294 ON THE PROPAGATION OF LIGHT 



of the medium Is parallel to the plane of polarization, agreeably 

 to the supposition first advanced by M. Cauchy. 



If we admit the existence of extraneous pressures, it will 

 be necessary in addition to the single restriction before noticed, 

 to suppose that for three plane waves parallel to three orthogonal 

 sections of our medium, and which may be denominated principal 

 sections, the wave-velocities shall be the same for any two of 

 the three waves whose fronts are parallel to these sections, pro- 

 vided the direction of the corresponding disturbances are parallel 

 to the line of their intersection. With this additional sup- 

 position, the directions of the actual disturbances by which any 

 plane wave will propagate itself without subdivision, and the 

 wave-velocities, agree exactly with those given by Fresnel, sup- 

 posing, with him, that these directions are perpendicular to the 

 plane of polarization. The last, or Fresnel's hypothesis, was 

 adopted in our former paper. But as that paper relates merely 

 to the"* intensities of the waves reflected and refracted at the 

 surface of separation of two media, and as these intensities 

 may depend upon physical circumstances, the consideration of 

 which was not introduced into our former investigations, it 

 seems right, in the present paper, considering the actual situa- 

 tion of the theory of light, when the partial differential equations 

 on which the determination of the motion of the luminiferous 

 ether depends are yet to discover, to state fairly the results of 

 both hypotheses. 



It is hoped the analysis employed on the present occasion 

 will be found sufficiently simple, as a method has here been 

 given of passing immediately and without calculation from the 

 function due to the internal forces of our medium to the equation 

 of an ellipsoidal surface, of which the semi-axes represent in 

 magnitude the reciprocals of the three wave-velocities, and in 

 direction the directions of the -three corresponding disturbances 

 by which a wave can propagate itself in one medium without 

 subdivision. This surface, which may be properly styled the 

 ellipsoid of elasticity, must not be confounded with the one 

 whose section by a plane parallel to the wave's front gives the 

 reciprocals of the wave-velocities, and the corresponding direc- 



