282 
MR. MACQUORN RANKINE ON AXES OF 
30. Mutual Independence of the Euthytatic and Heterotatic Axes, and of the Homotatic 
and Heterotatic Coefficients. 
The fifteen Homotatic Coefficients of the Biquadratic Surface, on which the 
Euthytatic Axes depend, and the six Heterotatic Differences, coefficients of the 
Heterotatic Ellipsoid, constitute twenty-one independent quantities ; so that the 
Euthytatic Axes may possess any kind or degree of symmetry or asymmetry, and the 
Heterotatic Axes any other kind or degree, in the same solid. 
Hence if it be true that crystalline form depends on the arrangement of Euthytatic 
Axes, it follows that two substances may be exactly alike in crystalline form, and yet 
differ materially in the laws of their elasticity, owing to differences in their respective 
Heterotatic Coefficients. 
It may be observed, however, that this complete independence of those two systems 
of axes and coefficients is mathematical only ; and that their physical dependence or 
independence is a question for experiment. 
31. On Real and Alleged Diffierences between the Laws of the Elasticity of Solids, and 
those of the Luminiferous Force. 
For every conceivable system of tasinomic coefficients in a solid, the plane of 
polarization of a wave of distortion is that which includes the direction of the 
molecular vibration and the direction of its propagation, being, in fact, the plane of 
distortion. 
On the other hand, it appears to be impossible to avoid concluding, from the laws 
of the Diffraction of Polarized Light, as discovered by Professor Stokes, and from 
those of the more minute phenomena of the reflexion of light, as investigated 
theoretically by M. Cauchy and experimentally by M. Jamin, that in plane-polarized 
light the plane of polarization is perpendicular to the direction of vibration, or rather 
(to avoid hypothetical language) to the direction of some physical phenomenon whose 
laws of communication are to a certain extent analogous to those of a vibratory 
movement. 
This constitutes an essential difference between the laws of the Elastic Forces in a 
solid, and those of the luminiferous force. 
In order to frame, in connexion with the wave-theory of light, a mechanical 
hypothesis which should take that difference into account, it has been proposed to 
consider the elasticity of the luminiferous medium to be the same in all substances, 
and for all directions, or Pantatically Isotropic, and to ascribe the various retardations 
of light to variations in the inertia of the mass moved in luminiferous waves, in dif- 
ferent substances, and for different directions of motion*. 
Anotlier essential difference between the laws of Solid Elasticity and those of the 
* Philosophical Magazine, June 1851, December 1853. 
