in MacCullagh's theory the difference between the contiguous media is represented by a difference of their elastic constants, 80 in the electromagnetic theory it may be represented by a difference in their specific inductive capacities. From a letter which Maxwell wrote to Stokes in 1864, and which has been preserved,[1] it appears that the problem of reflexion and refraction was engaging Maxwell's attention at the time when he was preparing his Royal Society memoir on the electromagnetic field; but he was not able to satisfy himself regarding the conditions which should be satisfied at the interface between the media. He seems to have been in doubt which of the rival elastic-solid theories to take as a pattern; and it is not unlikely that he was led astray by relying too much on the analogy between the electric displacement and an elastic displacement.[2] For in the elastic-solid theory all three components of the displacement must be continuous across the interface between two contiguous media; but Maxwell found that it was impossible to explain reflexion and refraction if all three components of the electric displacement were supposed to be continuous across the interface; and, unwilling to give up the analogy which had hitherto guided him aright, yet unable to disprove[3] the Greenian conditions at bounding surfaces, he seems to have laid aside the problem until some new light should dawn upon it.
This was not the only difficulty which beset the electromagnetic theory. The theoretical conclusion, that the specific inductive capacity of a medium should be equal to the square of its refractive index with respect to waves of long period, was not as yet substantiated by experiment; and the theory of displacement-currents, on which everything else depended, was
- ↑ Stokes's Scientific Correspondence, ii, pp. 25, 26.
- ↑ It must be remembered that Maxwell pictured the electric displacement as a real displacement of a medium. "My theory of electrical forces," he wrote, "is that they are called into play in insulating media by slight electric displacements, which put certain small portions of the medium into a state of distortion, which, being resisted by the elasticity of the medium, produces an electromotive force." Campbell and Garnett's Life of Maxwell, p. 244.
- ↑ The letter to Stokes already mentioned appears to indicate that Maxwell for a time doubted the correctness of Green's conditions.
