229 
Royal Irish Academy, 
oscillations of the barometer in Ireland be confirmed by the experi- 
ments of other observers, it will either lead to new views of this 
phsenomenon 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 MacCullagh 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 
vibrations 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 
known 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 crystal 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 
where rj, are the displacements at the time ^ of a particle whose 
co-ordinates are x, y, z, and where the density of the aether is sup- 
posed to be unity, as being constant for all media, the author deter- 
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 
