FRESNEL ON DOUBLE REFRACTION. 331 



dependence of the strata of aether between which they are 

 situated, and that they may be arranged in such a manner that 

 they weaken this mutual dependence^ or elasticity of the sether, 

 more in one direction than another. 



The phaenomenon of dispersion proves that the rays of diflferent 

 colours or Avaves of different lengths do not traverse bodies with 

 the same velocity, which arises doubtless from this, that the 

 elasticity put in play by the luminous waves varies with their 

 length. When the sphere of activity of the molecular actions is 

 supposed infinitely small with regard to the extent of an undu- 

 lation, analysis shows that the elasticity by which the waves are 

 propagated does not vary with thf ir breadth [largeur) ; but 

 this is no longer true when the mutual dependence of the mole- 

 cules extends to a sensible distance with regard to the length of 

 an undulation. It is easy to prove that, in this case, the elasti- 

 city put in play is rather less for narrow waves [etroites) than 

 for broader waves, and that consequently the former must be 

 propagated rather more slowly than the second, conformably to 

 experiment*. It hence results that the three semi-axes a, b, c, 

 w-hich represent the square roots of the elasticities put in play 

 by the parallel vibrations, or the corresponding velocities of pro- 

 pagation, must vary a little for waves of different breadths [lar- 

 geurs), according to the theory as well as to experiment ; now it 

 is possible that this variation may not take place according to 

 the same ratio between the three axes, in which case the angle 

 formed by the two circular sections of the ellipsoid with each 

 other, and therefore the angle between the two optic axes, 

 may no longer be the same for rays of different colours, as Sir 

 David Brewster and Sir J. Herschel have remarked in the greater 

 number of bi-axal ciystals. 



The phaenomenon of dispersion has perhaps yet other causes 

 than that which we have just indicated ; but whatever they may 

 be, we must still conclude from the observations of these two 

 skilful experimenters, that the lengths of the semi-axes {a), (b), 

 (c) do not vary in the same ratio for waves of different breadths 

 [largeurs) in crystals where the optic axes change their direction 



♦ The demonstration of this consequence of the theory forms the object of 

 Note II. at the end of the memoir. [There are no notes at all to the memoir. 

 Prof. Lloyd, in liis Report on Physical Optics to the British Association, has 

 remarked that "this demonstration is more than once referred to by the author 

 as contained in a note appended to Iiis memoir on double refraction. The note, 

 however, probably by some oversight, has never been printed." — Trans.] 



