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]