Royal hisJi Academy. ■ 229 



oscillations of the barometer in Ireland be confirmed by the experi- 

 ments of other observers, it will either lead to new views of this 

 phEenomenon generally, or show that the quantity of aqueous va- 

 pour existing in Ireland is so great as to cause the horary barome- 

 tric oscillations to present themselves in a different form from that 

 in which they are recognised in drier climates. 



The author adverted, in the last place, to the hypothesis of 

 Priestley and Beccaria, — that the upper regions of our atmosphere 

 were the chief depositories of the electric fluid, — an opinion which 

 he conceived must fall, if the origin of atmospheric electricity be 

 due (as his experiments prove) to the existence of vapour ; as these 

 elevated parts of our atmosphere are far above the region of per- 

 manent vapour, or even of vapour at all. 



Professor MacCuUagh read a paper " on the Dynamical Theory 

 of crystalline Reflexion and Refraction." 



In a former paper, presented to the Academy in January, 1837, 

 and printed in volume xviii. of the Transactions, the author had 

 reduced all the complicated phsenomena of reflexion and refrac- 

 tion at the surfaces of crystals to the utmost regularity and order, 

 by means of a simple rule, comprised in his theorem of the polar 

 plane. This rule, which was verified by its agreement with exact 

 experiments, he had deduced from a set of hypotheses relative to the 

 \'ibrations of light in their passage through a given medium, and 

 out of one medium into another ; but he had not attempted to ac- 

 count for his hypotheses, nor to connect them together by any 

 knowTi principles of mechanics ; and the only evidence in favour of 

 their truth, was the truth of the results to which they led. He 

 had observed, however, that these hypotheses were not independent 

 of each other ; he had ascertained that the laws of reflexion at the 

 surface of a crj^stal were connected with the laws of propagation in 

 its interior ; and he had thence been led to conclude that all these 

 laws and hypotheses " had a common source in other and more inti- 

 mate laws not yet discovered." He became impressed, in short, 

 with the idea, " that the next step in physical optics would lead to 

 those higher and more elementary principles by which the laws 

 of reflexion and the laws of propagation are linked together as parts 

 of the same system." 



This step the author has now made ; and the present paper 

 realizes the anticipations scattered through the former. Setting 

 out with the general dynamical theorem expressed by the equation 



f/fdxdy^^(^Jl+'^^Jn+^J^\=^fffdxdydz6x, (1). 



where ^,7^, '(, are the displacements at the time f of a particle whose 

 co-ordinates are x, y, z, and where the density of the sether is sup- 

 posed to be unity, as being constant for all media, the author detei*- 

 mines the form of the function v, for the particular case of luminife- 

 rous vibrations, by means of the property which may be regarded as 

 distinguishing them from all others — namely, that they take place 



