We must begin, however, with stating the mechanical phenomena of these sciences, and the reduction of such phenomena to laws. In this point of view, the phenomena of which we have to speak are those in which bodies exhibit attractions and repulsions, peculiarly determined by their nature and circumstances; as the magnet, and a 192 piece of amber when rubbed. Such results are altogether different from the universal attraction which, according to Newton’s discovery, prevails among all particles of matter, and to which cosmical phenomena are owing. But yet the difference of these special attractions, and of cosmical attraction, was at first so far from being recognized, that the only way in which men could be led to conceive or assent to an action of one body upon another at a distance, in cosmical cases, was by likening it to magnetic attraction, as we have seen in the history of Physical Astronomy. And we shall, in the first part of our account, not dwell much upon the peculiar conditions under which bodies are magnetic or electric, since these conditions are not readily reducible to mechanical laws; but, taking the magnetic or electric character for granted, we shall trace its effects.

The habit of considering magnetic action as the type or general case of attractive and repulsive agency, explains the early writers having spoken of Electricity as a kind of Magnetism. Thus Gilbert, in his book De Magnete (1600), has a chapter,1 De coitione Magniticâ, primumque de Succini attractione, sive verius corporum ad Succinum applicatione. The manner in which he speaks, shows us how mysterious the fact of attraction then appeared; so that, as he says, “the magnet and amber were called in aid by philosophers as illustrations, when our sense is in the dark in abstruse inquiries, and when our reason can go no further. Gilbert speaks of these phenomena like a genuine inductive philosopher, reproving2 those who before him had “stuffed the booksellers’ shops by copying from one another extravagant stories concerning the attraction of magnets and amber, without giving any reason from experiment.” He himself makes some important steps in the subject. He distinguishes magnetic from electric forces,3 and is the inventor of the latter name, derived from ἤλεκτρον, electron, amber. He observes rightly, that the electric force attracts all light bodies, while the magnetic force attracts iron only; and he devises a satisfactory apparatus by which this is shown. He gives4 a considerable list of bodies which possess the electric property; “Not only amber and agate attract small bodies, as some think, but diamond, sapphire, carbuncle, opal, amethyst, Bristol gem, beryli, crystal, glass, glass of antimony, spar of various kinds, sulphur, mastic, sealing-wax,” and other substances which he mentions. Even his speculations on the general laws of these phenomena, though vague and erroneous, as 193 at that period was unavoidable, do him no discredit when compared with the doctrines of his successors a century and a half afterwards. But such speculations belong to a succeeding part of this history.

In treating of these Sciences, I will speak of Electricity in the first place; although it is thus separated by the interposition of Magnetism from the succeeding subjects (Galvanism, &c.) with which its alliance seems, at first sight, the closest, and although some general notions of the laws of magnets were obtained at an earlier period than a knowledge of the corresponding relations of electric phenomena: for the theory of electric attraction and repulsion is somewhat more simple than of magnetic; was, in fact, the first obtained; and was of use in suggesting and confirming the generalization of magnetic laws.

CHAPTER 1.

Discovery of Laws of Electric Phenomena.

WE have already seen what was the state of this branch of knowledge at the beginning of the seventeenth century; and the advances made by Gilbert. We must now notice the additions which it subsequently received, and especially those which led to the discovery of general laws, and the establishment of the theory; events of this kind being those of which we have more peculiarly to trace the conditions and causes. Among the facts which we have thus especially to attend to, are the electric attractions of small bodies by amber and other substances when rubbed. Boyle, who repeated and extended the experiments of Gilbert, does not appear to have arrived at any new general notions; but Otto Guericke of Magdeburg, about the same time, made a very material step, by discovering that there was an electric force of repulsion as well as of attraction. He found that when a globe of sulphur had attracted a feather, it afterwards repelled it, till the feather had been in contact with some other body. This, when verified under a due generality of circumstances, forms a capital fact in our present subject. Hawkesbee, who wrote in 1709 (Physico-Mechanical Experiments) also observed various of the effects of attraction and repulsion upon threads hanging loosely. But the person who appears to have first fully seized the general law of these facts, is 194 Dufay, whose experiments appear in the Memoirs of the French Academy, in 1733, 1734, and 1737.5 “I discovered,” he says, “a very simple principle, which accounts for a great part of the irregularities, and, if I may use the term, the caprices that seem to accompany most of the experiments in electricity. This principle is, that electric bodies attract all those that are not so, and repel them as soon as they are become electric by the vicinity or contact of the electric body. . . . Upon applying this principle to various experiments of electricity, any one will be surprised at the number of obscure and puzzling facts which it clears up.” By the help of this principle, he endeavors to explain several of Hawkesbee’s experiments.

A little anterior to Dufay’s experiments were those of Grey, who, in 1729, discovered the properties of conductors. He found that the attraction and repulsion which appear in electric bodies are exhibited also by other bodies in contact with the electric. In this manner he found that an ivory ball, connected with a glass tube by a stick, a wire, or a packthread, attracted and repelled a feather, as the glass itself would have done. He was then led to try to extend this communication to considerable distances, first by ascending to an upper window and hanging down his ball, and, afterwards, by carrying the string horizontally supported on loops. As his success was complete in the former case, he was perplexed by failure in the latter; but when he supported the string by loops of silk instead of hempen cords, he found it again become a conductor of electricity. This he ascribed at first to the smaller thickness of the silk, which did not carry off so much of the electric virtue; but from this explanation he was again driven, by finding that wires of brass still thinner than the silk destroyed the effect. Thus Grey perceived that the efficacy of the support depended on its being silk, and he soon found other substances which answered the same purpose. The difference, in fact, depended on the supporting substance being electric, and therefore not itself a conductor; for it soon appeared from such experiments, and especially6 from those made by Dufay, that substances might be divided into electrics per se, and non-electrics, or conductors. These terms were introduced by Desaguliers,7 and gave a permanent currency to the results of the labors of Grey and others.

Another very important discovery belonging to this period is, that 195 of the two kinds of electricity. This also was made by Dufay. “Chance,” says he, “has thrown in my way another principle more universal and remarkable than the preceding one, and which casts a new light upon the subject of electricity. The principle is, that there are two distinct kinds of electricity, very different from one another; one of which I call vitreous, the other resinous, electricity. The first is that of glass, gems, hair, wool, &c.; the second is that of amber, gum-lac, silk, &c. The characteristic of these two electricities is, that they repel themselves and attract each other.” This discovery does not, however, appear to have drawn so much attention as it deserved. It was published in 1735; (in the Memoirs of the Academy for 1733;) and yet in 1747, Franklin and his friends at Philadelphia, who had been supplied with electrical apparatus and information by persons in England well acquainted with the then present state of the subject, imagined that they were making observations unknown to European science, when they were led to assert two conditions of bodies, which were in fact the opposite electricities of Dufay, though the American experimenters referred them to a single element, of which electrized bodies might have either excess or defect. “Hence,” Franklin says, “have arisen some new terms among us: we say B,” who receives a spark from glass, “and bodies in like circumstances, is electrized positively; A,” who communicates his electricity to glass, “negatively; or rather B is electrized plus, A minus.” Dr. (afterwards Sir William) Watson had, about the same time, arrived at the same conclusions, which he expresses by saying that the electricity of A was more rare, and that of B more dense, than it naturally would have been.8 But that which gave the main importance to this doctrine was its application to some remarkable experiments, of which we must now speak.

Electric action is accompanied, in many cases, by light and a crackling sound. Otto Guericke9 observes that his sulphur-globe, when rubbed in a dark place, gave faint flashes, such as take place when sugar is crushed. And shortly after, a light was observed at the surface of the mercury in the barometer, when shaken, which was explained at first by Bernoulli, on the then prevalent Cartesian principles; but, afterwards, more truly by Hawkesbee, as an electrical phenomenon. Wall, in 1708, found sparks produced by rubbing amber, and Hawkesbee observed the light and the snapping, as he calls it, under various modifications. But the electric spark from a living body, which, as 196 Priestley says,10 “makes a principal part of the diversion of gentlemen and ladies who come to see experiments in electricity,” was first observed by Dufay and the Abbé Nollet. Nollet says11 he “shall never forget the surprise which the first electric spark ever drawn from the human body excited, both in M. Dufay and in himself.” The drawing of a spark from the human body was practised in various forms, one of which was familiarly known as the “electrical kiss.” Other exhibitions of electrical light were the electrical star, electrical rain, and the like.

As electricians determined more exactly the conditions of electrical action, they succeeded in rendering more intense those sudden actions which the spark accompanies, and thus produced the electric shock. This was especially done in the Leyden phial. This apparatus received its name, while the discovery of its property was attributed to Cunæus, a native of Leyden, who, in 1746, handling a vessel containing water in communication with the electrical machine, and happening thus to bring the inside and the outside into connexion, received a sudden shock in his arms and breast. It appears, however,12 that a shock had been received under nearly the same circumstances in 1746, by Von Kleist, a German prelate, at Camin, in Pomerania. The strangeness of this occurrence, and the suddenness of the blow, much exaggerated the estimate which men formed of its force. Muschenbroek, after taking one shock, declared he would not take a second for the kingdom of France; though Boze, with a more magnanimous spirit, wished13 that he might die by such a stroke, and have the circumstances of the experiment recorded in the Memoirs of the Academy. But we may easily imagine what a new fame and interest this discovery gave to the subject of electricity. It was repeated in all parts of the world, with various modifications: and the shock was passed through a line of several persons holding hands; Nollet, in the presence of the king of France, sent it through a circle of 180 men of the guards, and along a line of men and wires of 900 toises;14 and experiments of the same kind were made in England, principally under the direction of Watson, on a scale so large as to excite the admiration of Muschenbroek; who says, in a letter to Watson, “Magnificentissimis tuis experimentis superasti conatus omnium.” The result was, that the transmission of electricity through a length of 12,000 feet was, to sense, instantaneous.

197 The essential circumstances of the electric shock were gradually unravelled. Watson found that it did not increase in proportion either to the contents of the phial or the size of the globe by which the electricity was excited; that the outside coating of the glass (which, in the first form of the experiment, was only a film of water), and its contents, might be varied in different ways. To Franklin is due the merit of clearly pointing out most of the circumstances on which the efficacy of the Leyden phial depends. He showed, in 1747,15 that the inside of the bottle is electrized positively, the outside negatively; and that the shock is produced by the restoration of the equilibrium, when the outside and inside are brought into communication suddenly. But in order to complete this discovery, it remained to be shown that the electric matter was collected entirely at the surface of the glass, and that the opposite electricities on the two opposite sides of the glass were accumulated by their mutual attraction. Monnier the younger discovered that the electricity which bodies can receive, depends upon their surface rather than their mass, and Franklin16 soon found that “the whole force of the bottle, and power of giving a shock, is in the glass itself.” This they proved by decanting the water out of an electrized into another bottle, when it appeared that the second bottle did not become electric, but the first remained so. Thus it was found “that the non-electrics, in contact with the glass, served only to unite the force of the several parts.”

So far as the effect of the coating of the Leyden phial is concerned, this was satisfactory and complete: but Franklin was not equally successful in tracing the action of the electric matter upon itself, in virtue of which it is accumulated in the phial; indeed, he appears to have ascribed the effect to some property of the glass. The mode of describing this action varied, accordingly as two electric fluids were supposed (with Dufay,) or one, which was the view taken by Franklin. On this latter supposition the parts of the electric fluid repel each other, and the excess in one surface of the glass expels the fluid from the other surface. This kind of action, however, came into much clearer view in the experiments of Canton, Wilcke, and Æpinus. It was principally manifested in the attractions and repulsions which objects exert when they are in the neighborhood of electrized bodies; or in the electrical atmosphere, using the phraseology of the time. At present we say that bodies are electrized by induction, when they are 198 thus made electric by the electric attraction and repulsion of other bodies. Canton’s experiments were communicated to the Royal Society in 1753, and show that the electricity on each body acts upon the electricity of another body, at a distance, with a repulsive energy. Wilcke, in like manner, showed that parts of non-electrics, plunged in electric atmospheres, acquire an electricity opposite to that of such atmospheres. And Æpinus devised a method of examining the nature of the electricity at any part of the surface of a body, by means of which he ascertained its distribution, and found that it agreed with such a law of self-repulsion. His attempt to give mathematical precision to this induction was one of the most important steps towards electrical theory, and must be spoken of shortly, in that point of view. But in the mean time we may observe, that this doctrine was applied to the explanation of the Leyden jar; and the explanation was confirmed by charging a plate of air, and obtaining a shock from it, in a manner which the theory pointed out.

Before we proceed to the history of the theory, we must mention some other of the laws of phenomena which were noticed, and which theory was expected to explain. Among the most celebrated of these, were the effect of sharp points in conductors, and the phenomena of electricity in the atmosphere. The former of these circumstances was one of the first which Franklin observed as remarkable. It was found that the points of needles and the like throw off and draw off the electric virtue; thus a bodkin, directed towards an electrized ball, at six or eight inches’ distance, destroyed its electric action. The latter subject, involving the consideration of thunder and lightning, and of many other meteorological phenomena, excited great interest. The comparison of the electric spark to lightning had very early been made; but it was only when the discharge had been rendered more powerful in the Leyden jar, that the comparison of the effects became very plausible. Franklin, about 1750, had offered a few somewhat vague conjectures17 respecting the existence of electricity in the clouds; but it was not till Wilcke and Æpinus had obtained clear notions of the effect of electric matter at a distance, that the real condition of the clouds could be well understood. In 1752, however,18 D’Alibard, and other French philosophers, were desirous of verifying Franklin’s conjecture of the analogy of thunder and electricity. This they did by erecting a pointed iron rod, forty feet high, 199 at Marli: the rod was found capable of giving out electrical sparks when a thunder-cloud passed over the place. This was repeated in various parts of Europe, and Franklin suggested that a communication with the clouds might be formed by means of a kite. By these, and similar means, the electricity of the atmosphere was studied by Canton in England, Mazeas in France, Beccaria in Italy, and others elsewhere. These essays soon led to a fatal accident, the death of Richman at Petersburg, while he was, on Aug. 6th, 1753, observing the electricity collected from an approaching thunder-cloud, by means of a rod which he called an electrical gnomon: a globe of blue fire was seen to leap from the rod to the head of the unfortunate professor, who was thus struck dead.

[2nd Ed.] [As an important application of the doctrines of electricity, I may mention the contrivances employed to protect ships from the effects of lightning. The use of conductors in such cases is attended with peculiar difficulties. In 1780 the French began to turn their attention to this subject, and Le Roi was sent to Brest and the various sea-ports of France for that purpose. Chains temporarily applied in the rigging had been previously suggested, but he endeavored to place, he says, such conductors in ships as might be fixed and durable. He devised certain long linked rods, which led from a point in the mast-head along a part of the rigging, or in divided stages along the masts, and were fixed to plates of metal in the ship’s sides communicating with the sea. But these were either unable to stand the working of the rigging, or otherwise inconvenient, and were finally abandoned.19

The conductor commonly used in the English Navy, till recently, consisted of a flexible copper chain, tied, when occasion required, to the mast-head, and reaching down into the sea; a contrivance recommended by Dr. Watson in 1762. But notwithstanding this precaution, the shipping suffered greatly from the effects of lightning.

Mr. Snow Harris (now Sir William Snow Harris), whose electrical labors are noticed above, proposed to the Admiralty, in 1820, a plan which combined the conditions of ship-conductors, so desirable, yet so difficult to secure:—namely, that they should be permanently fixed, and sufficiently large, and yet should in no way interfere with the motion of the rigging, or with the sliding masts. The method which he proposed was to make the masts themselves conductors of electricity, 200 by incorporating with them, in a peculiar way, two laminæ of sheet-copper, uniting these with the metallic masses in the hull by other laminæ, and giving the whole a free communication with the sea. This method was tried experimentally, both on models and to a large extent in the navy itself; and a Commission appointed to examine the result reported themselves highly satisfied with Mr. Harris’s plan, and strongly recommended that it should be fully carried out in the Navy.20]

It is not here necessary to trace the study of atmospheric electricity any further: and we must now endeavor to see how these phenomena and laws of phenomena which we have related, were worked up into consistent theories; for though many experimental observations and measures were made after this time, they were guided by the theory, and may be considered as having rather discharged the office of confirming than of suggesting it.

We may observe also that we have now described the period of most extensive activity and interest in electrical researches. These naturally occurred while the general notions and laws of the phenomena were becoming, and were not yet become, fixed and clear. At such a period, a large and popular circle of spectators and amateurs feel themselves nearly upon a level, in the value of their trials and speculations, with more profound thinkers: at a later period, when the subject is become a science, that is, a study in which all must be left far behind who do not come to it with disciplined, informed, and logical minds, the cultivators are far more few, and the shout of applause less tumultuous and less loud. We may add, too, that the experiments, which are the most striking to the senses, lose much of their impressiveness with their novelty. Electricity, to be now studied rightly, must be reasoned upon mathematically; how slowly such a mode of study makes its way, we shall see in the progress of the theory, which we must now proceed to narrate.

[2nd Ed.] [A new mode of producing electricity has excited much notice lately. In October, 1840, one of the workmen in attendance upon a boiler belonging to the Newcastle and Durham Railway, reported that the boiler was full of fire; the fact being, that when he placed his hand near it an electrical spark was given out. This drew the attention of Mr. Armstrong and Mr. Pattinson, who made the circumstance publicly known.21 Mr. Armstrong pursued the investigation 201 with great zeal, and after various conjectures was able to announce22 that the electricity was excited at the point where the steam is subject to friction in its emission. He found too that he could produce a like effect by the emission of condensed air. Following out his views, he was able to construct, for the Polytechnic Institution in London, a “Hydro-electric Machine,” of greater power than any electrical machine previously made. Dr. Faraday took up the investigation as the subject of the Eighteenth Series of his Researches, sent to the Royal Society, Jan. 26, 1842; and in this he illustrated, with his usual command of copious and luminous experiments, a like view;—that the electricity is produced by the friction of the particles of the water carried along by the steam. And thus this is a new manifestation of that electricity, which, to distinguish it from voltaic electricity, is sometimes called Friction Electricity or Machine Electricity. Dr. Faraday has, however, in the course of this investigation, brought to light several new electrical relations of bodies.]

CHAPTER II.

The Progress of Electrical Theory.

THE cause of electrical phenomena, and the mode of its operation, were naturally at first spoken of in an indistinct and wavering manner. It was called the electric fire, the electric fluid; its effects were attributed to virtues, effluvia, atmospheres. When men’s mechanical ideas became somewhat more distinct, the motions and tendencies to motion were ascribed to currents, in the same manner as the cosmical motions had been in the Cartesian system. This doctrine of currents was maintained by Nollet, who ascribed all the phenomena of electrized bodies to the contemporaneous afflux and efflux of electrical matter. It was an important step towards sound theory, to get rid of this notion of moving fluids, and to consider attraction and repulsion as statical forces; and this appears to have been done by others about the same time. Dufay23 considered that he had proved the existence of two electricities, the vitreous and the resinous, and conceived each 202 of these to be a fluid which repelled its own parts and attracted those of the other: this is, in fact, the outline of the theory which recently has been considered as the best established; but from various causes it was not at once, or at least not generally adopted. The hypothesis of the excess and defect of a single fluid is capable of being so treated as to give the same results with the hypothesis of two opposite fluids and happened to obtain the preference for some time. We have already seen that this hypothesis, according to which electric phenomena arose from the excess and defect of a generally diffused fluid, suggested itself to Watson and Franklin about 1747. Watson found that when an electric body was excited, the electricity was not created, but collected; and Franklin held, that when the Leyden jar was charged, the quantity of electricity was unaltered, though its distribution was changed. Symmer24 maintained the existence of two fluids; and Cigna supplied the main defect which belonged to this tenet in the way in which Dufay held it, by showing that the two opposite electricities were usually produced at the same time. Still the apparent simplicity of the hypothesis of one fluid procured it many supporters. It was that which Franklin adopted, in his explanation of the Leyden experiment; and though after the first conception of an electrical charge as a disturbance of equilibrium, there was nothing in the development or details of Franklin’s views which deserved to win for them any peculiar authority, his reputation, and his skill as a writer, gave a considerable influence to his opinions. Indeed, for a time he was considered, over a large part of Europe, as the creator of the science, and the terms25 Franklinism, Franklinist, Franklinian system, occur in almost every page of continental publications on the subject. Yet the electrical phenomena to the knowledge of which Franklin added least, those of induction, were those by which the progress of the theory was most promoted. These, as we have already said, were at first explained by the hypothesis of electrical atmospheres. Lord Mahon wrote a treatise, in which this hypothesis was mathematically treated; yet the hypothesis was very untenable, for it would not account for the most obvious cases of induction, such as the Leyden jar, except the atmosphere was supposed to penetrate glass.

The phenomena of electricity by induction, when fairly considered by a person of clear notions of the relations of space and force, were seen to accommodate themselves very generally to the conception 203 introduced by Dufay;26 of two electricities each repelling itself and attracting the other. If we suppose that there is only one fluid, which repels itself and attracts all other matter, we obtain, in many cases, the same general results as if we suppose two fluids; thus, if an electrized body, overcharged with the single fluid, act upon a ball, it drives the electric fluid in the ball to the further side by its repulsion, and then attracts the ball by attracting the matter of the ball more than it repels the fluid which is upon the ball. If we suppose two fluids, the positively electrized body draws the negative fluid to the nearer side of the ball, repels the positive fluid to the opposite side, and attracts the ball on the whole, because the attracted fluid is nearer than that which is repelled. The verification of either of these hypotheses, and the determination of their details, depended necessarily upon experiment and calculation. It was under the hypothesis of a single fluid that this trial was first properly made. Æpinus of Petersburg published, in 1759, his Tentamen Theoriæ Electricitatis et Magnetismi; in which he traces mathematically the consequences of the hypothesis of an electric fluid, attracting all other matter, but repelling itself; the law of force of this repulsion and attraction he did not pretend to assign precisely, confining himself to the supposition that the mutual force of the particles increases as the distance decreases. But it was found, that in order to make this theory tenable, an additional supposition was required, namely, that the particles of bodies repel each other as much as they attract the electric fluid.27 For if two bodies, A and B, be in their natural electrical condition, they neither attract nor repel each other. Now, in this case, the fluid in A attracts the matter in B and repels the fluid in B with equal energy, and thus no tendency to motion results from the fluid in A; and if we further suppose that the matter in A attracts the fluid in B and repels the matter in B with equal energy, we have the resulting mutual inactivity of the two bodies explained; but without the latter supposition, there would be a mutual attraction: or we may put the truth more simply thus; two negatively electrized bodies repel each other; if negative electrization were merely the abstraction of the fluid which is the repulsive element, this result could not follow except there were a repulsion in the bodies themselves, independent of the fluid. And thus Æpinus found himself compelled to assume this mutual repulsion of material particles; he had, in fact, the 204 alternative of this supposition, or that of two fluids, to choose between, for the mathematical results of both hypotheses are the same. Wilcke, a Swede, who had at first asserted and worked out the Æpinian theory in its original form, afterwards inclined to the opinion of Symmer; and Coulomb, when, at a later period, he confirmed the theory by his experiments and determined the law of force, did not hesitate to prefer28 the theory of two fluids, “because,” he says, “it appears to me contradictory to admit at the same time, in the particles of bodies, an attractive force in the inverse ratio of the squares of the distances, which is demonstrated by universal gravitation, and a repulsive force in the same inverse ratio of the squares of the distances; a force which would necessarily be infinitely great relatively to the action of gravitation.” We may add, that by forcing us upon this doctrine of the universal repulsion of matter, the theory of a single fluid seems quite to lose that superiority in the way of simplicity which had originally been its principal recommendation.

The mathematical results of the supposition of Æpinus, which are, as Coulomb observes,29 the same as of that of the two fluids, were traced by the author himself in the work referred to, and shown to agree, in a great number of cases, with the observed facts of electrical induction, attraction, and repulsion. Apparently this work did not make its way very rapidly through Europe; for in 1771, Henry Cavendish stated30 the same hypothesis in a paper read before the Royal Society; which he prefaces by saying, “Since I first wrote the following paper, I find that this way of accounting for the phenomena of electricity is not new. Æpinus, in his Tentamen Theoriæ Electricitatis et Magnetismi, has made use of the same, or nearly the same hypothesis that I have; and the conclusions he draws from it agree nearly with mine as far as he goes.”

The confirmation of the theory was, of course, to be found in the agreement of its results with experiment; and in particular, in the facts of electrical induction, attraction, and repulsion, which suggested the theory. Æpinus showed that such a confirmation appeared in a number of the most obvious cases; and to these, Cavendish added others, which, though not obvious, were of such a nature that the calculations, in general difficult or impossible, could in these instances be easily performed; as, for example, cases in which there are plates or globes at the two extremities of a long wire. In all these cases of 205 electrical action the theory was justified. But in order to give it full confirmation, it was to be considered whether any other facts, not immediately assumed in the foundation of the theory, were explained by it; a circumstance which, as we have seen, gave the final stamp of truth to the theories of astronomy and optics. Now we appear to have such confirmation, in the effect of points, and in the phenomena of the electrical discharge. The theory of neither of these was fully understood by Cavendish, but he made an approach to the true view of them. If one part of a conducting body be a sphere of small radius, the electric fluid upon the surface of this sphere will, it appears by calculation, be more dense, and tend to escape more energetically, in proportion as the radius of the sphere is smaller; and, therefore, if we consider a point as part of the surface of a sphere of imperceptible radius, it follows from the theory that the effort of the fluid to escape at that place will be enormous; so that it may easily be supposed to overcome the resisting causes. And the discharge may be explained in nearly the same manner; for when a conductor is brought nearer and nearer to an electrized body, the opposite electricity is more and more accumulated by attraction on the side next to the electrized body; its tension becomes greater by the increase of its quantity and the diminution of the distance, and at last it is too strong to be contained, and leaps out in the form of a spark.

The light, sound, and mechanical effects produced by the electric discharge, made the electric fluid to be not merely considered as a mathematical hypothesis, useful for reducing phenomena to formulæ (as for a long time the magnetic fluid was), but caused it to be at once and universally accepted as a physical reality, of which we learn the existence by the common use of the senses, and of which measures and calculations are only wanted to teach us the laws.

The applications of the theory of electricity which I have principally considered above, are those which belong to conductors, in which the electric fluid is perfectly moveable, and can take that distribution which the forces require. In non-conducting or electric bodies, the conditions to which the fluid is subject are less easy to determine; but by supposing that the fluid moves with great difficulty among the particles of such bodies,—that nevertheless it may be dislodged and accumulated in parts of the surface of such bodies, by friction and other modes of excitement; and that the earth is an inexhaustible reservoir of electric matter,—the principal facts of excitation and the like receive a tolerably satisfactory explanation. 206

The theory of Æpinus, however, still required to have the law of action of the particles of the fluid determined. If we were to call to mind how momentous an event in physical astronomy was the determination of the law of the cosmical forces, the inverse square of the distance, and were to suppose the importance and difficulty of the analogous step in this case to be of the same kind, this would be to mistake the condition of science at that time. The leading idea, the conception of the possibility of explaining natural phenomena by means of the action of forces, on rigorously mechanical principles, had already been promulgated by Newton, and was, from the first, seen to be peculiarly applicable to electrical phenomena; so that the very material step of clearly proposing the problem, often more important than the solution of it, had already been made. Moreover the confirmation of the truth of the assumed cause in the astronomical case depended on taking the right law; but the electrical theory could be confirmed, in a general manner at least, without this restriction. Still it was an important discovery that the law of the inverse square prevailed in these as well as in cosmical attractions.

It was impossible not to conjecture beforehand that it would be so. Cavendish had professed in his calculations not to take the exponent of the inverse power, on which the force depended, to be strictly 2, but to leave it indeterminate between 1 and 3; but in his applications of his results, he obviously inclines to the assumption that it is 2. Experimenters tried to establish this in various ways. Robison,31 in 1769, had already proved that the law of force is very nearly or exactly the inverse square; and Meyer32 had discovered, but not published, the same result. The clear and satisfactory establishment of this truth is due to Coulomb, and was one of the first steps in his important series of researches on this subject. In his first paper33 in the Memoirs of the Academy for 1785, he proves this law for small globes; in his second Memoir he shows it to be true for globes one and two feet in diameter. His invention of the torsion-balance, which measures very small forces with great certainty and exactness, enabled him to set this question at rest for ever.