January 13, 1840. 
SIR Wa. 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 
