408 — Royal Irish Academy: Prof. MacCullagh on a 
but by the scientific world generally, to have already afforded the 
only satisfactory explanation of the laws of double refraction in the 
common and well-known case where the vibrations are rectilinear. 
This supposed explanation was obtained, as has been said, by re- 
stricting the application of M. Cauchy’s principles to the hypothesis 
of a vibrating medium arranged symmetrically, in which case it was 
shown that the vibrations were necessarily rectilinear ; andof course 
the removal of this restriction was the only way in which it was 
possible, on those principles, to account for the existence of circular 
and elliptical vibrations. Accordingly, when M. Cauchy perceived 
that, on the hypothesis of unsymmetrical arrangement, the existence 
of rectilinear vibrations became impossible, and that of elliptic vibra- 
tions, generally speaking, possible, he found it very easy to persuade 
himself that he had obtained a new proof of the correctness of his 
views, and a new and most important application of the fundamental 
equations by which his general principles were analytically expressed. 
To have supposed otherwise would have been to admit that his ge- 
neral principles were false. If the elliptical or quasi-circular vibra- 
tions which he was now contemplating were not capable of being 
identified with those which had been recognized in the phenomena 
presented by quartz and the rotatory fluids—if their laws were es- 
sentially or very considerably different—his theory would be incon- 
sistent with a wide range of well-known facts, and, notwithstanding 
its so-called explanations of other laws, should be finally abandoned. 
Under these circumstances, therefore, he very naturally supposed 
that his new results must be in complete harmony with the pheno- 
mena discovered by M. Arago, and analysed so successfully by 
MM. Biot and Fresnel ; although, had he taken the precaution of ac- 
quiring such a clear notion of the phenomena as would have enabled 
him to translate them into analytical language, he must have per- 
ceived that they were entirely opposed to his results, and that this 
opposition furnished an argument which swept away the very founda- 
tions of his theory. For, if the constitution of the luminiferous me- 
dium were such as M. Cauchy supposes, the well-known phenomena 
of circular and elliptic polarization would, as we have seen, be ab- 
solutely impossible. 
Thus the argument which overturns the particular theory of el- 
liptical polarization destroys at the same time all the other optical 
theories of M. Cauchy, because they are all built on the principles 
which we have now demonstrated to be false. But though the prin- 
ciples of M. Cauchy are now, for the first time, formally refuted, 
they were objected to, on general grounds, so long ago as the year 
1830, by a person whose opinion, on a question of mechanics, ought 
to have had considerable weight. ‘This was M. Poisson, who, having 
deduced from the equations of motion of an elastic solid the conse- 
quence that such a body admitted vibrations perpendicular to the 
direction of their propagation, thought it right to remark that this 
conclusion could not be supposed to account for transversal vibra- 
tions in the theory of light, because (as he expressed himself) ‘‘ the 
same equations of motion could not possibly apply to two systems 
