Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/174

Thus it $\textstyle {\bar {B}}/{\bar {A}}$ denote the modulus of B/A, we have

$\left({\frac {\bar {B}}{\bar {A}}}\right)^{2}={\frac {\left({\frac {\rho _{2}}{\rho _{1}}}+1\right)^{2}\left({\frac {\rho _{2}}{\rho _{1}}}-{\frac {l_{1}}{l}}\right)^{2}+\left({\frac {\rho _{2}}{\rho _{1}}}-1\right)^{4}{\frac {m^{2}}{l^{2}}}}{\left({\frac {\rho _{2}}{\rho _{1}}}+1\right)^{2}\left({\frac {\rho _{2}}{\rho _{1}}}+{\frac {l_{1}}{l}}\right)^{2}+\left({\frac {\rho _{2}}{\rho _{1}}}-1\right)^{4}{\frac {m^{2}}{l^{2}}}}}$

This expression represents the ratio of the intensity of the transverse reflected wave to that the incident wave. It does not agree with Fresnel's tangent-formula: and both on this account and also because (as we shall see) this theory of reflexion does not harmonize well with the clastic-solid theory of crystal-optics, it must be concluded that the vibrations of a Greenian solid do not furnish an exact parallel to the vibrations which constitute light.

The success of Green's investigation from the standpoint of dynamics, set off by its failure in the details last mentioned, stimulated MacCullagh to fresh exertions. At length he succeeded in placing his own theory, which had all along been free from reproach so far as agreement with optical experiments was concerned, on a sound dynamical basis; thereby effecting that reconciliation of the theories of Light and Dynamics which had been the dream of every physicist since the days of Descartes.

The central feature of MacCullagh's investigation,^[1] which was presented to the Royal Irish Academy in 1839, is the introduction of a new type of elastic solid. He had, in fact, concluded from Green's results that it was impossible to explain optical phenomena satisfactorily by comparing the aether to an elastic solid of the ordinary type, which resists compression, and distortion; and he saw that the only hope of the situation was to devise a medium which should be as strictly conformable to dynamical laws as Green's elastic solid, and yet should have its properties specially designed to fulfil the requirements of the theory of light. Such a medium he now described.

If as before we denote by e the vector displacement of a point of the medium from its equilibrium position, it is well

1. Trans. Roy. Irish Acad. xxi.: MacCullagh's Coll. Works, p. 145.