58 FBESNEL ON THE COLOURS PRODUCED IN 



may consequently suppose all their principal sections inclined 

 at an angle of 45° to the plane of primitive polarization, so 

 that their planes of entrance or of exit coincide with that plane. 

 1 shall suppose, for example, that they are the planes of en- 

 trance. Having thus turned all the principal sections in the 

 same direction, we may suppress all the 

 planes of entrance and of exit, excepting 

 the first and last. The first coincides with 

 P P' by hypothesis, and the last, repre- 

 sented in the figure by N N', is perpen- 

 dicular to it. Let RR' be the plane in 

 which the light is twice reflected in the 

 glass parallelopiped, after having traversed 

 the oil of turpentine ; let, lastly, S S' be the principal section of 

 the rhomboid of calcareous spar with which the colours are 

 produced. I represent the angle P C R by r, and the angle 

 PCS by i. 



The plane of entrance, coinciding with that of primitive po- 

 larization, does not modify the light. By the double refraction 

 of the particles it is divided into two systems of waves, polarized, 

 the one in the principal section O O', the other in the perpen- 

 dicular plane E E'. If F represents the velocity of the aetherial 

 molecules in the vibrations of the incident pencil, their veloci- 

 ties, in the ordinary and extraordinary waves, will be 



\/fF. and y^l.F, 



P.O. P . E'. 



and e always representing the numbers of the ordinary and 

 extraordinary undulations completed in the oil of turpentine by 

 the kind of rays under consideration. By the action of the plane 

 of exit N N', each of these pencils divides itself into two others, 

 which gives in all the four following pencils : 



-F , , -F -F j-i -F 



2 »+i' 2 ' 2 2 ' 



P.O.N. P.O. P. P.E'.N'. P.E'.P. 



The double reflexion in the glass parallelopiped divides then 

 each of these four pencils into two others, polarized, the one in 

 the plane of reflexion R R', the other in the perpendicular plane 

 T T'. Lastly, by the action of the rhomboid of calcareous spar, 

 each of these eight pencils is divided into two others, polarized 



