[61] It is difficult to explain without analysis exactly what is measured by Maxwell’s Vector Potential. Its rate of change at any point of space measures the electromotive force at that point, so far as it is due to variations of the electric current in neighbouring conductors; the magnetic induction depends on the first differential coefficients of the components of the electro-tonic state; the electric current is related to their second differential coefficients in the same manner as the density of attracting matter is related to the potential it produces. In language which is now frequently used in mathematical physics, the electromotive force at a point due to magnetic induction is proportioned to the rate of change of the Vector Potential, the magnetic induction depends on the “curl” of the Vector Potential, while the electric current is measured by the “concentration” of the Vector Potential. From a knowledge of the Vector Potential these other quantities can be obtained by processes of differentiation.
[62] The 4 π is introduced because of the system of units usually employed to measure electrical quantities. If we adopted Mr. Oliver Heaviside’s “rational units,” it would disappear, as it does in (B).
[63] For an exact statement as to the relation between the directions of the lines of electric displacement and of the magnetic force, reference must be made to Professor Poynting’s paper, Phil. Trans., 1885, Part II., pp. 280, 281. The ideas are further developed in a series of articles in the Electrician, September, 1895. Reference should also be made to J. J. Thomson’s “Recent Researches in Electricity and Magnetism.”
[64] Preface to Newton’s “Principia,” 2nd edition.
[65] “Lezioni Accademiche” (Firenze, 1715), p. 25.
[66] In his sentence μ stands for the refractive index.
[67] Hertz’s papers have been translated into English by D. E. Jones, and are published under the title of Electric Waves.
[68] Some of the consequences of this electrical resonance have been very strikingly shown by Professor Oliver Lodge. See Nature, February 20th, 1890.
[69] Hertz’s original results were no doubt affected by waves reflected from the walls and floor of the room in which he worked. An iron stove also, which was near his apparatus, may have had a disturbing influence; but for all this, it is to his genius and his brilliant achievements that the complete establishment of Maxwell’s theory is due.
[70] The analogy does not consist only in the agreement between the more or less accurately measured velocities. The approximately equal velocity is only one element among many others.