134 Mr GREEN, ON THE PROPAGATION OF LIGHT 



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 <p. 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 ve- 

 locities 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 C 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, b — 0, c = 0, and the equation (8) of our ellipsoid becomes 



1 = iux* + A (x 2 + f + z 2 ) + Mz 2 + Ny 2 -, 



and that of a section by a plane through its centre parallel to the wave's 

 front, will be 



1 = {A + N)y* + (A + M) z 2 ; 



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

 polarized waves will be 



V 'A + iV. The disturbance being parallel to the axis of y. 



\/A + M. to the axis of x. 



Similarly, if the plane of the wave's front is parallel to the plane 

 (xz), the wave-velocities are, 



\/B + JV. The disturbance being parallel to the axis x. 



y/ B -t- L. to the axis z. 



Or, if the plane of the wave's front is parallel to (xy), the velo- 

 cities are, 



V C + M. The disturbance being parallel to x. 



W+L y. 



