FRESNEL, ON DOUBLE REFRACTION. 251 



fraction, which have been calculated on the supposition that the 

 vibrations of the interfering raj^s were performed in a common 

 direction. 



I come now to the third principle of interference of polarized 

 rays. When two portions of a luminous beam, which had at 

 first the same plane of polarization, PP', receive a new polariza- 

 tion in two different planes, OO' and EE', and are afterwards 

 brought back to a common plane 

 of polarization, SS' or TT', their 

 agreement or disagreement answers 

 precisely to the difference of the 

 routes described, when the two 

 planes of polarization OC and E'C, 

 starting from the primitive direc- 

 tion CP, after having been sepa- 

 rated one from the other, approach 

 each other afterwards by a contrary 

 movement so as to reunite in CS; but 

 when the two planes CO and CE' continue to widen their distance 

 from each other until they become situated one on the pro- 

 longation of the other, in CT and CT' for example, it is no 

 longer sufficient to take into account the difference of paths de- 

 scribed ; it is necessary also to change the signs of the absolute 

 velocities of one of the interfering beams by giving a contrary 

 sign to their constant coefficient, or, which comes to the same 

 thing, adding a semi-undulation to the difference of paths 

 described. 



It is easy to see the reason of this rule. In order not to com- 

 plicate the figure, we shall suppose that the lines there drawn, 

 instead of representing the planes of polarization, indicate the 

 direction of the luminous vibrations which are perpendicular to 

 those planes. This is as if we had turned the figure thi'ough a 

 quarter of a circumference round its centre C ; which alters 

 nothing in the relative positions of the planes of polarization. 

 Let us consider, at any point whatever of the luminous ray pro- 

 jected in C, the absolute velocity which animates the astherial 

 molecules at a given instant in the primitive beam, whose vibra- 

 tions are performed in the direction PP' ; and suppose that at 

 this instant the molecule C is pushed from C towards P, that is 

 to say, that its absolute velocity acts in the direction CP, its 

 components along CO and CE' will act, one in the direction CO, 



