130 Mr GREEN, ON THE PROPAGATION OF LIGHT 



B >'= (Z, * F)bc, 

 E'= (M + Q) ac, 

 F' = (N + R)ab\ 



we get 



= (A'- e*)a + F'fl + E'y, 

 = F'a + (JT-/)/9 + ^7, 

 =.E'a + Z>/3 + (C- e>)y, 



(6.) 



These last equations will serve to determine three values of e", and three 

 corresponding ratios of the quantities a, /3, y, and hence we know the 

 directions of the disturbance by which a plane wave will propagate 

 itself without subdivision, and also the corresponding velocities of pro- 

 pagation. From the form of the equations (6), it is well known, that 

 if we conceive an ellipsoid whose equation is 



1 = A' a? + B'f + CV + 2D'yz + %E' x% + ZF'xy* (7.) 



and represent its three semi-axes by /•', r", and r", the directions of these 

 axes will be the required directions of the disturbance, and the corre- 

 sponding velocities of propagation will be given by 



Fresnel supposes those vibrations of the particles of the luminiferous 

 ether which affect the eye, to be accurately in the front of the wave. 



* If we reflect on the connexion of the operations by which we pass from the function 

 (4) to the equation (7), it will be easy to perceive that the right side of the equation (7) may 

 always be immediately deduced from that portion of the function which is of the second 

 degree by changing u, v and w into x, y and z. 



«i d d , d . , 



Also, -=- , -=- and -p- into a, b and c. 

 ax ay dz 



This remark will be of use to us afterwards, when we come to consider the most general 

 form of the function due to the internal actions. 



