254 FBESNEL ON DOUBLE REFRACTION. 



tained between C O and C P. Tlie same will be the case for all 

 the other points taken along the ray projected in C. Thus the 

 whole light composed of the two emergent beams will still be 

 polarized on leaving the crystal, since all its vibrations will be 

 parallel to a constant direction ; but its plane of polarization, 

 instead of coinciding with the primitive plane, as in the preceding 

 case, will be found separated from it by an angle equal to (2i). 

 It is this new direction of the plane of polarization which 

 M. Biot has called the azimuth 2 i. 



It is seen with what simplicity the theory we have set forth 

 explains how the union of two beams of light, polarized at right 

 angles, the one in a direction parallel, the other perpendicular, 

 to the principal section of a crystal, form by their reuniting a 

 light polarized in the primitive plane or in the azimuth (2 i), 

 according as the difference of route between the two beams is 

 equal to an even or uneven number of semi-undulations. We 

 cannot imagine how one could conceive, on the emission system, 

 this remarkable phaenomenon ; which nevertheless cannot be 

 called into doubt after it has been proved by an experiment so 

 decisive as that of the two rhomboids, given in the Annates de 

 Chimie et de, Physique, tom. xvii. p. 94 et seq. 



Let us consider now the case in \^ hich the difference of route 

 is no longer a whole number of semi-undulations ; then the cor- 

 responding velocities in the two systems of waves are no longer 

 applied simultaneously to the same points of the ray projected 

 in C ; the result is, that the two forces, which solicit each of 

 these points at the same instant, have not the same ratio of 

 magnitude along the whole length of the ray, and consequently 

 that their resultants are no longer in the direction of the same 

 plane; thus, the reunion of the two systems of waves presents 

 no longer the characters of polarized light. Call their difference 

 of route («) ; the constant coefficients of their absolute velocities 

 are respectively equal to cos i and sin i, taking for unity that of 

 the primitive beam, whose vibrations are performed in a direc- 

 tion parallel to P P'. 



Then, the absolute velocities excited by the two component 

 beams, in the same point of the ray projected in C, at the instant 



[t), will be cos i . sin 2 tt (/) and sin i . sin 2 tt f / j : and the 



square of the resultant of these two rectangular forces will be 

 equal to 



