A History of the Theories of Aether and Electricity/Chapter 3

by Edmund Taylor Whittaker

CHAPTER III.

GALVANISM, THOM GALVANI TO OHM.

Until the last decade of the eighteenth century, electricians were occupied solely with statical electricity. Their attention was then turned in a different direction.

In a work entitled Recherches sur l'origine des sentiments agréables et désagréables, which was published^[1] in 1752, Johann Georg Sulzer (b. 1720, d. 1779) had mentioned that, if two pieces of metal, the one of lead and the other of silver, be joined together in such a manner that their edges touch, and if they be placed on the tongue, a taste is perceived "similar to that of vitriol of iron," although neither of these metals applied separately gives any trace of such a taste. "It is not probable," he says, “that this contact of the two metals causes a solution of either of them, liberating particles which might affect the tongue; and we must therefore conclude that the contact sets up a vibration in their particles, which, by affecting the nerves of the tongue, produces the taste in question."

This observation was not suspected to have any connexion with electrical phenomena, and it played no part in the inception of the next discovery, which indeed was suggested by a mere accident.

Luigi Galvani, born at Bologna in 1737, occupied from 1775 onwards a chair of Anatomy in his native city. For many years before the event which made him famons he had been studying the susceptibility of the nerves to irritation; and, having been formerly a pupil of Beccaria, he was also interested in electrical experiments. One day in the latter part of the year 1780 he had, as he tells us,^[2] “dissected and prepared a frog, and laid it on a table, on which, at some distance from the frog, was an electric machine. It happened by chance that one of my assistants touched the inner crural nerve of the frog with the point of a scalpel; whereupon at once the muscles of the limbs were violently convulsed.

“Another of those who used to help me in electrical experiments thought he had noticed that at this instant a spark was drawn from the conductor of the machine. I myself was at the time occupied with a totally different matter; but when he drew my attention to this, I greatly desired to try it for myself, and discover its hidden principle. So I, too, touched one or other of the crural nerves with the point of the scalpel, at the same time that one of those present drew a spark; and the same phenomenon was repeated exactly as before."^[3]

After this, Galvani conceived the idea of trying whether the electricity of thunderstorms would induce muscular contractions equally well with the electricity of the machine. Having successfully experimented with lightning, he “wished," as he writes,^[4] “to try the effect of atmospheric electricity in calm weather. My reason for this was an observation I had made, that frogs which had been suitably prepared for these experiments and fastened, by brass hooks in the spinal marrow, to the iron lattice round a certain hanging-garden at my house, exhibited convulsions not only during thunderstorms, but sometimes even when the sky was quite serene. I suspected these effects to be due to the changes which take place during the day in the electric state of the atmosphere, and so, with some degree of confidence, I performed experiments to test the point; and at different hours for many days I watched frogs: which I had disposed for the purpose; but could not detect any motion in their muscles. At length, weary of waiting in vain, I pressed the brass hooks, which were driven into the spinal marrow, against the iron lattice, in order to sec whether contractions could be excited by varying the incidental circumstances of the experiment. I observed contractions tolerably often, but they did not seem to bear any relation to the changes in the electrical state of the atmosphere.

"However, at this time, when as yet I had not tried the experiment except in the open air, I came very near to adopting a theory that the contractions are due to atmospheric electricity, which, having slowly entered the animal and accumulated in it, is suddenly discharged when the hook comes in contact with the iron lattice. For it is easy in experimenting to deceive ourselves, and to imagine we see the things we wish to see.

"But I took the animal into a closed room, and placed it on an iron-plate; and when I pressed the hook which was fixed in the spinal marrow against the plate, behold! the same spasmodic contractions as before. I tried other metals at different hours on various days, in several places, and always with the same result, except that the contractions were more violent with some metals than with others. After this I tried various bodies which are not conductors of electricity, such as glass, guns, resins, stones, and dry wood; but nothing happened. This was somewhat surprising, and led me to suspect that electricity is inherent in the animal itself. This suspicion was strengthened by the observation that a kind of circuit of subtle nervous fluid (resembling the electric circuit which is manifested in the Leyden jar experiment) is completed from the nerves to the muscles when the contractions are produced.

"For, while I with one hand held the prepared frog by the hook fixed in its spinal marrow, so that it stood with its feet on a silver box, and with the other hand touched the lid of the box, or its sides, with any metallic body, I was surprised to see the frog become strongly convulsed every time that I applied this artifice."^[5]

Galvani thus ascertained that the limbs of the frog are convulsed whenever a connexion is made between the nerves and muscles by a metallic arc, generally formed of more than one kind of metal; and he advanced the hypothesis that the convulsions are caused by the transport of a peculiar fluid from the nerves to the muscles, the are acting as a conductor. To this fluid the names Galvonism and Animal Electricity were soon generally applied. Galvani himself considered it to be the same as the ordinary electric fluid, and, indeed, regarded the entire phenomenon as similar to the discharge of a Leyden jar.

The publication of Galvani's views soon engaged the attention of the learned world, and gave rise to an animated controversy between those who supported Galvani's own view, those who believed galvanism to be a fluid distinct from ordinary electricity, and a third school who altogether refused to attribute the effects to a supposed fluid contained in the nervous system. The leader of the last-named party was Alessandro Volta (b. 1745, d. 1827), Professor of Natural Philosophy in the University of Pavia, who in 1792 put forward the view^[6] that the stimulus in Galvani's experiment is derived essentially from the connexion of two different metals by a moist body. “The metals used in the experiments, being applied to the moist bodies of animals, can by themselves, and of their proper virtue, excite and dislodge the electric fluid from its state of rest; so that the organs of the animal act only passively." At first he inclined to combine this theory of metallic stimulus with a certain degree of belief in such a fluid as Galvani had supposed, but after the end of 1793 he denied the existence of animal electricity altogether.

From this standpoint Volta continued his experiments and worked out his theory. The following quotation from a letter^[7] which he wrote later to Gren, the editor of the Neues Journal d. Physik, sets forth his view in a more developed form:—

“The contact of different conductors, particularly the metallic, including pyrites and other minerals, as well as charcoal, which I call dry conductors, or of the first class, with moist conductors, or conductors of the second class, agitates or disturbs the electric fluid, or gives it a certain impulse. Do not ask in what manner: it is enough that it is a principle, and a general principle. This impulse, whether produced by attraction or any other force, is different or unlike, both in regard to the different metals and to the different moist conductors; so that the direction, or at least the power, with which the electric fluid is impelled or excited, is different when the conductor A is applied to the conductor B, or to another C. In a perfect circle of conductors, where either one of the second class is placed between two different from each other of the first class, or, contrariwise, one of the first class is placed between two of the second class different from each other, an electric stream is occasioned by the predominating force either to the right or to the left-a circulation of this fluid, which ceases only when the circle is broken, and which is renewed when the circle is again rendered complete."

Another philosopher who, like Volta, denied the existence of a fluid peculiar to animals, but who took a somewhat different view of the origin of the phenomenon, was Giovanni Fabroni, of Florence (b. 1752, d. 1822), who,^[8] having placed two plates of different metals in water, observed that one of them was partially oxidized when they were put in contact; from which he rightly concluded that some chemical action is inseparably connected with galvanic effects.

The feeble intensity of the phenomena of galvanism, which compared poorly with the striking displays obtained in electrostatics, was responsible for some falling off of interest in them towards the end of the eighteenth century; and the last years of their illustrious discoverer were clouded by misfortune. Being attached to the old order which was overthrown by the armies of the French Revolution, he refused in 1798 to take the oath of allegiance to the newly constituted Cisalpine Republic, and was deposed from his professorial chair. A profound melancholy, which had been induced by domestic bereavement, was aggravated by poverty and disgrace; and, unable to survive the loss of all he held dear, he died broken-hearted before the end of the year.^[9]

Scarcely more than a year after the death of Galvani, the new science suddenly regained the eager attention of philosophers. This renewal of interest was due to the discovery by Volta, in the early spring of 1800, of a means of greatly increasing the intensity of the effects. Hitherto all attempts to magnify the action by enlarging or multiplying the apparatus had ended in failure. If a long chain of different metals was used instead of only two, the convulsions of the frog were no more violent. But Volta now showed^[10] that if any number of couples, each consisting of a zinc disk and a copper disk in contact, were taken, and if each couple was separated from the next by a disk of moistened pasteboard (so that the order was copper, zinc, pasteboard, copper, zinc, pasteboard, &c.), the effect of the pile this formed was much greater than that of any galvanic apparatus previously introduced. When the highest and lowest disks were simultaneously touched by the fingers, a distinct shock was felt; and this could be repeated again and again, the pile apparently possessing within itself an indefinite power of recuperation. It thus resembled a Leyden jar endowed with a power of automatically re-establishing its state of tension after each explosion; with, in fact, "an inexhaustible charge, a perpetual action or impulsion on the electric fluid."

Volta unhesitatingly pronounced the phenomena of the pile to be in their nature electrical. The circumstances of Galvani's original discovery had prepared the minds of philosophers for this belief, which was powerfully supported by the similarity of the physiological effects of the pile to those of the Leyden jar, and by the observation that the galvanic influence was conducted only by those bodies—e.g. the metals—which were already known to be good conductors of static electricity. But Volta now supplied a still more convincing proof. Taking a disk of copper and one of zinc, he held each by an insulating handle and applied them to each other for an instant. After the disks had been separated, they were brought into contact with a delicate electroscope, which indicated by the divergence of its straws that the disks were now electrified—the zinc had, in fact, acquired a positive and the copper a negative electric charge.^[11] Thus the mere contact of two different metals, such as those employed in the pile, was shown to be sufficient for the production of effects undoubtedly electrical in character.

On the basis of this result Volta in the same year (1800) put forward a definite theory of the action of the pile. Suppose first that a disk of zinc is laid on a disk of copper, which in turn rests on an insulating support. The experiment just described shows that the electric fluid will be driven from the copper to the zinc. We may then, according to Volta, represent the state or "tension" of the copper by the number -1/2, and that of the zinc by the number +1/2, the difference being arbitrarily taken as unity, and the sum being (on account of the insulation) zero. It will be seen that Volta's idea of "tension" was a mingling of two ideas, which in modern electric theory are clearly distinguished from each other-namely, electric charge and electric potential.

Now let a disk of moistened pasteboard be laid on the zinc, and a disk of copper on this again. Since the uppermost copper is not in contact with the zinc, the contact-action does not take place between them; but since the moist pasteboard is a conductor, the copper will receive a charge from the zinc. Thus the states will now be represented by -2/3 for the lower copper, +1/3 for the zinc, and +1/3 for the upper copper, giving a zero sum as before.

If, now, another zinc disk is placed on the top, the states will be represented by -1 for the lower copper, 0 for the lower zine and upper copper, and +1 for the upper zinc.

In this way it is evident that the difference between the numbers indicating the tensions of the uppermost and lowest disks in the pile will always be equal to the number of pairs of metallic disks contained in it. If the pile is insulated, the sum of the numbers indicating the states of all the disks must be zero; but if the lowest disk is connected to earth, the tension of this disk will be zero, and the numbers indicating the states of all the other disks will be increased by the same amount, their mutual differences remaining unchanged.

The pile as a whole is thus similar to a Leyden, jar; when the experimenter touches the uppermost and lowest. disks, he receives the shock of its discharge, the intensity being proportional to the number of disks.

The moist layers played no part in Volta's theory beyond that of conductors.^[12] It was soon found that when the moisture is acidified, the pile is more efficient; but this was attributed solely to the superior conducting power of acids.

Volta fully understood and explained the impossibility of constructing a pile from disks of metal alone, without making use of moist substances. As he showed in 1801, if disks of various metals are placed in contact in any order, the extreme metals will be in the same state as if they touched each other directly without the intervention of the others; so that the whole is equivalent merely to a single pair. When the metals are arranged in the order silver, copper, iron, tin, lead, zinc, each of them becomes positive with respect to that which precedes it, and negative with respect to that which follows it; but the moving force from the silver to the zinc is equal to the sum of the moving forces of the metals comprehended between them in the series.

When a connexion was maintained for some time between the extreme disks of a pile by the human body, sensations. were experienced which seemed to indicate a continuous activity in the entire system. Volta inferred that the electric current persists during the whole time that communication by conductors exists all round the circuit, and that the current is suspended only when this communication is interrupted. "This endless circulation or perpetual motion of the electric fluid," he says, "may seem paradoxical, and may prove inexplicable; but it is none the less real, and we can, so to speak, touch and handle it."

Volta announced his discovery in a letter to Sir Joseph Banks, dated from Como, March 20th, 1800. Sir Joseph, who was then President of the Royal Society, communicated the news to William Nicholson (b. 1753, d. 1815), founder of the Journal which is generally known by his name, and his friend Anthony Carlisle (b. 1768, d. 1840), afterwards a distinguished surgeon. On the 30th of the following month, Nicholson and Carlisle set up the first pile made in England. In repeating Volta's experiments, having made the contact more secure at the upper plate of the pile by placing a drop of water there, they noticed^[13] a disengagement of gas round the con- «ducting wire at this point; whereupon they followed up the matter by introducing a tube of water, into which the wires from the terminals of the pile were plunged. Bubbles of an inflammable gas were liberated at one wire, while the other wire became oxidised; when platinum wires were used, oxygen and hydrogen were evolved in a free state, one at each wire. This effect, which was nothing less than the electric decomposition of water into its constituent gases, was obtained on May 2nd, 1800.^[14]

Although it had long been known that frictional electricity is capable of inducing chemical action,^[15] the discovery of Nicholson and Carlisle was of tho first magnitude. It was at once extended by William Cruickshank, of Woolwich (b. 1745, d. 1800), who^[16] showed that solutions of metallic salts are also decomposed by the current; and William Hyde Wollaston (b. 1766, d. 1828) seized on it as a test^[17] of the identity of the electric currents of Volta with those obtained by the discharge of frictional electricity. He found that water could be decomposed by currents of either type, and inferred that all differences between them could be explained by supposing that voltaic electricity as commonly obtained is "less intense, but produced in much larger quantity." Later in the same year (1801), Martin van Marum (b, 1750, d. 1837) and Christian Heinrich Pfaff (b. 1773, d. 1852) arrived at the same conclusion by carrying out on a large scale^[18] Volta's plan of using the pile to charge batteries of Leyden jars.

The discovery of Nicholson and Carlisle made a great impression on the mind of Humphry Davy (b. 1778, d. 1829), a young Cornishman who about this time was appointed Professor of Chemistry at the Royal Institution in London. Davy at once began to experiment with Voltaic piles, and in November, 1800,^[19] showed that they give no current when the water between the pairs of plates is pure, and that their power of action is "in great measure proportional to the power of the conducting fluid substance between the double plates to oxydate the zinc." This result, as he immediately perceived, did not harmonize well with Volta's views on the source of electricity in the pile, but was, on the other hand, in agreement with Fabroni's idea that galvanic effects are always accompanied by chemical action. After a series of experiments he definitely concluded that "the galvanic pile of Volta acts only when the conducting substance between the plates is capable of oxydating the zinc; and that, in proportion as a greater quantity of oxygen enters into combination with the zinc in a given time, so in proportion is the power of the pile to decompose water and to give the shock greater. It seems therefore reasonable to conclude, though with our present quantity of facts we are unable to explain the exact mode of operation, that the oxydation of the zinc in the pile, and the chemical changes connected with it, are somehow the cause of the electrical effects it produces." This principle of oxidation guided Davy in designing many new types of pile, with elements chosen from the whole range of the known metals.

Davy's chemical theory of the pile was supported by Wollaston^[20] and by Nicholson,^[21] the latter of whom urged that the existence of piles in which only one metal is used (with more. than one kind of fluid) is fatal to any theory which places the seat of the activity in the contact of dissimilar metals.

Davy afterwards proposed^[22] a theory of the voltaic pile. which combines ideas drawn from both the "contact" and "chemical" explanations. Ho supposed that before the circuit is closed, the copper and zinc disks in each contiguous pair assume opposite electrostatic states, in consequence of inherent.

"electrical energies" possessed by the metals; and when a communication is made between the extreme disks by a wire, the opposite electricities annihilate each other, as in the discharge of a Leyden jar. If the liquid (which Davy compared to the glass of a Leyden jar) were incapable of decomposition, the current would cease after this discharge. But the liquid in the pile is composed of two elements which have inherent attractions for electrified metallic surfaces: hence arises chemical action, which removes from the disks the outermost layers of molecules, whose energy is exhausted, and exposes new metallic surfaces. The electrical energies of the copper and zinc are consequently again exerted, and the process of electromotion continues. Thus the contact of metals is the cause which disturbs the equilibrium, while the chemical changes of continually restore the conditions under which the contact energy can be exerted.

In this and other memoirs Davy asserted that chemical affinity is essentially of an electrical nature. "Chemical and electrical attractions," he declared,^[23] "are produced by the same cause, acting in one case on particles, in the other on masses, of matter; and the same property, under different modifications, is the cause of all the phenomena exhibited by different voltaic combinations."

The further elucidation of this matter came chiefly from researches on electro-chemical decomposition, which we must now consider.

A phenomenon which had greatly surprised Nicholson and Carlisle in their early experiments was the appearance of the products of galvanic decomposition at places remote from each other. The first attempt to account for this was made in 1806 by Theodor von Grothusst^[24] (b.1785, d. 1822) and by Davy ^[25] who advanced a theory that the terminals at which water is decomposed have attractive and repellent powers; that the pole whence resinous electricity issues has the property of attracting hydrogen and the metals, and of repelling oxygen and acid substances, while the positive terminal has the power of attracting oxygen and repelling hydrogen; and that these forces are sufficiently energetic to destroy or suspend the usual operation of chemical affinity in the water-molecules nearest the terminals. The force due to each terminal was supposed to diminish with the distance from the terminal. When the molecule nearest one of the terminals has been decomposed by the attractive and repellent forces of the terminal, one of its constituents is liberated there, while the other constituent, by virtue of electrical forces (the oxygen and hydrogen being in opposite electrical states), attacks the next molecule, which is then decomposed. The surplus constituent from this attacks the next molecule, and so on. Thus a chain of decompositions and recompositions was supposed to be set up among the molecules intervening between the terminals.

The hypothesis of Grouhuss and Davy was attacked in 1825 by Anguste De La Rive^[26] (b. 1801, d. 1873) of Geneva, on the ground of its failure to explain what happens when different liquids are placed in series in the circuit. If, for example, a solution of zinc sulphate is placed in one compartment, and water in another, and if the positive pole is placed in the solution of zinc sulphate, and the negative pole in the water, De La Rive found that oxide of zinc is developed round the latter; although decomposition and recomposition of zine sulphate could not take place in the water, which contained none of it. Accordingly, he supposed the constituents of the decomposed liquid to be bodily transported across the liquids, in close union with the moving electricity. In the electrolysis of water, one current of electrified hydrogen was supposed to leave the positive pole, and become decomposed into hydrogen and electricity at the negative pole, the hydrogen being there liberated as a gas. Another current in the same way carried electrified oxygen from the negative to the positive pole. In this scheme the chain of successive decompositions imagined by Grothuss does not take place, the only molecules decomposed being those adjacent to the poles.

The appearance of the products of decomposition at the separate poles could be explained either in Grothuss' fashion by assuming dissociations throughout the mass of liquid, or in De La Rive's by supposing particular dissociated atoms to travel considerable distances. Perhaps & preconceived idea of economy in Nature deterred the workers of that time from accepting the two assumptions together, when either of them separately would meet the case. Yet it is to this apparent redundancy that later researches have pointed as the truth. Nature is what she is, and not what we would make her,

De La Rive was one of the most thoroughgoing opponents of Volta's contact theory of the pile; even in the case when two metals are in contact in air only, without the intervention of any liquid, he attributed the electric effect wholly to the chemical affinity of the air for the metals.

During the long interval between the publication of the rival hypotheses of Grothuss and De La Rive, little real progress was made with the special problems of the cell; but meanwhile electric theory was developing in other directions. One of these, to which our attention will first be turned, was the electro-chemical theory of the celebrated Swedish chemist, Jöns Jacob Berzelius (b. 1779, d. 1848).

Berzelius founded his theory,^[27] which had been in one or two of its features anticipated by Davy,^[28] on inferences drawn from Volta's contact effects. "Two bodies," he remarked, "which have affinity for each other, and which have been brought into mutual contact, are found upon separation to be in opposite electrical states. That which has the greatest affinity for oxygen usually becomes positively electrified, and the other negatively."

This seemed to him to indicate that chemical affinity arises from the play of electric forces, which in turn spring from electric charges within the atoms of matter. To be precise, he supposed each atom to possess two poles, which are the seat of opposite electrifications, and whose electrostatic field is the cause of chemical affinity.

By aid of this conception Berzelius drew a simple and vivid picture of chemical combination. Two atoms, which are about to unite, dispose themselves so that the positive pole of one touches the negative pole of the other; the electricities of these two poles then discharge each other, giving rise to the heat and light which are observed to accompany the act of combination.^[29] The disappearance of these leaves the compound molecule with the two remaining poles; and it cannot be dissociated into its constituent atoms again until some means is found of restoring to the vanished poles their charges. Such a means is afforded by the action of the galvanic pile in electrolysis: the opposite electricities of the current invade the molecules of the electrolyte, and restore the atoms to their original state of polarization,

If, as Berzelius taught, all chemical compounds are formed by the mutual neutralization of pairs of atoms, it is evident that they must have a binary character. Thus he conceived a salt to be compounded of an acid and an oxide, and each of these to be compounded of two other constituents. Moreover, in any compound the electropositive member would be replaceable only by another electropositive member, and the electronegative member only by another member also electronegative; so that the substitution of, e.g., chlorine for hydrogen in a compound would be impossible—an inference which was overthrown by subsequent discoveries in chemistry.

Berzelius succeeded in bringing the most curiously diverse facts within the scope of his theory. Thus "the combination of polarized atoms requires a motion to turn the opposite poles to each other; and to this circumstance is owing the facility with which combination takes place when one of the two bodies is in the liquid state, or when both are in that state; and the extreme difficulty, or nearly impossibility, of effecting an union between bodies, both of which are solid. And again, since each polarized particle must have an electric atmosphere, and as this atmosphere is the predisposing cause of combination, as we have seen, it follows, that the particles cannot act but at certain distances, proportioned to the intensity of their polarity; and hence it is that bodies, which have affinity for each other, always combine nearly on the instant when mixed in the liquid state, but less easily in the gaseous state, and the union ceases to be possible under a certain degree of dilatation of the gases; as we know by the experiments of Grothuss, that a mixture of oxygen and hydrogen in due proportions, when rarefied to a certain degree, cannot be set on fire at any temperature whatever."

And again: "Many bodies require an elevation of temperature to enable them to act upon each other. It appears, therefore, that heat possesses the property of augmenting the polarity of these bodies."

Berzelius accounted for Volta's electromotive series by assuming the electrification at one pole of an atom to be somewhat more or somewhat less than what would be required to neutralize the charge at the other pole. Thus each atom would possess a certain net or residual charge, which might be of either sign; and the order of the elements in Volta's series could be interpreted simply as the order in which they would stand when ranged according to the magnitude of this residual charge. As we shall see, this conception was afterwards overthrown by Faraday.

Berzelius permitted himself to publish some speculations on the nature of heat and electricity, which bring vividly before us the outlook of an able thinker in the first quarter of the nineteenth century. The great question, he says, is whether ✓ the electricities and caloric are matter or merely phenomena. If the title of matter is to be granted only to such things as are ponderable, then these problematic entities are certainly not matter; but thus to narrow the application of the term is, he believes, a mistake; and he inclines to the opinion that caloric is truly matter, possessing chemical affinities without obeying the law of gravitation, and that light and all radiations consist in modes of propagating such matter. This conclusion makes it easier to decide regarding electricity. "From the relation which exists between caloric and the electricities," he remarks, "it is clear that what may be true with regard to the materiality of one of them must also be true with regard to that of the other. There are, however, a quantity of phenomena produced by electricity which do not admit of explanation without admitting at the same time that electricity is matter. Electricity, for instance, very often detaches everything which covers the surface of those bodies which conduct it. It, indeed, passes through conductors without leaving any trace of its passage; but it penetrates non-conductors which oppose its course, and makes a perforation precisely of the same description as would have been made by something which had need of place for its passage. We often observe this when electric jars are broken by an overcharge, or when the electric shock is passed through a number of cards, etc. We may therefore, at least with some probability, imagine caloric and the electricities to be matter, destitute of gravitation, but possessing affinity to gravitating bodies. When they are not confined by these affinities, they tend to place themselves in equilibrium in the universe. The suns destroy at every moment this equilibrium, and they send the re-united electricities in the form of luminous rays towards the planetary bodies, upon the surface of which the rays, being arrested, manifest themselves as caloric; and this last in its turn, during the time required to replace it in equilibrium in the universe, supports the chemical activity of organic and inorganic nature."

It was scarcely to be expected that anything so speculative as Berzelius' electric conception of chemical combination would be confirmed in all particulars by subsequent discovery; and, as a matter of fact, it did not as a coherent theory survive the lifetime of its author. But some of its ideas have persisted, and among them the conviction which lies at its foundation, that chemical affinities are, in the last resort, of electrical origin.

While the attention of chemists was for long directed to the theory of Berzelius, the interest of electricians was diverted from it by a discovery of the first magnitude in a different region.

That a relation of some kind subsists between electricity and magnetism had been suspected by the philosophers of the eighteenth century. The suspicion was based in part on some curious effects produced by lightning, of a kind which may be illustrated by a paper published in the Philosophical Transactions in 1735.^[30] A tradesman of Wakefield, we are told, "having put up a great number of knives and forks in a large box, and having placed the box in the corner of a large room, there happen'd in July, 1731, a sudden storm of thunder, lightning, etc., by which the corner of the room was damaged, the Box split, and a good many knives and forks melted, the sheaths being untouched. The owner emptying the box upon a Counter where some Nails lay, the Persons who took up the knives, that lay upon the Nails, observed that the knives took up the Nails."

Lightning thus came to be credited with the power of magnetizing steel; and it was doubtless this which led Franklin^[31] in 1751 to attempt to magnetize a sewing-needle by means of the discharge of Leyden jars. The attempt was indeed successful; but, as Van Marum afterwards showed, it was doubtful whether the magnetism was due directly to the current.

More experiments followed.^[32] In 1805 Jean Nicolas Pierre Hachette (b. 1769, d. 1834) and Charles Bernard Desormes (b. 1777, d. 1862) attempted to determine whether an insulated voltaic pile, freely suspended, is oriented by terrestrial magnetism; but without positive result. In 1807 Hans Christian Oersted (b. 1777, d. 1851), Professor of Natural Philosophy in Copenhagen, announced his intention of examining the action of electricity on the magnetic needle; but it was not for some years that his hopes were realized. If one of his pupils is to be believed,^[33] he was "a man of genius, but a very unhappy experimonter; he could not manipulate instruments. He must always have an assistant, or one of his auditors who had easy hands, to arrange the experiment."

During a course of lectures which he delivered in the winter of 1819-20 on "Electricity, Galvanism, and Magnetism," the idea occurred to him that the changes observed with the compass-needle during a thunderstorm might give the clue to the effect of which he was in search; and this led him to think that the experiment should be tried with the galvanic circuit closed instead of open, and to inquire whether any effect is produced on a magnetic needle when an electric current is passed through a neighbouring wire. At first he placed the wire at right angles to the needle, but observed no result. After the end of a lecture in which this negative experiment had been shown, the idea occurred to him to place the wire parallel to the needle: on trying it, a pronounced deflexion was observed, and the relation between magnetism and the electric current was discovered. After confirmatory experiments with more powerful apparatus, the public announcement was made in July, 1820.^[34]

Oersted did not determine the quantitative laws of the action, but contented himself with a statement of the qualitative effect and some remarks on its cause, which recall the magnetic speculations of Descartes: indeed, Oersted's conceptions may be regarded as linking those of the Cartesian school to those which were introduced subsequently by Faraday. "To the effect which takes place in the conductor and in the surrounding space," he wrote, "we shall give the name of the conflict of electricity." "The electric conflict acts only on the magnetic particles of matter. All non-magnetic bodies appear penetrable by the electric conflict, while magnetic bodies, or rather their magnetic particles, resist the passage of this conflict. Hence they can be moved by the impetus of the contending powers.

"It is sufficiently evident from the preceding facts that the electric conflict is not confined to the conductor, but dispersed pretty widely in the circumjacent space.

"From the preceding facts we may likewise collect, that this conflict performs circles; for without this condition, it seems impossible that the one part of the uniting wire, when placed below the magnetic pole, should drive it toward the east, and when placed above it toward the west; for it is the nature of a circle that the motions in opposite parts should have an opposite direction."

Oersted's discovery was described at the meeting of the French Academy on September 11th, 1820, by an academician (Arago) who had just returned from abroad. Several investigators in France repeated and extended his experiments; and the first precise analysis of the effect was published by two of these, Jean-Baptiste Biot (b. 1774, d. 1862) and Félix Savart (b.1791, d. 1841), who, at a meeting of the Academy of Sciences. on October 30th, 1820, announced^[35] that the action experienced by a pole of austral or boreal magnetism, when placed at any distance from a straight wire carrying a voltaic current, may be thus expressed: "Draw from the pole a perpendicular to the wire; the force on the pole is at right angles to this line and to the wire, and its intensity is proportional to the reciprocal of the distance." This result was soon further analysed, the attractive force being divided into constituents, each of which was supposed to be due to some particular element of the current; in its new form the law may be stated thus: the magnetic force due to an element ds of a circuit, in which a current i is flowing, at a point whose vector distance from ds is r, is (in suitable units)

${\frac {i}{r^{3}}}[\mathbf {ds,r} ]$^[36] or $\mathrm {curl} {\frac {i\mathbf {ds} }{r}}$.^[37]

It was now recognized that a magnetic field may be produced as readily by an electric current as by a magnet; and, as Arayo soon showed,^[38] this, like any other magnetic field, is capable of inducing magnetization in iron. The question naturally suggested itself as to whether the similarity of properties between currents and magnets extended still further, e.g. whether conductors carrying currents would, like magnets, experience ponderomotive forces when placed in a magnetic field, and whether such conductors would consequently, like magnets, exert ponderomotive forces on each other.

The first step towards answering these inquiries was taken by Oersted^[39] himself. "As," he said, "a body cannot put another in motion without being moved in its turn, when it possesses the requisite mobility, it is easy to foresee that the galvanic arc must be moved by the magnet"; and this he verified experimentally.

The next step came from André Marie Ampère (b. 1775, d. 1836), who at the meeting of the Academy on September 18th, exactly a week after the news of Oersted's first discovery had arrived, showed that two parallel wires carrying currents' attract each other if the currents are in the same direction, and repel each other if the currents are in opposite directions. During the next three years Ampère continued to prosecute the researches thus inaugurated, and in 1825 published his collected results in one of the most celebrated memoirs^[40] in the history of natural philosophy.

Ampère introduces his work by proclaiming himself a follower of that school which explained all physical phenomena in terms of equal and oppositely directed forces between pairs of particles; and he renounces the attempt to seek more speculative, though possibly more fundamental, explanations in terms of the motions of ultimate fluids and aethers. Nevertheless, he indicates two conceptions of this latter character, on which such explanations might be founded.

In the first^[41] he suggests that the ponderomotive forces between circuits carrying electric currents may be due to "the reaction of the elastic fluid which extends throughout all space, whose vibrations produce the phenomena of light," and which is "put in motion by electric currents." This fluid or aether can, he says, "be no other than that which results from the combination of the two electricities."

In the second conception,^[42] Ampère suggests that the interspaces between the metallic molecules of a wire which carries a current may be occupied by a fluid composed of the two electricities, not in the proportions which form the neutral fluid, but with an excess of that one of them which is opposite to the electricity peculiar to the molecules of the metal, and which consequently masks this latter electricity. In this inter-molecular fluid the opposite electricities are continually being dissociated and recombined; a dissociation of the fluid within one inter-molecular interval having taken place, the positive electricity thus produced unites with the negative electricity of the interval next to it in the direction of the current, while the negative electricity of the first interval unites with the positive electricity of the next interval in the other direction, Such interchanges, according to this hypothesis, constitute the electric current.

Ampère's memoir is, however, but little occupied with the more speculative side of the subject. His first aim was to investigate thoroughly by experiment the ponderomotive forces on electric currents.

"When," he remarks, "M. Oersted discovered the action which a current exercises on a magnet, one might certainly have suspected the existence of a mutual action between two circuits carrying currents; but this was not a necessary consequence; for a bar of soft iron also acts on a magnetized needle, although there is no mutual action between two bars of soft iron."

Ampère, therefore, submitted the matter to the test of the laboratory, and discovered that circuits carrying electric currents exert ponderomotive forces on each other, and that ponderomotive forces are exerted on such currents by magnets. To the science which deals with the mutual action of currents he gave the name electro-dynamics;^[43] and he showed that the action obeys the following laws:—

(1) The effect of a current is reversed when the direction of the current is reversed.

(2) The effect of a current flowing in a circuit twisted into small sinuosities is the same as if the circuit were smoothed out.

(3) The force exerted by a closed circuit on an element of another circuit is at right angles to the latter.

(4) The force between two elements of circuits is unaffected when all linear dimensions are increased proportionately, the current-strengths remaining unaltered.

From these data, together with his assumption that the force between two elements of circuits acts along the line joining them, Ampère obtained an expression of this force: the deduction nay be made in the following way:—

Let ds, ds′ be the elements, r the line joining them, and i, i′ the current-strengths. From (2) we see that the effect of ds on ds′ is the vector sum of the effects of dx, dy, dz on ds′, where these are the three components of ds: so the required force must be of the form—

Γ x a scalar quantity which is linear and homogeneous in ds; and it must similarly be linear and homogeneous in ds′; so using (1), we see that the force must be of the form

$\mathbf {F} =ii\prime \mathbf {r} \left\{(\mathbf {ds} .\mathbf {ds\prime } )\phi (r)+(\mathbf {ds} .\mathbf {r} )(\mathbf {ds\prime } .\mathbf {r} )\psi (r)\right\}$

where φ and ψ denote undetermined functions of r.

From (4) it follows that when ds, ds′', r are all multiplied by the same number, F is unaffected: this shows that

$\phi (r)={\frac {A}{r^{3}}}$ and $\psi (r)={\frac {B}{r^{5}}}$

where A and B denote constants. Thus we have

$\mathbf {F} =ii\prime \mathbf {r} \left\{{\frac {A(\mathbf {ds} .\mathbf {ds\prime } )}{r^{3}}}+{\frac {B(\mathbf {ds} .\mathbf {r} )(\mathbf {ds\prime } .\mathbf {r} )}{r^{5}}}\right\}$

Now, by (3), the resolved part of F along ds′ must vanish when integrated round the circuit s, i.e. it must be a complete differential when dr is taken to be equal to -ds. That is to say,

${\frac {A(\mathbf {ds.ds\prime } )(\mathbf {r.ds\prime } )}{r^{3}}}+{\frac {B(\mathbf {ds.r} )(\mathbf {ds\prime .r} )^{2}}{r^{5}}}$

must be a complete differential; or

$-{\frac {A}{2r^{3}}}d.(\mathbf {r.ds\prime } )^{2}+{\frac {B}{r^{5}}}(\mathbf {ds.r} )(\mathbf {r.ds\prime } )^{2}$

must be a complete differential; and therefore

$d.{\frac {A}{2r^{2}}}=-{\frac {B}{r^{5}}}(\mathbf {ds.r} )$,

or${\frac {3A}{2r^{4}}}dr={\frac {B}{r^{4}}}dr$,

or$B=-{\frac {3}{2}}A$

Thus finally we have

$\mathbf {F} =\mathrm {Constant} \times ii\prime \mathbf {r} \left\{{\frac {2}{r^{3}}}(\mathbf {ds.ds\prime } )-{\frac {3}{r^{5}}}(\mathbf {ds.r} )(\mathbf {ds\prime .r} )\right\}$

This is Ampère's formula: the multiplicative constant depends of course on the units chosen, and may be taken to be - 1.

The weakness of Ampère's work evidently lies in the assumption that the force is directed along the line joining the two elements: for in the analogous case of the action between two magnetic molecules, we know that the force is not directed along the line joining the molecules. It is therefore of interest to find the form of F when this restriction is removed.

For this purpose we observe that we can add to the expression already found for F any term of the form

$\phi (r).(\mathbf {ds.r} ).\mathbf {ds\prime }$,

where φ(r) denotes any arbitrary function of r; for since

$(\mathbf {ds.r} )=-r.ds.{\frac {dr}{ds}}$,

this term vanishes when integrated round the circuit s; and it contains ds and ds′ linearly and homogeneously, as it should. We can also add any terms of the form

$d\{\mathbf {r} .(\mathbf {ds\prime .r} ).\chi (r)\}$,

where χ(r) denotes any arbitrary function of r, and d denotes differentiation along the arc s, keeping ds′ fixed (so that dr = - ds); this differential may be written

$-\mathbf {ds} .\mathbf {ds\prime .r} .\chi (r)-\mathbf {r} \chi (r)(\mathbf {ds\prime .ds} )-{\frac {1}{r}}\chi \prime (r)\mathbf {r} (\mathbf {ds.r} )(\mathbf {ds\prime .r} )$.

In order that the law of Action and Reaction may not be violated, we must combine this with the former additional term so as to obtain an expression symmetrical in ds and ds′: and hence we see finally that the general value of F is given by the equation

$\mathbf {F} =-ii\prime \mathbf {r} \left\{{\frac {2}{r^{3}}}(\mathbf {ds.ds\prime } )-{\frac {3}{r^{3}}}(\mathbf {ds.r} )(\mathbf {ds.r} )\right\}$

$+\chi (r)(\mathbf {ds\prime .r} )\mathbf {ds} +\chi (r)(\mathbf {ds.r} )\mathbf {ds\prime } +\chi (r)(\mathbf {ds.ds\prime } )\mathbf {r}$

$+{\frac {1}{r}}\chi \prime (r)(\mathbf {ds.r} )(\mathbf {ds\prime .r} )\mathbf {r}$.

The simplest form of this expression is obtained by taking

$\chi (r)={\frac {ii\prime }{r^{3}}}$,

when we obtain

$\mathbf {F} ={\frac {ii\prime }{r^{3}}}\{(\mathbf {ds.r} ).\mathbf {ds\prime } +(\mathbf {ds\prime .r} )\mathbf {ds} +(\mathbf {ds.ds\prime } )\mathbf {r} \}$.

The comparatively simple expression in brackets is vector part of the quaternion product of the three vectors ds, r, ds′. ^[44]

From any of these values of F we can find the ponderomotive force exerted by the whole circuit s on the element ds': it is, in fact, from the last expression,

$ii\prime \int {\frac {1}{r^{5}}}(\mathbf {ds\prime .r} ).\mathbf {ds} -(\mathbf {ds.ds\prime } )\mathbf {r}$,

or $ii\prime \int _{s}\left[\mathbf {ds\prime .} {\frac {[\mathbf {ds.r} ]}{r^{3}}}\right]$,

or $i\prime [\mathbf {ds\prime .B} ]$,

Where $\mathbf {B} =i\int _{s}{\frac {1}{r^{3}}}[\mathbf {ds.r} ]$.

Now this value of B is precisely the value found by Biot and Savart^[45] for the magnetic intensity at ds′ due to the current i in the circuit s. Thus we see that the ponderomotive force on a current-element ds′ in a magnetic field B is i′[ds′.B].

Ampère developed to a considerable extent the theory of the equivalence of magnets with circuits carrying currents; and showed that an electric current is equivalent, in its magnetic effects, to a distribution of magnetism on any surface terminated by the circuit, the axes of the magnetic molecules being everywhere normal to this surface:^[46] such a magnetized surface is called a magnetic shell. He preferred, however, to regard the current rather than the magnetic fluid as the fundamental entity, and considered magnetism to be really an electrical phenomenon: each magnetic molecule owes its properties, according to this view, to the presence within it of a small closed circuit in which an electric current is perpetually flowing.

The impression produced by Ampère's memoir was great and lasting. Writing half a century afterwards, Maxwell speaks of it as "one of the most brilliant achievements in science." "The whole," he says, "theory and experiment, seems as if it had leaped, full-grown and full-armed, from the brain of the 'Newton of electricity.' It is perfect in form and unassailable in accuracy; and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electrodynamics."

Not long after the discovery by Oersted of the connexion between galvanism and magnetism, a connexion was discovered between galvanism and heat. In 1822 Thomas Johann Seebeck (b. 1770, d. 1831), of Berlin discovered^[47] that an electric current can be set up in a circuit of metals, without the interposition of any liquid, merely by disturbing the equilibrium of temperature Let a ring be formed of copper and bismuth soldered together at the two extremities; to establish a current it is only necessary to heat the ring at one of these junctions. To this new class of circuits the name thermo-electric was given.

It was found that the metals can be arranged as thermo-electric series, in the order of their power of generating currents when thus paired, and that this order is quite different from Volta's order of electromotive potency. Indeed antimony and bismuth, which are near each other in the latter series, are at opposite extremities of the former.

The currents generated by thermo-electric means generally feeble: and the mention of this fact brings us to the question, which was about this time engaging attention, of the efficacy of different voltaic arrangements.

Comparisons of a rough kind had been instituted soon after the discovery of the pile. The French chemists Antoine François de Fourcroy (b. 1755, d. 1809), Louis Nicolas Vauquelin (b. 1763, d. 1829), and Louis Jacques Thénard (b. 1777, d. 1857) found^[48] in 1801, on varying the size of the metallic disks constituting the pile, that the sensations produced on the human frame were unaffected so long as the number of disks remained the same, but that the power of burning finely drawn wire was altered; and that the latter power was proportional to the total surface of the disks employed, whether this were distributed among a small number of large disks, or a large number of small ones. This was explained by supposing that small plates give a small quantity of the electric fluid with a high velocity, while large plates give a larger quantity with 10 greater velocity. Shocks, which were supposed to depend on the velocity of the fluid alone, would therefore not be intensified by increasing the size of the plates.

The effect of varying the conductors which connect the terminals of the pile was also studied. Nicolas Gautherot (b. 1753, d. 1803) observed^[49] that water contained in tubes which have a narrow opening does not conduct voltaic currents so well as when the opening is more considerable. This experiment is evidently very similar to that which Beccaria had performed half a century previously^[50] with electrostatic discharges.

As we have already seen, Cavendish investigated very completely the power of metals to conduct electrostatic discharges; their power of conducting voltaic currents was now examined by Davy.^[51] His method was to connect the terminals of a voltaic battery by a path containing water (which it decomposed), and also by an alternative path consisting of the metallic wire under examination. When the length of the wire was less than a certain quantity, tho water ceased to be decomposed; Davy measured the lengths and weights of wires of different materials and cross-sections under these limiting circumstances; and, by comparing them, showed that the conducting power of a wire formed of any one metal His inversely proportional to its length and directly proportional to its sectional area, but independent of the shape of the crosssection^[52]. The latter fact, as he remarked, showed that voltaic currents pass through the substance of the conductor and not along its surface.

Davy, in the same memoir, compared the conductivities of various metals, and studied the effect of temperature: he found that the conductivity varied with the temperature, being "lower in some inverse ratio as the temperature was higher."

He also observed that the same magnetic power is exhibited by every part of the same circuit, even though it be formed of wires of different conducting powers pieced into a chain, so that "the magnetism seems directly as the quantity of electricity which they transmit."

The current which flows in a given voltaic circuit evidently depends not only on the conductors which form the circuit, but also on the driving-power of the battery. In order to form a complete theory of voltaic circuits, it was therefore necessary to extend Davy's laws by taking the driving-power into account. This advance was effected in 1826 by Georg Simon Ohm^[53] (b. 1787, d. 1854).

Ohm had already carried out a considerable amount of experimental work on the subject, and had, e.g., discovered that if a number of voltaic cells are placed in series in a circuit, the current is proportional to their number if the external resistance is very large, but is independent of their number if the external resistance is small. He now essayed the task of combining all the known results into a consistent theory.

For this purpose he adopted the idea of comparing the flow of electricity in a current to the flow of heat along a wire, the theory of which had been familiar to all physicists since the publication of Fourier's Théorie analytique de la chaleur in 1822. "I have proceeded," he says, "from the supposition that the communication of the electricity from one particle takes place directly only to the one next to it, so that no immediate transition from that particle to any other situate at a greater distance occurs. The magnitude of the flow between two adjacent particles, under otherwise exactly similar circumstances, I have assumed to be proportional to the difference of the electric forces existing in the two particles; just as, in the theory of heat, the flow of caloric between two particles is regarded as proportional to the difference of their temperatures."

The comparison between the flow of electricity and the flow of heat suggested the propriety of introducing a quantity whose behaviour in electrical problems should resemble that of temperature in the theory of heat. The differences in the values of such a quantity at two points of a circuit would provide what was so much needed, namely, a measure of the "driving-power" acting on the electricity between these points. To carry out this idea, Ohm recurred to Volta's theory of the electrostatic condition of the open pile. It was customary to measure the "tension" of a pile by connecting one terminal to earth and testing the other terminal by an electroscope. Accordingly Ohm says: "In order to investigate the changes which occur in the electric condition of a body A in a perfectly definite manner, the body is each time brought, under similar circumstances, into relation with a second moveable body of invariable electrical condition, called the electroscope; and the force with which the electroscope is repelled or attracted by the body is determined. This force is termed the electroscopic force of the body A."

"The same body A may also serve to determine the electroscopic force in various parts of the same body. For this purpose take the body A of very small dimensions, so that when we bring it into contact with the part to be tested of any third body, it may from its smallness be regarded as a substitute for this part: then its electroscopic force, measured in the way described, will, when it happens to be different at the various places, make known the relative differences with regard to electricity between these places."

Ohm assumed, as was customary at that period, that when two metals are placed in contact, "they constantly maintain at the point of contact the same difference between their electroscopic forces." He accordingly supposed that each voltaic cell possesses a definite tension, or discontinuity of electroscopic force, which is to be regarded as its contribution to the driving-force of any circuit in which it may be placed. This assumption confers a definite meaning on his use of the term "electroscopic force"; the force in question is identical with the electrostatic potential. But Ohm and his contemporaries did not correctly understand the relation of galvanic conceptions to the electrostatic functions of Poisson. The electroscopic force in the open pile was generally identified with the thickness of the electrical stratum at the place tested; while Ohm, recognizing that electric currents are not confined to the surface of the conductors, but penetrate their substance, seems to have thought of the electroscopic force at a place in a circuit as being proportional to the volume-density of electricity there—an idea in which he was confirmed by the relation which, in an analogous case, exists between the temperature of a body and the volume-density of heat supposed to be contained in it.

Denoting, then, by S the current which flows in a wire of conductivity γ, when the difference of the electroscopic forces at the terminals is E, Ohm writes

$S=\gamma E$.

From this formula it is easy to deduce the laws already given by Davy. Thus, if the area of the cross-section of a wire is A, we can by placing a such wires side by side construct a wire of cross-section nA. If the quantity E is the same for each, equal currents will flow in the wires; and therefore the current in the compound wire will be n times that in the single wire; so when the quantity E is unchanged, the current is proportional to the cross-section; that is, the conductivity of a wire is directly proportional to its cross-section, which is one of Davy's laws.

In spite of the confusion which was attached to the idea of electroscopic force, and which was not dispelled for some years, the publication of Ohm's memoir marked a great advance in electrical philosophy. It was now clearly understood that the current flowing in any conductor depends only on the conductivity inherent in the conductor and on another variable which bears to electricity the same relation that temperature bears to heat; and, moreover, it was realized that this latter variable is the link connecting the theory of currents with the older theory of electrostatics. These principles were a sufficient foundation for future progress; and much of the work which was published in the second quarter of the century was no more than the natural development of the principles laid down by Ohm.^[54]

It is painful to relate that the discoverer had long to wait before the merits of his great achievement were officially recognized. Twenty-two years after the publication of the memoir on the galvanic circuit, he was promoted to a university professorship; this he held for the five years which remained until his death in 1854.

Notes

1. Mém. de l'Acad. de Rerlin, 1752, p. 356.
2. Author:Luigi Aloisio Galvani|Aloisii Galvani]], De Viribus Electricitatis in Matu · Inculari : Commentarii Bononiensi, vii (1791), p. 363.
3. According to a story which has often been repeated, but which rests on no sufficient evidence, the frog was one of a number which had been procured for the Signora Galvani, who, being in poor health, bad been recommended to take a soup made of these animals as a restorative.
4. Loo. cit., p. 377.
5. This observation was made in 1786.
6. Phil. Trans., 1793, pp. 10, 27.
7. Phil. Mag. iv (1799), pp. 59, 163, 306-
8. Phil. Journal, 4to, iii, 308; iv. 120; Journal de Physique, vi. 318.
9. A degree of reinstatement had been grunted, but had not come into operation at the time of Galvani's death.
10. Phil. Trans., 1800, p. 403.
11. Abraham Bennet (b. 1750, d. 1799) had previously shown (New Experiments in Electricity, 1789, PP. 86-102) that many bodies, when separated after contact, are oppositely electrified; he conceived that different bodies have different attractions or capacities for electricity.
12. Volta had inclined, in his earlier experiments on galvanism, to locate the seat of power at the interfaces of the metals with the moist conductors. Cf. bis letter to Greu, Phil. Mag. iv (1799), p. 62.
13. Nicholson's Journal (4to), iv, 179 (1800); Phil. Mag. vii, 337 (1800).
14. It was obtained independently four months later ly J. W. Ritter.
15. Beccaria (Lettere dell' elettricismo, Bologna, 1768, p. 282) had reduced mercury and other detals fron their oxides by discharges of frictional electricity; and Priestley had obtained an inflammable gas from certain organic liquids in the same way. Cavendish in 1781 had established the constitution of water by electrically exploding hydrogen and oxygen.
16. Nicholsan's Journal (4to), iv (1800), pp. 187, 215: Phil. Mag, vii (1800), p. 337.
17. Phil. Mag., 1801, p. 427.
18. Phil. Mag., xii (1802), p. 161.
19. Nicholson's Journal (4t0), iv (1800); Davy's Works, ii, p. 155.
20. Phil. Trans., 1801, p. 427.
21. Nicholson's Journal, i (1802), p. 142.
22. Phil. Trans., 1807, p. 1.
23. Phil. Trans., 1826, p. 383.
24. Ann. do Chim., Ivili (1806), p. 54.
25. Bakerian lecture for 1806, Phil. Trans., 1807, p. 1. theory similar to that of Grothusa and Davy was communicated by Peter Mark Roget (b. 1779, d. 1869) in 1807 to the Philosophical Society of Manchester; cf. Roget's Galvanism, § 106.
26. Anuales de Chimie, xxvii, 190.
27. Memoirs of the Acad. of Stockholm, 1812; Nicholson's Journal of Nat. Phil., xxxiv (1913), 142, 153, 240, 319; XXXF, 38, 118, 159.
28. Phil. Trans., 1807.
29. This idea was Davy's.
30. Phil. Trans. xxxix (1736), p. 74.
31. Letter vi from Franklin to Collinson.
32. In 1774 the Electoral Academy of Bavaria proposed the question, "Is there a real and physical analogy between electric and magnetic forces?" as the subject of a prize.
33. Cf.a letter from Hansteen inserted in Bence Jones' Life of Faraday, ii, p. 395.
34. Schweigger's Journal für Chemie und Physik, xxix (1820), p. 275; Thomson's Annals of Philosophy, xvi (1820), p. 273; Ostwald's Klassiker der ezaktan -Wissenschaften, Nr. 83.
35. Annales de Chimie, xv (1820), p. 222; Journal de Phys., xli, p. 51.
36. If a and b denote two vectors, the vector whose components are ($a_{y}b_{z}-a_{z}b_{y},a_{z}b_{x}-a_{x}b_{z},a_{x}b_{y}-a_{y}b_{x}$) is called the vector product of a and b, and is denoted by [a, b]. Its direction is at right angles to those of a and b, and its magnitude is represented by twice the area of the triangle formed by them.
37. If a denotes any vector, the vector whose components are ${\frac {\partial \alpha _{z}}{\partial y}}-{\frac {\partial \alpha _{y}}{\partial z}},{\frac {\partial \alpha _{x}}{\partial z}}-{\frac {\partial \alpha _{z}}{\partial x}},{\frac {\partial \alpha _{y}}{\partial x}}-{\frac {\partial \alpha _{x}}{\partial y}}$ is denoted by curl a.
38. Annales de Chimie, x1 (1820), p. 93.
39. Schweigger's Journal für Chem. u. Phys., xxix (1820), p. 364; Thomson's Annals of Philosophy, xvi (1820), p. 375.
40. Mém. de l'Acad., vi, p. 175.
41. Recueil d'observations électro-dynamiques, p. 215; and the memoir just cited, pp. 285, 370.
42. Recueil d'observations électro-dynamiques, pp. 297, 300, 371.
43. Loc. cit., p. 298.
44. The simpler form of F given in the text is, if the term in ds′ be omitted, the form given by Grassmann, Ann. d. Phys. lxiv (1845), p. 1. For further work on this subject cf. Tait, Proc. R. S. Edio. viii (1873), p. 220, and Korteweg, Journal für Math. xe (1881), p. 45.
45. See ante, p. 86.
46. Loc. cit., p. 367.
47. Abhandl. d. Berlin Akad. 1822-3; Ann. d. Phys. lxxiii (1823), pp. 115, 430; vi (1826), pp. 1, 133, 253.
    Volta had previously noticed that a silver plate whose ends were at different temperatures appeared to act like a voltaic cell.
    Further experiments were performed by James Cumming (b. 1777, d. 1861), Professor of Chemistry at Cambridge, Trans, Camb. Phil. Soc. ii (1823), p. 47, and by Antoine César Becquerel (b. 1788, d. 1878), Annales de Chimie, xxxi (1826), p. 371.
48. Ann. de Chimie, xxxix (1801), p. 103.
49. Annales de Chim., xxxix (1801), p. 203.
50. See p. 53.
51. Phil. Trans., 1821, p. 433. His results were confirmed afterwards by Becquerel, Annales de Chimie, xxxii (1826), p. 423.
52. These results had been known to Cavendish.
53. Ann. d. Phys. vi (1826), p. 459; vii. pp. 45, 117; Die Galvanische Kette mathematisch bearbeitet: Berlin, 1827; translated in Taylor's Scientific Memoirs, ii (1841), p. 401. Ci. also subsequent papers by Ohm in Kastner's Archiv für d. ges. Naturlehre, and Schweigger's Jahrbuch,
54. Ohm's theory was confirmed experimentally by several investigators, among whom may be mentioned Gustav Theodor Fechner (b. 1801, d. 1887) (Maassbestimmungen über die Galvanische Kette, Leipzig, 1831), and Charles Wheatstone (b. 1802, d. 1875) (Phil. Trans., 1843, p. 303).