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ROYAL IRISH ACADEMY. 
Noy. 8, 1841.—Sir Wm. R. Hamilton, LL.D., President, in the 
Chair. 
Professor MacCullagh read the following note on some points in 
the Theory of Light. 
I1.—On a Mechanical Theory which has been proposed for the Explana- 
tion of the Phenomena of Circular Polarization in Liquids, and of 
Circular and Elliptic Polarization in Quartz or Rock-crystal ; with 
Remarks on the corresponding Theory of Rectilinear Polarization. 
The theory of elliptic polarization, which I feel myself called upon 
to notice, was first stated by M. Cauchy, and has been made the sub- 
ject of elaborate investigation by other writers. That celebrated 
analyst, conceiving (though without sufficient reason, as will pre- 
sently appear) that he had fully explained the known laws of the pro- 
pagation of rectilinear vibrations by the hypothesis that the luminife- 
rous ether, in media transmitting such vibrations, consists of separate 
molecules symmetrically arranged with respect to each of three rect- 
angular planes, and acting on each other by forces which are some 
function of the distance, was led very naturally to imagine that he 
would find the laws of circular and elliptic vibrations, in other media, 
to be included in the more general hypothesis of an unsymmetrical ar- 
rangement. Accordingly, in a letter read to the French Academy 
on the 22nd of February, 1836, a letter to which he attached so much 
importance that he desired it might not only be published in the Pro- 
ceedings, but also “‘ deposited in the Archives” of that body (see the 
Comptes rendus des Séances de l Académie des Sciences, tom. ii. p.182), 
he gave a precise statement of his more extended views, informing 
the Academy that he had submitted his new theory to calculation, 
and that, among other remarkable results, he had obtained (with a 
slight variation or correction) the laws of circular polarization, dis- 
covered by Arago, Biot, and Fresnel. Referring to his Memoir on 
Dispersion, published at Prague under the title of Nouveaux Evercices 
de Mathématiques, he observes, that the results therein contained 
may be generalized, by ‘ceasing to neglect” in the, equations of 
motion [the equations marked (24) in § 2 of that memoir] certain 
terms which vanish in the case of a symmetrical distribution of the 
wether. He then goes on to say— 
“Nos formules ainsi généralisées représentent les phénoménes de 
Yabsorption de la lumiére ou de certains rayons, produite par les 
verres colorés, la tourmaline, &c., le phénoméne de la polarisation 
circulaire produite par le cristal de roche, l’huile de térébenthine, 
&c. (Voir les expériences de MM. Arago, Biot, Fresnel). Elles ser- 
vent méme a déterminer les conditions et les lois de ces phénoménes ; 
elles montrent que généralement,"dans un rayon de lumiére po- 
larisée, une molecule d’éther décrit une ellipse. Mais dans certains 
cas particuliers, cette ellipse se change en une droite, et alors on 
obtient la polarisation rectiligne.” ‘Enfin le calcul prouve que, 
dans le cristal de roche, l’huile de térébenthine, &c., la polarisation 
des rayons transmis parallélement a l’axe (s'il s’agit du cristal de 
