DISCOVERY OF THE LAWS OF DOUBLE REFRACTION.
THE laws of refraction which we have hitherto described, were simple
and uniform, and had a symmetrical reference to the surface of the
refracting medium. It appeared strange to men, when their attention
was drawn to a class of phenomena in which this symmetry was
wanting, and in which a refraction took place which was not even in
the plane of incidence. The subject was not unworthy the notice and
admiration it attracted; for the prosecution of it ended in the
discovery of the general laws of light. The phenomena of which I now
speak, are those exhibited by various kinds of crystalline bodies;
but observed for a long time in one kind only, namely, the
rhombohedral calc-spar; or, as it was usually termed, from the
country which supplied the largest and clearest crystals, _Iceland
spar_. These {70} rhombohedral crystals are usually very smooth and
transparent, and often of considerable size; and it was observed, on
looking through them, that all objects appeared double. The
phenomena, even as early as 1669, had been considered so curious,
that Erasmus Bartholin published a work upon them at
Copenhagen,[36\9] (_Experimenta Crystalli Islandici_, Hafniæ, 1669.)
He analysed the phenomena into their laws, so far as to discover
that one of the two images was produced by refraction after the
usual rule, and the other by an unusual refraction. This latter
refraction Bartholin found to vary in different positions; to be
regulated by a line parallel to the sides of the rhombohedron; and
to be greatest in the direction of a line bisecting two of the
angles of the rhombic face of the crystal.
[Note 36\9: Priestley's _Optics_, p. 550.]
These rules were exact as far as they went; and when we consider how
geometrically complex the law is, which really regulates the unusual
or extraordinary refraction;--that Newton altogether mistook it, and
that it was not verified till the experiments of Haüy and Wollaston
in our own time;--we might expect that it would not be soon or
easily detected. But Huyghens possessed a key to the secret, in the
theory, which he had devised, of the propagation of light by
undulations, and which he conceived with perfect distinctness and
correctness, so far as its application to these phenomena is
concerned. Hence he was enabled to lay down the law of the phenomena
(the only part of his discovery which we have here to consider),
with a precision and success which excited deserved admiration, when
the subject, at a much later period, regained its due share of
attention. His Treatise was written[37\9] in 1678, but not published
till 1690.
[Note 37\9: See his _Traité de la Lumière_. Preface.]
The laws of the _ordinary_ and the _extraordinary_ refraction in
Iceland spar are related to each other; they are, in fact, similar
constructions, made, in the one case, by means of an imaginary
sphere, in the other, by means of a spheroid; the spheroid being of
such oblateness as to suit the rhombohedral form of the crystal, and
the axis of the spheroid being the axis of symmetry of the crystal.
Huyghens followed this general conception into particular positions
and conditions; and thus obtained rules, which he compared with
observation, for cutting the crystal and transmitting the rays in
various manners. "I have examined in detail," says he,[38] "the
properties of the {71} extraordinary refraction of this crystal, to
see if each phenomenon which is deduced from theory, would agree
with what is really observed. And this being so, it is no slight
proof of the truth of our suppositions and principles; but what I am
going to add here confirms them still more wonderfully; that is, the
different modes of cutting this crystal, in which the surfaces
produced give rise to refractions exactly such as they ought to be,
and as I had foreseen them, according to the preceding theory."
[Note 38\9: See Maseres's _Tracts on Optics_, p. 250; or Huyghens,
_Tr. sur la Lum._ ch. v. Art. 43.]
Statements of this kind, coming from a philosopher like Huyghens,
were entitled to great confidence; Newton, however, appears not to
have noticed, or to have disregarded them. In his _Opticks_, he
gives a rule for the extraordinary refraction of Iceland spar which
is altogether erroneous, without assigning any reason for rejecting
the law published by Huyghens; and, so far as appears, without
having made any experiments of his own. The Huyghenian doctrine of
double refraction fell, along with his theory of undulations, into
temporary neglect, of which we shall have hereafter to speak. But in
1788, Haüy showed that Huyghens's rule agreed much better than
Newton's with the phenomena: and in 1802, Wollaston, applying a
method of his own for measuring refraction, came to the same result.
"He made," says Young,[39\9] "a number of accurate experiments with
an apparatus singularly well calculated to examine the phenomena,
but could find no general principle to connect them, until the work
of Huyghens was pointed out to him." In 1808, the subject of double
refraction was proposed as a prize-question by the French Institute;
and Malus, whose Memoir obtained the prize, says, "I began by
observing and measuring a long series of phenomena on natural and
artificial faces of Iceland spar. Then, testing by means of these
observations the different laws proposed up to the present time by
physical writers, I was struck with the admirable agreement of the
law of Huyghens with the phenomena, and I was soon convinced that it
is really the law of nature." Pursuing the consequences of the law,
he found that it satisfied phenomena which Huyghens himself had not
observed. From this time, then, the truth of the Huyghenian law was
universally allowed, and soon afterwards, the theory by which it had
been suggested was generally received.
[Note 39\9: _Quart. Rev._ 1809, Nov. p. 338.]
The property of double refraction had been first studied only in
Iceland spar, in which it is very obvious. The same property
belongs, {72} though less conspicuously, to many other kinds of
crystals. Huyghens had noticed the same fact in rock-crystal;[40\9]
and Malus found it to belong to a large list of bodies besides; for
instance, arragonite, sulphate of lime, of baryta, of strontia, of
iron; carbonate of lead; zircon, corundum, cymophane, emerald,
euclase, felspar, mesotype, peridote, sulphur, and mellite. Attempts
were made, with imperfect success, to reduce all these to the law
which had been established for Iceland spar. In the first instance,
Malus took for granted that the extraordinary refraction depended
always upon an oblate spheroid; but M. Biot[41\9] pointed out a
distinction between two classes of crystals in which this spheroid
was oblong and oblate respectively, and these he called _attractive_
and _repulsive_ crystals. With this correction, the law could be
extended to a considerable number of cases; but it was afterwards
proved by Sir D. Brewster's discoveries, that even in this form, it
belonged only to substances of which the crystallization has
relation to a single axis of symmetry, as the rhombohedron, or the
square pyramid. In other cases, as the rhombic prism, in which the
form, considered with reference to its crystalline symmetry, is
_biaxal_, the law is much more complicated. In that case, the sphere
and the spheroid, which are used in the construction for uniaxal
crystals, transform themselves into the two successful convolutions
of a single continuous curve surface; neither of the two rays
follows the law of ordinary refraction; and the formula which
determines their position is very complex. It is, however, capable
of being tested by measures of the refractions of crystals cut in a
peculiar manner for the purpose, and this was done by MM. Fresnel
and Arago. But this complex law of double refraction was only
discovered through the aid of the theory of a luminiferous ether,
and therefore we must now return to the other facts which led to
such a theory.
[Note 40\9: _ Traité de la Lumière_, ch. v. Art. 20]
[Note 41\9: Biot, _Traité de Phys._ iii. 330.]