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 based upon Faraday’s fundamental law of induction, that the rate of change of the total magnetic flux linked with a conductor is a measure of the electromotive force created in it (see ). Maxwell also introduced in this connexion the notion of the vector potential. Coupling together these ideas he was finally enabled to prove that the propagation of electric and magnetic force takes place through space with a certain velocity determined by the dielectric constant and the magnetic permeability of the medium. To take a simple instance, if we consider an electric current as flowing in a conductor it is, as Oersted discovered, surrounded by closed lines of magnetic force. If we imagine the current in the conductor to be instantaneously reversed in direction, the magnetic force surrounding it would not be instantly reversed everywhere in direction, but the reversal would be propagated outwards through space with a certain velocity which Maxwell showed was inversely as the square root of the product of the magnetic permeability and the dielectric constant or specific inductive capacity of the medium.

These great results were announced by him for the first time in a paper presented in 1864 to the Royal Society of London and printed in the ''Phil. Trans.'' for 1865, entitled “A Dynamical Theory of the Electromagnetic Field.” Maxwell showed in this paper that the velocity of propagation of an electromagnetic impulse through space could also be determined by certain experimental methods which consisted in measuring the same electric quantity, capacity, resistance or potential in two ways. W. E. Weber had already laid the foundations of the absolute system of electric and magnetic measurement, and proved that a quantity of electricity could be measured either by the force it exercises upon another static or stationary quantity of electricity, or magnetically by the force this quantity of electricity exercises upon a magnetic pole when flowing through a neighbouring conductor. The two systems of measurement were called respectively the electrostatic and the electromagnetic systems (see ). Maxwell suggested new methods for the determination of this ratio of the electrostatic to the electromagnetic units, and by experiments of great ingenuity was able to show that this ratio, which is also that of the velocity of the propagation of an electromagnetic impulse through space, is identical with that of light. This great fact once ascertained, it became clear that the notion that electric phenomena are affections of the luminiferous ether was no longer a mere speculation but a scientific theory capable of verification. An immediate deduction from Maxwell’s theory was that in transparent dielectrics, the dielectric constant or specific inductive capacity should be numerically equal to the square of the refractive index for very long electric waves. At the time when Maxwell developed his theory the dielectric constants of only a few transparent insulators were known and these were for the most part measured with steady or unidirectional electromotive force. The only refractive indices which had been measured were the optical refractive indices of a number of transparent substances. Maxwell made a comparison between the optical refractive index and the dielectric constant of paraffin wax, and the approximation between the numerical values of the square of the first and that of the last was sufficient to show that there was a basis for further work. Maxwell’s electric and magnetic ideas were gathered together in a great mathematical treatise on electricity and magnetism which was published in 1873. This book stimulated in a most remarkable degree theoretical and practical research into the phenomena of electricity and magnetism. Experimental methods were devised for the further exact measurements of the electromagnetic velocity and numerous determinations of the dielectric constants of various solids, liquids and gases, and comparisons of these with the corresponding optical refractive indices were conducted. This early work indicated that whilst there were a number of cases in which the square of optical refractive index for long waves and the dielectric constant of the same substance were sufficiently close to afford an apparent confirmation of Maxwell’s theory, yet in other cases there were considerable divergencies. L. Boltzmann (1844–1907) made a large number of determinations for solids and for gases, and the dielectric constants of many solid and liquid substances were determined by N. N. Schiller (b. 1848), P. A. Silow (b. 1850), J. Hopkinson and others. The accumulating determinations of the numerical value of the electromagnetic velocity (v) from the earliest made by Lord Kelvin (Sir W. Thomson) with the aid of King and McKichan, or those of Clerk Maxwell, W. E. Ayrton and J. Perry, to more recent ones by J. J. Thomson, F. Himstedt, H. A. Rowland, E. B. Rosa, J. S. H. Pellat and H. A. Abraham, showed it to be very close to the best determinations of the velocity of light (see ). On the other hand, the divergence in some cases between the square of the optical refractive index and the dielectric constant was very marked. Hence although Maxwell’s theory of electrical action when first propounded found many adherents in Great Britain, it did not so much dominate opinion on the continent of Europe.

—With the publication of Clerk Maxwell’s treatise in 1873, we enter fully upon the fourth and modern period of electrical research. On the technical side the invention of a new form of armature for dynamo electric machines by Z. T. Gramme (1826–1901) inaugurated a departure from which we may date modern electrical engineering. It will be convenient to deal with technical development first.

Technical Development.—As far back as 1841 large magneto-electric machines driven by steam power had been constructed, and in 1856 F. H. Holmes had made a magneto machine with multiple permanent magnets which was installed in 1862 in Dungeness lighthouse. Further progress was made in 1867 when H. Wilde introduced the use of electromagnets for the field magnets. In 1860 Dr Antonio Pacinotti invented what is now called the toothed ring winding for armatures and described it in an Italian journal, but it attracted little notice until reinvented in 1870 by Gramme. In this new form of bobbin, the armature consisted of a ring of iron wire wound over with an endless coil of wire and connected to a commutator consisting of copper bars insulated from one another. Gramme dynamos were then soon made on the self-exciting principle. In 1873 at Vienna the fact was discovered that a dynamo machine of the Gramme type could also act as an electric motor and was set in rotation when a current was passed into it from another similar machine. Henceforth the electric transmission of power came within the possibilities of engineering.

Electric Lighting.—In 1876, Paul Jablochkov (1847–1894), a Russian officer, passing through Paris, invented his famous electric candle, consisting of two rods of carbon placed side by side and separated from one another by an insulating material. This invention in conjunction with an alternating current dynamo provided a new and simple form of electric arc lighting. Two years afterwards C. F. Brush, in the United States, produced another efficient form of dynamo and electric arc lamp suitable for working in series (see : Electric), and these inventions of Brush and Jablochkov inaugurated commercial arc lighting. The so-called subdivision of electric light by incandescent lighting lamps then engaged attention. E. A. King in 1845 and W. E. Staite in 1848 had made incandescent electric lamps of an elementary form, and T. A. Edison in 1878 again attacked the problem of producing light by the incandescence of platinum. It had by that time become clear that the most suitable material for an incandescent lamp was carbon contained in a good vacuum, and St G. Lane Fox and Sir J. W. Swan in England, and T. A. Edison in the United States, were engaged in struggling with the difficulties of producing a suitable carbon incandescence electric lamp. Edison constructed in 1879 a successful lamp of this type consisting of a vessel wholly of glass containing a carbon filament made by carbonizing paper or some other carbonizable material, the vessel being exhausted and the current led into the filament through platinum wires.