In the twenty years which have elapsed since the first appearance of Maxwell's Treatise on Electricity and Magnetism great progress has been made in these sciences. This progress has been largely—perhaps it would not be too much to say mainly—due to the influence of the views set forth in that Treatise, to the value of which it offers convincing testimony.

In the following work I have endeavoured to give an account of some recent electrical researches, experimental as well as theoretical, in the hope that it may assist students to gain some acquaintance with the recent progress of Electricity and yet retain Maxwell's Treatise as the source from which they learn the great principles of the science. I have adopted exclusively Maxwell's theory, and have not attempted to discuss the consequences which would follow from any other view of electrical action. I have assumed throughout the equations of the Electromagnetic Field given by Maxwell in the ninth chapter of the second volume of his Treatise.

The first chapter of this work contains an account of a method of regarding the Electric Field, which is geometrical and physical rather than analytical. I have been induced to dwell on this because I have found that students, especially those who commence the subject after a long course of mathematical studies, have a great tendency to regard the whole of Maxwell's theory as a matter of the solution of certain differential equations, and to dispense with any attempt to form for themselves a mental picture of the physical processes which accompany the phenomena they are investigating.

1.] The influence which the notation and ideas of the fluid theory of electricity have ever since their introduction exerted over the science of Electricity and Magnetism, is a striking illustration of the benefits conferred upon this science by a concrete representation or ‘construibar vorstellung’ of the symbols, which in the Mathematical Theory of Electricity define the state of the electric field. Indeed the services which the old fluid theory has rendered to Electricity by providing a language in which the facts of the science can be clearly and briefly expressed can hardly be over-rated. A descriptive theory of this kind does more than serve as a vehicle for the clear expression of well-known results, it often renders important services by suggesting the possibility of the existence of new phenomena.

The descriptive hypothesis, that of displacement in a dielectric, used by Maxwell to illustrate his mathematical theory, seems to have been found by many readers neither so simple nor so easy of comprehension as the old fluid theory; indeed this seems to have been one of the chief reasons why his views did not sooner meet with the general acceptance they have since received. As many students find the conception of ‘displacement’ difficult, I venture to give an alternative method of regarding the processes occurring in the electric field, which I have often found useful and which is, from a mathematical point of view, equivalent to Maxwell's Theory.

35.] The importance which Maxwell attached to the study of the phenomena attending the passage of electricity through gases, as well as the fact that there is no summary in English text books of the very extensive literature on this subject, lead me to think that a short account of recent researches on this kind of electric discharge may not be out of place in this volume.

Can the Molecule of a Gas be charged with Electricity?

36.] The fundamental question as to whether a body if charged to a low potential and surrounded by dust-free air at a low temperature will lose any of its charge, and the very closely connected one as to whether it is possible to communicate a charge of electricity to air in this condition, have occasioned considerable divergence of opinion among physicists.

Coulomb (Mémoïres de l'Académie des Sciences, 1785, p. 612), who investigated the loss of electricity from a charged body suspended by insulating strings, thought that after allowing for the leakage along the supports there was a balance over, which he accounted for by a convective discharge through the air; he supposed that the particles of air when they came in contact with a charged body received a charge of electricity of the same sign as that on the body, and that they were then repelled by it. On this view the molecules of air, just like small pieces of metal, can be charged with electricity.