II. On certain remarkable Instances of deviation from Newton's Scale in the Tints developed by Crystals, with one Axis of Double Refraction, on exposure to Polarized Light.

By J. F. W. HERSCHEL, M. A.

FELLOW OF THE ROYAL SOCIETIES OF LONDON AND EDINBURGH,

THE discovery of crystals which possess two axes of double refraction, which we owe to Dr. Brewster, is perhaps the greatest step which has been made in physical optics since the discovery of double refraction itself by Bartholin, and its reference to an axis by Huygens. It has opened new views on the structure of crystals, and will in all probability be the means of leading us to a more intimate knowledge of the nature and laws of those forces by which the ultimate particles of matter act on light and on each other. When we reflect on the situation of these axes in different crystallized media, we cannot fail to be struck by the variety of the angles they include, and of the positions they hold with respect to the prominent lines or axes of symmetry of the primitive molecules, and the question immediately suggests itself, what are the circumstances which determine their position in the interior of a crystal?

It seems to have been all along taken for granted that, whatever these circumstances may be, the nature of the ray must at least be a matter of indifference; in other words, that a red and a violet ray

similarly polarized and incident in the same direction on the same point of a doubly refracting surface, will either both undergo or both not undergo a separation into two pencils, without any distinction arising from the place of the ray in the prismatic spectrum. Were this the case, the two axes would be fixed lines within the primitive form, absolutely determined by the nature of the body, as much so as the lines which bound the primitive form itself, and any attempt to substitute for them hypothetical axes coinciding with remarkable lines in the latter figure, however ingeniously devised, must be regarded as mere speculation. The fact however is otherwise. In a paper recently presented to the Royal Society, I have shewn that the axes of double refraction in one and the same crystal differ in their position according to the colour of the intromitted ray, a violet ray being separated into two pencils, when incident in the same direction in which a red one would be refracted singly. This remarkable fact, which is almost universal in crystals with two axes places the question in a very different light. It appears that the nature of the ray as well as that of the medium, has its share in determining the position of the axes, and that the intensity of the action of the medium on the ray is one of the elements involved in this problem. Now it is hardly possible to conceive the neutral axis of a crystal otherwise than as a position of equilibrium, or direction in which the axis of translation of a luminous molecule (if such exist) must be placed, that certain forces may act in opposition, and balance one another; but since forces which balance will likewise counteract each other when increased or diminished all in the same ratio, it follows that the partial or elementary forces so held in equilibrium do not observe the law of proportionality when the colour of the incident ray varies. If we suppose then with Dr. Brewster that these partial forces emanate from certain fixed axes coincident with remarkable lines in the primitive form, it will follow that each separate axis has a peculiar specific law which

regulates the intensity of its action on the differently coloured rays, and that each axis, supposing the others not to interfere with it, would exhibit separately a set of circular rings of which the tints would manifest a more or less marked deviation from the Newtonian Scale of Colours, as displayed by their uncrystallized laminæ.

This view of the subject will be remarkably supported by the facts about to be described, by which it will appear that among crystals with one axis only, there exists the greatest, I might almost say, the most capricious diversity in this respect, and that probably no two crystals, either with one or two axes, have the same scale of action, or polarize the differently coloured rays with an energy varying according to the same law precisely.

To this it may be objected, that from the result of a most elaborate examination of the colours exhibited by sulphate of lime, rock crystal, and mica, M. Biot has concluded that they follow in their action on coloured light, precisely the order and proportions stated in the Table of Newton, for the colours of thin plates of air. This coincidence is certainly extremely remarkable, supposing it rigorously exact, and antecedent to further experience, would appear to authorize the conclusion, that the proportional lengths of the periods performed by differently coloured rays within crystallized bodies depend essentially on the nature of the rays themselves, and not at all on the interior constitution of the crystal. Indeed in a case very analogous, M. Biot himself has attributed great and decisive weight to a presumption resting on the very same grounds. I allude to his Memoir on the Rotatory Phenomena exhibited by rock crystal and certain liquids, where having observed that in the former substance, the rotatory velocities impressed on the planes of polarization of differently coloured rays, are inversely as the squares of the lengths of their fits; he argues that this relation being independent of any datum involving the

peculiar constitution of rock crystal, ought to be the general law for all other subtances which possess the rotatory property.

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"Où

pourrait considérer d'abord que la rotation dans le cristal de roche " s'étant trouvée réciproque aux carrés des longueurs des accés des "divers rayons simples, cette loi se présente comme une propriété "des rayons mêmes, et non comme un résultat dépendant de la "nature des corps qui agissent sur eux. Ou doit donc s'attendre, "d'après cette remarque, que la même loi subsistera dans toutes "les substances, comme on y voit se maintenir les rapports des "accès mêmes dont la seul longueur absolue varie."

However convincing this line of argument may appear, and however exactly supported by experiment in the case of the rotatory phenomena, its conclusions are not verified in that of the polarized rings, to which it nevertheless applies with as much or greater force as in the other instance, and this may serve to shew how very cautious we ought to be in our attempts to generalize antecedently to experience in this branch of optical science. In the paper above alluded to, I have demonstrated that this law of proportionality admits of exceptions, and to the instances there adduced, I have now to add other still more remarkable ones, which if I mistake not, afford abundant proof that it has no foundation whatever in the nature of light. Indeed it may be observed, that the last sentence in the passage just quoted, is sufficient to destroy in a great measure the force of the argument in the former part of it: for, since Newton has demonstrated that for rays of a given colour, the lengths of the fits in different media are proportional to the sines of refraction corresponding to a given angle of incidence out of a vacuum, and since the more recent discovery of the different dispersive powers of substances has proved that media differ very considerably in the proportion of these sines for the different rays of the spectrum, it follows that the proportional lengths of the fits must differ in every different medium. Hence will arise a difference

in the scale of colours which their laminæ of different media should exhibit, and though we may certainly fix on one (that exhibited by a vacuum for instance) as a standard, and call it the Newtonian Scale, yet this, though convenient, is nevertheless in some degree arbitrary, as we know not the nature of the media, with which what we call a vacuum may be filled, nor their action on light. Nor is this cause of deviation so small as to be safely neglected in all cases. In oil of Cassia the difference in the refractions of red and violet rays amounts to no less than of the whole refraction, and the colours exhibited by thin or thick plates of this liquid should therefore deviate very sensibly from those in air or in Various solids too as chromate of lead, realgar, &c. could they be obtained by any means in sufficiently thin leaves, ought to exhibit a scale of colour differing altogether from that of Newton.

vacuo.

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The very remarkable succession of colours exhibited by that variety of the Fish-eye Stone (Apophyllite) which possesses a single axis of double refraction, has been noticed by Dr. Brewster, and since shewn in my paper already alluded to, to indicate an action on polarized light very nearly the same for all the colours, being equal upon the red and indigo-blue rays, a little greater for the yellow and green, and a little less for the violet, being the only instance yet adduced in the whole circle of optical phenomena of a maximum taking place between the extreme limits of the spectrum. I was led by this to conceive the possible existence of bodies, in which the law of proportional action should be so far subverted, as to render the periods performed by a red ray, within their substances, actually shorter than those passed through by a violet one; but certainly did not expect to find any conjecture almost immediately verified in the striking manner I am now to detail, and on the very substance which first gave rise to it.

By the kindness of my friend Mr. Lowry, (to whose liberality in rendering his invaluable collection accessible to scientific

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