410 Royal Irish Academy: Prof. MacCullagh on a 
and promises, for the satisfaction of philosophers, to make known 
the means of ascertaining its existence (Jid. p. 305). But he after- 
wards contented himself with observing that as its vibrations are in 
the direction of propagation they prubably make no impression on 
the eye, and he then gave it the mame of the “ invisible ray.” 
(Nouveaux Exercices, p. 40.) 
In these investigations, the suppositions which M. Cauchy had 
made respecting the constants, led to the result that the vibrations 
of a polarized ray are parallel to its plane of polarization ; but in 
the year 1836 he changed his opinion on this point, and then, by 
reinstating the constants that he had before supposed to vanish, and 
establishing proper relations amongst them and the rest, he arrived at 
the conclusion that the vibrations are perpendicular to the plane of po- 
larization (Comptes Rendus, tom. ii. p. 342). All his other results, of 
course, underwent some corresponding change; and it is this new 
theory which must now be regarded as rigorous, while that of Fresnel 
is to be looked on as approximate. But it is needless to say, that if 
the accuracy of Fresnel’s law of double refraction is to be disputed, 
it must be on much better grounds than these; and the results of M. 
Cauchy are certainly too far removed from that law to have any 
chance of being consonant with truth. Although, for example, his 
new views respecting the direction of the vibrations agree, in a ge- 
neral way, with those of Fresnel, there is yet, in one particular, an 
important difference between them; for according to Fresnel, the 
vibrations are always exactly in the surface of the wave, while, ac- 
cording to M. Cauchy (in his old theory as well as the new), they 
are only so in ordinary media. In a biaxal crystal he finds—and 
this is one of the ways in which the “invisible ray” manifests its 
influence—that the direction of vibration, in each of the two rays ° 
that are visible, is inclined at a certain angle to the wave-plane ; but 
this angle, though small, is by no means inconsiderable, as M. Cauchy 
seems to intimate, overlooking the fact, which appears from his own 
equations, that it is of the same order of magnitude as the quantities 
on which the double refraction depends. It is true, the deviation 
measured by this angle cannot, if it exists, be directly observed in 
the refracted light; but its indirect effects on reflected light ought 
to be very great, since the action of the crystal on a ray reflected at 
its surface differs from that of an ordinary medium by a quantity of 
the same order merely as the aforesaid angle; and as the problem 
of crystalline reflexion has been already solved (Transactions of the 
Royal Irish Academy, vol. xviii. p.31) on the supposition (which is 
an essential one in the solution) that the vibrations are ewactly in the 
plane of the wave, it is highly improbable, considering the complex 
nature of the question, that it will be solved, in any satisfactory way, 
on a supposition so different as that which is required by the theory 
of M. Cauchy. However, as the laws of such reflexion are now 
well known, by means of the solution alluded to, it is possible that M. 
Cauchy may, as in the case of double refraction, succeed in deducing 
the same laws, or, if not the same, what may seem to be more exact 
