# A History of the Theories of Aether and Electricity/Chapter 6

CHAPTER VI.

At Davy's recommendation Faraday was in the following spring appointed to a post in the laboratory of the Royal Institution, which had been established at the close of the eighteenth century under the auspices of Count Rumford; and here he remained for the whole of his active life, first as assistant, then as director of the laboratory, and from 1833 onwards as the occupant of a chair of chemistry which was founded for his benefit.

For many years Faraday was directly under Davy's influence, and was occupied chiefly in chemical investigations. But in 1821, when the new field of inquiry opened by Oersted's discovery was attracting attention, he wrote an Historical Sketch of Electro-Magnetism,[1] as a preparation for which he carefully repeated the experiments described by the writers he was reviewing, and this seems to have been the beginning of the researches to which his fame is chiefly due.

The memoir which stands first in the published volumes of Faraday's electrical work[2] was communicated to the Royal Society on November 24th, 1831. The investigation was inspired, as he tells us, by the hope of discovering analogies between the behaviour of electricity as observed in motion in currents, and the behaviour of electricity at rest on conductors. Static electricity was known to possess the power of "induction"—i.e., of causing an opposite electrical state on bodies in its neighbourhood; was it not possible that electric currents might show a similar property? The idea at first was that if in any circuit a current were made to flow, any adjacent circuit would be traversed by an induced current, which would persist exactly as long as the inducing current. Faraday found that this was not the case; a current was indeed induced, but it lasted only for an instant, being in fact perceived only when the primary current was started or stopped. It depended, as he soon convinced himself, not on the mere existence of the inducing current, but on its variation.

Faraday now set himself to determine the laws of induction of currents, and for this purpose devised a new way of representing the state of a magnetic field, Philosophers had been long accustomed[3] to illustrate magnetic power by strewing iron filings on a sheet of paper, and observing the curves in which they dispose themselves when a magnet is brought underneath. These curves suggested to Faraday[4] the idea of lines of magnetic force, or curves whose direction at every point coincides with the direction of the magnetic intensity at that point; the curves in which the iron filings arrange themselves on the paper resemble these curves so far is possible subject to the condition of not leaving the plane of the paper.

With these lines of magnetic force Faraday conceived all space to be filled. Every line of force is a closed curve, which in some part of its course passes through the magnet to which it belongs.[5] Hence if any small closed curve be taken in space, the lines of force which intersect this curve must form a tubular surface returning into itself, such a surface is called a tube of force. From a tube of force we may derive information not only regarding the direction of the magnetic intensity, but also regarding its magnitude; for the product of this magnitude[6] and the cross-section of any tube is constant along the entire length of the tube.[7] On the basis of this result, Faraday conceived the idea of partitioning all space into -compartments by tubes, each tube being such that this product has the same definite value. For simplicity, each of these tubes may be called a "unit line of force"; the strength of the field is then indicated by the separation or concentration of the unit lines of force,[8] so that the number of them which intersect a unit area placed at right angles to their direction at any point measures the intensity of the magnetic field at that point.

Faraday constantly thought in terms of lines of force. "I cannot refrain," he wrote, in 1851,[9] "from again expressing my conviction of the truthfulness of tho representation, which the idea of lines of force affords in regard to magnetic action. All the points which are experimentally established in regard to that action—i.e. all that is not hypothetical—appear to be well and truly represented by it."[10]

Faraday found that a current is induced in a circuit either when the strength of an adjacent current is altered, or when a magnet is brought near to the circuit, or when the circuit itself is moved about in presence of another current or a magnet. He saw from the first[11] that in all cases the induction depends on the relative motion of the circuit and the lines of magnetic force in its vicinity. The precise nature of this dependence was the subject of long-continued further experiments. In 1832 he found[12] that the currents produced by induction under the same circumstances in different wires are proportional to the conducting powers of the wires—a result which showed that the induction consists in the production of a definite electromotive force, independent of the nature of the wire, and dependent only on the intersections of the wire and the magnetic curves. This electromotive force is produced whether the wire forms a closed circuit (so that a current flows) or is open (so that electric tension results).

All that now remained was to inquire in what way the electromotive force depends on the relative motion of the wire and the lines of force. The answer to this inquiry is, in Faraday's own words,[13] that "whether the wire moves directly or obliquely across the lines of force, in one direction or another, it sums up the amount of the forces represented by the lines it has crossed," so that "the quantity of electricity thrown into a current is directly as the number of curves intersected."[14] The induced electromotive force is, in fact, simply proportional to the number of the unit lines of magnetic force intersected by the wire per second.

This is the fundamental principle of the induction of currents. Faraday is undoubtedly entitled to the full honour of its discovery; but for a right understanding of the progress of electrical theory at this period, it is necessary to remember that many years elapsed before all the conceptions involved in Faraday's principle became clear and familiar to his contemporaries; and that in the meantime the problem of formulating the laws of induced currents was approached with success from other points of view. There were indeed many obstacles to the direct appropriation of Faraday's work by the mathematical physicists of his own generation; not being himself a mathematician, he was unable to address them in their own language; and his favourite mode of representation by moving lines of force repelled analysts who had been trained in the school of Laplace and Poisson. Moreover, the idea of electromotive force itself, which had been applied to currents a few years previously in Ohm's memoir, was, as we have seen, still involved in obscurity and misapprehension.

A curious question which arose out of Faraday's theory was whether a bar-magnet which is rotated on its own axis carries its lines of magnetic force in rotation with it. Faraday himself believed that the lines of force do not rotate[15]: on this view a revolving magnet like the earth is to be regarded as moving through its own lines of force, so that it must become charged at the equator and poles with electricity of opposite signs, and if a wire not partaking in the earth's rotation were to have sliding contact with the earth at a pole and at the equator, a current would steadily flow through it. Experiments confirmatory of these views were made by Faraday himself;[16] but they do not strictly prove his hypothesis that the lines of force remain at rest; for it is easily seen[17] that, if they were to rotate, that part of the electromotive force which would be produced by their rotation would be derivable from a potential, and so would produce no effect in closed circuits such as Faraday used.

Three years after the commencement of Faraday's researches on induced currents he was led to an important extension of them by an observation which was communicated to him by another worker. William Jenkin had noticed that an electric shock may be obtained with no more powerful source of electricity than a single cell, provided the wire through which the current passes is long and coiled; the shock being felt when contact is broken.[18] As Jenkin did not choose to investigate the matter further, Faraday took it up, and showed[19] that the powerful momentary current, which was observed when the circuit was interrupted, was really an induced current governed by the same laws as all other induced currents, but with this peculiarity, that the induced and inducing currents now flowed in the same circuit. In fact, the current in its steady state establishes in the surrounding region a magnetic field, whose lines of force are linked with the circuit; and the removal of these lines of force when the circuit is broken originates an induced current, which greatly reinforces the primary current just before its final extinction. To this phenomenon the name of self-induction has been given.

The circumstances attending the discovery of self-induction occasioned a comment from Faraday on the number of suggestions which were continually being laid before him. He remarked that although at different times a large number of authors had presented him with their ideas, this case of Jenkin was the only one in which any result had followed. "The volunteers are serious embarrassments generally to the experienced philosopher."[20]

The discoveries of Oersted, Ampère, and Faraday had shown the close connexion of magnetic with electric science. But the connexion of the different branches of electric science with each other was still not altogether clear. Although Wollaston's experiments of 1801 had in effect proved the identity in kind of the currents derived from frictional and voltaic sources, the question was still regarded as open thirty years afterwards,[21] no satisfactory explanation being forthcoming of the fact that frictional electricity appeared to be a surface-phenomenon, whereas voltaic electricity was conducted within the interior substance of bodies. To this question Faraday now applied himself; and in 1833 he succeeded[22] in showing that every known effect of electricity-physiological, magnetic, luminous, calorific, chemical, and mechanical-may be obtained indifferently either with the electricity which is obtained by friction or with that obtained from a voltaic battery. Henceforth the identity of the two was beyond dispute.

Some misapprehension, however, has existed among later writers as to the conclusions which may be drawn from this identification. What Faraday proved is that the process which goes on in a wire connecting the terminals of a voltaic cell is of the same nature as the process which for a short time goes on in a wire by which a condenser is discharged. He did not prove, and did not profess to have proved, that this process consists in the actual movement of a quasi-substance, electricity, from one plate of the condenser to the other, or of two quasi-substances, the resinous and vitreous electricities, in opposite directions. The process had been pictured in this way by many of his predecessors, notably by Volta; and it has since been so pictured by most of his successors: but from such assumptions Faraday himself carefully abstained.

What is common to all theories, and is universally conceded, is that the rate of increase in the total quantity of electrostatic charge within any volume-element is equal to the excess of the influx over the efflux of current from it. This statement may be represented by the equation

${\displaystyle {\frac {\partial \rho }{\partial t}}+\mathrm {div} \ \mathbf {i} =0}$,

where ρ denotes the volume-density of electrostatic charge, and i the current, at the place (x, y, z) at the time t. Volta's assumption is really one way of interpreting this equation physically: it presents itself when we compare equation (1) with the equation

${\displaystyle {\frac {\partial \rho }{\partial t}}+\mathrm {div} (\rho \mathbf {v} )=0}$,

which is the equation of continuity for a fluid of density ρ and velocity v: we may identify the two equations by supposing i to be of the same physical nature as the product ρv; and this is precisely what is done by those who accept Volta's assumption.

But other assumptions might be made which would equally well furnish physical interpretations to equation (1). For instance, if we suppose ρ to be the convergence of any vector of which i is the time-flux,[23] equation (1) is satisfied automatically; 196 Faraday. we can picture this vector as being of the nature of a displacement. By such an assumption we should avoid altogether the necessity for regarding the conduction-current as an actual flow of electric charges, or for speculating whether the drifting charges are positive or negative; and there would be no longer anything surprising in the production of a null effect by the coalescence of electric charges of opposite signs.

Faraday himself wished to leave the matter open, and to avoid any definite assumption.[24] Perhaps the best indication of his views is afforded by a laboratory note[25] of date 1837:—

"After much consideration of the manner in which the electric forces are arranged in the various phenomena generally I have come to certain conclusions which I will endeavour to note down without committing myself to any opinion as to the cause of electricity, i.e., as to the nature of the power. If electricity exist independently of matter, then I think that the hypothesis of one fluid will not stand against that of two fluids. There are, I think, evidently what I may call two elements of power, of equal force and acting toward each other. But these powers may be distinguished only by direction, and may be no more separate than the north and south forces in the elements of a magnetic needle. They may be the polar points of the forces originally placed in the particles of matter."

It may be remarked that since the rise of the mathematical theory of electrostatics, the controversy between the supporters of the one-fluid and the two-fluid theories had become manifestly barren. The analytical equations, in which interest was now largely centred, could be interpreted equally well on either hypothesis; and there seemed to be little prospect of discriminating between them by any new experimental discovery. But a problem does not lose its fascination because it appears insoluble. "I said once to Faraday," wrote Stokes to his father-in-law in 1879, "as I sat beside him at a British Association dinner, that I thought a great step would be made when we should be able to say of electricity that which we say of light, in saying that it consists of undulations. He said to me he thought we were a long way off that yet."[26]

For his next series of researches,[27] Faraday reverted to subjects which had been among the first to attract him as an apprentice attending Davy's lectures: the voltaic pile, and the relations of electricity to chemistry.

It was at this time generally supposed that the decomposition of a solution, through which an electric current is passed, is due primarily to attractive and repellent forces exercised on its molecules by the metallic terminals at which the current enters and leaves the solution. Such forces had been assumed both in the hypothesis of Grothuss and Davy, and in the rival hypothesis of De La Rive;[28] the chief difference between these Being that whereas Grothuss and Davy supposed a chain of decompositions and recompositions in the liquid, De La Rive supposed the molecules adjacent to the terminals to be the only ones decomposed, and attributed to their fragments the power of travelling through the liquid from one terminal to the other.

To test this doctrine of the influence of terminals, Faraday moistened a piece of paper in a saline solution, and supported it in the air on wax, so as to occupy part of the interval between two needle-points which were connected with an electric machine. When the machine was worked, the current was conveyed between the needle-points by way of the moistened paper and the two air-intervals on either side of it; and under these circumstances it was found that the salt underwent decomposition. Since in this case no metallic terminals of any kind were in contact with the solution, it was evident that all hypotheses which attributed decomposition to the action of the terminals were untenable.

The ground being thus cleared by the demolition of previous theories, Faraday was at liberty to construct a theory of his He retained one of the ideas of Grothuss' and Davy's doctrine, namely, that a chain of decompositions and recombinations takes place in the liquid; but these molecular processes he attributed not to any action of the terminals, but to a power possessed by the electric current itself, at all places in its course through the solution. If as an example we consider neighbouring molecules A, B, C, D, ... of the compound—say water, which was at that time believed to be directly decomposed by the current—Faraday supposed that before the passage of the current the hydrogen of A would be in close union with the oxygen of A, and also in a less close relation with the oxygen atoms of B, C, D, ...: these latter relations being conjectured to be the cause of the attraction of aggregation in solids and fluids.[29] When an electric current is sent through the liquid, the affinity of the hydrogen of A for the oxygen of B is strengthened, if A and B lie along the direction of the current; while the hydrogen of A withdraws some of its bonds from the oxygen of A, with which it is at the moment combined. So long as the hydrogen and oxygen of A remain in association, the state thus induced is merely one of polarization; but the compound molecule is unable to stand the strain thus imposed on it, and the hydrogen and oxygen of A part company from each other, Thus decompositions take place, followed by recombinations: with the result that after each exchange an oxygen atom associates itself with a partner nearer to the positive terminal, while a hydrogen atom associates with a partner nearer to the negative terminal.

This theory explains why, in all ordinary cases, the evolved substances appear only at the terminals; for the terminals are the limiting surfaces of the decomposing substance; and, except. at them, every particle finds other particles having a contrary tendency with which it can combine. It also explains why, in numerous cases, the atoms of the evolved substances are not retained by the terminals (an obvious difficulty in the way of all theories which suppose the terminals to attract the atoms): for the evolved substances are expelled from the liquid, not drawn out by an attraction.

Many of the perplexities which had harassed the older theories were at once removed when the phenomena were regarded from Faraday's point of view. Thus, mere mixtures (as opposed to chemical compounds) are not separated into their constituents by the electric current; although there would seem to be no reason why the Grothuss-Davy polar attraction should not operate as well on elements contained in mixtures as on elements contained in compounds.

In the latter part of the same year (1833) Faraday took up the subject again.[30] It was at this time that he introduced the terms which have ever since been generally used to describe the phenomena of electro-chemical decomposition. To the terminals by which the electric current passes into or out of the decomposing body he gave the name electrodes. The electrode of high potential, at which oxygen, chlorine, acids, &c., are evolved, he called the anode, and the electrode of low potential, at which metals, alkalis, and bases are evolved, the cathode. Those bodies which are decomposed directly by the current he named electrolytes; the parts into which they are decomposed, ions; the acid ions, which travel to the anode, he named anions; and the metallic ions, which pass to the cathode, cations,

Faraday now proceeded to test the truth of a supposition which he had published rather more than a year previously,[31] and which indeed had apparently been suspected by Gay-Lussac and Thénard[32] so early as 1811; namely, that the rate at which an electrolyte is decomposed depends solely on the intensity of the electric current passing through it, and not at all on the size of the electrodes or the strength of the solution. Having established the accuracy of this law,[33] he found by a comparison of different electrolytes that the mass of any ion liberated by a given quantity of electricity is proportional to its chemical equivalent, i.e. to the amount of it required to combine with some standard mass of some standard element. If an element is n-valent, so that one of its atoms can hold in combination n atoms of hydrogen, the chemical equivalent of this element may be taken to be 1/n of its atomic weight; and therefore Faraday's result may be expressed by saying that an electric current will liberate exactly one atom of the element in question in the time which it would take to liberate n atoms of hydrogen.[34]

The quantitative law seemed to Faraday[35] to indicate that "the atoms of matter are in some way endowed or associated with electrical powers, to which they owe their most striking qualities, and amongst them their mutual chemical affinity."

Looking at the facts of electrolytic decomposition from this point of view, he showed how natural it is to suppose that the electricity which passes through the electrolyte is the exact equivalent of that which is possessed by the atoms separated at the electrodes; which implies that there is a certain absolute quantity of the electric power associated with each atom of matter.

The claims of this splendid speculation he advocated with conviction. "The harmony," he wrote,[36] "which it introduces into the associated theories of definite proportions and electro-chemical affinity is very great. According to it, the equivalent weights of bodies are simply those quantities of them which contain equal quantities of electricity, or have naturally equal electric powers; it being the electricity which determines tho equivalent number, because it determines the combining force. Or, if we adopt the atomic theory or phraseology, then the atoms of bodies which are equivalent to each other in their ordinary chemical action, have equal quantities of electricity naturally associated with them. "But," he added, "I must confess I am jealous of the term atom: for though it is very easy to talk of atoms, it is very difficult to form a clear idea of their nature, especially when compound bodies are under consideration."

These discoveries and ideas tended to confirm Faraday in preferring, among the rival theories of the voltaic cell, that one to which all his antecedents and connexions predisposed him. The controversy between the supporters of Volta's contact hypothesis on the one hand, and the chemical hypothesis of Davy and Wollaston on the other, had now been carried on for a generation without any very decisive result. In Germany and Italy the contact explanation was generally accepted, under the influence of Christian Heinrich Pfaff, of Kiel (b. 1773, d. 1852), and of Ohm, and, among the younger men, of Gustav Theodor Fechner (b. 1801, d. 1887), of Leipzig,[37] and Stefano Marianini (b. 1790, d. 1866), of Modena. Among French writers De La Rive, of Geneva, was, as we have seen, active in support of the chemical hypothesis; and this side in the dispute had always been favoured by the English philosophers.

There is no doubt that when two different metals are put in contact, a difference of potential is set up between them without any apparent chemical action; but while the contact party regarded this as a direct manifestation of a "contact-force" distinct in kind from all other known forces of nature, the chemical party explained it as a consequence of chemical affinity or incipient chemical action between the metals and the surrounding air or moisture. There is also no doubt that the continued activity of a voltaic cell is always accompanied by chemical unions or decompositions; but while the chemical party asserted that these constitute the efficient source of the current, the contact party regarded them as secondary actions, and attributed the continual circulation of electricity to the perpetual tendency of the electromotive force of contact to transfer charge from one substance to another.

One of the most active supporters of the chemical theory among the English physicists immediately preceding Faraday was Peter Mark Roget (b. 1779, d. 1869), to whom are due two of the strongest arguments in its favour. In the first place, carefully distinguishing between the quantity of electricity put. into circulation by a cell and the tension at which this electricity is furnished, he showed that the latter quantity depends on the "energy of the chemical action"[38]—a fact which, when taken together with Faraday's discovery that the quantity of electricity put into circulation depends on the amount of chemicals consumed, places the origin of voltaic activity beyond all question. Roget's principle was afterwards verified by Faraday[39] and by De La Rive[40]; "the electricity of the voltaic pile is proportionate in its intensity to the intensity of the affinities concerned in its production," said the former in 1834; while De La Rive wrote in 1836, "The intensity of the currents developed in combinations and in decompositions is exactly proportional to the degree of affinity which subsists between the atoms whose combination or separation has given rise to these currents."

Not resting here, however, Roget brought up another argument of far-reaching significance. "If," he wrote,[41] "there could exist a power having the property ascribed to it by the [contact] hypothesis, namely, that of giving continual impulse to a fluid in one constant direction, without being exhausted by its own action, it would differ essentially from all the other known powers in nature. All the powers and sources of motion, with the operation of which we are acquainted, when producing their peculiar effects, are expended in the same proportion as those effects are produced; and hence arises the impossibility of obtaining by their agency a perpetual effect; or, in other words, a perpetual motion. But the electro-motive force ascribed by Volta to the metals when in contact is a force which, as long as a free course is allowed to the electricity it sets in motion, is never expended, and continues to be exerted with undiminished power, in the production of a never-ceasing effect. Against the truth of such a supposition the probabilities are all but infinite."

This principle, which is little less than the doctrine of conservation of energy applied to a voltaic cell, was reasserted by Faraday. The process imagined by the contact school would," he wrote, "indeed be a creation of power, like no other force in nature." In all known cases energy is not generated, but only transformed. There is no such thing in the world as "a pure creation of force; a production of power without a corresponding exhaustion of something to supply it."[42]

As time went on, each of the rival theories of the cell became modified in the direction of the other. The contact party admitted the importance of the surfaces at which the metals are in contact with the liquid, where of course the chief chemical action takes place; and the chemical party confessed their inability to explain the state of tension which subsists before the circuit is closed, without introducing hypotheses just as uncertain as that of contact force.

Faraday's own view on this point[43] was that a plate of amalgamated zine, when placed in dilute sulphuric acid, "has power so far to act, by its attraction for the oxygen of the particles in contact with it, as to place the similar forces already active between these and the other particles of oxygen and the particles of hydrogen in the water, in a peculiar state of tension or polarity, and probably also at the same time to throw those of its own particles which are in contact with the water into a similar but opposed state. Whilst this state is retained. no further change occurs: but when it is relieved by completion of the circuit, in which case the forces determined in opposite directions, with respect to the zine and the electrolyte, are found exactly competent to neutralize each other, then a series of decompositions and recompositions takes place amongst the particles of oxygen and hydrogen which constitute the water, between the place of contact with the platina and the place where the zine is active: these intervening particles being evidently in close dependence upon and relation to each other. The zinc forms a direct compound with those particles of oxygen which were, previously, in divided relation to both it and the hydrogen: the oxide is removed by the acid, and a fresh surface of zinc is presented to the water, to renew and repeat the action."

These ideas were developed further by the later adherents of the chemical theory, especially by Faraday's friend Christian Friedrich Schönbein,[44] of Basle (b. 1799, d. 1868), the discoverer of ozone. Schönbein made the hypothesis more definite by assuming that when the circuit is open, the molecules of water adjacent to the zinc plate are electrically polarized, the oxygen side of each molecule being turned towards the zinc and being negatively charged, while the hydrogen side is turned away from the zinc and is positively charged. In the third quarter Faraday. 205 of the nineteenth century, the general opinion was in favour of some such conception as this. Helmholtz[45] attempted to grasp the molecular processes more intimately by assuming that the different chemical elements have different attractive powers (exerted only at small distances) for the vitreous and resinous electricities: thus potassium and zinc have strong attractions for positive charges, while oxygen, chlorine, and bromine have strong attractions for negative electricity. This. differs from Volta's original hypothesis in little else but. in assuming two electric fluids where Volta assumed only one. It is evident that the contact difference of potential between two metals may be at once explained by Helmholtz's. hypothesis, as it was by Volta's; and the activity of the voltaic cell may be referred to the same principles: for the two ions. of which the liquid molecules are composed will also possess: different attractive powers for the electricities, and may be supposed to be united respectively with vitreous and resinous. charges. Thus when two metals are immersed in the liquid, the circuit being open, the positive ions are attracted to the negative metal and the negative ions to the positive metal, thereby causing a polarized arrangement of the liquid molecules near the metals. When the circuit is closed, the positively charged surface of the positive metal is dissolved into the fluid;. and as the atoms carry their charge with them, the positive: charge on the immersed surface of this metal must be perpetually renewed by a current flowing in the outer circuit.

It will be seen that Helmholtz did not adhere to Davy's's doctrine of the electrical nature of chemical affinity quite as: simply or closely as Faraday, who preferred it in its most direct and uncompromising form. "All the facts show us," he wrote,[46] "that that power commonly called chemical affinity can be communicated to a distance through the metals and certain forms of carbon; that the electric current is only another form of the forces of chemical affinity; that its power is in proportion. to the chemical affinities producing it; that when it is deficient in force it may be helped by calling in chemical aid, the want in the former being made up by an equivalent of the latter; that, in other words, the forces termed chemical affinity and electricity are one and the same."

In the interval between Faraday's earlier and later papers on the cell, some important results on the same subject were published by Frederic Daniell (b. 1790, d. 1845), Professor of Chemistry in King's College, London.[47] Daniell showed that when a current is passed through a solution of a salt in water, the ions which carry the current are those derived from the salt, and not the oxygen and hydrogen ions derived from the water; this follows since a current divides itself between different mixed electrolytes according to the difficulty of decomposing each, and it is known that pure water can be electrolysed only with great difficulty. Daniell further showed that the ions arising from (say) sodium sulphate are not represented by Na2O and SO3, but by Na and SO4, and that in such a case as this, sulphuric acid is formed at the anode and soda at the cathode by secondary action, giving rise to the observed evolution of oxygen and hydrogen respectively at these terminals.

The researches of Faraday on the decomposition of chemical compounds placed between electrodes maintained at different potentials led him in 1837 to reflect on the behaviour of such substances as oil of turpentine or sulphur, when placed in the same situation. These bodies do not conduct electricity, and are not decomposed; but if the metallic faces of a condenser are maintained at a definite potential difference, and if the space between them is occupied by one of these insulating substances, it is found that the charge on either face depends on the nature of the insulating substance. If for any particular insulator the charge has a value ε times the value which it would have if the intervening body were air, the number ε may be regarded as a measure of the influence which the insulator exerts on the propagation of electrostatic action through it: it was called by Faraday the specific inductive capacity of the insulator.[48]

The discovery of this property of insulating substances or dielectrics raised the question as to whether it could be harmonized with the old ideas of electrostatic action. Consider, for example, the force of attraction or repulsion between two small electrically-charged bodies. So long as they are in air, the force is proportional to the inverse square of the distance; but if the medium in which they are immersed be partly changed—e.g., if a globe of sulphur be inserted in the intervening space—this law is no longer valid: the change in the dielectric affects the distribution of electric intensity throughout the entire field.

The problem could be satisfactorily solved only by forming a physical conception of the action of dielectrics: and such a conception Faraday now put forward.

The original idea had been promulgated long before by his master Davy. Davy, it will be remembered,[49] in his explanation of the voltaic pile, had supposed that at first, before chemical decompositions take place, the liquid plays a part analogous to that of the glass in a Leyden jar, and that in this is involved an electric polarization of the liquid molecules.[50] This hypothesis was now developed by Faraday. Referring first to his own work on electrolysis, he asserted[51] that the behaviour of a dielectric is exactly the same as that of an electrolyte, up to the point at which the electrolyte breaks down under the electric stress, a dielectric being, in fact, a body which is capable of sustaining the stress without suffering decomposition.

"For," he argued,[52] "let the electrolyte be water, a plate of ice being coated with platina foil on its two surfaces, and these coatings connected with any continued source of the two electrical powers, the ice will charge like a Leyden arrangement, presenting a case of common induction, but no current will pass. If the ice be liquefied, the induction will now fall to a certain degree, because a current can now pass; but its passing is dependent upon a peculiar molecular arrangement of the particles consistent with the transfer of the elements of the electrolyte in opposite directions As, therefore, in the electrolytic action, induction appeared to be the first step, and decomposition the second (the power of separating these steps from each other by giving the solid or fluid condition to the electrolyte being in our hands); as the induction was the same in its nature as that through air, glass, wax, &c., produced by any of the ordinary means; and as the whole effect in the electrolyte appeared to be an action of the particles thrown into a peculiar or polarized state, I was glad to suspect that common induction itself was in all cases an action of contiguous particles, and that electrical action at a distance (i.e., ordinary inductive action) never occurred except through the influence of the intervening matter."

Thus at the root of Faraday's conception of electrostatic induction lay this idea that the whole of the insulating medium through which the action takes place is in a state of polarization similar to that which precedes decomposition in an electrolyte. "Insulators," he wrote,[53] "may be said to be bodies whose particles can retain the polarized state, whilst conductors are those whose particles cannot be permanently polarized."

The conception which he at this time entertained of the polarization may be reconstructed from what he had already written concerning electrolytes. He supposed[54] that in the ordinary or unpolarized condition of a body, the molecules consist of atoms which are bound to each other by the forces of chemical affinity, these forces being really electrical in their nature; and that the same forces are exerted, though to a less degree, between atoms which belong to different molecules, thus producing the phenomena of cohesion. When an electric field is set up, a change takes place in the distribution of these forces; some are strengthened and some are weakened, the effect being symmetrical about the direction of the applied electric force.

Such a polarized condition acquired by a dielectric when placed in an electric field presents an evident analogy to the condition of magnetic polarization which is acquired by a mass of soft iron when placed in a magnetic field; and it was therefore natural that in discussing the matter Faraday should introduce lines of electric force, similar to the lines of magnetic force which he had employed so successfully in his previous researches. A line of electric force he defined to be a curve whose tangent at every point has the same direction as the electric intensity.

The changes which take place in an electric field when the dielectric is varied may be very simply described in terms of lines of force. Thus if a mass of sulphur, or other substance of high specific inductive capacity, is introduced into the field, the effect is as if the lines of force tend to crowd into it: as W. Thomson (Kelvin) showed later, they are altered in the same way as the lines of flow of heat, in a case of steady conduction of heat, would be altered by introducing a body of greater conducting power for heat. By studying the figures of the lines of force in a great number of individual cases, Faraday was led to notice that they always dispose themselves as if they were subject to a mutual repulsion, or as if the tubes of force had an inherent tendency to dilate.[55]

It is interesting to interpret by aid of these conceptions the law of Priestley and Coulomb regarding the attraction between two oppositely-charged spheres. In Faraday's view, the medium intervening between the spheres is the seat of a system of stresses, which may be represented by an attraction or tension along the lines of electric force at every point, together with a mutual repulsion of these lines, or pressure laterally. Where a line of force ends on one of the spheres, its tension is exercised on the sphere: in this way, every surface-element of each sphere is pulled outwards. If the spheres were entirely removed from each other's influence, the state of stress would be uniform round each sphere, and the pulls on its surface-elements would balance, giving no resultant force on the sphere. But when the two spheres are brought into each other's presence, the unit lines of force become somewhat more crowded together on the sides of the spheres which face than on the remote sides, and thus the resultant pull on either sphere tends to draw it Loward the other, When the spheres are at distances great compared with their radii, the attraction is nearly proportional to the inverse square of the distance, which is Priestley's law.

In the following year (1838) Faraday amplified[56] his theory of electrostatic induction, by making further use of the analogy with the induction of magnetism. Fourteen years previously Poisson had imagined[57] an admirable model of the molecular processes which accompany magnetization; and this was now applied with very little change by Faraday to the case of induc- tion in dielectrics. "The particles of an insulating dielectric," he suggested,[58] "whilst under induction may be compared to a series of small magnetic needles, or, more correctly still, to a series of small insulated conductors. If the space round a charged globe were filled with a mixture of an insulating dielectric, as oil of turpentine or air, and small globular conductors, as shot, the latter being at a little distance from each other so as to be insulated, then these would in their condition and action exactly resemble what I consider to be the condition and action of the particles of the insulating dielectric itself. If the globe were charged, thcso little con- ductors would all be polar; if the globe were discharged, they would all return to their normal state, to be polarized again upon the recharging of the globe."

That this explanation accounts for the phenomena of specific inductive capacity may be seen by what follows, which is substantially a translation into electrostatical language of Poisson's theory of induced magnetism.[59]

Let ρ denote volume-density of clectric charge. For each of Faraday's "small shot" the integral

${\displaystyle \iiint \rho dx\ dy\ dz}$,

integrated throughout the shot, will vanish, since the total charge of the shot is zero: but if r denote the vector (x, y, z), the integral

${\displaystyle \iiint \rho \mathbf {r} dx\ dy\ dz}$

will not be zero, since it represents the electric polarization of the shot: if there are N shot per unit volume, the quantity

${\displaystyle \mathbf {P} =N\iiint \rho \mathbf {r} dx\ dy\ dz}$

will represent the total polarization per unit volume. If d denote the electric force, and E the average value of d, P will be proportional to E, say

${\displaystyle \mathbf {P} =(\epsilon -1)\mathbf {E} }$.

By integration by parts, assuming all the quantities concerned to vary continuously and to vanish at infinity, we have

${\displaystyle \iiint \left(P_{x}{\frac {\partial }{\partial x}}+P_{y}{\frac {\partial }{\partial y}}+P_{z}{\frac {\partial }{\partial z}}\right)\phi (x,y,z)dx\ dy\ dz=-\iiint \phi \mathrm {div} \ \mathbf {P} \ dx\ dy\ dz}$,

where φ denotes an arbitrary function, and the volume-integrals are taken throughout infinite space. This equation shows that the polar-distribution of electric charge on the shot is equivalent to a volume-distribution throughout space, of density

${\displaystyle {\overline {\rho }}=-\mathrm {div} \ \mathbf {P} }$.

Now the fundamental equation of electrostatics may in suitable units be written,

${\displaystyle \mathrm {div} \ \mathbf {d} =\rho }$;

and this gives on averaging

${\displaystyle \mathrm {div} \ \mathbf {E} =\rho _{1}+{\overline {\rho }}}$,

where ρ1 denotes the volume-density of free electric charge, i.e. excluding that in the doublets; or

${\displaystyle \mathrm {div} \ (\mathbf {E} +\mathbf {P} )=\rho _{1}}$,

or ${\displaystyle \mathrm {div} \ (\epsilon \mathbf {E} )=\rho _{1}}$. This is the fundamental equation of electrostatics, as modified in order to take into account the effect of the specific inductive capacity ε.

The conception of action propagated step by step through a medium by the influence of contiguous particles had a firm hold on Faraday's mind, and was applied by him in almost every part of physics. "It appears to me possible," he wrote in 1838,[60] "and even probable, that magnetic action may be communicated to a distance by the action of the intervening particles, in a manner having a relation to the way in which the inductive forces of static electricity are transferred to a distance, the intervening particles assuming for the time more or less of a peculiar condition, which (though with a very imperfect idea) I have several times expressed by the term electro-tonic state."[61]

The same set of ideas sufficed to explain electric currents. Conduction, Faraday suggested,[62] might be "an action of contiguous particles, dependent on the forces developed in electrical excitement; these forces bring the particles into a state of tension or polarity;[63] and being in this state the contiguous particles have a power or capability of communicating these forces, one to the other, by which they are lowered and discharge occurs."

After working strenuously for the ten years which followed the discovery of induced currents, Faraday found in 1841 that his health was affected; and for four years he rested. A second period of brilliant discoveries began in 1845.

Many experiments had been made at different times by various investigators[64] with the purpose of discovering a connexion between magnetism and light. These had generally taken the form of attempts to magnetize bodies by exposure in particular ways to particular kinds of radiation; and a successful issue had been more than once reported, only to be negatived on re-examination.

The true path was first indicated by Sir John Herschel After his discovery of the connexion between the outward form of quartz crystals and their property of rotating the plane of polarization of light, Herschel remarked that a rectilinear electric current, deflecting a needle to right and left all round it, possesses a helicoidal dissymmetry similar to that displayed by the crystals. "Therefore," he wrote,[65] "induction led me to conclude that a similar connexion exists, and must turn up somehow or other, between the electric current and polarized light, and that the plane of polarization would be deflected by magneto-electricity."

The nature of this connexion was discovered by Faraday, who so far back as 1834[66] had transmitted polarized light through an electrolytic solution during the passage of the current, in the hope of observing a change of polarization, This early attempt failed; but in September, 1845, he varied the experiment by placing a piece of heavy glass between the poles of an excited electro-magnet; and found that the plane of polarization of a beam of light was rotated when the beam traveiled through the glass parallel to the lines of force of the magnetic field.[67]

In the year following Faraday's discovery, Airy[68] suggested a way of representing the effect analytically; as might have been expected, this was by modifying the equations which had been already introduced by MacCullagh for the case of naturally active bodies. In MacCullagh's equations

${\displaystyle {\begin{cases}{\frac {\partial ^{2}Y}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Y}{\partial x^{2}}}+\mu {\frac {\partial ^{2}Z}{\partial x^{3}}}\\{\frac {\partial ^{2}Z}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Z}{\partial x^{2}}}-\mu {\frac {\partial ^{2}Y}{\partial x^{3}}}\end{cases}}}$,

the terms ${\displaystyle {\tfrac {\partial ^{3}Z}{\partial x^{3}}}}$ and ${\displaystyle {\tfrac {\partial ^{3}Y}{\partial x^{3}}}}$ change sign with x, so that the rotation of the plane of polarization is always right-handed or always left-handed with respect to the direction of the beam. This is the case in naturally-active bodies; but the rotation due to a magnetic field is in the same absolute direction whichever way the light is travelling, so that the derivations with respect to x must be of even order. Airy proposed the equations

${\displaystyle {\begin{cases}{\frac {\partial ^{2}Y}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Y}{\partial x^{2}}}+\mu {\frac {\partial Z}{\partial t}}\\{\frac {\partial ^{2}Z}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Z}{\partial x^{2}}}-\mu {\frac {\partial Y}{\partial t}}\end{cases}}}$,

where μ denotes a constant, proportional to the strength of the magnetic field which is used to produce the effect. He remarked, however, that instead of taking ${\displaystyle \mu {\tfrac {\partial Z}{\partial t}}}$ and ${\displaystyle \mu {\tfrac {\partial Y}{\partial t}}}$ as the additional terms, it would be possible to take ${\displaystyle \mu {\tfrac {\partial ^{3}Z}{\partial t^{3}}}}$ and ${\displaystyle \mu {\tfrac {\partial ^{3}Y}{\partial t^{3}}}}$, or ${\displaystyle \mu {\tfrac {\partial ^{3}Z}{\partial x^{2}\partial t}}}$ and ${\displaystyle \mu {\tfrac {\partial ^{3}Z}{\partial x^{2}\partial t}}}$, or any other derivates in which the number of differentiations is odd with respect to t and even with respect to x. It may, in fact, be shown by the method previously applied to MacCullagh's formulae that, if the equations are ${\displaystyle {\begin{cases}{\frac {\partial ^{2}Y}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Y}{\partial x^{2}}}+\mu {\frac {\partial ^{r+s}Z}{\partial x^{r}\partial t^{s}}}\\{\frac {\partial ^{2}Z}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Z}{\partial x^{2}}}-\mu {\frac {\partial ^{r+s}Y}{\partial x^{r}\partial t^{s}}}\end{cases}}}$, where (r + s) is an odd number, the angle through which the plane of polarization rotates in unit length of path is a numerical multiple of

${\displaystyle {\frac {\mu }{\tau ^{r+s-1}c_{1}^{r+1}}}}$,

where τ denotes the period of the light. Now it was shown by Verdet[69] that the magnetic rotation is approximately proportional to the inverse square of the wave-length; and hence we must have

${\displaystyle r+s=3}$;

so that the only equations capable of correctly representing Faraday's effect are either

${\displaystyle {\begin{cases}{\frac {\partial ^{2}Y}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Y}{\partial x^{2}}}+\mu {\frac {\partial ^{3}Z}{\partial x^{2}\partial t}}\\{\frac {\partial ^{2}Z}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Z}{\partial x^{2}}}-\mu {\frac {\partial ^{3}Y}{\partial x^{2}\partial t}}\end{cases}}}$,

or ${\displaystyle {\begin{cases}{\frac {\partial ^{2}Y}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Y}{\partial x^{2}}}+\mu {\frac {\partial ^{3}Z}{\partial t^{3}}}\\{\frac {\partial ^{2}Z}{\partial t^{2}}}=c_{1}^{2}{\frac {\partial ^{2}Z}{\partial x^{2}}}-\mu {\frac {\partial ^{3}Y}{\partial t^{3}}}\end{cases}}}$,

The former pair arise, as will appear later, in Maxwell's theory of rotatory polarization: the latter pair, which were suggested in 1868 by Boussinesq.[70] follow from that physical theory of the phenomenon which is generally accepted at the present time.[71]

Airy's work on the magnetic rotation of light was limited in the same way as MacCullagh's work on the rotatory power of quartz; it furnished only an analytical representation of the effect, without attempting to justify the equations. The earliest endeavour to provide a physical theory seems to have been made in 1858, in the inaugural dissertations of Carl Neumann, of Halle.[72] Neumann assumed that every element of an electric current exerts force on the particles of the aether; and in particular that this is true of the molecular currents which constitute magnetization, although in this case the force vanishes except when the aethereal particle is already in motion. If e donote the displacement of the aethereal particle m, the force in question may be represented by the term

${\displaystyle km[\mathbf {e.K} ]}$

where K denotes the imposed magnetic field, and k denotes a magneto-optic constant characteristic the body. When this term is introduced into the equations of motion of the aether, they take the form which had been suggested by Airy; whence Neumann's hypothesis is seen to lead to the incorrect conclusion that the rotation is independent of the wave-length.

The rotation of plane-polarized light depends, as Fresnel had shown,[73] on a difference between the velocities of propagation of the right-handed and left-handed circularly polarized waves into which plane-polarized light may be resolved. In the case of magnetic rotation, this difference was shown by Verdet to be proportional to the component of the magnetic force in the direction of propagation of the light; and Cornu[74] showed further that the mean of the velocities of the right-handed and left-handed waves is equal to the velocity of light in the medium when there is no magnetic field. From these data, by Fresnel's geometrical method, the wave-surface in the medium may be obtained; it is found to consist of two spheres (one relating to the right-handed and one to the left-handed light), each identical with the spherical wave-surface of the unmagnetized medium, displaced from each other along the lines of magnetic force.[75]

The discovery of the connexion between magnetism and light gave interest to a short paper of a speculative character which Faraday published[76] in 1846, under the title "Thoughts on Ray-Vibrations." In this it is possible to trace the progress of Faraday's thought towards something like an electro-magnetic theory of light.

Considering first the nature of ponderable matter, he suggests that an ultimate atom may be nothing else than a field of force—electric, magnetic,and gravitational—surrounding a point-centre; on this view, which is substantially that of Michell and Boscovich, an atom would have no definite size, but ought rather to be conceived of as completely penetrable, and extending throughout all space; and the molecule of a chemical compound would consist not of atoms side by side, but of "spheres of power mutually penetrated, and the centres even coinciding."[77]

All space being thus permeated by lines of force, Faraday suggested that light and radiant heat might be transverse vibrations propagated along these lines of force. In this way he proposed to "dismiss the aether," or rather to replace it by lines of force between centres, the centres together with their lines of force constituting the particles of material substances.

If the existence of a luminiferous aether were to be admitted, Faraday suggested that it might be the vehicle of magnetic force; " for," he wrote in 1851,[78] "it is not at all unlikely that if there be an aether, it should have other uses than simply the conveyance of radiations." This sentence may be regarded as the origin of the electro-magnetic theory of light.

At the time when the "Thoughts on Ray-Vibrations" were published, Faraday was evidently trying to comprehend everything in terms of lines of force; his confidence in which had been recently justified by another discovery. A few weeks after the first observation of the magnetic rotation of light, he noticed[79] that a bar of the heavy glass which had been used in this investigation, when suspended between the poles of an electro-magnet, set itself across the line joining the poles: thus behaving in the contrary way to a bar of an ordinary magnetic substance, which would tend to set itself along this line. A simpler manifestation of the effect was obtained when a cube or sphere of the substance was used; in such forms it showed a disposition to move from the stronger to the weaker places of the magnetic field. The pointing of the bar was then seen to be merely the resultant of the tendencies of each of its particles to move outwards into the positions of weakest magnetic action.

Many other bodies besides heavy glass were found to display the same property; in particular, bismuth.[80] The name diamagnetic was given to them.

"Theoretically," remarked Faraday, "an explanation of the movements of the diamagnetic bodies might be offered in the supposition that magnetic induction caused in them a contrary state to that which it produced in magnetic matter; i.e. that if a particle of each kind of matter were placed in the magnetic field, both would become magnetic, and each would have its axis parallel to the resultant of magnetic force passing through it; but the particle of magnetic matter would have its north and south poles opposite, or facing toward the contrary poles of the inducing magnet, whereas with the diamagnetic particles the reverse would be the case; and hence would result approximation in the one substance, recession in the other. Upon Ampère's theory, this view would be equivalent to the supposition that, as currents are induced in iron and magnetics parallel to those existing in the inducing magnet or battery wire, so in bismuth, heavy glass, and diamagnetic bodies, the currents induced are in the contrary direction."[81][errata 1]

This explanation became generally known as the "hypothesis of diamagnetic polarity"; it represents diamagnetism as similar to ordinary induced magnetism in all respects, except that the direction of the induced polarity is reversed. It was accepted by other investigators, notably by W. Weber, Plücker, Reich, and Tyndall; but was afterwards displaced from the favour of its inventor by another conception, more agreeable to his peculiar views on the nature of the magnetic field. In this second hypothesis, Faraday supposed an ordinary magnetic or para- magnetic[82] body to be one which offers a specially easy passage to lines of magnetic force, so that they tend to crowd into it in preference to other bodies; while he supposed a dia- magnetic body to have a low degree of conducting power for the lines of force, so that they tend to avoid it. "If, then," he reasoned,[83] "a medium having a certain conducting power occupy the magnetic field, and then a portion of another medium or substance be placed in the field having a greater conducting power, the latter will tend to draw up towards the place of greatest force, displacing the former." There is an electrostatic effect to which this is quite analogous ; a charged body attracts a body whose specific inductive capacity is greater than that of the surrounding medium, and repels a body whose specific inductive capacity is less; in either case the tendency is to afford the path of best conductance to the lines of force.[84]

For some time the advocates of the "polarity" and "conduction" theories of diamagnetism carried on a contro- versy which, indeed, like the controversy between the adherents of the one-fluid and two-fluid theories of electricity, persisted after it had been shown that the rival hypotheses were mathe- matically equivalent, and that no experiment could be suggested which would distinguish between them.

Meanwhile new properties of magnetizable bodies were being discovered. In 1847 Julius Plücker (b. 1801, d. 1868), Professor of Natural Philosophy in the University of Bonn, while repeating and extending Faraday's magnetic experiments, observed[85] that certain uniaxal crystals, when placed between the two poles of a magnet, tend to set themselves so that the optic axis has the equatorial position. At this time Faraday was continuing his researches; and, while investigating the diamagnetic properties of bismuth, was frequently embarrassed by the occurrence of anomalous results. In 1848 he ascertained that these were in some way connected with the crystalline form of the substance, and showed[86] that when a crystal of bismuth is placed in a field of uniform magnetic force (so that no tendency to motion arises from its diamagnetism) it sets itself so as to have one of its crystalline axes directed along the lines of force.

At first he supposed this effect to be distinct from that which had been discovered shortly before by Plücker. "The results," he wrote,[87] "are altogether very different from those produced by diamagnetic action. They are equally distinct from those discovered and described by Plücker, in his beautiful researches into the relation of the optic axis to magnetic action; for there the force is equatorial, whereas here it is axial. So they appear to present to us a new force, or a new form of force, in the molecules of matter, which, for convenience sake, I will conventionally designate by a new word, as the magnecrystallic force." Later in the same year, however, he recognized[88] that "the phaenomena discovered by Plücker and those of which I have given an account have one common origin and cause."

The idea of the "conduction" of lines of magnetic force by different substances, by which Faraday had so successfully explained the phenomena of diamagnetism, he now applied to the study of the magnetic behaviour of crystals. "If," he wrote[89] "the idea of conduction be applied to these magnecrystallic bodies, it would seem to satisfy all that requires explanation in their special results. A magnecrystallic substance would then be one which in the crystallized state could conduct onwards, or permit the exertion of the magnetic force with more facility in one direction than another; and that direction would be the magnecrystallic axis. Hence, when in the magnetic field, the magnecrystallic axis would be urged into a position coincident with the magnetic axis, by a force correspondent to that difference, just as if two different bodies were taken, when the one with the greater conducting power displaces that which is weaker."

This hypothesis led Faraday to predict the existence of another type of magnecrystallic effect, as yet unobserved. "If such a view were correct," he wrote,[90] "it would appear to follow that a diamagnetic body like bismuth ought to be less diamagnetic when its magnecrystallic axis is parallel to the magnetic axis than when it is perpendicular to it. In the two positions it should be equivalent to two substances having different conducting powers for magnetism, and therefore if submitted to the differential balance ought to present differential phaenomena." This expectation was realized when the matter was subjected to the test of experiment.[91]

The series of Faraday's "Experimental Researches in Electricity" end in the year 1855. The closing period of his life was quietly spent at Hampton Court, in a house placed at his disposal by the kindness of the Queen; and here on August 25th, 1867, he passed away.

Among experimental philosophers Faraday holds by universal consent the foremost place. The memoirs in which his discoveries are enshrined will never cease to be read with admiration and delight; and future generations will preserve with an affection not less enduring the personal records and familiar letters, which recall the memory of his humble and unselfish spirit.

## Notes

1. Original: was amended to [81]
1. Published in Annals of Philosophy, ii (1821), pp. 195, 274; iii (1822), p. 107
2. Experimental Researches in Electricity, by Michael Faraday: 3 vols.
3. The practice goes back at least as far as Niccolo Cabeo; indeed the curves traced by Petrus Peregrinus on his globular lodestone (cf. p. 8) were projections of lines of force. Among eighteenth-century writers La Hire mentions the use of iron filings, Mém. de l'Acad., 1717. Faraday had referred to them in his electromagnetic paper of 1821, Exp. Res. ii, p. 127.
4. They were first defined in Exp. Res., § 114: "By magnetic curves, I mean the lines of magnetic forces, however modified by the juxtaposition of poles, which could be depicted by iron filings; or those to which a very small magnetic needle would form a tangent."
5. Exp. Res. iii, p. 405.
6. Within the substance of magnetized bodies we must in this connexion understand the magnetic intensity to be that experienced in a crevice whose sides are perpendicular to the lines of magnetization: in other words, we must take it to be what since Maxwell's time has been called the magnetic induction.
7. Exp. Res., 3073. This theorem was first proved by the French geometer Michel Chasles, in bis memoir on the attraction of an ellipsoidal sheet, Journal de l'Ecole Polyt. xv (1837), p. 266.
8. Ibid., § 3122. "The relative amount of force, or of lines of force, in a given space is indicated by their concentration or separation—i.e., by their number in that space."
9. Exp. Res., § 3174.
10. Some of Faraday's most distinguished contemporaries were far from sharing this conviction. "I declare," wrote Sir George Airy in 1853, "that I can hardly imagine anyone who practically and numerically knows this agreement" between observation and the results of calculation based on action at a distance, "to hesitate an instant in the choice between this simple and precise action, on the one hand, and anything so vague and varying as lines of force, on the other hand." Cf. Bence Jones's Life of Faraday, ii, p. 353.
11. Exp. Res., § 116.
12. Ibid., § 213.
13. Exp. Res., § 3082.
14. Ibid., § 3116.
15. Ibid., § 3090.
16. Exp. Res., §§ 218, 3109, &c.
17. Cf. W. Weber, Ann. d. Phys. lii (1841); S. Tolver Preston, Phil. Mag. xix (1885), p. 131. In 1891 S. T. Preston, Phil. Mag. xxxi, p. 100, designed a crucial experiment to test the question; but it was not tried for want of a sufficiently delicate electrometer.
18. A similar observation had been made by Henry, and published in the Amer. Jour. Sci. xxii (1832), p. 408. The spark at the rupture of a spirally-wound circuit had been often observed, e.g., by Pouillet and Nobili,
19. Exp. Res., § 1048.
20. Benee Jones's Life of Faraday, ii, p. 45.
21. Cf. John Davy, Phil. Trans., 1832, p. 259; W. Ritchie, ibid., p. 279. Davy suggested that the electrical power, "according to the analogy of the solar ray," might be "not a simple power, but a combination of powers, which may occur variously associated, and produce all the varieties of electricity with which we are acquainted."
22. Exp. Res., Series iii.
23. In symbols,

${\displaystyle \mathrm {div} \ \mathbf {s} =-\rho }$ ,

${\displaystyle {\frac {\partial \mathbf {s} }{\partial t}}=i}$ ,

where s denotes the vector in question.

24. "His principal aim," said Helmholtz in the Faraday Lecture of 1881, "was to express in bis new conceptions only facts, with the least possible use of hypothetical substances and forces. This was really & progress in general scientific method, destined to purify science from the last remains of metaphysics."
25. Bence Jones's Life of Faraday, ii, p. 77.
26. Stokes's Scientific Correspondence, vol. i, p. 363.
27. Exp. Res., § 450 (1833).
28. Cf. pp. 78-9.
29. Exp. Res., § 523.
30. Exp. Res., § 661.
31. Ibid., § 377 (Dec. 1832).
32. Recherches physico-chimiques faites sur la pile; Paris, 1811, p. 12.
33. Exp. Res., §§ 713-821.
34. In the modern units, 96580 coulombs of electricity must pass round the circuit in order to liberate of each ion a number of grams equal to the quotient of the atomic weight by the valenoy.
35. Exp. Res., § 852.
36. Ibid., § 869.
37. Jobanu Christian Poggendorff (b, 1796, d. 1877), of Berlin, for long the editor of the Annalen der Physik, leaned originally to the chemical side, but in 1838 became convinced of the truth of the contact theory, which he afterwards actively defended. Moritz Hermann Jacobi (b.1801, d. 1874), of Dorpat, is also to be mentioned among its advocates.
Faraday's first series of investigations on this subject were made in 1834: Exp. Res., series viii. In 1836 De La Rive followed on the same side with his Recherches sur la Cause de l'Eleels. Voltaique. The views of Faraday and De La Rive were criticized by Pfaff, Recision der Lehre van Galvanismus, Kiel, 1837, and by Fechner, Ann. d. Phys., xlii (1837), p. 481, and xliii (1838), p. 433: translated Phil. Mag., xiii (1838), pp. 208, 367. Faraday returned to the question in 1840, Exp. Res., series xvi and xvii.
38. "The absolute quantity of electricity which is thus developed, and made to circulate, will depend upon a variety of circumstances, such as the extent of the surfaces in chemical action, the facilities afforded to its transmission, &c. But its degree of intensity, or tension, as it is often termed, will be regulated by other causes, and more especially by the energy of the chemical action." Roget's Galvanism (1832), § 70.
39. Exp. Res., §§ 908, 909, 916, 988, 1958.
40. Annales de Chim., lxi (1836), p. 38.
41. Roget's Galvanism (1832), § 113.
42. Exp. Res., § 2071 (1840).
43. Exp. Res., § 949.
44. Ann. d. Phys., lxxviii (1849), P, 289, translated Archives des sc. phys., xiii (1860), p. 192. Faraday and Schönbein for many years carried on a correspondence, which has been edited by G. W. A, Kahlbaum and F. V. Darbishire: London, Williams and Norgate.
45. In his celebrated memoir of 1847 on the Conservation of Energy.
46. Exp. Res., § 918.
47. Phil. Trans., 1839, p. 97.
48. Exp. Res., § 1252 (1837). Cavendish bad discovered specific inductive capacity long before, but bis papers were still unpublished.
49. Cf. p. 77.
50. This is expressly stated in Davy's Elements of Chemical Philosophy (1812), Div. i, § 7, where he lays it down that an essential "property of non-conductors" is "receive electrical polarities."
51. Exp. Res., §§ 1164, 1338, 1343, 1621.
52. Exp. Res., § 1164.
53. Exp. Res., § 1338.
54. This must not be taken to be more than an idea which Faraday mentioned as present to his mind. He declined as yet to formulate a definite hypothesis.
55. Esp. Res., §§ 1224, 1297 (1837).
56. Exp. Res., Series xiv.
57. Cf. p. 65.
58. Exp. Res., § 1679.
59. W. Thomson (Kelvin), Camb. and Dub. Math. Journal, November, 1845; W. Thomson's Papers on Electrostatics and Magnetism, § 43 sqq.; F. O. Mossotti, Arch. des sc. phys. (Geneva) vi (1847), p. 193: Mem. della Soc. Ital. Modena, (2) xiv (1850), p. 49.
60. Exp. Res., § 1729.
61. This name had been devised in 1831 to express the state of mutter subject to magneto-electrio induction; ef. Exp. Res., § 60.
62. Exp. Res. iii, p. 513.
63. As in electrostatic induction in dielectrics.
64. e.g. by Morichini, of Rome, in 1813, Quart. Journ. Sci. xix, p. 338; by Samuel Hunter Christie, of Cambridge, in 1825, Phil. Trans., 1826, p. 219; and by Mary Somerville in the same year, Phil. Trans., 1826, p. 132.
65. Sir. J. Herschel in Bence Jones's Life of Faraday, p. 205.
66. Exp. Res., § 951.
67. Ib., § 2152
68. Phil. Max. xxviii (1848) p. 469.
69. Comptes Rendus, lvi (1863), p. 630.
70. Journal de Math., xi (1868), p. 430.
71. Y and Z being interpreted as components of electric force.
72. Explicare tentatur, quomodo fiat, ut lucis planum polarisationis per vires el. vel mag. declinetur. Halis Saxonum, 1858. The results were republished in a tract Die magnetische Drehung der Polarisationaebere des Lichtes. Hallo, 1863.
73. Cf. p. 174.
74. Comples Rendus, xcii (1881), p. 1368.
75. Cornui, Comptes Rendus, xeix (1884), p. 1045.
76. Phil. Mag. (3), xxviii (1846): Exp. Res., iii, p. 447.
77. Cf. Bence Jones's Life of Faraday, ii, p. 178.
78. Exp. Res., § 3075.
79. Phil. Trans., 1846, p. 21: Exp. Res., § 2253.
80. The repulsion of bismuth in the magnetic field had been previously observed by A. Brugmans in 1778; Antonii Brugmans Magnetismus, Lugd. Bat., 1778.
81. Exp. Res., § 2429.
82. This term was introduced by Faraday, Exp. Res., § 2790.
83. Exp. Res., § 2798.
84. The mathematical theory of the motion of a magnetizable body in a non-uniform field of force was discussed by W. Thomson (Kelvin) in 1947.
85. Ann. d. Phys. lxxii (1847), p. 316; Taylor's Scientific Memoirs, v, p. 353.
86. Phil. Tranz., 1819, p. 1; Exp. Res., § 2454.
87. Exp. Res., § 2469.
88. Ibid., § 2605.
89. Ibid., § 2837.
90. Exp. Res., § 2839.
91. Ibid., § 2841.