385 



January IS* 1840. 



SIR Wm. R. HAMILTON, LL. D., President, in the Chair. 



Sir Philip Crampton, Bart., William J. Lloyd, Esq., 

 and John Mollan, M. D. were elected members of the 

 Academy. 



Professor Mac Cullagh made a communication respecting 

 the optical Laws of Rock-crystal (Quartz). 



In a paper read to the Academy in February 1836, and 

 published in the Transactions, (vol. xvii. p. 461,) he had 

 shown how the peculiar properties of that crystal might be 

 explained, by adding, to the usual equations of vibratory 

 motion, certain terms depending on differential coefficients 

 of the third order, and containing only one new constant c. 

 This hypothesis, which was very simple in itself, not only 

 involved as consequences all the laws that were previously 

 known, but led to the discovery of a new one — the law, 

 namely, by which the ellipticity of the vibrations depends 

 on the direction of the ray within the crystal. He was not 

 able, however, to account for his hypothesis, nor has it 

 since been accounted for by any one. 



But the theory developed in the paper which he read at 

 the last meeting of the Academy, now enables him to assign, 

 with a high degree of probability, the origin of the addi- 

 tional terms above-mentioned, and, if not to account for 

 them mechanically, at least to advance a step higher in the 

 inquiry. In that theory it was supposed, (and the sup- 

 position holds good in all known crystals, except quartz,) 

 that the molecules of the ether vibrate in right lines, the 

 displacements remaining always parallel to each other as the 

 wave is propagated ; and it was shown that the function v, 

 by which the motion is determined, then depends only on 

 the relative displacements of the molecules. But when this 



