tints.

curious phenomena to anything like a law. It was evident almost from the first, that the axes in question (which he termed axes of no polarization) are only the resultants of remoter fundamental actions of the crystalline constitution. For example, these axes vary in position according to the colour of the light used to display them; their position within the crystal varies (as was shown by Mitscherlich) with the temperature of the body, nor is it obviously related to any of the geometrical lines of crystallizaLaw of the tion. Sir David Brewster succeeded in finding the law of the tints expressed upon the surface of a sphere of which the directions of the two axes form diameters. M. Biot expressed the law more elegantly by saying, that the tint developed by a biaxal crystal in any ray, is proportional to the product of the sines of the angles which the ray in question makes with the two optic axes. The tints are consequently arranged round the two poles of the axes, in a series of curves resembling the figure 8, having each this property, that the product of the sines of the angular distances of each point of one curve from the two poles is equal to a constant quantity. Such curves are called lemniscates, and are beautifully seen in nitre, especially when viewed by homogeneous light.

(532.)

racters to

A series of researches of the most elaborate Relation of description led Sir David Brewster to this addioptical cha- tional and admirable discovery, viz., that the optical crystalline characters of single refraction, double refraction forms. with one axis, and double refraction with two axes, have reference invariably to the primitive crystalline form of the mineral, and that the complexity of the optical character is as invariably related in degree to the complexity of the crystalline figure. Cubical and regularly octahedral crystals (as rock salt and fluor spar) being possessed of perfect symmetry in three principal directions, possess also simple refraction. Crystals with one predominant line or axis of symmetry -as rhombohedrons, octahedrons with square bases, right prisms with square or hexagonal bases-have a single axis of double refraction. Such, for instance, are Iceland spar, zircon, ice, beryl. Finally, all crystals unsymmetrical in the three principal directions, including prisms and octahedrons whose bases are not square, and those which are oblique, have two axes of double refraction. The rarity and minuteness of many crystals, the difficulty of cutting them, and when cut, of detecting their optic axes, evidently made the research one of extreme labour, yet highly remunerative, not only through the discovery of the general principle, but by the vast amount of beautiful and varied optic displays witnessed in the course of it. Sir David Brewster was nearly, if not quite, alone in this research, and after a short resistance on the part of some mineralogists, his principle of discrimination of primitive forms of crystallization by optical characters has been perfectly established.

reflection.

reflect is very peculiar. Malus, who at first believed Laws of that they were incapable of polarizing it in any de-metallic gree, afterwards changed his opinion, and ingeniously suggested that whilst transparent bodies reflect, at the polarizing angle, light polarized only in one plane, metals reflect rays oppositely polarized and then mixed. Sir David Brewster has the merit of having, after several unsuccessful attempts, deduced the leading empirical laws of metallic polarization, having been partly guided (as he states in his paper in the Philosophical Transactions for 1830) by Fresnel's remarkable experiments on circular polarization produced by total reflection in glass (see Art. 491). Having found qualities somewhat analogous in light reflected one or several times from metallic plates at various angles depending on the nature of the substance, he gave to the light so reflected the name of elliptically polarized light. It was afterwards satisfactorily proved by Mr Airy that the light so named by Sir D. Brewster is in fact identical in its qualities with the elliptically polarized light of Fresnel.

tion.

The subject of metallic polarization is rather too (534.) abstruse to be explained in a popular way; and the Metallic phenomena produced with depolarizing plates of dif-polarizaferent metals are not so well known as, according to their discoverer, they deserve to be. My limits only permit me at present to state that the care and accuracy of Sir D. Brewster's results are unquestionable; that they have formed almost the sole data upon which M. Cauchy and other mathematicians have based their theories of metallic reflection; and that, by generalizing the more limited views entertained by Fresnel as to the constitution of media and the nature of reflected light, they have been mainly instrumental in fixing the later views of optical writers as to the precise phenomena of polarization as produced, not only by metals, but by other substances. To these views I shall briefly advert in the next section.

The laws of the reflection of light at crystallized (535.) surfaces have also been studied by Sir D. Brewster. In this case observation is still in advance of theory.

V. Of Sir David Brewster's experiments on the (536.) absorption of light we must speak much more Absorption briefly. White light is coloured or analyzed by of light. refraction (as in a prism); by simple interference, as in Newton's rings; by double refraction combined with polarization. But it is also decomposed in a way which, primarily at least, seems different from all these,-by passing through coloured, or ratner, colouring media, whether solids, liquids, or gases, as red glass, ink, chlorine. This, the most familiar mode of coloration, is the most difficult to account for, and has been (on account of its obscurity) less studied than the others. In some instances, the complementary colour (that which, added to the transmitted tint, makes up white light) is entirely absorbed or lost; in other cases it is reflected at or near the first surface of the medium. Sometimes

action of

nitrous acid gas

the transmitted light is made up of different portions of the spectrum curiously blended, whilst rays intermediate in the order of refrangibility are wholly stifled. Many crystals have the curious property of dichroism, that is, of transmitting light of different colours in different directions. All these facts have been very carefully studied by Sir David Brewster. (537.) But the most remarkable phenomenon to be noticed Singular under this head is the wonderful action of nitrous acid gas upon light. When a beam, either of sunlight, or the light of a lamp, is passed through a bottle containon light. ing a small quantity of fuming nitrous acid, the light emerges of a tawny orange colour, which may be deepened indefinitely by heating the acid. If this light be then analyzed by a common prism, a wonderful spectacle is seen. The spectrum appears traversed by countless bands or dark spaces, whilst the blue and violet colours are nearly absorbed. The effect of the gas, then, is this,--to stifle or absorb countless minute portions of light seemingly selected at random from every part of every colour in the whole spectrum. Some of these deficient rays are broad and palpable, but most of them are so fine as to be visible only with the telescope. To understand the full import of this discovery, it is necessary to describe first the lines of Fraunhofer.

the spec

trum.

(538.) JOSEPH FRAUNHOFER, born in Bavaria, of humble Fraunhofer parents, in 1787, raised himself by his unassisted -Lines of efforts to be the first practical optician of the day. He had also the merit of devoting his leisure and the fine apparatus at his command to the observation and discovery of many optical phenomena, particularly those diffractive colours produced by fine gratings, which are known under the name of Fraunhofer's spectra. His principal discovery, however, was (in 1814) that of countless deficient or dark lines in the solar spectrum, resembling those which, as we have mentioned, were afterwards observed by Sir D. Brewster, to be produced in any kind of light by the action of nitrous gas. The deficient rays of solar light had, indeed, been observed still earlier (in 1802) by Dr Wollaston, but he counted only a very few of the more conspicuous ones; he described them merely incidentally, and (unusually with him) seems not to have perceived the great value of the discovery both in a theoretical and practical point of view. Fraunhofer's beautiful map of the spectrum, traTheir num- versed by lines of every grade of darkness, and clustered with every conceivable variety of distribution, was published in the Munich Transactions. He counted 590 lines, but Sir D. Brewster states that he has carried the number to 2000. Like the stars, they are probably countless. These lines characterize solar light. The light of the fixed stars and that of the

(539.)

ber and im. portance.

1 Edinburgh Transactions, vol. xii. (1833).

electric spark have their peculiar deficiencies different from those of our sun. These were discovered by Fraunhofer, as well as their occurrence in certain coloured flames. The order and number of the lines is, in each case, independent of the kind of prism used; but the angular distribution of the deficient rays varies with the material. Thus an oil of cassia prism expands most in proportion the less refrangible end of the spectrum; while water and sulphuric acid act with disproportionate dispersive energy on blue and violet light. This property of substances had been already studied by Sir D. Brewster with his usual diligence; but the importance of Fraunhofer's discovery was this, that the lines (the larger of which he distinguished by letters of the alphabet) furnish landmarks which define special rays of light invariably recognisable under all circumstances, which the vague description of their tints is quite incompetent to do. This enabled, on the one hand, the practical optician to discover the kinds of glass most fit for achromatic combination; and, on the other, it afforded precise numerical measures of the quality of dispersiveness in bodies which have been partly already, and will yet much more become, tests of some of the more obscure and difficult portions of the theory of light,-those, namely, which are connected with dispersion and absorption. Fraunhofer was, after Dollond, the most eminent and scientific manufacturer of achromatic telescopes, of which he vastly increased the aperture. He died at Munich in 1826.

nitrous gus

spectrum.

Returning to Sir David Brewster's discovery of the (540.) artificial production of analogous lines or deficient Action of rays in light from any source, its importance is easily and of the perceived:-for, in the first place, it so far accounts earth's atfor the strange phenomenon of the deficient rays mosphere of the sun's light, by showing that it may be caused on the by a gas resembling nitrous acid gas in its properties existing in the solar atmosphere; and, farther, if so astonishing a result of absorption is ever to be explained by theory, the first step is to be able to produce the phenomenon at pleasure, and to examine the qualities of the bodies producing it. The phenomena of coloured flames which possess standard deficient rays, present perhaps a closer analogy to the sidereal spectra. Sir David Brewster has farther found that the absorptive action of the earth's atmosphere (detected by the varying character of the spectrum for different angular altitudes of the sun) increases the number and also the breadth of these lines.

analysis of

trum.

Fresnel.

laboriously accurate. One of his papers fills an entire volume of the Academy's Memoirs. Even the astronomical hieroglyphics of the Egyptians, and the chronology of Chinese eclipses, have drawn from his pen learned treatises; and he has expounded the labours and discoveries of his countrymen and others with almost as much care and effort as if they had been proper to himself. But his subject by predilection was optics, and here he made his most considerable discovery, and that which he has followed out with most minute industry, namely, the rotatory action of fluids, in which he had Seebeck for a co-discoverer. (See Art. 512.) He studied the colours of crystallized plates with exemplary patience, and as we have seen in the preceding section, by his accurate observations on the law of the tints, prepared the way for the theory of transverse vibrations; but his own doctrine of moveable polarization, which he imagined to explain them, made no impression on the progress of science. He was the first who divided doubly-refracting crystals into positive (as

quartz), and negative (as calcareous spar). In the former the extraordinary wave is a prolate spheroid, and inclosed within the ordinary spherical wave; in the latter the spheroid is oblate, and exterior to the sphere. He also discovered (very approximately) the law regulating the plane of polarization of the rays in biaxal crystals.

M. Biot has for about half a century been an active professor and member of the Institute. His researches, always marked by precision, are perhaps deficient in bold conjecture and happy generalization. They are conducted with a mathematical stiffness which allows little play to the fancy, and in hypothetical reasoning he rarely indulges. His style is formal yet diffuse, and consequently somewhat repulsive to the student. His works are consequently not easily read, and have contributed less to the progress of knowledge than the scrupulous care often evinced in their compilation might seem to warrant. Yet the name of Biot will be ever associated with devotion to science, and especially with the progress of optics in our own day.

(547.) It would not be possible, in one short section, to Progress of do justice to the various improvements and additions the undula- which the undulatory theory of light-the joint crealatory theory since tion of Huygens, Young, and Fresnel—has received since the nearly simultaneous decease of the two lastnamed philosophers. But while a vast amount of labour and of mathematical and experimental skill has been thus expended, of which it would be in vain to attempt within our limits to give an account, we may pause upon two or three of the more conspicuous results of these researches, which, in conformity with the plan of this dissertation, may give a tolerable idea of their general tendency.

ties in its

history.

(548.) Looking at the history generally, we find one cuPeculiari- rious peculiarity in the progress of this remarkable theory. Its origin in the seventeenth century was unattended with sympathy or success. It received little support, and was well nigh forgotten for more than an hundred years: it was then resumed (we might almost say re-invented) in England, but it remained unpopular and almost unknown until re-echoed from a foreign land; while in France itself the views of Fresnel were (with one or two exceptions) as little appreciated as those of Young had been in England. From this period England became the place of its chief development; and with the exception of one eminent philosopher, M. Cauchy, its supporters and extenders, whether by analysis or experiment, have

(546.)

Sir J. Her schel and Mr Airy.

belonged to Great Britain,' a few of the most conspicuous of whom are named at the head of this section. The attention of the British public was forcibly (549.) called to the theory of Young and Fresnel, by an able treatise on Light, contributed by Sir John Herschel in 1827 to the Encyclopædia Metropolitana. The excellent method, lucid explanations, and intelligent zeal which marked this essay compelled the notice of men of science, too long deterred from the study of the fragmentary and abstruse writings of Young. It was followed four years later by a most able and precise mathematical exposition of the theory, and its application to optical problems, by Mr AIRY (now Astronomer Royal), who was then Plumian Professor at Cambridge, and who introduced this part of optics as a branch of study in that university. Whilst the excellent tract on the undulatory theory (published in 1831 in his Mathematical Tracts) opened up the subject in a most accessible form to British mathematicians, his original papers in the Cambridge Transactions confirmed the doctrines of Fresnel by a number of new and admirably contrived experiments, some in connection with interference, some with polarization, and all were confronted with the rigorous results of the mathematical theory. The paper on Quartz, and that on the Rainbow, have been already referred to (art. 466, 512). The writings of Mr Airy and of Sir John Herschel have continued to be the

(550.) Sir Wm. R. Hamil

main sources of information on this subject, and on physical optics generally, not only in this country but on the Continent. It is remarkable that in France, which possesses so many admirable scientific books, there should not exist a single good treatise on optics. Had not Mr Airy's attention been necessarily withdrawn from optics to astronomy, it is very evident that the theory of light would have received from him many farther important additions.

Whilst an impulse was thus given to the mathematical theory of light in the University of Camton and Dr bridge, a similar progress was being made in the Lloyd. sister University of Dublin, where three of her most eminent professors, Sir WILLIAM ROWAN HAMILTON and Professors LLOYD and MACCULLAGH devoted themselves energetically to its improvement and verification.

fraction in biaxal

1

(551.) To the two former of these we owe the prediction and Conical re- ocular demonstration of the most singular and critical of all the results of Fresnel's theory. Sir William crystals. Hamilton, a geometer of the first order, having undertaken the more complete discussion of the wave surface of Fresnel (see Section Third of this Chapter), to the equation of which he gave a more elegant form than heretofore, ascertained the exact nature of that surface, and consequently the exact direction of refracted rays in the neighbourhood of the "optic axes." It had been shown by Fresnel that, in the case of crystals with two axes, a plane section in a certain direction cuts the two sheets of the wave surface in a circle and in an ellipse, which necessarily intersect each other in four places. (See the annexed figure.) In the lines joining these four points with the centre of the figure the velocity of the two rays is equal. Now the cusps or sharp inflections of the wave surface in these particular directions, occur not only in the particular plane of section which we have considered, but in any section of the wave surface passing through these lines of equal ray-velocity. In the figure, therefore, of the compound sheet there is not a furrow, as Fresnel had supposed, but a pit or dimple, with arched sides something like the flower of a convolvulus, and the surfaces meet at the bottom of the pit at a definite angle. Let the circle and ellipse, in the annexed figure, represent the section of the wave surface we have described; then O P is the line of uniform propagation, and P is the bottom of the

Quaternions.

1 The equation is—

Now

M

N

conoidal pit M P N. suppose a slender ray of light to move through the crystal in the line OP, and to emerge into air at a surface of the crystal cut perpendicular or nearly so to the direction of single ray-velocity O P. If we confine our attention at first to the plane of the figure only, that ray having intersecting tangents both proper to the wave surface, would give rise, on Huygens' construction (art. 475), to two emergent rays inclined at an angle. But since this is the case, not only in the plane of the figure, but (as has been stated) in any plane passing through the ray in question, the emergent light must form a conical luminous sheet, the angle of the cone being determined by the refractive properties of the crystal. This beautiful and unexpected result was verified with great skill and address by Dr Lloyd in the case of Arragonite, which is a biaxal crystal, and he found the position, dimensions, and conditions of polarization of the emerging cone of light to be exactly such as theory assigns. When all the necessary corrections are attended to, the angle of the cone of light is about 3°. There is another case of conical (or it might be called cylindrical) refraction, which occurs nearly in the same portion of a crystal, which was predicted and discovered in like manner, but which we will not stop to particularize. The observations of Dr Lloyd have been extended by M. Haidinger to the case of Diopside, a crystal also having two optic axes.

Sir W. Ha

Every one capable of appreciating such evidence, (552.) will feel the irresistible impression which so curious Other an anticipation, so accurately fulfilled, gives us of the works of positive truth of a theory admitting of such veri-milton and fications. The names of Sir W. Hamilton and Dr Dr Lloyd. Lloyd will be handed down to posterity in connection with this admirable discovery. But they have also other claims to our respect, to which we can here only refer in the most general terms. The former has generalized the most complicated cases of common geometrical optics by a peculiar analysis developed in his essays on "Systems of Rays" (Irish Academy Transactions, vols. xv.-xvii.)3 To Dr Lloyd