143 



efficients multiplied by the same constant c, this constant 

 having opposite signs in the two equations. The quantities 

 % and i) are, at any time t, the displacements parallel to the 

 axes of a; and y, which are supposed to be the principal di- 

 rections in the plane of the wave, one of them being there- 

 fore perpendicular to the axis of the crystal. The constants 

 A and B are given by the expressions 



A = a^, B = a^ — (o^ — b"^) sin ^j//, 



where « and b are the principal velocities of propagation, 

 ordinary and extraordinary, and t// is the angle made by the 

 wave-normal (or the direction of ^) with the axis of the crys- 

 tal. The only new constant introduced is c, which, though 

 the peculiar phenomena of quartz depend entirely on its ex- 

 istence, is almost inconceivably small ; its value is determined 

 in the paper just referred to. The equations are there proved 

 to .afford a strict geometrical representation of the facts ; not 

 only connecting together all the laws discovered by the dis- 

 tinguished observers to whom M. Cauchy refers, and in- 

 cluding the subsequent additions for which we are indebted 

 to Mr. Airy, but leading to new results, one of which esta- 

 bhshes a relation between two different classes of pheno- 

 mena, and is verified by the experiments of M. Biot and Mr. 

 Airy. Having, therefore, such conclusive proofs of the truth 

 of these equations, we are entitled to assume them as a 

 standard whereby to judge of any theory ; so that any me- 

 chanical hypothesis which leads to results inconsistent with 

 them may be at once rejected. 



Now I assert that the mechanical hypothesis of M. 

 Cauchy contradicts these equations, and therefore contra- 

 dicts all the phenomena and experiments which he supposed 

 it to represent. But before we proceed to the proof of this 

 assertion, it may perhaps be proper to remark, that pre- 

 viously to the date of M. Cauchy's communication, and of my 

 own paper, I had actually tried and rejected this identical 



