ON DOUBLE REFRACTION. 257 
now under consideration, must be the plane of polarization. The incident 
vibrations are parallel to the surface, and accordingly inclined at angles of 
9° 50’ and 80° 10’ to the directions of the nearly transversal and nearly nor- 
mal vibrations, respectively, within the crystal. Hence it seems evident that 
the amplitude of the latter must be of the order of magnitude of sin 9° 50’, 
or about a5 the amplitude of vibration in the incident light being taken as 
unity. The velocity of propagation of the nearly normal vibrations being to 
that of the nearly transversal roughly as /3 to 1, as will immediately be 
shown, it follows that the vis viva of the nearly normal would be to that 
of the nearly transversal vibrations in a ratio comparable with that of 
¥3xsin? 9° 50' to 1, or about 4, to 1. Hence the intensity of the nearly 
normal vibrations is by no means insignificant, and therefore it is a very 
serious objection to the theory that no corresponding phenomenon should 
have been discovered. It has been suggested by some of the advocates of 
this theory that the normal vibrations may correspond to heat. But the fact 
of the polarization of heat at once negatives such a supposition, even without 
insisting on the accumulation of evidence in favour of the identity of radiant 
heat and light of the same refrangibility. 
But the objections to the theory on the ground of the absence of some un- 
known phenomenon corresponding with the third ray, to which the theory 
necessarily conducts, are not the only ones which may be urged against it in 
connexion with that ray. The existence of normal or nearly normal vibra- 
tions entails consequences respecting the transversal which could hardly fail 
to have been detected by observation. In the first place, the vis viva belong- 
ing to the normal vibrations is so much abstracted from the transversal, which 
alone by hypothesis constitute light, so that there is a loss of light inherent 
in the very act of passage from air into the crystal, or conversely, from the 
erystal into air. About th of the whole might thus be expected to be lost 
at a single surface of Iceland spar, the surface being inclined 45° to the axis, 
and the light being incident perpendicularly, and being polarized in the prin- 
cipal plane; and the loss would amount to somewhere about ;/-th in passage 
across a plate bounded by parallel surfaces, by which amount the sum of 
the reflected and transmitted light ought to fall short of the incident. And 
it is evident that something of the same kind must take place at other incli- 
nations to the axis and at other incidences. The loss thus occasioned in mul- 
tiplied reflexions could hardly have escaped observation, though it is not quite 
so great as might at first sight appear, as the transversal vibrations produced 
back again by the normal would presently become sensible. 
But the most fatal objection of all is that urged by Green* against the 
supposition that normal vibrations could be propagated with a velocity com- 
parable with those of transversal. As transversal vibrations are capable 
(according to the suppositions here combated) of giving rise at incidence on a 
medium to normal or nearly normal vibrations within it, so conversely the 
latter on arriving at the second surface are capable of giving rise to emergent 
transversal vibrations; so that not only would normal vibrations entail a loss 
of light in the quarter in which light is looked for, but would give rise to 
light (of small intensity it is true, but by no means imperceptible) in a quar- 
ter in which otherwise there would have been none at all. Thus in the case 
supposed above, the intensity of the light produced by nearly normal vibra- * 
tions giving rise on emergence to transversal vibrations would be somewhere 
about the (.\,)* or the 51, of ,the incident light. In the case of light trans- 
* Cambridge Philosophical Transactions, vol, vii. p. 2. 
1862, _ 8 
