260 SENARMONT ON THE OPTICAL CHARACTERS OP 



optical elasticity which does not coincide with an axis of sym- 

 metry, generally has a direction a little different for different 

 colours. They scarcely appear, however, to have been led to the 

 comparative investigation of the phaenomena of double refraction 

 presented by crystals similar in form but different in substance. 

 And this is the object I have had in view in the experiments I 

 am about to describe. 



Fresnel has demonstrated that the optical characters of all 

 doubly-refracting media admit of being accounted for by the 

 unequal elasticity of the aether in three fixed rectangular direc- 

 tions throughout the entire extent of that medium, which he has 

 denominated the axes of optical elasticity. The elements which 

 it is necessary to compare together for this purpose are, the posi- 

 tion of these three axes in the crystalline form, the relative values 

 of the elasticity in their three directions, and the crystallographic 

 data which define the crystal ; all of them dependent equally, 

 although perhaps in a different manner, upon the molecular con- 

 stitution and the internal structure of the crystal; and it is 

 necessary to ascertain how it happens that the different effects 

 of the same cause present themselves as functions of each other. 



Before proceeding further, it will perhaps be advisable to state 

 in a few words the definition of the optical characters which it 

 was necessary to determine. 



Let a^, U^, c^ be the three coefficients of elasticity correspond- 

 ing to the axes of optical elasticity A, B, C. The numerical 

 constants «, h, c are directly proportional to the velocities, con- 

 sequently inversely proportional to the indices of refraction of a 

 ray of light perpendicular to the axis of elasticity in question, 

 and at the same time polarized. 



Let a>h>c, then both of the optical axes are included within 

 the plane of the axes A and C of the maximum and minimum 

 elasticity, and both make with the axis A an angle a determinable 

 by the formula — 



tana = +A /^^~^\ 



The axes A and C, of maximum and minimum elasticity, there- 

 fore divide the acute and obtuse angle included between the two 

 optical axes. The line which divides the acute angle is specially 

 denominated the bisecting line. 



When therefore « is less than 45°, the bisecting hne is the 



