FRESNEL ON DOUBLE REFRACTION'. 257 



the right or left of that of the system of waves succeeding {en 

 arriere), the difference of route being equal to a quarter of an 

 undulation^ or to a whole number of undulations plus a quarter; 

 it is the inverse when this difference is three-quarters of an 

 undulation, or a whole number of undulations plus three- 

 quarters. 



There are certain refracting media, such as rock-crystal in the 

 direction of its axis, the essential oil of turpentine, of lemons, 

 &c., which have the property of not transmitting with the same 

 velocity the circular vibrations from right to left and those from 

 left to right. Such a result may be conceived to arise from a 

 particular constitution of the refracting medium or of its inte- 

 grant molecules, which produces a difference between the direc- 

 tion from right to left and that from left to right; such would 

 be, for example, a helicoidal arrangement of the molecules of the 

 medium, which would offer contrar}' properties according as the 

 helices were dextrorsum or sinistrorsum. 



The mechanical definition which we have just given of circular 

 polarization enables us to conceive how the singular double 

 refraction presented by rock-crystal in the direction of its axis 

 may take place ; namely, that the arrangement of the molecules 

 of this crystal is not the same apparently from right to left and 

 from left to right; so that the luminous beam whose circular 

 vibrations are performed from right to left puts into play an 

 elasticity or force of propagation slightly differing from that ex- 

 cited by another beam whose vibrations are perfoi'med from left 

 to right. 



Such is the principal theoretical advantage which may be de- 

 rived from the geometrical considerations we have just given on 

 the circular vibrations of light resulting from the combination 

 of rectilinear vibrations. But in the calculation of the phaeno- 

 mena presented by light polarized rectilinearly or circularly 

 after having traversed the media by which it is modified, it is 

 useless to investigate, for example, what are the curvilinear 

 vibrations resulting from the reunion of two systems of waves 

 on leaving a crystalline plate ; we are, on the contrary, obliged 

 to decompose into rectilinear motions the circular vibrations of 

 the two systems of waves emerging from a plate of rock-crystal 

 perpendicular to its axis, when we wish to determine the intensi- 

 ties of the ordinary and extraordinary images produced by this 

 emergent light across a rhomboid of calcareous spar. The cal- 



