The history of these subjects contains an account of the rise and fall of a multiplicity of theories; of these the earlier consisted mainly of crude conceptions in which effluvia fluids and corpuscles played their part. These theories were designed to appeal to familiar images of the sensuous imagination. Later on the same rivalries are to be found as we have already observed in other branches of Physical Science between the notions of action at a distance action by contact and propagation through media. Such theories imperfect contradicting one another and sometimes even self-contradictory served in various degrees the all-important functions of fixing the direction of future observation of facts and of predicting results by which the theories could be verified or refuted. This subjection of rival theories to the law of the survival of the fittest is an essential element in the life of Natural Science.

In ancient times the sole knowledge of Electricity and Magnetism was confined to the facts that amber ἤλεκτρον when rubbed has the power of attracting light substances and that a certain iron are (λίθος μαγνη̑τις) has the power of attracting small pieces of iron. The use of the magnetic needle for indicating directions at sea was known at the time of the crusades and it appears also to have been known in China at an early period. One discovery of importance was made in the thirteenth century by Petrus Peregrinus; that of the polarity of the natural magnet or loadstone. Experimenting with a loadstone of globular shape Peregrinus showed by placing needles in contact with it in various positions all over the surface that the positions of the needles all pointed towards two points at opposite ends of the stone; and these points he proposed to call the poles. He then observed that the way in which magnets set themselves and attract each other depends only on the position of the poles as if the magnetic power were concentrated in these points. No corresponding increase of knowledge of electric phenomena was obtained until the sixteenth century; these were known only as a few bare facts connected with amber and one or two other substances. The first considerable increase of knowledge both of electric and magnetic phenomena was due to the researches of William Gilbert (1540–1603) of Colchester. He made the highly important discovery that the orientation of magnets may be accounted for by regarding the earth itself as a great magnet with its poles in high northern and southern latitudes in accordance with the general principle that the north-seeking pole of every magnet attracts the south-seeking pole of every other magnet and repels its north-seeking pole. In Electricity Gilbert discovered that a whole class of bodies such as glass sulphur sealing-wax etc. have the same property as amber that of being electrified by friction. The contrast in various respects between magnetic and electric forces which Gilbert observed especially in respect of screening and polarity led him to set up the theory that electrical phenomena are due to an atmosphere of effluvia round an electrified body; the effluvia consisting of material liberated from the body by the process of friction. As he regarded action at a distance as inconceivable the effluvia provided for the necessary contact with the attracted bodies in analogy with his view of the phenomena of falling bodies as due to the atmosphere acting as an effluvium by means of which the earth draws all bodies towards itself. This theory was generally accepted by those Natural Philosophers of the period who were interested in the subject but there was some difference of opinion amongst them as to the manner in which the effluvia acted on the neighbouring small bodies. Gilbert himself imagined that the effluvia had an inherent tendency to return to the body from which they emanated. Moreover the fact that electrified bodies exercise repulsion as well as attraction did not remain unobserved. Notwithstanding the rise of the Newtonian theory of gravitation which shattered that emanation theory of falling bodies which had suggested the emanation theory of electricity the latter theory remained unaffected into the eighteenth century.

The first attempt to set up a theory of Magnetism was due to Descartes who connected it with his general theory of vortices. He postulated the existence of vortex of fluid matter round the magnet; this fluid entering the magnet at one pole and leaving it at the other. The fluid matter was regarded as acting upon iron on account of resistance offered by the particles of iron to the motion of the fluid. Even in the eighteenth century Euler and two of the brothers Bernoulli worked out theories of magnetism based upon the hypothesis of vortices.

A very important discovery that of conduction of Electricity was published in 1729 by Stephen Gray a pensioner of the Charterhouse who showed as he describes in his own words:

No other mode of electrification than that by friction had been previously known. It was found that this property of conduction belongs only to a certain class of bodies especially to metals. To these bodies Desaguliers in 1736 gave the name of non-electrics or conductors. The view that electric effluvia are inseparably connected with the body that has been rubbed became untenable in consequence of the discovery of conduction; and thus the notion of an electric fluid of an imponderable character was substituted for the effluvium; and this fluid came to be regarded as one of the chemical elements although it was thought by some Physicists to be closely connected with caloric the substance of which heat was then supposed to consist. This last idea was refuted by an experiment of Stephen Gray who showed that the electrification of two similar bodies one of which was solid and the other hollow produced exactly similar effects. From this it was concluded that only the surface of a body has to do with its electrification whereas caloric is diffused through the whole substance of the body. The next important discovery made by Charles Francois du Fay (1698–1739) was that there are two species of electrification. He showed that an electrified body repels another one that has been electrified in the same way as itself but that two bodies whose electricities are of different species attract one another. To the two kinds of electricity the existence of which his experiments proved he gave the names “vitreous” and “resinous” by which they are still known. In 1745 Pieter van Musschenbroek (1692–1761) a Professor at Leyden as the result of an attempt to prevent the electric charge of a body from undergoing the decay which had been observed to take place when the charged body is surrounded by air was led to the discovery of the Leyden phial or jar as a means of accumulating the effect of electrification; at the same time the physiological effect of the discharge of the phial through the human body was discovered. Soon after this discovery a London apothecary William Watson in the course of experiments with the Leyden jar and its discharge was led to propound in 1746 the theory that the phenomena are due to the presence of an “electrical aether” which is transferred but not created or destroyed during the process of charging and discharging the Leyden jar. In accordance with his theory the electrification of a body is due to its receiving at the expense of some other body an excess of electric fluid over the normal amount that belongs to the body; the fluid in the other body being correspondingly depleted. The two species of electrification correspond on this theory respectively to an excess or a defect of the electric fluid belonging to the body that is electrified.

The same theory was independently proposed a few months later by Benjamin Franklin (1706–1790) of Philadelphia as the result of various experiments. The principle of Watson and Franklin may be stated as that of the conservation of electric charge indicating that in any isolated system the total quantity of electric fluid is invariable. In view of this principle Franklin was led to regard electrification as being either positive or negative according as it denoted an excess or defect of electric fluid in the electrified body; he attributed the positive sign to vitreous and the negative sign to resinous electricity. In considering the theory of the Leyden jar Franklin was led to assume that the glass in the jar is impenetrable to the electric fluid although the attractive effect between one electrified body and another body is not destroyed by interposing a glass plate between them. He was thus led to the idea that the surface of the glass nearest the electrified body is able to influence its other surface through the glass and that this effect then accounts for the influence on the other body. In the case of the jar the excess of fluid on the inner face exercises through the glass a repulsion which causes a defect of fluid on the outer face. This interpretation of fact was in accordance with a theory the one-fluid theory of electricity which unlike the older conception of effluvia involved the notion of action at a distance. The view that glass is impermeable to the electric fluid was extended by Aepinus (1724–1802) so as to apply to all non-conductors. In order to account for the repulsion between two resinously charged bodies Aepinus who also held the one-fluid theory set up the hypothesis that the particles of ordinary matter repel each other but that when bodies are unelectrified this repulsive force is balanced by the attraction which he like Franklin assumed to exist between matter and electric fluid. He suggested that gravitation might be due to a slight inequality between these attractive and repulsive forces. He applied his theory to the explanation of the induction of electric charges a phenomenon which had been previously observed by others and had been studied a little earlier by John Canton (1718–1772) and by Wilcke.

I have spoken of the facts known at an early period relating to electricity and magnetism as trivial. There is however one phenomenon that cannot be so described although it fortunately occurs only occasionally. I mean the phenomenon of lightning in thunderstorms. The important discovery that lightning is an electric phenomenon akin to the spark observed when a Leyden jar is discharged is due to Benjamin Franklin. Experimenting during thunderstorms with kites he was able to establish the electric character of the occurrence by charging a Leyden jar by means of electricity conducted from the kite.

The discovery of the law of force between two electric charges was made by Joseph Priestley (1733–1804) the discoverer of Oxygen. He showed experimentally that when a hollow metal vessel is electrified there is no charge on the inner surface and no electric force in the interior; and he inferred from this fact that the law of force is that of the inverse square of the distance the same as that of gravitation. This discovery of Priestley taken in conjunction with Franklin's law of the conservation of electric charge brought the phenomena of Electrostatics for the first time to a completeness of description sufficient to render them accessible to Mathematical calculation. The first to take advantage of the possibility of applying calculation to electrical phenomena was the Hon. Henry Cavendish (1731–1810). In a memoir presented in 1771 to the Royal Society he adopted the one-fluid theory of Aepinus and Franklin which he had however discovered independently. In this memoir he assumed the law of electric force between charges to be inversely as some less power of the distance than the cube and virtually introduced under the term intensity of electrification the notion of the potential which later became fundamental in electrical theory although its use was hindered by the fact that he did not definitely assume the law of force to be that of the inverse square. Unfortunately Cavendish's researches remained for the most part unknown until 1879 when they were published at the instance of Lord Kelvin who had examined the manuscripts. It then appeared that Cavendish had not only rediscovered the law of the inverse square but had even determined the correct value for the ratio of the electric charges carried by a circular disc and a sphere of the same radius in metallic connection with one another; thus he introduced the conception of electrostatic capacity. Moreover he anticipated the later discovery by Faraday of specific inductive capacity and investigated experimentally the conducting powers of different materials for electrostatic discharges.

Whilst the progress I have described of knowledge of electric phenomena was made the subject of Magnetism had not been neglected. The law of force between magnetic poles was discovered by John Michell (1724–1793) a Fellow of Queens' College Cambridge who published his researches in 1750. It had been previously believed that the attraction between opposite poles followed a different law from that of the repulsion between like poles. A theory of magnetic fluid similar to that of the one-fluid theory of electricity was propounded in 1759 by Aepinus who regarded the two poles of a magnet as places where the magnetic fluid existed in excess and in defect of the normal amount respectively. He supposed that the particles of the fluid repel each other but attract particles of iron and steel; moreover he saw that it was necessary to assume that the material particles of the magnet repel each other. By later investigators a two-fluid theory of magnetism was employed; these fluids were taken to have properties of attraction and repulsion similar to those of vitreous and resinous electricity.

Exact measurements both electric and magnetic were made by Charles Augustin Coulomb (1736–1806) who employed for this purpose the torsion balance. By this means he verified decisively the law that the force between two small globes charged electrically is inversely as the square of the distance between their centres and is repulsive or attractive according as the electricity is of the same or of the opposite kinds. Instead of the one-fluid theory which had been accepted as the basis of the explanation of electrostatic phenomena by Franklin Aepinus and Cavendish Coulomb postulated the existence of two fluids corresponding respectively to the two kinds of electrification. He supposed that in an uncharged body these fluids were both present in equal amounts and thus neutralized each other; but when in an electric field a decomposition of the neutral fluid takes place into equal amounts of the separated fluids which can then be separately located. The controversy which took place between the upholders of the rival one-fluid and two-fluid theories was in reality one between the merits of two conceptual descriptions of the phenomena and no experimental evidence was forthcoming which was capable of deciding between them in respect of their power of representing the facts of observation. Coulomb also verified the law of force of magnetic poles on one another by means of the torsion balance. He endeavoured to explain the fact that the two magnetic fluids unlike the two electric fluids cannot be divided between different substances so as to obtain a magnetic pole in isolation. He propounded the view that the magnetic fluids cannot move from one molecule of the magnetic body to another so that each molecule always contains equal amounts of the two fluids which are separated within the molecule when the substance is magnetized giving rise to two poles in each molecule.

At the end of the eighteenth century the theory of effluvia in Electricity and that of vortices in Magnetism had been eliminated and had in each case been replaced by a theory which involved the postulation of the existence of either one or two fluids and in which the notion of attractive and repulsive forces acting at a distance was a fundamental element. The Sciences had now arrived at a point which made them accessible to Mathematical Analysis. A complete mathematical development of Electrostatics on the basis of the two-fluid theory was published in 1812 by Simeon Denis Poisson (1781–1840). He showed that on the basis of the theory of attractions and repulsions between particles of the fluids which were supposed capable of moving freely in conductors there is no electric force in the interior of the conductor; and that a charge of such a body which consists of an excess of one kind of fluid over the other distributes itself over the surface of the conductor as a layer of which the thickness at every point depends upon the shape of the surface. He showed that in simple cases it is possible to determine the distribution of electricity over the surface of the conductor; and for these purposes he transferred to electric theory various results which had been obtained in the theory of gravitational attraction in which the same law of force is involved as in the case of electricity. Of special importance was the introduction into electrostatics of the potential function which had been previously introduced into gravitational theory by Lagrange who showed that an attractive force at a point can be expressed as the gradient of this unction. In all later developments of electricity and in their practical applications this notion of potential or of potential difference has proved to be of fundamental importance; upon it depends the whole theory of the distribution of electrical charges upon conductors and it was seen later that this is but a small part of the function which this conception fulfils in electrical theory. In 1824 Poisson published a corresponding complete mathematical theory of Magnetism of which the notion of the potential is the basis. He showed that the effect of a magnetized body can be represented by fictitious surface- and volume-distributions of magnetic matter. At the same time he gave a theory of the temporary magnetization induced in a body made of soft iron by the approach of a permanent magnet. Very important developments and extensions of the mathematical theory of electricity and of magnetism were published in 1828 by George Green (1793–1841) to whom the term potential is due which has ever since been employed to designate the function introduced into the theory by Lagrange and Poisson. The celebrated theorem known as Green's theorem was established in this memoir; of this theorem Poisson's resolution of the effect of magnetization of a body into the sum of parts due to surface- and volume-distributions is simply a particular case.

The theories of Electrostatics and of Magnetism had now been so far developed that they had been subsumed under schemes of conceptual description which represented the ascertained facts and which were sufficient for mathematical calculation of the details of the phenomena in cases which were sufficiently simple and for the ascertainment in the form of mathematical theorems of a variety of the more general aspects of those phenomena. The stage of development of Electrical Science in general which comes next for consideration arose from the discovery in the latter part of the eighteenth century of a set of phenomena belonging to a quite new class.

Luigi Galvani Professor of Anatomy at Bologna by an accidental observation made in 1780 whilst dissecting a frog was led to the discovery that if the nerves and the muscles of the frog are connected by a metallic arc formed of more than one kind of metal the limbs of the frog became violently convulsed. He was led to the conclusion that this was due to a flow of electric fluid and he considered the phenomenon as essentially similar to what happens when a Leyden jar is discharged. This view did not receive universal acceptance; some physicists thinking that this so-called galvanism or animal electricity was a fluid different from the electric fluid which was regarded as functioning in electrostatic phenomena. In 1792 the opinion was maintained by Alessandro Volta (1745–1827) Professor at Pavia that the essential element in Galvani's experiment was the connection of two different metals by a moist body and that the supposed animal electricity due to the nervous system of the frog had nothing to do with the phenomenon. Shortly afterwards Fabroni of Florence placed two plates of different metals in water and observed that when they were put in contact one of them became partially oxidized; from this he concluded that some chemical action is connected with the galvanic phenomenon. In 1800 Volta showed that the galvanic effect could be made much greater by constructing a pile in which a number of pairs of zinc and copper discs were used each pair being separated from the next by a disc of moist pasteboard. This pile is the parent of the battery employed in electric telegraphy. A distinct shock could be felt when the highest and the lowest discs were simultaneously touched by the fingers; and it appeared that this shock could be repeated any number of times. As the result of this and further experiments Volta set up his electrical theory of the pile as due to the contact of each copper disc with a zinc disc the pasteboard discs acting merely as conductors. He recognised the existence of a continuous electric current so long as the circuit is completed by joining the highest and lowest discs. When Volta's discovery had been communicated in 1800 to Sir Joseph Banks president of the Royal Society Volta's experiment was repeated by Nicholson and Carlisle who having placed a drop of water on the upper plate of the pile in order to make the electric contact of the highest and lowest discs more efficient observed that round the wire there was at the drop of water a disengagement of gas. They then introduced a tube of water into which the wires from the two terminals of the pile were immersed and observed that an inflammable gas hydrogen was liberated at one wire whilst the other became oxidized.

This observation of the effect of the decomposition of the water constituted the great discovery of electrolysis which was soon extended to the decomposition of various metallic salts in solution. It was shown by Wollaston that water could be decomposed by the discharge of frictional electricity thus identifying the currents of the electricity of Volta's currents with those of frictional electricity. There were two views as to the mode in which the current in the pile is produced the so-called contact theory that it is due to molecular action between the two different metals in contact with one another and the chemical theory that it is due to chemical action involving oxidation of the zinc in the pile. The chemical theory was supported by Humphry Davy (1778–1829) Professor of Chemistry at the Royal Institution. He showed that there is no current when the water between the pair of plates is quite pure and that their power of action is in great measure proportional to the power of the conducting fluid between the plates to oxidize the zinc. Davy afterwards proposed a theory of the voltaic pile in which the contact and chemical actions were both recognized as contributing to the effect; the contact of the metals disturbing equilibrium whilst the chemical changes in the liquid constantly tend to restore the conditions under which the contact energy is exerted. He was led to make the assertion that chemical affinity is essentially electrical in its nature. A comprehensive chemical theory of the electric current and of chemical combination was advanced by the Swedish chemist Berzelius (1779–1848) dependent on the hypothesis of the existence of electric charges within the atoms of matter. This was an anticipation in some respects of conceptions which have become of fundamental importance in recent decades although the detailed theory of Berzelius did not survive him. He was inclined to regard both electricity and caloric as substances devoid of gravitation but possessing affinity to gravitating substances.

So far as I have at present proceeded in the account of the gradual increase of knowledge of electrical and magnetic phenomena no connection between the two sets of phenomena had been exhibited. A discovery made in 1820 by the Danish physicist Hans Christian Oersted (1777–1851) produced in its ultimate implications a revolutionary effect upon the whole future of the Sciences of Electricity and Magnetism exhibiting as it did the closest connection between the two sets of phenomena. It had been for some time suspected that an electric discharge has an effect upon the magnetic needle but Oersted was the first to demonstrate its existence by his observation that a magnetic needle when placed in the neighbourhood of a continuous electric current in a straight wire parallel to the needle tends to set itself at right angles to the wire. It thus appeared that the phenomenon of an electric current could not be localized entirely in the conducting wire but had an effect which spread itself through the surrounding space and produced an alteration in the orientation of the magnetic needle. Oersted's discovery was described at a meeting of the French Academy shortly after it was made and this led to further investigation by physicists. Two of these Biot and Savart shortly afterwards announced their discovery of the law of force of the straight current upon the magnetic pole; that the force on a pole is at right angles to the plane through the wire and the pole and its intensity is inversely proportional to the distance of the pole from the wire. It was shown by Arago that a magnetic field produced by an electric current may be employed in the same manner as one produced by a magnet to induce magnetization in iron and thus that an electric current is a magnet.

Almost immediately after Oersted's discovery had become known André Marie Ampére (1775–1836) showed that two parallel wires carrying currents attract each other when the currents are in the same direction and repel each other when the currents are in opposite directions. Ampére set himself the work of developing a complete theory of the pondero-motive forces which act between circuits carrying electric currents on the basis of the conception of forces acting at a distance between pairs of elements of the two currents. He showed in particular that an electric circuit is equivalent in its magnetic effects to what is called a magnetic shell that is a distribution of elementary magnets on a surface bounded by the circuit with the axes of the magnets normal to that surface. He regarded magnetism as essentially an electrical phenomenon; each magnetic molecule being looked upon as having a small closed circuit within it in which a permanent electric current flows. Ampére succeeded in developing upon this basis a complete mathematical theory of the mechanical interaction of circuits carrying electric currents that is of electromagnets. Of this theory Maxwell wrote¹ several decades later:

The theory of Ampére is like the similar theories developed later by Grassmann Stefan and Korteweg based upon the conception of action at a distance; no account being taken of the medium between the electric circuits. The essential assumption in these theories is that the whole effect of one circuit on another can be represented as the resultant effect of forces acting between pairs of elements of the two circuits. These theories differ from one another in respect of the nature of the forces which they assume to act between pairs of elements but they all agree in representing the actual forces between complete circuits which alone can be submitted to the direct test of observation. They make no explicit use of the principle of the conservation of energy and indeed that principle would imply the existence of couples between pairs of elements which are not taken into account in Ampére's theory. Ampére's theory cannot accordingly be regarded as a dynamical theory although it like the other theories of the same type affords a sufficient representation of the interaction of complete circuits. Theories of another type which also take no account of the medium between the circuits were developed later by Gauss W. E. Weber Riemann and Clausius. These represent the action of currents by assuming that the forces acting at a distance between electrified bodies depend upon the velocities and accelerations of those bodies. In all these theories except that of Clausius Fechner's hypothesis is adopted that an electric current consists of a flow of positive electricity in one direction and a flow of negative electricity with the same velocity and of equal amount in the opposite direction. They differ from one another in respect of the law of force which they assume to exist between pairs of moving elements of electricity. The theories of Weber and Clausius unlike that of Gauss are consistent with the principle of the conservation of energy and consequently suffice to represent the induction of currents as well as the mechanical forcive between the circuits.

Another theory of electrodynamical forces was developed by F. E. Neumann and extended by Helmholtz. This was a dynamical theory based upon the assumption of a law of the mutual energy between elements of currents but like those I have hitherto mentioned it took no account of the dielectric medium. The power possessed by different metals to conduct electric currents was investigated by Humphry Davy but a complete theory of this conduction was formulated by George Simon Ohm (1787–1854) based upon a large amount of experimental work. Ohm compared the flow of electricity in a current with the flow of heat in a wire of which the theory had been given in a complete form by Fourier in his Analytical Theory of Heat. He introduced the notion of electroscopic force as a conception which plays a part analogous to that of temperature in the conduction of heat. Tension or difference of electroscopic force at two places in a conductor he regarded as effective in producing a current between those places just as conduction of heat is dependent on difference of temperature. Each voltaic cell he regarded as possessing a definite tension which is a contribution to the driving force of a current in any circuit in which it is placed. He did not however relate differences of electroscopic force with differences of potential (or as we now say with electromotive force) as that conception appears in Poisson's theory of electrostatics. Notwithstanding this defect the publication of what has since been known as Ohm's law constituted a considerable advance in knowledge of the conduction of electric currents and much of the later development of the subject up to the middle of the nineteenth century was dependent upon it.

A complete transformation of the whole manner in which the phenomena of Electricity and Magnetism are conceived was the ultimate result of the researches of Michael Faraday whose genius as an experimental investigator in accordance with the inductive method has certainly never been surpassed and perhaps never been equalled. Only a study of his great work the Experimental Researches can lead to a just appreciation of the profound insight which led him to the discovery of a multitude of facts in an orderly succession under the guidance of novel conceptions radically different from those which had guided previous investigators. Upon his discoveries rest ultimately not only the modern theory of Electromagnetic Science but also in its practical applications the Science of electrical engineering as we know it. The first question which Faraday set himself was to discover whether an electric current in one circuit can induce a current in another circuit in analogy with the known fact of Electrostatics that a charged conductor induces a charge in neighbouring conductors. In 1831 he published a memoir in which he gave an account of the answer he had obtained to this question. He found that such a current was in fact induced but that it lasted only for an instant when the primary current was started or stopped; no induced current existing whilst the primary current flowed steadily. With a view to a formulation of the laws of the induction of currents he took the step of concentrating his attention on the dielectric or nonconducting medium which surrounded the circuits thus initiating the breach with the older conception that the phenomena are localized in the conductors in accordance with the notion of action at a distance; with Faraday the phenomena are localized mainly in the dielectric. He constructed for his guidance the conception of lines of force which he conceived to fill the space in the neighbourhood of magnets or electromagnets; the direction of each such line at any point being that of the magnetic force which would act upon a magnetic pole at that point. Every such line of force he regarded as a closed curve which at some part of its length passed through the magnet or electromagnet with which it was associated. These lines of force he conceived to form unit tubes of force such that for any one tube the product of its cross-section into the magnetic force is constant along its whole length. In this manner he formed an intuitional geometrical representation of the phenomena of magnetism which assisted greatly in directing his investigations. On the basis of his experiments he obtained a formulation of the law of induction of currents in circuits–that the electromotive force induced in a circuit is measured by the rate of change of the number of unit tubes which pass through the circuit. The full import of this important result was only understood later when the theory of electromagnetic induction was formulated mathematically by Maxwell and others A few years later this fruitful discovery was followed by that of self-conduction in which the effect of the electromotive force in an electric circuit due to a change in the magnitude of a current through that same circuit was established. Faraday also completed the identification of currents as exhibited by an electrostatic discharge with those due to voltaic cells by showing that the magnetic calorific and other effects are the same in the two cases. A very important set of Faraday's investigations were concerned with the chemical decomposition in the cells leading to a statement of the quantitative laws of electrolysis. In this connection he made the statement of great significance at the present day that” the atoms of matter are in some way endowed or associated with electrical powers to which they owe their most striking qualities and amongst them their mutual chemical affinity.”

The concentration of Faraday's attention on the dielectric media was rewarded by the discovery that such a medium has a definite specific inductive capacity the magnitude of which is different for various dielectric substances. He regarded electrostatic induction as consisting of a certain polarized state of the particles of the medium similar to that which precedes the decomposition of an electrolyte into which they are thrown by the inducing surfaces or particles. This state of polarization disappears when the inducing force is removed; it can exist continuously only in insulators because a conductor is incapable of retaining this state of its particles; an immediate discharge taking place if it be set up in the conductor.

Among many other investigations of Faraday were those connected with his discovery of diamagnetism and his investigations of the magnetization of crystals to which attention had been called by the discovery made by Plücker of the University of Bonn that certain uniaxal crystals placed between the poles of a magnet tend to set themselves so that the optic axis has the equatorial position.

One surmise of Faraday is of extreme interest in view of its later realization in the hands of his great disciple and successor James Clerk Maxwell. In 1851 Faraday suggested that if the hypothesis of a luminiferous ether be admitted that ether may have other uses than simply the conveyance of radiant light and heat. He had in 1845 made the important discovery that the plane of polarization of a ray of light is rotated when it passes through a magnetic field when the polarized ray passes in the direction of the lines of magnetic force. This established a direct connection between optical and electromagnetic phenomena and is of the highest interest in view of the later amalgamation of the theories of light and electromagnetism. It was found by Joule in 1841 that the amount of heat evolved in a given time in a wire through which a current is passing is proportional to the resistance of the wire and to the square of the strength of the current that is to the product of the current into the electromotive force on the wire. This enabled him to perfect the theory which had been developed by Roget and Faraday that the chemical energy derived from the cell has its equivalent in work done in the outer part of the circuit. Thus the amount of energy transformed from the potential energy of chemical affinity into an electrical form has its equivalent in the heat evolved and dissipated in the circuit and in any work done otherwise in connection with the outer circuit. It was however shown by Kelvin and Helmholtz that the electrical energy furnished by a voltaic cell need not be derived exclusively from the chemical energy of the cell but may also depend upon the abstraction of energy from neighbouring bodies which is also converted into electrical energy. Helmholtz applied also the principle of energy to the case of systems containing electric currents and showed that the phenomenon of magneto-electric induction can thus be taken into account. His theory was however defective in that he did not take into account the electro-kinetic energy of the currents themselves.

It was largely to the researches of Lord Kelvin that the complete theories of the magnetic and electromagnetic fields are due. He introduced into Magnetism the distinction between the vectors afterwards named by Maxwell the magnetic force and the magnetic induction and he extended his theory to take account of magneto-crystallic phenomena. Ohm's theory of linear conduction of currents was generalized by Kirchhoff (1824–1887) to include the case of conduction in three dimensions the analogy with Fourier's theory of the conduction of heat being useful for this purpose. Kirchhoff showed that in a system of conductors the currents so distribute themselves as to produce the minimum amount of heat. Hitherto there had been no complete identification between the electroscopic force of Ohm and difference of electrostatic potential; this hiatus in electric theory was filled up in 1849 by Kirchhoff.

The theoretical investigations of Electrical Science in the last half century have in a very large degree been dominated by the conceptions of James Clerk Maxwell and by the mathematical formulation of the phenomena in the electromagnetic field to which he was led by those conceptions. The modes of geometrical representation of the state of the electromagnetic field which were devised by Faraday and which guided him in his researches show that his mode of thinking was essentially of a mathematical kind and indeed he possessed constructive mathematical power of a high order. He lacked however that command of the technique of Mathematical Analysis the possession of which enabled Maxwell to follow out Faraday's conception of the localization of the phenomena in the dielectric medium surrounding conducting substances and to develop in mathematical form the geometrical notion which Faraday employed of lines of force and by an enrichment of Faraday's ideas with conceptions of his own to give a dynamical theory of the electromagnetic field. In this work he was appreciably influenced by the ideas and mathematical analogies contained in the work of Lord Kelvin. In particular he accepted Kelvin's idea that Magnetism is essentially a phenomenon of rotation in the form of the conception that in a magnetic field there is rotation of the medium about the lines of magnetic force and that electric currents are to be regarded as a phenomenon of translation.

One of his most fundamental conceptions is that an electrostatic field involves “electric displacement” in the direction of the lines of force and that when the field is varied the variation of this electric displacement whatever precise interpretation the term may receive must be regarded as an electric current. This notion of electric displacement is a development of the notion of Faraday that in a ponderable dielectric there is an actual displacement of electric charge on the small conducting particles of which he assumed the dielectric to consist; whereas with Maxwell the displacement occurs even in free ether devoid of ponderable matter. Maxwell was thus led to one of his most characteristic assumptions that every current forms a closed circuit; thus a current employed in charging a condenser is closed being completed by the displacement-current in the dielectric between the coatings of the condenser. Another fundamental conception of Maxwell's scheme is that magnetic energy is the kinetic energy of a medium occupying the whole of space whilst electric energy is to be regarded as the energy of a system of strains of the same medium. In his great memoir A Dynamical Theory of the Electromagnetic Field published in 1864 he gave his theory in the form of equations connecting vectors in the electromagnetic field. In his treatise published in 1871 he gave a fuller account of his theory of stresses in the ether and in dielectrics but he was not completely successful in conceiving a mechanism by which such systems of stresses could be sustained. Space will not allow me to give even in outline an account of Maxwell's various investigations in this great branch of Physics or of the very important developments of the subject made by his successors. I accordingly turn to the great step which Maxwell made in the unification of Science when he set up his electromagnetic theory of light. The theory of Optics has a long and intensely interesting history but I must confine myself to a summary account of the later stages of that history leading up to the state of the subject when Maxwell introduced his great unification.

The first Natural Philosopher who made any advance upon the crude Cartesian theory of light as consisting of a propagation of pressure not of motion through a set of globules which constitute space was Robert Hooke (1635–1703) one of the founders of the Royal Society. He appears to have initiated the wave theory of light: regarding light as consisting of a system of minute vibrations propagated in a medium or ether. He introduced the notion of a wave surface as a sphere with centre at the luminous point and he made an attempt on these principles to explain reflection and refraction. On the other hand Newton supposed light not to be constituted by the vibrations of an ether although he regarded such vibrations as existing in close connection with light but by streams of corpuscles emitted by luminous bodies; the various colours being due to differing corpuscles which excite vibrations of differing types in the ether. One side of Newton's views of the matter constituted the celebrated emission theory which was for a long time the rival of the wave theory. The important fact was established by Roemer in 1675 that light requires a finite time for its transmission.

The undulatory theory was greatly improved by Christian Huygens (1629–1695) who gave satisfactory accounts on that basis of the phenomena of reflection and refraction and who explained the varying velocity of light in different substances. He concerned himself with the study of the double refraction of light by such crystals as Iceland spar; and explained the phenomenon as due to the propagation of two waves in the crystal with different fronts a sphere and a spheroid. The ultimate triumph of the wave theory over the rival emission theory was largely due to the labours of Thomas Young (1773–1829) who showed that the former theory gives the more satisfactory explanation of the phenomena of reflection and refraction of interference fringes in shadows of the colours of thin plates and of the behaviour of light in crystals. The important discovery of polarization by reflection at the surface of water at a certain angle was made by Etienne Louis Malus (1775–1812) who showed that such a reflected ray has the same peculiarities as one of the rays which has suffered double refraction. The discovery of biaxal crystals is due to David Brewster (1781–1868). The vibrations of the ether were for the most part conceived as longitudinal in the direction of propagation of the light on the analogy of sound-waves. The important step was taken by Augustin Fresnel (1788–1827) of conceiving the vibrations to be in a direction perpendicular to that of the direction of propagation of the light. His theory the first attempt at the construction of a dynamical theory of the phenomena was the first of a series of theories based upon the view that the ether behaves more like an elastic solid and not like a compressible fluid. Fresnel supposed that no longitudinal wave exists and that in a polarized pencil the direction of the vibrations is perpendicular to the plane of polarization. A celebrated instance of the power of prediction even of an imperfect theory such as that of Fresnel is the fact that it enabled Sir William Rowan Hamilton to predict the occurrence of conical refraction in which a single ray proceeding in a crystal in a certain direction would on emergence give rise to a whole bundle of rays forming a conical surface; this prediction was verified experimentally by Humphry Lloyd of Dublin. Investigators were confronted with the difficulty that the ether appears to behave like an elastic solid in relation to such rapid vibrations as those of light but at the same time to yield freely to such comparatively slow motions as those of the planets; that there is no necessary inconsistency involved in this was pointed out by Stokes who referred to the analogy of such substances as pitch and shoemaker's wax which have both rigidity and plasticity. The exigencies of the theory of the luminiferous ether naturally led to mathematical investigation of the vibrations which can be propagated in elastic solids. Theories of such vibrations were given by Navier Cauchy and Poisson the last of whom established the existence of two types of wave one transverse and the other longitudinal propagated with different velocities both of which he determined in terms of the elastic constants of the medium. In 1828 this theory was so extended by Cauchy as to take account of crystalline substances. The difficulties in the way of conceiving a type of medium in which the vibrations propagated would accord with the known properties of light especially the difficulties as regards the conditions which would hold at the interface of two media led to the development of further theories of the matter by James MacCullagh (1809–1847) by F. E. Neumann (1798–1895) and by George Green. MacCullagh developed the theory of a new kind of medium endowed with rotational elasticity; this theory appears to be sound as a dynamical theory and to accord with the properties of light; Kelvin afterwards devised a model to illustrate this kind of rotational elasticity. From the point of view of Dynamics the theory of George Green was superior to the pre-existing theories but the vibrations of Green's type do not accord very well with optical phenomena. Cauchy in a 'later theory which he advanced in 1839 introduced a type of ether! so designed that longitudinal waves are suppressed; this type of ether was designated by Lord Kelvin labile ether.

At this stage the difficulties in the way of conceiving a substantial ether as the vehicle of conveyance of light in a manner capable of being completely represented in accordance with a dynamical scheme had become parallel to the corresponding difficulties relating to electromagnetic phenomena. The great merit of Maxwell consists in his perception that the difficulties of both departments can be concentrated upon a single scheme. He showed that in his electromagnetic medium electromagnetic oscillations can be propagated with a velocity in agreement with the known velocity of light. He established the fact that his equations of the electromagnet field accord with the formulation obtained by the elastic-solid theory and that it thus affords a general explanation of metallic reflection. There still remained various difficulties which Maxwell did not completely overcome and these have led to a great amount of subsequent investigation; but that light is to be regarded as an electromagnetic phenomenon to be investigated as a portion of the phenomena of electromagnetism has been generally accepted by all recent investigators. The discovery by Hertz in the light of this order of ideas of the long waves employed in wireless telegraphy identical in most respects except their physiological properties with those of light is a striking example of the value of the unification of ideas which is due to Maxwell.

Amidst the differences of opinion which have prevailed as to the precise manner in which electromagnetic phenomena may be best conceived Maxwell's equations remain endowed with an undoubted power of representation of what can be actually observed. It would appear that the time may have arrived at which the scaffolding constituted by notions of a substantial ether with properties difficult to formulate precisely and consistently may be removed. The theory of electro-magnetism and of light would then have reached the stage of abstraction in which the electromagnetic field would be regarded solely as a field of vectors distributed and changing in accordance with definite mathematical laws; the notion of a substantial ether having served its purpose as a guide and been superseded by a more highly abstract scheme in which all such models are discarded. If this be done the theory will have reached the high stage of abstraction towards which all conceptual theories tend as they approach completion. The development of such a theory necessarily involves the previous existence of a series of attempts to represent the phenomena by means of sensuous images which always contain elements of inadequacy and often of contradiction. The existence of a series of successive grades of abstraction is a law of the mental evolution of scientific theories. The question whether this gradual increase of abstractness in scientific theories represents a recession from or an approach towards “reality” in any metaphysical sense of the term is a question which will receive differing answers from Philosophers of different schools. Natural Science has no direct concern with the answer which may be given to such a question.