on the Unduhtory Hypothesis of Light. 477 



Since e 2 , which measures the elasticity of the refracting medium, 

 is extremely small compared with cc> which measures the elas- 

 ticity of the aether, and since we have shown that y- is a nega- 

 tive quantity, it follows that the right-hand side of this equation 

 is negative. Hence, the variations of e 2 and jn having opposite 

 signs, the greater the elasticity of the medium the less the refrac- 

 tive index, and therefore the greater the velocity of propagation 

 in the medium. 



From the foregoing argument we may conclude generally, that 

 the velocity of transmission of light in any diaphanous medium 

 depends in part on the elasticity of the medium. 



But experiments have been considered to indicate that the 

 elasticity of certain crystals is different in different directions; 

 and it may reasonably be supposed that this is generally the case 

 in regularly crystallized bodies. We have therefore now to 

 inquire what effect this circumstance may have on the trans- 

 mission of light in crystals. In the first place, from the facts of 

 crystallography it may be presumed that the elasticity is in some 

 manner connected with atomic arrangement. It does not seem 

 possible to account for planes of cleavage on any other principle. 

 If, then, the atomic arrangement should be such as to be sym- 

 metrical about any straight line drawn parallel to a fixed direc- 

 tion in the crystal, it seems to be a necessary consequence that 

 the elasticity of the crystal will be the same in all directions 

 perpendicular to that line. For instance, in a uniaxal crystal, 

 as Iceland spar, the elasticities in directions perpendicular to the 

 crystallographical axis would all be equal. But it is allowable 

 to make a more comprehensive supposition respecting the atomic 

 arrangement. We may suppose it to be symmetrical with respect 

 to three planes drawn always parallel to three fixed planes at 

 right angles to each other in the crystal. Taking the intersec- 

 tion of the planes for the axes of coordinates, if a surface be 

 described such that a radius vector drawn in any direction from 

 the origin represents the elasticity of the crystal in that direction, 

 the above-mentioned condition of symmetry of atomic arrange- 

 ment would require the equation of this surface to be of the form 

 z 2 =f(x~, ?/ 2 ). Hence, as the elasticity (e 2 ) is a function of the 

 radius vector (r), we have 



This equality shows that e may have a maximum or minimum 

 value independently of the forms of the functions </> and/. For by 

 differentiating, 



