As to direct measurements on electric waves, there were none; the value of the velocity with which, if Maxwell’s theory were true, they must travel had been determined from electrical observations of quite a different character. Weber and Kohlrausch had measured the value of K for air, for which μ is unity, and from their observations it follows that the value of the wave velocity for electro-magnetic waves is about 31 × 10⁹ centimetres per second. The velocity of light was known, from the experiments of Fizeau and Foucault, to have about this value, and it was the near coincidence of these two values which led Maxwell to write in 1864:—
“The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electro-magnetic disturbance propagated through the field according to electro-magnetic laws.”
By the time the first edition of the “Electricity and Magnetism” was published, Maxwell and Thomson (Lord Kelvin) had both made determinations of K, and had shewn that for air at least the resulting value for the velocity of electro-magnetic waves was very nearly that of light.
For other substances at that date the observations were fewer still. Gibson and Barclay had determined the specific inductive capacity of paraffin, and found that its square root was 1·405, while its refractive index for long waves is 1·422. Maxwell himself thought that if a similar agreement could be shewn to hold for a number of substances, we should be warranted in concluding that “the square root of K, though it may not be the complete expression for the index of refraction, is at least the most important term in it.”
Between this time and Maxwell’s death enough had been done to more than justify this statement. It was clear from the observations of Boltzmann, Silow, Hopkinson, and others that there were many substances for which the square root of the specific inductive capacity was very nearly indeed equal to the refractive index, and good reason had been given why in some cases there should be a considerable difference between the two.
Hopkinson found that in the case of glass the differences were very large, and they have since been found to be considerable for most solids examined, with the exception of paraffin and sulphur. For petroleum oil, benzine, toluene, carbon-bisulphide, and some other liquids the agreement between Maxwell’s theory and experiment is close. For the fatty oils, such as castor oil, olive oil, sperm oil, neatsfoot oil, and also for ether, the differences are considerable.
It seems probable that the reason for this difference lies in the fact that, in the light waves, we are dealing with the wave velocity of a disturbance of an extremely short period. Now, we know that the substances mentioned shew optical dispersion, and we have at present no completely satisfactory theory from which we can calculate, from experiments on very short waves, what the velocity for very long waves will be. In most cases Cauchy’s formula has been used to obtain the numbers given. The value of K, however, as found by experiment, corresponds to these infinitely long waves, and to quote Professor J. J. Thomson’s words, “the marvel is not that there should not be substances for which the relation K = μ² does not hold, but that there should be any for which it does.”[66]
It has been shewn, moreover, both by Professor J. J. Thomson himself and by Blondlot, that when the value of K is measured under very rapidly varying electrifications, changing at the rate of about 25,000,000 to the second, the value of the inductive capacity for glass is reduced from about 6·8 or 7 to about 2·7; the square root of this is 1·6, which does not differ much from its refractive index. The values of the inductive capacity of paraffin and sulphur, which it will be remembered agree fairly with Maxwell’s theory, were found to be not greatly different in the steady and in the rapidly varying field.
On the other hand, some experiments of Arons and Rubens in rapidly varying fields lead to values which do not differ greatly from those given by other methods. The theory, however, of these experiments seems open to criticism.
To attempt anything like a complete account of modern verifications of Maxwell’s views and modern developments of his theory is a task beyond our limits, but an account of Maxwell written in 1895 would be incomplete without a reference to the work of Heinrich Hertz.