A History of the Theories of Aether and Electricity/Chapter 2

by Edmund Taylor Whittaker

CHAPTER II.

ELECTRIC AND MAGNETIC SCIENCE PRIOR TO THE INTRODUCTION OF THE POTENTIALS.

The magnetic discoveries of Peregrinus and Gilbert, and the vortex-hypothesis by which Descartes had attempted to explain them,^[1] had raised magnetism to the rank of a separate science by the middle of the seventeenth century. The kindred science of electricity was at that time in a less developed state; but it had been considerably advanced by Gilbert, whose researches in this direction will now be noticed.

For two thousand years the attractive power of amber had been regarded as a virtue peculiar to that substance, or possessed by at most one or two others. Gilbert proved^[2] this view to be mistaken, showing that the same effects are induced by friction in quite a large class of bodies; among which he mentioned glass, sulphur, sealing-wax, and various precious stones.

A force which was manifested by so many different kinds of matter seemed to need a name of its own; and accordingly Gilbert gave to it the name electric, which it has ever since retained.

Between the magnetic and electric forces Gilbert remarked many distinctions. The lodestone requires 110 stimulus of friction such as is needed to stir glass and sulphur into activity. The lodestone attracts only magnetizable substances, whereas electrified bodies attract everything. The magnetic attraction between two bodies is not affected by interposing a sheet of paper, or a linen cloth, or by immersing the bodies in water; whereas the electric attraction is readily destroyed by screens. Lastly, the magnetic force tends to arrange bodies in definite orientations; while the electric force merely tends to heap them together in shapeless clusters.

These facts appeared to Gilbert to indicate that electric phenomena are due to something of a material nature, which under the influence of friction is liberated from the glass or amber in which under ordinary circumstances it is imprisoned. In support of this view he adduced evidence from other quarters. Being a physician, he was well acquainted with the doctrine that the human body contains various humours or kinds of moisture-phlegm, blood, choler, and melancholy,—which, as they predominated, were supposed to determine the temper of mind; and when he observed that electrifiable bodies were almost all hard and transparent, and therefore (according to the ideas of that time) formed by the consolidation of watery liquids, he concluded that the common menstruum of these liquids must be a particular kind of humour, to the possession of which the electrical properties of bodies were to be referred. Friction might be supposed to warn or otherwise excite or liberate the hunour, which would then issue from the body as an effluvium and form an atmosphere around it. The effluvium must, he remarked, be very attenuated, for its emission cannot be detected by the senses.

The existence of an atmosphere of effluvia round every electrified body indeed indeed have been inferred, according to Gilbert's ideas, from the single fact of electric attraction. For he believed that matter cannot act where it is not; and hence if a body acts on all surrounding objects without appearing to touch them, something must have proceeded out of it unseen.

The whole phenomenon appeared to him to be analogous to the attraction which is exercised by the earth on falling bodies. For in the latter case he conceived of the atmospheric air as the effluvium by which the earth draws all things downwards to itself.

Gilbert's theory of electrical emanations commended itself generally to such of the natural philosophers of the seventeenth century as were interested in the subject; among whom were numbered Niccolo Cabeo (b. 1585, d. 1650), an Italian Jesuit who was perhaps the first to observe that electrified bodies repel as well as attract ; the English royalist exile, Sir Kenelm Digby (b. 1603, d. 1665); and the celebrated Robert Boyle (b. 1627, d. 1691). There were, however, some differences of opinion as to the manner in which the effluvia acted on the small bodies and set them in motion towards the excited electric; Gilbert himself had supposed the emanations to have an inherent tendency to reunion with the parent body; Digby likened their return to the condensation of a vapour by cooling; and other writers pictured the effluvia as forming vortices round the attracted bodies in the Cartesian fashion.

There is a well-known allusion to Gilbert's hypothesis in Newton's Opticks.^[3]

"Let him also tell me, how an electrick body can by friction emit an exhalation so rare and subtle,^[4] and yet so potent, as by its emission to cause no sensible diminution of the weight of the electrick body, and to be expanded through a sphere, whose diameter is above two feet, and yet to be able to agitate and carry up leaf copper, or leaf gold, at a distance of above a foot from the electrick body?”

It is, perhaps, somewhat surprising that the Newtonian doctrine of gravitation should not have proved a severe blow to the emanation theory of electricity; but Gilbert's doctrine was now so firmly established as to be unshaken by the overthrow of the analogy by which it had been originally justified. It was, however, modified in one particular about the beginning of the eighteenth century. In order to account for the fact that electrics are not perceptibly wasted away by excitement, tho earlier writers had supposed all the emanations to return ultimately to the body which had emitted them; but the corpuscular theory of light accustomed philosophers to the idea of emissions so subtle as to cause no perceptible loss; and after the time of Newton the doctrine of the return of the electric effluvia gradually lost credit.

Newton died in 1727. Of the expositions of his philosophy which were published in his lifetime by his followers, one at least deserves to be noticed for the sake of the insight which it affords into the state of opinion regarding light, heat, and electricity in the first half of the eighteenth century. This was the Physices elementa mathematica experimentis confirmata of Wilhelm Jacob s'Gravesande (b. 1688, d. 1742), published at Leyden in 1720. The Latin edition was afterwards reprinted several times, and was, moreover, translated into French and English: it seems to have exercised a considerable and, on the whole, well-deserved influence on contemporary thought.

s'Gravesande supposed light to consist in the projection of corpuscles from luminous bodies to the eye; the motion being very swift, as is shown by astronomical observations. Since many bodies, e.g. tho metals, become luminous when they are heated, he inferred that every substance possesses a natural store of corpuscles, which are expelled when it is heated to incandescence; conversely, corpuscles may become united to a material body; as happens, for instance, when the body is exposed to the rays of a fire. Moreover, since the heat thus acquired is readily conducted throughout the substance of the body, he concluded that corpuscles can penetrate all substances, however hard and dense they be.

Let us here recall the ideas then current regarding the nature of material bodies. From the time of Boyle (1626-1691) it had been recognized generally that substances perceptible to the senses may be either elements or compounds or mixtures; the compounds being chemical individuals, distinct from mere mixtures of elements. But the substances at that time accepted as elements were very different from those which are now known by the name. Air and the calees^[5] of the metals figured in the list, while almost all the chemical elements now recognized were omitted from it; some of them, such as oxygen and hydrogen, because they were as yet undiscovered, and others, such as the metals, because they were believed to be compounds.

Among the chemical elements, it became customary after the time of Newton to include light-corpuscles.^[6] That something which is confessedly imponderable should ever have been admitted into this class may at first sight seem surprising. But it must be remembered that questions of ponderability counted for very little with the philosophers of the period. Three-quarters of the eighteenth century had passed before Lavoisier enunciated the fundamental doctrine that the total weight of the substances concerned in a chemical reaction is the same after the reaction as before it. As soon as this principle came to be universally applied, light parted company from the true elements in the scheme of chemistry.

We must now consider the views which were held at this time regarding the nature of heat. These are of interest for our present purpose, on account of the analogies which were set up between heat and electricity.

The various conceptions which have been entertained concerning heat fall into one or other of two classes, according as heat is represented as a mere condition producible in bodies, or as a distinct species of matter. The former view, which is that universally hell at the present day, was advocated by the great philosophers of the seventeenth century. Bacon maintained it in the Novum Oryanum: "Calor," he wrote, “est motus expansiviis, cohibitus, et nitens per partes minores."^[7] Boyle^[8] affirmed that the “Nature of Heat” consists in "a various, vehement, and intestine commotion of the Parts among themselves." Hooke^[9] declared that "Heat is a property of a body arising from the motion or agitation of its parts." And Newton^[10] asked: “Do not all fixed Bodies, when heated beyond a certain Degree, emit light and shine; and is not this Emission performed by the vibrating Motion of their Parts?" and, moreover, suggested the converse of this, namely, that when light is absorbed by a material body, vibrations are set up which are perceived by the senses as heat.

The doctrine that heat is a material substance was maintained in Newton's lifetime by a certain school of chemists. The most conspicuous member of the school was Wilhelm Homberg (b. 1652, d. 1715) of Paris, who^[11] identified heat and light with the sulphureous principle, which he supposed to be one of the primary ingredients of all bodies, and to be present even in the inter- planetary spaces. Between this view and that of Newton it might at first seem as if nothing but sharp opposition was to be expected.^[12] But a few years later the professed exponents of the Principia and the Opticks began to develop their system under the evident influence of Homberg's writings. This evolution may easily be traced in s'Gravesande, whose starting-point is the admittedly Newtonian idea that heat bears to light a relation similar to that which a state of turmoil bears to regular rectilinear motion; whence, conceiving light as a projection of corpuscles, he infers that in a hot body the material particles and the light-corpuscles^[13] are in a state of agitation, which becomes more violent as the body is more intensely heated.

s'Gravesande thus holds a position between the two opposite camps. On the one hand he interprets heat as a mode of motion; but on the other he associates it with the presence of a particular kind of matter, which he further identifies with the matter of light. After this the materialistic hypothesis made rapid progress. It was frankly advocated by another member of the Dutch school, Hermann Boerhaave^[14] (b. 1668, d. 1738), Professor in the University of Leyden, whose treatise on chemistry was translated into English in 1727.

Somewhat later it was found that the heating effects of the rays from incandescent bodies may be separated from their luminous effects by passing the rays through a plate of glass, which transmits the light, but absorbs the heat. After this discovery it was no longer possible to identify the matter of heat with the corpuscles of light; and the former was consequently accepted as a distinct element, under the name of calorie.^[15] In the latter part of the eighteenth and early part of the nineteenth centuries^[16] caloric was generally conceived as occupying the interstices between the particles of ponderable matter—an idea which fitted in well with the observation that bodies commonly expand when they are absorbing heat, but which was less competent to explain the fact^[17] that water expands when freezing. The latter difficulty was overcome by supposing the union between a body and the calorie absorbed in the process of melting to be of a chemical nature; so that the consequent changes in volume would be beyond the possibility of prediction.

As we have already remarked, the imponderability of heat did not appear to the philosophers of the eighteenth century to be a sufficient reason for excluding it from the list of chemical elements; and in any case there was considerable doubt as to whether caloric was ponderable or not. Some experimenters believed that bodies were heavier when cold than when hot; others that they were heavier when lot than when cold. The century was far advanced before Lavoisier and Rumford finally proved that the temperature of a body is without sensible influence on its weight.

Perhaps nothing in the history of natural philosophy is more amazing than the vicissitudes of the theory of heat. The true hypothesis, after having met with general acceptance throughout a century, and having been approved by a succession of illustrious men, was deliberately abandoned by their successors in favour of a conception utterly false, and, in some of its developments, grotesque and absurd.

We must now return to s'Gravesande's book. The phenomena of combustion he explained by assuming that when a body is sufficiently heated the light-corpuscles interact with the material particles, some constituents being in consequence separated and carried away with the corpuscles as flame and smoke. This view harmonizes with the theory of calcination which had been developed by Becher and his pupil Stahl at the end of the seventeenth century, according to which the metals were supposed to be composed of their calces and an element phlogiston. The process of combustion, by which a metal is changed into its calx, was interpreted as a decomposition, in which the phlogiston separated from the metal and escaped into the atmosphere; while the conversion of the calx into the metal was regarded as a union with phlogiston.^[18]

s'Gravesande attributed electric effects to vibrations induced in effluvia, which he supposed to be permanently attached to such bodies as amber. "Glass," he asserted,"contains in it, and has about its surface, a certain atmosphere, which is excited by Friction and put into a vibratory motion; for it attracts and repels light Bodies. The smallest parts of the glass are agitated by the Attrition, and by reason of their elasticity, their motion is vibratory, which is communicated to the Atmosphere above-mentioned: and therefore that Atmosphere exerts its action the further, the greater agitation the Parts of the Glass receive when a greater attrition is given to the glass."

The English translator of s'Gravesando's work was himself destined to play a considerable part in the history of electrical science. Jean Théophile Desaguliers (b. 1683, d. 1744) was an Englishman only by adoption. His father had been a Huguenot pastor, who, escaping from France after the revocation of the Edict of Nantes, brought away the boy from La Rochelle, concealed, it is said, in a tub. The young Desaguliers was afterwards ordained, and became chaplain to that Duke of Chandos who was so ungratefully ridiculed by Lope. In this situation he formed friendships with some of the natural philosophers of the capital, and amongst others with Stephen Gray, an experimenter of whom little is known^[19] beyond the fact that he was a pensioner of the Charterhouse.

In 1729 Gray communicated, as he says,^[20] "to Dr. Desaguliers and some other Gentlemen” a discovery he had lately made, "showing that the Electrick Vertue of a Glass Tube may be conveyed to any other Bodies so as to give them the same Property of attracting and repelling light Bodies as the Tube does, when excited by rubbing: and that this attractive Vertue might be carried to Bodies that were many Feet distant from the Tube."

This was a result of the greatest importance, for previous workers had known of no other way of producing the attractive emanations than by rubbing the body concerned.^[21] It was found that only a limited class of substances, among which the metals were conspicuous, had the capacity of acting as channels for the transport of the electric power; to these Desaguliers, who continued the experiments after Gray's death in 1736, gave^[22] the name non-electrics or conductors.

After Gray's discovery it was no longer possible to believe that the electric effluvia are inseparably connected with the bodies from which they are evoked by rubbing; and it became necessary to admit that these emanations have an independent existence, and can be transferred from one body to another. Accordingly we find them recognized, under the name of the electric fluid,^[23] as one of the substances of which the world is constituted. The imponderability of this fluid did not, for the reasons already mentioned, prevent its admission by the side of light and caloric into the list of chemical elements.

The question was actively debated as to whether the electric fluid was an element sui generis, or, as some suspected, was another manifestation of that principle whose operation is seen in the phenomena of heat. Those who held the latter view urged that the electric fluid and heat can both be induced by friction, can both induce combustion, and can both be transferred from one body to another by mere contact; and, moreover, that the best conductors of heat are also in general the best conductors of electricity. On the other hand it was contended that, the electrification of a body does not cause any appreciable rise in its temperature; and an experiment of Stephen Gray's brought to light a yet more striking difference. Gray,^[24] in 1729, made two oaken cubes, one solid and the other hollow, and showed that when electrified in the same way they produced exactly similar effects; whence he concluded that it was only the surfaces which had taken part in the phenomena. Thus while heat is disseminated throughout the substance of a body, the electric fluid resides at or near its surface. In the middle of the eighteenth century it was generally compared to an enveloping atmosphere. “The electricity which a non-electric of great length (for example, a hempen string 800 or 900 feet long) "receives, runs from one end to the other in a sphere of electrical Effluvia," says Desaguliers in 1740^[25] and a report of the French Academy in 1733 says:^[26] "Around an electrified body there is formed a vortex of exceedingly fine matter in a state of agitation, which urges towards the body such light substances as lie within its sphere of activity. The existence of this vortex is more than a mere conjecture; for when an electrified body is brought close to the face it causes a sensation like that of encountering a cobweb."^[27]

The report from which this is quoted was prepared in connexion with the discoveries of Charles-François du Fay (b. 1698, d. 1739), superintendent of gardens to the King of France. Du Fay^[28] accounted for the behaviour of gold leaf when brought near to an electrified glass tube by supposing that at first the vortex of the tube envelopes the gold-leaf, and so attracts it towards the tube. But when contact occurs, the gold-leaf acquires the electric virtue, and so becomes surrounded by a vortex of its own. The two vortices, striving to extend in contrary senses, repel each other, and the vortex of the tube, being the stronger, drives away that of the gold-leaf. “It is then certain," says du Fay,^[29] "that bodies which have become electric by contact are repelled by those which have rendered them electric; but are they repelled likewise by other electrified bodies of all kinds? And do electrified bodies differ from each other in no respect save their intensity of electrification? An examination of this matter has led me to a discovery which I should never have foreseen, and of which I believe no one hitherto has had the least idea."

He found, in fact, that when gold-leaf which had been electrified by contact with excited glass was brought near to an excited piece of copal,^[30] an attraction was manifested between them. "I had expected," he writes, "quite the opposite effect, since, according to my reasoning, the copal and gold-leaf, which both electrified, should have repelled each other." Proceeding with his experiments he found that the gold-leaf, when electrified and repelled by glass, was attracted by all electrified resinous substances, and that when repelled by the latter it was attracted by the glass. “We see, then," he continues, "that there are two electricities of a totally different nature — namely, that of transparent solids, such as glass, crystal, &e., and that of bituminous or resinous bodies, such as amber, copal, sealing-wax, &e. Each of them repels bodies which have contracted an electricity of the same nature as its own, and attracts those whose electricity is of the contrary nature. We see even that bodies which are not themselves electrics can acquire either of these electricities, and that then their effects are similar to those of the bodies which have communicated it to them."

To the two kinds of electricity whose existence was thus demonstrated, du Fay gave the names vitreous and resinous, by which they have ever since been known.

An interest in electrical experiments seems to have spread from du Fay to other members of the Court circle of Louis XV; and from 1745 onwards the Memoirs of the Academy contain a series of papers on the subject by the Abbé Jean-Antoine Nollet (b. 1700, d. 1770), afterwards preceptor in natural philosophy to the Royal Family. Nollet attributed electric phenomena to the movement in opposite directions of two currents of a fluid, "very subtle and inflammable," which he supposed to be present in all bodies under all circumstances.^[31] When all electric is excited by friction, part of this fluid escapes from its pores, forming an effluent stream; and this loss is repaired by an afluent stream of the same fluid entering the body from outside. Light bodies in the vicinity, being caught in one or other of these streams, are attracted or repelled from the excited electric.

Nollet's theory was in great vogue for some time; but six or seven years after its first publication, its author came across a work purporting to be a French translation of a book printed originally in England, describing experiments said to have been made at Philadelphia, in America, by one Benjamin Franklin. “He could not at first believe," as Franklin tells us in his Autobiography, "that such a work came from America, and said it must have been fabricated by his enemies at Paris to decry his system. Afterwards, having been assured that there really existed such a person as Franklin at Philadelphia, which he had doubted, he wrote and published a volume of letters, chiefly addressed to me, defending his theory, and denying the verity of my experiments, and of the positions deduced from them."

We must now trace the events which led up to the discovery which so perturbed Nollet.

In 1745 Pieter van Musschenbroek (b. 1692, d. 1761), Professor at Leyden, attempted to find a method of preserving electric charges from the decay which was observed when the charged bodies were surrounded by air. With this purpose he tried the effect of surrounding a charged mass of water by an envelope of some non-conductor, e.g., glass. In one of his experiments, a phial of water was suspended from a gun-barrel by a wire let down a few inches into the water through the cork; and the gun-barrel, suspended on silk lines, was applied so near an excited glass globe that some metallic fringes inserted into the gun-barrel touched the globe in motion. Under these circumstances a friend named Cunaeus, who happened to grasp the phial with one hand, and touch the gun-barrel with the other, received a violent shock, and it became evident that a method of accumulating or intensifying the electric power had been discovered.^[32]

Shortly after the discovery of the Leyden phial, as it was named by Nollet, had become known in England, a London apothecary named William Watson (b. 1715, d. 1787)^[33] noticed that when the experiment is performed in this fashion the observer feels the shock "in no other parts of his body but his arms and breast"; whence he inferred that in the act of discharge there is a transference of something which takes the shortest or best-conducting path between the gun-barrel and the phial. This idea of transference seemed to him to bear some similarity to Nollet's doctrine afflux and efflux; and there can indeed be little doubt that the Abbé's hypothesis, though totally false in itself, furnished some of the ideas from which Watson, with the guidance of experiment, constructed a correct theory. In a memoir^[34] read to the Royal Society in October, 1746, he propounded the doctrine that electrical actions are due to the presence of an "electrical aether," which in the charging or discharging of a Leyden jar is transferred, but is not created or destroyed. The excitation of an electric, according to this view, consists not in the evoking of anything from within the electric itself without compensation, but in the accumulation of a surplus of electrical aether by the electric at the expense of some other body, whose stock is accordingly, depleted All bodies were supposed to possess a certain natural store, which could be drawn upon for this purpose.

"I have shewn," wrote Watson, "that electricity is the effect of a very subtil and elastic fluid, occupying all bodies in contact with the terraqueous globe; and that every-where, in its natural state, it is of the same degree of density; and that glass and other bodies, which we denominate electrics per se, have the power, by certain known operations, of taking this fluid from one body, and conveying it to another, in a quantity sufficient to be obvious to all our senses; and that, under certain circumstances, it was possible to render the electricity in some bodies more rare than it naturally is, and, by communicating this to other bodies, to give them an additional quantity, and make their electricity more dense."

In the same year in which Watson's theory was proposed, a certain Dr. Spence, who had lately arrived in America from Scotland, was showing in Boston some electrical experiments. Among his audience was a man who already at forty years of age was recognized as one of the leading citizens of the English colonies in America, Benjamin Franklin of Philadelphia (b. 1706, d. 1790). Spence's experiments "were," writes Franklin,^[35] “imperfectly performed, as he was not very expert; but, being on a subject quite new to me, they equally surprised and pleased me." Soon after this, the “Library Company” of Philadelphia (an institution founded by Franklin himself) received from Mr. Peter Collinson of London a present of a glass tube, with some account of its use. In a letter written to Collinson on July 11th, 1747,^[36] Franklin described experiments made with this tube, and certain deductions which he had drawn from them.

If one person A, standing on wax so that electricity cannot pass from him to the ground, rubs the tube, and if another person B, likewise standing on wax, passes his knuckle along near the glass so as to receive its electricity, then both A and B will be capable of giving a spark to a third person C standing on the floor; that is, they will be electrified. If, however, A and B touch each other, either during or after the rubbing, they will not be electrified.

This observation suggested to Franklin the same hypothesis that (unknown to him) had been propounded a few months previously by Watson : namely, that electricity is an element present in a certain proportion in all matter in its normal condition; so that, before the rubbing, each of the persons A, B, and C has an equal share. The effect of the rubbing is to transfer some of A's electricity to the glass, whence it is transferred to B. Thus A has a deficiency and B a superfluity of electricity; and if either of them approaches C, who has the normal amount, the distribution will be equalized by a spark. If, however, A and B are in contact, electricity flows between them so as to re-establish the original equality, and neither is then electrified with reference to C.

Thus electricity is not created by rubbing the glass, but only transferred to the glass from the rubber, so that the rubber loses exactly as much as the glass gains; the total quantity of electricity in any insulated system is invariable. This assertion is usually known as the principle of conservation of electric charge.

The condition of A and B in the experiment can evidently be expressed by plus and minus signs: A having a deficiency - e and B a superfluity + e of electricity. Franklin, at the commencement of his own experiments, was not acquainted with du Fay's discoveries: but it is evident that the electric fluid of Franklin is identical with the vitreous electricity of du Fay, and that du Fay's resinous electricity is, in Franklin's theory, merely the deficiency of a stock of vitreous electricity supposed to be possessed naturally by all ponderable bodies. In Franklin's theory we are spared the necessity for admitting that two quasi-material bodies can by their union annihilate each other, as vitreous and resinous electricity were supposed to do.

Some curiosity will naturally be felt as to the considerations which induced Franklin to attribute the positive character to vitreous rather than to resinous electricity. They seem to have been founded on a comparison of the brush discharges from conductors charged with the two electricities; when the electricity was resinous, the discharge was observed to spread over the surface of the opposite conductor "as if it flowed from it." Again, if a Leyden jar whose inner coating is electrified vitreously is discharged silently by a conductor, of whose pointed ends one is near the knob and the other near the outer coating, the point which is near the knob is seen in the dark to be illuminated with a star or globule, while the point which is near the outer coating is illuminated with a pencil of rays; which suggested to Franklin that the electric fluid, going from the inside to the outside of the jar, enters at the former point and issues from the latter. And yet again, in some cases the flame of a wax taper is blown away from a brass ball which is discharging vitreous electricity, and towards one which is discharging resinous electricity. But Franklin remarks that the interpretation of these observations is somewhat conjectural, and that whether vitreous or resinous electricity is the actual electric fluid is not certainly known.

Regarding the physical nature of electricity, Franklin held much the same ideas as his contemporaries; he pictured it as an elastic^[37] fluid, consisting of "particles extremely subtle, since it can permeate common matter, even the densest metals, with such ease and freedom as not to receive any perceptible resistance." He departed, however, to some extent from the conceptions of his predecessors, who were accustomed to ascribe all electrical repulsions to the diffusion of effluvia from the excited electric to the body acted on; so that the tickling sensation which is experienced when a charged body is brought near to the human face was attributed to a direct action of the effluvia on the skin. This doctrine, which, as we shall see, practically ended with Franklin, bears a suggestive resemblance to that which nearly a century later was introduced by Faraday; both explained electrical phenomena without introducing action at a distance, by supposing that something which forms an essential part of the electrified system is present at the spot where any electric action takes place; but in the older theory this something was identified with the electric fluid itself, while in the modern view it is identified with a state of stress in the aether. In the interval between the fall of one school and the rise of the other, the theory of action at a distance was dominant.

The germs of the last-mentioned theory may be found in Franklin's own writings. It originated in connexion with the explanation of the Leyden jar, a matter which is discussed in his third letter to Collinson, of date September 1st, 1747. In charging the jar, he says, a quantity of electricity is taken away from one side of the glass, by means of the coating in contact with it, and an equal quantity is communicated to the other side, by means of the other coating. The glass itself he supposes to be impermeable to the electric fluid, so that the deficiency on the one side can permanently coexist with the redundancy on the other, so long as the two sides are not connected with each other; but when a connexion is set up, the distribution of fluid is equalized through the body of the experimenter, who receives a shock.

Compelled by this theory of the jar to regard glass as impenetrable to electric effluvia, Franklin was nevertheless well aware^[38] that the interposition of a glass plate between an electrified body and the objects of its attraction does not shield the latter from the attractive influence. He was thus driven to suppose^[39] that the surface of the glass which is nearest the excited body is directly affected, and is able to exert an influence through the glass on the opposite surface; the latter surface, which thus receives a kind of secondary or derived excitement, is responsible for the electric effects beyond it.

This idea harmonized admirably with the phenomena of the jar; for it was now possible to hold that the excess of electricity on the inner face exercises a repellent action through the substance of the glass, and so causes a deficiency on the outer faces by driving away the electricity from it.^[40]

Franklin had thus arrived at what was really a theory of action at a distance between the particles of the electric fluid; and this he was able to support by other experiments. “Thus," he writes,^[41] "the stream of a fountain, naturally dense and continual, when electrified, will separate and spread in the form of a brush, every drop endeavouring to recede from every other drop.' In order to account for the attraction between oppositely charged bodies, in one of which there is an excess of electricity as compared with ordinary matter, and in the other an excess of ordinary matter as compared with electricity, he assumed that "though the particles of electrical matter do repel each other, they are strongly attracted by all other matter", so that "common matter is as a kind of spunge to the electrical fluid."

These repellent and attractive powers he assigned only to the actual (vitreous) electric fluid; and when later on the mutual repulsion of resinously electrified bodies became known to him,^[42] it caused him considerable perplexity.^[43] As we shall sec, the difficulty was eventually removed by Aepinus.

In spite of his belief in the power of electricity to act at a distance, Franklin did not abandon the doctrine of effluvia. "The form of the electrical atmosphere," he says,^[44] "is that of the body it surrounds. This shape may be rendered visible in a still air, by raising a smoke from dry rosin dropt into a hot teaspoon, under the electrified body, which will be attracted, and spread itself equally on all sides, covering and concealing the body, And this form it takes, because it is attracted by all parts of the surface of the body, though it cannot enter the substance already replete. Without this attraction, it would not remain round the body, but dissipate in the air." HC observed, however, that electrical effluvia do not seem to affect, or be affected by, the air; since it is possible to breathe freely in the neighbourhood of electrified bodies; and moreover a current of dry air does not destroy electric attractions and repulsions.^[45]

Regarding the suspected identity of electricity with the matter of heat, as to which Nollet had taken the affirmative position, Franklin expressed no opinion. "Common fire," he writes,^[46] "is in all bodies, more or less, as well as electrical fire. Perhaps they may be different modifications of the same element; or they may be different elements. The latter is by some suspected. If they are different things, yet they may and do subsist together in the same body."

Franklin's work did not at first receive from European philosophers the attention which it deserved; although Watson generously endeavoured to make the colonial writer's merits known,^[47] and inserted some of Franklin's letters in one of his own papers communicated to the Royal Society. But an account of Franklin's discoveries, which had been printed in England, happened to fall into the hands of the naturalist Buffon, who was so much impressed that he secured the issue of a French translation of the work; and it was this publication which, as we have seen, gave such offence to Nollet. The success of a plan proposed by Franklin for drawing lightning from the clouds soon engaged public attention everywhere; and in a short time the triumph of the one-fluid theory of electricity, as the hypothesis of Watson and Franklin is generally called, was complete. Nollet, who was obdurate, "lived to see himself the last of his sect, except Monsieur B— of Paris, his élève and immediate disciple."^[48]

The theory of effluvia was finally overthrown, and replaced by that of action at a distance, by the labours of one of Franklin's continental followers, Francis Ulrich Theodore Aepinus^[49] (b. 1724, d. 1802). The doctrine that glass is impermeable to electricity, which had formed the basis of Franklin's theory of the Leyden phial, was generalized by Aepinus^[50] and his co-worker Johann Karl Wilcke (b. 1732, d. 1796) into the law that all non-conductors are impermeable to the electric fluid. That this applies even to air they proved by constructing a machine analogous to the Leyden jar, in which, however, air took the place of glass as the medium between two oppositely charged surfaces. The success of this experiment led Aepinus to deny altogether the existence of electric effluvia surrounding charged bodies:^[51] a position which he regarded as strengthened by Franklin's observation, that the electric field in the neighbourhood of an excited body is not destroyed when the adjacent air is blown away. The electric fluid must therefore be supposed not to extend beyond the excited bodies themselves. The experiment of Gray, to which we have already referred, showed that it does not penetrate far into their substance; and thus it became necessary to suppose that the electric fluid, in its state of rest, is confined to thin layers on the surfaces of the excited bodies. This being granted, the attractions and repulsions observed between the bodies compel us to believe that electricity acts at a distance across the intervening air.

Since two vitreously charged bodies repel each other, the force between two particles of the electric fluid must con Franklin's one-fluid theory, which Aepinus adopted) be repulsive: and since there is an attraction between oppositely charged bodies, the force between electricity and ordinary matter must be attractive. These assumptions had been made, as we have seen, by Franklin; but in order to account for the repulsion between two resinously charged bodies, Aepinus introduced a new supposition—namely, that the particles of ordinary matter repel each other. This, at first, startled his contemporaries; but, as he pointed out, the "unelectrified" matter with which we are acquainted is really matter saturated with its natural quantity of the electric fluid, and the forces due to the matter and fluid balance each other; or perhaps, as he suggested, a slight want of equality between these forces might give, as a residual, the force of gravitation.

Assuming that the attractive and repellent forces increase as the distance between the acting charges decreases, Aepinus applied his theory to explain a phenomenon which bad been more or less indefinitely observed by many previous writers, and specially studied a short time previously by John Canton^[52] (b. 1718, d. 1772) and by Wilcket^[53]—namely, that if a conductor is brought into the neighbourhood of an excited body without actually touching it, the remoter portion of the conductor acquires an electric charge of the same kind as that of the excited body, while the nearer portion acquires a charge of the opposite kind. This effect, which is known as the induction of electric charges, had been explained by Canton himself and by Franklin^[54] in terms of the theory of electric effluvia. Aepinus showed that it followed naturally from the theory of action at a distance, by taking into account the mobility of the electric fluid in conductors; and by discussing different cases, so far as was possible with the means at his command, he laid the foundations of the mathematical theory of electrostatics.

Aepinus (lid not succeed in determining the law according to which the force between two electric charges varies with the distance between them; and the honour of having first accomplished this belongs to Joseph Priestley (b. 1733, d. 1804), the discoverer of oxygen. Priestley, who was a friend of Franklin's, had been informed by the latter that he had found cork balls to be wholly unaffected by the electricity of a metal cup within which they were held; and Franklin desired priestley to repeat and ascertain the fact. Accordingly, on December 21st, 1766, Priestley instituted experiments, which showed that, when a hollow metallic vessel is electrified, there is no charge on the inner surface (except near the opening), and no electric force in the air inside. From this he at once drew the correct conclusion, which was published in 1767.^[55] "May we not infer," he says, "from this experiment that the attraction of electricity is subject to the same laws with that of gravitation, and is therefore according to the squares of the distances; since it is easily demonstrated that were the earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another?"

This brilliant inference seems to have been insufficiently studied by the scientific men of the day; and, indeed, its author appears to have hesitated to claim for it the authority of a complete and rigorous proof. Accordingly we find that the question of the law of force was not regarded as finally settled for eighteen years afterwards.^[56]

By Franklin's law of the conservation of electric charge, and Priestley's law of attraction between charged bodies, electricity was raised to the position of an exact science. It is impossible to mention the names of these two friends in such a connexion without reflecting on the curious parallelism of their lives. In both men there was the same combination of intellectual boldness and power with moral earnestness and public spirit. Both of them carried on a long and tenacious struggle with the reactionary influences which dominated the English Government in the reign of George III; and both at last, when overpowered in the conflict, reluctantly exchanged their native flag for that of the United States of America. The names of both have been held in honour by later generations, not more for their scientific discoveries than for their services to the cause of religious, intellectual, and political freedom.

The most celebrated electrician of Priestley's contemporaries in London was the Hon. Henry Cavendish (b. 1731, d. 1810), whose interest in the subject was indeed hereditary, for his father, Lord Charles Cavendish, had assisted in Watson's experiments of 1747.^[57] In 1771 Cavendish^[58] presented to the Royal Society an "Attempt to explain some of the principal phenomena of Electricity, by means of an elastic fluid." The hypothesis adopted is that of the one-fluid theory, in much the same form as that of Aepinus. It was, as he tells us, discovered independently, although he became acquainted with Aepinus' work before the publication of his own paper.

In this memoir Cavendish makes no assumption regarding the law of force between electric charges, except that it is "inversely as some less power of the distance than the cube"; but he evidently inclines to believe in the law of the inverse square. Indeed, he shows it to be "likely, that if the electric attraction or repulsion is inversely as the square of the distance, almost all the redundant fluid in the body will be lodged close to the surface, and there pressed close together, and the rest of the body will be saturated"; which approximates closely to the discovery made four years previously by Priestley. Cavendish did, as a matter of fact, rediscover the inverse square law shortly afterwards; but, indifferent to fame, he neglected to communicate to others this and much other work of importance. The value of his researches was not realized until the middle of the nineteenth century, when William Thomson (Lord Kelvin) found in Cavendish's manuscripts the correct value for the ratio of the electric charges carried by a circular disk and a sphere of the same radius which had been placed in metallic connexion. Thomson urged that the papers should be published; which came to pass ^[59] in 1879, a hundred years from the date of the great discoveries which they enshrined. It was then seen that Cavendish had anticipated his successors in several of the ideas which will presently be discussed—amongst others, those of electrostatic capacity and specific inductive capacity.

In the published memoir of 1771 Cavendish worked out the consequences of his fundamental hypothesis more completely than Aepinus; and, in fact, virtually introduced the notion of electric potential, though, in the absence of any definite assumption as to the law of force, it was impossible to develop this idea to any great extent.

One of the investigations with which Cavendish occupied himself was a comparison between the conducting powers of different materials for electrostatic discharges. The question hall been first raised by Beccaria, who had shown^[60] in 1753 that when the circuit through which a discharge is passed contains tubes of water, the shock is more powerful when the cross-section of the tubes is increased. Cavendish went into the matter much more thoroughly, and was able, in a memoir presented to the Royal Society in 1775,^[61] to say: "It appears from some experiments, of which I propose shortly to lay an account before this Society, that iron wire conducts about 400 million times better than rain or distilled water—that is, the electricity meets with no more resistance in passing through a piece of iron wire 400,000,000 inches long than through a column of water of the same diameter only one inch long. Sea—water, or a solution of one part of salt in 30 of water, conducts 100 times, or a saturated solution of sea—salt about 720 times, better than rain-water."

The promised account of the experiments was published in the volume edited in 1879. It appears from it that the method of testing by which Cavendish obtained these, results was simply that of physiological sensation, but the figures given in the comparison of iron and sea—water are remarkably exact.

While the theory of electricity was being established on a sure foundation by the great investigators of the eighteenth century, a no less remarkable development was taking place in the kindred science of magnetism, to which our attention must now be directed.

The law of attraction between magnets was investigated at an earlier date than the corresponding law for electrically charged bodies. Newton,^[62] in the Principia, says: "The power of gravity is of a different nature from the power of magnetism, For the magnetic attraction is not as the matter attracted. Some bodies are attracted more by the magnet, others less; most bodies not at all. The power of magnetism, in one and the same body, may be increased and diminished; and is sometimes far stronger, for the quantity of matter, than the power of gravity; and in receding from the magnet, decreases not in the duplicate, but almost in the triplicate proportion of the distance, as nearly as I could judge from some rude observations,"

The edition of the Principia which was published in 1742 by Thomas Le Seur and Francis Jacquier contains a note on this corollary, in which the correct result is obtained that the directive couple exercised on one magnet by another is proportional to the inverse cube of the distance.

The first discoverer of the law of force between magnetic t poles was John Michell (b. 1724, d. 1793), at that time a young Fellow of Queen's College, Cambridge,^[63] who in 1750 published A Treatise of Artificial Magnets; in which is shown an easy and expeditious method of making them superior to the best natural ones. In this he states the principles of magnetic theory as follows^[64]:—

"Wherever any Magnetism is found, whether in the Magnet itself, or any piece of Iron, etc., excited by the Magnet, there are always found two Poles, which are generally called North and South; and the North Pole of one Magnet always attracts the South Pole, and repels the North Pole of another; and vice versa."

This is of course adopted from Gilbert.

"Each Pole attracts or repels exactly equally, at equal distances, in every direction." This, it may be observed, overthrows the theory of vortices, with which it is irreconcilable. "The Magnetical Attraction and Repulsion are exactly equal to each other." This, obvious though it may seem to us, was really a most important advance, for, as he remarks, "Most people, who have mention'd any thing relating to this property of the Magnet, have agreed, not only that the Attraction and Repulsion of Magnets are not equal to each other, but that also, they do not observe the same rule of increase and decrease."

"The Attraction and Repulsion of Magnets decreases, as the Squares of the distances from the respective poles increase."

This great discovery, which is the basis of the mathematical theory of Magnetism, was deduced partly from his own obscrvations, and partly from those of previous investigators (e.g. Dr. Brook Taylor and P. Musschenbroek^{[errata 1]}), who, as he observes, had made accurate experiments, but had failed to take into account all the considerations necessary for a sound theoretical discussion of them,

After Michell the law of the inverse square was maintained by Tobias Mayer^[65] of Göttingen (b. 1723, d. 1762), better known as the author of Lunar Tables which were long in use; and by the celebrated mathematician, Johann Heinrich Lambert^[66] (b. 1728, d. 1777)

The promulgation of the one-fluid theory of electricity, in the middle of the eighteenth century, naturally led to attempts to construct a similar theory of magnetism; this was effected in 1759 by Aepinus,^[67] who supposed the "poles" to be places at which a magnetic fluid was present in amount exceeding or falling short of the normal quantity. The permanence of magnets was accounted for by supposing the fluid to be entangled in their pores, so as to be with difficulty displaced. The particles of the fluid were assumed to repel each other, and to attract the particles of iron and steel; but, as Aepinus saw, in order to satisfactorily explain magnetic phenomena it was necessary to assume also a mutual repulsion among the material particles of the magnet.

Subsequently two imponderable magnetic fluids, to which the names boreal and austral were assigned, were postulated by the Hollander Anton Brugmans (b. 1732, d. 1789) and by Wilcke. These fluids were supposed to have properties of mutual attraction and repulsion similar to those possessed by vitreous and resinous electricity.

The writer who next claims our attention for his services both to magnetism and to electricity is the French physicist, Charles Augustin Coulomb^[68] (b. 1736, d. 1806). By aid of the torsion-balance, which was independently invented by Michell and himself, he verified in 1785 Priestley's fundamental law that the repulsive force between two small globes charged with the same kind of electricity is in the inverse ratio of the square of the distance of their centres. In the second memoir he extended this law to the attraction of opposite electricities.

Coulomb did not accept the one-fluid theory of Franklin, Aepinus, and Cavendish, but preferred a rival hypothesis which had been proposed in 1759 by Robert Symmer.^[69] "My notion," said Symmer, "is that the operations of electricity do not depend upon one single positive power, according to the opinion generally received; but upon two distinct, positive, and active powers, which, by contrasting, and, as it were, counteracting each other, produce the various phenomena of electricity; and that, when a body is said to be positively electrified, it is not simply that it is possessed of a larger share of electric matter than in a natural state; nor, when it is said to be negatively electrified, of a less; but that, in the former case, it is possessed of a larger portion of one of those active powers, and in the latter, of a larger portion of the other; while a body in its natural state remains unelectrified, from an equal balance of those two powers within it."

Coulomb developed this idea: "Whatever be the cause of electricity," he says,^[70] "we can explain all the phenomena by supposing that there are two electric fluids, the parts of the same fluid repelling each other according to the inverse square of the distance, and attracting the parts of the other fluid according to the same inverse square law." "The supposition of two fluids," he adds, "is moreover in accord with all those discoveries of modern chemists and physicists, which have made known to a various pairs of gases whose elasticity is destroyed by their admixture in certain proportions—an effect which could pot take place without something equivalent to a repulsion between the parts of the same gas, which is the cause of its elasticity, and an attraction between the parts of different gases, which accounts for the loss of elasticity on combination."

According, then, to the two-fluid theory, the "natural fluid" contained in all matter can be decomposed, under the influence of an electric field, into equal quantities of vitreous and resinous electricity, which, if the matter be conducting, can then fly to the surface of the body. The abeyance of the characteristic properties of the opposite electricities when in combination was sometimes further compared to the neutrality manifested by . the compound of an acid and an alkali.

The publication of Coulomb's views led to some controversy between the partisans of the one-fluid and two-fluid theories; the latter was soon generally adopted in France, but was stoutly opposed in Holland by Van Marum and in Italy by Volta. The chief difference between the rival hypotheses is that, in the two-fluid theory, both the electric fluids are movable within the substance of a solid conductor; while in the one-fluid theory the actual electric fluid is mobile, but the particles of the conductor are fixed. The dispute could therefore be settled only by a determination of the actual motion of electricity in discharges; and this was beyond the reach of experiment.

In his Fourth Memoir Coulomb showed that electricity in equilibrium is confined to the surface of conductors, and does not penetrate to their interior substance; and in the Sixth Memoir^[71] he virtually establishes the result that the electric force near a conductor is proportional to the surface-density of electrification,

Since the overthrow of the doctrine of electric eflluvia by Aepinus, the aim of electricians had been to establish their science upon the foundation of a law of action at a distance, resembling that which had led to such triumphs in Celestial Mechanics. When the law first stated by Priestley was at length decisively established by Coulomb, its simplicity and beauty gave rise to a general feeling of complete trust in it as the best attainable conception of electrostatic phenomena. The result was that attention was almost exclusively focused on action-at-a-distance theories, until the time, long afterwards, when Faraday led natural philosophers back to the right: path.

Coulomb rendered great services to magnetic theory. It was he who in 1777, by simple mechanical reasoning, completed the overthrow of the hypothesis of vortices.^[72] He also, in the second of the Memoirs already quoted,^[73] confirmed Michell's law, according to which the particles of the magnetic fluids attract or repel each other with forces proportional to the inverse square of the distance. Coulomb, however, went beyond this, and endeavoured to account for the fact that the two magnetic fluids, unlike the two electric fluids, cannot be obtained separately; for when a magnet is broken into two pieces, one containing its north and the other its south pole, it is found that each piece is an independent magnet possessing two poles of its own, so that it is impossible to obtain a north or south pole in a state of isolation. Coulomb explained this by supposing^[74] that the magnetic fluids are permanently imprisoned within the molecules of magnetic bodies, so as to be incapable of crossing from one molecule to the next; each molecule therefore under all circumstances contains as much of the boreal as of the austral fluid, and magnetization consists simply in a separation of the two fluids to opposite ends of each molecule. Such a hypothesis evidently accounts for the impossibility of separating the two fluids to opposite ends of a body of finite size. The same idea, here introduced for the first time, has since been applied with success in other departments of electrical philosophy.

In spite of the advances which have been recounted, the mathematical development of electric and magnetic theory was scarcely begun at the close of the eighteenth century; and many erroneous notions were still widely entertained. Report^[75] which was presented to the French Academy in 1800, it was assumed that the mutual repulsion of the particles of electricity on the surface of a body is balanced by the resistance of the surrounding air; and for long afterwards the electric force outside a charged conductor was confused with a supposed additional pressure in the atmosphere.

Electrostatical theory was, however, suddenly advanced to quite a mature state of development by Siméon Denis Poisson (b. 1781, d. 1840), in a memoir which was read to the French Academy in 1812.^[76] As the opening sentences show, he accepted the conceptions of the two-fluid theory.

"The theory of electricity which is most generally accepted," he says, "is that which attributes the phenomena to two different fluids, which are contained in all material bodies. It is supposed that molecules of the same fluid repel each other and attract the molecules of the other fluid; these forces of attraction and repulsion obey the law of the inverse square of the distance; and at the same distance the attractive power is equal to the repellent power; whence it follows that, when all the parts of a body contain equal quantities of the two fluids, the latter do not exert any influence on the fluids contained in neighbouring bodies, and consequently no electrical effects are discernible. This equal and uniform distribution of the two fluids is called the natural state; when this state is disturbed in any body, the body is said to be electrified, and the various phenomena of electricity begin to take place.

"Material bodies do not all behave in the same way with respect to the electric fluid: some, such as the metals, do not appear to exert any influence on it, but permit it to move about freely in their substance: for this reason they are called conductors. Others, on the contrary—very dry air, for example—oppose the passage of the electric fluid in their interior, so that they can prevent the fluid accumulated in conductors from being dissipated throughout space."

When an excess of one of the electric fluids is communicated to a metallic body, this charge distributes itself over the surface of the body, forming a layer whose thickness at any point depends on the shape of the surface. The resultant force due to the repulsion of all the particles of this surface-layer must vanish at any point in the interior of the conductor, since otherwise the natural state existing there would be disturbed; and Poisson showed that by aid of this principle it is possible in certain cases to determine the distribution of electricity in the surface-layer. For example, a well-known proposition of the theory of Attractions asserts that a hollow shell whose bounding surfaces are two similar and similarly situated ellipsoids exercises no attractive force at any point within the interior hollow; and it may thence be inferred that, if an electrified metallic conductor has the form of an ellipsoid, the charge will be distributed on it proportionally to the normal distance from the surface to an adjacent similar and similarly situated ellipsoid.

Poisson went on to show that this result was by no means all that might with advantage be borrowed from the theory of + Attractions. Lagrange, in a memoir on the motion of gravitating bodies, had shown^[77] that the components of the attractive force at any point can be simply expressed as the derivates of the function which is obtained by adding together the masses of all the particles of an attracting system, each divided by its distance from the point; and Laplace had shown^[78] that this function V satisfies the equation

${\frac {\partial ^{2}V}{\partial x^{2}}}+{\frac {\partial ^{2}V}{\partial y^{2}}}+{\frac {\partial ^{2}V}{\partial z^{2}}}=0$

in space free from attracting matter. Poisson himself showed later, in 1813,^[79] that when the point (x, y, z) is within the substance of the attracting body, this equation of Laplace must be replaced by

${\frac {\partial ^{2}V}{\partial x^{2}}}+{\frac {\partial ^{2}V}{\partial y^{2}}}+{\frac {\partial ^{2}V}{\partial z^{2}}}=4\pi \rho$

where ρ denotes the density of the attracting matter at the point. In the present memoir Poisson called attention to the utility of this function V in electrical investigations, remarking that its value over the surface of any conductor must be constant.

The known formulae for the attractions of spheroids show that when a charged conductor is spheroidal, the repellent force acting on a small charged body immediately outside it will be directed at right angles to the surface of the spheroid, and will be proportional to the thickness of the surface-layer of electricity at this place. Poisson suspected that this theorem might be true for conductors not having the spheroidal form—a result which, as we have seen, had been already virtually given by Coulomb; and Laplace suggested to Poisson the following proof, applicable to the general case. The force at a point immediately outside the conductor can be divided into a part S due to the part of the charged surface immediately adjacent to the point, and a part due to the rest of the surface. At a point close to this, but just inside the conductor, the force S will still act; but the forces will evidently be reversed in direction. Since the resultant force at the latter point vanishes, we must have S=s; so the resultant force at the exterior point is 2s. But s is proportional to the charge per unit area of the surface, as is seen by considering the case of an infinite plate; which establishes the theorem.

When several conductors are in presence of each other, the distribution of electricity on their surfaces may be determined by the principle, which Poisson took as the basis of his work, that at any point in the interior of any one of the conductors, the resultant force due to all the surface-layers must be zero. He discussed, in particular, one of the classical problems of electrostatics— namely, that of determining the surface-density on two charged conducting spheres placed at any distance from each other. The solution depends on Double Gamma Functions in the general case; when the two spheres are in contact, it depends on ordinary Gamma Functions. Poisson gave a solution in terms of definite integrals, which is equivalent to that in terms of Gamma Functions; and after reducing his results to numbers, compared them with Coulomb's experiments.

The rapidity with which in a single memoir Poisson passed from the barest elements of the subject to such recondite problems as those just mentioned may well excite admiration. His success is, no doubt, partly explained by the high state of development to which analysis had been advanced by the great mathematicians of the eighteenth century; but even after allowance has been made for what is due to his predecessors, Poisson's investigation must be accounted a splendid memorial of his genius.

Some years later Poisson turned his attention to magnetism; and, in a masterly paper^[80] presented to the French Academy in 1824, gave a remarkably complete theory of the subject.

His starting-point is Coulomb's doctrine of two imponderable magnetic fluids, arising from the decomposition of a neutral fluid, and confined in their movements to the individual elements of the magnetic body, so as to be incapable of passing from one element to the next.

Suppose that an amount m of the positive magnetic fluid is located at a point (x, y, z); the components of the magnetic intensity, or force exerted on unit magnetic pole, at a point (ξ, η, ζ) will evidently be

$-m{\frac {\partial }{\partial \xi }}\left({\frac {1}{r}}\right)$, $-m{\frac {\partial }{\partial \eta }}\left({\frac {1}{r}}\right)$, $-m{\frac {\partial }{\partial \zeta }}\left({\frac {1}{r}}\right)$,

where r denotes |(ξ-x)² + (η-y)² + (ζ-z)²|^{${\frac {1}{2}}$}. Hence if we consider next a magnetic element in which equal quantities of the two magnetic fluids are displaced from each other parallel to the x-axis, the components of the magnetic intensity at (ξ, η, ζ) will be the negative derivates, with respect to ξ, η, ζ respectively, of the function

$A{\frac {\partial }{\partial x}}\left({\frac {1}{r}}\right)$,

where the quantity A, which does not involve (ξ, η, ζ), may be called the magnetic moment of the element: it may be measured by the couple required to maintain the element in equilibrium at a definite angular distance from the magnetic meridian.

If the displacement of the two fluids from each other in the element is not parallel to the axis of s, it is easily seen that the expression corresponding to the last is

$A{\frac {\partial }{\partial x}}\left({\frac {1}{r}}\right)+B{\frac {\partial }{\partial y}}\left({\frac {1}{r}}\right)+C{\frac {\partial }{\partial z}}\left({\frac {1}{r}}\right)$,

where the vector (A, B, C) now denotes the magnetic moment of the element.

Thus the magnetic intensity at an external point (ξ, η, ζ) due to any magnetic body has the components

$\left(-{\frac {\partial V}{\partial \xi }},-{\frac {\partial V}{\partial \eta }},-{\frac {\partial V}{\partial \zeta }}\right)$,

where

$V=\iiint \left(A{\frac {\partial }{\partial x}}+B{\frac {\partial }{\partial y}}+C{\frac {\partial }{\partial z}}\right)\left({\frac {1}{r}}\right)dxdydz$

integrated throughout the substance of the magnetic body, and where the vector (A, B, C) or I represents the magnetic moment per unit-volume, or, as it is generally called, the magnetization. The function V was afterwards named by Green the magnetic potential.

Poisson, by integrating by parts the preceding expression for the magnetic potential, obtained it in the form

$\iint (\mathbf {I.} d\mathbf {S} ){\frac {1}{r}}-\iiint {\frac {1}{r}}\mathrm {div} \mathbf {I} dxdydz$,^[81]

the first integral being taken over the surface S of the magnetic body, and the second integral being taken throughout its volume. This formula shows that the magnetic intensity produced by the body in external space is the same as would be produced by a fictitious distribution of magnetic fluid, consisting of a layer over its surface, of surface-charge (I.ds) per element dS, together with a volume-distribution of density — div I throughout its substance. These fictitious magnetizations are generally known as Poisson's equivalent surface- and volume-distributions of magnetism.

Poisson, moreover, perceived that at a point in a very small cavity excavated within the magnetic body, the magnetic potential has a limiting value which is independent of the shape of the cavity as the dimensions of the cavity tend to zero; but that this is not true of the magnetic intensity, which in such a small cavity depends on the shape of the cavity. Taking the cavity to be spherical, he showed that the magnetic intensity within it is

$\mathrm {grad} V+{\frac {4}{3}}\pi \mathbf {I}$,^[82]

where I denotes the magnetization at the place.

This memoir also contains a discussion of the magnetism temporarily induced in soft iron and other magnetizable metals by the approach of a permanent magnet. Poisson accounted for the properties of temporary magnets by assuming that they contain embedded in their substance a great number of small spheres, which are perfect conductors for the magnetic fluids; 80 that the resultant magnetic intensity in the interior of one of these small spheres must be zero. He showed that such a sphere, when placed in a field of magnetic intensity F,^[83] must acquire a magnetic moment of amount ${\frac {3}{4\pi }}\mathbf {F} \times$ the volume of the sphere, in order to counteract within the sphere the force F. Thus if k_p denote the total volume of these spheres contained within a unit volume of the temporary magnet, the magnetization will be I, where ${\frac {3}{4}}\pi \mathbf {I} =k_{p}\mathbf {F}$, and F denotes the magnetic intensity within a spherical cavity excavated in the body. This is Poisson's law of induced magnetism.

It is known that some substances acquire a greater degree of temporary magnetization than others when placed in the same circumstances: Poisson accounted for this by supposing that the quantity k_p varies from one substance to another. But the experimental data show that for soft iron k_p must have a value very near unity, which would obviously be impossible if k_p is to mean the ratio of the volume of spheres contained within a region to the total volume of the region.^[84] The physical interpretation assigned by Poisson to his formulae must therefore be rejected, although the formulae themselves retain their value.

Poisson's electrical and magnetical investigations were generalized and extended in 1828 by George Green^[85] (b. 1793, d. 1841). Green's treatment is based on the properties of the function already used by Lagrange, Laplace, and Poisson, which represents the sum of all the electric or magnetic charges in the field, divided by their respective distances from some given point: to this function Green gave the name potential, by which it has always since been known.^[86]

Near the beginning of the memoir is established the celebrated formula connecting surface and volume integrals, which is now generally called Green's Theorem, and of which Poisson's result on the equivalent surface- and volume-distributions of magnetization is a particular application. By using this theorem to investigate the properties of the potential, Green arrived at many results of remarkable beauty and interest. We need only mention, as an example of the power of his method, the following:—Suppose that there is a hollow conducting shell, bounded by two closed surfaces, and that a number of electrified bodies are placed, some within and some without it, and let the inner surface and interior bodies be called the interior system, and the outer surface and exterior bodies be called the exterior system. Then all the electrical phenomena of the interior system, relative to attractions, repulsions, and densities, will be the same as if there were no exterior system, and the inner surface were a perfect conductor, put in communication with the earth; and all those of the exterior system will be the same as if the interior system did not exist, and the outer surface were a perfect conductor, containing a quantity of electricity equal to the whole of that originally contained in the shell itself and in all the interior bodies.

It will be evident that electrostatics had by this time attained a state of development in which further progress could be hoped for only in the mathematical superstructure, unless experiment should unexpectedly bring to light phenomena of an entirely new character. This will therefore be a convenient place to pause and consider the rise of another branch of electrical philosophy.

Notes

1. Original: Muschenbroek was amended to Musschenbroek

1. Cf. pp. 7-9.
2. De Magnete, lib. ii., cap. 2.
3. Query 22.
4. "Subtlety," says Johnson, "which in its original import means exility of particles, is taken in its metaphorical meaning for nicety of distinction."
5. i.e, oxides.
6. Newton himself (Opticks, p. 349) suspected that light-corpuscles and ponderable matter might be transmuted into each other: much later, Boscovich (Theoria, pp. 216, 217) regarded the matter of light as a principle or element in the constitution of natural bodies.
7. Nov. Org., Lib. II., Aphor. xx.
8. Mechanical Production of Heat and Cold
9. Micrographia, p. 37.
10. Opticks
11. Mém. de l'Acad., 1705, p. 88.
12. Though it reminds us of a curious conjecture of Newton's: "Is not the strength and vigour of the action between light and sulphureous bodies one reason why sulphureous bodies take fire more readily and burn more vehemently than other bodies do?"
13. I have thought it best to translate s'Gravesande's ignis by "light-corpuscles." This is, I think, fully justified by such of his statements as Quando ignis per lineas rectax oculos nostros intrat, ex motu quem fibris in fundo oculi communicat ideam luminis excital.
14. Boerhaave followed Homberg in supposing the matter of heat to be present in all so-called vacuous spaces.
15. Scheele in 1777 supposed calorie to be a compound of oxygen and phlogiston, and light to be oxygen combined with a greater proportion of phlogiston.
16. In spite of the experiments of Benjamin Thompson, Count Rumford (5. 1753, d. 1814), in the closing years of the eighteenth century. These should have sufficed to re-establish the older conception of heat.
17. This had been known since the time of Boyle.
18. The correct idea of combustion had been advanced by Hooke. "The dissolution of inflammable bodies," he asserts in the Micrographia, "is performed by a substance inherent in and mixed with the air, that is like, if not the very same with, that which is fixed in saltpetre." But this statement met with little favour at the time, and the doctrine of the compound nature of metals survived in full vigour until the discovery of oxygen by Priestley and Scheele in 1771-5. In 1775 Lavoisier reaffirmed Hooke's principle that a metallic calx is not the metal minus phlogiston, but the metal plus oxygen; and this idea, which carried with it the recognition of the elementary nature of metals, was generally accepted by the end of the eighteenth century.
19. Those who are interested in the literary history of the eighteenth century will recall the controversy as to whether the verses on the death of Stephen Gray were written by Anna Williams, whose name they bore, or by her patron Johnson.
20. Phil. Trans. xxxvii (1731), pp. 18, 227, 285, 397.
21. Otto von Guericke (b. 1602, d. 1686) bad, as a matter of fact, observed the conduction of electricity along a linen thread; but this experiment does not seem to have been followed up. Cf. Experimenta novu magdeburgica, 1672.
22. Phil. Trans. xli. (1739), PP. 186, 193, 200, 209: Dissertation concerning Electricity, 1742
23. The Cartesians defined a fluid to be a body whose minute parts are in a continual agitation
24. Phil. Trans. xxxvii., p. 35.
25. Phil. Trans. xli., p. 636.
26. Hist, de l'Acad., 1733, p. 6.
27. This observation had been made first by Hawksbee at the beginning of the century.
28. Mém. de l'Acad. des Sciences, 1733, pp. 23, 73, 233, 467; 1734, pp. 341, 503; 1737, p. 86; Phil. Trans. xxxviii. (1734), p. 258.
29. Mém. de l'Acad., 1733, p. 464.
30. A hard transparent resin, used in the preparation of varnish.
31. Cf. Nollet's Recherches, 1749, p. 245.
32. The discovery was niade independently in the same year by Ewald Georg von Kleist, Dean of Kumpin.
33. Watson afterwards rose to eminence in the medical profession, and was knighted
34. l'hil. Trans. xliv.. p, 718. It may here be noted that it was Watson who improved the phial by coating it nearly to the top, both inside and outside, with tinfoil.
35. Franklin's Autobiography.
36. Franklin's New Experiments and Observations on Electricity, letter ii.
37. i.e., repulsive of its own particles.
38. New Experiments, 1750, §28.
39. New Experiments, 1750, §34,
40. New Experiments, 1750, §32.
41. Letter v.
42. He refers to it in his Paper read to the Royal Society, December 18, 1755.
43. Cf. letters xxxvii and xxxviii, dated 1761 und 1762.
44. New Experiments, 1750, §15,
45. Letter vii, 1751.
46. Letter y.
47. Phil. Trans. xlvii, p. 202. Watson agreed with Nollet in rejecting Franklin's theory of the impermeability of glass.
48. Franklin's Autobiography.
49. This philosopher's surname had been hellenized from its original form Hoeck to αἰπεινός by one of his ancestors, a distinguished theologian.
50. F. V. T. Aepinus Tentamen Theoriae Electricitatis et Magnetismi: St. Petersburg, 1759.
51. This was also maintained about the same time by Giacomo Battista Beccaria of Turin (b. 1716, d. 1781).
52. Phil. Trans. xlviii (1763), p. 350.
53. Disputatio physica experimentalis de electricitatibus contrariis: Rostock, 1757.
54. In his paper read to the Royal Society on Dee. 1811, 1766.
55. Priestley, The History and Present State of Electricity, with Original Experimens; London, 1767: page 732. That electrical attraction follows the law of the inverse square had been suspected by Daniel Bernoulli in 1700: Cr. Socin's Experiments, Acta Helvetica, iv, p. 214.
56. In 1769 Dr. John Robison (b. 1739, d. 1805). of Edinburgh, endeavoured to determine the law of force by direct experiment, and found it to be that of the inverse 2.06^th power of the distance.
57. Phil. Trans. xlv, p. 67 (1750).
58. Phil. Trans. Ixi, p. 084 (1771).
59. The Electrical Researches of the Hon, Henry Cavendish, edited by J. Clerk Maxwell, 1879.
60. G. B. Becuaria, Dell' elettricismo artificiale o naturale, Turin, 1753, p. 113.
61. Phil. Trans. Ixvi (1776), p. 196.
62. Book iii, Prop. vi, cor. 5.
63. Michell had taken bis degree only two years previously. Later in life he was on terms of friendship with Priestley, Cavendish, and William Herschel; it was he who taught Herschel the art of grinding mirrors for telescopes. The plan of determining the density of the earth, which was carried out by Cavendish in 1999, and is generally known as the "Cavendish Experiment," was due to Michell. Michell was the first inventor of the torsion-balance; he also made many valuable contributions to Astronomy. In 1767 he became Rector of Thornhill, Yorks, and lived there until his death.
64. 4 Loc. cit., p. 17.
65. Noticed in Göttinger Gelehrter Anzeiger, 1760: ef. Aepinus, Nov. Comm. Aead. Petrop., 1768, and Mayer's Opera Inedita, herauag. von G. C. Lichtenberg.
66. Histoire de l'Acad. de Berlin, 1766, PP. 22, 49.
67. In the Tentamen, to which reference has already been made.
68. Coulomb's First, Second, and Third Memoirs appear in Mémoires de l'Acad., 1785; the Fourth in 1786, the Fifth in 1787, the Sixth in 1788, and the Seventh in 1789.
69. Phil. Trans. li (1759), p. 371.
70. Sixth Memoir, p. 561.
71. Page 677.
72. Mém. présentés par divers Savans, ix (1780), p. 166.
73. Mém de 1'Acad., 1785, p. 593. Gauss finally established the law by a much more refined method.
74. In his Seventh Memoir, Mém, de l'Acad., 1789, p. 488.
75. On Volta's discoveries.
76. Mém. de l'Institut, 1811, l'art i., p. 1, Part ii., p. 163.
77. Mém. de Berlin, 1777. The theorem was afterwards published, and ascribed to Laplace, in a memoir by Legendre on the Attractions of Spheroids, which will be found in the Mém, par divers Savans, published in 1785.
78. Mém. de l'Acad., 1782 (published in 1785), p. 113.
79. Bull. de la Soc. Philomathique. iii. (1813), p. 388.
80. Mem, de l'Acad., v, p. 247.
81. If the components of a vector a are denoted by (a_x, a_y, a_z), the quantity a_xb_x, a_yb_y, a_zb_z is called the scalar product of two vectors a and b, and is denoted by (a.b).

    The quantity ${\frac {\partial \alpha x}{\partial x}}+{\frac {\partial \alpha y}{\partial y}}+{\frac {\partial \alpha z}{\partial z}}$ is called the divergence of the vector a, and is denoted by div a.

82. The vector whose components are $-{\frac {\partial V}{\partial x}},-{\frac {\partial V}{\partial y}},-{\frac {\partial V}{\partial z}}$ is denoted by grad V.
83. In the present work, vectors will generally be distinguished by heavy type.
84. This objection was advanced by Maxwell in § 480 of his Treatise. An attempt to overcome it was made by Betti: cf. p. 377 of his Lessons on the Potential.
85. An essay on the application of mathematical analysis to the theories of electricity and magnetism, Nottingham, 1828: reprinted in The Mathematical Papers of the late George Green, p. I.
86. Euler in 1744 (De methodis inveniendi ...) had spoken of the vis potentialis—would now be called the potential energy—possessed by an elastic body when bent.