too soft and pliant to support the form of a spiral.
Will he say a spiral of steel is no more elastic than a strait line of steel? Has a watch spring wound up, no more elastic force than when it is run down?
The contrary is evident. Mr. Colden mistakes the argument. It is not denied that the power of sustaining the form of a spiral, lies in the component parts and composition of the steel, but it is not said that a greater elasticity is given to the steel itself, by its being formed into a spiral than it had before. No alteration is made in that arrangement of parts, in consequence of which steel differs specifically from lead, or any other metal.
If I take a piece of strait wire and turn it three or four times round my finger, the steel is still steel, and of the same temper as before; though it has acquired a spiral form. It is not the essential arrangement of the constituent parts of the steel, but the local arrangement of the parts of the strait line that is affected.
It is this new arrangement of parts that generates a new being, whose mode of resistance is peculiar to its form; and which, so long as that arrangement endures, will endure also, subsisting and ceasing with it.
An inattention to this circumstance has occasioned innumerable disappointments to mechanicians, endeavouring to profit by the elasticity of springs. Attentive to the general rule that springs unbend with the same force with which they are bent; and that their elastic force in general depends on the temper of the metal; they forget that the elasticity of each particular spring depends immediately on its form, and that such form is varied according as the spring is bent with a greater or less velocity. The compression of the same piece of steel is therefore not always that of the same spring; nor will its dilatation have an equal effect, unless directly on the same body that compresses it.— This, and this only, seems to be the reason why professor 'sGravesande's clear demonstration of the possibility of the perpetual motion, has not been long since confirmed by practice.
This error is the common effect of the popular notion of supposing the properties of things attached to some substratum or substance, distinct from those properties.
The specific powers of every palpable body in nature are the effect of the arrangement or motion of its constituent parts.
Even from the primary homogeneous elements exclusive, to the complicated body of the whole universe, the arrangement of the parts of one thing constitutes the essence of another. The very existence and different properties of fossiles, minerals, vegetables, brutes, all depend on, and are the immediate effect of, the arrangement of their specific corpuscles; in like manner dependent on that of the primary elements.
Thus it is not pretended that the different arrangement of the parts of any thing, can give new powers to that very thing: a different arrangement would constitute a new thing. If a watch spring and the steel of which it is composed were one and the same thing, there would be no occasion for watch-spring makers; the artist and his art would be useless.
The propriety of conceiving the action of the primary elements exerted spirally, is further evident from the reflection that, we thence avoid the contradiction of supposing one and the same influence exerted in two contrary directions at one and the same time; as would be the case in conceiving it exerted by emanation in strait lines on every side from a centre; whereas in the case presumed, the action of such element is one simple undivided action, the exertion of the influence of a single indivisible power; from the necessary effect of which, its reaction upon the contiguous elements, is nevertheless exerted on every side in recti-linear radii from its centre.
Thus when I compress a watch spring between my fingers and thumb, the resistance or reaction of the spring is exerted each way from the centre of the coil in the line of its diameter; but the action of the spring is exerted only in the single direction of the coil; the ends of it moving backwards and forwards in dilatation and contraction solely in that direction.
More depends on this individuality or identity of objects than may readily occur, both with respect to their action and motion. It is the property or horologary power of a clock or watch to divide the time, and point out the hours of night and day. Will any one doubt that such a thing as a clock exists? or that its essential property is the mechanical effect of its arrangement of parts?
Separate those parts from each other or give them a different arrangement; they have no longer the same property. The clock is annihilated, though every wheel and pinion of it remain, uninjured, whole and entire. I might pursue the allusion through all nature; but shall confine myself to the immediate object of this lecture.
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.
In animals the blood circulates freely through their veins and arteries in all positions of the containing vessels; every globule of blood in the body has a centre of gravity of its own, independent of the centre of gravity of the whole body. A considerable quantity of blood may be taken away, and, thence diminish the weight of the body, without putting a stop to its motion, or diminishing its activity; which, if the perpetual motion were on this account impracticable, could not be. Indeed were such the case, on this or any other account, the blood in a man's body, when standing erect, would fall into the legs and feet, nor could the wisdom of the wisest and the strength of the strongest man united, raise it up again. This circulation indeed is generally imputed to the dilatation and contraction of the heart. But to what is the motion of the heart imputed? Neither to the wit of the wise, nor the will of the wilful.
It is shewn by Dr. Keil that if the circulation of the blood were once stopped, not all the muscular force of the heart would put it again in motion.
It is, in fact, the circulation of the blood that keeps up the motion of the heart, not the heart the circulation of the blood. The incumbent pressure of the atmosphere on the blood vessels cannot possibly be the cause, as some suppose, of the rise of the blood in the veins. A partial compression indeed might cause a partial stagnation of the blood, but an undequaque pressure can never be the cause of its general circulation. Besides, Mr. Boyle hath shewn that the heart of a frog beats as regularly, and as strongly, in vacuo, as in the open air.— The circulation of the blood, and, in consequence of that, all the animal functions, are, and must be, kept up by some mechanism in the body by means of which the blood rises, either in smaller globules or by some other means, so as to gain a force on gravity, to repair the motion dissipated by its friction against the containing vessels. And that such force is to be so gained, I shall hereafter prove by the most incontestible experiment.
At present I shall only beg leave to exhibit a very simple one universally conceived to be as much an impossibility as the perpetuol motion itself; by which however that impossibility as well as the absurdity exploded by De la Hire, appears to be really a fact. It is notorious that the pressure of a small quantity of a fluid is the same against the sides of the containing vessel as that of the greatest quantity at equal depths; the pressure of fluids following simply the proportion of their depth. Hence if the area of a vessel be small and its depth great, a very small weight of water will press against the bottom with prodigious force. Nay, by means of a vessel of different areas, at different heights, as a barrel with a perpendicular pipe carried through its head: if the head of the barrel be moveable and yet water-tight, a little water, poured into the pipe, will actually raise up a vast weight laid upon the head of the barrel. Here a small quantity of a fluid hath comparatively as much weight or gravitating force as a greater. Now I shall shew that this is not only the case with different quantities of a fluid; but that the same individual solid will, in like circumstances, appear to have a less and a greater weight than itself.
I must first however beg leave to observe, that there are two methods of estimating the weight of bodies. One is by the common ballance, by which their comparative weight only is determined; being weighed one against another or against some third body, which is made the common standard of comparison between both.
The other is by the elasticity of springs, which sustain weights equal to their elastic force. This determines the real weight: one body not descending as in the ballance, in proportion as another rises; but descending in proportion as the spring is bent; the elastic force of the spring being opposed to the gravitating force of the body. Hence it appears evidently impossible that the perpendicular pressure of the same body, should not equally compress the same spring: the elastic force of the spring being the measure of the gravitating force of the body. Yet see, Gentlemen, here is a ring of tempered steel; which, being placed within the edges of this box, is compressed by means of this fulcrum.
See plate 1. fig. I.
The fulcrum itself is nothing more than a strait piece of brass, projecting horizontally from two parallel perpendicular sliders, on the top of which is placed the weight. Till the spring be placed under the fulcrum, the latter will support no weight at all; but both the sliders may be moved up and down, together with the fulcrum, with the same ease: A proof that when the spring is placed under the fulcrum, no opposition is made from any other cause to either. And yet when the weight is laid on the different sliders, the spring will support it on the top of one, on being bent very little; whereas, if laid on the other, the spring will be bent very considerably. If then the elastic force of the spring, be the measure of the weight of the body, we have here a piece of lead apparently heavier and lighter than itself. The proportion in this instance is just as two to one, but it might be encreased as an hundred to one.
You seem surprized, Gentlemen, but there is no absurdity, no contradiction in all this. The weight of bodies, as estimated by the ballance, is as before observed merely comparative; their weight as estimated by the resistance of a spring is real; and there is no more reason why the real and comparative weight of bodies should be equal, than why their specific weights should be so too, which are universally admitted to differ. In the present case, when the weight is laid on one slider, the spring acts against its real weight; when on the other, against its comparative weight. The matter, if you will, may be called paradoxical; but so was for a long time the equality between the comparative weight of a heavy body at the end of a short lever and a light one at the end of a long lever.
This equilibrium between bodies so situated, that in other circumstances are of different weights, was for ages looked upon as a kind of miracle in mechanics; though, now we are we are better acquainted with the laws of gravitation and motion, it would be miraculous if it were otherwise.
It is every day experienced, with the common steel-yard, that one pound at the end of ten inches from the centre of suspension, is comparatively of equal weight to ten pound at the end of one inch.
The difference between the real and comparative weight or gravitating force of a body, will appear yet more plainly, if we suppose that the body, instead of barely pressing the spring, should fall from any height perpendicularly down upon it. Let us suppose, for instance, a weight of four pound to fall from the height of four feet. As the space described by falling bodies is as the square of their velocity, it will in falling four feet acquire two degrees of velocity, and of course being four pound bend the spring with eight degrees of force; which is in thi
case the real momentum of the motion acquired by its gravitating force in falling that distance.
Now it is well known that, it would require exactly the same force to throw the same body up again in the same time to the same height. But it is as well known that the weight of one pound, and ever so little more, at the end of a ballance beam of sixteen feet, would weigh up four pound to the height of four feet, from which it fell.—It is equally as well known and certain that, if one pound be freely let fall sixteen feet, it will acquire but four degrees of velocity, and of course have acquired but four degrees of momentum by its gravitating force; which is but half the force of the greater weight; which nevertheless it counterballances both in motion and at rest: the effects of the comparative gravity therefore of the two weights, is in this case equal, while those of their real gravity differ as two to one.
It is on the mechanical advantages to be taken of this difference between the real and relative weight of bodies that the perpetual motion is founded. It is in fact nothing more than the weighing a heavy body up by a small comparative weight, and letting it fall with its own real weight: while, on the other hand, the light body rises with its real weight and falls with i
comparative weight: by which means a force may be gained on gravity, at every rise and fall, proportional to the difference between the real weight of both.
To explain more fully the difference between the elasticity and weight of bodies, on which both the theory and practice of all mechanic powers depend; it will be necessary to recur to the action of the primary elements; whose elasticity I have endeavoured to illustrate; by imputing their action to the exertion of a power in a spiral form.
The spiral indeed is usually considered in physicks, like the circle, as a composition of imperceptibly small right lines. But the difference is obvious. Let us suppose for instance, the periphery of a circle to have real existence, and to be divisible; every divided segment of that circle would describe the same curve as the whole: that is, it would have the same property or bear the same geometrical relation to a right line, of the same length, as the whole circle would to a right line of its whole length. It is otherwise with the spiral.
For, suppose it divisible into parts, as in the case of the periphery of a circle, every part of it would be a different kind of curve. They would not each bear the same geometrical relation to a right line proportional to their length.
A spiral indeed may with greater propriety be called the generative part of a line, than a line itself: as the physical elements may be, in like manner, more properly called extending than extended; the elements of extension rather than extended elements; as will appear from conceiving the distance between any two mathematical points described by spiral motion. The moving object would not, in any part of that distance, move in the line of direction between those two points. But, if they lay east and west, it would move in all directions of the compass, in moving ever so little eastward or westward in that line. If the line were eastward it would move westward first, as well as northward and Southward; and, if westward vice versâ; because it must describe a circle round the point, from which it moves, before it arrives at the point to which it is moving. Hence it is plain that each such element, circumscribing its centre on all sides, will constitute an indivisible, incommenfutable, elastic, spherical form; whose diameter, if I may so call it, will be less than any physical right line whatever. Because a right line being divisible, it must of necessity comprehend at least three mathematical points, a beginning, a middle and end. But a primary element describing only the necessary distance between two, must of necessity be still less.
Every actual motion, is, as I have said, recti-linear, though not every action. The undequaque resistance, or elasticity of matter, is the effect of its spiral action; its change of place in any particular direction is the effect of some partial reaction, or impulse and is its motion.
An elementary power may act spirally from a point, though it cannot move, or change its place, but in a right line. Its dimensions also, in consequence of such actions being exerted uniformly round its centre, would assume a spherical form; and, though its contraction and dilatation should be effected, as in the case of a watch spring, spirally, and not in a diversity of right lines, emaning in different directions from such centre; yet the reaction of such elements, or the resistance they would make to each other, would be exerted in such right lines from and to the centres of each.
Such elements also might thus act and react, and yet be perfectly indifferent either to rest or motion. Their mere change of place in any particular direction, would not at all interfere with their internal action; or their mutual reactions with the action of each other. At the same time that their undequaque resistance, or reaction, would be still the same whether in motion or at rest; as we find indeed to be universally the case with all bodies.
Again, every such power might so act independently of any other; so that, as we can form no idea of the existence of a power that does not act, we hence avoid the absurdity of admitting passive powers, and negative properties in physicks.
The propriety of the distinction between action and motion appears hence also, more evident; in that each single element might act of itself, by virtue of its inherent power or principle of activity; whereas it is impossible that motion can be generated among simple elements, without a partial inequality in the reactions of two or more such elements; or propagated among compound bodies without the equal and contrary motion of at least two such bodies.
Mr. Locke, indeed, calls motion, action; and says there are but two species of action; motion and thinking; and talks of the possibility of a capacity of thinking being annexed to simple, inert matter.
Dr. Stewart, on the other hand, though he absolutely rejects, on the authority of Clarke and Wollaston, the latter notion, as well as the more plausible opinion of Hobbes, that a kind of obscure sense or perception is inherent in all matter; yet conceives, that a power of beginning motion seems necessarily to infer a power of thinking. At the same time, however, he admits that, for ought we know, there may exist some species of thinking beings, destitute of the power of motion altogether. Oysters, in particular he observes, have very little of this power. But might we not ask this learned professor, how he knows that they have the power of thinking in a greater degree than that of motion? For my own part, I must own, I have no great opinion of the intellectual abilities of an oyster: nay, though it were the most sagacious of a whole barrel; and that the most sensible that ever came from Colchester. I could almost as readily impute ingenuity to vegetables and fossiles; to the sensitive plant and the loadstone; as meditation to muscles or cogitabundity to cockles, periwinkles and rock oysters.
Neither Mr. Locke nor Dr. Stewart, did, in this particular, distinguish with their usual accuracy. It is foreign to our purpose, or it would be easy to prove that, whether thinking be properly termed an action or not, it cannot be the action of a simple uncompounded substance; and still less is it the immediate cause of motion. We are led into this error from our very naturally attributing intelligence to the great first cause. But, though we are obliged to make use of the same terms, to express wisdom and design in the deity as in ourselves, intelligence divine and human must differ as much as cause and effect. For high as the heavens are above the earth, are his thoughts above our thoughts; his ways above our ways. One essential difference at least, is evident in the thoughts of the creature and the creator. The design of a created being determines only the mode in which it will exert the physical power, whether of elasticity or weight, that it is possessed of in common with inanimate bodies of the same quantity of both. But the design of the creator carries with it the immediate power of execution to any degree. The design of the creator is his fiat, his fiat the execution of his will, whatever it be, it is no sooner designed than it is done. The creature, however ingenious, may form projects and designs innumerable beyond his powers of execution. The human imagination may form ideas; but mere ideas are all it can form. The will of the deity is omnipotent it hath made a material universe of immense momentum and moves gravitating worlds through elastic media with amazing velocity; the will of man cannot create a material atom, or give motion even to the gossamer that idles in the wanton summer air. So weak humanity!
Lord Kaims makes no distinction between action and motion; but considers motion as a continued action; and controverts the capacity of inert matter to preserve a motion once impressed on it. But in illustrating this, he contradicts known experience. When the cause of motion ceases, says he, we seek no other cause for the ceasing of the motion. Walking or running requires a continued exertion of power. It requires no exertion of power to put an end to these motions.
Dr. Stewart, on the contrary, opposes this doctrine; and very justly defends the continuation of motion, on the Newtonian principle of the vis inertiae, or the indifference of matter to motion and rest. But a man who should walk, or run with any considerable degree of velocity, particularly down-hill, will want no authority to be convinced that it does require a considerable effort to put a stop to his motion. He does not stop the moment he ceases to exert his power to move forward; but must exert a contrary power and that for some time before he will cease to move. If during that time he throws his legs forward, it is only to keep himself upright, and prevent his falling on his nose; not to carry the center of gravity of his body forward, but rather to throw it backward.
Motion, on the other hand, says the last mentioned philosopher is not action; but the effect of an action; and pertinently asks, Why may not an active being communicate motion to matter, without moving itself? Judiciously observing, that, whether the agent itself moves or not, it must have a power of acting, previous to all motion; otherwise it would be impossible for matter, or any other being, to begin motion of itself.
I have already answered his question, by shewing the impossibility of communicating motion to solid matter by mere impulse. And as to his observation, we may, in our turn, observe, that no finite created being, whether solid or fluid, active or inactive, animate or inanimate, can begin to move of itself.
Motion, as he truly asserts, is the effect of action; but it is only a secondary effect. The motion of any individual is not the direct and sole effect of the action of that individual. Two active elements may, by their mutual resistance or reaction, put each other in motion; but the reaction of the one, is reciprocally and jointly the cause of the motion of the other; and not the simple action of either. Nor is this all. There must be some inequality in their mutual resistance, arising either from the inequality of their own density, or that of the ambient medium; otherwise neither would move.
The fore-finger of my right hand, pressing against that of my left, will put it in motion; provided there be any inequality in their mutual pressure, but if they press each other equally; that is, if their reactions be equal; being in opposite directions, no motion of either ensues, with whatsoever force they may press against each other: Motion being ever generated in the direction of the least resistance.
Motion therefore is not the direct effect of the simple action of any single individual; or even the equal reactions of two; but of a partial and temporary inequality in the resistance or reaction of two or more.
This will appear still more clearly, on adverting to the propagation of motion among palpable bodies. These are usually distinguished, on this occasion, into animate and inanimate; the animate body being supposed capable, by virtue of its consciousness or power of thinking, to begin motion of itself, and the inanimate only of continuing the motion given it.
But though I impute that physical action, which is the primary generative cause of motion, to the constant exertion of an universal, metaphysical cause; to the great creator and governor of the universe; though I do not join with Hobbes or Leibnitz, in imputing consciousness or intelligence to monades or physical atoms, it does not by any means appear to me than even animated bodies are capable of originally generating motion in and of themselves. Indeed we distinguish an animate from an inanimate body, only by its apparently-voluntary or involuntary motion. If all its motions are the simple and obvious effect of some other body moving it, we say it is inanimate and its motion is called involuntary. If they are more complicated, and we do not see into the motives of its change of place, we say it is animated; its motion is voluntary, and we impute to it a capacity of thinking. Dr. Hill tells us, in speaking of microscopical observations, and I dare say, he tells us truly, that certain late philosophers of the royal society, hence mistook the seeds of a certain plant for living insects. On the same grounds it was, that the Mexicans mistook the Spanish ships when they first approached their coast, for huge fish or sea-monsters rising out of the ocean; as for the like reason the Indian-of-the-lakes took the first watch, he saw, for a demon or the familiar of a conjurer.
But the motion of a body, as I have before hinted, is not immechanical, merely because we cannot explore its mechanism. Even voluntary motion itself is imputed to some motive. A man does not move this way or that without some inducing cause; and, whether it be metaphysical and mental, or mechanical and material, is determined only from its apparent modus operandi: by its producing its effect by means of the internal organs of conception and reflection, or the external organs of sensation and motion. The one may be anatomized; the other eludes dissection; but we neither know nor can know that there is any essential difference in their mode of action.
Nothing however is more certain than that animals do not move merely because they have a capacity of feeling, thinking, and willing; though perhaps they may feel, think and will, for the same reason that they are capacitated to move. Even Dr. Stewart admits that, though a power of beginning motion seems necessarily to infer a power of thinking, we cannot inversely affirm that a power of thinking must infer a power of beginning motion.
The anatomists agree that, in the voluntary motion of the limbs of animals, the influence of their will serves only to turn the scale, if I may so term it, between two mechanic powers, vibrating in equilibrio; as the muscles, serving for voluntary motion, have each its antagonist; and would be in a state of perpetual contraction, notwithstanding the strongest exertion of the will, were it not for the equipollent libration of these antagonists.
But let thought or design proceed from what it may; whether it be, or not, the action of any particular substance; it is not the generative cause of motion, any more than motion, as Colden and others have conceived, is an inherent quality in any thing. The motion of a thing is a temporary and adventitious circumstance, and not a mode of existence or constant essential property of any simple being. Even as to palpable bodies, 'tis plain, they may be now at motion and now at rest, and sometimes in a state between both; as they are in the propagation and communication of motion by percussion; during which interval, the direction and velocity of the motion is generated by the percussion and repercussion of their component parts. For, however uncommon may be the observation, that bodies are sometimes neither in a state of motion nor rest, but between both; it is very true, considering them, as they are, compounds and individuals at the same time. Were they perfectly solid and simple indeed, they could not: they must be in motion or at rest; but being compounded, there must be some time, however small, between the moment in which their parts are struck with a certain velocity on one side, and the motion of their parts with a different velocity on the other; during this interval the body is neither wholly in motion nor wholly at rest: an interval very perceptible in the collision of compound elastic bodies; and, as I have said, we know not that bodies perfectly hard and unelastic exist in nature. Admitting even the existence of such bodies, motion could be no more communicated from one to another, in the manner it is, by percussion, than, as I have before shewn, they could originally receive it by simple impulse. For, being indifferent equally to motion and rest, the solid at rest, impelled by another in motion, would either change its place, with infinite velocity, or move forward in the same direction with the same velocity.—But this is not the case. The momentum of the motion is divided between the two bodies; which if equal, move on after collision with only half the velocity of the first mover. This division, therefore, is effected by the successive action and reaction of the parts of the two bodies; by which means those of one are impeded in their motion, as much as those of the other are impelled to move.
It is admitted, indeed, that the action and reaction of the specific parts of palpable bodies consists of actual motion. It may therefore be pertinently asked, how these, if once repelled, are brought to move forward again in the direction of the impelling body? I answer, by the repulsion of the medium in which they exist, and by virtue of which they cohere.—For it is to be observed that the gravity or weight of bodies, though always proportional to their quantity of resistance, is not proportional to their elasticity or the number of primary elastic elements contained within their dimensions. On the contrary, the heaviest and hardest body in nature, will contain the fewest elastic particles in its composition: so that in the centre of a secondary element, generated by motion, the hardest, heaviest and most impenetrable of all bodies, there would be a vacuum almost as perfect as that supposed by the Newtonians, in mere space.
For I shall prove mechanically to be true, what Sir Isaac Newton suggested that the aether or the elastic medium is the densest, where there are the fewest and lightest palpable solids.
But this I shall explain more fully, when I come to shew, why the parts of bodies gravitate and cohere; and how the resistance, which arises merely from elasticity or action in the primary elements, is supplied by motion in the secondary ones.—But to return—Though a contender for the perpetual motion, I am so far from being an advocate for what may be strictly called self-motion, that I do affirm no finite created being whatever is capable of such self-motion. Even the most nimble animal in the creation, exert what force it will, cannot move an inch without the assistance of some other body; which in its turn must be moved by it equally in a contrary direction.
This is a certain and necessary consequence of the mechanical principle of action and reaction, prevailing throughout all nature: The universal equality of this action and reaction in opposite directions, being itself the necessary consequence of bodies being composed of, and moving in, an elastic medium.
This is a critical point, Gentlemen; and, I own, I do not expect you will readily give up your privilege, of self-motion; or condescend to think yourselves obliged to stocks and stones for their assistance in moving yourselves. And yet, humiliating as may be the reflection, man, in his present state is so incumbered with matter, and so dependent on the objects about him, that he cannot stir a foot without them. What, you will say, cannot we, impatient of such discourse, rise up and go about our business at pleasure? Doubtless, Gentlemen, the will is free and your disgust will be a sufficient motive of action: but you cannot, by any action of your own, put yourselves in motion, without putting, at the same time, some other body in equal motion a contrary way; whose reaction must jointly determine the way you are to go. So far from being capable of changing your place, and going out of the room; you cannot even change your posture, and rise from your seats, without the assistance of the very chairs on which you sit. Have you the patience to permit me farther to explain myself?—I am obliged to you, Gentlemen, I see you are not sufficiently disgusted. Your chairs do not move you. I find, I may go on.
Professor Stewart, whom I have so often quoted, talks, indeed, on a similar occasion, of a man's giving himself a push, when he wants to go forward; and tells us that the common account of the progressive motion of animals, as given by Borelli, and admitted by most other authors, is too concise, if not false; videlicet, that in walking, flying, or swimming, the animal acts upon the ground, air, or water, in one direction; and that the reaction of the medium carries the animal forward, in another direction.
This theory, adopted by Sir Isaac Newton and almost all experimental philosophers, is controverted by the professor; who tells us, on the other hand, that the only immediate cause of the motion, is the active force of the animal; which presses the medium one way and its own body another. But were this the case, it is evident, on the very face of the proposition, that the same body might actively tend to one side, and also actively tend to the other, at the same time.—This the professor himself allows to be a contradiction in terms. A man indeed may, with one hand, press against one object in one direction; and with the other against another in a contrary direction, and may move both: but, if their resistance to his pressure be equal, he himself will not move, or be moved at all. And, if unequal, he would be moved, like every other body, in the direction of least resistance. If a man could move, or change his place, merely of himself, he could of himself put an end to any motion into which he might be put. But this we find impossible. A man hurried along by a force superior to his own, cannot stop himself, till he meets with some obstacle of greater resistance; a stone, post, or a brick-wall, for instance; by whose friendly aid he might be stopped.
A philosopher falling from the top of a house, with all his sagacity, resolution and activity, cannot stop himself, at least now the sign irons are taken away, till he comes to the ground.—I have indeed heard of a man, who once undertook to jump off the monument, for a wager; but when half way down, found he could not do it; slunk up again and yielded the wager lost.
You may smile, Gentlemen, but unless any of you will avouch the truth of this story, I cannot admit that, without assistance, any of you can actually move yourselves. It is pretty obvious, in the case of leaping, dancing and jumping, that we do not altogether move ourselves. To instance only the simple case of the tight rope: let the dancer cut the same capers if he can, by pressing his feet in the same manner and with the same force against an inflexible rod of iron. Would he be able, think you, to spring so high? And yet, if our motion be the immediate and sole effect of our own activity; Why not?
It may be imagined that when a man holds out his arm at length, that it is done merely by a simple and single act of volition.—Not so.— It is raised, perhaps by a single act of the will, determining the direction of least resistance among the equilibrating muscles; but it must be sustained by repeated acts of volition; that keep the sustaining muscles and their antagonists in constant vibration; or it would descend in the direction of gravity.
Hence we see that animals cannot support even the weight of their own limbs, for a length of time, without fatigue and weariness. And hence the reason and evident use of rest and sleep; to give the fibres of the muscles time to recover their elasticity, when their tone is too much relaxed by vigilance and labour. All this is merely mechanical.
So very mechanical, indeed, is the whole business of animal motion, that I should not wonder if some ingenious artist, versed in the practical expedients of machinery, should, under the direction of a Cox, or a Pinchbeck, contrive an inanimate automaton, that might be led about the room by a boy, as a blind beggar is about the streets by a dog and a string.
That sceptical smile, Gentlemen, carries with it, a Credat Judaeus Apella. And yet it is certain no greater exertion of animal power would be required, than just to incline the centre of the automaton's gravity in the line of direction, and at the same time to throw one leg forward to keep it from falling, and press the other downwards to raise the centre of gravity; and this the weight of the boy might be able to perform by pulling at the end of a string. Nay, we often see live animals so pulled along even against their inclination; but their centre of gravity being drawn forward, they are obliged to move their legs or fall down; in the mean while they are dragged on by the action of the body pulling them, as much as a cart is by the horses; the motion of the legs in one case and the wheels in the other, serving only to keep the centre of gravity from falling.
Let us suppose, Gentlemen, that, instead of sitting upon common chairs, the weight of your bodies were sustained by elastic springs: if, in order to rise, you were to press with the sedentary muscles against such springs, as forcibly as you would against a chair, you would not only be thrown up into an erect posture, but would be tumbled forward on your faces upon the carpet.
But it may be necessary to illustrate this matter still farther; as more depends on it, respecting the perpetuity of communicated motion, than may at first be imagined.
Lord Kaims, who too readily admits, on the fallacious evidence of a single sense, that an animal may move itself; argues, in order to prove it, against the universal equality of action and reaction, and objects to Sir Isaac Newton's illustration of it: saying we should make a distinction between moveable and immoveable obstacles. But no such distinction really exists. Motion, as it is not the essential property, or mode of existance, of any simple substance; so neither is it the durable state of any such substance. The object, indeed, which is resisted on all sides, is, so long as it is so equally resisted, at rest. But all physical obstacles are not only moveable, but in actual motion: their rest is only relative. Bodies equally resisted on all sides, or those moving with the same velocity the same way, are indeed at rest, with respect to each other: though with respect to another combination or system of bodies, they may be in motion with prodigious velocity. With regard to each other, Gentlemen, and the apparently immoveable objects about you; so long as you remain in any particular place, you are relatively at rest; and yet nothing is more certain than that the room itself, with all that are in it, is moved by the diurnal revolution of the earth many thousand miles in a minute.
This every body knows, and yet almost every body inadvertently concludes, that men are at rest, when they are not put in motion by themselves, or some other animated being: the obstacle, indeed, is called immoveable when, being apparently at rest, its quantity of matter is prodigiously great, in proportion to that by which it is pushed, or pulled, drawn or impelled: because in that case, its velocity is comparatively so slow as to be imperceptible; the force of the action and reaction being in all cases equal; which it would not be, if the velocity of the motion were not always reciprocally as the quantity of the moving matter.
Hence the famous position, drawn as a corollary from that of the vis inertiae, or indifference of matter to motion and rest; viz. that the leg of a fly moves the whole globe of the earth.
This instance, however, has the common fault of familiar illustrations. It does not fully apply; as it would do, if the globe of the earth were a perfectly solid body. For an obstacle may also be called immoveable (as it is to all intents and purposes equally so respecting the moving body) when, being of the same weight, it meets it with the same velocity in a contrary direction.
It stops the body as much in one case as the other, and is therefore an equal obstacle to its motion. The putting a stop to any motion, by moving in an opposite direction before collision, requires the same force and is in effect the same thing, as moving a contrary way after collision. The various motions therefore of the component parts of the earth in a contrary direction, prevent the fly's actually moving the whole.
It has been often remarked, by writers on this subject, that the animate body differs from the inanimate, with respect to motion; in that the thinking being can determine the quantity of its motion, on any occasion. But this is true only to a certain degree. An animal indeed may exert his power in various degrees, within that of its own weight, and the weight it is capable of sustaining; but no farther. It might divide and diversify the direction or tendency of that power; but it cannot encrease its momentum, or exert as much more force on any occasion as it will. When we see a waggoner belabouring a poor horse, to make him draw a weight, which he is incapable of stirring: The Brute (I don't mean the horse) seems to think, with such philosophers, that the animal can exert as much power as he pleases. But he finds the contrary, while the willing beast is cruelly loaden with stripes, for supposed stubbornness or sloth; when his only fault is the want of food to fill his belly, by which he might acquire a little more flesh on his back. Animal resolution is not a mechanic power. An animal without weight, how great soever its good will, would not be able to lift, or draw a single feather.
The objections indeed which have been started to the universal equality between the action and reaction of bodies, have taken their rise chiefly from the defective manner in which it has been illustrated.
Thus it has been said that, when a horse draws along a stone, the stone draws the horse backward with a force equal to that with which the horse draws the stone forwards.
To this it has been objected,
By Dr. Stewart. See Edinburg Essays
that "nothing more can be meant by it than that the horse loses as much force as the stone gains; and that with respect to the horse the effect is the same as if there was no stone tied behind him; but that he was pushed back with a force equal to that acquired by the stone. The active force of the horse's limbs presses forwards, it is said, both the horse and the stone; what is called the reaction of the stone is not equal to the whole force exerted by the horse; for then indeed there could be no progression, it is only equal to what is impressed upon the stone."
But the truth is that neither the illustration nor the objection are applicable to the point. As to the first, in pulling or drawing, we do not directly act, or impress any motion, on the thing pulled or drawn, as in pushing or thrusting. In the case of the horse and the stone; the horse acts only against the ground; and even in that not in a direction immediately contrary to that in which he moves. As to the stone, it is entirely passive, and though it cannot help following the horse to which it is fastened, does not exert any action affecting its motion in any direction whatever. That the several parts of the ground, the horse, the rope, and the stone, do reciprocally react on each other during the generation of the motion, I grant; for hence are its direction and velocity determined, but when the rope is stretched to its utmost degree of tension, both the horse and stone move together as one body. The horse would certainly move faster without the stone, as the stone would lie at rest without the horse; but for no other reason than that the same force of reaction could not move a mass equal to both, with the same velocity as it would move either.
In like manner, it is said, that when a person in a boat pulls a rope, which is fastened to the shore; the man acts upon the shore in one direction, and that the shore, by its reaction in the opposite direction, pulls the man and boat towards it.
To this it is also, in the same manner, objected that it is evidently the force of the man extending himself that draws the shore, with his hands, one way, and at the same time pushes the vessel with equal force, with his feet, the opposite way.
In reply to this it may be said that, though a man by extending himself, as professor Stewart terms it, might push bodies in different directions from him, it can only be by contracting himself or by moving in a contrary direction he can draw any thing toward him. He thinks no man can seriously maintain "that the shore can draw the man in the boat," yet tells us that the man in the boat really draws the shore. But the shore is certainly as much at rest, as it is inactive. The truth is, that drawing and pulling are popular and unphilosophical terms; they express rather the concomitant effect, than the cause of motion; which is originally generated by direct repulsion and not by indirect attraction. Nothing can act where it is not: the man is at a distance from the shore and neither of them acts upon the other. When the man pulls the rope indeed, the shore, the man, and the boat, are all one body: and neither act nor react on each other. The immediate cause of the motion of the boat, is the action of the boat on the water, and the reaction of the water against the boat; the inequality of which determines the boat to move on the side of least resistance. This is plain, for a man with the strength of Sampson might not be able with his hands to draw either the shore to him, or with his feet to push the boat to the shore, against an opposing tide or current. Were the reactions of the boat and the water equal, the activity of the man would no more move the boat, than if he were sitting at one end of it, and that activity were exerted in pulling a rope fastened to the other: while on the other hand, if they were unequal, and that of the current the greatest, the boat would move, notwithstanding all the man's pulling, in the direction of the current. So that, instead of taking in the rope with his hands, he must let it out; or he would himself be pulled overboard and fall into the stream.
That the motions of the stone, in one case, and of the boat in the other, are not the only immediate effect of the action of the horse, or the man, will be farther evident from considering the manner in which the motion of the animal itself is generated.
First, it is induced from some motive, either apparent or occult, to move. It must, of necessity move one way—This direction is determined by the will, or the internal active power of the animal. But it does not actually move in consequence of this determination. To put its design in execution it must press against some other resisting body. If it press in a direction contrary to that of its intended motion, and its centre of gravity rest on a slippery surface, it will, of course, be moved by the reaction of the obstacle in the direction intended. Thus a man, standing on skaits upon the ice, may, by pushing with his hands or feet against a resisting obstacle, cause it to move him, or as it is called, move himself, a considerable while, in a direction contrary to that he pushed. But, in order to avoid the wear and tear of tender bodies moving on rough surfaces, the necessary consequence of so much friction, nature has provided that the loco-motion of animals should be progressive. It becomes necessary, therefore, that the centre of gravity should alternately rise and fall. A man may slip or slide, but he cannot walk or run, without raising his centre of gravity at every step, in order to give it an inclination of descent in the direction of his motion.
This alternate rise and fall of the centre of gravity is effected by the pressure of the foot, in an oblique direction against the ground, to raise the body, and by the descent of the body when raised; during which the feet are alternately thrown forward to keep the animal from falling. Hence we see that its progressive motion in walking or running is so far from being the only immediate effect of its own motion, that it is not even the sole effect of the reaction of the medium on which it acts, but the joint effect of that reaction and the action of gravity; in the compound direction of both which it moves.
And hence we see the reason why in pulling and drawing, effected by the alternate motion of the hands or feet, the power of the animal is ever proportional to its weight and the weight it sustains. Thus in the case of the boat, the force with which it would oppose the water, would be proportional to the weight of the man pulling the rope. So that a heavy man, equally willing and active, would pull the boat a-shore, not only sooner than a light one, but when a light one, of equal activity in proportion to his bulk, would not do it all. A light animal, be its strength and activity what it will, cannot pull or draw so great a weight as an heavy animal of the same activity.
A practical and useful conclusion may be inferred from hence, not only respecting the properties of the animals best adapted for different kinds of labour; but also the method of applying those properties to the greatest advantage: every animal being capable only of exerting a power proportional to its weight, and the weight it is capable of supporting. It will, indeed, move its own limbs with an agility proportional to the elasticity of its muscles; but, caeteris paribus, an heavy animal will always be stronger, or capable of greater labour than a light one; and that in proportion to their difference of weight. Hence we see, also, why men exert their greatest strength, either in carrying burthens, or in working engines, where the whole weight of the body is employed.
The doctrine of the equality of action and reaction, has been as imperfectly illustrated, with regard to the more immediate cause of motion by impulse.
Thus, in rowing or pushing along a barge, or lighter, by means of a pole; it is commonly said the oars, in the one case, act against, or upon, the water in one direction; while the water, reacting on the oars, in a contrary direction produce the motion of the boat. In the other case, they say, that the reaction of the ground against the pole, makes the boat move. To these, it is objected, that the motion is in both cases intirely produced by the man, whose active force is the only moving power. Professor Stewart, says this, in contradiction to Sir Isaac Newton.
As to the business of rowing, it is a compound action, consisting of both pulling and pushing. A waterman pulls with one end of his oar, and pushes with the other. Not to take up your time unnecessarily, therefore, as I have already explained the mechanism of the former, I shall confine myself to the latter, viz. his pushing a barge along with a pole. In this case he exerts the the same force as if he walked by the side of the canal and dragged the boat after him. The only difference in the operation is that, in walking along the ground and pulling his boat along, the man moves constantly as fast as the boat, and may be considered as one body with it; being connected by the hawser. Here the immediate cause of motion is the inequality between the reaction of the ground against one part of this compound body, and the opposite reaction of the water against another part of it: the generative force of the motion being still merely the weight of the man. On the other hand, in pushing the barge, the man does not move always with the same velocity, though he must be always considered as part of the same body. When he rests with his shoulder on his pole, he may be considered, likewise, together with the barge and pole, as one body with the ground; to which (notwithstanding he moves his legs to keep himself from falling) he is attached, as well as to the barge; and does not move; though, by the action of his legs against the deck, the barge is partially moved from under him. When he takes up his pole, he is no longer one body with the ground, nor does he contribute to the motion of the barge. The immediate cause of which is, as before, the inequality between the reactions of the vessel and the water, and the generative force merely the weight of the man, pressing the ground, by means of the pole in one direction, and the water, by means of the barge, in another; in the compound of which two directions the barge moves; while the man himself descends in the line of gravity, and would fall flat on his face, if his centre were not repeatedly raised, by the alternate motion of his legs. Thus we see that, in this case, as in the former, neither the illustration nor the objection are strictly applicable.
That the action or voluntary motion of the man originally determines in both, the direction in which the boat is to move, is admitted. But, so does that of the man at the helm, on board a ship; and yet nobody pretends that a ship is moved solely by its pilot. The wind or tide is at least equally necessary. We are indeed our own pilots, Gentlemen; but, quo rapit tempestas—without assistance we can make no way, and even with it we cannot always make our own way.
On this consideration, though merely a mechanical one, I flatter myself with your assistance, to enable me to remove that enormous weight of public prejudice, which prevails against the perpetual motion.
This, Gentlemen, I presume to hope from your candour, as I have endeavoured to make it appear, as well as a single lecture would permit, 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 boody—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) with the difference only of being incapable of thinking or diversifying its action. And this is all that is, or can be, expected of a perpetual motion; the momentum of which may, for the reasons before given, be encreased to any degree, according to the weight of the bodies employed, and the work required to be done.
If I have failed in any particular of giving conviction, a future lecture may probably elucidate what may seem obscure in the present. In the mean time, I hope enough hath been said, to convince my auditors, that I have not excited their attention to a subject I have not long considered; and that they will at least conclude, in my favour, that a man of very moderate abilities may, during an intense application for fifteen or twenty years to one object, have taken a view of it in more lights, than the most ingenious philosopher may have done, by making it only a cursory and occasional object of his attention.
But here I must beg leave to put an end to the first part of my Lecture.
In my next (of which I shall take the liberty to give you early notice) I shall enter farther into the mechanical effects of motion: among which I place all the Phaenomena, great and small, of palpable bodies. Even their Extension, Gravitation, and Cohesion, with all their specific differences, as also their various appearances under different circumstances, I propose to prove to be the mechanical effects of one general principle of all natural perpetual motions; and that the very same on which I found my pretensions to an artificial one: Indeed, if such principle did not, or should cease to, exist in nature, we ourselves, with all the objects around us,
Would, like the baseless fabrick of a vision,
Melt into air, into thin air.
The cloud-capt towers, the gorgeous palaces,
The solemn temples— the great globe itself
Yea, all which it inherit, would dissolve,
And, like an insubstantial pageant fading,
Leave not a wreck behind.
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Perpetual Motion, Will shortly be READ, an INTRODUCTION TO A New System OF NATURAL PHILOSOPHY.
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By WILLIAM KENRICK.
Juris utriusque et Philosophiae Doctor.
Omnis enim philosophiae difficultas in eo versari videtur ut a phaenomenis motuum investigemus vires naturae; deinde ab his viribus demonstremus phaenomena reliqua: quibus viribus ignotis, philosophi hactenus naturam frustra tentarunt.
Sir ISAAC NEWTON.
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