FRESNEL ON DOUBLE REFRACTION. 309 



periment gives immediately the difference between the numbers 

 of the undulations performed within the thickness of the plates ; 

 whence it is easy to conclude immediately the difference of route 

 of the two systems of waves, since these numbers are equal to 

 the thickness of the plate divided by the two lengths of undula- 

 tion, or the two velocities measured perpendicularly to the plane 

 of the waves, whatever besides may be the obliquity of the rays 

 to the surface of the waves. Suppose, for example, that a plate 

 of crystal with parallel faces AB FD (fig. 11) is traversed per- 

 pendicularly by a beam of light coming from a point so distant 

 that we may consider as a plane the small extent of the incident 

 wave A B, which undergoes refraction : the refracted wave will 

 be in all its successive positions ^. , , 

 plane and parallel to A B ; conse- 

 quently it will be sufficient to know 

 the velocity of propagation of this 

 wave measured along C D perpen- 

 dicularly to A B, to ascertain what 

 relative time it has employed in tra- 

 versing the thickness of the plate, 



or what number of undulations it 

 has performed in it. It is useless 

 to calculate the oblique direction 



E D, by which the refracted rays have arrived at D, opposite the 

 slit T made in the screen ; but if this route were known, instead 

 of employing the velocity deduced from the equation to which we 

 have referred, and in which it is supposed to be reckoned on the 

 normal to the wave, it would be necessary to make use of the 

 velocity given by equation (D.), where it is reckoned on the direc- 

 tion of the ray E D, and we should evidently arrive at the same 

 result. 



Definition of the word " Ray." 



The word "ray" in the wave theory must always be applied 

 to the line which goes from the centre of the wave to a point of 

 its surface, whatever besides may be the inclination of this line 

 to the element on which it abuts, as Huygens has remarked ; 

 for this line offers, in fact, all the optical properties of that which 

 is called the ray in the emission system. Hence, when it is 

 wished to translate the results of the former theory into the lan- 

 guage of the latter, it must always be supposed that the line 



