Kinetic Theories of Gravitation/Faraday, 1844

by William Bower Taylor

Although the views announced by Professor Michael Faraday on the subject of gravitation were undoubtedly very vague, he must be classed with the kinetic theorists ; and the very influence necessarily attaching to his well-earned reputation as an investigator and experimental physicist, renders a full discussion and a free criticism of his published reflections all the more imperative in the interests of scientific truth.

In "A Speculation on the Nature of Matter," dated January 25, 1844, Faraday remarks: "The safest course appears to be to assume as little as possible ; and in that respect, the atoms of Boscovich appear to me to have a great advantage over the usual notion...A mind just entering on the subject may consider it difficult to think of the powers of matter independent of a separate something to be called the matter, but it is certainly far more difficult, and indeed impossible, to think of or imagine that matter, independent of the powers. Now the [230] powers we know and recognize in every phenomenon of the creation ; the abstract matter in none ; why then assume the existence of that of which we are ignorant, which we cannot conceive, and for which there is no philosophical necessity ? .... Doubtless the centers of force vary in their distance one from another, but that which is truly the matter of one atom touches the matter of its neighbors. Hence matter will be continuous throughout, and in considering a mass of it, we have not to suppose a distinction between its atoms and any intervening space. The powers around the centers give these centers the properties of atoms of matter; and these powers again, when many centers by their conjoint forces are grouped into a mass, give to every part of that mass the properties of matter The view now stated of the constitution of matter would seem to involve necessarily the conclusion that matter fills all space, or at least all space to which gravitation extends ; for gravitation is a property of matter dependent on a certain force, and it is this force which constitutes matter. In that view, matter is not merely mutually penetrable, but each atom extends, so to say, throughout the whole of the solar system, yet always retaining its own centre of force."^[1]

This result of "assuming as little as possible" thus appears to commence with the Berkeleyan negation of matter, only to conclude that it is omnipresent. When it is inferred however, that every atom separately includes every other atom, it is obviously only influence that is conceived of, and not matter at all in any intelligible sense. If we call this multitudinous infinitely-extended and mutually-inclusive influence " matter," there still remains the inexorable necessity of designating by some distinctive title that other form of influence inclosed within the visible tangible surfaces bounding those appearances which are characterized by inertia, which are accurately measurable in mass, and which are the objects of all our direct observation and experiment. Neither in formula, nor in idea, therefore, — neither in nominalism, nor in realism, — are we advanced a particle by such speculations.

In a memoir "On the Possible Relation of Gravity to Electricity," read before the Royal Society, November 28, 1850, Faraday remarks: "The long and constant persuasion that all the forces of nature are mutually dependent, having one common origin, or rather being different manifestations of one fundamental power, has made me often think upon the possibility of establishing by experiment, a connection between gravity and electricity, and so introducing the former into the group, the chain of which (including magnetism, chemical force, and heat,) binds so many and such varied exhibitions of force together by common relations." He then records experiments with a tubular helix of covered copper wire of considerable length, and having its extremities connected with long covered wires which were brought to a very sensitive galvanometer, the said coil or helix being allowed to fall about [231] thirty six feet. No indications however, were perceived in the needle.^[2] Experiments with solid cylinders of copper, iron, glass, &c., secured within the helix were successively made without result. Similar cylinders were then dropped through a fixed helix, and also reciprocating motion by mechanical devices was tried, but equally without any effect on the galvanometer needle. Faraday concludes, " Here end my trials for the present. The results are negative. They do not shake my strong feeling of the existence of a relation between gravity and electricity, though they give no proof that such a relation exists."^[3] These experiments were skillfully devised to detect a correlation between the two, if any such existed. Were gravity either a form or a resultant of molecular motion we should certainly expect to find evidence of an expenditure of such motion, proportioned to the energy of the "fall."

Several years later, in a memoir "On the Conservation of Force," Professor Faraday thus states the result of his further meditations on the "attractive" theme of gravitation: "I believe I represent the received idea of the gravitating force aright in saying that it is a simple attractive force exerted between any two or all the particles or masses of matter at every sensible distance, but with a strength varying inversely" as the square of the distance. The usual idea of the force implies direct action at a distance ; and such a view appears to present little difficulty except to Newton, and a few, including myself, who in that respect may be of like mind with him.^[4] This idea of gravity appears to me to ignore entirely the principle of the conservation of force; and by the terms of its definition, if taken in an absolute sense, varying inversely as the square of the distance,' to be in direct opposition to it."^[5]

This singular misconception of his theme, which underlies all his subsequent reasoning, may be briefly rebutted by the simple averment that the conservation of force has no relation whatever to the law of force, and can have no relation to it. All that the established doctrine affirms, is that be the law what it may, "conservation" demands that none of the resultant effects shall vanish, and that the action of the law shall be absolutely the same in the same conditions. In the ease of a dynamic radiation — indeed, through a perfectly elastic medium, —[232] conservation requires that all the successive spheres described by increasing radii of action shall represent precisely the same amount of energy, which is the expression of "inverse squares." But in the case of a primitive force which is not radiation, (as in gravity, elasticity, cohesion, or affinity,) the law of increment or decrement with distance may have any mathematical value, and may be entirely different and incommensurable with every variety of force.

Unfortunately the human mind has been gifted with no insights or intuitions which can determine the ft priori certainty of a single fact of natural law. After twenty-five centuries of vainly-struggling speculation, the true law of one kind of force was laboriously ascertained only two little centuries ago. And this result is justly regarded as the most brilliant achievement of the highest human intellect. Did experience teach us that the law of gravity was one of simple decrease of intensity directly with the distance, (in which case the periodic times of the planets would be directly as their distances and their orbital velocities the same at all distances,) or did it teach us that its energy was precisely the same at all distances, as Faraday thinks to be the true desideratum, (in which case the periodic times as well as the orbital velocities would be as the square roots of the distances,) or did it teach us that its intensity increased directly as the distance, as by an elastic bond,^[6] (in which case the periods of revolution would be the same for all distances, and the orbital velocities therefore, proportional to the distance,) in each and every case it would still be unalterably true that the energy expended in separating two bodies would be exactly equal to the energy given out in their return to the antecedent position. And this is what is meant by the "conservation of force."

Probably no generalization of science has been the occasion of more misapprehension and confusion than this of " conservation. Properly speaking, " Force " is not conserved at all ! It is the offspring of Force, or " work " that is really conserved. As words necessarily follow thought practically no less than genetically, (and sometimes longo intervallo,) it results that with the increasing specializations of scientific conception, many words continue to retain their more primitive or "comprehensive type" cf meaning, without originating the required varieties or differentiations of expression ; and such has been the case with the very useful word "force;" which is employed sometimes in its more generalized sense, as including any stress or action whatever; sometimes as limited to quantity of motion ; sometimes as synonymous with energy, (in which sense alone is "conservation" applicable to it;) sometimes as expressing " the mere rate of conversion or transference of energy per unit length of that motion," (with a strong suspicion that " there is probably no such tiling as force at all;")^[7] and sometimes as signifying [233] primitive innate tension, exclusive of all motion, although the parent of all motion. So that while one would limit the word to designate a purely kinetic condition of matter, another would limit it on the opposite side to designate a purely static quality in matter.

Elasticity is a natural force, having always an entirely different spacepotential from gravity, and yet is equally removed in every case from that ratio of uniformity supposed to be the true representation of conservation. In the case of tensile elasticity, (as of a rubber baud or of a long spiral spring,) the tension increases directly with the distance of elongation.

Professor Faraday thus proceeds to illustrate the difficulty he finds in the ordinary definition of gravity : " Assume two particles of matter, A and B, in free space. . . . Then at the distance of 10 the force may be estimated at 1, whilst at the distance of 1, i. e., one-tenth of the former, the force will be 100; and if we suppose an elastic spring to be introduced between the two as a measure of the attractive force, the power compressing it will be a hundred times as much in the latter case as in the former. But from whence can this enormous increase of the power come? The answer is, that this increase of "power" comes from either particle being so much nearer the source of the influence. Why this increase should be just one hundred-fold in the case supposed, the present state of science does not furnish any explanation. The result is accepted simply as a very rigorously verified " fact."

"Suppose the two particles A and B removed back to the greater distance of 10, then the force of attraction would be only a hundredth part of that they previously possessed ; this, according to the statement that the force varies inversely as the square of the distance, would double the strangeness of the above results ; it would be an annihilation of force." Here again, the law of intensity, as a function of distance, is confounded with absolute quantity in the agent. Such a confusion could hardly have occurred in discussing the action of a permanent magnet. The actually existing gravity decrement no more involves any "annihilation of force," than would an equality of ratio irrespective of distance involve a creation of force, were it found in any case to be true. So far from there being any destruction or loss of force in the crucial case supposed, the doctrine of "conservation" teaches us that the separation of the two particles could be effected only by the expenditure of an adequate amount of energy; and that at their greater distance of 10, these particles would possess a potential of position precisely equivalent thereto.

Faraday continues : "According to the definition, the force depends upon both particles ; and if the particle A or B were by itself, it could not gravitate, i. e. it could have no attraction, no force of gravity. . . . As the particles can be separated, we can easily conceive of the particle B being removed to an infinite distance from A, and then the power in A will be infinitely diminished. Such removal of B will be as if it were [234] annihilated in regard to A, and the force in A will be annihilated at the same time."^[8] Although it is certainly true that when B is removed to an infinite distance from A, the power of A upon B will be infinitely diminished, it is not a sound inference that "the power in A will be infinitely diminished." The same inaccuracy occurs in the assumption that if an isolated particle " could not gravitate" it could have " no force of gravity." This is but another expression of the not unusual sophism that force has no existence unless in active exercise.

Varying his illustration to attack the problem of mass, Professor Faraday thus further unfolds his difficulties: "The particle A will attract the particle B at the distance of a mile with a certain degree of force ; it will attract the particle C at the same distance of a mile, with a power equal to that by which it attracts B. If myriads of like particles be placed at the given distance of a mile, A will attract each with equal force. . . . How are we to conceive of this force growing up in A to a million-fold or more ? And if the surrounding particles be then removed, of its diminution in an equal degree? Or how are we to look upon the power raised up in all these outer x^articles by the action of A on them, or by their action one on another, without admitting (according to the limited definition of gravitation) the facile generation and annihilation of force ?" The substance of this enigma is comprised in the corollary to our second proposition. Striking out the fallacious expression "of this force growing up in A," which has already been sufficiently criticised, surely the case as stated, is a very good illustration of " conservation." The hypothetical generation and annihilation of the distant particles surrounding A are just as "facile" as the hypothetical " generation and annihilation of force " exercised by them; but no whit more so. As if one should say, imagine the clock wound up, and it will run a week. The equation is correct only on condition that both the terms are equally real or equally imaginary.

Inasmuch as the accepted definition of gravitative force (deemed by Faraday so objectionable) is merely the summation of an over^'helming induction derived from a ceaseless observation, the question naturally arises, to what point are the difficulties imagined by him supposed to tend ? " The principle of the conservation of force would lead us to assume that when A and B attract each other less because of increasing distance, then some other exertion of power, either within or without them, is proportionately growing up. And again that when their distance is diminished, as from 10 to 1, the power of attraction, now increased a hundred-fold, has been produced out of some other form of power which has been equivalently reduced."^[9] Were gravity merely a dynamic energy, generated in time and space by an anterior and exterior force, the inference would undoubtedly be correct. Conversely, the utter falsity of the inference, as established by all experience, in which [235] experience, as a question of fact, the keenest of experimental investigators, Faraday himself, has been able to detect no flaw, the utter falsity of the inference may be taken as conclusive against the premiss. Gravity is thereby proved to be a static tension^ — incessant, inconvertible, inexhaustible; as affirmed by our fifth and sixth propositions. Whatever a priori conceptions may be indulged therefore, as to the natural fitness of a central force having the same tension at all distances, it has been definitely established by two centuries of continuous and irreversible demonstration, that gravity is not such a force. And this announcement is the subject of our third proposition.

" It will not be imagined for a moment," says Faraday, " that I am opposed to what may be called the law of gravitative action; that is, the law by which all the known effects of gravity are governed. What I am considering is the definition of the force of gravitation. . . . That the totality of a force can be employed according to that law I do not believe, either in relation to gravitation, or electricity, or magnetism, or any other supposed form of power."^[10] But the most refined and varied observations (even when conducted by a Faraday) have failed to detect any such supposed residuum of effect, and have substantiated as one of the largest results of our present knowledge the received formula as expressing the "totality" of the force recognized as gravity. Our "beliefs" should always be based upon, and conform to, the observed order of nature. "The safest course appears to be to assume as little as possible."

Faraday thus sums up his own impressions: "For my own part, many considerations urge my mind toward the idea of a cause of gravity which is not resident in the particles of matter merely, but constantly in them and all space." (p. 231.) " I would much rather incline to believe that bodies affecting each other by gravitation act by lines of force of definite amount, or by an aether pervading all parts of space, than admit that the conservation of force could be dispensed with." (238.) Fortunately, the alternative presented possesses no relation of its terms. The unqualified assertion of " conservation" has no bearing whatever on either "lines of force" or the supposed action of " an aether;" and a choice is therefore quite unnecessary.^[11]

On no subject, perhaps, have the distinguished author's ideas been more vague and intangible than on the favorite one of " lines of force." After exhibiting the familiar magnetic curves or chains of iron-filings as a typical phenomenon, he says : " The term line of force, as defined above, is restricted to mean no more than the condition of the force in a given place as to strength and direction; and not to include any idea of the nature of the physical cause of the phenomena. At the same time, if [236] reason should arise to think that the physical condition of the force partakes generally of the nature of a current or of a ray, a view which the author inclines to, he sees no objection in the term."^[12]

" In the action of gravity, for instance, the line of force is a straight line, as far as we can test it by the resultant phenomena. It cannot be deflected or even affected, in its course. Neither is the action in one line at all influenced, either in direction or amount, by a like action in another line."^[13] This is the affirmation made by our first proposition.

Faraday continues : " There is one question in relation to gravity, which, if we could ascertain or touch it, would greatly enlighten us. It is, whether gravitation requires time. If it did, it would show undeniably, that a physical agency existed in the course of the line of force. It seems equally impossible to prove or disprove this point, since there is no capability of suspending, changing, or annihilating the power, or annihilating the matter in which the power resides."^[14] Some six years before the date of this latter paper. Professor Faraday, in "Thoughts on Ray-vibrations," had suggested more doubtingly, the same inquiry : " I am not aware whether there are any data by which it has been or could be ascertained whether such a power as gravitation acts without occupying time."^[15]

This query finds its answer in our fourth proposition. The writer was evidently not aware that it had been definitely settled by the astronomers, and with a delicacy of precision infinitely beyond the reach of any direct or instrumental' research ; and not being a mathematician, he very naturally supposed the problem insoluble. Those not trained in the higher operations of the science of " necessary conclusions," have no conception of the resources of mathematical investigation applied to judicious comparisons of accurate observations. And just here the reminder may be permitted, that did the influence of gravitation occupy the millionth part of a second in traversing the distance of a million miles, the astronomer's analysis would easily detect it. This would represent only.one-ninth of the velocity estimated by Laplace and Arago, as previously stated.

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1. L. E. D. Philosophical Magazine, 1844, vol. xxiv, pp. 140-143.
2. It is evident that whether the earth be contemplated as an electrically-charged globe or as a permanent magnet, the delicate experiments of Faraday, above described, would necessarily give indications thereof in the galvanometer : and it is an interesting illustration of the scientific conscientiousness of the experimenter, to observe with what caution these collateral results were eliminated.
3. Philosophical Transactions Roy. See, 1851, vol. 141, pp. 1-6. A Mr. Zalewski presented to the French Academy of Sciences, (April 22, and August 19, 1850, and again July 5 and 19, 1852,) memoirs "On Electricity as the Cause of the Effects attributed to Universal Gravitation." {Comptes Rendtis, 1850, vol. xxx, p. 485; vol. xxxi, p. 255; and for 18.52, vol. xxxv, pp. 49 and 95.) " Faraday's insight was so profound, that we cannot assert that something may not yet be discovered by such experiments, but it will assuredly not be conservation of force." Professor Tait's Lecture on "Force," Nature, 21st September, 1876, vol. xiv, p. 452.
4. Referring, of course, to the "third Bentley letter."
5. L. E. D. Phil. Mag., 1857, vol. xiii, p, 228.
6. There is reason to believe that this is actually the law of the atomic orbits.
7. Lecture on "Force," by Professor Tait, of Edinburgh. Nature, 21st September, 1876, vol. xiv, pp. 459, 463. It is certain that Newton did not employ the word Vis in any such restricted sense, as the learned professor would imply.
8. L. E. D. Phil. Mag. 1857, vol. xiii, pp. 228, 229.
9. Loco citat., pp. 230, 231.
10. Loco citat., p. 233.
11. An excellent review and criticism of Professor Faraday's Memoir on Gravitation, by Professor Brücke, of Vienna, was published in the L. E.D., Phil. Mag., 1858, vol. xv, p. 81.
12. L. E. D., Phil. Mag., 1852, vol. iii, p. 67. Dr. P. M. Roget showed in 1831, by a very neat geometrical demonstration, that these so-called " lines of force " in the magnetic field, are simply the tangential resultants of the directive action by the two magnetic poles exerted in straight or radial lines with a ratio of diminished intensity as the square of the distance from either pole, on the minute iron particles regarded as needles. (Journal of the Royal Institution, February, 1831, vol. 1, pp. 311-318; and also a treatise on " Magnetism " by the same author, in vol. ii of the " Library of Useful Knowledge," chap, ii, sect. 3, pp. 19-21.) M. Ch. Cellerier has also, by an analytical discussion of the "magnetic curves," established the same conclusion mathematically. (A Treatise on Electricity, by Aug. De La Rive, London, 2 vols., 8vo, 18.53. part iii, chap. i. Note D, vol. i, pp. 542-544.)
13. Phil. Mag., 1852, vol. iii, p. 403.
14. Ibidem, p. 403.
15. Phil. Mag., May, 1846, vol. xxviii, p. 349.