122 Mr GREEN, ON THE PROPAGATION OF LIGHT 



in the front of the wave. This fundamental principle of FresnePs Theory 

 gives fourteen relations between the twenty-one constants originally enter- 

 ing into our function ; and it seems worthy of remark, that when 

 there are no extraneous pressures, the directions of polarization and the 

 wave-velocities given by our theory, when thus limited, are identical 

 with those assigned by Fresnel's general construction for biaxal crystals ; 

 provided we suppose the actual direction of disturbance in the particles 

 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 ne- 

 cessary, 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 foi» any two of the three waves whose fronts 

 are parallel to these sections, provided the direction of the corresponding 

 disturbances are parallel to the line of their intersection. With this 

 additional supposition, 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, supposing, 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 inten- 

 sities 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 situation 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- 



