Reference: A Logical Approach to Theoretical Physics
Reference: Fundamentals of Physics
This is a talk by Michael Faraday delivered on February 27, 1857. It is available at the Proceedings of the Royal Institution, Vol. II. p. 352.
Here is a brief summary of my comments.
In this lecture Faraday presents the concept of conservation of force. To him, Force is the cause of a physical action, and not just the tendency of the body to pass from one place to another. Force is the source or sources of all possible changes amongst the particles or materials of the universe. To Faraday force is an indicator of the substantialness of substance, much like inertia.
These ideas were opposed by many scientists of his time, who viewed Faraday’s ideas to contradict Newton’s. But Faraday believed that he was expanding upon Newton’s ideas to address the dilemma of action at a distance. Action at a distance was troublesome to Newton as well.
Faraday was an experimentalist. He did not have deep knowledge of mathematics, and could not verify his conclusions accordingly. Therefore he was criticized by other scientists. But Faraday did not think that he had any less capability for perceiving the nature and power of a natural principle of action.
Extensive and painstaking experiments had led Faraday to implicitly trust the principle of conservation of force. This principle went beyond the conservation of energy, mass and momentum put together, as it meant the conservation of the very substance underlying all forms. To him there was no absolute destruction or creation of such force of substance.
Faraday saw consistency in all forms of physical power, whether it was static electricity, electric current, magnetism, chemical action, or heat. Therefore, consistency was expected between gravitation and any of these forms of force. Faraday believed that bodies affecting each other by gravitation acted by lines of force of definite amount (somewhat in the manner of magnetic or electric induction but without polarity).
In Faraday’s view, the principle of conservation of force (in its broadest sense of inertia) could greatly aid experimental philosophers in the enunciation of problems to be solved.
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The contents of Faraday’s talk follow. My comments follow the paragraphs in bold color italics.
On the Conservation of Force
Various circumstances induce me at the present moment to put forth a consideration regarding the conservation of force. I do not suppose that I can utter any truth respecting it that has not already presented itself to the high and piercing intellects which move within the exalted regions of science; but the course of my own investigations and views makes me think that the consideration may be of service to those persevering labourers (amongst whom I endeavour to class myself), who, occupied in the comparison of physical ideas with fundamental principles, and continually sustaining and aiding themselves by experiment and observation, delight to labour for the advance of natural knowledge, and strive to follow it into undiscovered regions.
There is continuity of substance from neutron to proton to electron to light. Faraday sees this continuity as lines of force that are centered at, let’s say, neutrons. These lines of force represent the substance. The overall force is conserved. Faraday’s concept of force includes both mass and energy. Therefore, it is different from Newton’s concept of force.
There is no question which lies closer to the root of all physical knowledge, than that which inquires whether force can be destroyed or not. The progress of the strict science of modern times has tended more and more to produce the conviction that “force can neither be created nor destroyed,” and to render daily more manifest the value of the knowledge of that truth in experimental research. To admit, indeed, that force may be destructible or can altogether disappear, would be to admit that matter could be uncreated; for we know matter only by its forces: and though one of these is most commonly referred to, namely gravity, to prove its presence, it is not because gravity has any pretension, or any exemption amongst the forms of force, as regards the principle of conservation; but simply that being, as far as we perceive, inconvertible in its nature and unchangeable in its manifestation, it offers an unchanging test of the matter which we recognize by it.
The force of gravity is one of these forces. Gravity is most commonly referred to prove the presence of matter because it is inconvertible in its nature and unchangeable in its manifestation. It offers an unchanging test of the matter which we recognize by it.
Agreeing with those who admit the conservation of force to be a principle in physics as large and sure as that of the indestructibility of matter, or the invariability of gravity, I think that no particular idea of force has a right to unlimited or unqualified acceptance, that does not include assent to it; and also, to definite amount and definite disposition of the force, either in one effect or another, for these are necessary consequences: therefore, I urge, that the conservation of force ought to be admitted as a physical principle in all our hypotheses, whether partial or general, regarding the actions of matter.
The conservation of force ought to be admitted as a physical principle in all our hypotheses, whether partial or general, regarding the actions of matter.
I have had doubts in my own mind whether the considerations I am about to advance are not rather metaphysical than physical. I am unable to define what is metaphysical in physical science; and am exceedingly adverse to the easy and unconsidered admission of one supposition upon another, suggested as they often are by very imperfect induction from a small number of facts, or by a very imperfect observation of the facts themselves: but, on the other hand, I think the philosopher may be bold in his application of principles which have been developed by close inquiry, have stood through much investigation, and continually increase in force.
The philosopher may be bold in his application of principles which have been developed by close inquiry, have stood through much investigation, and continually increase in force.
For instance, time is growing up daily into importance as an element in the exercise of force. The earth moves in its orbit in time; the crust of the earth moves in time; light moves in time; an electro-magnet requires time for its charge by an electric current: to inquire, therefore, whether power, acting either at sensible or insensible distances, always acts in time, is not to be metaphysical; if it acts in time and across space, it must act by physical lines of force; and our view of the nature of the force may be affected to the extremest degree by the conclusions, which experiment and observation on time may supply; being, perhaps, finally determinable only by them. To inquire after the possible time in which gravitating, magnetic, or electric force is exerted, is no more metaphysical than to mark the times of the hands of a clock in their progress; or that of the temple of Serapis in its ascents and descents; or the periods of the occultations of Jupiter’s satellites; or that in which the light from them comes to the earth.
If power acts in time and across space it must act by physical lines of force (continuity of substance). To inquire after the possible time in which gravitating, magnetic, or electric force is exerted, is no more metaphysical than to mark the times of the hands of a clock in their progress.
Again, in some of the known cases of action in time, something happens whilst the time is passing which did not happen before, and does not continue after: it is therefore not metaphysical to expect an effect in every case, or to endeavour to discover its existence and determine its nature. So in regard to the principle of the conservation of force; I do not think that to admit it, and its consequences, whatever they may be, is to be metaphysical: on the contrary, if that word have any application to physics, then I think that any hypothesis, whether of heat, or electricity, or gravitation, or any other form of force, which either wittingly or unwittingly dispenses with the principle of conservation, is more liable to the charge, than those which, by including it, become so far more strict and precise.
Any hypothesis, whether of heat, or electricity, or gravitation, or any other form of force, which either wittingly or unwittingly dispenses with the principle of conservation, is more liable to the charge of being metaphysical.
Supposing that the truth of the principle of the conservation of force is assented to, I come to its uses. No hypothesis should be admitted nor any assertion of a fact credited, that denies the principle. No view should be inconsistent or incompatible with it. Many of our hypotheses in the present state of science may not comprehend it, and may be unable to suggest its consequences; but none should oppose or contradict it.
No hypothesis should be admitted nor any assertion of a fact credited, that denies the principle of the conservation of force.
If the principle be admitted, we perceive at once, that a theory or definition, though it may not contradict the principle cannot be accepted as sufficient or complete unless the former be contained in it; that however well or perfectly the definition may include and represent the state of things commonly considered under it, that state or result is only partial, and must not be accepted as exhausting the power or being the full equivalent, and therefore cannot be considered as representing its whole nature; that, indeed, it may express only a very small part of the whole, only a residual phenomenon, and hence give us but little indication of the full natural truth. Allowing the principle its force, we ought, in every hypothesis; either to account for its consequences by saying what the changes are when force of a given kind apparently disappears, as when ice thaws, or else should leave space for the idea of the conversion. If any hypothesis, more or less trustworthy on other accounts, is insufficient in expressing it or incompatible with it, the place of deficiency or opposition should be marked as the most important for examination; for there lies the hope of a discovery of new laws or a new condition of force. The deficiency should never be accepted as satisfactory, but be remembered and used as a stimulant to further inquiry; for conversions of force may here be hoped for. Suppositions may be accepted for the time, provided they are not in contradiction with the principle. Even an increased or diminished capacity is better than nothing at all; because such a supposition, if made, must be consistent with the nature of the original hypothesis, and may, therefore, by the application of experiment, be converted into a further test of probable truth. The case of a force simply removed or suspended, without a transferred exertion in some other direction, appears to me to be absolutely impossible.
If any hypothesis, more or less trustworthy on other accounts, is insufficient in expressing the conservation of force or incompatible with it, the place of deficiency or opposition should be marked as the most important for examination; for there lies the hope of a discovery of new laws or a new condition of force.
If the principle be accepted as true, we have a right to pursue it to its consequences, no matter what they may be. It is, indeed, a duty to do so. A theory may be perfection, as far as it goes, but a consideration going beyond it, is not for that reason to be shut out. We might as well accept our limited horizon as the limits of the world. No magnitude, either of the phenomena or of the results to be dealt with, should stop our exertions to ascertain, by the use of the principle, that something remains to be discovered, and to trace in what direction that discovery may lie.
No magnitude, either of the phenomena or of the results to be dealt with, should stop our exertions to ascertain, by the use of the principle, that something remains to be discovered, and to trace in what direction that discovery may lie.
I will endeavour to illustrate some of the points which have been urged, by reference, in the first instance, to a case of power, which has long had great attractions for me, because of its extreme simplicity, its promising nature, its universal presence, and its invariability under like circumstances; on which, though I have experimented and as yet failed, I think experiment would be well bestowed: I mean the force 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.
Gravitating force is defined as 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. This idea of direct action at a distance is troublesome.
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; and it becomes my duty, now, to point out where this contradiction occurs, and to use it in illustration of the principle of conservation. Assume two particles of matter A and B, in free space, and a force in each or in both by which they gravitate towards each other, the force being unalterable for an unchanging distance, but varying inversely as the square of the distance when the latter varies. Then, at the distance of 10 the force may be estimated as 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? If we say that it is the character of this force, and content ourselves with that as a sufficient answer, then it appears to me, we admit a creation of power, and that to an enormous amount; yet by a change of condition, so small and simple, as to fail in leading the least instructed mind to think that it can be a sufficient cause:—we should admit a result which would equal the highest act our minds can appreciate of the working of infinite power upon matter; we should let loose the highest law in physical science which our faculties permit us to perceive, namely, the conservation of force. 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 ; an effect equal in its infinity and its consequences with creation, and only within the power of Him who has created.
This idea of gravity appears to ignore the principle of the conservation of force; and the statement “varying inversely as the square of the distance” seems to be in direct opposition to it. It assumes a force in the body by which it gravitates towards another body. This force varies with the distance between the bodies. It means “creation of tremendous power” with lessening of distance, and “annihilation of power” with increasing distance.
We have a right to view gravitation under every form that either its definition or its effects can suggest to the mind; it is our privilege to do so with every force in nature; and it is only by so doing, that we have succeeded, to a large extent, in relating the various forms of power, so as to derive one from another, and thereby obtain confirmatory evidence of the great principle of the conservation of force. Then let us consider the two particles A and B as attracting each other by the force of gravitation, under another view. 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. Supposing A to exist in that isolated state and without gravitating force, and then B placed in relation to it, gravitation comes on, as is supposed, on the part of both. Now, without trying to imagine how B, which had no gravitating force, can raise up gravitating force in A; and how A, equally without force beforehand can raise up force in B, still, to imagine it as a fact done, is to admit a creation of force in both particles; and so to bring ourselves within the impossible consequences which have already been referred to.
From another view, the force of gravity depends on two particles. A particle cannot gravitate by itself. How does the force of gravity arise just because of the presence of another particle?
It may be said we cannot have an idea of one particle by itself, and so the reasoning fails. For my part I can comprehend a particle by itself just as easily as many particles; and though I cannot conceive the relation of a lone particle to gravitation, according to the limited view which is at present taken of that force, I can conceive its relation to something which causes gravitation, and with which, whether the particle is alone, or one of a universe of other particles, it is always related. But the reasoning upon a lone particle does not fail; for 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 annihilated in regard to A, and the force in A will be annihilated at the same time: so that the case of a lone particle and that where different distances only are considered become one, being identical with each other in their consequences. And as removal of B to an infinite distance is as regards A annihilation of B, so removal to the smallest degree is, in principle, the same thing with displacement through infinite space: the smallest increase in distance involves annihilation of power; the annihilation of the second particle, so as to have A alone, involves no other consequence in relation to gravity; there is difference in degree, but no difference in the character of the result.
When two particles move away from each other to infinite distance, their power annihilate by degrees until it completely disappears.
It seems hardly necessary to observe, that the same line of thought grows up in the mind if we consider the mutual gravitating action of one particle and many. The particle A will attract the particle B at the distance of a mile with a certain degree of force ; it will attract a 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 ; and if other particles be accumulated round it, within and without the sphere of two miles diameter, it will attract them all with a force varying inversely with the square of the distance. 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 particles 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?
With the limited definition of gravitation we have to admit to the facile generation and annihilation of power.
The assumption which we make for the time with regard to the nature of a power (as gravity, heat, &c.), and the form of words in which we express it, i.e, its definition, should be consistent with the fundamental principles of force generally. The conservation of force is a fundamental principle; hence the assumption with regard to a particular form of force, ought to imply what becomes of the force when its action is increased or diminished, or its direction changed; or else the assumption should admit that it is deficient on that point, being only half competent to represent the force; and, in any case, should not be opposed to the principle of conservation. The usual definition of gravity as an attractive force between the particles of matter VARYING inversely as the square of the distance, whilst it stands as a full definition of the power, is inconsistent with the principle of the conservation of force. If we accept the principle, such a definition must be an imperfect account of the whole of the force, and is probably only a description of one exercise of that power, whatever the nature of the force itself may be. If the definition be accepted as tacitly including the conservation of force, then it ought to admit, that consequences must occur during the suspended or diminished degree of its power as gravitation, equal in importance to the power suspended or hidden; being in fact equivalent to that diminution. It ought also to admit, that it is incompetent to suggest or deal with any of the consequences of that changed part or condition of the force, and cannot tell whether they depend on, or are related to, conditions external or internal to the gravitating particle; and, as it appears to me, can say neither yes nor no to any of the arguments or probabilities belonging to the subject.
The current definition of gravity is an imperfect account of the whole of the force. It does not tell us about the nature of the force. During the diminishing of the power of gravitation, equivalent consequences must occur. Such consequences may be related to conditions external or internal to the gravitating particle.
If the definition denies the occurrence of such contingent results, it seems to me to be unphilosophical; if it simply ignores them, I think it is imperfect and insufficient; if it admits these things, or any part of them, then it prepares the natural philosopher to look for effects and conditions as yet unknown, and is open to any degree of development of the consequences and relations of power: by denying, it opposes a dogmatic barrier to improvement; by ignoring, it becomes in many respects an inert thing, often much in the way; by admitting, it rises to the dignity of a stimulus to investigation, a pilot to human science.
By admitting to its limitation, the current idea of gravity would stimulate further scientific investigation for effects and conditions as yet unknown.
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. This enlarged assumption of the nature of gravity is not more metaphysical than the half assumption; and is, I believe, more philosophical, and more in accordance with all physical considerations. The half assumption is, in my view of the matter, more dogmatic and irrational than the whole, because it leaves it to be understood, that power can be created and destroyed almost at pleasure.
When gravitational attraction is changing because of change in distance, then some other exertion of power, either within or without the particles, must also be changing proportionately.
When the equivalents of the various forms of force, as far as they are known, are considered, their differences appear very great; thus, a grain of water is known to have electric relations equivalent to a very powerful flash of lightning. It may therefore be supposed that a very large apparent amount of the force causing the phenomena of gravitation may be the equivalent of a very small change in some unknown condition of the bodies, whose attraction is varying by change of distance. 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. I have already put forth considerations regarding gravity which partake of this idea, and it seems to have been unhesitatingly accepted by Newton.
It may be supposed that a very large apparent amount of the force causing the phenomena of gravitation may be the equivalent of a very small change in some unknown condition of the bodies, whose attraction is varying by change of distance.
There is one wonderful condition of matter, perhaps its only true indication, namely inertia; but in relation to the ordinary definition of gravity, it only adds to the difficulty. For if we consider two particles of matter at a certain distance apart, attracting each other under the power of gravity and free to approach, they will approach; and when at only half the distance each will have had stored up in it, because of its inertia, a certain amount of mechanical force. This must be due to the force exerted, and, if the conservation principle be true, must have consumed an equivalent proportion of the cause of attraction; and yet, according to the definition of gravity, the attractive force is not diminished thereby, but increased four-fold, the force growing up within itself the more rapidly, the more it is occupied in producing other force. On the other hand, if mechanical force from without be used to separate the particles to twice their distance, this force is not stored up in momentum or by inertia, but disappears; and three-fourths of the attractive force at the first distance disappears with it: How can this be?
There appears to be an anomaly of gravitational force with respect to the concept of inertia.
In Faraday’s example, two particle’s can maintain a certain distance between them only when they are moving with a certain velocity about each other. In that case the centripetal force shall balance the force of gravitational attraction. The natural motion is tied to the consistency of the particle. If the motion increases the consistency must decrease and vice versa. Looks like the general concept of consistency is similar to the concept of inertia in matter. A slight change in inertia shall create a very large change in the natural motion of a mass particle. It appears to me that as the force of gravitation increases as the mass particles are brought closer to each other, their inertia must decrease by a corresponding amount.
We know not the physical condition or action from which inertia results; but inertia is always a pure case of the conservation of force. It has a strict relation to gravity, as appears by the proportionate amount of force which gravity can communicate to the inert body; but it appears to have the same strict relation to other forces acting at a distance as those of magnetism or electricity, when they are so applied by the tangential balance as to act independent of the gravitating force. It has the like strict relation to force communicated by impact, pull, or in any other way. It enables a body to take up and conserve a given amount of force until that force is transferred to other bodies, or changed into an equivalent of some other form; that is all that we perceive in it: and we cannot find a more striking instance amongst natural, or possible, phenomena of the necessity of the conservation of force as a law of nature; or one more in contrast with the assumed variable condition of the gravitating force supposed to reside in the particles of matter.
Inertia restrains the acceleration, which results in constant speed for the particle.
Even gravity itself furnishes the strictest proof of the conservation of force in this, that its power is unchangeable for the same distance; and is by that in striking contrast with the variation which we assume in regard to the cause of gravity, to account for the results at different distances.
When inertia is smaller the constant speed is higher.
It will not be imagined for a moment that I am opposed to what may be called the law of gravitating 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 result of one exercise of a power may be inversely as the square of the distance, I believe and admit; and I know that it is so in the case of gravity, and has been verified to an extent that could hardly have been within the conception even of Newton himself when he gave utterance to the law: but 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.
Only an aspect of the force of gravitation, and not the totality of it, follows the law of inverse squares.
I might have drawn reasons for urging a continual recollection of, and reference to, the principle of the conservation of force from other forms of power than that of gravitation; but I think that when founded on gravitating phenomena, they appear in their greatest simplicity; and precisely for this reason, that gravitation has not yet been connected by any degree of convertibility with the other forms of force. If I refer for a few minutes to these other forms, it is only to point in their variations, to the proofs of the value of the principle laid down, the consistency of the known phenomena with it, and the suggestions of research and discovery which arise from it. Heat, for instance, is a mighty form of power, and its effects have been greatly developed; therefore, assumptions regarding its nature become useful and necessary, and philosophers try to define it. The most probable assumption is, that it is a motion of the particles of matter; but a view, at one time very popular, is, that it consists of a particular fluid of heat. Whether it be viewed in one way or the other, the principle of conservation is admitted, I believe, with all its force. When transferred from one portion to another portion of like matter the full amount of heat appears. When transferred to matter of another kind an apparent excess or deficiency often results; the word “capacity” is then introduced, which, whilst it acknowledges the principle of conservation, leaves space for research. When employed in changing the state of bodies, the appearance and disappearance of the heat is provided for consistently by the assumption of enlarged or diminished motion, or else space is left by the term “capacity” for the partial views; which remains to be developed. When converted into mechanical force, in the steam or air-engine, and so brought into direct contact with gravity, being then easily placed in relation to it, still the conservation of force is fully respected and wonderfully sustained. The constant amount of heat developed in the whole of a voltaic current described by M. P. A. Favre, and the present state of the knowledge of thermo-electricity, are again fine partial or subordinate illustrations of the principle of conservation. Even when rendered radiant, and for the time giving no trace or signs of ordinary heat action, the assumptions regarding its nature have provided for the belief in the conservation of force, by admitting, either that it throws the ether into an equivalent state, in sustaining which for the time the power is engaged; or else, that the motion of the particles of heat is employed altogether in their own transit from place to place.
There is no convertibility from gravitation to other forces because it is the simplest case. Heat exists in the motion of particles of matter. A concept of ‘capacity’ is used when heat is transferred to unlike matter. This leaves space for research. Heat converting change in state of bodies or into mechanical force also needs further research. Thermo-electricity and black-body radiation is also partially understood.
It is true that heat often becomes evident or insensible in a manner unknown to us; and we have a right to ask what is happening when the heat disappears in one part, as of the thermo-voltaic current, and appears in another; or when it enlarges or changes the state of bodies; or what would happen, if the heat, being presented, such changes were purposely opposed. We have a right to ask these questions, but not to ignore or deny the conservation of force; and one of the highest uses of the principle is to suggest such inquiries. Explications of similar points are continually produced, and will be most abundant from the hands of those who, not desiring to ease their labour by forgetting the principle, are ready to admit it either tacitly, or better still, effectively, being then continually guided by it. Such philosophers believe that heat must do its equivalent of work: that if in doing work it seem to disappear, it is still producing its equivalent effect, though often in a manner partially or totally unknown; and that if it give rise to another form of force (as we imperfectly express it), that force is equivalent in power to the heat which has disappeared.
Many aspects of heat appearing and disappearing along with other changes are not fully explored. Such enquiries are suggested by the principle of conservation of force.
What is called chemical attraction, affords equally instructive and suggestive considerations in relation to the principle of the conservation of force. The indestructibility of individual matter, is one case, and a most important one, of the conservation of chemical force. A molecule has been endowed with powers which give rise in it to various qualities, and these never change, either in their nature or amount. A particle of oxygen is ever a particle of oxygen—nothing can in the least wear it. If it enters into combination and disappears as oxygen,—if it pass through a thousand combinations, animal, vegetable, mineral,—if it lie hid for a thousand years and then be evolved, it is oxygen with its first qualities, neither more nor less. It has all its original force, and only that; the amount of force which it disengaged when hiding itself, has again to be employed in a reverse direction when it is set at liberty; and if, hereafter, we should decompose oxygen, and find it compounded of other particles, we should only increase the strength of the proof of the conservation of force, for we should have a right to say of these particles, long as they have been hidden, all that we could say of the oxygen itself.
Further exploration of chemical attraction is also suggested by the principle of the conservation of force. There exists conservation of chemical force. The atomic structure of elements is conserved within the various molecules.
Again, the body of facts included in the theory of definite proportions, witnesses to the truth of the conservation of force; and though we know little of the cause of the change of properties of the acting and produced bodies, or how the forces of the former are hid amongst those of the latter, we do not for an instant doubt the conservation, but are moved to look for the manner in which the forces are, for the time, disposed, or if they have taken up another form of force, to search what that form may be.
At the time of Faraday, the words ‘force’ and ‘energy’ were used interchangeably. In either case, Faraday is taking the word ‘force’ to far greater depth, which can only be expressed as ‘substance’ and all its properties.
Even chemical action at a distance, which is in such antithetical contrast with the ordinary exertion of chemical affinity, since it can produce effects miles away from the particles on which they depend, and which are effectual only by forces acting at insensible distances, still proves the same thing, the conservation of force. Preparations can be made for a chemical action in the simple voltaic circuit, but until the circuit be complete that action does not occur; yet in completing we can so arrange the circuit, that a distant chemical action, the perfect equivalent of the dominant chemical action, shall be produced; and this result, whilst it establishes the electro chemical equivalent of power, establishes the principle of the conservation of force also, and at the same time suggests many collateral inquiries which have yet to be made and answered, before all that concerns the conservation in this case can be understood.
The conservation of force applies even to chemical action at a distance and suggests many collateral inquiries.
This and other instances of chemical action at a distance, carry our inquiring thoughts on from the facts to the physical mode of the exertion of force; for the qualities which seem located and fixed to certain particles of matter appear at a distance in connexion with particles altogether different. They also lead our thoughts to the conversion of one form of power into another: as for instance, in the heat which the elements of a voltaic pile may either show at the place where they act by their combustion or combination together; or in the distance, where the electric spark may be rendered manifest; or in the wire or fluids of the different parts of the circuit.
It makes us curious about different modes of manifestation of force and their conversion.
When we occupy ourselves with the dual forms of power, electricity and magnetism, we find great latitude of assumption; and necessarily so, for the powers become more and more complicated in their conditions. But still there is no apparent desire to let loose the force of the principle of conservation, even in those cases where the appearance and disappearance of force may seem most evident and striking. Electricity appears when there is consumption of no other force than that required for friction; we do not know how, but we search to know, not being willing to admit that the electric force can arise out of nothing. The two electricities are developed in equal proportions; and having appeared, we may dispose variously of the influence of one upon successive portions of the other, causing many changes in relation, yet never able to make the sum of the force of one kind in the least degree exceed or come short of the sum of the other. In that necessity of equality, we see another direct proof of the conservation of force, in the midst of a thousand changes that require to be developed in their principles before we can consider this part of science as even moderately known to us.
The forms of power become increasingly complicated, but their total sum is always the same. Thus, force is conserved but we need to develop principles to describe the thousand of other changes.
One assumption with regard to electricity is, that there is an electric fluid rendered evident by excitement in plus and minus proportions. Another assumption is, that there are two fluids of electricity, each particle of each repelling all particles like itself, and attracting all particles of the other kind always, and with a force proportionate to the inverse square of the distance, being so far analogous to the definition of gravity. This hypothesis is antagonistic to the law of the conservation of force, and open to all the objections that have been, or may be, made against the ordinary definition of gravity. Another assumption is, that each particle of the two electricities has a given amount of power, and can only attract contrary particles with the sum of that amount, acting upon each of two with only half the power it could in like circumstances exert upon one. But various as are the assumptions, the conservation of force, (though wanting in the second,) is, I think, intended to be included in all. I might repeat the same observations nearly in regard to magnetism,—whether it be assumed as a fluid, or two fluids or electric currents,—whether the external action be supposed to be action at a distance, or dependent on an external condition and lines of force—still all are intended to admit the conservation of power as a principle to which the phenomena are subject.
The idea of plus and minus electricity, which exerts a force proportional to inverse square of distance, is inadequate like the ordinary definition of gravity, when examined for conservation of force. The principle of conservation of force takes priority over all these assumptions applied to electricity and magnetism.
The principles of physical knowledge are now so far developed as to enable us not merely to define or describe the known, but to state reasonable expectations regarding the unknown; and I think the principle of the conservation of force may greatly aid experimental philosophers in that duty to science, which consists in the enunciation of problems to be solved. It will lead us, in any case where the force remaining unchanged in form is altered in direction only, to look for the new disposition of the force; as in the cases of magnetism, static electricity, and perhaps gravity, and to ascertain that as a whole it remains unchanged in amount:—or, if the original force disappear, either altogether or in part, it will lead us to look for the new condition or form of force which should result, and to develop its equivalency to the force that has disappeared. Likewise, when force is developed, it will cause us to consider the previously existing equivalent to the force so appearing; and many such cases there are in chemical action. When force disappears, as in the electric or magnetic induction after more or less discharge, or that of gravity with an increasing distance; it will suggest a research as to whether the equivalent change is one within the apparently acting bodies, or one external (in part) to them. It will also raise up inquiry as to the nature of the internal or external state, both before the change and after. If supposed to be external, it will suggest the necessity of a physical process, by which the power is communicated from body to body; and in the case of external action, will lead to the inquiry whether, in any case, there can be truly action at a distance, or whether the ether, or some other medium, is not necessarily present.
In Faraday’s view, the principle of conservation of force could greatly aid experimental philosophers in the enunciation of problems to be solved. Faraday lays out the details of possible ways.
We are not permitted as yet to see the nature of the source of physical power, but we are allowed to see much of the consistency existing amongst the various forms in which it is presented to us. Thus if, in static electricity, we consider an act of induction, we can perceive the consistency of all other like acts of induction with it. If we then take an electric current, and compare it with this inductive effect, we see their relation and consistency. In the same manner we have arrived at a knowledge of the consistency of magnetism with electricity, and also of chemical action and of heat with all the former; and if we see not the consistency between gravitation with any of these forms of force, I am strongly of the mind that it is because of our ignorance only. How imperfect would our idea of an electric current now be, if we were to leave out of sight its origin, its static and dynamic induction, its magnetic influence, its chemical and heating effects? or our idea of any one of these results, if we left any of the others unregarded? That there should be a power of gravitation existing by itself, having no relation to the other natural powers, and no respect to the law of the conservation of force, is as little likely as that there should be a principle of levity as well as of gravity. Gravity may be only the residual part of the other forces of nature, as Mossotti has tried to show; but that it should fall out from the law of all other force, and should be outside the reach either of further experiment or philosophical conclusions, is not probable. So we must strive to learn more of this outstanding power, and endeavour to avoid any definition of it which is incompatible with the principles of force generally, for all the phenomena of nature lead us to believe that the great and governing law is one. I would much rather incline to believe that bodies affecting each other by gravitation act by lines of force of definite amount (somewhat in the manner of magnetic or electric induction, though without polarity), or by an ether pervading all parts of space, than admit that the conservation of force could be dispensed with.
There is consistency in all the forms of physical power, whether it is static electricity, electric current, magnetism, chemical action, or heat. Therefore, consistency is expected between gravitation with any of these forms of force. Faraday concludes that bodies affecting each other by gravitation may act by lines of force of definite amount (somewhat in the manner of magnetic or electric induction but without polarity).
It may be supposed, that one who has little or no mathematical knowledge should hardly assume a right to judge of the generality and force of a principle such as that which forms the subject of these remarks. My apology is this, I do not perceive that a mathematical mind, simply as such, has any advantage over an equally acute mind not mathematical, in perceiving the nature and power of a natural principle of action. It cannot of itself introduce the knowledge of any new principle. Dealing with any and every amount of static electricity, the mathematical mind can, and has balanced and adjusted them with wonderful advantage, and has foretold results which the experimentalist can do no more than verify. But it could not discover dynamic-electricity, nor electromagnetism, nor magneto-electricity, or even suggest them; though when once discovered by the experimentalist, it can take them up with extreme facility. So in respect of the force of gravitation, it has calculated the results of the power in such a wonderful manner as to trace the known planets through their courses and perturbations, and in so doing has discovered a planet before unknown; but there may be results of the gravitating force of other kinds than attraction inversely as the square of the distance, of which it knows nothing, can discover nothing, and can neither assert nor deny their possibility or occurrence. Under these circumstances, a principle, which may be accepted as equally strict with mathematical knowledge, comprehensible without it, applicable by all in their philosophical logic whatever form that may take, and above all, suggestive, encouraging, and instructive to the mind of the experimentalist, should be the more earnestly employed and the more frequently resorted to when we are labouring either to discover new regions of science, or to map out and develop those which are known into one harmonious whole; and if in such strivings, we, whilst applying the principle of conservation, see but imperfectly, still we should endeavour to see, for even an obscure and distorted vision is better than none. Let us, if we can, discover a new thing in any shape; the true appearance and character will be easily developed afterwards.
A mathematical mind, simply as such, has no advantage over an equally acute mind not mathematical, in perceiving the nature and power of a natural principle of action. It cannot of itself introduce the knowledge of any new principles, such as, dynamic-electricity, electromagnetism, or magneto-electricity. The conservation of force is a principle that is comprehensible without mathematical knowledge and applicable by all in their philosophical knowledge whatever form that may take. It encourages the experimentalist to discover a new thing in any shape, which may then be developed later by the mathematical mind.
Some are much surprised that I should, as they think, venture to oppose the conclusions of Newton: but here there is a mistake. I do not oppose Newton on any point; it is rather those who sustain the idea of action at a distance, that contradict him. Doubtful as I ought to be of myself, I am certainly very glad to feel that my convictions are in accordance with his conclusions. At the same time, those who occupy themselves with such matters ought not to depend altogether upon authority, but should find reason within themselves, after careful thought and consideration, to use and abide by their own judgment. Newton himself, whilst referring to those who were judging his views, speaks of such as are competent to form an opinion in such matters, and makes a strong distinction between them and those who were incompetent for the case.
Faraday’s ideas on gravitation do not oppose the conclusions of Newton, as Newton did not sustain the idea of action at a distance either. But Faraday was thought to oppose Newton by those who simply depended altogether upon authority, and made no effort to find reason within themselves, after careful thought and consideration, to use and abide by their own judgment.
But after all, the principle of the conservation of force may by some be denied. Well, then, if it be unfounded even in its application to the smallest part of the science of force, the proof must be within our reach, for all physical science is so. In that case, discoveries as large or larger than any yet made, may be anticipated. I do not resist the search for them, for no one can do harm, but only good, who works with an earnest and truthful spirit in such a direction. But let us not admit the destruction or creation of force without clear and constant proof. Just as the chemist owes all the perfection of his science to his dependence on the certainty of gravitation applied by the balance, so may the physical philosopher expect to find the greatest security and the utmost aid in the principle of the conservation of force. All that we have that is good and safe, as the steam-engine, the electric-telegraph, &c., witness to that principle,—it would require a perpetual motion, a fire without heat, heat without a source, action without reaction, cause without effect, or effect without a cause, to displace it from its rank as a law of nature.
Faraday was convinced about the principle of conservation of force though many theoretical scientists denied it. To him there was no absolute destruction or creation of force.
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ADDENDUM
June 1958
During the year that has passed since the publication of the preceding views regarding gravitation, &c., I have come to the knowledge of various observations upon them, some adverse, others favorable; these have given me no reason to change my own mode of viewing the subject, but some of them make me think that I have not stated the matter with sufficient precision. The word “force” is understood by many to mean simply “the tendency of a body to pass from one place to another,” which is equivalent, I suppose, to the phrase “mechanical force;” those who so restrain its meaning must have found my argument very obscure. What I mean by the word “force,” is the cause of a physical action; the source or sources of all possible changes amongst the particles or materials of the universe.
After getting feedback from Maxwell, Faraday is clarifying his position publicly. He is giving here the same clarifications that he wrote to Maxwell. I see Faraday’s force as the “innate impulse” that makes up the continuum of substance in this universe..
It seems to me that the idea of the conservation of force is absolutely independent of any notion we may form of the nature of force or its varieties, and is as sure and may be as firmly held in the mind, as if we, instead of being very ignorant, understood perfectly every point about the cause of force and the varied effects it can produce. There may be perfectly distinct and separate causes of what are called chemical actions, or electrical actions, or gravitating actions, constituting so many forces; but if the “conservation of force” is a good and true principle, each of these forces must be subject to it: none can vary in its absolute amount; each must be definite at all times, whether for a particle, or for all the particles in the universe; and the sum also of the three forces must be equally unchangeable. Or, there may be but one cause for these three sets of actions, and in place of three forces we may really have but one, convertible in its manifestations; then the proportions between one set of actions and another, as the chemical and the electrical, may become very variable, so as to be utterly inconsistent with the idea of the conservation of two separate forces (the electrical and the chemical), but perfectly consistent with the conservation of a force being the common cause of the two or more sets of action.
To Faraday the idea of the conservation of force is absolutely independent of any notion about the nature of force. It means complete understanding and accounting of the causes and effects that constitute a phenomena. For example, a decrease in something must be explained by proportional increase in something else. Faraday’s “conservation of force” may be called “conservation of substance” where that substance forms the single continuum of the universe.
It is perfectly true that we cannot always trace a force by its actions, though we admit its conservation. Oxygen and hydrogen may remain mixed for years without showing any signs of chemical activity; they may be made at any given instant to exhibit active results, and then assume a new state, in which again they appear as passive bodies. Now, though we cannot clearly explain what the chemical force is doing, that is to say, what are its effects during the three periods before, at, and after the active combination, and only by very vague assumption can approach to a feeble conception of its respective states, yet we do not suppose the creation of a new portion of force for the active moment of time, or the less believe that the forces belonging to the oxygen and hydrogen exist unchanged in their amount at all these periods, though varying in their results. A part may at the active moment be thrown off as mechanical force, a part as radiant force, a part disposed of we know not how; but believing, by the principle of conservation, that it is not increased or destroyed, our thoughts are directed to search out what at all and every period it is doing, and how it is to be recognized and measured. A problem, founded on the physical truth of nature, is stated, and, being stated, is on the way to its solution.
Mechanical force is only a part of the total force just as the radiant and other forms of force are. Faraday is talking about the conservation of the very substance of the phenomenon. When things don’t add up it is time to look for the missing ‘force’.
Those who admit the possibility of the common origin of all physical force, and also acknowledge the principle of conservation, apply that principle to the sum total of the force. Though the amount of mechanical force (using habitual language for convenience sake) may remain unchanged and definite in its character for a long time, yet when, as in the collision of two equal inelastic bodies, it appears to be lost, they find it in the form of heat and whether they admit that heat to be a continued mechanical action (as is most probable), or assume some other idea, as that of electricity, or action of a heat-fluid, still they hold to the principle of conservation by admitting that the sum of force, i. e. of the “cause of action,” is the same, whatever character the effects assume. With them the convertibility of heat, electricity, magnetism, chemical action and motion is a familiar thought; neither can I perceive any reason why they should be led to exclude, a priori, the cause of gravitation from association with the cause of these other phenomena respectively. All that they are limited by in their various investigations, whatever directions they may take, is the necessity of making no assumption directly contradictory of the conservation of force applied to the sum of all the forces concerned, and to endeavour to discover the different directions in which the various parts of the total force have been exerted.
We commonly think of the convertibility of heat, electricity, magnetism, chemical action and motion. All these are “causes of different actions.” There is no reason to exclude cause of gravitation from this list. The only limiting necessity is the principle of the conservation of force applied to the sum of all the forces concerned. .
Those who admit separate forces inter-unchangeable, have to show that each of these forces is separately subject to the principle of conservation. If gravitation be such a separate force, and yet its power in the action of two particles be supposed to be diminished fourfold by doubling the distance, surely some new action, having true gravitation character, and that alone, ought to appear; for how else can the totality of the force remain unchanged? To define the force as “a simple attractive force exerted between any two or all the particles of matter, with a strength varying inversely as the square of the distance,” is not to answer the question; nor does it indicate or even assume what are the other complementary results which occur; or allow the supposition that such are necessary: it is simply, as it appears to me, to deny the conservation of force.
If the force of gravitation is not interchangeable with other forces, then it must be conserved in itself. If gravitation is changing with distance then some new action having true gravitation character must appear.
As to the gravitating force, I do not presume to say that I have the least idea of what occurs in two particles when their power of mutually approaching each other is changed by their being placed at different distances; but I have a strong conviction, through the influence on my mind of the doctrine of conservation, that there is a change; and that the phenomena resulting from the change will probably appear someday as the result of careful research. If it be said that “‘twere to consider too curiously to consider so,” then I must dissent. To refrain to consider, would be to ignore the principle of the conservation of force, and to stop the inquiry which it suggests: whereas to admit the proper logical force of the principle in our hypotheses and considerations, and to permit its guidance in a cautious yet courageous course of investigation, may give us power to enlarge the generalities we already possess in respect of heat, motion, electricity, magnetism, &c.; to associate gravity with them; and perhaps enable us to know whether the essential force of gravitation (and other attractions) is internal or external as respects the attracted bodies.
When two particles are placed at different distances, their power of mutually approaching each other is changed. It must be compensated by some other change. Careful research may tell us about this change someday. This is not “thinking too much”. It is necessary inquiry.
Returning once more to the definition of the gravitating power as “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” I ought perhaps to suppose there are many who accept this as a true and sufficient description of the force, and who therefore, in relation to it, deny the principle of conservation. If both are accepted and are thought to be consistent with each other, it cannot be difficult to add words which shall make “varying strength” and “conservation” agree together. It cannot be said that the definition merely applies to the effects of gravitation as far as we know them. So understood, it would form no barrier to progress; for, that particles at different distances are urged towards each other with a power varying inversely as the square of the distance, is a truth; but the definition has not that meaning; and what I object to is the pretense of knowledge which the definition sets up, when it assumes to describe, not the partial effects of the force, but the nature of the force as a whole.
Faraday is basically objecting to ‘action at a distance’ belief present among scientists. There are things here, which are not known, and which needs to be researched.
NOTE: When the force of gravity changes with change in distance, it seems to be compensated by a change in inertia or consistency of substance. In other words, as two masses approach each other, they “thin out” as the gravitation increases; and as they move away from each other, they “thicken up” as the gravitation decreases. The universe is expanding means that the galaxies are thinning out as they try to approach each other due to gravitation.
June, 1858. M. F.
