Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/182

 of the aether are supposed to vanish, and the vibrations of the aether are supposed to be executed parallel to the plane of polarization of the light; in the other theory, the initial stresses are not supposed to vanish, and the aether-vibrations are at right angles to the plane of polarization. The two investigations are generally known as Green's First and Second 'Theories of crystal-optics.

The foundations of both theories are, however, the same. Green first of all determined the potential energy of a strained crystalline solid; this in the most general case involves 27 constants, or 21 if there is no initial stress. If, however, as is here assumed, the medium possesses the planes of symmetry at right angles to each other, the number of constants reduces to 12, or to 9 if there is no initial stress; if e denote the displacement, the potential energy per unit volume may be written The usual variational equation