IN CRYSTALLIZED MEDIA. 305 



a plane wave to propagate itself without subdivision, and the 

 velocity of propagation parallel to its own front. The change 

 of position here made in the elliptical section, is evidently 

 equivalent to supposing the actual disturbances of the ethereal 

 particles to be parallel to the plane usually denominated the 

 plane of polarization. 



This hypothesis, at first advanced by M. Cauchy, has since 

 been adopted by several philosophers ; and it seems worthy of 

 remark, that if we suppose an elastic medium free from all 

 extraneous pressure, we have merely to suppose it so constituted 

 that two of the wave-disturbances shall be accurately in the 

 wave's front, agreeably to Fresnel's fundamental hypothesis, 

 thence to deduce his general construction for the propagation of 

 waves in biaxal crystals. In fact, we shall afterwards prove 

 that the function < 2 , which in its most general form contains 

 twenty-one coefficients, is, in consequence of this hypothesis, 

 reduced to one containing only seven coefficients; and that, from 

 this last form of our function, we obtain for the directions of 

 the disturbance and velocities of propagation precisely the same 

 values as given by Fresnel's construction. 



The above supposes, that in a state of equilibrium every 

 part of the medium is quite free from pressure. When this is 

 not the case, A, B, and G will no longer vanish in the equation 

 (8). In the first place, conceive the plane of the wave's front 

 parallel to the plane (yz) then a = 1, 5 = 0, c = 0, and the equa- 

 tion (8) of our ellipsoid becomes 



* -f 



and that of a section by a plane through its centre parallel to 

 the wave's front, will be 



and hence, by what precedes, the velocities of propagation of 

 our two polarized waves will be 



+ N. The disturbance being parallel to the axis of y t 



+ M. ..................................... to the axis of z. 



20 



