I LECTURES ON POLARIZED LIGHT, DELIVERED BEFORE THE PHARMACEUTICAL SOCIETY OF GREAT BRITAIN; AND IN THE MEDICAL SCHOOL OF THE LONDON HOSPITAL. S!lu8trateii ti» atiobe J^iftg JUaoo&cutsi. LONDON: LONGMAN, BROWN, GREEN, AND LONGMANS. 1843. C. WHITINO, BEAUFORT HOUSB, STRAND. TO CHARLES WOODWARD, ESQ., F.R.S., fRESIDENT OF THE ISLINGTON LITERARY & SCIENTIFIC SOCIETY, THIS WORK, ON A SUBJECT WITH WHICH HE IS INTIMATELY ACQUAINTED, IS INSCRIBED, AS A TESTIMONY OF RESPECT AND ESTEEM, BY HIS SINCERE FRIEND, THE AUTHOR. PREFACE. The following Lectures were delivered in the spring of 1843, before the Members of the Pharmaceutical Society of Great Britain, and are now in course of publication in the Pharmaceu- tical Journal. The substance of them has formed, for some years past, a portion of the Annual Course on Chemistry, delivered in the Medical School of the London Hospital. To the undermentioned eminent philosophers the author has been principally indebted for the information contained in the following pages : Sir Isaac Neivfon. — Opticks ; or, a Treatise of the Reflections^ Refractions, Inflections, and Colours of Light. Dr. Thomas Young. — A Course of Lectures on Natural Philo- sophy and the Mechanical Arts. Sir D. Brewster. — Various papers in the Transactions of the Royal Societies of London and Edinburgh. Also two numbers on the Double Refraction and Polarization of Light, published under the superintendence of the Society for the Diff"usion of Useful Knowledge. Likewise, a Treatise on Optics, in Lardner's Cyclo- paedia, and the article " Optics" in the Encyclopaedia Britannica, 7th edition. Fresnel. — Elementary View of the Undulatory Theory of Light, in the Quarterly Journal of Science for 1827, 1828, 1829, trans- lated and annotated by Dr. Thomas Young. Also various papers in the Annales de Chimie et de Physique. Likewise, Extrait du Bulletin de la Societe Philomatique, D6cembre, 1822, and Fevrler, 1823. Sir J. Herschel. — Article "Light," in the Encyclopajdia Metropolitana. Also, Transactions of the Cambridge Philosophical Society, and Philosophical Transactions. Biot. — Various papers in the Memolres de 1' Academic Royalc des Sciences, and in the Annales de Chimie et de Physique. vi PREFACE. Airy. — Mathematical Tracts. 2d edit. 1831. Also, Transac- tions of the Cambridge Philosophical Society. Pouillet. — Elemens de Physique Experimentale et de Meteoro- logi^, 2 vols. 1827. Peclet. — Traite Elementaire de Physique. 2™'- ed. 2 vols. 1830. Quetelet. — Notes to the French Translation of Herschel's Article on Light. Also, Positions de Physique. 1 834. Lloyd, Rev. H. — Report on the Progress and Present State of Physical Optics, in the Report of the Fourth Meeting of the Bri- tish Association. 1835. Also, Lectures on the Wave Theory of Light. 1841. Powell, Rev. Professor. — Elementary Treatise on Experimental and Mathematical Optics. 1833. Also, a General and Elementary View of the Undulatory Theory, as applied to the Dispersion of Light. 1841. Likewise, various papers in the Philosophical Magazine. Rose, Gustav. — Elemente der Krystallographie. 2'^- Aufl. 1838. (A French translation of the 1st edition of this work). Dove. — On the Circular Polarization of Light : translated in Taylor's Scientific Memoirs, vol. i. Soubeiran. — Journal de Pharmacie. 1842. Ventzke. — Annals of Chemistry. December, 1842. The author takes this opportunity of offering his warmest thanks to his friend, Mr. Woodward, for his valuable assistance and advice on many occasions, in the performance of experiments on Polarized Light ; as well as for the loan of various pieces of apparatus, contrived and adapted by Mr. Woodward, for the public illustration of the phenomena of Polarized Light. To Mr. Darker, optician and manufacturer of polarizing ap- paratus, of Paradise Street, Lambeth, the thanks of the author are also justly due, for his disinterested zeal, skill, and attention in promoting the objects of the author in the preparation of the present course of Lectures. J. P. 47, FiNSBURY Square, September, 1843. TABLE OF CO^^TENTS. LECTUEE I. PACK. Introductory Remarks 1 1. General Statement of the Physical Properties of Light. — 1. Propagation. 2. Intensity, Photometry, Wheatstone's Photometer. 3, Transparency and Opacity. 4. Reflection. 5. Refraction. 6. Dis- persion, the spectrum, primitive and compound colours, comple- mentary tints, formation of white light, possible existence of a second spectrum, achromatism, Fraunhofer's lines. 7. Diffraction. 8. Colours of thin plates, of filths, and of grooved surfaces, Newton's Pits, NobiWs Metallo- Chromes, Reade's Iriscope. 9. Double Refraction. 10. Polarization, methods of eifecting it, by reflection, by single refraction, by double refraction, by the tourmaline 3—20 2. Wave Hypothesis. — Light a property or motion, not a matter. Ether, its existence assumed, its supposed resistance to the motions of the planets, retardation of Encke's comet. Ethereal Molecules. TFawes, lengths for different colours ; comparative range of sensibility of the eye and ear. Vibrations, rectihnear, circular, elUptical. Powell's machine. Doctrine of transversal vibrations. Partially polarized light. Interferences of Light, Young's experiments ; his sliders, circular and elliptical waYes how formed. Wheatstone's illustrative apparatus 20—33 LECTURE n. 3. Coloured Polarization. — Polariscope ; polarizer, depolarizer, and analyzer. Colours of thin plates by polai-ized lights. Theory of their production. Selenite, description of, its optical properties, devices of 34 — 41 Double refraction, test of, its cause. Effect of compression, and unequal heating or cooling in producing double refraction, chromatic dyna- mometer, chromatic thermometer. Properties of unannetiled glass. Practical application of the preceding statements. Argument for the vegetable origin of the Diamond. Doubly refractive power of starch grains and other organic substances 41 — 50 LECTURE III. Crystals, their doubly refractive power ; uniaxial and biaxial crystals ; positive and negative axes. Forms of crystals ; crystallographical axes, classification of crystalline forms. Expansibility of crystals ; Mitscherlich's experiments. Atoms of crystals; opinions as to their shape, probability that the atoms are susceptible of alteration of form. Molecular forces ; elasticity of crystals, Savart's experiments thereon. General conclusions 50 — 64 VUl TABLE OF CONTENTS. Systems of Crystals. Individual considerations of the sjoionymes, forms, crystals, properties, and exceptions of each of these : 1. Cubic or Octohedral System. — Boracite, Analcime 64 2. Square Prismatic System. — Ferrocyanide of Potassium, Zircon, ApophyUite 67 3. Rhombohedric System. — Mica Cuniaxial)Iceland Spar (production of rings and cross in uniaxial crystals), Tourmaliiie, Ice and Crystals of Snow, Beryl, Quartz, Amethyst, Chabasite 68 4. Right Prismatic System. — Nitre (production of lemniscates and cross in biaxial crystals). Carbonate of Lead, Arragonite, Kochelle Salt, and Topaz 77 5. Oblique Prismatic System. — Borax, Selenite, Sugar Candy 82 6. Doubly Oblique Prismatic System. — Sulphate of Copper 84 LECTUKE IV. 4. Circular Polarization. — General explanation. Conditions neces- sary for its production. Different methods of effecting it. Fresnel's method, his rhomb. Airy's method. Dove's method. Quartz, its peculiar optical properties. Eight-handed and left-handed quartz. Plagie- hedral quartz. Circular Polarization of Fluids; liquids possessing this property, others which do not. Description of the apparatus for ob- serving the circular polarization of Mquids, Blot's, Powell's, Ventzke's. Volatile oils, their power of rotating the planes of polarization ; ap- plication. Sugar, rotative powers of solutions of different kinds of saccharine substances. Applications, sugar-refining, fictitious manna, vinous fermentation, diabetic urine. Dextrine. Properties of circu- larly polarized light ; its reflection, transmission through tourmaline plates, double refraction, conversion into plane polarized light by two internal reflections, uniform tints and coloured rings produced by its transmission through crystalline films, transmission unchanged through circularly polarizing liquids, action of quartz, production of spirals, Earnshaw's theoretical deduction, and Powell's verification of it. Airy's analyzer for circularly polarized light 86 — 106 5. Elliptical Polarization. — Conditions for its production. Dif- ferent modes of effecting it. Distinguishina characters of eUiptically polarized light 106—108 6. Macles and Compound Crystals. — Hemitropes, intersecting crystals, twin or double crystals, tesselated or composite crystals. Nitre, Arragonite, Amethyst, Topaz, Sulphate of Potash, ApophyUite, Analcime, idiocyclophanous crystals of Iceland spar, &c 108 — 110 Conclusion , no THE POLAEIZAHON OF LIGHT, &c. &c. &c. LECTURE I. With the concurrence of the Council of your Society, I have undertaken to deliver three lectures on the Phenomena of Pola- rized Light. I have done so, because I believe that their singularity, variety, splendor, and useful applicability will create great and universal interest in the minds of my auditors, what- ever be their pursuits, occupations, or acquirements. I am acquainted with no branch of experimental philosophy capable of presenting such brilliant and gorgeous phenomena, and which are so well adapted for illustration in the lecture-room, as polarized light. In its power of unfolding to our view the intimate structure and constitution of natural bodies, it certainly has no superior, if indeed it have any equal. It furnishes us with characters for recognizing and distinguishing many bodies, and it gives us the means of determining the nature of the changes going on in some of the recondite operations of nature. It is a subject whose phenomena are so complicated and intricate, that it not only admits of, but actually requires, the highest departments of mathematics to elucidate them ; and it is, therefore, very properly placed in the very first rank of the physico-mathe- matical sciences. But in all societies and associations, the lovers of knowledge are of two kinds, philosophers and utilitarians. The first pursue science for its own sake, the second for its usefulness. With the latter every step they take in the acquirement of knowledge is accompanied with the question " cui bono?^' With such, all scientific researches which have no immediately practical bearing, which, according to their narrow views, cannot be at once shown to be useful, are neglected, perhaps even sneered at. Though with such I profess to hold no community of feeling ; yet as I am desirous of combining in these lectures, the utile with the dulce, I think I can venture to hold out to them ample remune- ration for the time they may devote to the study of polarized light, by attending these lectures. 2 ON THE POLARIZATION OF LIGHT. If I can show them that this agent furnishes us with a more intimate knowledge of the nature and properties of those sub- stances, by the commerce in which most of the Members of this Society gain their bread ; if I can demonstrate its applicability to the detection of adulteration of foods, drugs, and chemicals ; if I can*point out its application to the determination of the commercial value of saccharine juices ; if I show how it has been applied to determine the nature of the changes which occur in certain chemical and vital processes, in which ordinary che- mical analysis completely fails us; if I prove that it may aid members of my own profession in detecting the existence of certain diseases ; and, lastly, if we show the possibility of its use to the mariner in aiding him, under certain circumstances, to avoid shoals and rocks — I trust even the utilitarians will admit that the study of polarized light is both advantageous and pro- fitable, and that the time of this Society has not been unprofitably occupied by these lectures. Tliese are only a portion of the valuable and practical uses of which polarized light is susceptible. Its phenomena are so in- tricate, and at present so little understood by the public, that a very large number of persons, who might otherwise perhaps beneficially avail themselves of its services, are ignorant alike of its powers and of its uses. We may, therefore, hope that when it becomes better known it will be found more extensively useful. Common and polarized light agree in several of their leading properties, and though these lectures are intended to illustrate the peculiarities of polarized light, yet before we can prove what is peculiar to the one, we must be acquainted with the general properties of the other, and thus, I conceive, I must introduce polarized light to your notice, by a ■preliminary general view of the physical properties of light. Moreover, the phenomena of polarized light are so numerous, various, and intricate, that the student is very apt to become bewildered with an immense multitude of facts, and to forget, if indeed he ever knew, the conditions which are requisite for the production of each phenomenon. Hence, then, it becomes desi- rable that we should give him some artificial aid to assist in the conception of facts, and the modes of observing them ; as well as to show him how these manifold phenomena are mutually connected and dependent. We require in fact some means of generalization. Such will be found, I think, in the undulatory hypothesis of light. . 1 propose, therefore, to occupy this lecture with a brief statement and demonstration of the properties of light, and to take a hasty glance at the hypothesis of waves or undulations ; so that I trust you will leave this room to-night with some general notions ON THE POLARIZATION OF LIGHT. 3 of the possible physical causes of common and polarized light, and almost anticipate some of the statements which I shall have to make in the next lecture. 1. GENERAL STATEMENT OF THE PHYSICAL PROPERTIES OF LIGHT. 1 . Propagation of Light. — Light emanates from luminous bodies with the enormous rapidity of above 190,000 miles per second. This has been ascertained in two ways ; first, by observation of the times at which the eclipses of the satellites of Jupiter are perceived by us at different seasons, according to the part of its orbit which the earth happens to be in ; and, secondly, by the phenomenon called the aberration of the fixed stars. The' first method gives 192,500 — the second, 191,515 — miles per second. 2. Variation of Intensity. — The intensity of light decreases as the square of the distance increases. At twice the distance, it has only | of the intensity, at thrice the distance ^ the intensity, at four times the distance ^g- of the intensity, and so on. The reason of this is, that being highly expansile, it illumi- nates four times the space at twice the distance, nine times at thrice, and sixteen times at four times the distance ; hence, its intensity must be inversely as the square of the distance. The law is aptly illustrated by a quadrangular pyramid of wood, divided horizontally at equal distances, into four parts or segments of equal height. The upper segment has a square base, whose area we shall call 1. The second segment has also a square base, but its area is 4. The area of the square base of the third segment is 9, and that of the lowest or fourth segment, 16. Here the distances of the bases of the segments from the apex of the pyramid, are as 1, 2, 3, 4, while the areas of these bases are as 1, 4, 9, 16. The readiest demonstration of the law for the lecture-room, is the following : — Let the light from a lantern pass out through a square aperture, and be received on a semi-transparent screen, on which square spaces are marked. Notice at what distance the beam of light illuminates one of these squares. At double the distance, it will illuminate 4, at treble 9, at quadruple 16 squares. In Photometry, we avail ourselves of this law. If two lumi- nous bodies, at unequal distances, produce the same amount of illumination, the relative quantities of light evolved by these bodies, are as the squares of the distances. Thus, if a lamp, at four feet distance, give as much light as a candle at one foot, the lamp actually evolves 1 6 times as much light as the candle. Count Rumford's photometrical process of observing at what distances two lights gave two shadows of equal intensities, as well as the photometers of the late Mr. Ritchie and of Professor Wheatstone, are on this principle. But all these modes of measuring light B 2 4 ON THE POLARIZATION OF LIGHT. are objectionable, since they are based on the imperfect and varying judgment of the eye. Professor Wheatstone's recently-constructed photometer is a very ingenious contrivance. It is a cylindrical box, of about two inches diameter, and one inch in depth, and which con- tains a system of two wheels and pinions. On the face of the box, and near to its external border, is a circle of cogs. In the centre of the face is an axis, to which is attached an hori- zontal arm, carrying a toothed wheel or disk, the teeth of which fit into the cogs of the outer cir- cle. This wheel has a double motion, it rotates on its own axis, and also revolves within the cogged circle. To this disk is attached a small, hollow, glass bead, silvered internally, and which moves with great rapidity backwards and forwards across the face of the cylinder. The motion is communicated by turning the handle on the opposite face of the box. If this photometer be placed between two lights, and the bead put in rapid motion, we observe two parallel luminous lines, about the -^^ of an inch apart. By adjusting the relative distances of the two lights from the photometer, so that the brightness of the lumi- nous lines may be equalized as determined by the eye, and then squaring the distances, their comparative intensity may be ascer- tained*. 3. Transparency and Opacity. — Some bodies allow light to penetrate them, as air, water, glass, crystal, &c. These are called transparent bodies. Others, however, refuse to give passage to light, as the metals. The latter are termed opake bodies. But some substances, which in the mass are opake, become transparent when reduced to thin films. Gold is an instance of this : in the lump it is opake, but as gold leaf it allows light to traverse it. 4. Reflection. — When a beam of light falls on a smooth- polished surface, a portion of it is reflected. The incident and the reflected ray make each the same angle with the reflecting surface, hence the law of reflection is, that the angles of inci- dence and reflexion are equal This law holds good under all circumstances, whether the reflector be plain or curved. A polished metallic plate as a speculum is a good reflector. Glass, being t ransparent, reflects both from its anterior and * This instrument is made by Messrs. Watkins and Hill, of Charing Cross. ON THE POLARIZATION OP LIGHT. 5 posterior surface. Hence in some optical experiments, where it is desirable to avoid the confusion from a double reflexion, the posterior surface of the glass is either ground, or blackened by means of soot, candle-smoke, or size and lamp-black. This proceeding is especially desirable in experiments on polarized light. Silvered glass, that is, glass covered on the posterior surface by an amalgam of tin, as the common looking-glass, is not adapted for accurate optical experiments, on account of the reflection from the metal as well as from the glass. 5. Refraction. — When a ray of light passes obliquely out of one medium into another of a different density or combustibility, it changes its direction, or is bent out of its course ; in optical language it is refracted. If the second medium be denser, or more combustible than the first, the refraction is towards the perpendicular ; but if the density or combustibility of the second medium is less than that of the first, the refraction is from the perpendicular. If the ray fall perpendicularly on the refracting surface, it suffers no change in its direction, in other words, it undergoes no refraction. In most optical instruments in which refracting media are required, glass is employed, as in the camera obscura, astro- nomical and terrestrial telescopes, microscopes, magic lanterns, common spectacles, eye-glasses, &c. The oxyhydrogen appa- ratus, which I shall use in these lectures for illustrating the phenomena of polarized light, serves, when deprived of its polarizing part, for use as a microscope (oxyhydrogen or gas microscope^ the images of the objects being thrown on a screen. Used in this form, it is simply a refracting instrument. Its structure I shall hereafter explain. Quartz or rock crystal is used, under the name of Brazil pebble, as a refracting medium for spectacles, on account of its greater hardness, and its being less liable to scratch. The diamond and other precious gems have been occasionally used for microscopic lenses. Jewellers employ a glass globe filled with water, to concentrate the rays from the lamp which they use to work by. The water is generally coloured pale blue, to counteract the reddish yellow tint of the artificial light. Amber, when cut and polished, is sometimes used for spectacles. When the object is to concentrate rays of light, and to exclude those of heat, lenses of alum or sulphate of copper may be employed. I have already stated, that the law of reflection, as regards the direction of the reflected ray, is the same for all reflecting media. But the law of refraction is very different, each refracting medium having its own peculiar action on light. A variety of curious and well-known phenomena result from the unequal refracting powers of different bodies, or of the same 6 ON THE POLARIZATION OF LIGHT, body in different states of density. Thus the apparent crooked- ness of a stick placed obliquely in water ; the difficulty of hitting a body, as a fish, in water, when we take an oblique aim ; the deception experienced in estimating the depth of water, except when viewed perpendicularly; and the altered position of a body (as a piece of money) contained in a basin, when viewed obliquely, first when the basin contains no water, and afterwards when water has been put in — these, and many other phenomena, result from the greater refractive powers of water than of air, and the consequent change of direction which the luminous rays suffer when passing from one medium to the other. Again, the tremulous motions of bodies, when yiewed through an ascending current of heated air, and by which an excise-officer is said to have, on one occasion, discovered a subterranean still in the Highlands of Scotland, result from the unequal refracting power of air in different states of density. 6. Dispersion. — If a ray of white light be made to traverse a refracting medium, or, in other words, to suffer refraction, it is found to have undergone a remarkable change — it is no longer perfectly white, but more or less coloured. It is assumed, there- fore, that white light is made up of coloured lights, and that these, being unequally refrangible, are separated, or, in optical language, are dispersed. In this way, seven colours are ob- tained, viz. violet, indiyo, blue, green, yellow, orange, and fed. These are usually procured by a triangular piece of glass, called a prism — the seven colours constituting the prismatic or solar spectrum. This mode of producing colours from white light is called the decomposition, the analysis, or the dispersion of light. If we allow the oxyhydrogen lime-light to pass out of the lantern through a slit, and receive it on a prism, the spectrum may be thrown on the cieling of the lecture-room, or on the screen before us. To persons unacquainted with philosophical investigations, few facts seem more astonishing, and even improbable, than that of white light being compounded of differently coloured lights. I shall, therefore, dwell for a few minutes on this topic. Every one is familiar with the fact, that, by mixture, colours are altered. Thus blue and yellow form green ; red and yellow form orange; while blue, with different proportions of red, yields indigo or violet. You will, therefore, readily believe, that of the seven prismatic colours into which the prism decomposes white light, three only may be primitive, and four compounded. Primitives. Compounds. Ked Orange Yellow Green Blue Indigo Violet ON THE POLARIZATION OP LIGHT. 7 If the seven prismatic colours be rudely printed on a circular disk of card, and then be made to rotate rapidly, the union of these colours on the retina gives us an impression of greyish-white. If we paint the three supposed primitive colours, viz., red, yellow, and blue on a similar disk, and cause this to revolve, we also obtain an impression of greyish white. These experiments, therefore, favour the notion that the sen- sation of white light depends on the simultaneous impression of differently-coloured lights on the retina ; and, secondly, that three of the prismatic colours being capable of giving the sensa- tion of white light, they probably are the primitive colours, the others being compounds. Hence, white light is called com- pound or heterogeneous light; while the three colours, red, yellow, and blue, are termed simple or homogeneous lights. Each of these may be termed a monochromatic light. Orange, green, indigo, and violet, on the other hand, are mixed colours. It follows, from this view of the subject, that two colours (one of which must be a ?nia;e Orange. Yellow ...< Newtonian Spectrum. Hypothetical Spectrum... Blue. * An apparatus for the exhibition of these lines, lent by Messrs. Watkins and Hill, was exhibited to the meeting. 10 ON THE POLAHTZATION OF LIGHT. existence of a calorific, magnetic, and chemical influence beyond the confines of the coloured spectrum, is a fact of considerable importance in any enquiries which may be instituted into the nature of light. Moreover, the splendid and interesting pictures caWed Daguerreotypes, Calofypes*, Chrysotypes, and Ferrotypes, or Cyanotypes,now behve me, produced by the chemical influence of light on gross or ponderable matter, show the high importance of investigations respecting the chemical powers of the spectrum. 7. Diffraction. — When light passes near the edges of bodies, it suffers certain modifications, included by opticians under the denomination of inflection or diffraction. If an opake body be placed in a cone of light admitted into a dark chamber through a very small aperture, its shadow is larger than its geometric pro- jection. Moreover, its shadow is bordered with fringes, and similar fringes are obse ved within the shadows of narrow bodies. If the light be lio'.iogeneous or monochromatic, the fringes consist of dark and li ;ht spaces of the same colour, and are of different breadths, red yielding the broadest, violet the narrowest fringes, but in white li,;ht the fringes are prismatic or iris-coloured. The iris fringes msy be readily observed by looking through the slit, between the almost closed fingers, at a candle, placed at a distance of several yards. It may be seen still better by looking at the same luminous body through a feather, or through a fine wire gauze. I have before me Schwerd's very complete apparatus for examining the complicated and difficult phenomena of diffraction. When I tell you that the immortal Newton failed to perceive the internal fringes, and that he left the subject altogether in an imperfect, unsatisfactory, and unfinished state, I need scarcely add, that the phenomena are very complicated, and their study exceedingly difficult. 8. Colours of thin plates, of films, and of grooved surfaces. A variety of curious and brilliant optical phenomena were attributed by Newton to what he called flts of transmission, And flts of reflection; but which Dr. Young and most subsequent writers ascribe to interference of light. I refer now to the phenomena of thin plates, of films, and of grooved surfaces. Excessively thin plates of air, liquids, or solids, appear co- loured when viewed by reflected and transmitted light ; but the colour seen by reflection is complementary to that seen by trans- mission. If the plate be of uniform thickness, the colour is uniform ; but if the thickness varies, the colo ur also varies, * Some beautiful Calotype portraits, taken by Mr. Collen, of Somerset Street, Portman Square, miniature painter to the Queen, were exhibited to the meeting. ON THE rOLAKTZATION OP LIGHT. 11 Very much thinner plates than those which present colours, do not reflect light, and when viewed in this position, appear black. But they still transmit light, and when viewed by trans- mitted light, appear white. Wedge-shaped plates present a series of parallel bands or fringes of colour. A plate having the form of a plano-concave lens, the thinnest part of the plate being in the centre, gives a series of concentric rings of brilliant colours. Those seen by reflected light, have a black spot in the centre, while the transmitted rings have a white spot in the centre. These different phenomena of thin plates are brilliantly illus- trated in the lecture-room by the oxyhydrogen lime-light, which, after passing through the condensers of the lantern, ia polarized, then passed through films of selenite (of uniform thinness, or wedge-shaped plates, or plano-concave films) afterwards through the two lenses called the powers, and ultimately analysed by a plate of tourmaline, or a bundle of plates of thin glass. The nature of the changes will be explained hereafter. The squares of the diameters of the reflected coloured rings are as the odd numbers, 1, 3, 5, 7, 9, &c.; while the squares of the diameters of the transmitted rings are as the even numbers, 0, 2, 4, 6, 8, 10, &c. The brilliant colours, produced by thin plates of air between the laminae of mica, of selenite, and of Iceland spar, and between plates of glass, are familiar illustrations of the colours caused by thin plates of a gaseous substance. The colours caused by thin films of oil of turpentine or other essential oils, of alcohol or of water, and by soap-bubbles, are well- known examples of the colours caused by thin plates of liquids. The iridescent hues produced on copper or steel by heat, and which depend on the formation of a thin film of metallic oxide, are good illustrations of the colours caused by thin plates of solids. But the most brilliant are those caused by thin films of peroxide of lead, formed upon polished steel plates, by the electrolytic de- composition of acetate of lead. These splendid prismatic tints were discovered by Nobili*, and are commonly known as Nobilis colours or metallo-chromes. The mode of producing them has been described by my friend Mr. Gassiot, in a paper read before the Royal Societyf. If we place on the polished steel plate a card screen in which some device is cut out,very beautiful figures, having a splendid iridescent appearance, are produced. In all the cases hitherto alluded to, I have supposed white or * See Taylor's Scientific Memoirs, vol. i. part 1. t See the Proceedings of the Royal Society, for March, 1840; also Brande's Manual of Chemistry, 5th edit., p. 836. 12 ON THE POLARIZATION OP LIGHT. compound light to be used ; and then the colours are iridescent or prismatic. But if monochromatic or homogeneous light be employed, the rings are of a uniform tint or colour, and are sepa- rated by obscure bands or rings. Red light yields the broadest, violet light the narrowest rings. Minute particles, fibres, and grooved surfaces also produce prismatic or iridescent colours by white light. Thus, minute par- ticles of condensed vapour, obtained by breathing on glass, give rise to this effect. A familiar illustration is to be found in the halos observed around the street-lamps, when viewed at night through a coach-window, on the glass of which vapour is depo- sited. In this case the colours are seen by transmission. Dr. Joseph Reade's beautiful instrument, called the Iriscope^ brilliantly displays the colours produced by reflection from a plate covered with condensed vapour. It consists of a plate of highly-polished black glass, having its surface smeared with a so- lution of fine soap, and subsequently dried by rubbing it clean with a piece of chamois leather. If the surface, thus prepared, be breathed on, through a glass tube, the vapour is deposited in brilliant coloured rings. But as, in this mode of experimenting, the plate of vapour is thickest in the middle,and thin nest in the circumference, the rings have black circumferences instead of black centres. Minute fibres of silk, wool, and of the spider's web, also present in sunshine a most vivid iridescence. A very minutely grooved surface also presents a prismatic or iridescent appearance in white light. Of this mother-of-pearl is a familiar instance — as also opal. Micrometer scales frequently present the same appearances ; and Barton's buttons and other iris ornaments owe their resplendence to the numerous minute grooves cut in the surface of the metal. If a beam of light from the oxyhydrogen apparatus be received on one of Barton's buttons, an iridescent image may be thrown on a screen several yards distant ; thus furnishing a good lecture-room illustration of the colours of grooved surfaces. 9. Double Refraction.—When a pencil of light falls in certain directions on any crystals, which do not belong to the cubical system, it is split or divided into two other pencils, which diverge and follow different paths ; and when their divergence is considera- ble, objects viewed through them appear doubled. The change thus effected on a ray of light is denominated double refraction. The substance which is commonly used to produce this effect is that variety of transparent crystallized carbonate of lime, called Ice- land spar, or sometimes calcareous spar, or, for brevity, caZc-fpar. In every double refracting crystal there are, however, one or more directions in which double refraction does not take place. These are called axes of double refraction : they might with more propriety be termed axes of no double refraction. ON THE POLARIZATION OP LIGHT. 13 I now pass a beam of light (produced by throwing the oxy- hydrogen flame on lime) through a rhombohedron of Iceland spar, and we obtain two images on the screen. By rotating the crystal on its axis, one of the images revolves around the other, but neither disappears during the revolution. Now this fact proves that the light which falls on the crystal is unpolarized ; for if it had been polarized, one image would have disappeared in certain positions, as 1 shall hereafter prove. 10. Polarization. — When submitted to certain influences, the rays of common light acquire peculiar properties, designated by the term polarization. These peculiarities are not distinguishable by the unassisted eye. A very common question, put by persons who have not studied the subject, is, " What is polarized light?" and the philosopher feels very considerable difficulty in giving a concise and intelli- gible reply ; so that the enquirer, perhaps after listening to a lengthened detail, frequently goes away, without obtaining as he says, a direct and short answer to his question. There are two modes of reply : one is to describe, independent of all hypotheses, the properties by which polarized light is dis- tinguished from common light ; the other, is to adopt some hypothesis of the nature of light, and, therefore, to give an hypo- thetical explanation of the nature of polarized light. Whichever method we adopt — and I shall give both — lengthened details are necessary to enable the uninitiated to comprehend the subject. There'are four methods of polarizing light, viz. a. Reflection. b. Simple refraction. c. Double refraction. d. Transmission through 'a plate of tourmaline. In the following table I have contrasted some of the distin- guishing characteristics of common and polarized light : A Ray of Common Light, A Ray of Polarized Light, 1. Is capable of reflection, at oblique 1. Is capable of reflection, at oblique angles of incidence, in every po- angles of incidence, mcertom/wst- sition of the reflector. tions only of the reflector. 2. Penetrates a plate of tourmaline 2. Penetrates a plate of tourmaline (cut parallel to the axis of the (cut parallel to the axis of the crystal) in every position of the crystal) in certain positions of the plate. plate, but in others is wholly in- tercepted. 3. Penetrates a bundle of parallel 3. Penetrates a bundle of parallel glass plates, in every position of glass plates, in certain positions of the bundle. the bundle, but not in others. 4. Suflers double refraction by Ice- 4. Does not sufier double refraction land spar in every direction, ex- by Iceland spar in every direction, cept that of the axis of the except that of the axis of the crystal. crystal. In certain positions, it siiSers single refraction only. 14 ON THE POLARIZATION OF LIGHT. Thus, then, one mode of replying to the before-mentioned question would be, by recapitulating the facts stated in this se- cond column. This reply would form what I may term a matter- of-fact answer, being independent of all hypothesis. The naked or unassisted eye cannot then distinguish common from polarized light. Every person must have repeatedly seen polarized light, but not knowing how to recognize it, has failed to distinguish it from common light. If you look at a polished maho- gany table, placed between you and the window, part of the light reflected from the table is polarized. When you look obliquely at the goods in a linendraper's shop, through the plate-glass window, part of the light by which you see the articles is polarized. When you see two images by a crystal of Iceland spar the transmitted light is polarized. The atmospheric light is frequently polarized, especially in the earlier and later periods of the day when the solar rays fall very obliquely on the atmo- sphere. At the present season, the effect may be perceived at eight or nine o'clock in the morning and five or six o'clock in the afternoon, the observer standing with his back to the sun, or with his face north or south. 1 have found that the effect is best per- ceived when the sun is shining, and the atmosphere more or less misty. It is obvious, therefore, that after we have polarized a ray of light, we must employ some agent to detect its peculiar pro- perties. This agent is called the analyser. It would be better understood if it were termed the test. It may be a reflecting plate, a plate oj tourmaline, a bundle of glass plates, a Nichol's prism, or a double refracting prism ; in fact, the analyser or test must be a polarizer. Thus, then, a. polariscope consists of two parts : one for polariz- ing, the other for analysing or testing the light. There is no essen- tial difference between the two parts, except what convenience or economy may lead us to adopt ; and either part, therefore, may be used as polarizer or analyser; but whichever we use as the polarizer, the other then becomes the analyser. a. Polarization by reflection. — This method of polarizing light was discovered by Mains, in 1 8U8. He was viewing, through a double refracting prism, the light of the setting sun reflected from the glass windows of the Luxemburgh palace in Paris ; and, on turning round the prism, he was surprised to observe a re- markable difference in the intensity of the two images : the most refracted alternately surpassing and falling short of the least re- fracted in brightness. Polarizing reflectors are usually glass. This should be either ground or blackened at the back to prevent posterior reflection. Water is seldom made use of. Mica may be employed instead ON THE POLARIZATION OP LIGHT. 15 of glass. A well-polished or var- nished piece of wood (as a table, top of a pianoforte, or a counter) is very convenient. Marble also answers tolerably well. The shining back of a book is oft- Polarization by Rejlection. entimes Serviceable. Metallic a. Incident ray of common or unpo- plates are objectionable ; since '"Al^Ratfof glass (-polarizing plate). ^ne reflection Only from them , c. Reflected ray of polariisecl llRht. the light is found tO be ellipti- cally polarized ; though by successive reflections it becomes plane polarized. The polarizing angle varies for different substances, as the following table shows : Angles of Polarization by reflection. Water ... 52° 45' Glass .... 56° 45' Sulphate of lime 56° 45' Rock crystal . 56° 58' Iceland spar . . 58° 51' Diamond ... 68° I' Fronn a very extensive series of experiments, made to determine the maximum polarizing angles of various bodies, Dr. Brewster arrived at the following law : the index of refraction is the tangent of the angle of polarization. It follows, therefore, that the re- flected polarized ray forms a right angle with the t efracted ray. Here, perhaps, is the most convenient place for referring to a suggested application of polarized light. I have slated that light is polarized by water, at an angle of 52° 45'. By the analyser (as a tourmaline, or Nichol's prism, or a bundle of glass plates) the whole of this reflected polarized light may be intercepted \yithout oflTering any impediment to the unpolarized but refracted light which has traversed the water ; so that objects may be more readily seen at the bottom of ponds, rivers, and the sea, by this expedient than otherwise, since the glare of the reflected light is prevented. Hence anglers, and those fond of fish-spearing, may employ this property of polarized light in the discovery of the objects of their sport; and commanders of vessels may avail themselves of it to detect rocks and shoals in the bottom of the ocean, which are not otherwise visible except by viewing them from the mast-head, by which the angle of reflexion is diminished, and consequently the quantity of light reflected is thereby lessened. I proceed now to demonstrate the polarization of light by re- flection, and the essential properties of the polarized ray. For this purpose, I obtain an intense light by throwing the flame of a jet of mixed oxygen and hydrogen gases on a cylinder of lime. 16 ON THE POLARIZATION OF LIGHT. This light, which I shall, for brevity, call the lime-lightyk condensed by two crossed lenses (called condensers), and thrown on a plate of glass, blackened at the back, and placed at an angle of 56° 45'. The lig;ht is polarized by this plate, and being then refracted by two plano-convex glasses (termed the power), is afterwards re- ceived on a semi-transparent calico screen, strained on a wooden frame, and moistened with water. A bundle of glass plates is sometimes used as a reflecting polarizer : it has the advantage of reflecting more light, but a portion of it is unpolarized. The light thus polarized is not distinguishable by the eye from common light,- but to prove its nature, I proceed to test it. For this purpose, I place a plate of tourmaline on the front of the polariscope, and on revolving it, you observe the light on the screen is alternately cut off and admitted. At 0 the tourmaline transmits the light, at 90'^ it absorbs it, at 180° it transmits it, at 270° it absorbs it. I remove the tourmaline, and substitute a bundle of glass plates, placed at an angle of 56° 45'. On revolving this, the light is observed to be alternately cut off and transmitted, as in the case of the tourmaline. I now substitute a double refracting prism for the bundle of glass, and on revolving this, it is seen that in two positions double refraction takes place, and two images are produced on the screen, while in two intermediate positions, one image is cut off. Thus, then, the light reflected from the blackened glass plate of the polari- scope, is polarized, since it possesses the characters assigned to ^his kind of light. Common crown or window glass serves well enough for ordi- nary purposes. The flattest, thinnest, most colourless, and per- fect pieces are to be selected. A very convenient mode of using them is the following : — Take two one ounce paper pill- boxes, remove the lids and the bottoms, and then paste together the two cylinders of the boxes, so as to form a tube. Into this, place obliquely sixteen pieces of window glass. oppositely polarized to c. Polarization by single Refraction, a. Ray of common or unpolarized light. b. Bundle of glass plates. c. Reflected polarized ray. d. Refracted polarized ray. This ray is 2. Polarization by single Refraction. — If light be trans- mitted obliquely through a bun- dle of diaphanous laminse, it suffers polarization. The very thin parallel glass plates used for microscopes, and sold by Bromley and Drake, at 315, Oxford Street, form the best medium. Sixteen or more of these are to be placed parallel, and the bundle then placed at an angle of 56° 45' to the ray to be polarized. ON THE POLARIZATIOX OF LIGHT. 17 Having cut in each of the lids a circular hole, of about the size of a sixpence, place a lid at each end of the cylinder Ihe I.ght by passing obliquely through the glass-plates in this cylinder, becomes polarized. A bundle of mica plates may be used for polarizing, but it is interior to the bundle of microscope glass above referred to 3. Polarization by Double Refraction.— I have already demonstrated the double refractive power of Iceland spar- though 1 have not hitherto said anything of the nature of the light of which the two pencils are made up. I now proceed to demonstrate that the two pencils or rays produced by this process are polarized; but the polarized state of the one ray is of an opposite kind to that of the other ; so that the two rays are said to be oppositely polarized. That this is the case is proved by applying our tests to them. Thus if J apply a plate of tourmaline, you observe that, as this is rot'ated one of the luminous rays is alternately cut oflT, which would not be the case were the rays composed of common light; while if both were similarly polarized they would be simultaneously and not alternately absorbed. If I substitute the bundle of glass plates for the tourmaline, one of the rays is reflected, and the other transmitted ; and by revolving the bundle 90° the rav which was reflected is now transmitted, and that which was transmitted is now reflected. ^^^^^^'^ prism, or NichoVs eye-piece*, is a most valuable and convenient polarizer. It is an oblique rhombic prism, whose terminal planes form an angle of 68° with the adjoining obtuse lateral edges. It is formed by joining, by means of Canada balsam, two wedge-shaped pieces of Iceland spar. It is a double l^oiible Refraction by a rhombohedron of Vtihactor, but the two rays are a. The obteatf^r-Aline drawn ^^^''^^^ «° that Only cryTta? ^ * ^^epresents. the axis of the image IS SCen in itS USUal c. fncident ray of unpolarized or com- P^^'t'O"- The cause of this is ^r"??'- , , . Canada balsam, whose index e.o. Oppositely polarized transmitted ^( rf>?v:,ni\r.,. ^^ K^nx • • . rays, e IS called the extraordinary, 0 the rerraction (1.549) IS Ulterme- 7.rffie^which.henviewedthro„.h ^i^te between that for the ordi- ^herhombohedron, appears doubled./^ "^O' ray (1.654), and that for *r . "^he extraordinary ray (1.483) so that t his substance changes the direct ion of the two rays in an * See Jameson's Journal, vols. 6, 16, and 27. ~~ ~* 18 ON THE POLARIZATION OF LIGHT. opposite manner, before they enter the posterior half of the prism. Over the tourmahne this prism has the advantage of being perfectly free from colour, but it has the great objection of giving a very limited field of vision. 4. Poiarizatiou by the Tourmaline. The last mode of polarizing light to which I shall have occasion to allude, is by transmission through a plate of tourmaline, cut parallel to the axis of the crystal. The substance called tourmaline, and to which I have al- ready referred, is a precious stone, which is occasionally cut and polished, and worn as a jewel. There is good reason for supposing that it is the substance to which Theophrastus alludes under the name of lyncurium (XvyKvpiov). It is found in various parts of Europe, Asia, Africa, and America. Much of that found in commerce comes from the Brazils. It occurs in thick and short, as well as in acicular prismatic crystals, belong- ing to the rhombohedric system, and which have three, six, or more sides and dissimilar summits. Thus in most tourmalines the extremities or summits of the crystal differ from each other in the number or situation of the planes ; and like other unsymmetrical crystals, the tourmaline becomes electrical while changing its temperature, one extremity becoming positive, the other negative. a. Brazilian tourmaline. By cooling, the upper end becomes positively ( + ), lower negatively ( — ) electrical. O. Anotner tourmaline. , , , . , j a c. Tourmaline slit, parallel to the axis, into four plates, which, when ground and polished, are used as either polarizers or analysers. ^ a d. Tourmaline cut at right angles to its axis. The plates, thus obtained, are ground and polished, and then used in the polariscope for producing coloured rings. The colour of the tourmaline is various, but green and brown are the prevailing tints. Curiously enough, there appears to be a remarkable connection between the colour and the other optical, as well as the electrical properties of the tourmaline. Green, blue, and yellow colours are, in general, imperfect polarizers. The brown and pinkish tints are the best. White colourless tourma- lines do not polarize. The principal constituents of the tourmaline, are silica and ON THE POLARIZATION OP LIGHT. 19 alumina, Boracic acid is alway., present, as also magnesia, iron, potash, soda, Sfc, are not constant ingredients For optical purposes, the tourmaline is cut in two directions yiz. parallel, and likewise at right angles to the crystallo^raphi- cat axis Tourmaline plates for polarizing or analyzing, ,,ve cut parallel to the axis about of an inch thick ; but for depolanzing or showing coloured rings, at right angles to the axis. Considerable care and experience are required to pre- pare good plates.* If they be not cut perfectly parallel to the axis, their polarizing and analyzing powers are greatly impaired. In buying plates, avoid cracks, flaws, and deep colours, and select those which by experiment you find to be good polarizers, for as the po anzing powers are very unequal in different crystals, no- thing but a trial of each plate can determine its goodness 1 he light which is transmitted by a plate of tourmaline (a or a') (cut parallel to the axis), is plane-polarized. A second plate of tourmaline {b), if held in the same position, transmits the light polanzed by the first plate ; but if the second plate ilj) be turned round, so that its axis is at right angles with the axis of the first plate, no light is transmitted. Action of Toxirmalme Plates on Light. ,.nf;.;rf JT° tourmaline (cut parallel to the axis of the crystal), with their axes coincident ; a. is called the polarizer, and b. the analyser. c. Incident ray of mipolarized light. d. Transmitted ray of light polarized by a. e. Ray polarized by a, and transmitted by b. hy'a'% ?nTe° cS b/fi''!'''"'"''^ '''''' '° ^^^^^ "S^**' POl^i^^ The great objection to the tourmaline, as a polarizer, is, that the transmitted polarized beam is more or less coloured. If laro-e, transparent, and colourless polarizing tourmalines could be ob- tained, they would be invaluable to the optician. That common light is polarized by transmission through a plate of tourmaline, as above described, is proved thus : — A second tourmaline, placed with its axis at right angles to the first, does not permit light to pass. But when the axes of the plates comcide, the light p olarized by the first plate is trans- * Mr. Darker, of Paradise Street, Lambeth, prepares tourmaline plates lor most of the opticians. r^a^ca c 2 20 ON THi: POLAHTZATION OF LIGHT. mitted by the second. Moreover, if the light transmitted through the first tourmaline be received at an oblique angle on a plate of glass, blackened at the back, it is reflected only on two sides of the ray, and at an angle of 56" 45'. Lastly, if it be tested by a double refracting prism, it is found to produce double refraction in two positions only of the ray, for on rotating the double refracting prism on its axis, we find that one of the images is alternately cut ofl^, and in intermediate positions, two faint images only are produced. 2.. WAVE HYPOTHESIS OF LIGHT. There are two hypotheses or theories which have been formed to account for the phenomena of light; one of these is called, the projectile theory, or the theory of emission ; — while the second is denominated the wave, or undulatory theory of light. The first is sometimes called the material or Newtonian theory of light. But as on both hypotheses a fine subtile form of matter is required to account for luminous phenomena, the one hypothesis equally deserves the name of material with the other. Moreover, I cannot understand why the projectile theory is to be exclusively honoured with the name of the Newtonian ; fortbough on some occasions Newton certainly adopts it, yet on others he appears to support the theory of waves. On the present occasion it is not my intention to enter into any details respecting the projectile theory ; for however ably and plausibly it accounts for some optical phenomena, it is manii'estly incompetent to explain those which it is the object of this course of lectures to describe. Light, a Property or Motion. — The wave- theory supposes that light is a property — a motion — a vibration of something. But of what? Euier imagined that the vibrating medium, in dense bo- dies, was the body itself ; through the gross particles of which he supposed the light to be propagated in the same manner as sound. This hypothesis, Dr. Young* declares to be " liable to strong objections;" and he adds, that " on this supposition, the refrac- tion of the rays of light, on entering the atmosphere from the pure ether which he describes, ought to be a million times greater than it is." Ether. — To account for the phenomena of light, philosophers have assumed the existence of a vibrating medium, which has been called the ethereal medium, the luminiferous ether, or simply • A Course of Lectures on Natural Philosophy, vol. ii., p. 542. Also Phil. Trans, for 1800. WAVE HYrOTHESlS^ 21 ether. It is supposed to be a rare, highly elastic, subtile fluid, which occupies all space and pervades all bodies. As the sen- sation of light is supposed to be excited by the undulations of this medium, so, where light exists, there ether must be. Hence it fills ail space. It is between the sun and the earth, the earth and the stars, and so on. If it did not exist in water, diamonds, glass, &c., these bodies would not be diaphanous; So that it must pervade all bodies. Even opake substances roust contain it, since, as in the case of gold, these become transparent when excessively thin. Existence of an Ether. — We have no independent evidence to adduce of the existence of this medium. It is, therefore, an as- sumption ; but one which is sanctioned by the high authority of Descartes, Huyghens, Euler, Hooke, Newton, Young, Fresnel, and some of the most distinguished philosophers of the present day, among whom are Sir John Herschel and Arago. These eminent men have seen in this assumption nothing inconsistent with their knowledge of the constitution of the universe. The electrician and the magnetician have assumed, respectively, an electric and a mag- netic fluid, and there can be no impropriety, therefore, in the op- tician assuming a luminiferous ether, provided, however, that it be compatible with well ascertained facts, and do not violate known laws. Moreover, it is by no means improbable that the fluids ■which have been respectively assumed as the causes of electrical, magnetical, calorific, and luminous phenomena, may be one and the same. Even gravity, perhaps, may be referable to the same cause. Newton* himself has thrown out a speculation of this kind. Alluding to the ether, he says, '* Is not this medium much rarer within the dense bodies of the sun, stars, planets, and comets, than in the empty celestial spaces between them ? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies ; every body endeavouring to go from the denser parts of the medium towards the rarer?" Very recently, Dr. Rogett and MosottiJ have shown how, on the assumption of an ethereal medium, the phenomena of gravitation and elec- tricity, may be included in the same law. It has been said, that if the universe contained a fluid of the kind here referred to, the planets must experience some resist- ance to their motions, and, therefore, that as no resistance can be detected, there can be no ethereal medium. This conclusion, » Opticks, p. 325. Query 21. t Electricity. Published in the Library of Useful Knowledge. X On the Forces which regulate the Internal Constitution of Bodies, in Taylor's Scientijic Memoirs, part iii. 22 ON THE POLARIZATION OF LIGHT. however, is by no means. a necessary one, for " if this ether," says Newton*, "should be supposed 700,0i^0 times more elastic than our air, and above 700,000 times more rare, its resistance would be above 600,000,000 times less than that of water. And so small a resistance would scarce make any sensible alteration in the motions of the planets in ten thousand years." The most satisfactory evidence of this resistance, if indeed it exist, might be expected to be found in the case of the comets, bodies made up of the lightest materials, in fact, masses of vapour, and, there- fore, from their less momentum, more likely to suffer retardation. In the case of Encke's comet, evidence of this resistance is be- lieved to have been obtained. The mean duration of one entire revolution of this comet is about 1207 days, and the " magnitude of the resistance is such as to diminish the periodic time about of the whole at each revolution ; a quantity so large that there can be no mistake about its existence.f" The following table of the mean duration of one entire revolu- tion of this comet, allowance being made for perturbations occa- sioned by the action of neighbouring planets, is taken from a memoir by Encke+. Days. From 1786 to 1795 1208.112 " 1795 to 1805 1207.879 " 1805 to 1819 1207.424 Sir John Herschel § observes, that " on comparing the intervals between the successive perihelion passages of this comet, after al- lowing, in the most careful and exact manner, for all the disturb- ances due to the actions of the planets, a very singular fact has come to light, viz., that the periods are continually diminishing, or, in other words, the mean distance from the sun, or the major axis of the ellipse, dwindling by slow but regular degrees. This is evidently the effect which would be produced by a resistance expe- rienced by the comet from a very rare ethereal medium pervading the regions in which it moves, for such resistance, by diminishing its actual velocity, would diminish also its centrifugal force, and thus give the sun more power over it to draw it nearer. Accord- ingly (no other mode of accounting for the phenomenon in ques- tion appearing) this is the solution proposed by Encke, and gene- rally received. It will, therefore, probably fall ultimately into the sun, should it not first be dissipated altogether, a thing no way improbable, when the lightness of its materials is considered, and which seems authorized by the observed fact of its having been less and less conspicuous at each reappearance." * Opticks, p. 327. Query 22. t Airy, JReport on the Progress of Astroyiomy, in the Report of the British Association for 1833. J Astrcnomische Nachrichten, Nos. 210, 211. § Treatise on Astronomy (in Lardner's Cyclopaedia^, p. 309. WAVE HYPOTHESIS. 23 Leaving these speculations, and assuming, then, the existence of a luniiniferous ether, I proceed to point out the properties such a fluid must be supposed to possess. Ethereal Molecules. — The ether consists, or is made up of mi- nute parts, which we call molecules, between which there must exist attractive and repulsive forces*, in virtue of which the ether possesses extreme elasticity. Moreover, there appears to exist some attractive force between the ethereal molecules and the par- ticles of the grosser forms of matter. Indeed, Dr. Young supposed that the vibrating medium is the ether and ponderable matter conjointly. But instead of insisting on the actual existence of an ethereal medium composed of molecules, we " may be content to look at the theory simply as a mathematical system, which faithfully represents, at least, a wide range of phenomena, and to some extent connects the laws so made out with dynamical principles regulating the motions of a system of points, combined to form an elastic system, which, for brevity and illustration, we call molecules, constituting an cethereal medium f." Ethereal Waves. — If we suppose the existence of attractive and repulsive forces between the ethereal molecules, it follows, that when these molecules are at rest or have attained a state of equi- librium, any attempt to move one molecule must be attended with the displacement of several ; for the motion is extended to adjacent molecules. So that if a vibratory movement be commu- nicated to one, it is extended to several. Now, an assemblage of vibrating molecules, in all phases of vibration, constitutes an ethe- real wave. These vibrations being communicated through succes- sive portions of the ethereal medium, reach the retina or expanded optic nerve, and are propagated along the optic nerve to the brain, where they excite in us the sensation of light, just as the vibrations of the air communicated to the auditory nerve, and from thence to the brain, produce the sensation of sound. The number of impulses made by the ethereal molecules on the retina in a given time, determines the colour of the light, just as the number of impulses by the aerial molecules on the auditory nerves determines the pitch, note, or tone of sound, lience co- lours are to the eye what tones are to the ear. "From Newton's measures of the thicknesses reflecting the difFerenl colours, the breadth and duration of their respective * See a paiper by Mr. Earnshaw, On the Nature of the Molecular Forces which regulate the Constitution of the Luminiferous Ether, in the Transactions of the Cambridge Philosophical Society, vol. vii., part 1. t A Geneiral and Elementary View of the Undidatory Theory, as applied to the Dispersion of Light. By the Rev. Baden Powell, 1841, pp. 4 and 5, 24 ON THE POLARIZATION OF LIGHT. undulations may be very accurately determined. The whole visible spectrum appears to be comprised within the ratio of three to five, which is that of a major sixth in music ; and the undulations of red, yellow, and blue, to be related in magnitude- as the numbers 8, 7, and 6 ; so that the interval from red to blue is a fourth. The absolute frequency expressed in numbers is too great to be distinctly conceived, but it may be better imagined by a comparison with sound. If a chord sounding the tenor c, could be continually bisected forty times, and should then vibrate, it would afford a yellow green light : this being denoted by c, the extreme red would be f, and the blue q. The absolute length and frequency of each vibration is expressed in the table*;" supposing light to travel at the rate of 192,000 miles per second. Colours. Length of an Undulation in parts of an inch in Air. Number of Undulations in an inch. Number of Undulations in a second. .0000266 37640 458 millions of millions. Eed .0000256 39180 477 ii Interraediate ... .0000246 40720 495 a .0000240 41610 506 Intermediate . . . .0000235 42510 517 YeUow .0000227 44000 535 Intermediate . . . .0000219 45600 555 .0000211 47460 577 Intermediate ... .0000203 49320 600 it .0000196 51110 622 a Intermediate . . . .0000189 52910 644 <( .0000185 54070 658 Intermediate . . . .0000181 55240 672 C( .0000174 57490 699 Extreme .0000167 597.50 727 Mean of all, or white .0000225 44440 541 n There is a limit to the sensibility of both ear and eye; that is, a certain number of impulses must be made in a given time on these organs before we become sensible of them ; and if we go on augmenting the number, we cease to be sensible of them after a certain time. Now, the limits of sensibility of the eye are much more confined than those of the ear ; or, in other words, the sen- sibility ceases much sooner in the case of the eye than in that of the ear. * Dr. Young's Course of Lectures on Natural Philosophy, vol. ii. p. 627. The above table is also taken from this work. Dr. Young calculated the velocity of Ught at 500,000 million feet in 8^ minutes ; but I have adopted Sir John Herschel's assumption of 192,000 miles per second, which makes the numbers in the fourth column of the table different to those given by Young. WAVE HYPOTHESIS. 25 The following is the range of the human hearing according to Biot*.— Number of Length Vibrations in of Sonorous one second. Waves. Feet in. Commencement of appreciable Sounds 32 32 0 64 16 0 128 8 0 256 4 0 512 2 0 1024 1 0 2048 0 6 4096 0 3 8192 0 li But the actual range varies in different individuals, and we shall not be far from the truth if we assume, with Dr. WoUastonf and Sir John Herschel^, that the whole range of human hearing includes about nine octaves. ^ Now on comparing the range of human hearing with that of vision, we find the relative limits of the two senses to be as follows : — Et/e. Ear. Commencement of sensibility . 1 . . . . 1 Cessation of ditto , . ]024 It is highly probable, however, that the range of human vision, like that of hearing, is subject to variation in different individuals. From these observations, then, it will be understood, that, according to the undulatory theory, the colour of the light depends on the lengths of the waves, or on their number in a given time. Thus red has the largest waves, and, therefore, the smallest number in a given time ; while violet has the shortest waves, and, therefore, the greatest number in a given time. The intensity of the light depends on the amplitude or extent of excursion of the ethereal molecules from their points of rest ; or in other words, on the height of the wave. Just as when we make a cord sound, we find that the sound diminishes in pro- portion to the diminution of the amplitude of the oscillations. Vibrations. — The vibrations of the ethereal molecules may be rectilinear or curvilinear. It is not easy to give a popular illus- tration of the first, which, however, may be easily conceived ; but the motion of a pendulum is an excellent example of curvi- * Precis Elementaire de Physique, vol. i. p. 324. t Phil Trans. 1820, p. 306. J Enci/clopcEdia Metropolitana, art. Sound, p. 7S2. 26 ON THE POLARIZATION OF LIGHT. linear motion. A ball, suspended by a string, describes in vibrating a curved line, or, in other words, it vibrates in the arc of a circle. An assemblage of molecules, vibrating rectilinearly , in the same plane, and in all phases of their vibrations, constitutes a plane wave. An assemblage of molecules, vibrating curvilinear ly or rotating, the rotation or vibration of every molecule being made in parallel planes, constitutes what may be termed a spiral or helicoidal wave. If the molecule revolve in a circle, the wave is circular ; if in an ellipse, the wave is elliptical. All motion being naturally rectilinear, it follows, that when we see a body moving in a curve of any kind, we conclude that it must be under the influence of at least two forces ; one putting it in motion, and another drawing it off from the rectilinear course, which it would otherwise have continued to move in. The cause of these curvilinear movements of the ethereal molecules will be subsequently explained. g The Rev. Professor Baden Powell has contrived an ingenious machine, for showing in what manner rec- tilinear and curvilinear vibrations produce respectively plane and helicoidal (circular or elliptical) waves. It is founded upon this geometrical construction : a finite line, P Q, moves always through the point C, and with its end P always in the circumference of a given circle, whose centre is A ; the end Q will describe a certain curve, which appears upon analysis to be one of a high order, but having in general some sort of oval form, which varies as the distance ^ C is altered. If J. C be very great compared with the radius of the circle, Q will move up and down, almost in a straight line : if A C he somewhat less, its path will resemble an ellipse; if still less, it will be more rounded or re- semble a circle. Upon this the machine is constructed as follows (/I and C cor- respond in both diagrams) : The lower part consists of a stout iron wire bent into a series of cranks, of which the two extremes are in the same position, e. g. downwards ; the middle one vertical, and the intermediate ones at intermediate inclinations. Attached to each crank by a hinge or joint, is a long rod, R R', &c., which passes through an aper- ture in a cross-bar, C C, at the top. The top of this rod is made conspicuous by an ivory ball or a ball painted white, B, the rest of I he apparatus being painted black. The bar C C is attached to the supports A C A' C, by screws, and can be removed (without changing the rods) from D D to the positions D' D', or D" D". The proportions of the machine are not essential, but WAVE HYPOTHESIS. 27 only that the length of the rods should be great compared with that of the cranks. When the bar is at 2) D, on turning the handle a plane polarized wave is produced by the balls; when at D' D' an elliptical one ; and when at D" D" a circular one — that is, what, for illustration, and to the eye, may be considered so. If the distance A D" be eighteen inches, A V should be about twenty-four, and A D about thirty-six inches ; but these are not material as to exactness. Mr. E. M. Clarke, philosophical instrument-maker, of the Strand, has constructed this instrument without cranks. The upright rods are attached inferiorly to metallic rings, through each of which runs an axis, A A' ; and on this axis the rings are fixed in a spiral or helicoidal manner. Fig. 9. Pnifessor Powell's Machine, as constructed by Mr. Clarke. Transversal Vibrations. — I come now to a most important part of the undulatory hypothesis — that by which the phenomena of polarized, as distinguished from those of common or un- polarized, light are accounted for. I refer now to the hijpothesis of transversal vibrations, first suggested, [ believe, by Dr. Young, but most admirably developed and applied by Fresnel. " The existence of an alternating motion of some kind, at minute intervals along a ray, is," says Professor Powell,* " as real as the motion of translation by which light is propagated through space. Both must essentially be combined in any cor- rect conception we form of light. That this alternating motion * A General and Elementary View of the Undiilaturi/ Theory, p. 4. 28 ON THE POLARIZATION OF LIGHT. must have reference to certain directions transverse to that of the ray is equally established as a consequence of phenomena — and these two principles must form the basis of any explanation which can be attempted." In order to understand transversal vibrations, let us first con- sider how waves of water, and of other liquids, are formed. If a stone be thrown into a pond, there is formed a system or group of waves, which commences at the spot where the stone impinges, and gradually extends outwards in the form of concentric circles. The aqueous particles in the centre are forced down, and the surrounding ones thereby urged upwards above the normal level of the water. In this way the central depression, and the first or innermost circular heap, are formed. But gravity soon causes this heap to subside, and fill up the central depression, while by its downward progress it acquires momentum, and thereby descends below its normal level, thus not only giving rise to a circular depression, but causing the formation of another and outer circular heap by the elevation of the neighbouring particles. In this way the waves gradually extend outwards. It is obvious, then, that in waves of liquids, the directions of vibration of the molecules is vertical, or nearly so, while the propagation of the waves is horizontal. In a vibrating cord, the vibrations ore rectangular to the •propagation of the undulations along the cord. In luminous waves, the direction of vibration is supposed by Fresnel to be transverse to the direction of propagation ; and the more recent researches of Cauchy seem to have established the doctrine of transversal vibrations; but he assumes a third vibra- tion, namely, one parallel to the ray, so that, according to him, the motions of the molecules take place in three rectangular axes. The necessity for this third axis of vibration, parallel to the ray, seems to be derived from the phenomena of dispersion. Now, polarized light, on the wave hypothesis, is light which has only one plane of vibration ; whereas common or unpolarized light consists of light having two or more planes of vibrations, of which two must be rectangular — that is, after the molecules have vibrated in one plane, they change their vibration to another plane. So that common light consists in a rapid suc- cession of waves in which the vibrations take place in different planes. It does not, however, appear that the planes of vibration are continually changing; but that in each system of waves, there are probably several hundred successive vibrations, which are all performed in the same |)lane ; although the vibrations of one system bear no relation to those of another. Thus, then, we call that light polarized, in which all the vibrations take place in one plane; but when vibrations are succeeded rapidly WAVE HYPOTHESIS. 29 by other vibrations in an opposite plane, the two waves though separately called polarized, are together, termed unpolarized or common light ; so that, as Fresnel has observed, common light is merely polarize'l light, having two planes of polarization at right angles to each other. Thus, then, I have now replied theoretically, as well as prac- tically, to the question, What is polarized light ?" Partially polarized light consists, according to Sir John Herschel, of two unequally intense portions; one completely polarized, the other not at all. Sir David Brewster, however, re- gards it as light whose planes of polarization are inclined at an- gles less than 90°. But to the latter view some objections have been raised by Mr. Lloyd. In the following diagram, let the straight lines represent the directions in which the ethereal molecules are supposed to vibrate. Then A B and CD will represent the direction of vibration ot the ethereal molecules of two oppositely polarized rays ; A B' C D' the two rectangular directions of vibration of a ray of com- mon or unpolarized light ; and A" B" C" D" a ray of partially po- larized light, according to Sir D. Brewster's hypothesis. Fig. 10. ''The difference between a polarized and an ordinary ray of light," says Sir John Herschel, "can hardly be more readily conceived than by assimilating the latter to a cylindrical, and the former to a four-sided prismatic rod, such as a lath or a ruler, or other long, flat, straight stick." In order to illustrate Fresnel's notion of transversal vibrations, and of the hypothetical difference between common and polarized light, painted card models are very convenient. A piece of card- board is cut out in a waved or undulated form, so that the curves of the upper and lower edges accord. Then, midway be- tween these edges, a row of circular black spots is painted on the card : these are to represent the ethereal molecules, while the card-board represents the plane of vibration. A single card thus cut and painted serves to illustrate a ray of plane-polarized light (Fig A) : two of them placed side by side, with their planes at right angles to each other, B, represent the two oppositely-polarized rays produced by a double refracting prism, while two so placed that they mutually cross, represent common light, C 30 ON THE POLAllIZATION OF LIGIIT. Fig. 11. We are now prepared to understand bow common light becomes polarized. In the case of tlie doubly refracting bodies the two planes separate, for reasons that will be explained in the next lecture ; and as the two waves have the planes of their vibrations at right angles to each other, we see now how the rays are said to be oppositely polarized. As these two waves are propagated with different velocities, they in consequence follow different paths. The tourmaline likewise separates the two planes ; but it gradually extinguishes the one, by offering such an impediment to its progress that its vibrations are destroyed. The agency of the rejlecfing plate in polarizing light may also be readily ac- counted for. When a ray of common light falls on a transparent surface, at a certain angle, its planes of vibration are resolved into two, one of which is transmitted^ the other reflected; both are polarized, but oppositely. The action of the analyzer or test may also be easily under- stood. Suppose the analyzer to be a reflecting plate': if this plate be at the same angle to the ray as the polarizing plate, the vibrations will be reflected when the planes of reflexion of the polarizing and analyzing plates coincide — but will be trans- mitted (that is not reflected) when the planes are at right angles to each other. Suppose the analyzer to be a tourmaline plate : in one position this plate permits the vibrations to be transm.itted, but in a position perpendicular to this it destroys them. So that in these two rectangular directions, the crystal of tourmaline must possess unequal elasticities ; for the motion or vibration is transmitted in the one, but stifled or destroyed in the other direction. Suppose the analyzer to be a rhombohedron of Ice- land spar; in either of two rectangular directions the vibrations of the polarized incident ray are propagated unchanged, but at an angle of 45*^ to either of these positions, the plane of vibration of the incident ray is resolved into two rectangular planes, each of which forms an angle of 45° with the incident ray. WAVE HYPOTHESIS. 31 Interferences of Light. — It is a law in dynamics, that the velocity produced by two joint forces,- when they act in the same direction, will be as the sum of the forces. Hence if two waves, all of whose parts respectively coincide, meet, it is evident that their velocities will be doubled. Whether the vibrating medium be water, air (sound), or ether {light), this statement holds good : the intensity of the waves is doubled. But the velocity of two joint forces, when they act in opposite directions, will be as their differences. Hence, if a wave (of water, air, or ether) be half an undulation behind another wave, the velocities of the two are mutually destroyed. When stones are thrown into a pond, and two groups of waves cross each other on its surface, there are points at which the water remains immove- able when the two systems are nearly of the same magnitude, while there are other places in which the force of the water is augmented by their concurrence. If two sonorous undulations differ a little from each other in frequency, they alternately tend to destroy each other, and to acquu-e a double, or, perhaps, a quadruple force ; and the sound gradually increases and dimi- nishes in continued succession at equal intervals. This alternate intension and remission is called a beat. Pjj^ In the same way, the waves of the luminiferous ether interfere, and, mutu- ally destroying each other, cause dark- ness. This important fact, that under some circumstances, light added to light ^ causes darkness — a fact apparently fatal to the projectile theory of light — was first established by Dr. Young. This distin- guished philosopher — whose attainments and knowledge were insufBciently esti- mated while he was living — passed a sun- beam through a hole (0) made with a fine needle in thick paper, and brought 7 into the diverging beam a slip of card (A B) one-thirtieth of an inch in breadth, and observed its shadow (E F) on a white screen, at different distances. The shadow was divided by parallel bands, but the central line (X) was always white. That these bands originated in the interference of the light passing on both sides of the card, Dr. Young demonstrated by simply intercepting the light on one side by a screen (C D), leaving the rays on the other side to pass freely. In this arrange- ment all the fringes which had before existed in the shadow im- mediately disappeared, although the light inflected on the edge 32 ON THE POLAllIZATION OP LIGHT. (A) was allowed to retain its course. The same result took place when the intercepting body was at C D, before the edge B of the body. By a series of wooden sliders, originally contrived by Young*, but jput into a very convenient form for use in the lecture-room, by my friend Mr. Woodward, the interference of waves may be neatly illustrated. By this apparatus it will be seen that when the difference amounts to 2, 4, 6, or other even number of half undulations, the waves coincide and mutually augment their intensities; while, when the difference amounts to 1, 3, 5, or other odd number of half undulations, there is discordance and mutual destruction. Now it will be perceived, that these num- bers coincide with those referred to by Newton, as expressive of his fits of transmission and reflection. If two waves of homogeneous or monochromatic light interfere, the result will be an augmentation or diminution of brilliancy, or complete destruction. The light is augmented when the waves accord— but is lessened or destroyed when they are mutually opposed. Hence Newton's rings, seen by homogeneous light, are merely dark and light bands of one and the same colour. But if two waves of heterogeneous or white light interfere, the result will be the production of vivid coloured fringes. Certain colours are destroyed, while others remain, or have their brilliancy augmented. It is a law in dynamics, that a body acted upon by two forces united, will describe the diagonal of a parallelogram in the same time in which it would have described its sides by the separate action of those forcesf. Hence, if two waves, whose molecules are in the same phases of vibration, but whose planes of vibra- tion are more or less angular, say rectangular, to each other, the only effect produced is an alteration of the plane of vibration. This is an explanation of a fact discovered by Fresnel, and laid down by him as a law, that " two rays of light, polarized at right angles to each other, exhibit none of the phenomena of interference," that is, they produce no colours or fringes. If both the forces act upon a body in such a manner as to move it uniformly, the diagonal described will be a straight line ; but if one of the forces acts so as to make the body move faster and faster, then the line described will be a curve. Now this dynamical law explains how two plane luminous waves, whose molecules are vibrating in rectangular planes, by their mutual action, produce a circula r or elliptical wave. For if two * Lectures on Natural Philosophy, vol. i., p. 390, plate xxv., fig. 352 D. t This fact was demonstrated by a neat machine, invented by Mr. E. M. Clarke, of the Strand. WAVE HYPOTHESIS. 33 systems of waves of equal intensity, and polarized in rectangular planes, differ in their progress ^ of an undulation, the compound movement which they will communicate to each molecule, instead of bemg rectilinear, as in the two fasciculi considered separately, mil be circular, and will be performed with uniform velocity. But if the difference of progress, instead of being an even or an uneven number of |thof undulations, be a fractional number, the vibratory movements will be neither rectilinear, nor circular, but elliptical. Here is an apparatus (fig. 13), contrived, I am informed, by Professor Wheatstone, which illustrates how two rectangularly polarized rays of light may influence each other. It consists of a series of rods disposed horizontally in an undulated form, so as to represent a system of plane waves. One end of each rod is ren- dered conspicuous by a white ball, and it will be seen, that, as now arranged, all the balls (which represent a line of etherial mole- cules) are in one plane, A. If now a block of wood, B, cut so as to represent a system of plane waves of equal size to those repre- sented by the rods, be pressed against the balls, so that the two systems of waves acton each other in a rectangular direction, then, when the waves coincide, the plane, in which the balls lie, changes, and becomes diagonal, as in C ; whereas, if the block be so applied to the balls, that the two systems of waves do not coincide, then the balls no longer remain in one plane, but become placed in a helicoidal manner, representing a circular or elliptical wave, as in D. Fig. 13. With these remarks I finish the theory of light, and have now arrived at the subject of Coloured Polarization. D 34 ON THE POLARIZATION OF LIGHT. lp:cture II. 3. COLOURED POLARIZATION. When an excessively thin film of a doubly refracting crystal is placed in the polariscope, that is, between the polarizing and analyzing plates, the most gorgeous colour or colours appear, and when the analyzer is rotated on its axis they change to complementary tints. If the film be of uniform thickness, the co- lour is uniform •, but if the film be of irregular thickness, dif- ferent colours are perceived. In order to produce colour, it is necessary to use, first, bl po- larizer, as a tourmaline, a doubly refracting prism, or a reflecting plate ; secondly, a Jilm of a doubly refracting crystal, called the depolarizer ; and, thirdly, an analyzer or test, as a tourmaline, a reflecting plate, or a doubly refracting prism. The office of the polarizer is indicated by its name ; it po- larizes the light. Without this no colour is perceived, for a reason which will be hereafter explained. The doubly refracting Jilm, called the depolarizer, receives the light thus polarized, and doubly refracts it. That is, a sys- tem of waves, constituting the incident ray, entering the crystal- line film, is resolved into two systems of equal intensities within it. These form respectively the ordinary and extraordinary rays (fig. 14, 0 and E). They are polarized in planes +45° and — 45® to that of the incident system, so that the plane of polarization of the ordinary system forms an angle of 90° with that of the ex- traordinary system. Now, the two systems of waves thus produced traverse the crystal in different directions and with different velocities ; but as the film or plate is excessively thin, they emerge superposed. One set proceeds through the crystal more slowly than the other ; or, in the language of a distinguished writer on this subject, one set lags behind the other: so that at their emergence they are found to be in different phases of vibration. By the analyzer each of the two systems (O and E) is resolved into two other systems {Oo Oe and Ee Eo), so that now four systems or two pairs are produced. But the vibrations of these four systems are made in two planes : that is, two in one plane, and the other two in a second plane, which is rectangular to the first. Now, as the two vibrations which are made in the same plane, are not in the same phase (the one system having suffered a greater retardation than the other), the waves interfere and produce colour (if the incident light be white). But the two vibrations of the one plane conspire, while those of the other plane are opposed. Hence the tint or colour produced by the interference of the waves, in one plane, is com- COLOURED POLARIZATION. 35 plementary to that produced in the other plane. So that if the analyzer be a doubly refracting prism, both complementary co- lours are seen by transmission; but if it be a reflector, one is reflected and the other transmitted ; whereas, if it be a tourmaline, one is transmitted, while the other is suppressed, extinguished or stifled. Fig. 14. JilJJ "ililinin 1 o Production of Compkmentary Tints, A . A ray of common or unpolarized light incident on B. B. The polarizer (a plate of tourmaline), C. A ray of plane polarized light incident on D. D. The doubly refracting film or depolarizer, O The o^dmary ra7 } P''°'l'»<=ed by the double refraction of the ray C. G. The analyzer (a doubly refracting prism). JE^.The ordinary ray \ produced by the double refraction of the extraordinary ~ '5 lay S. Oo. The ordinary ray j produced by the double refraction of the ordinary ray O. Ee. The extraordinary ray Oo. The ordinary ray Oe. The extraordinary ray To render somewhat more intelligible the cause of the colours being complementary, and, therefore, to explain what is meant by the conspiration and opposition of vibrations, let us suppose the vibrations of the polarized light (C, fig. 14) to be made in the plane, C P, fig. 15; and to give more precision to our ideas, let us further suppose that the molecule C is, at a given instant, moving from C towards P. The doubly refracting film resolves this motion into two other motions, performed at right angles to each other, one in the direction C 0, the other in the direction C E. The waves pro- duced by the vibrations in the plane C 0, we shall suppose to constitute the ordinary system, while those in the plane C E form the extraordinary system. But the plate is much too thin to have produced between these two systems any sensible separation. Each of these motions is resolved, by the analyzer, into two others at right angles to each other. That is, the vibration C O is resolved into the vibrations C Oo and C Oe; while the vibra- tion CE \s resolved into the vibrations C Eo and C Ee. Now, it is obvious, that the two motions C Oo and C Eo act in the same direction, or, in other words, they conspire, or strengthen each other; while the motions C Oe and C Ee, though performed in the same plane, oppose or destroy each other. d2 36 ON THE POLARIZATION OF LIGHT. P< 9 C E Fig. 15. c Oo Oe Ee By rotating the analyzer the reverse happens : C Oo and C Eo oppose or deslroy each other, while C Oe and C'JE'e conspire, or strengthen each other, as in fig. 16. Fig. 16. Oe Oo Ee 'J% C Thus, then, the original polarized ray(C, fig. 14) has been resolved into four rays, two polarized in one plane, and the other two polar- ized in a plane rectangular to this. The two rays which interfere and destroy each other, diflfer by half an undulation. The colour produced by the interference of the conspiring rays, corresponds to the difference of the routes of the two polarized rays in the plate or film, while that which results from the interference of the opposing rays, is that which is due to the same difference augmented or diminished by half an undulation. In the case above noticed, in which CO e and C Ee (fig. 15) are opposed, the colour corresponds to the difference plus half an undulation. But it may be asked, What is the use of the polarizing plate? What is the reason that no colour is perceived if the light which is incident on the double refracting film be common orunpolarized ? To explain this, let us suppose that a ray of common or unpo- larized light consists of two rays rectangularly polarized. Each of these rays will sufter the same series of divisions, subdivisions, and interferences as the former ; but the tints produced by the one COL0T3RED POLARIZATION. 37 ray will be complementary to those of the other; so that we shall thus obtain two pairs of complementary tints, and as the tints of each pair will emerge superposed, they will neutralize each other, and the resulting light will be of uniform whiteness. Thus 1st PAIR OK ad PAIR Of ' TINTS. TINTS. Suppose the two complementary tints produced by one ray to be Green and Eed. Those produced by the second ray will be Red " Green. And the sum of each pair will be White. White. For red and green are complementary tints, and produce by their union white light, as I have already demonstrated. The office of the doubly refracting film, called the depolarizer, is to doubly refract the polarized light. It prepares the rays for the changes which they have ultimately to undergo and by which colour is to be produced. The thickness of the film or crystalline plate determines the tint; but the actual thickness required to produce a given tint depends on the nature of the crystal. By this plate or film two rectangularly polarized systems of waves are produced, which traverse the plate in different directions and with different velocities, and emerge in different phases of vibra- tion. Now as they are superposed, and as the retardation amounts only to a few undulations and parts of an undulation, it might be supposed that colour would be produced by their interference. But I have already stated that two rectangularly polarized rays do not interfere, so as to produce colour. In order, therefore, to make them interfere, their planes of polarization must be made to coincide; and to do this is the function of the analyzer. In order to assist us in comprehend- ing how a polarized ray may be resolved into two others polarized in different planes, we may take, as an illustration, a stretched cord, fig. 17 ^ 5, dividing at B into B C and B D, making a small angle with each other at B, and having either equal or unequal tension. Let us suppose the extremity A of the single cord to be made to vibrate regu- larly in cither a horizontal or vertical plane; now, b;y means of two polished guiding-planes, E F and G H, in- clined at different angles to the horiijon, and making a right angle with each other, the horizontal vibrations of the cord A B, will give rise to two other vibrations, parallel respectively to E F Tig. 17. 38 ON THE POLARIZATION OF LIGHT. and G H. And if we assume the two branches B C and B D to be unequally tense, the waves produced by the vibration of A B will be propagated along ihem with unequal velocity. So that this illustration, which I have adopted from Sir John Herschel's able treatise on light, serves to explain not only how a vibration in one plane may be resolved into vibrations in two other planes, but also why the two resulting waves are propa- gated with unequal velocity. Though a thin plate of Iceland-spar or of any other doubly refracting crystal serves, when placed in the polariscope, for the production of colour; yet certain crystals are preferable to others on account of the facility with which they may be split into thin laminse. Selenite and mica are especially convenient for this purpose ; and the former of these is extensively employed by op- ticians in the preparation of a variety of beautiful and ingenious polariscope illustrations. On this account a brief notice of it is requisite. Selenite, ov sparry-gypsum, is \.\\Q.7iative crystallized hydrated sulphate of lime (Ca O. S 03 + 2 Aq.) It occurs imbedded in London clay. It is found also at Shotover Hill, near Oxford, where the labourers call it quarry glass, and likewise at the Isle of Sheppy. Very large crystals of it are found at Montmartre, near Paris. The crystalline forms in which it occurs belong to the oblique rectangular prismatic system. Haiiy and the late Mr. William Phillips describe its primary form as a right oblique- angled prism ; so that the lateral faces of the crystal are regarded by them as the terminal planes. But the optical characters of the crystal prove the incorrectness of the description of these cele- brated mineralogists : and here, I would observe, is an excellent illustration of the great value of polarized light to the crystallo- grapher. In this particular instance it enables him to distinguish a lateral face, from a terminal plane, of a prism. The crystals of selenite which are most frequently met with, are oblique rectangular prisms, with ten rhomboidal faces, of which two are considerably larger than the others (fig. 18 A). They are very easily slit into thin laminse (a b, fig. 18 B), parallel to these larger lateral faces (terminal planes of Haiiy and W. Phillips). Macles or hemitrope crystals of selenite are very common. By hemitrope, a word derived from the Greek (from rjni half, and rpcTTO) / turn), is meant a figure produced by cutting the primary crystal in two, causing one of the fragments to make half a revolution, and then uniting the sides actually in contact. The most singular and common hemitrope variety of selenite is that called arrow headed selenite (fig. 18 C), and which is so called because the crystal is formed like the barbed head of an COLOURED POLARIZATION. 39 arrow. Its nature may be easily explained. Cut a card or ihin board in a rhomboidal form to represent one of the laminae taken from lateral faces of the prism (fig. 18 D). Then divide it in the direction of its greater diagonal (a 6), and transpose the separated parts in such a manner, that two of the alternate angles, produced by the diagonal division, shall make the point — the other two, the barbs — of the arrow-head. The optical structure of films or thin plates of selenite, having a thickness of from -^^ih. to the ^V^h of an inch, is very curious. In two rectangular directions they allow perpendical^rays of polarized light to traverse them unchanged : these directions are called the neutral axes. In two other directions, however, which form respectively angles of 45° with the neutral axes, these films have the property of double refraction. These directions are usually denominated depolarizing axes ; but they might be more correctly termed doubly refracting axes. In order to render these properties more intelligible, suppose the structure of the film to be that represented by fig. 19, in which the film IS seen to be crossed by two series of light lines, or passages, the one perpendicular to the other. These are to represent the neutral axes. We may imagine, that in these directions only can the ethereal molecules vibrate. A ray of incident polarized light whose vibrations coincide with either of these lines, is trans- mitted through the film unchanged. But a ray of incident polarized light whose vibrations form an angle of 45° with these lines, or, in other words, which coincide with the diagonals of the square spaces, suffers double refraction ; that is, it is resolved into two vibrations, one parallel with a b, the other parallel with c d, and, therefore, the directions of the diagonals of the squares are called the doubly refracting or depolarizing axes. But the two resulting vibrations are not propagated, in these two rectan- gular directions, with equal velocity, the one suffering greater retardation than the other, so that the waves, at their emergence, are in different phases of vibration, though they do not interfere Fig. 18. Selenite. 40 ON THE POLARIZATION OP LIGHT. Fig. 19. Imaginary Structure of a Plate of Selenite. 9^ otO'f'' so as to produce colour, because their planes of vibration are rectangular. By the analyzer, however, iheir planes are made to coincide, and colour is produced ; and on rotating the analyzer on its axis, the colour changes and becomes complementary. To illustrate these statements, place a film of selenite, of uniform thickness, in the polariscope. On rotating the film (the analyzer and polarizer remaining still), a brilliant colour is perceived at every quadrant of a circle, but in intermediate positions it vanishes altogether. We observe, however, that the tint does not change, but only varies in intensity. If, now, the film be fixed and the analyzer rotated, we also observe colour at every quadrant of a revolution ; but the tint changes and becomes complementary at every quadrant — the same lint reappearing at every half revolu- tion : so that when the film alone is revolved one colour only is seen, but when the analyzer alone is revolved, two colours are seen. Effect of revolving the film of Selenite. Effect of revolving the Analyzer. % Colour. cP Colour. I J Colour, ^ Colour. O 4° \ 4. Colour. Colour. \ I Colour. ^ov° Colour. COLOURED POLARIZATION. 41 If we employ, as the analyzer, a double refracting prism, we observe two complennentary disks of colour, and these may be made to cross and produce white light as before shown. The thickness of the film of selenite determines the particular tint. If, therefore, we use a film of irregular thickness, different colours are presented by different thicknesses. A wedge-shaped piece will produce parallel bands of colours, and two wedges crossed present diagonal bands. A plano-concave film, as well as a plano-convex nim, gives concentric rings of colour, the former with a black, the latter with a white, centre. Two films superposed, do not give the colour which would arise from the mixture of the two colours, but either the colour which corresponds to the joint thickness of the films, or that which belongs to the difference of their thickness. When the two films are put together, as they lie in the crystal, the resulting colour depends on the sum of the thicknesses. But when the two films are crossed, so that similar lines in the one are at right angles to similar lines in the other, the resulting tint depends on the difference of the thicknesses. These facts admit of very beau- tiful, curious, and interesting illustrations. Thin films of selenite of uniform thickness are so arranged as to slide over figures also formed of films of selenite. The changes of colour effected in the tints are most striking, and to unphilosophical minds almost magical. In the opticians' shops are met with a great variety of devices prepared with films of selenite of different thicknesses, and which constitute philosophical toys illustrative of the before- mentioned facts. Gothic ivindows, stars, flowers, fruits^ animals (butterflies, parrots, dolphins, and chameleons), and theatrical figures (Jim Crow, harlequin, &c.), are some of the ingenious, and often laughable illustrations contrived by Mr. Darker. Test of Double Refraction. — From the preceding statements then, it appears, that the polariscope becomes a very delicate test of double refraction. A very large number of crystalline, and other bodies, possess a doubly refractive property ; but com- paratively few of these have it in so high a degree as to present, under ordinary circumstances, the phenomenon of double images ; that is, the separation of the two systems of ethereal waves is not, in general, suflftciently great to be visible to the eye. In such cases, therefore, the polariscope is of great value, since it enables us to detect the slightest degree of double refraction. Some doubly refracting bodies present, in the polariscope, most gorgeous colours, as selenite. Others, however, which possess the doubly refractive property in a much slighter degree, require the aid of a thin film of selenite, of uniform thickness. Their double refractive property then becomes evident by the chang-e' 42 ON THE POLARIZATION OP LIGHT. which they induce in the colour of the film. Without this, we see light or dark fringes or bands, or black or white crosses, but no colour. Cause of Double Refraction. — Being now in possession of an exceedingly delicate test of double refraction, we are prepared to enter into an inquiry into the cause of this property. Now we shall find that every body endowed with equal elas- ticity in every direction, is a single refractor. Alter its elasticity in any one direction, put it in a state of unequal tension, and immediately it acquires the property of double refraction. Hence then, double refraction may be temporarily or permanently com- municated to bodies, by temporarily or permanently disturbing the equality of their elasticity in different directions. 1 . Pressure produces double refraction. — In fluids (gases and liquids) pressure is equally distributed in all directions, which is obviously owing to the facility with which the molecules shift their places. Hence pressure on fluids does not communicate to them the power of double refraction. In solids, however, matters are far otherwise. Owing to cohe- sion, the molecules cannot change their relative positions; and, therefore, in this form of matter unequal degrees of tension may exist in different directions : so that pressure may be communi- cated in any desired direction without being equally or uniformly distributed. Now a transparent solid, as a well-annealed piece of glass, all of whose parts possess equal elasticity, is a single refractor ; but if we subject such a body to the influence of a compressing force, it becomes a double refractor, and acquires neutral and doubly refracting (depolarizing) axes ; the former parallel and perpen- dicular to the direction of pressure, the latter 45° inclined to them. Let us consider for a moment what must be the effect of pressure in Fig. 20. any given direction. Suppose a rectangu- I' d G lar piece of glass (fig. 20) to be subjected • to pressure in the direction A B: the im- mediate effect will be to urge the conti- guous particles nearer together in this c ." direction, and thereby to call into action ° their repulsive forces. But it will also urge the particles asunder in the direction C D, — that is, in a direction perpendicu- \ lar to that of the pressure, and thereby to H c F call into operation their attractive forces. Thus then, it is obvious, that a force, which when applied to a solid, causes a condensation in the direction of the force {A B), is jittended with dilatation or expansion in a direction perpendicular COLOURED POLARIZATION. 43 to it (CD). In the first direction the elasticity is a maximum — in the second direction it is a minimum. Incident light polarized in a plane parallel with either of these directions passes through unchanged, and these directions are called the neutral axes. But if it be polarized in a plane inclined 45° to either of these directions (that is, in the direction E F ov G H) it is resolved into two systems of waves, one polarized in the direction A B, the other in the direction C D. The directions E F and GH, are, therefore, the doubly refracting or depolarizing axes. But the system polarized in the plane A B, will proceed more slowly (owing to the maximum elasticity in that direction) than the system C D (which is polarized in the direction of the minimum elasticity). Hence, at their emergence, the two systems of waves are in different phases of vibration, but they do not interfere so as to produce colours, owing to the plane of vibration of the one being rectangular or perpendicular to that of the other. When, however, we apply the analyzer, and restore these two rectangular planes to a common plane, interference takes place and colour results. Let us now take the case of a flexed body. When I bend a cane or other solid, the convex surface is in a state of expansion or dilatation, while the concave surface is compressed. The molecules on the convex surface are urged asunder, and their attractive forces called into operation, while those on the concave surface are pressed together, and their repulsive forces brought into action. Between these two oppositely affected surfaces, there is a neutral line where equilibrium exists, and on both sides of this the degree of strain augments as we recede from the line. Now, if a well annealed, and, therefore, single refracting plate of glass be bent, and examined while in the polariscope, it will be found to have acquired, while in the bent state, double re- fracting properties. Two sets of coloured fringes are perceived, one on the convex or dilated side of the plate, and the other on the con- cave or compressed side. Between these two sets of fringes is a black line, indicating the situation where neither compression nor dilatation exists, and where, therefore, double refraction is absent. Thus then the polariscope becomes a valuable means of detect- ing the existence of unequal tension or strains in transparent bodies, and Dr. Brewster has suggested its useful application to the determination of the intensity and direction of all the forces which are excited by a superincumbent load -in different parts of the arch, as also the intensity and direction of the compressing and dilating forces which are excited in loaded framings of car- pentry. For these purposes, models in glass or copal are to be prepared, and the effects are rendered visible by exposing the models to polarized light. He has likewise constructed a chro- 44 ON THE POLARIZATION OF LIGHT. matic dynamometer for measuring the intensities of forces, founded on the facts ah-eady stated. It consists of a bundle of narrow and thick plates of glass, fixed at each end in brass caps. Then when any force is applied to a ring in the middle of the plates, the ends being fixed, the plates of glass will be bent, and the force thus produced is measured by the tints that appear on each side of the black line. By the gradual induration, as well as by the mechanical com- pression and dilatation of animal jellies, fringes may be produced, as in glass. 2.' Unequal heating causes double refraction. — When heat is applied to bodies, it causes them to expand or dilate. If the substance to which the heat is applied be a bad conductor, the part in contact with the heated body becomes hot, and expands before heat is communicated to the neighbouring parts. Hence the bad conductor endeavours to curve, just as when we hear a compound bar of iron and brass, a curvature is induced, owing to the unequal expansile power of these two metals, and as the brass expands more than the iron, the latter forms the inner or concave side of the curved bar, while the brass forms the outer or convex side. On this principle is constructed the compensation balance of a watch. Glass is a bad conductor of caloric, and when a heated body is applied to it, the part in contact with this becoming hot, expands, but owing to the bad conducting quality of the medium, the surrounding parts not being influenced by the heat, do not expand, but resist the dilatation of the heated portion. In this way, therefore, the immediate effect of heat on one part of a piece of glass, is to put all the surrounding parts into a strained state, one part is expanding, and other parts are resisting the dilatation. When the difference of temperature is extreme, the violence of the strain is such that very thick pieces of glass are sometimes rent asunder. It is very desirable that we should be acquainted with the precise mechanical condition of the glass thus partially subjected to caloric. A knowledge of this would greatly assist us in com- prehending the optical phenomena. But the subject is replete with difficulties. Perhaps, some assistance may be obtained from the following considerations : — Fig. 21. Let A B C B (fig. 21), he a rectan- B gular plate of glass, subjected to heat along its edge, A B. This portion of the glass being heated, tends to expand ; but on account of its connection with other portions of the glass, cannot do D so without forcing these to participate Compressed. ^ I e. Dilated. Compressed. COLOURED POLARIZATIOil. 45 in its augmented bulk. These, however, owing to the bad conducting power of the glass, retain their original tempera- ture, and consequently refuse to expand, so that the stratum is subjected to compression ; that is, it is prevented from ac- quiring that volume which is natural to it, in this heated state. The central stratum e /, is in a state of dilatation or expansion, owing to its particles being urged asunder by the tendency of the upper stratum, A B, to expand. The resist- ance offered to the expansion by e /, tends to produce pres- sure on the lower stratum C D, the particles of which will be urged together. This lower stratum C D, like the upper one A B, will then be in a state of compression. As the tension of e/is sustained at .4 ^ and C D, it will tend to send inwards the lateral columns A C and B D, dilating them at the convex portion of the bend, and compressing them at the concave portion. By these strains, therefore, the rectangular plate of glass will assume a figure concave on all its edges. It is obvious then, from the unequal states of tension of the difFerent parts of a piece of glass thus partially heated, that it ought to acquire doubly refracting properties, and the polari- scope shows that it does so. In this state, the glass exhibits distinct neutral and doubly refracting {depolarizing) axes, the neutral ones being parallel and perpendicular to the direction in which the heat is propagated. The black fringes, sometimes called lines, of no polarization, indicate the neutral axes, or those portions of the glass which are destitute of the property of double refraction. It deserves especial notice that fringes make their appearance in the part of the glass most distant from the heated body, before they have received any sensible accession of heat, and which, therefore, must depend on the state of strain into which they are thrown by the eftect of the heat on the other parts of the mass, in the way I have already endeavoured to explain. Dr. Brewster has suggested the construction of two kinds of chromatic thermometers, for measuring changes of temperature by the production of coloured fringes, exhibited by glass plates when exposed to heat; for " every tint in the scale of colours has a corresponding numerical value, which becomes a correct measure of the temperature of the fluid." In the one instru- ment, the tints originate immediately from the changes of tem- perature ; in the other, they are produced by the difference of pressures upon the glass, occasioned by the difference of expan- sions arising from changes of temperature. I must refer you to his paper in the Philosophical Transactions for 1816, for details respecting them. 3. Unequal cooling causes double refraction. — If a piece of 46 ON THE rOLAHlZATION OV LIGHT. hot glass of uniform temperature be unequally cooled, as by placing one of its edges on a cold mass of iron, it acquires doubly refracting properties, and when examined by polarized liglit, presents fringes, &c. similar to those observed in glass un- equally heated. It is obvious, however, that as the physical condition produced by cold is diametrically opposite to that caused by heat, so the structure of the corresponding parts of the two glasses (the one which has been cooled, and the other which has been heated) must be opposite. 4. Unannealed glass is a double refractor. — If glass be sud- denly cooled after having been melted, it possesses certain remarkable properties, which unfit it for ordinary use. Some- times it splits or flies to pieces in the act of cooling ; or if it fail to do this, a very moderate change of temperature, a slight external force, a scratch, or a slight fracture, is sufficient to cause it to crack and fly to pieces. The glass tears called Rupert's drops, or hand-crackers, and the proofs, or philosophical phials, are familiar illustrations of this kind of glass. In order to pre- vent it acquiring this remarkable condition, glass, after being fashioned, is submitted to the process called annealing, that is to very slow cooling in the annealing oven or Her. Glass which has undergone this process is said to be annealed, while that which has not is termed unannealed. But the so-called unan- nealed glasses sold by the opticians are in fact annealed glasses, which have been reheated until they begin to soften, then cooled by placing them on the ashes beneath the furnace, and after- wards ground and polished. The optical properties of unannealed glass are very remark- able. To comprehend them let us consider the mechanical con- dition of the glass. When a mass of red-hot and soft glass is exposed to a cool air, its external portion becomes cold and rigid, while the inner parts are still hot and soft. After a short time, however, the latter solidify and cool, but are prevented from contracting themselves into the smaller bulk which is natural to them in their cooled state, by the rigid crust, which acts like an arch or vault, and keeps them distended, but which is to a ceitain extent strained and drawn somewhat inwards by the tension exercised on it by the internal parts. It is obvious then that the different parts of a mass of unannealed glass are unequally and differently strained ; the internal being in a state of distention or dilatation, the external in that of compression. So that the state of the different parts, and the distribution of the forces, will be almost exactly similar to those already de- scribed, in the case of annealed glass which has been unequally heated. " The analogy between the cases," says Sir John Herschel, "would be complete, if, instead of supposing the COLOURED POLARIZATION. 47 annealed plate heated at one edge only, the heat were applied to all the four simultaneously, by surrounding it with a frame of hot iron." There is one very important point in reference to these unan- nealed glasses, to which I must beg your attention ; I refer now to the circumstance that in them, the polarizing (doubly refract- ing) structure depends entirely on the external form of the glass plate, and on the mode of aggregation of its particles. This will be very obvious by observing the different shapes of the fringes respectively presented by square, circular, oval, rectangular, and other shaped plates. The circular and square plates have only one axis of [no] double refraction ; whereas the oval and rectan- gular plates have, two axes. By dividing and subdividing these plates, the doubly refractive property is not only greatly dimi- nished, but sometimes even destroyed, if the portion be very small. Moreover, it is distributed in a new manner, according to the shape of the fragment. The dissected unannealed glasses, sold in the opticians' shops, beautifully illustrate the dependence of the form of the coloured fringes on the external shape of the glass. Thus the pattern produced by one circular piece of unannealed glass, is very different to that of a circle formed by joining four segments. In these particulars, the unannealed plates of glass differ very widely from doubly refracting crystals. The fringes and colours, presented by the latter, are unaltered by the changes we may effect in the external form of the crystal — the smallest fragment producing the same system of fringes as the largest ; and, pro- vided the thickness remains the same, the polarizing force suffers no diminution by the reduction in size. We are then constrained to infer that the optical properties of crystals are those of their integrant molecules ; while those of the unannealed glasses depend on the mode of arrangement of the molecules, and on the external form of the mass. The effects produced by superposing similarly shaped pieces of unannealed glass are striking, and, at first, surprising; but, on consideration, may be easily understood. If they be symmetrically superposed, similar points being laid together, the tints will be equal to the sum of the separate tints : — but, if superposed cross- wise, the resulting tints will be the difference of the separate tints. This may be conveniently shown by causing an unannealed glass bar to rotate in front of another unannealed bar. Applications. — These facts respecting the properties of unan- nealed or imperfectly annealed glasses, admit of some valuable practical applications. To the optician it is of the highest im- portance that the glass, of which lenses and prisms are made, ishould possess uniform density, and be free from all defects 48 ON THE POLARIZATION OF LIGHT. arising from irregularities in the annealing process. To detect these the glass should be carefully examined by polarized light previous to being ground and polished ; and by this agent the slightest defects are made appreciable. So also glass vessels employed for domestic purposes may be advantageously tested by the same agent. The facility with which tumblers, &c. crack, sometimes spontaneously, at other times while in the hands of the glass-cutter, or when warm water is poured into them, or when exposed to a slight blow, depends on some imperfection in the annealing process. Hence, also, the reason why run glass (that is, glass made without paying the duty) is very apt to crack ; for owing to the rapidity with which all the stages of its manufacture have been hurried on, it is not well made, and sufficient time has not been allowed for the annealing process. It is probable, also, that manufacturers, or rather the mounters of electrical machines, might beneficially avail themselves of po- larized light in the selection of glass cylinders and plates. E-e- cently made cylinders, when mounted, will sometimes crack, or fly, as it is termed, without any obvious agency, owing, I presume, to some defect in the annealing process, which, per- haps, might have been previously discovered by means of polar- ized light. An argument in favour of the vegetable origin of the diamond has been founded by Dr. Brewster, on the phenomena presented by this substance, when examined by means of polarized light. It is well known that various opinions have been held by different writers on the mode of formation of this mineral. All of them, however, may be included under two divisions : those which as- sume the diamond to be the direct produce of heat on carbonic acid or carbon, and those which ascribe it to the slow decomposition of plants. Dr. Brewster, who adopts the latter notion, met with a diamond which contained a globule of air, while the surrounding substance of the diamond had a polarizing (doubly refracting) structure, displayed by four sectors of polarized light encircling the globule. He, therefore, inferred that this air bubble had been heated, and by expansion had produced pressure on the surround- ing parts of the diamond, and thereby communicated to them a polarizing structure. Now for this to have happened, the diamond must have been soft and susceptible of compression. But as va- rious circumstances contribute to prove that this softness was the effect of neither solvents nor heat, he concluded that the diamond must have been formed, like amber, by the consolidation of vege- table matter, which gradually acquired a crystalline form by the influence of time and the slow action of corpuscular forces. Starch grains have a laminated texture, and possess a doubly. COLOURED POLARIZATION. 49 refractive power. They are composed of concentric layers of amylaceous matter. On some part of the surface of each o-rain IS a circular spot, called the hilum. This appears to be an aperture or transverse section of the tube or passage leading into the inte- rior of the grain, and by which the amylaceous matter, forming- the internal laminse, was conveyed. On examining the grains by the polarizing microscope, unequivocal evidence of their doubly refractive power may be obtained. At least I have found this to be the case in all the starches which I have yet examined, viz., tons les OTozs, potato-starch. West Indian arrow-root, sago-meal, Tahiti arrow-root (obtained from a species of Tacca), tapioca-meal, East Indian arrow-root (CMrcwma anf/ws^i/oZm), wheat-starch, Portland arrovy-root(yl rwm maculatum), and rice-starch. The larc^er grained starches form splendid objects for the polarizing microscope ; tous Ics mois being the largest may be taken as the type of the others. It presents a black cross, the arms of which meet at the hilum. A. Fig. 22. n. On rotating the analyzer the black cross disappears, and at 90'=' is replaced by a white cross ; another, but much fainter black cross, being perceived between the arms of the white cross. Hitherto, however, no colour is perceptible. But if a thin plate Grains of Tous les Mois viewed by the selenite be interposed be- Polarizing Microscope. .4 , represents the tween the starch sfrains and the appearance when the planes of polarization i • ^ , , , of the polarizer and analyzer are at right pOlanzer, moSt Splendid and angles to each other J £.when they coincide gorgeOUS colours make their appearance. The arms of the cross acquire the colour which the selenite plate yields in polarized light. The four spaces between the arms also appear coloured ; but their tint is different to that of the cross. The colours of the first and the third spaces are identical, but different to those of the second and fourth, both of which have the same tint. At the point where the colours of the arms and of the interspaces meet, the tints blend. All the colours change by revolving the analyzer ; and become complementary at every 90^*. The appearances presented by potato-starch are similar to those of tous les mois. Several other starches (as West Indian ar- row-root, sago-meal, Tahiti arrow-root, tapioca-meal, and East Indian arrow-root) present black and white crosses, and, when a selenite plate is used, also colours ; but in proportion as the grains are small, are their appearances less distinct. I have not hitherto detected the black and white crosses in wheat-starch, Portland arrow-root, and rice-starch. Their double refractive power, however, is proved by the change they effect in the colour yielded by a plate of selenite, A great variety of animal structures possess a doubly refracting or depolarizing structure, as a quill cut and laid out flat on glass, E 50 ON THE POLARIZATION OF LIGHT. the cornea of a sheep's eye, a piece of bladder, gold-beaters' skin, human hair, a slice of a toe or finger nail, sections of bones, of teeth, &c. The crystalline lenses of animals also possess this pro- perty in a high degree, owing to their central portion being denser and firmer than the external portion. If the lens of a cod-fish be placed in a glass trough of oil or Canada balsam, it presents twelve luminous sectors separated from each other by a black cross. Even living animals present double refracting properties. The aquatic larvse of a gnat, commonly called skeleton larvce, form a very amus- ing exhibition. They are to be placed in water in a very narrow water-trough. In certain positions, they give no evidence of double refraction, but in others, and especially when they are exerting much muscular energy, they possess it in a very marked degree. LECTURE III. DOUBLY REFRACTIVE AND OTHER ALLIED PROPERTIES OF CRYSTALS. In my last lecture I explained the nature and cause of double refraction ; and I now proceed to examine the double refractive property of crystals, and to show how this is connected with, or related to, other properties of crystalline substances. 1. Double Refraction of Crystals.— Bvery transparent crystalline body refracts the rays of light which are incident on it at oblique angles ; and the degree of its refractive power de- pends on two circumstances; viz., the angle of incidence, and the nature of the crystalline substance. In these respects crystals agree with all other transparent media. But a very large number of crystals possess the property of double refraction ; and they are, therefore, called doubly refract- ing crystals, to distinguish them from others which have not this property, and which are denominated singly refracting crystals. The double refraction of some crystals is immediately mani- fested by the production of duplicate images ; either through two parallel surfaces, as Iceland spar, or through two surfaces which are more or less inclined on each other. Thus to observe the double refraction of a crystal of quartz, it is necessary to look through a pyramidal and lateral plane at the same time. By this contrivance the surface of emersion is inclined to that of admission, which causes the two pencils to emerge at different inclinations, and so become further separated as they proceed. Many crystals, however, possess the property of double refrac- tion in so feeble a degree that it is impossible to see, under ordi- nary circumstances, two images ; and in such cases we are con- strained to employ the polariscope to detect this property. In every doubly refracting crystal there are one or more posi- tions or directions in which the two images become superposed ; DOUBLY REPRACTIVB PROPERTIES OP CRYSTALS. 51 or, in other words, in which no double refraction exists or is evident. These directions are called the optic axes or Ihe axes of double refraction. I have already stated that the phrase axes of NO double refractionwould be more intelligible. These axes may be regarded as positions of equilibrium where certain forces, which exist within the crystal and act in opposition, balance each other. In crystals of certain forms they coincide with the geometrical or crystallographical axes,whereas in crystals of other shapes they do not ; but to these points I shall again have to beg your attention. If we consider doubly refracting crystals in regard to the number of their optic axes we may divide them into two orders ; one including those that possess only one axis, and another com- prehending such as have two axes. The first are called uniaxial, the second biaxial crystals. As this distinction is connected with other remarkable optical peculiarities, as well as with the geometric and thermotic properties of crystals, it will be neces- sary to notice it a little more in detail. a. Uniaxial Crystals. — Those crystals which have only one axis of [no] double refraction, and which, in consequence, are termed uniaxial crystals, or crystals with one optic axis, belong to the square prismatic or rhombohedric systems. In them the geometric or crystallographic axis is coincident with the optical one ; that is, the line or direction in the crystal, around which the figure is symmetrically disposed, or about which every thing occurs in a similar manner on all sides, is coincident with the optic axis, or the axis around which the optical phenomena are the same in all directions. You must not, however, suppose that the axis is a single line ; for there must be as many axes as there may be lines parallel to each other, so that the word is merely synonymous with a fixed direction. In all other directions but the one called the optic axis, these crystals doubly refract; and of the two rays thus produced, one follows the ordinary laws of simple refraction, and is accordingly called the ordinary ray, while the other, being subject to an extraordinary law, is denominated the extraordinary ray. These two rays advance with unequal degrees of velocity; the one suffering greater retardation than the other. When the ordinary ray advances more rapidly than the extraordinary one, the crystal is said to have a negative or repulsive axis of [wo] double refraction; but when the ordinary ray advances less rapidly, the crystal is said to possess a posifzue or attractive axis In other words, when the extraordinary ray is refracted towards the axis, the crystal is said to have a positive axis; but when the ray is refracted from the axis, the crystal is said to have a negative axis. These terms are not very expressive of the property they are intended to represent. Biot used the terms £ 2 52 ON THE POLARIZATION OP LIGHT. attractive and repulsive to designate the attractive or repulsive forces which he supposed to emanate from the axes of crystals. For it is obvious that if the extraordinary ray be most retarded, it will be refracted from the axis, that is, it will appear to be repelled by a force emanating from the axis; whereas, if it be the least retarded, it will be refracted towards the axis, or will appear to be attracted by a force emanating from the axis. Now it was to obviate the hypothesis which these terms involve, that Brewster substituted the words positive and negative for the terms attractive and repulsive, merely meaning to denote by them the opposition, but not the nature, of the forces. Table of Uniaxial Crystals. Positive {+) or attractive Crystals. (Ordinary ray most retarded). Zircon Negative (— ) or repttlsive Crystals (Extraordinary ray most retarded^. Iceland Spar Tourmaline Nitrate of Soda Bicyanide of Mercury Quartz Oxide of Tin Ice In uniaxial crystals the position of the optic axis is constant, whatever be the colour of the light ; whereas in biaxial crystals this is not the case, as I shall presently show. b. Of Biaxial Crystals.— A very large number of crystals, including all which belong to the right rhombic prismatic, oblique prismatic, and doubly oblique systems, have two axes of double refraction, which are more or less inclined to each other. Such crystals are, in consequence, denominated biaxial crystals, or crystals with two optic axes. In them there is no single line or axis around which the figure is symmetrical, as in uniaxial crys- tals ; and the optic axes do not always, or even frequently, coin- cide with any fixed line in the crystals. Now this fact has led Dr. Brewster to believe that the optic axes are not the real axes of the crystals, but only the resultants of the real, or polarising, axes, or lines, in which the opposite actions of the two real axes compensate each other. Hence he terms them the resultant axes, or axes of no polarization, or of compensation. The following is a list of a few biaxial crystals ; and for a more extensive one I must refer my auditors to Dr. Brewster's works : TaUe of Biaxial Crystals. Character of Principal Inclination of Resultant Axes*. Axes. Glaubcrite Negative 2° or S"* Nitrate of Potash Negative 5° 20 Carbonate of Lead Negative lO^ 35| Arragonite Negative IS" 18 Borax Positive 28" 42' Sugar Negative 50° Selenite Positive eO"* Rochelle Salt Positive 80° * The principal axis is, according to Dr. Brewster, the middle point between the two nearest poles of no polarization.— PA//. Tc^ns., 1818. DOUBLY REFRACTIVE PROPERTIES OP CRYSTALS. 53 Of the two rays produced by the double refraction of biaxial crystals, neither can be strictly denominated the ordinary one, since neither of them is refracted according to the ordinary law of single refraction. Both of them then are extraordinary rays, since they are refracted according to the laws of extraordinary refraction. Another peculiarity of biaxial crystals is that the position of the optic axes is not constant, but varies in the same crystal, according- to the colour of the intromitted ray, and the temperature of the crystal. Thus a violet ray is separated into two pencils when incident in the same direction in which a red one is refracted singly. Sir John Herschel, to whom we are indebted for this discovery, found that the inclination of the resultant axes, in Rochelle salt, is for violet light .56°, and for red light IQ^, but in the case of nitre, the inclination of the axes for violet light is greater than for red light, and Dr. Brewster discovered that glauberite has two axes for red light inclined about 5°, and only one axis for violet light. The changes produced on the inclina- tions of these axes by heat, I shall hereafter have occasion to notice. In conclusion, then, crystals considered with respect to their singly or doubly refractive properties may be thus arranged : OPTICAL CLASSIFICATION OF CRYSTALS. Class i. Singly refracting crystals. Doubly refracting crystals .. \ ^.''f-Z l' Uniaxial,. •> jy V a. Repulsive fnegative) or " ' < Orrfer 2. Biaxial .. J (6. Attractive (positive) 2. Form of Crystals. — A remarkable connexion exists between the optical properties and the geometrical forms of crystals ; and to this I have now to beg your attention. A crystal, like every other solid, possesses length, breadth, and thickness ; and the measures of these are three imaginary lines which pass through the centre of the crystal, and are termed the axes. They may be denominated crystallographical or geome- trical axes, to distinguish them from the optic axes with which they do not always coincide. Rose defines them to be "certain lines which pass through the centre of the crystal, and around which the faces are symmetrically disposed." In some forms all these axes are equal in length, as in the cube ; and in such cases it is said, that the axes are similar or alike. Such crystals are termed equiaxed. But in a very large proportion of cases the axes are not all equal, and these crystals are said to be uneqidaxed. Now it is a remarkable circumstance, that the equiaxed crystals are single refractors, while the unequi- axed are double refractors. This is the first fact demonstrative of the connexion between the forms and the optical properties of crystals. 54 ON THE POLARIZATION OF LIGHT. Of the uneqiiiaxed crystals some have two, others three kinds of axes. If, for example, the length and the breadth of a crystal be alike, but the thickness different, the axes are of two kinds. Such crystals are usually said to have two dissimilar axes, but I shall term them di-unequiaxed. Other unequiaxed crystals have all their axes unequal; in other words, their length, their breadth, and their thickness are all unequal. Such crystals are generally said to have three dissimilar axes, but I shall call them tri-unequiaxed. Now, it is most remarkable that the di-unequiaxed crystals are double refractors, with one axis of [no] double refraction, while the tri-unequiaxed are double refractors Avith two axes of [no] double refraction. Here is another curious fact, illustrative of the relation which exists between the shape and optical properties of crystals. Modern crystallographers arrange crystals in six groups, called systems. The equiaxed crystals constitute one system, called the cubic, octohedral or tessular system. The di-unequiaxed crystals comprehend two systems ; one termed the square prismatic or pyramidal system, the other called the rhombohedric or rhombo- hedral system. The tri-unequiaxed crystals include three sys- tems : one denominated the right rhombic or rectangular prismatic system ; a second termed the oblique rhombic or rec- tangular prismatic system; and a third, called the doubly oblique prismatic system. The following table will, perhaps, render these statements more intelligible ; GBOMKTRICAL CLASSIFICATION OF CRYSTALS. Systems. Olass 1» 1 Equiaxed crystals > i. Cufcic or Octohedral. (single refractors)] . [Order l. Di-unequiaxed {one axts Si. Square Prismatic. Class 2. of \no'\ double refraction) 1 3. Rhombohedric. Unequiaxedcrystals^ orrf^t-o Tri iinPnniaxedCtooaare* f^- Rhombic Prismatic, (dotible refractors) I fJraer2. Ui nneq,maxea{iteoaxes } ob ique Rhombic Pnsmatie. {double rejractors) y ^^^^^^ refractiorC) . . . . 'j^gj ^^^^^ 0^^^^ prismatic. I shall not at present enter into any further details respecting the geometrical peculiarities of each of these systems, as the subject will be more appropriately considered presently. 3. Expansibility. — Between the particles of matter there exist two classes of forces, the one attractive, the other repulsive. By the first, particles are approximated and united to form masses ; by the second, they are separated to greater or less dis- tances. Hence attraction and repulsion are antagonizing forces. Caloric or heat is a repulsive force. It augments the distance between particles and thereby weakens their attractive force ; for molecular attraction rapidly diminishes as the distance between the particles increases. Hence solids and fluids, when heated, expand or dilate; But the force of attraction which exists between the particles DOUBLY REFRACTIVE PROPERTIES OF CRYSTALS. 55 of different bodies (solids and liquids) varies considerably: in some being much greater than in others. Hence, the same amount of heat gives rise to a very different degree of expansion in dif- ferent bodies. In other words, each solid or liquid has an expan- sion peculiar to itself, owing to the greater or less attractive force which exists between the molecules. Some crystals, when heated, expand equally in all directions, and such I shall accordingly denominate equiexpanding. Now it is obvious that in these the existence of equally attractive forces in all directions must be inferred ; and it is a curious and striking confirmation of this inference that crystals, which suffer equal expansion in all directions, are singly refracting and equiaxed. A very large number of crystals, however, dilate, when heated, unequally in different directions; and such may be conve- niently denominated unequiexpanding . In them expansion in one direction is accompanied in some, if not in all cases, with contraction in another direction; and it is, therefore, obvious, that the force of attraction between their particles must be unequal in different directions, the attractive or cohesive force being least in that direction in which the expansion is the greatest. Crystals of this class are doubly refracting and unequiaxed. The essential difference in shape between an equiexpanding and an unequiexpanding crystal is, that the first can be inscribed within a sphere, the second cannot. We may rudely illustrate this in the lecture-room, by diagram, substituting planes for solids, by inscribing a square, or an equilateral triangle in a circle (fig. 23, A and B). The first will represent the face of a cube, the second that of the regular tetrahedon. Now, it will be perceived that the circumference of the circle passes through all the angular points of the figure about which it is described. All these forms are equiexpanding. Fia. 23. The regular six-sided prism expands unequally in some direc- tions, but equally in others. If now we describe a circle around the terminal faces, it will be perceived that it passes through all the angular points of this face (fig. 23, C), and in all directions, in this plane, the crystal expands equally. The rhombohedron can- not be inscribed within the sphere, because its axes are unequal. If, for example, we attempt to describe a circle around the 56 ON THE POLARIZATION OF LIGHT. rhombic face of Iceland spar (fig. 23, D), it will be found that while the obtuse angles (a a' ) are contained within the circle, the acute ones (6 V ) project beyond it. Now, under the influence of heat, this face expands in the direction of the shortest axis, but contracts in that of the longest axis, by which the rhomb approaches to the square, the obtuse angles becoming more acute, the acute ones more obtuse (fig. 23, E). These illustrations will serve to give some general notions of the relations which exist between the forms and expansibilities of crystals. The di-uneguiaxed crystals — that is, the doubly-refracting crystals, which have only one axis of [no] double refraction — expand equally in the direction of the equal crystallographical axes, but differently in that of the remaining one; and we may, therefore, denominate them di-unequiexpanding crystals. If, for example, a rhombohedron of Iceland spar be subjected to heat, it expands in the direction of its shortest axis, but contracts in all directions perpendicular to this, and in an intermediate direction it neither dilates nor contracts. Thus, according to Mitscherlich and Dulong, when heated from 32° to 212° Fahr, it actually expands, in the direction of the shorter axis, 0.00286, and contracts in a direction perpendicular to this 0.00056 ; so that its apparent or relative expansion in this axis is 0.00342 (that is 0.00286 + 0.00056). Now a necessary con- sequence of this unequal expansion is an alteration in the angles of the crystal : the obtuse ones become more acute, the acute ones more obtuse. In other words, the rhombohedron approximates to the cube ; and in proportion to this change of form is the diminution of doubly refracting energy. Mitscher- lich had conjectured that the latter effect would take place, and Rudberg has verified the conjecture. The last mentioned philosopher found, that while the ordinary refraction of Iceland spar underwent little or no change, the extraordinary refraction was considerably diminished by an augmentation of temperature. Fic. 21. The tri-unequiaxed crystals expand when heated, unequally in the direction of all their axes, and, therefore, they may be denominated tri- une quiexpa7iding crystals. When the temperature of selenite is augmented, the inclinations of all its faces suffer changes. Thus according to Mitscher- lich by heating it from 32° to 212°, the inclination of the faces cc' was altered 10'50", that of the faces a a 8'25", and that of the edges b b' only 7'26". I have already explained what is meant by the terms positive or attractive, and repulsive , , or neqative axes. They refer to optical differences selenite. in crystals, for which we find no correspondnig DOUBLY REFRACTIVE PROPERTIES OP CRYSTALS. 57 geometric or crystallograpliical differences. Now there have been observed, in the effects of heat on crystals, differences analogous to the optical ones just referred to. Thus, in crystals with a repul- sive or negative axis, as Iceland spar, expansion is greatest in the direction of the shortest axis, showing that the molecular attraction in this direction is the weakest; whereas in positive or attractive crystals, as selenite, heat produces less dilatation in a direction parallel to the axis than in a direction perpendicular to it. " The inchnation of the optic axes, in biaxial crystals," says Mr. Lloyd, " is a simple function of the elasticities of the vibrat- ing medium in the direction of three rectangular axes, and the plane of the optic axes is that of the greatest and least elasticities. If, then, these three principal elasticities be altered by heat in different proportions, the inclination of the axes will likewise vary ; and if, in the course of this change, the difference between the greatest elasticity and the mean, or between the mean and the least, should vanish and afterwards change sign, the two axes will collapse into one, and finally open out in a plane perpen- dicular to their former plane. All these variations have been actually observed. Professor Mitscherlich found, that in sulphate of lime the angle between the axes (which is about 60° at the ordinary temperature) diminishes on the application of heat; that, as the temperature increases, these axes approach until they unite ; and that, on a still further augmentation of heat, they again separate, and open out in a perpendicular plane. The primitive form of the crystal undergoes a corresponding change, the dila- tation being greater in one direction than in another at right ano-les to it. Sir David Brewster has observed an analogous and even yet more remarkable property in glauberite. At the freezini>- tem- perature, this crystal has two axes for all the rays of the spectrum, the inclination of the axes being greatest in red light and least in violet. As the temperature rises, the two axes approach, and those of different colours unite in succession ; and at the ordinary temperature of the atmosphere, the crystal possesses the singular property of being tiniaxial for violet light, and biaxial for red. When the heat is further increased, the axes which have united open out in order, and in a plane at right angles to that in which they formerly lay, and at a temperature much below that of boiling water, the planes of the axes for all colours are perpen- dicular to their first position.* The inclination of the optic axes in topaz, on the other hand, augments with the increase of tem- perature, and the variation M. Marx has observed, is much greater in the coloured than in the colourless varieties of this mineralf." • Edin. Trans,, vol. xi. ; and Phil. Mag., 3d series, vol. i., 417. t Jahrb. der Chemie, vol. ix. 5b ON THE POLARIZATION OF LIGHT. In conclusion, then, crystals considered with reference to the effects of heat on them, may be thus arranged : — THEEMOTIC CLASSIFICATION OF CBYSTALS. Class 1. Equiexpanding crystals (single refractors, equiaxed). Class 2. ") Unequiexpanding Order 1. Di-unequiexpanding (one optic axis, di-untquiaxed). crystals !> (double refractors, Order 2. Tii-\xneciuieij)aniiBg(tuio optic axes,tri-unequiaxed). unequiaxed) J 4. Atoms or Molecules. — It has been correctly stated by Dr. Brewster,* that the polarizing or doubly refracting structure of crystals must ''depend on the form of their integrant molecules, and the variation in their density." A few observations on the atoms or molecules of crystals, will not, therefore, be out of place on the present occasion. Like all other aggregates, crystals are made up of certain small parts conventionally called atoms or molecules. It is un- necessary to discuss the question of their finite or infinite divisi- bility; and to obviate the necessity of this, I shall assume with Dumas,t that an atom is the smallest particle of a body, which by mere juxtaposition with the particles of other bodies, gives rise to a combination. Hence, therefore, the small parts of any one body which combine chemically with certain small parts of another body, without suflTering further division, are what we understand by the terms atoms or molecules. As these small parts or atoms are invisible, even when we aid the eye by the most powerful microscope, it is obvious that all observations on their size and shape must be speculative. Two opinions, however, have prevailed with respect to their form, Haliy and others have adopted the notion of their angular shape, while Hooke, Wollaston, and other more recent writers, assume them to be rounded. If we were to deduce the form of the miSle- cules from that of their aggregates, Ave should adopt the angular hypothesis ; for the most minute fragment of a crystal which we can procure and see, is angular. On the other hand, the spheroidal form of the planetary bodies, the tendency which liquids manifest to assume the spherical sha})e, and the mechanical facilities which the hypothesis of rounded atoms offers in the grouping of the atoms, have led later writers to adopt almost exclusively the views of Hooke and Wollaston. But it may be asked. Is the shape of an atom constant? or can it suffer change ? May not the atoms of liquids be spherical or ellipsoidal and those of crystals angular ? Ellip- soidal forms become angular by mutual compression ; and hence may not the ellipsoidal atoms of a liquid become angular in the act of crystallization? The idea has not, to my knowledge, oc- * Phil. Jrans. for 1818, p. 264. t Traite de Chimie, t. 1, p. 33, 1828. DOUBLY KEFRACTIVE PROPERTIES OF CRYSTALS. 59 curred to crystallogTaphers, but it appears to me that the subject well deserves consideration. A spheroid is said to be oblate, when, as in the case of the earth, the shortest diameter is its axis of revolution, but it h prolate or oblong, when the longer diameter is its axis of revolution. Now the shorter diameter may be regarded as the direction of the greatest attraction, or of compression, while the longer diameter is the direction of least attraction or of dilatation. In the case of the earth it is well known that gravity is greater at the poles than at the equator, a body weighing about xg-jth more at the former than at the latter. It might, therefore, be supposed that crystals with one positive or attractive axis of double refraction would be formed of oblate spheroids, while those with one nega- tive or repulsive axis, would be made up of prolate spheroids. But an objection exists to this hypothesis. According to it, obtuse rhombohedra ought to have one positive axis, while acute rhombohedra should have one negative axis of double refraction. Now the crystalline form of Iceland spar is an obtuse rhombo- hedron, but the optic axis of this substance is negative, so that its crystalline form is that which is produced by an oblate spheroid, while its optical property is that of a prolate spheroid. To obviate this objection, Dr. Brewster* suggests that the molecules have the form of oblate spheroids, whose polar is to their equatorial axis as 1 to 2.8204, and that they were originally more oblate, but have been rendered less so by the force of aggregation, which dilated them in the direction of the smaller axis. In point of fact, however, this assumption does not entirely obviate the difficulty, as the spheroids are still supposed to be oblate, though their axis is a negative one ; and it appears pro- bable, that the same force which would render the axis negative, should change the shape of the spheroid from the oblate to the prolate. Moreover, Dr. Brewster's explanation involves the im- probable supposition that the original very oblate spheroids if ''placed together without any forces which would alter their form," would *' compose a rhombohedron with a greater angle, and having no double refraction." On the assumption that the axes of the atoms of crystals bear the same relations to each other that the axes of the systems of crystals themselves do, I have drawn up the following table of the supposed shapes of the atoms : TABLE OF THE SHAPES OF THE ATOMS OF CRYSTALS. Systems of Crystals. Class 1. Equiaxed {spheres) j. Cubic fOrderx. Twoequalaxes(.M.m-rf.){^; HZ^.^^I^^,^^ p.] Class 2. Unequiaxed< (i. Right Prismatic 3 I Order 2. Three unequal axes \b. Oblique Prismatic " V ^ I.6. Doubly Oblique * Phil. Trans., 1830. ■ If 60 ON THE POLARIZATION OF LIGHT. The doubly refracting structure is not inherent in the mole- cules themselves. Quartz or crystallized silica doubly refracts; but tabasheer, opal, and melted quartz, all siliceous substances, do not. Ice doubly refracts, while water singly refracts. What is the reason of this ? It will be generally admitted, I presume, that the double refrac- tion of ice is a molecular property, and is associated with the shape of the atom ; and hence, if the atoms of water have the same form as those of ice, they ought also to possess the doubly refracting property of the latter. Now, the advocates for the hypothesis of the unchangeability of atomic forms contend, that in ice the atoms are symmetrically and regularly arranged, with their axes pointing in the same direction ; while in water they are unsymmetrically or irregularly arranged or jumbled together in such a manner that their axes have every possible direction, so as to create a general equilibrium of the polarizing forces. But, if this were the case, two specimens of water would scarcely ever present the same optical properties. If, by any accident, the axes of a large majority of the molecules should happen to be arranged in the same direction, the liquid would then possess a doubly refracting property. Now, it appears to me, that no hypothesis can be correct which ascribes to accident or chance a constant and invariable property of a body ; for I hold, that, except when approaching the freezing point, liquid water is invariably a single refractor. But on the assumption that the shapes of atoms are, to a cer- tain extent, capable of change, the difficulty is easily obviated. Suppose the atoms of liquid water to be spheres, and that in the act of freezing they become spheroids, the expansion of water in the act of freezing, the doubly refracting property, and the crys- talline form of ice would then be readily explicable. A consistent explanation of Dimorphism can scarcely be offered except on the assumption of the changeability of the shapes of the atoms. Carbonate of lime, for example, crystal- lizes in two distinct and incompatible forms, the one belonging to the rhombohedric, the other to the right prismatic system. In the first case, we call it Iceland-spar; in the other, arragonite. Iceland-spar has one negative optic axis, arragonite has two negative optic axes. The shapes of the atoms of these bodies must, therefore, be different. Admit that, under certain circum- stances, the atom of carbonate of lime can change its shape, and all difficulty as to the production of these forms is at an end. We suppose, therefore, that " when in the process of evapora- tion or cooling, any two molecules are brought together by the forces or polarities which produce a crystalline arrangement, and strongly adhere, they will mutually compress one another." If the compression in three rectangular directions be equal, the DOUBLY REFRACTIVE PROPERTIES OF CRYSTALS. 61 crystal will be a singly refracting one : if the compression in two directions be equal but different in the third, the crystal will be a doubly refracting one with one optic axis : and, lastly, if the compression be difl'erent in each of the threo directions, the crystal will doubly refract, and have two optic axes. 5. Molecular Forces. — Between the molecules of crystals, as well as of other bodies, there exist attractive and repulsive forces, in virtue of which the molecules are retained, not in contact, but within certain distances of each other. These forces are an- tagonists, and, therefore, the molecules acting under their influ- ence, take up a position of equilibrium, where the two opposing powers counterbalance each other. But in crystals it is necessary to admit, besides ordinary attrac- tion and repulsion, a third molecular force called poZanVy, which may be regarded either as an original or a derivative property. Without this it is impossible to account for the regularity of crystal- line forms. Under the influence of a mutually attractive force particles would adhere together and form masses ; the shapes of which, however, would be subject to the greatest variety ; and though occasionally they might happen to be regular, yet this could not constantly be the case. The simplest conception we can form of polarity is that it de- pends on the unequal action of molecular attraction or repulsion in different directions. A molecule endowed with unequal at- tractive forces in different directions may be said to be possessed of polarity. A crystal has length, breadth, and depth or thickness. It is composed of molecules accumulated in three different directions corresponding to these three measurements ; and it is obvious, therefore, that to account for their cohesion we must suppos'e that they attract each other in three directions ; moreover, as the relative intensity of their attraction in these directions is, in many cases, unequal, it might be even supposed that they are three different kinds of attractions. To render this subject intelligible I shall make use of some illustrations employed by Dr. Prout in one of the Bridgewater Treatises. Fia. 24. Fio.25. Fro. 26, 62 ON THE POLARIZATION OF LIGHT. Suppose three molecules to adhere together to form a single roiu, line, or string of molecules, in virtue of an attractive force vk^hich I shall distinguish by the name of the length force. The points AAA or a a a are supposed to mutually repel each other, while AaAaAa mutually attract (fig. 24). Let us further suppose that three such rows of particles cohere in virtue of an attractive force acting in a direction perpendicular to the first. We may distinguish this as the breadth force. The points B B B or hbb are supposed to mutually repel, while Bb Bb Bb mutually attract. These three rows of particles by their cohesion form a -plane (fig. 25). Again let us assume, that three such planes cohere together, in virtue of an attractive force acting in a direction perpendicular to both the other forces. Tliis force we may denominate the depth force. The points C C C or cc c are assumed mutually to repel, while Cc Cc Cc mutually attract. These three planes by their union form a solid (fig. 26). Thus, then, we suppose that the molecules of crystals have three rectangular axes of attraction, or *' lines along which they are most powerfully attracted, and in the direction of which they cohere with different degrees of force." Though for convenience and facility of explanation I have employed the terms length-force, breadth-force, and depth-force, I by no means wish you to suppose that I adopt the notion of the distinct nature of these forces. They may be, perhaps they are, one force acting in three directions. These forces may be equal or unequal, and in the latter case two only, or all three, may be unequal. That is, in some crystals the length-force may be equal to the breadth-force, and this to the depth-force. Or two only of the forces may be equal, the third being unequal : or, lastly, all three may be unequal. _ As I have already had frequent occasion to speak of the elas- ticity of crystals, and as I shall again have to refer to it, I think it proper to explain what is meant by it. I have stated that the molecules of bodies are not in actual contact, but are separated by greater or less intervals. They are kept from actual contact to which attraction urges them, by repulsion, while their further separation is opposed by attraction. Now we may disturb their state of equilibrium. We may, for example, by some compressing force, compel the particles to approach nearer to each other ; but when the distflrbing cause ceases to act, the particles after a few oscillations take up their original position. This then is what we mean by elasticity, which is obviously a consequence of attraction and repulsion. An elastic body is one which has the property of restoring itself to its former figure after any force which has disturbed it is withdrawn. DOUBLY REFRACTIVE PROPERTIES OP CRYSTALS. 63 If by any force we approximate the particles of an elastic body, we augment its elasticity, and vice versa. Now, as it is repulsion which opposes the approximation of particles, it appears that it is this force principally which confers on bodies the property called elasticity. In some crystals their elasticity is equal in three rectangular directions. Such crystals may be denominated equielastic. Others, however, have unequal elasticities in different directions, and may be termed unequielastic. The first are single refractors, the latter are double refractors. Of the unequielastic crystals, some have two of their three elasticities equal, others have all three of their elasticities unequal: the first may be termed di-unequielastic — the second, tri-unequielastic. The elasticity in the crystallographical axis may fall short of or exceed that in other directions : in the first case, crystals are said to have a negative or repulsive axis, or an axis of dilatation ; in the latter case, they are said to have a positive or attractive axis, or an axis of compression. By experiments made by Savart*, on the mode of sonorous vibration of crystalline substances, it has been shown, that the negative or repulsive axis is the axis of least elasticity, while tlje positive or attractive axis is the axis of greatest elasticity. " In carbonate'of lime," he observes, '*it is the small diagonal of the rhombohedron which is the axis of least elasticity, whilst it is that of greatest elasticity in quartz." To be convinced of the accuracy of this assertion, it is sufficient to cut, in a rhombo- hedron of carbonate of lime, a plate taken parallel to one of its natural faces, and to examine the arrangement of its two nodal systems, one of which consists of two lines crossed rectangularly, which are always placed on the diagonals of the lozenge, the primitive outline of the plate ; and the other is formed of two hyperbolic branches, to which the preceding lines serve as axes, (fig. 27), but with this peculiarity, that it is the small diagonal Flo. 27. Fia. 28. / ) I j M'odal Systems of Calc Spar. Ditto of Quartz. * Taylor's Scientific Memoirs, vol. 1. 64 ON THE POLARIZATION OF LIGHT. which hecomes the first axis of the hyperbola, wliilst it is its second axis in the corresponding plate of rock crystal (fig. 28). The following table shows the relation between the elasticities and shapes of crystals : TABLE OF THE ELASTICITIES OF CRYSTALS. Class I. "l Systems. Equielastic V 1. Cubic. , . crystals ... J { Order i. r 2. Rhombohodric...") .S <^ 2" f Di-unequielastic. . 1.3. Square Prismatic '(^ia'S «.Minus(negative (-4. Right Prismatic. 1-3 S «! or repulsive) or Order 2. J 5. Oblique Prismatic f I 5. Plus (positive Tri-unequielastic.'l 6. Doubly Oblique \ S^-^" \ or attractive) L Prismatic J S b p. L Conclusions. — From the preceding remarks it will appear, 1. That singly refracting crystals are equiaxed, eqiiiexpand- ing, equielastic, and, on the ellipsoidal hypothesis of molecules, may be assumed to be made up of spherical atoms. 2. That doubly refracting crystals are unequiaxed, unequi- expanding, unequielastic, and, on the ellipsoidal hypothesis of molecules, may be assumed to be made up of either spheroidal atoms or ellipsoids with three unequal axes. 3. That uniaxial crystals are di-unequiaxed, di-unequiexpand- ing, di-unequielastic, and, on the ellipsoidal hypothesis of mole- cules, may be assumed to be made up of spheroidal atoms. 4. That biaxial crystals are tri-unequiaxed, tri-uneqniexpand- ing, tri-unequielastic"; and, on the ellipsoidal hypothesis of mole- cules, may be assumed to be made up of ellipsoids having three unequal axes. 5. That doubly refracting crystals, having a negative or repul- sive axis, expand more, and have less elasticity in the direction of the axis than in directions perpendicular to this. 6. Lastly, that doubly refracting crystals, having a positive or attractive axis, expand less, and have more elasticity in the direc- tion of the axis than in directions perpendicular to this. I shall now go through the six systems of crystals, separately pointing out the most important of their optical and other pro- perties. SYSTEM I. THE CUBIC OR OCTOHEDRAL SYSTEM? Synonyrnes. — The regular, the tessular, the tesseral, or the isometric system. Forms. — The forms of this system are either homohedral or whole forms, or hemihedral or half forms. DOUBLY REFRACTIVE PROPERTIES OF CRYSTALS. 65 Ilomohedral Farms. 1. Regular Octoliedron. 2. Cube or Hexahedron. 3. Rhombic Dodecahedron. 4. Icositetrahedron. 5. Triakisoctohedron. G. Tetrakishexahedron. 7. Ilexakisoctoliedron. Ilemlhedral Forms. 1. Tetrahedron or Ilemioctohedron. 2. Hemicositetrahedron or Pyra- midal Tetrahedron. 3. Hemitriakisoctohedron. 4. Hemihexakisoctohedron. 5. Hemitetrakishexahedron or Pen- tagonal Dodecaliedron. 6. Hemioctakishexahedron. Fig. 29. Four forms of the Cubic System ; viz.. Cube, Reeular Tetrahedron, Rhombic Dodecahedron, and Regular Octohedron. aa, b I), c c. The three rectangular equal axes. Crystals. — Of the fifty-five or fifty-six simple or elementary bodies which have been hitherto discovered, the crystalline forms of not more than eighteen have been ascertained. Of this number, no less than thirteen are referable to the cubic system, namely bismuth, copper, silver, gold, platinum, iridiuyyi (?), iron, lead, titanium, mercury, sodium, phosphorus and diamond. Now it appears d, priori probable that simple bodies would have spherical atoms, and, therefore, the fact that the above named substances crystallize in forms belonging to the cubic system, has been adduced as an additional evidence of their simple nature. A considerable number of binary compounds also belong to this system^ — as the chlorides of sodium, potassium, and silver; sal ammoniac ; the bromide and iodide of potassium ; fluor-spar, and the sulphurets of zinc (blende), lead (galena), silver, and iron (pyrites). Some substances, which contain more tlian two elements, also belong to this system, as alum and garnet. Now, if the cubical form be an argument for the simple nature of the metals, why, it may be asked, do so many compound bodies present the same form ? To this we can offer no satisfactory reply ; and I think, therefore, we may conclude with Dr.WolIaston, " that any attempts to trace a general correspondence between the crystallographical and supposed chemical elements of nature, must, in the present state of the sciences, be premature." F 66 ON THE POLARIZATION OF LIGHT. Properties.— The crystals of this system have the following properties : they are equiaxed singly refracting, equiexpanding and eqiiielastic. We assume their molecules to be spherical. When examined in the polariscope they present no traces of colour. Exceptions.— A few exceptions exist to some of the preceding statements ; but they are probably more apparent than real. 1. Several crystals of this system, as the diamond, fluor-spar, alum, and common salt, sometimes exhibit traces of a doubly refracting structure. But this is ascribable to irregularities of crys- tallization, or to the operation of compressing or dilating forces. 2. Boraciie (a compound of boracic acid and magnesia) crys- tallizes in the general form of the cube ; the edges of which are replaced, and the diagonally opposed solid angles dissimilarly modified. Instead, however, of being merely a single refractor, as its shape would lead us to expect, Dr. Brewster found that it was a double refractor, with one positive axis of double refraction in the direction of a line joining two opposite solid angles of the cube. So that, in point of fact, it possesses the properties of a rhombohedric crystal. We may, therefore, regard it as a rhombo- hedron, whose angles differ from a right angle by an infinitely small quantity. 3. Analclme or cicbizite (hydrated silicate of alumina and soda) constitutes another remarkable exception to the general rule, that crystals of the cubic system are devoid of a doubly refracting struc- ture. The m.ost usual form of this crystal is the icositetrahedron. Now if we suppose, says Dr. Brewster, its contained cube " to be dissected by planes passing through all the twelve diagonals of its six faces, each of these planes will be found to be a plane of no double refraction or polarization." All intermediate portions doubly refract. From every other known doubly refracting crystal, analcime differs in the circumstance, that ^11 its particles do not equally possess the property of double refraction, those in the planes above mentioned being devoid of this power, and the others possessing it in proportion to the squares of their distances from these planes. It differs from unannealed glass in the fact that a change in its external form does not give rise to a change in its polarizing power; but each fragment possesses the same optical property, when it is detached from the mass, that it had when naturally connected with its adjacent parts. Analcime, therefore, is a complete optical anomaly. It has been suggested, that these curious optical properties may depend on the presence of both a doubly and a singly re- fracting mineral ; and the fact, that the large opake crystals of analcime, found in the valley of Fassa in the Tyrol, are traversed by plates of apophyllite (a doubly refracting crystal), lends sup- ort to this hypothesis. DOUBLY REFRACTIVE PROPERTIES OP CRYSTALS. 67 SYSTEM II. THE SQUARE PRISMATIC SYSTEM. Synonymes.—The four-membered or two- and one-axed, the pyramidal, the tetragonal, or the monodimetric system. Forms.— The forms of this system are either homo kedral or whole forms, or hemihedral or half forms. Homohedral Forms. Hemihedral Forms. 1. Octohedron with square base. 1. Hemioctoliedron or Tetrahedron- 2. lerminal Face or Horizontal 2. Hemi-dioctohedron. Plane. 3. Square Prism (of two positions). 4. Dioctohedron or Eight-sided Py- ramid. 5. Eight-sided prism. Fig. 30. Four forms of the Square Prismatic System ; viz.. Two Square Piisma i?i different positions. Mid Tivo Octohedra with square bases, a a. Principal axis. bb,cc. Secondary axes. Crystals. — Among the crystals * of this system are chloride of mercury (calomel), bicyanide of mercury, ferrocyanide of potassium (yellow prussiate of potash), peroxide of tin, copper pyrites, zircon, and apophyllite. Properties. — The crystals of this system have the following properties: They are di-unequiaxed, doubly refracting with one optic axis, di-unequiexpanding-, and di-unequielastic. We assume their molecules to be either prolate or oblate spheroids. The two equal rectangular geometric axes of this system are called secondary axes ; while the third or odd one, which may be greater or less than the others, is the principal or prismatic axis, or the crystallographical axis, or the axis of symmetry. The' optical characters of this system are the following: The crystals are doubly refracting, with one optic axis which coincides with the principal axis. If a thin slice of a crystal of this system, cut perpendicularly * Sowerby (^wn, P/h7. xvi. 223.) mentions crystals oi Palladium in the torm of octohedra with a square base and of symmetrical prisms. F 2 68 ON THE POLARIZATION OP LIGHT. to the principal axis, be placed in the polariscope, it presents a system of circular rings, with a cross, which is either black or white, according to the relative positions of the polarizer and analyzer. Ferrocyanide of potassium (commonly called prussiate of potash) may be conveniently used -to show these effects. As found in commerce it usually occurs in the form of truncated octohedrons having a square base. It should be split with a lancet in the direction of its laminae, that is, perpendicularly to its principal axis. Plates, of about a quarter of an inch or more in thickness, serve for the polariscope. They present a cross, and a negative system of circular rings ; but the yellow colour of the crystal affects the brilliancy of the tints. Zircon (a compound of silica and zirconia) is valuable for op- tical purposes, on account of its being a positive uniaxial crystal. Hence if a plate of it, which gives a system of rings of the very same size as that produced by a plate of Iceland spar {^negative uniaxial crystal) be superposed over the latter plate, the one system of rings is completely obliterated by the other ; and the combined system exhibits neither double refraction nor polari- zation. 1 shall defer all explanation respecting the rings and cross of this system, until I speak of Iceland spar (a crystal of the rhombohedric system). Exceptions.— Some exceptions to the above mentioned pro- perties of the crystals of this system exist, and require to be noticed. 1. Ferrocyanide of potassium is subject to irregularities of crystallization ; and certain specimens present a double system of rings, or, in other words, are biaxial. Certain uniaxial specimens give a positive system of rings. 2. Apophyllite or Fisheyc-stone (a compound of silica, lime, potash, and water) possesses some remarkable properties. In the most common variety, that from Cipit in the Tyrol, the diameters of the rings are nearly alike for all colours — those of the green rings being a little less. Some specimens of apophyllite, called by Dr. Brewster tesselated apophyllite, present, in the polari- scope, a tesselated or composite structure, instead of the ordinary cross and circular rings. They will be described hereafter among ihe tesselated or intersected crystals. SYSTEM III. THE RHOMBOHEDRIC SYSTEM. Synonymes. — The three- and one-axed, the klinohedric, the hexagonal, or the trimetric system. Forms, — ^The forms of this system are either homohedral or hemihedrdl. DOUBLY REFEACTIVJE PROP-ERTIES OF CRYSTALS. 69 Homohedral Forms. 1 . Double Six-sided Pyramid (Hcxa- gondodecahedron). 2. Eight Terminal Face (Horizontal Plane), 3. Hexagonal Prism, 4. Double Twelve-sided Pyramid ( Didodecaliedron ) , 5. Twelye-sided Prism. Ilemihedral Forms. 1. Rliomboliedrou ( Hemidodecalie- dron). 2, Scalenohcdron. Fig, 31. Three forms of the Rhomhohedric Si/stem ; vis., the Hexagonal Prism, the Scalene Dodecahedron and the Rhomhohedron. a a. The principal axis. bb,cc, d d. The secondary axes. Crystals, — To this system belong some bodies supposed to be simple or elementary; viz., antimony, arsenicum, and tellurium.* Plumbago or graphite and the native alloy of iridium and osmium also belong to this system. Ice, magnetic iron pyrites, cinnabar , chloride of calcium, Ice- land spar, carbonates of iron and zinc, dolomite (magnesian car- bonate of lime), nitrate of soda, hydrate of magnesia, tourtnaline, talc, beryl, chabasite, quartz, and one-axed mica belong to this system. And here it may be necessary to remark, that the sub- stance known to mineralogists by the name of mica, and which, in trade, is usually but improperly termed talc-\, varies in its crystalline forms and optical properties. One kind crystallizes in regular hexagonal prisms, which cleave with extreme facility in one direction, viz., perpendicularly to their axis. This has only one axis of [no] double refraction, and consequently when a lamina of it is placed in the polariscope it presents only one system of circular rings traversed by a cross. This is the kind called rhombohedral or uniaxial mica, the majority of spe- cimens of which have a negative or repulsive axis, though some have a positive or attractive one. But there is another kind of mica, of more frequent occurrence in the shops, and which is called by mineralogists prismatic or diaxial mica. It has two * Rose inserts " Palladium (?) " among rhombohedric crystals. t Talc is readily distinguished from mica by its greasy or unctuous feel. The most familiar kind of talc is that sold in the shops under the name of French chalk. It is talc in an indurated earthy form. 70 ON THE POLARIZATION OF LIGHT. axes of double refraction, and consequently when a plate of it is placed in the polariscope, two systems of coloured rings are per- ceived. This kind of mica exists in two forms; one is crystallized in right prisms, the other in oblique prisms. Hence I shall dis- tinguish the one as right prismatic mica, the other as oblique prismatic mica. They will be described hereafter. In conclusion, then, the kinds of mica may be thus arranged : fRhombohedric or Uniaxial i ™^ ^ ^^^.^^^^ ^i^' j^- I \ With a positive axis. I Prismatio or Diaxial / ^^^^^^ Prismatic. L Prismatic or Diaxial j ObHq.ue Prismatic, The principal constituents of mica are silica and alumina. But it also contains potash and sesquioxide of iron. Properties. — ^The forms of this system possess four axesf ; viz., three equal ones, called the secondary axes, placed in one plane, and crossing in the centre at an angle of 60°; and a fourth, termed the principal axis, or the axis of symmetry , or the crystallographical axis, perpendicular to the others, from which it differs in length. They are double refractors, with one optic axis coincident with the principal axis. They are di-unequiexpanding bodies, the expansion being different (greater or less) in the principal axis from that in the secondary ones. They are di-unequielastic ; the elasticity in the principal axis being either more or less than that in the secondary axes. With regard to the atoms, we may assume their shape to be spheroids. Iceland spar (Ca O. CO2) may be conveniently used to illustrate the optical properties of the crystals of this system. It occurs in rhomboidal masses, which by cleavage yield obtuse rhombohedra. The line which joins the two obtuse summits of one of these rhombohedra, is called the shortest or principal axis, the crys- tallographical axis, the axis of the rhomboid, or simply the axis. A plane drawn through this axis, perpendicularly to a face of the crystal, is called the principal section. This section belongs rather to a face than to the entire crystal, for each face has its own. Now when the incident rays are perpendicular to the face of the crystal, both the ordinary and extraordinary rays are always found in the same plane, so that the deviation of the extraordinary pencil takes place in the plane of the principal section. Every plane in the interior of the crystal, which is perpendicular to the axis, is called a section perpendicular to the axis, or the equator of double refraction. In this plane the t The description adopted in the lectures is that of Weiss and Rose; some other writers admit only tliree axes. Thus, Turner {Elements of Chemistry 7tli ed,, p, 588) describes three equal but not rectangular axes; while GrilQn {System of Crystallography, pp, 151 and 258) admits three rectangular but unequal axes. Neither of these modes of descriptions appear to me so com- pletely to connect the form with the optical and other properties of the crystals, as Weiss and Rose's method. DOUBLY REFRACTIVE PROPERTIES OF CRYSTALS, 71 doubly refracting force is at a maximum, and when a ray is incident in this plane, the resulting extraordinary and ordinary rays are both in the same plane. If a plate of Iceland spar, cut perpendicularly to the principal or shortest axis, be placed in the polariscope, the polarizing and analyzing- plates being crossed, we observe coloured curves or concentric rings intersected by a rectangular black cross, the arms of which meet at the centre of the rings (fig. 32). Fig. 32. Fig. 33. Fio. 34. h The coloured curves or rings are called the lines of equal tint, or isochromatic lines (from icros equal and ;^po)jaariK6s coloured). In this and other uniaxial crystals, they are disposed in concentric circles, and are similar to Newton's rings seen by reflection. If we revolve the plate of Iceland spar on its axis, the rings and cross preserve the same position ; but if either the polarizing or analyzing plate be rotated, some remarkable changes occur. Suppose the analyzing plate to be turned 45^ round the incident ray in a left-handed direction, we observe that the original or primary coloured rings grow fainter or more dilute, and the cross seems to shift its position to the left, while its blackness lessens and is replaced by another set of rings, which alternate with, and are complementary to, the original curves (fig. 33). If the analyzing plate be rotated 45° further in the same direction, that is 90° to the first or original position, the black cross is replaced by a white one, and the original set of coloured rings is succeeded by a second or complementary set, the rings of which are intermediate to the original ones, and are similar to Newton's rings seen by transmission (fig. 34). If the system of rings with a black cross (fig. 32) were super- posed in the system with the white cross (fig. 34) white light would be reproduced. If the incident polarized light be white, the rings consist of com- pound tints produced by the superposition on each other of rings formed by each of the homogeneous rays composing white light. 72 ON THE POLARIZATION OF LIGHT. Of course, if the rings of all the colours were of the same size, the resulting system would consist of black and white rings ; but being of different dimensions, we obtain a system of different colours. In this case, the cross is either black or white, not coloured. If the incident polarized light be homogeneous the rings consist of rings of the colour of the light employed separated by black rings. Thus, suppose red light to be used, the rings will be alter- nately red and black; whereas if blue light be employed, they will he alternately blue and black. Their size varies with the colour of the light : red produces the largest, violet the smallest system of rings. In all cases in which homogeneous light is employed the cross is either a black or a coloured one. The radii of the bright rings are as the square roots of the odd numbers, 1, 3, 5, 7, &c.; while those of the dark rings are as the square roots of the even numbers, 2, 4, 6, 8, &c. In other words, the squares of the diameters of the bright rings are as the odd numbers, 1, 3, 5, 7, &c. ; while the squares of the diameters of the dark rings are as the even numbers, 2, 4, 6, 8, &c. Sijuares of the dia- ( Bright rings meters of the ... i Dark rings 1 3 _ 5 7 2 4 6 : 8 The actual diameter and breadth of the rings are increased by diminishing the thickness of the crystalline plate. To speak more precisely, the radii of the rings are inversely as the square root of the thickness of the plate; and, therefore, the rings are smaller with a thick plate than with a thin one. Thus while a plate of a given thickness will produce a system of rings, the whole of which can be seen at once, a plate considerably thinner will give rings of so much larger diameter and greater breadth, that the whole system cannot be taken in at once by the eye. It is obvious, therefore, that the comparative doubly refracting power of two uniaxial crystals may be ascertained by observing the size of the rings produced by plates of equal thickness : with a powerful doubly refracting crystal the rings are less than with a crystal possessing this property in a weaker degree. In fact, the radii of the rings are inversely as the doubly refracting power of the crystal. Let us now endeavour to explain generally the origin of the coloured rings and of the cross, according to the undulatory hypothesis ; and, for precision and brevity of description, I shall suppose that tourmaline plates are used in the polariscope both for polarizing and analyzing. The first tourmaline plate polarizes the light which is then incident on the Iceland spar. In their progress through the latter, some of the polarized rays suffer double refraction, others are transmitted without undergoing this change. For there are DOUBLY REFRACTIVE PROPERTIES OP CRYSTALS. 73 Fig. 35. two rectangular planes of polarization of the luminous rays in Iceland spar, one of the plane of polarization of the ordinary rays, the other of the extraordinary rays ; and in those parts of the crystal in which the plane of polarization of the incident light coincides with either of the planes of polarization of the rays in the crystal, no double refraction occurs. On the other hand, in those parts of the crystal in which neither of its planes of polarization coincide with the plane of the incident polarized light, double refraction ensues. All the ordinary rays which emerge from thecrystal, are polarized in planes which pass through the principal axis of thecrystal: while the extraordinary rays will be polarized in planes per- pendicular to these. Let fig. 35 re- present the crystalline plate cut per- MMgg'j;sSgJjBl^ pendicularly to the axis e. The =^'^^'^^^-'^-'^==^~ radiating white lines represent the planes of polarization for the ordinary rays, and the circular white Tmes the planes of polarization for the extraor- dinary rays. The two sets of rays (that is, the ordinary and the extraordinary) form two cones of refracted rays, having a common axis coincident with the axis of the crystal. The summit, or apex of each cone, will be at the eye of the observer ; and the diameter of the base of the cone will of course vary according to its distance from the eye. The difierent rays, of which each cone is made up, undergo different changes. Those which form the axis of the cone, traverse the plate at a perpen- dicular incidence, and, therefore, are not refracted ; while those which pass through the plate obliquely,undergo double refraction. The ordinary or the extraordinary rays forming the same cone have not all an equal intensity at different parts of its circum- ference. For if the plane of polarization of the incident light be identical with or parallel to a b, fig. 35, it is evident, that while the intensity of the ordinary rays will be at a maximum in the plane a b, and at a viinimum or nil in a direction perpendicular to this c d, the intensity of the extraordinary rays will be at a maximum in the plane c d, and at a minimum or vil in a direction perpendicular to this, a b. Hence those rays which are incident on the crystal in the plane a b, traverse the plate without having their plane of polarization charged, emerge as ordinary rays, and, by the subsequent action of the analyzing plate, form two arms of the rectangular cross, a b (fig. 36). Those rays which are incident on the crystal at any point of the line c d also traverse the crystal without having their plane of 74 ON THE POLARIZATION OP LIGHT. Fig. 36. polarization changed, but they emerge as ex- a traordinary rays, and , by the subsequent ac- tion of the analyzer, form the remaining two S arms of the rectangular cross c d (fig. 36). c Extraordinary rays, a The two sets of polarized incident rays which 1 thus traverse the crystal,without having their ^ plane of polarization changed, and emerge, O the one as the ordinary, the other as the ^ extraordinary rays, form either a black or a white cross, according as they are either suppressed or trans- mitted by the second or analyzing tourmaline. If the two tourmalines be crossed the rays are suppressed — if they coincide the rays are transmitted. In the first case we perceive a black cross, in the second a white one. Fig- 37. Tilus, tlien, all the rays which emerge from the second surface of the crystal, at any point of the two lines ab, cd (fig. 37), will not be divided into two, nor have c their planes of polarization altered. But all the polarized rays which are incident on the crystal in any direction intermediate between the positions a h and c d suffer * double refraction, since their planes of pola- rization coincides neither with the plane of polarization of the ordinary, nor with that of the extraordinary rays ; that is, the vibrations of the incident rays are resolved into two sets, one which forms the ordinary rays, and the other perpendicular to it, which forms the extraordinary rays. The two systems of waves, produced by these two sets of vibrations, proceed through the crystal with unequal velocities and describe different paths; consequently they emerge in different phases, that is, in a condition for suffering interference by the action of the analyzer. In my last lecture, however, I so fully explained the agency of the analyzer in giving rise to the phenomena of colour, that I need not now enter further into it. I shall, therefore, only add, that the coloured rings owe their origin to interference. A circumstance which affects the formation of the rings, is the inclination of the polarized rays to the optic axis of the crystal. In the axis itself, where the arms of the cross pass athwart each Other, no colour is produced, consequently there can be, in this position, no double refraction. But those rays which suffer double refraction and produce colour, traverse the crystal obliquely, and at an inclination to the optic axis, and the obliquity or inclination augments in proportion as we recede from the centre or axis. Now the effect of an increase in the inclination of the rays to the optic axis is equivalent to an increase of thickness in the crystal. Hence it is obvious why we have rings, DOUBLY KEFBACTIVE PROPERTIES OF CRYSTALS. 75 and not an uniform tint, as in the case of the thin films of sele- nite described in our last lecture. Moreover, it is obvious that at equal distances around the axis the inclinations will be the same, and consequently the similar tints will be found at equal distances from the axis ; in other words, the lines of equal tint or isochro- matic lines will be disposed in concentric circles. That the tints of the system of rings accompanying- the black cross should be complementary to those which accompany the white cross, will be readily understood from what was stated in the last lecture respecting the office of the analyzing plate. The rings of the two systems do not occupy the same position, but are transposed ; that is, the bright rings of the one system occupy the position of the dark rings of the other system. The cause of this is obvious — the rings of the two systems are produced by different rays. The two sets, of rays which successively pass through the tourmaline analyzing plate in its two positions, would, if this plate were not interposed, pass simultaneously and produce an uniform tint of the same colour as that of the incident light. In other words, without the analyzer neither cross nor rings would be perceived. But why, it may be asked, is the maximum brilliancy of the rings at the middle of the four quadrants; that is, in lines or directions which are equidistant from the two nearest arms of the cross ? Because it may be replied, it is at these spots that the ordinary and extraordinary rays (produced by double refraction) are equal. On either side of these directions, the ordinary ray has either a greater or less intensity than the extraordinary one. Iceland spar has, as I have already stated, a negative or repulsive axis ; and I shall take this opportunity of explaining the method used by Dr. Brewster for distinguishing whether the axis of a crystal be positive or negative. Take a film of selenite (sulphate of lime), and mark on it the neutral axes ; then, by a little wax, attach it to a plate of Iceland spar (cut so as to show the rings), and place them in the polariscope. If the film by itself produces the red of the second order, it will now, when combined with the Iceland spar, obliterate part of the red ring of the second order in two alternate and opposite quadrants (either a c and h d, ox ad and b c, figs. 32 and 34). The line of the film which crosses these two quadrants at right angles to the rings is the principal axis of selenite, and should be marked as such. Then if we wish to examine whether any other system of rings is positive or negative, we have only to cross the rings with the principal axis *' by in- terposing the film: and if it obliterates the red ring of the second order in the quadrant which it crosses, the system will be nega- tive; but if it obliterates the same ring in the other two quadrants which it does not cross, then the system will be positive. It is of no consequence what colour the film polarizes, as it wiH always •76 ON THE POLARIZATION OF LIGHT. obliterate the tint of the same nature in the system of rings under examination." Plates of tourmaline, obtained by cutting the crystals at right angles to the principal or prismatic axis, as described in my first lecture (fig. 6, p. 18), present circular rings and a cross when examined by the polariscope. Ice belongs to the rhombohedric system. The beautiful and regular, though varied, crystalline forms of snow may be regarded as skeleton crystals of this system. 1 have here depicted (see fig. 38) a few forms taken from Captain Scoresby's work on the Arctic Regions ; and in them you may readily trace the three secondary axes {b b, cc, d d), placed in the same plane, and in- clined to each other at an angle of 60°, while the fourth or prin- cipal axis (a a) is perpendicular to the other three. Fio, 38. Crystals of Snow. Now, if you take a sheet of clear ice, about an inch thick, and which has been slowly formed in still weather, and examine it by the polariscope, you will readily detect the circular rings and cross. The system of rings formed by ice is positive or attractive ; and, therefore, is of an opposite kind to that of Iceland spar. Exceptions. — To the general properties of crystals of the rhombohedric system some exceptions exist. 1 . In Iceland spar, beryl, and other crystals of this system, the rings are not unfrequently distorted, owing to irregularities of crystalline structure. 2. Quartz belongs to this system, but its optical phenomena are very different to those of any other crystal, and will be described in my next Lecture, under the head of circular polarization. 3. Amethyst is another exception, which 1 shall hereafter describe. 4. Chabasite (a mineral compound of silica, alumina, lime water, and potash) is a rhombohcdral crystal, sometimes endowed with remarkable optical properties. *' In certain specimens of this mineral," says Dr. Brewster, " the molecules compose a regular central crystal, developing the phenomena of regular double refraction ; but in consequence of some change in the state of the solution, the molecules not only begin to form a hemitrope crystal on all the sides of the central nucleus, but each successive stratum has an inferior doubly refracting force DOUBLY REPHACTIVE PROPERTIES OP CRYSTALS. 77 till it wholly disappears. Beyond this limit it appears with an opposite character, and gradually increases till the crystal is complete. In this case the relative intensities of the axes or poles from which the forces of agrgregation emanate, have been gradually changed, probably by the introduction of some minute matter, which chemical analysis may be unable to detect. If we suppose these axes to be three, and the foreign particles to be introduced, so as to weaken the force of aggregation of the greater axis, then the doubly refracting force will gradually diminish with the intensity of this axis, till it disappears, when the three axes are reduced to equality. By continuing to dimi- nish the force of the third axis, the doubly refracting force will reappear with an opposite character, exactly as it does in the chabasite under consideration." SYSTEM IV. RIGHT PRISMATIC SYSTEM. Synonymes. — The right rhombic prismatic, or right rec- tangular prismatic system, the prismatic system, the two- and two-membered or one- and one-axed system, the orthotype system, the rhombic or the holohedric-rhombic system. Forms. — In this system are included the right rhombic prism, the right rhombic octohedron, the right rectangular prism, and the right rectangular octohedron. Rose enumerates the following forms as belonging to this system : Homohedral. Forms whose faces are inclined to all thi'ee axes (Octohedra). Forms whose faces are iucUiied to two axes, but are parallel to the third (Prisms), Forms whose faces are inclined to one axis but are parallel to the two others (Single Planes ). Fio. 39. Hemihedral, Rhombic Tetrahedron. Right Rectangular Prism. \ Right Rectangular Octohedron, Rill lit Rhombic Prism. j Right Rhombic Octohedron. u. Principal or prismatic axis, b b,cc. Secondary axes. 78 ON THE POLARIZATION OP LIGHT, Crystals. — The simple or elementary bodies which crystallize in forms belonging to this system are only three, namely, iodine^ native sulphur, and selenium. Among the binary compounds we have pyrolusite (binoxide of manganese), white antimony (sesquioxldeo^ antimony), bichloride of mercury, chloride of barium, orpiment, and grey antimony (sesquisulphuret of antimony). A considerable number of salts belong to this system, as the carbonates of lead, baryta, strontian, potash, and ammonia ; the bicarbonate of ammonia, and that variety of carbonate of lime called arragonite ; the nitrates of potash, ammonia, and silver ; the sulphates of magnesia, zinc, baryta, and strontian, and bisulphate of potash ; Rochelle salt (tartrate of potash and soda) and emetic tartar (tartrate of potash and antimony). To the above must be added the following substances : topaz, dichroite, citric acid and morphia. Properties. — The crystals of this system present the following properties: they have three rectangular axes all of different lengths: they are doubly refracting with two optic axes; and are tri-unequiexpanding. Consequently they have three rectan- gular unequal elasticities. On the eUipsoidal hypothesis, their atoms are ellipsoids, with three unequal axes. They present no crystallographical character by which the principal axis can be distinguished from the others called secondary axes ; so that in a geometrical point of view the choice of this axis is altogether arbitrary. But considered optically the principal axis is the middle point between the two nearest poles of no polarization. It corresponds with what is called by Mr, Brooke the prismatic axis ; that is, the axis which passes through the centres of the terminal planes of the prism. If you examine one of the simple or primary forms of this sys- tem — say this unmodified rectangular prism (the outer prism of figure 39), you observe there is no single line around which the figure is symmetrical ; nor any square plane, or plane which can be inscribed within the circle. But let each of the two opposite terminal edges be replaced by a square plane, both equally in- clined to the prismatic axis, and the line which passes through the centre of each of these planes will represent the direction of one of the optic axes. As the crystals of this system have two optic axes, they present, when examined by the polariscope, a double system of rings. In nitre, carbonate of lead, and arragonite the inclination of these axes is small ; and, therefore, both systems of rings may be seen at the same time. In order to examine these by the polariscope, we must, in the case of the three crystals just mentioned, cut slices of them DOUBLY REFRACTIVE PROPERTIES OP CRYSTAI.S. 79 perpendicularly to the principal or prismatic axis. But in topazr, right prismatic mica, and Rochelle salt, the inclination of the optic axes is too great to permit both of them to be seen simul- taneously ; and , therefore, only one of them can be seen at a time. Consequently if we examine, by the polariscope, a plate of any of these crystals, cut at right angles to the prismatic axis, we must incline it first on one side and then on the other, to see succes- sively the two systems of rings. To obviate this inconvenience, plates of these crystals should be prepared by grinding and polishing two parallel faces perpendicular to the axis of one system of rings. Nitrate of potash, also called nitre or saltpetre, (N O5 + K 0) is a very instructive crystal for illustrating the double system of rings. It is usually met with in the form of a six-sided prism, with diedral summits. For placing in the polariscope, we use plates of from -JLth to /3-th of an inch in thickness, cut perpendicular to the prismatic axis. If one of these be put in the polariscope in such a position that the plane passing through the optic axis is in the plane of primitive polarization, we shall then perceive a double system of coloured elliptical or oval rings, intersected by a cross, but the centre of the cross is equidistant from the centres of the two systems of rings, so that through the centre of each system passes one arm or bar of the cross, the other arm being at right angles to the former. When the polarizing and analyzing plates are crossed, we have a double system of coloured rings, with a black cross (fig. 40) ; but when the polarizing and analyzing plates coincide, we have another double system of coloured rings, exactly complementary to the first, with a white cross (fig. 41). Fig. 40. Fio. 41. If when the analyzing and polarizing tourmaline plates are crossed, we revolve the plate of nitre in its own plane (both the tourmaline plates remaining unmoved) the black cross opens into two black hyperbolic curves. When the angle of rotation is a quarter of a right angle, we have the appearance represented by 80 ON THE POLARIZATION OP LIGHT. (fig. 42) ; when it equals half of a right angle, the black arms have assumed the forms of fig. 43. FlO.42. FiC. 43. Here, then, is a remarkable distinction between biaxial and uniaxial crystals, for you will remember I demonstrated that when the uniaxial crystal was rotated iu the polariscope, the black cross retained its position and shape. The variation of form, as well as the general figure of the isochromatic lines, resembles the curve called by geometers the lemniscate. The inner rinas encircle one pole only, but the outer ones surround both poles. The number of rings which surround both poles augments, as we diminish the thickness of the plate of nitre, until all the rings surround both poles, and the system thus greatly resembles, in appearance, the rings of an uniaxial crystal, from which, however, they are distinguished by their oval form. I have already stated, that in biaxial crystals the optic axes for different colours do not coincide. In the case of nitre, the axes for red make with each other a smaller angle than the axes for blue. Hence the red ends of the rings are inward, that is, between or within the two optic axes, while the blue ends are outwards, or exterior to the two axes. But as the red rings are larger than the blue ones, it follows that there are points exterior to the axes where all the colours are mixed, or all are absent. At these spots, therefore, the rings are nearly white and black. Now if we trace the same rings to the positions between the axes, " the red rings will very much over-shoot the blue rings; and, therefore, the rings have the colour peculiar perhaps to a high order in Newton's scale *." Native crystallized carbonate of lead constitutes a splendid polariscope object. It is to be cut like nitre ; that is, perpen- dicularly to the prismatic axis. The optic axes are but slightly inclined (about 10^°) and, therefore, both of them may be simul- taneously perceived. The systems of rings have a similar form * Airy, Mathematical Tracts, p. 396. 2d ed. 1831. DOUBLY REFRACTIVE PROPERTIES OP CRYSTALS. 8i to those of nitre, and like the latter, the red ends of the rings are inwards, the blue ends outwards. Arragonite forms an interesting polariscope object. It is identical in chemical composition with calcareous or Iceland spar, but differs in crystalline form : calcareous spar belonging to the rhombohedric, arragonite to the right prismatic, system. According to Gustav Rose, both these forms of carbonate of lime may be artificially produced in the humid way, but calca- reous spar at a lower, arragonite at a higher, temperature. In the dry way, however, calcareous spar alone can be formed. The inclination of the optic axes of arragonite being small (about 18°) we can easily see, at the same time, the two negative systems of rings surrounding their two poles, but considerably more separated than in the case of nitre. For this purpose, a plate of the crystal is to be cut perpendicularly to the prismatic axis, that is, equally inclined (at about 9°) on each of the optic axes. If we rotate the plate of arragonite on its axis in the polariscope, the tourmaline plates being crossed and unmoved, the two sets of rings appear to revolve around each other. By superposing two plates of arragonite, we obtain four systems of rings. In Rochelle salt (tartrate of potash and soda) the optic axes of the differently refrangible or coloured rays are considerably separated. If a plate of this crystal, cut perpendicularly to the prismatic axis, be inclined first on one side and then on the other, both the systems of rings may be successively perceived. But to observe the separation of the axes for differently coloured rays, Sir J. Herschel directs the plate to be cut perpendicularly to one of its optic axes. If we view the rings with homogeneous light they appear to have a perfect regularity of form, and to be remarkably well defined. With differently coloured lights, how- ever, they not only differ in size but in position. If the light be " alternately altered from red to violet, and back again, the pole, with the rings about it, will also move backwards and for- wards, vibrating, as it were, over a considerable space. If homo- geneous rays of two colours be thrown at once on the lens, two sets of rings will be seen, having their centres more or less distant, and their magnitudes more or less different, according to the difference of refrangibility of the two species of light employed." Topaz (a fluosilicate of alumina) belongs to this system. As the inclination of its optic axes is great (about 50°), we can see at once only one of its two system of rings. It slits with facility in planes perpendicular to its prismatic axis, and equally inclined to its two optic axes. If we take a plate cut perpendicularly to G 82 ON THE POLARIZATION OP LIGHT. the prismatic axis, and incline it first on one side and then on the other, we shall see successively two systems of oval rings, which have been very elaborately described by Dr. Brewster. The plates of topaz sold in the opticians' shops, for polariscope purposes, have been obtained by cutting the crystal perpendicu- larly to one of the optic axes; that is, at an angle of about 25° to the prismatic axis. With these we only see one system of nearly circular rings traversed by a bar or arm of the cross. We observe also, that the optic axes for different colours are somewhat separated ; for the red ends of the rings are inwards, or within the resultant axes, while the blue ends are outwards. The topazes, which are cut for optical purposes, come from Australia, and are technically known as Nova Minas. They are colourless and remarkably free from flaws and macles. Exceptions. — In this system, as in the others, we meet with exceptions to some of the statements above made. 1. JVIacled crystals, especially of Nitre and Arragonite, are very common. Occasionally idiocyclophanous crystals of nitre are met with. These will be noticed subsequently. 2. Sulphate of potash is a tesselated or composite crystal, and as such will be described hereafter. 3. Some specimens of Brazilian topaz are tesselated. SYSTEM V. OBLIQUE PRISMATIC SYSTIiM, Synonymes. — ^The two- and one- member ed st/stem, the hemior- thotype system, the monoklinohedric system, or the hemihedric- rhombic system. Forms. — To this system belong the oblique octohedron with a rectangular base, the oblique rectangular prism, the oblique octohedron with a rhombic base, and the oblique rhombic prism. Mr. Brooke's right oblique-angled prism is referred to this system. Rose makes no distinction between the homohedral and hemi- hedral forms in this system ; but enumerates the following as the forms of the system : 1. Eorms whose faces are inclined to all the three axes {Octohedra). 2. Forms whose faces are inclined to two axes, and are parallel to the tliird axis (Prisms). 3. Eorras of which the faces are inclined towards one axis and parallel to the two others. DOUBLY REFRACTIVE PROPERTIES OF CRYSTALS. 83 FlO. 44. Oblique Rectangular Prism, Oblique Rhombic Prism, Oblique Rectangular Octahedron, and Oblique Rhombic Octohedron. a a. Principal axis. bb,cc. Secondary axes. Crystals. — ^To this system belong the crystals of sulphur, when obtained by slow cooling; realgar "(red sulphuret of arsenic), and red antimony (native Kermes). A considerable number of salts belong here also: as the sul- phates of soda, lime (selenite), and iron; carbonate and sesqui' carbonate (trona) of soda, bicarbonate of potash, chlorate of potash, phosphate of soda, borax (tincal), the acetates of soda, copper, zinc, and lead, binacetate of copper, binoxalate of potash, glauberite (sulphate of lime and soda), and ehromate of lead. To this system are also referred oblique pristnatic mica (one of the kinds of diaxial mica described by Count de Bournon), tartaric and oxalic acids, sugar candy, and the crystals fro7n oil of cubebs. Properties. — The forms of this system have three axes, all of which are unequal. Two of them cut one another obliquely, and are perpendicular to the third. From the forms of the pre- ceding system they are distinguished by this obliquity of two of their axes. As the three axes are unequal, it is indifferent which we take for the principal axis; but one of the inclined axes is usually selected, because, in general, the crystals are extended in the direction of one of these, so that in most cases the faces which are parallel to this axis greatly predominate. This axis, therefore, corresponds with that which Mr. Brooke calls the prismatic axis. The other two axes are called secondary axes . the one which is oblique being termed the first secondary axis ; the other, which is perpendicular to it, being denominated the second secondary axis. The crystals of this system are doubly refracting with two optic axes. They are tri-unequiexpanding, and tri-unequiaxed. On the ellipsoidal hypothesis their atoms are assumed to be ellipsoids with three unequal axes. G 2 84 ON THE POLARIZATION OP LIGHT. In the opticians' shops, plates, cut from several crystals of the this system, are sold for showing, in the polariscope, the systems of lernniscates. They are usually cut perpendicularly to one of the optic axes ; and, therefore, show but one system of rings traversed by a bar. Of these I shall notice three. Borax deserves especial notice on account of its optic axes for the different homogeneous colours lying in different planes, a fact for the knowledge of which we are indebted to Sir John Herschel. As in other biaxial crystals it will be observed that the rings, or lemniscates, are traversed by only one bar or arm of the cross. In the next place it will be perceived, that the axes for red light make a greater angle with each other than the axes for blue or purple; hence, unlike nitre and carbonate of lead, the red ends of the rings are outwards, while the blue ends are inwards. This fact, however, only proves that the axes for dif- ferent colours do not coincide; it does not show that they lie in different planes. But if, the tourmaline plates being crossed, the plate of borax be placed at such an azimuth that the bar or arm of the black cross distinctly traverses the centre of the system of lemniscates and leaves an interval perfectly obscure, we shall then see that the arm of the cross is not straight, as in nitre (fig. 40), but has a hyperbolic form. The reason of this difference is obvious: in nitre all the axes lie in the same straight line or plane, while in borax they are disposed obliquely, or in different planes. Selenite is sometimes cut to show one of its two systems of rings. I have already described this crystal, and demonstrated the uniform tints produced by films of selenite of equal thick- ness. To show the rings the crystal must be cut at right angles to one of its optic axes. Sugar Candy makes an interesting polariscope object. This crystal is also cut perpendicular to one of its optic axes, and, therefore, shows only one of its two systems of rings. Exceptions. — Owing to irregularities of crystallization, the rings of some of the crystals of this system are often seen more or less distorted. Macled selenite is very common, as I have before mentioned. Sir John Herschel states, that idiocyclophon- ous crystals of bicarbonate of potash are frequent. I shall hereafter notice them. SYSTEM VI. DOUBLY OBLIQUE PRISMATIC SYSTEM. Synonymes. — The one- and one-membered, the anorthotype, the triklinohedric, or the tetartohedric-rhombic system. Forms. — To this system belong the doubly oblique octohedron DOUBLY REFRACTIVE PROPERTIES OP CRYSTALS. 85 and the doubly obliq^ie prism. Rose makes no disthiction of homohedral and hemihedral forms; but arranges the forms of this system as follows: 1. Forms whose faces are inclined to all the three axes. {Octohedra.') 2. Forms whose faces are inclined to two axes, and are parallel to the third. (Prisms.) 3. Forms which have their faces inclined towards one axis only. These forms are the faces of truncation of the three kinds of angles of tha octehedron. Fig. 45. Tivo Doubly Oblique Prisms, and two Doubly Oblique Octohedra. a a. The Principal Axis, bb, cc. The Secondary axes. Vrystals — The most important substances, whose crystalline forms are referable to this system, are boracic acid, sulphate of copper*, nitrate of bismuth, sulphate of cinchonia, quadroxalate of potash, and gallic acid. Properties. — The forms belonging to this system have three axes all unequal and oblique-angular to one another ; they are doubly refracting, with two optic axes; and they are tri-unequi- expanding. Consequently they have three unequal elasticities. Of the three axes just referred to, one is taken for the prin- cipal axis, the other two for the secondary axes ; but geometri- cally considered the selection is altogether arbitrary. The principal axis coincides with Mr, Brooke s prismatic axis. " The forms of this system," says G. Rose, <' have not symmetri- cal faces. All the faces are unique, so that this system is the one which differs the most from the regular or cubic system, in which we find the greatest symmetry on account of the equality and perpendicularity of the axes." It is sometimes exceedingly dif- ficult to distinguish the forms of this system. " The "doubly oblique prism," observes Mr. Brooke, " will be found the most * Mr, Brooke {axt. Mineralogy, in the Encychpcedia Metropolitana), says, that the prmiary form of Sulphate of Copper is an oblique rhombic prism, and Mr. R. PhiUips (Translation of the Pharmacopeia, p. 237, 4th edit., 1841) has adopted Mr. Brooke's statement. If this be correct, sulphate ■of copper of course belongs to the oblique prismatic system, and not to the doubly oblique prismatic system, I have, however, referred it to the latter system on the authority of Gustav Rose, and most of the other eminent German crystallographcrs. 86 ON THE POLARIZATION OF LIGHT. difficult of all the primary forms to determine from its secondary crystals. It is distinguishable from all other forms, when its crystals are single, by the absence of symmetrical planes analo- gous to those of other prisms ; but it very frequently occurs in hemitrope or twin crystals, which must resemble some of the forms of the oblique rhombic prism, and can then be distin- guished only by some re-entering angle or other character on the surface of the crystal." Sulphate of Copper (Cu O. S O3. 5 Aq.) is sometimes cut to show the two sets of rings or lemniscates of this system ; but the blue colour of the crystal destroys their brilliancy. LECTURE IV. 4 CIKCULAU POLARIZATION. The name of circular or rotatory polarization has been ap- plied to a peculiar modification of light, first observed by Arago in the mineral called Quartz, and whose characteristic and distinc- tive properties I shall presently point out. On the wave hypothesis, the term circular or rotatory is pecu- liarly appropriate, since it is assumed that the ethereal molecules describe circles, in other words that they vibrate or revolve uni- formly in circles, and the form of the ethereal wave thereby produced, is that of a spiral or circular helix (that is, to a helix traced round a circular cylinder), of which a corkscrew and a bell-spring are familiar illustrations. But apart from all hypothetical considerations, the name is an appropriate one. For unlike the rays of common polarized (that is, plane or rectilinearly-polarized) light, those of circularly polar- ized light have no distinction of sides, or, in other words, they have " no particular relations to certain regions of space," but present similar properties on all sides, and the angles of reflection at which they are restored to plane polarized light, in different azimuths, are all equal, like the radii of a circle described round the ray. There are two varieties or kinds of circularly polarized light which have been respectively distinguished by the names of dextrogyrate or right-handed, and Iceuogyrate or left-handed. In one of these the vibrations are formed in an opposite direc- tion to those in the other. Unfortunately, however, writers are not agreed on the application of these terms ; and thus the polarization, called, by Biot, right-handed, is termed, by Herschel, left-handed, and vice versd. There is, however, no difference as to the facts, but merely as to theirdesignation. If, on turning the ana- lyzing prism or tourmaline from left to right, the colours descend in Newton's scale, that is, succeed each other in this order — red, orange, yellow, green, blue, indigo, and violet, Biot designates CIRCULAR POLARIZATION. 87 the polarization as right-handed, or +, or ; whereas if they descend in the scale by turning the analyzer from right to left, he terms it left-handed, or — , or • Sir John Herschel, on the other hand, supposes the observer lo look in the direction of the ray's motion. Let the reader, he observes, " take a common corkscrew, and holding '\iwith the head towards him, l€t him use it in the usual manner, as if to penetrate a cork. The head will then turn the same way with the plane of polarization as a ray in its progress from the spectator through a right-handed crystal may becunceived to do. If the thread of the corkscrew were reversed, or what is termed a left-handed thread, then the motion of the head, as the instrument advanced, would represent that of the plane of polarization in a left-handed specimen of rock crystal." I shall adopt Biot's nomenclature, and designate the polariza- tion right-handed or left-handed, according as we have to turn the analyzing prism to the right or to the left to obtain the colours in the descending order. In a former lecture I endeavoured to explain the nature of circularly polarized light, according to the wave hypothesis. Powell's machine (see p. 27) gives a very clear notion of the dif- ference between a circular and a plane wave. You may, perhaps, remember that I stated, that a circular wave is composed of two plane waves of equal intensity, polarized at right angles, and differing in their progress one quarter of an undulation. I endea- voured to demonstrate this fact by a machine invented, I believe, by Mr. Wheatstone (see p. 33). Now, in order that you may comprehend how we effect the circular polarization of light, I must beg of you to keep in mind these statements. Remember, that to convert plane-polarized into circularly-polarized light, two conditions are necessary, namely, 1st, the existence of two systems of luminous waves, of equal intensity, polarized perpendicularly to each other ; and, 2dly, a difference in the paths of these two systems of an odd or uneven number of quarter undulations. Now, whenever these two conditions are satisfied, circularly polarized light results. But how are we to satisfy them ? By so doubly refracting plane polarized light, that the two resulting waves shall differ in their path an odd quarter undulation. There are five modes of effecting the circular polarization of light, that is of satisfying the conditions above mentioned ; but they all agree in acting on the principle now laid down, namely, that by them plane polarized light is doubly refracted, and two rectangularly polarized waves produced, which differ in their path an odd quarter undulation. 88 ON THE POLARIZATION OF LIGHT. Fio. 46. 1. Fresnel's Method. — Fresnel effected the circular polarization of light by means of a parallelopiped of St. Gobin (crown) glass (fig. 46), whose acute angles, B and C, are about 54°, and consequently whose obtuse ones, A and D, are about 126°. This apparatus is commonly called FresneVs rhomb. If a ray, a, of plane polarized light be incident perpendicularly on the face, A B, it will suffer two total internal reflections, at an angle of about 54°, one at E, the other at F, and will emerge per- pendicularly from the face, D C. If the first plane, B D, of internal reflection, be inclined 45° to the plane of polarization A.B.t^'vlln^-^ti.om^.''^ the incident ray, « the emergent ray, a. Incident ray of plane ^' ^f^'^ ^6 CU-Cularly polariZCd. _ polarized light. Let US HOW cndeavour to explain this phe- c'. cfrcuiar^Vo^iarized nomenon according to the wave hypothesis, ray- So long as reflection is partial, whether performed at the first or second surface of the diaphanous medium, the incident light suffers only a deviation from its plane of polariza- tion, without having its primitive properties altered,whatever may be the azimuth of its plane relatively to that of the plane of reflection. But when the reflection is total the case is very different. The reflected rays then have, in general, suffered partial depolariza- tion, especially if the plane of reflection is in an azimuth of 45° relatively to the primitive plane of polarization. Now, a ray of light thus modified, or depolarized, as it is termed, may be repre- • sented by two rays polarized, the one according to the plane of reflection, the other perpendicularly to it. In other words, the incident-polarized ray (fig. 46, a) is resolved by reflection into two rectangularly plane-polarized rays (i), the planes of which are inclined respectively, the one 45° to the left, the other 45° to the right of the plane of polarization of the incident ray. But it is obvious that the reflection of these two rectangularly polarized rays must be effected at different depths, and, therefore, under very different circumstances. The ray whose vibrations are performed parallel to the reflecting surface will glide, as it were, on the surface, and be reflected in a stratum of uniform density ; whereas the ray, whose vibrations are performed per- pendicularly to the reflecting surface, will penetrate to a greater depth, and pass into strata of varying density. The latter ray will, therefore, suffer a greater retardation than the one whose vibrations are performed parallel to the reflecting surface. Now when, in the case of Fresnel's rhomb, the plane of the first reflecting surface is in an azimuth of 45° to that of the incident ray, CIRCULAR POLARIZATION. 89 the retardation is equal to |^th undulation. The same ray is farther retarded another ^th undulation by the second reflection ; and now differs in its phase from that of the other ray |th of an undulation. Thus are obtained the conditions necessary for the formation of a ray of circularly-polarized light; namely, two plane rays of equal intensity, polarized in planes perpendicular to each other, and differing in their path |th of an undulation. 2. Airy's Method. — If a ray of plane polarized light be trans- mitted through a lamina of either mica or selenite of such a thickness that, for a ray perpendicular to the lamina (that is, the ray polarized in the plane of one of the principal sections of the mica) the ordinary ray shall be retarded, an odd or uneven number of quarter undulations, as |th, |ths, or ^ths (according to the con- venience of splitting) more than the extraordinary ray (that is, the ray polarized in the plane of the other principal section), the emergent light will be found to be circularly-polarized. In this case the incident light is resolved into two sets of vibrations, at right angles to each other, and one of these is retarded in its phases more than the other. Between this and Fresnel's method of effecting circular pola- rization, there is this difference : in Fresnel's rhomb the retarda- tion of the one ray is nearly the same for all colours, that is, for waves of different lengths. But in the case of the lamina of mica or selenite, the retardation is greater for blue rays than for red rays. " This is seen most distinctly on putting several such laminee together [in the same crystalline position], when the light which is reflected from the analyzing plate is coloured, whereas, on putting together several of Fresnel's rhombs, there is no such colour. It is plain that in substituting such a lamina for Fresnel's rhomb, the plane of polarization of that ray which is least retarded, corresponds to the plane of reflection in the rhomb." 3. Dove's Method.— 'Th'is consists in transmitting plane polar- ized light through glass to which a certain degree of doubly - refracting power has been communicated by pressure, or by rapidly heating or cooling it. I have already shown that well annealed glass acquires doubly refracting properties when compressed ; that unannealed glass possesses similar properties ; and also that during the time that glass is rapidly heating or cooling it is likewise a double refractor. Of the two systems of waves which are thus obtained, one is polarized in a plane parallel to the axis of compression, the other in a plane perpendicular to it. Now, if the degree of doubly refracting power thus communi- cated to glass be just sufficient to effect the retardation of one of the systems of waves ^of an undulation, we obtain a structure fitted forconverting plane-polarized into circularly-polarized light. " If a square or circular plate of glass," says Dove, " be com- 90 ON THE POLARIZATION OF LIGHT. pressed so that the axis of compression forms an ang^le of 45° or 135° with the plane of primitive polarization, the light passing through the centre of the glass at a certain degree of the pressure will be circularly polarized. During a complete revolution of the plate in its plane round the perpendicular incident ray as an axis of revolution, the light is polarized four times rectilinearly and four times circularly : rectilinearly when the compressing screw acts on the points 0°, 90°, 180°, 270°, that is to say, when the axis of compression is perpendicular to the plane of pVimitive polarization, or lies within it ; and on the contrary, it is polarized circularly when that point of action corresponds to the points of division, 45°, 135°, 225«, 315°, whilst 45°, and 225°, as also 135" and 315°, exhibit a similar effect." These statements may be rendered more intelligible by the fol- lowing diagram : Fio. 47. If light, rectilinearly polarized in the plane 0° 180°, or in that of 90° 270°, be incident on a circular disk of compressed glass (fig. 47, A, B, C, D), the emergent light is rectilinearly polarized when the axis of compression is either 0'' 1 80°, or 90° 270'' ; but is circularly polarized when the axis of compression is either 45'' 225°, or 135° 315°. At all intermediate azimuths it is ellipti- cally polarized. CIRCULAR POLARIZATION, 91 Fig. 48. The degree of compression to which the glass is to be subjected, to produce these effects, is such that when the compressed glass is placed in the polariscope, with the tourmalines crossed, a black cross is seen with blond-white vacant spaces in the corners. Unannealed glass, possessing the same degree of doubly refracting power, acts in a similar manner to compressed glass. Annealed glass, while either rapidly heating or cooling, likewise gives rise to similar effects at the time when its doubly refracting power is just equal to that of thecompressed glass above described. 4. Quartz. — I now proceed to notice the remarkable optical properties of the substance denominated Quartz. This term, the etymological origin of which is not clearly made out, is applied to some of the crystalline forms of silica. The transparent variety, called rock or mountain crystal, is the kind used for optical purposes. Very perfect transparent crystals are found near Bristol and in Cornwall, and are called Bristol or Cornish diamonds. The opticians cut some of the most limpid and large crystals, which usually come from the Brazils, for making lenses for spectacles and eye-glasses, and which they denominate pebbles. Quartz belongs to the rhombohedric system . Its most common form is the six-sided prism, terminated by six-sided pyramids (fig. 48). Its fracture is conchoidal. Now, as quartz belongs to the same system of crystals to which Iceland spar belongs, it might be expected that when we place a plate of it, cut perpendicularly to its principal or prismatic axis (fig. 49 a a), in the polariscope, we should observe the cross and a system of circular rings, as in the case of Iceland spar and other crystals of the rhombohedric sys- tem. But this is not the case. We do, indeed, observe a system of rings, but the centre of the cross is wanting (fig. 50). Instead of the cross within the inner ring we observe an uni- form tint, the colour of which changes when the analyzer is revolved ; and, in succession. Different modes of slit- all the colours of the spectrum are brought purposes^r^ °' optical j^^j.^ yjew. But the order of succession (sup- aa. Plates transverse posing the direction Or revolution of the ana- to the pnsmatic axis, for r \ . ^, , . . showing (in the poiari- lyzcr to remain the same) varies in different cXrin\\(S)?^"'" crystals. Thus, suppose we turn the analyzer 66. Plates cut obliquely right-handed, that is, as we screw up, the ^L*stUghtban(fs^°'''''^ colours succced each other, either in this cc. Wedges for making order — red, orange, yellow, green, blue, in- WoUaston's quarts dou- j. -t. i *' . , biy refracting prisms. aigo, violet, red again, and so on ; or in the Ordinary Crystal of Quartz, Fio. 40- 92 ON THE POLARIZATION OF LIGHT. following order — red, violet, indigo, blue, green, yellow, orange, red again, and so on. So that to obtain the same order of succes- sion, the analyser must be turned in the one case right-handed, or as we screw up, in the other left-handed, or as we unscrew. This will be rendered more obvious by the follow- ing diagrams : Fig. 51. Right-handed. Red. Fig. 52. Left-handed. Red.. Red. Fig. 53. In each of these diagrams the arrow shows the direction in which the analyzer is to be rotated, in order to obtain the spec- tral tints in the descending order. In one complete revolution of the analyzer each of the colours of the spectrum occurs twice. In other words, all the colours are seen in one semi-revolution of the analyzer. Hence those specimens of quartz which present the colours in the descending order by a right-handed rotation of the analyzer, are denominated dextrogyrate, or right-handed quartz; while those which present them 'by a left-handed rotation are called Icb- vogyrate, or left-handed quartz. Between these two varieties there has been discovered by Sir John Herschel another dif- ference. In that form of quartz, termed by Haiiy plagiedral (from irXdyios oblique, and f'Bpa a base), it has been found that when the unsymmetrical or plagiedral faces (fig. .53 x) lean to the right, the polarization is right- handed, and vice versd, when they lean to the left the polarization is left-handed. So that the Plagiedral Quartx. cause, whatever it may be, which determines the optical phenomena is also connected with the production of the plagiedral faces. If, instead of using white light in our experiments, we employ homogeneous light, we find that the plane of polarization of the CIRCULAR POLARIZATION. 93 incident rays is turned or made to rotate either to the right or left, according as the quartz plate is either right-handed or left- handed. This rotation of the plane of polarization of the inci- dent ray is proportional to the thickness of the plate. The rings produced by thin plates are broader and less numerous than those produced by thick plates. If two plates be superposed the effect is, very nearly, the same as that produced by a single plate whose thickness is either the sum or the difference of the thicknesses of the two plates ; according as they are of the same kind (that is, both either right-handed or left-handed), or of opposite kinds (that is, one right-handed, the other left-handed). Thus, if the rotation of the red rays, effected by a plate of quartz of ^^^th of an inch thick be equal to 17|-°, that produced by two superposed plates of equal thickness, taken from the same crystal, will be 2xl7J°=35°. On the other hand, if we combine a plate of right-handed quartz of -^-^t-h. of an inch thick with a plate of left-handed quartz of -j^^^ths of an inch thick, the same effects are produced as if we had employed a left-handed plate of -jjths of an inch thick. When the thicknesses of the two dis- similar plates are equal " the plates of course destroy each other's effects, and the system of rings with the black cross will be dis- tinctly seen." {Brewster). The rotation of the plane of polarization increases with the refrangibility of the rays. Thus it is greater with violet than with blue, with blue than yellow, and with yellow than red. Homogeneous Ray. Arc of Rotation. Extreme Red 17" 29' 47" Limit of Red and Orange 20° 28' 47" " Orange and Yellow 22° 18' 49" " Yellow and Green 25° 40' 31" " Green and Blue 30° 2' 45" " Blue and Indigo 34° 34' 18" " Indigo and Violet 37" 51' 58" " Extreme Violet 44° 4' 58" I come now to the explanation which the wave hypothesis offers of these phenomena. When the light, rectilinearly polarized by the first tourmaline plate, is incident on the quartz plate, it suffers double refraction. To prove this, Fresnel contrived a combination of a right-handed prism, and two halves of a left-handed one, by which he doubled the separation of the two rays, and in this way managed to demonstrate the actual existence of double refraction in the principal or prismatic axis of quartz. This is a most remarkable fact. In the principal or prismatic axis of every other known crystal of the rhombohedric system double refraction does not exist. 94 ON THE POLABIZATION Of LIGHT. But the two rays thus obtained differ in their properties from those produced by Iceland spar and other doubly refracting crystals, for while the latter are rectilinearly polarized, those of quartz are circularly polarized. Now every circularly polarized ray is equal to two rectilinearly polarized waves, differing in their progress an odd number of | undulations. It follows therefore, that the two circularly polarized waves are equal to four rectilinearly polarized waves. Hence then to explain the phenomena, we must assume that the rectilinearly polarized ray (which I shall call R) incident on the quartz, is resolved into two others (A and B) of equal intensity, the one (A) polarized in a plane 45° inclined to the right, the other (J5) 45° inclined to the left of the plane of polarization of the primitive ray (R). Let us further conceive that each of the two rays (A and B) is resolved into two other rays, namely A into Aa and Ab, and B into Ba and Bb. Aa and Ab are polarized in one plane, viz., + 45°, while Ba and Bb are polarized in another plane, viz., — 45°. Aa and Ba have each their phases advanced, or + | undulation, while ^6 and Bb have each their phases retarded, or — ^ undulation *. Now if we suppose these four rays to be combined two and two in a cross order, we shall have resulting two circularly polarized rays, one right-handed, the other left-handed. Thus Aa and Bb combine to form a left-handed ray, while Ab and Ba form a right-handed one. For when the advanced system of waves has its plane of polarization to the right of that of the retarded system, the ethe- real molecules rotate from right to left ; whereas they rotate from left to right when the first plane is to the left of the second. These two circularly polarized rays are propagated along the axis of quartz with unequal velocities. In right-handed quartz, the right-handed ray is transmitted with greater velocity, in left- handed quartz with lesser velocity than the left-handed ray ; and thus at their emergence one is in advance of the other. If the surface of egress or ingress be oblique to the axis, the two circu- larly polarized rays will emerge in different directions ; but if it be perpendicular (as in the experiment under examination) they will emerge superposed, and will compound a single ray polarized * " It results from the laws of interference," says Fresnel, " that a sys- tem of -waves, polarized rectilinearly, may be replaced by two others, pola- rized at right angles to each other, and coinciding in their route ; and that for each of these we may substitute two other systems of waves having the same plane of polarization, but the one advanced, the other retarded Jth of an undulation ; and thus separated Jth of an undulation. In this way are obtained four systems of waves of equal intensity, of which two, polarized at right angles to each other, are |th of an undulation behind the two others polarized in the same planes." CIRCULAR POLARIZATION. 95 in a single plane. Now this plane is removed from the plane of primitive polarization by an angle proportional to the interval of retardation (therefore, proportional to the thickness of the crystal) and to the refrangibility of the ray. Thus then the differently coloured rays emerge from the quartz plate polarized ia different planes ; hence, by rotating the ana- lyzer, they are successively transmitted and brought into view. The following diagram may, perhaps, serve to render more intelligible the explanations of the action of a plate of quartz, of one millimetre (0.03937 of an English inch) in thickness, on the incident reclilinearly polarized red light. Incident Red Ray. Plane of Polarization Platte of Polarization. Phase. ^ |Aa...+45° +1 7 Left-handed Kay ■ +45 A6...+45° —J B6..,— 45° -4'' B L~^^° (^Ba...— 45^ +J ——^Eight-handed Eay. Emergrent Red Ray. Plane of Polarization 17J°. A succession of quartz prisms does not give a further multipli- cation of images — a circumstance which distinguishes the double refraction of quartz from that of Iceland spar and other crystals. The above explanation is applicable only when the direction of the rays coincides with the principal axis of the crystal. When it is inclined to this axis, Mr. Airy has shown that the two resulting rays are elliptically polarized, the elliptical vibrations in the two rays being in opposite directions (that is, one right- handed, the other left-handed), and the greater axis of the ellipse is for the extraordinary ray, in the principal plane of the crystal, and, for the ordinary ray, in a plane perpendicular to the principal one. The ratio of the axes in these ellipses, varies with the inclination of the ray to the principal axis of the crystal. When the direction of the ray coincides with this axis, the ratio is one of equality, and the ellipses become circles. But when the ray is inclined to the axis, the ratio increases indefinitely with the inclination. "It is also necessary to suppose that the axis of revolution of the spheroid (prolate for quartz) in which the extraordinary ray is supposed to diverge, is less than the radius of the sphere into which the ordinary wave diverges." Hitherto we have had no satisfactory theory of the cause of the unequal velocities with which the two rays are transmitted along the principal axis of quartz. We conceive that it must depend either on some peculiarity in the molecules themselves, 96 ON THE POLARIZATION OF LIGHT. or in their mode of arrangement. "The crystal," says Fresnel, ** cannot be constituted from right to left as it is from left to right, either in virtue of the arrangement of its particles, or of their individual constitution." If it be a molecular property, it must be acquired in the act of crystallization, by the mutual action of the molecules on each other, for other forms of siUca, as weW as melted quartz, are devoid of it. An helicoidal arrangement (right or left-handed, as the case may be) of the molecules furnishes a physical explanation of the fact above referred to. It has been objected to this hypothesis, that it is not applicable to the case of circularly polarizing liquids. But as the circular polarization of quartz is dependent on direction, while that of liquids is independent of it, it is tolerably clear that the cause must be different in the two cases. In the first, it may depend on the arrangement of the^molecules; in the second, on some peculiarity in the molecules themselves. If two plates of quartz, cut obliquely to the principal axis of the crystal (fig. 49, b b, bb),he superposed crosswise and examined in the polariscope, they present a series of parallel coloured bands or stripes, with a central black or white stripe. When the tourmaline plates are crossed, the central stripe is black, when they coincide, it is white. The lateral coloured stripes seen in the one case, are complementary to those seen in the other. Amethyst is a mixture of right and left-handed quartz, and will be hereafter noticed among tesselated crystals. 5. Circular Polarization by Fluids.— Some liquids possess the remarkable property of circularly polarizing light. The fol- lowing are the most important : Volatile oils (those of mustard and bitter almonds excepted). Naphtha. Aqueous solutions of several kinds of sugar, dextrine, tartaric acid, and tartrates (tartrate of alumina excepted). Diabetic urine. Albuminous urine. Alcoholic solutions of camphor and artificial camphor. Most vegetable juices. Biot found that vaporization did not destroy the circular pola- rization of oil of turpentine. The following liquids have been found devoid of this pro- perty : Water. Alcohol. Pyroxilic spirit. Pyroacetic spirit. Olive oil. CmCULAB POLARIZATION. 97 Volatile oil of mustard. ~~ bitter almonds. Claret ("perhaps a trace of "^^^^^ )• Champagne. Citric acid (dissolved in water). Mannite (ditto). Liquorice sugar (ditto). Glycerin. The apparatus necessary for observing this property of fluids consists essentially of three parts ; viz., a polarizer, a tube to contain the fluid, and an analyzer. The polarizer is an unsilvered glass mirror, a bundle of parallel glass plates or a Nichol's prism. Both Biot and Professor I'owell use the first, while Ventzke employs the last. A plate of glass, blackened at the posterior surface, answers very well Sometimes a second mirror (of silvered glass) is used to throw the light on the polarizing plate. The tube, to hold the liquid, should be from six to twenty-four inches long. In general, it is to be filled with the fluid under examination, and to be closed at each end by a flat glass plate. Professor Powell, however, employs a common test-tube, open at the top, and havmg the usual hemispherical bottom. In some cases It IS desirable to have two or three perforated diaphragms ot sheet silver or platinum, placed at intervals in the tube to exclude the light reflected from the sides of the tube, but to admit those rays which traverse the axis of the tube. The analyzer should be either an achromatic, doubly refracting prism, or a Nichol's prism. Biot uses a doubly refracting prism of calc spar, made of a rhombohedron of this substance! rendered achromatic by replacing a portion of the crystal by a glass prism. Achromatic quartz prisms are objectionable, since they are never so accurately prepared as to yield two images only but always four ; of which two, however, are very faint. Ir'rotessor Powell employs a rhombohedron of calc spar, in its natural state, as his analyzer, and a lens to magnify the separa- tion of the images. Ventzke uses a Nichol's prism as the ana- lyzer. ^ The amount of rotation which a ray of light suffers during its passage through the liquid, is measured by an index attached to the analyzer, and moving on a graduated circular metallic plate. Be- tore the tube containing the liquid is introduced, we must fix the zero, or O^. If a doubly refracting prism be the analyzer, the index IS made to point to zero, or 0°, when the ordinary imao-e alone is seen. If, however, a Nichol's prism be used as ana- 98 ON THE POLARIZATION OF LIGHT. lyzer, the index is arranged to point to C when the light is excluded ; or, in other words, when the light, transmitted by the polarizer, is extinguished by the analyzer. Homogeneous light is generally employed when we wish to measure the arc of rotation afFected by a liquid on a luminous ray. Red light is usually selected, because this is the only homogeneous light which can be isolated by coloured glass. We, therefore, place a plate of red glass between the eye and the analyzer. . . If, when the index points to zero 0**, the tube contaming a circularly polarizing liquid be introduced, the second or extra- ordinary image immediately becomes evident, if the doubly refracting prism be used as analyzer. By turning the latter round to the right or to the left, as the case may be, this second image disappears (when homogeneous light is used), and the arc traversed by the index from the zero 0°, measures the angle of deviation of the ray. If, however, a Nichol's prism be employed, it no longer excludes the light when the index stands at 0°,but requires to be rotated a certain number of degrees to do so, and the arc of rotation is here a measure of the rotative power of the liquid. , The explanation of the action of these liquids on the incident rectilinearly polarized light is similar to that already given for the axis of quartz ; with the exception, that in the case of quartz, the circular double refraction may depend on the arrangement of the molecules, whereas in liquids it must arise from some pro- perty of the molecules themselves. I proceed now to examine some of the liquids which posses* the property of circular polarization : First, with regard to the essential or volatile oils. Most ot these bodies are circular polarizers : indeed, I know but two exceptions to this statement, viz. oil of mustard and oil of bitter almonds. Some turn the planes of polarization to the right, others to the left, but the intensity of their rotative power varies considerably, as the following table shows ; CIRCULAR POLARIZATION OF THE VOLATILE OILS. 1. Left-handed, or Lavogyrate. Arc of Potation with the lied Rays through a thickness o/'20() Millimetres. Oil of Turpentine 59° 21' " Mint 32- 28' " Anise " Rue Naphtha • 21 CIRCULAK POLARIZATION. 99 2, Right-handed, or Dextrogyrate Oil of Lemon 110° 53' " Bergamot 38*> 16' Bigarade 157° 89' " Citron — " Limette — " Neroli — " Fennel 26« 32' " Caraway 131° 58' " Lavender 4° 04' " Rosemary 6° 58' " Knotted Marjorum 23° 68 ' " Sassafras 7° 06' " Savine 14° 12' This table is a' very instructive one. It shows that isomerism lias no connection with circular polarization, for of three iso- meric oils (turpentine, lemon, and bergamot) mentioned in this table, one is laevogyrate, the others dextrogyrate. We see also, that oils derived from plants of the same natural family (as the oils of anise, fennel, and caraway from the umbellifercB, and those of mint, lavender, and rosemary from the labiates) differ ia respect of their circular polarization. In some cases, perhaps, this fact might be available to the Pharmaceutical Chemist in detecting mixtures of one oil with another, as the adulteration of oil of peppermint with oil of rosemary, recently mentioned by Mr. Herring, (See Pharmaceutical Journal, vol. i., p. 263). Some kinds of sugar, when dissolved in water, yield solutions which have in a greater or less degree the property of rotating the planes of polarization, some to the right, others to the left. Hence polarized light may be sometimes used as a test of the presence of sugar, and the degree of rotation becomes an indica- tion of the quantity and even quality of the sugar present. Biot examined by this t«st a specimen of sugar-cane juice, and found that it indicated the presence of 20 or 21 per cent, of sugar. Peligot subsequently analyzed it, and found 20.9 per cent, of sugar. Biot, therefore, suggests that those who make, as well as those who refine sugar, might resort to this test as a means of determining the amount of sugar in different juices or solutions. To the colonist it would prove useful by pointing out the saccharine strength of the juice at the mill, and to the sugar refiner it would be valuable by enabling him to determine the absolute strength of raw sugar. The sugars are prepared for examination by dissolving thera in water, and decolorizing the solutions when necessary, by filtering them through purified granulated animal charcoal. Several sweet or saccharine substances do not indicate any circular polarization, and of those that do, some indicate right- handed, others left-handed circular polarization. H 2 100 ON THE POLARIZATION OF LIGHT. 3. Incrystallizable Sugar {Chulariose of Soubeiran) " 1. Cane Sugar Bight handed. 2. Grape Sugar (^Glucose of Dumas) ditto [ a. Incrystallizable Sugar of Honey Left handed. b. Incrystallizable Sugar, obtained by the action of acids on Cane Sugar ditto. c. Incrystallizable Sugar of the juices of Fruits ditto d. Incrystallizable Sugar, obtained by the alteration of Cane Sugar. This constitutes the greater part of Molasses ditto. 4. Mannite O 5. Glycerin O 6. Liquorice Sugar O The grape sugar referred to in this table exists ready formed in honey, and in diabetic urine. It is deposited when the acidulous juices of fruits have been saturated and sufficiently concentrated. Moreover, it is produced by the action of diastase on starch, as well as when syrup, obtained by the action of weak acids on starch or sugar, is abandoned to itself. The following table, taken from a memoir, by Biot, shows the extent of rotatory power possessed by different sugars : BOTATION OBSERVED WITH BED GLASS THROUGH A SOLUTION OF 152 MILLIMETRES IN LENGTH. Proportion of Sugar in one of the solution. Arc'oJ Rotation Sugar Candy 1. Aqueous solution 0.25 23" 28' 45* " 2. " 0.50 51" 28' 45" « 3. " 0.65 70^ ir 15" Cane Sugar syrup, boiled, and rapidly ? q 344 1 e** 50' 33" cooled 3 ■ Sugar of Milk, cryitallized (aqueous } lO" 2 1' 40 " solution) ) Starch Sugar, white grains (ditto)... 0.648 48<' 30' 0" Grape Sugar syrup — — — — in white grains (aque-7 ^ ^^^g _ ous solution) ) * ^ Crystallizable principle of Honey ... 0.34201... 16^ 47' 30 ' Uncrystallizable ditto — — — ~ Cane sugar, dissolved in water, causes n^/t/-handed polari- zation. A aitrong syrnp made with refined sugar shows the CIRCULAR POLARIZATION. 101 colours most brilliantly. When this kind of sugar is subjected to heat, especially in contact with acids, it loses its crystallizability, and then acquires /e/V-handed polarization. In the manufacture of barley- sugar, hard bake, &c., the makers of these kinds of hard confectionary use a little cream of tartar to destroy the crystal- lizability of sugar. Soubeiran found that a syrup of cane-sugar heated by a salt-water bath, the air being excluded, underwent a series of remarkable changes in respect of its rotative power. Arc of Rotation for mean Yellow Ray ^ . for a length of 100 Millimetres. byrup, primitive ^71 " After twenty hours O " After twenty-five hours —11 " After sixty -four hours O " After seventy-two hours 5 Here then it appears, that cane-sugar.^r^^ gradually lost its rotative power 0°, and then became In this latter state it was probably incrystallizable sugar. But this in its turn lost its rotative power 0°, and became^^^. The precise nature of the latter kind of sugar is not known. In sugar-refining the object is never to let the syrup get beyond tl e first zero; that is, not to convert crystallizable unto uncrystallizable sugar. Raw sugar contains, however, both crystallizable and uncrystallizable sugar : the latter alone should constitute treacle. But, from Soubeiran's optical examination, it appears that treacle contains a portion of crystallizable sugar. The optical characters of sugar have been made use of to detect fraud in Pharmacy. In 1842, more than a ton of a substance purporting to be manna was offered for sale in Paris at less than fivepence per pound, the excuse given for the unusually low price was, that cash was immediately required. Suspicion was raised, and the substance was submitted to careful examination, ihe result of which was the establishment of the fact, that it was not manna, but potato-sugar. Its aspect, taste, ferment- ibility (mannite not being fermentible), and the presence of sulphate of lime proved this. Biot submitted it to a very care- ful optical examination, and found its characters to be those of a starch-sugar. Manna contains two kinds of saccharine matter, one called mannite, and the other a fermentable sugar. Now mannite, when pure, has no rotative power on polarized 102 ON THE POLARIZATION OF LIGHT. light, but commercial manna has a slight effect, owing to the presence of a small quantity of fermentable sugar. This ficti- tious substance, however, had the same effect on plane polarized light, as sugar prepared by the action of acids on starch, when the action is arrested at the first phase of its transformation. Vinous fermentation has been studied by the aid of polarized light. Take a solution of cane-sugar which has right-handed circular polarization. As soon as it begins to ferment it loses this property, but acquires left-handed polarization. Polarized light has been prepared and used as a test of the presence of sugar in urine. To render diabetic urine available for this purpose, it must be decolorized by agitation with fresh prepared granulated animal charcoal, and subsequent filtration. The process is troublesome, tedious, and can only prove successful in the hands of persons familiar with the phenomena of polarized light. With all due deference to Biot, I do not think it will ever prove of much value in practical medicine. We have other, simpler, less laborious, and cheaper methods of detecting sugar in urine than the one now referred to. Moreover, it should be remembered, that albuminous urine possesses the property of circular polarization. The substance called dextrine is starch-gum, and is soluble in water. It is usually prepared from potato-starch, either by torrefaction or by the action of a small quantity of nitric acid. A solution of it possesses the property of right-handed circular polarization, hence the name dextrine applied to it by Payen and Persoz. Properties of circularly polarized Light. — Common, recti- linearly polarized, and circularly polarized, lights are undistin- guishable by the eye. All three may be coloured or white. The properties which distinguish the latter from the two former are as follows : 1. A ray of circularly polarized light is capable of reflection by a reflecting plane, as of glass, in every azimuth of the plane of reflection. For the circular vibrations of the ethereal mole- cules may be resolved into two equal rectilinear vibrations, one parallel, the other perpendicular, to any arbitrary plane. By this property, therefore, circularly polarized light differs from rectilinearly polarized light, but agrees with unpolarized light. 2. A ray of circularly polarized light is capable of transmis- sion through a plate of tourmaline (cut parallel to the axis of the crystal), in every azimuth of the axis of the crystal. For in this case also, the circular vibrations of the incident ray may be resolved into two equal rectilinearly vibrations, one parallel, the other perpendicular, to any azimuth. One of these vibrations is transmitted by the tourmaline, the other is suppressed. CIRCULAR POLARIZATION. 103 In this property also circularly polarized light agrees with common or unpolarized light, but differs from rectilinearly pola- rized light. 3. Analyzed by a doubly refracting prism of Iceland spar, a ray of circularly polarized light gives constantly two equal images, in whatever plane the principal section of the prism be placed. For, as I have already stated, a ray of circularly polarized light is the resultant of two rays placed at right angles and differing in their phase by a quarter undulation ; and, therefore, it must give equal images by the doubly refracting prism, in the same way that common or unpolarized light does, for the diiference of phases has nothing to do with this character. In this respect circularly polarized light agrees with common or unpolarized light ; but isdistinguished from rectilinearly (plane) polarized light, which in certain positions (before specified) yields one image only. 4. By tvs'o total internal reflections in the interior of glass, at an angle of about 54-1"^, circularly polarized light is converted into rectilinearly polarized light. Thus if light circularly polar- ized be incident on Fresnel's rhomb, it emerges rectilinearly polarized, and the position of the plane of polarization at emerg- ence makes au angle of +45^ or — 45°, with the plane of reflection according as the incident light was right-handed or left-handed. This experiment may be readily understood from the explanation already given of the action of Fresnel's rhomb in converting rectilinearly polarized light into circularly polarized light (fig. 46, p. 88). In fact, the two experiments are the converse of each other; the light called incident in the one case, being termed emergent in the other, and vice versd. In this character, circularly polarized light differs equally from both unpolarized and rectilinearly polarized lights. For by two reflections of this kind, common light suffers no obvious change ; while rectilinearly polarized light, under the same cir- cumstances, is converted into circularly polarized light, provided that the plane of reflection be at an azimuth of 45° to that of primitive polarization. 5. If a ray of circularly polarized light be transmitted through a thin film of a doubly refracting crystal, and the emergent light be analyzed by a doubly refracting prism, two rays of comple- mentary colours are produced. In this character, circularly polarized light is decidedly dif- ferent to common or unpolarized light, which when submitted to the same examination presents no colour. Rectilinearly polarized light, however, agrees with the circular light in producing com- plementary tints ; but they are not the same in the two cases ; those' produced by circular light differing from those of rectilinear 104 ON THE POLARIZATION OF LIGHT, light by an exact quarter of a tint, either in excess or defect, as the case may be. To illustrate these facts, place a film of selenite, of uniform thickness, in the polariscope, and observe the tint which it yields by rectilinearly polarized light. Then interpose, between the polarizing plate and the selenite film, a circularly polarizing appa- ratus (as Airy's mica plate, or Fresnel's rhomb), and the tint seen by the analyzer immediately changes. If a plate of calcareous spar, cut to show the circular rings and cross by rectilinearly polarized light, be placed in the po- lariscope, and circularly polarized light be used, we observe a system of rings and a cross (fig, 53), but which are very different to those seen by rectilinearly polarized light. " The rings are divided mto quadrants by the cross, every other quadrant being sinnilar, while the adjacent ones are dissimilar. The rings appear to be abruptly and absolutely dislocated, those in the two alternate quadrants being pushed outwards or from the centre, by J of an order, and those of the intermediate quadrants being as it were pulled inwards by ^ of an Spar produced by cir-^^^^^- Instead of a black cross, we have a cuiariy poiarixedjight.\\irn'mous One, the intensity of its light being uniform, and about equal to the mean intensity. If the plane of incidence pass througji 135" and 315°, the phenomena of adjacent quadrants are exactly interchanged. But the most important difference produced by circularly polarized light, is, that no alteration is made by turning the analyzing plate round the incident ray. If a plate of a biaxial crystal, as of nitre, be examined by circularly polarized light, we observe the double system of rings, but the black cross disappears. Every alternate semicircle of rings presents the appearance of dislocation. The origin of the tints produced by circularly polarized light, have been so clearly and concisely explained by Sir John Herschel, that I cannot do better than use his words : " When," says tins eminent philosopher, " a ray propagated by circular vibrations is incident on a crystallized lamina, it may be regarded as composed of two ; one polarized in the plane of the principal section, the other at right angles to it, of equal intensity, and differing in phase by a quarter midula- tion. Each of these will be transmitted mialtered ; and, therefore, at their emergence, and subsequent analysis, will comport themselves in respect of their interferences, just as would do the two portions of a ray primitively polarized in azimuth 45°, and divided into two by the double refraction of the lamina ; provided that a quarter undulation be added to the phase of one of these latter rays. Now, such rays will produce, by the interference of their doubly refracted positions, the ordinary and extraordinary tints due to the interval of retardation withm the crystallized lamina. Hence, in the CIRCULAR POLARIZATION. 105 present case, the tints produced will be those due to that interval, plus or minus the quarter of an undulation added to, or subtracted from, the phase of one of the portions ; and, consequently, will differ one-fourth of a tint in order from that which would arise from the use of a beam of ordinary polarized hght, incident in azimuth 45° in the lamina," f 6. If a ray of circularly-polarized light be transmitted through a column of syrup or oil of turpentine, lemon, &c., and then analyzed, either by a Nighol's prism, or a doubly-refracting prism, no colour is produced. For the circular wave is propa- gated along the liquid without suffering subdivision, and, there- fore, at its emergence, no colour can be produced by the analyzer. In this character circularly-polarized light agrees with common or unpolarized light ; but differs from plane polarized light. 7. *' Circularly-polarized light," says Fresnel, " differs from plane polarized light in not sensibly developing colours in plates of quartz perpendicular to the axis." According to the wave hypothesis this ought to be the case ; for " a ray propagated by circular vibrations, when incident on rock crystal in the direction of the axis, will (by hypothesis) be propagated along it by that elasticity which is due to the direction of its rotation, the wave then will enter the crystal without further subdivision, and there will be no difference of paths or interfering rays at its emergence ; and, of course, no colours produced on analyzing by double refraction." I confess, however, I have not been able precisely to verify this statement, though, I doubt not, my failure has arisen from some defect in the apparatus used to produce circular polariza- tion. I have always found a very feeble tint of colour in the axis. As Mr. Airy has very accurately described the phenomena which I myself have repeatedly seen, I prefer quoting his words : Fio. 54. " If circularly-polarized light pass through the quartz, on applying the analyzing plate, in- stead of rings, there are seen two spirals mu- tually enwrapping each other [as in fig. 54.]. If the [Fresnel* s] rhomb be placed in position 135°, the figure is turned through a quadrant. If the quartz be left-handed, the spirals are turned in the opposite direction. The central tint appears to be white. With the rhomb which I have commonly used (which is of plate- glass, but with the angles given by Fresnel for crown-glass), there is at the centre an extremely dilute tint of pink : I think it hkely that this arises from the error in the angles, as the in- tensity of the colour bears no proportion to that in other parts of the spiral." If a plate of right-handed quartz be superposed on a plate of left-handed quartz of equal thickness, and examined by circu- larly-polarized light, the left-handed slice being nearer to the Spirals of Quartz, produced by circularly- potarixed light. 106 ON THE POLARIZATION OF LIGHT. polarizing plate, we observe, by means of the analyzer, four spirals (proceeding from a black cross in the centre) which cut a series of circles at every quadrant. At some distance from the centre the black brushes are seen. If the right-handed slice be nearer the polarizing plate, the spirals are turned in the opposite directions. 8. Mr. Earnshaw inferred, theoretically, from Fresuel's formulae, that if right-handed circularly-polarized light be incident nearly perpendicularly upon a plane surface of glass, the reflected light will be left-handed circularly-polarized, and vice versa. The Rev. Professor Powell has subsequently verified experimentally Mr. Earnshaw's theoretical deduction. Airy's analyzer for Circularly -Polarized Light. — I have already stated and described twokinds of circularly-polarized light; theonecalled right-handed, the otherleft-handed. Todistinguish them, Mr. Airy contrived an analyzer which suppresses one and transmits the other. " It is well known," he observes, " that if circularly-polarized light is incident on Fresnel's rhomb, it emerges plane-polarized, and the position of the plane of polari- zation at emergence makes an angle of +45°, or — 45° with the plane of reflection, according as the incident light was right- handed or left-handed. Let the light emerging from the rhomb be received on an unsilvered glass at the polarizing angle, whose plane of reflection makes the angle +45^^ with that of the rhomb. Now it is plain that if the light incident on the rhomb was right- handed, it becomes plane-polarized in the plane of reflection of the glass, and, therefore, is wholly reflected ; if it was left- handed, it becomes plane-polarized in the plane perpendicular to the plane of reflection of the glass, and, therefore, is wholly suppressed." It is then obvious, that this combination of Fres- nel's rhomb and on unsilvered glass at +45°, or — 45^*, would form an analyzer for circularly-polarized light. But as Fresnel's rhomb is inconvenient, on account of its length, Mr, Airy has substituted " a plate of mica of such a thickness that the ray polarized in the plane of one of its principal sections is retarded either ^th, f ths, or -fths of a wave (^according to the convenience of splitting) more than that polarized in the plane of the other. The mica being attached to the unsilvered glass, so that its principal section makes an angle of 45** with the plane of reflec- tion, an analyzer is produced, which answers the same purposes, in general, as that described above." 6. ON ELLIPTICAL POLARIZATION. Time will permit to say a few words only respecting ellip- tically polarized light. ELLIPTICAL POLAKIZATION. 107 If two systems of waves of equal intensity, polarized rectan- gularly to each other, differ in their progress a fractional number of I undulation, the vibratory movements of the ethereal molecules will be neither rectilinear nor circular, but elliptical. The waves formed by such vibrations will be elliptical, and may be compared to an elliptical helix (that is, to a helix traced round an elliptical cylinder), right-handed or left-handed, as the case may be. Powell's machine gives a very good idea of elliptical vibrations and elliptical waves. The manner in which two rectangularly polarized waves interfere and produce elliptical waves, is shown by Wheatstone's apparatus. There are several modes of effecting the elliptical polarization of light. If in the experiments with Fresnel's rhomb (see Cir- cular Polarization) the planes of polarization and incidence be at any other angle than 45° the emergent ray will be elliptically polarized. Airy's mode of producing circular polarization may be used to obtain elliptical light ; but the mica plate, through which the ray is perpendicularly transmitted, must be placed at an azimuth between that which yields circularly polarized, and that which admits plane polarized light. Compressed, or unannealed glass, also yields elliptically po- larized light, under conditions which I have explained when describing Dove's method of circular polarization. Quartz also produces elliptical polarization when the direction of the incident ray is inclined to the axis. By reflection from metallic surfaces light becomes elliptically polarized. The elliptical light reflected from silver is nearly circular, while that from galena is almost plane : that is, the ellipsis in the one case is nearly a circle, in the other nearly a straight line. Elliptically polarized light is not distinguishable, by the eye, from other kinds of light. If it be analyzed by a Nichol's prism, an unsilvered glass mirror, or a plate of tourmaline, it never vanishes during the revolution of the analyzer. By this it may be known from rectilinearly polarized light. But at dif- ferent azimuths of the analyzer the intensity of the light varies; and by this it may be known from both unpolarized and circu- larly polarized light. If it be analyzed by a rhombohedron of calc spar, it gives two images in all positions of the analyzer. In this respect it differs from plane polarized light. But one of the images exhibits a defalcation of light, showing that the incident light is not common or unpolarized. If elliptically polarized light be transmitted through an uniaxial crystal (as 108 ON THE POLARIZATION OP LIGHT. Iceland spar) cut perpendicularly to its axis, and the emerg^ent light be afterwards analyzed, it presents a system of rings and cross different to those obtained from either plane or circularly polarized light. The preceding are some only of the peculiarities which distinguish this from other kinds of light; and in conclusion, I may observe, that elliptical polarization forms a connecting link between plane and circular polarization. 5. MACLES AND COMPOUND CRYSTALS. I have now arrived at the last part of my subject, viz., the consideration of the optical properties of those remarkable crys- talline structures commonly known by the name of macles, a term introduced into mineralogy by Rome de Lisle. Sometimes these structures appear to consist of one crystal, whose parts are transposed, dislocated, or displaced. When one-half of the crystal appears to have been turned partly round on an imaginary axis, passing through the centreof the crystal, and perpendicularly to the plane of section, and to have been united to the other half in this position, the body thus produced has been called the hemitrope (from r]HL half and TpeVo) / turn). Of this arrow- headed selenite is a familiar example. Sometimes two or more crystals are found intersecting each other, and are then called intersecting crystals. When two crystals are joined, they form the structure called a twin or double crystal. Many or most of the forms I have now referred to are irregu- lar, and might appear to be accidental. But there are some others which have great regularity, and cannot be ascribed to accident. Such are some specimens of apophyllite and sulphate of potash. They constitute what Dr. Brewster has termed tesselated or composite crystals; the real structure of many of which is only discoverable by the aid of polarized light; they consist of several crystals, or portions of crystals, juxtaposed, or united so as to form a compound crystal, the figure of which is very different from that of the crystals composing it. Macled crystals of nitre and arragonite are very common, and frequently their precise structure is undiscov^rable by the naked eye. In quartz we often find right and left-handed crystals inter- secting each other. Amethyst (by many mineralogists considered to be a variety of quartz), is a remarkable example of a combination of right and left-handed varieties of quartz. If a plate of amethyst, cut perpendicularly to the principal axis of the crystal, be examined by the polariscope, it presents a striped or fringed appearance, MACLES AND COMPOUND CRYSTALS. 109 variegated with the most gorgeous and brilliant tints. This is owing to its being composed of alternate minute strata of right and left-handed quartz, whose planes of polarization are parallel to the principal axis of the prism. Topaz sometimes presents a remarkably composite structure. It belongs to the right rhombic system, and presents, when re- gularly formed, two systems of rings. Cut at right angles to the axis it often presents a central rhomb, " surrounded by a border in which the optic meridians of the alternate sides are inclined at a quarter of a right angle to that of the central com- partment, and half of a right angle to each other. In conse- quence, when such a rhombic plate is held with its long diago- nal in the plane of primitive polarization, two opposite sides of the border appear bright, the other two black, and the central compartment of intermediate brightness. Such specimens often present the phenomena of dichroism in the central compartment, while the border is colourless in all positions*." Sulphate of potash is composed of six crystals belonging to the right prismatic system, joined so as to form a single or double six-sided pyramid, and simulating the crystals of the rhombo- hedric system. When, therefore, we put a slice of it, cut at right angles, to the axis of the pyramid, in the polariscope, we observe not a circular cross and rings, but a tesselated structure. One variety of apophyllite, called tesselite, presents a remark- able structure of the same kind ; but its phenomena are still more extraordinary. Apophyllite is composed principally of silicate of lime, with a little silicate of potash. It crystallizes in right square prisms. Plates cut transversely to the axis, and examined by polarized light, appear to consist of nine crystals contained within a number of parallel veins or plates. The cen- tral crystal has only one axis of no double refraction, the others two. (See p. 68). Analcime or Cubizite is another remarkable crystal. It consists principally of silicate of alumina with silicate of soda. It crystallizes in the form of the cube, or some form allied to this, as the icosatetrahedron. Instead of being without double refraction, as cubical crystals usually are, it presents a number of planes of no double refraction. It is, therefore, a compound crystal, that is, is composed of a number of crystalline parts disposed symmetrically. (See p. 66). And here also may be noticed what has been called mferrM/»^ec? Iceland spar. Some specimens of Iceland spar give four or even more images, which sometimes exhibit complementary tints. They owe this property to the presence of one or more intersecting * Herschel, Encycl, Metrop. 110 ON THE POLARIZATION OF LIGHT. or interrupting films or strata of the same substance, placed per- pendicularly to the short diagonal of the faces of the crystal. This film acts like the depolarizing plate in the polariscope, while the two portions of the crystal between which it is placed, act, the one as the polarizer, the other as the analyzer of the polari- scope. Crystals like these, which thus exhibit their colours and rings per se, that is without the polariscope, have been called by Sir John Herschel, idiocyclophanous (from 'Lbios proper, kvkKos a circle, and (^aiva I appear). Similar phenomena are sometimes exhibited by crystals of nitre, and still more frequently by bicarbonate of potash. Conclusion. — The lateness of the hour compels me to avoid any lengthened peroration. I shall, therefore, content myself with thanking my auditors for the great attention which they have manifested during the entire course. THE END. C. VHITING, BEAUFORT HOUSE, STRAND. October Z, 1843. NEW WORKS AND NEW EDITIONS PrinteU for LONGMAN, BROWN, GREEN, AND LONGMANS, LONDON. ANALYTICAL INDEX. AGRICULTURE AND RURAL AFFAIRS. Pages Bayldon On valuing Rents, &c. - 3 the Valuation of Pro- perty^for Poor's Rate - - - 4 Crocker's Land-Surveying - - 7 Davy's Agricultural Chemistry - 7 Johnson's Farmer's Encyclopsedia 14 Loudon's Encyclopaidia of Agri- culture - - - - - 17 Low's Elements of Asriculture - 18 " Breeds of the Domesticated Animals of Great Britain - 17 ARTS, MANUFACTURES, AND ARCHITECTURE. Brande's Dictionary of Science, Literature, and Art - - - 6 G%vilt's Encyclopsedia of Architec- ture 10 Loudon's Encyclopsedia of Cottage, Fai-m, and Villa Architecture and Furniture ----- 17 Porter's Manufacture of Silk - - 24 " Porcelain & Glass ib. Savage's Dictionary of Printing - 26 Ure's Dictionary o^ Arts, Manufac- tures, and Mines - - - - 31 Wathen's Egypt. Arts & Antiquities 32 BIOGRAPHY. Aikin's Life of Addison - - - 3 Bell's Lives of the most eminent British Poets - - - 4 Biographical Dictionary of the So- ciety for the Diffusion of Useful Knowledge - - - - - ib. Dover's Life of the King of Prussia 8 Dunham's Lives of the Early Wri- tei's of Great Britain - ib. « Lives of the British Dramatists - - ~ ib. Forster's Statesmen of the Com- monwealth of England - - 9 Glei^'s Lives of tlie most Eminent British Military Commanders - ib. Harford's Life of Dr. Burgess - 11 Jackson's Life of Wellington - - 13 James's Life of the Black Prince - 14 " Lives of the most Eminent Foreign Statesmen - - - ib. Maunder's Biographical Treasury- ^ Roscoe's Lives of eminent British Lawyers ----- 25 Russell's Correspondence of the Fourth Duke of Bedford - - 4 Shelley's Lives of the most eminent Literary Men of Italy, Spain, and Portugal - 26 " Lives of the most eminent French Writers - - ib. Smith's Memoirs of the Marquis de Pombal ----- 27 Southey's Lives of the British Ad- mirals - - - _ _ ib. Tate's Horatius Restitutus - - 29 BOOKS OF GENERAL UTILITY. Donovan's Domestic Economy General Catalogue - - - - Hand-book of Taste - - - Hints on Etiquette _ _ - Hudson's Parent's Hand-book " Executor's Guide - On Making Wills Pages Lorimer's Letters to a Young Master Mariner - - _ - 16 Manual for Mechanics' Institutions 18 Maunder's Treasury of Knowledge 20 ** Scientific and Literary Treasury - - - ib. " Treasury of History and Geography - - ib. ** Biographical Treasury - ib. Riddle's Diamond Latin-English Dictionary ----- 25 Short Whist 26 Thomson's Domestic Management of the Sick Room - 29 Tomlins's Law Dictionary - - 30 Waltzing, Reform your - - - 31 BOTANY AND GARDENING IN GENERAL. Callcott's Scripture Herbal - - 6 Conversations on Botany - 7 Drummond's First Steps to Botany 8 Glendinning On the Culture of tlie Pine Apple - - - - 9 Grigor's Eastern Arboretum - - 10 Heiislow's Botany - - - - 11 Hoare On Cultivation of the Grape Vine on Open Walls - - - ib. Hooker's British Flora - - - }^ " Icones Plantarum - - ib. " Compendium of English Flora - - - - ib. *' Ditto in Latin - - - ib. " and Taylor's Muscologia Britannica - - - 12 .lackson's Pictorial Flora - - 13 Knapp's Gramina Britannica - 15 Lindley's Theory of Horticulture - 16 " Outline of the First Prin- ciples of Horticulture - ib. " Guide to the Orchard and Kitchen Garden - - ib. " Introduction to Botany - 16 " Natural System of Botany ib. " Flora Medica - - - 16 " School Botany - - ib. " Synopsis of British Flora ib. Loudon's Hortus Britannicus - 17 " ** Lignosis Londinensis ib, " Encyclopsedia of Trees and Shrubs - - 16 *' " Gardening ib. " " Plants - 17 " Suburban Garden and Villa Companion - ib* " Cemeteries and Church- yards ------ ib. Repton's Landscape Gardening and Landscape Architecture - - 24 Rivers's Rose Amateur's Guide - 25 Roberts On the Vine - - - ib. Rogers's Vegetable Cultivator - 26 Smith's Introduction to Botany ** English Flora - ib. CHRONOLOGY. Blair's Chronological Tables - i Nicolas's Chronology of History - 22 Riddle's Ecclesiastical Chronology 25 Tate's Horatius Restitutus - 29 Wathen's Chronology of Anc. Egypt 32 COMIVIERCE AND MERCAN- TILE AFFAIRS. Young - 16 M'Culloch's Dictionary of Com- merce and Commer. Navigation - 20 Steel's Shipmaster's Assistant - 28 GEOGRAPHY X ATLASES. Butler's Sketch of Ancient and Modern Geography - 6 '* Atlas of Modern Geography ib " Ancient do. - - ib. Hall's New General Atlas - - 10 M'CuUoch's Dictionary, Geogra- phical, Statistical, and Historical 20 Malte-Bvun's Geography - - 18 Maunder's Treasury of Geography and History - - - - 20 Murray's Encyclop. of Geography - 22 Walker's British Atlas - - - 31 HISTORY, Addison's History of the Knights Templars - - - 3 Bell's History of Russia - - 4 Bloomfield's Translation of Thu- cydides - - - - - ib. Cooley's History of Maritime and Inland Discovery - - 7 Crowe's History of France - - ib. Dunham's History of Spain and Portugal - - - 8 " History of Europe dur- ingthe Middle Ages - ib. " History of the German Empire - - - ib. " History of Denmark, Sweden, and Norway- ib. " History of Poland - ib. Fergus's History of United States of America - - - - - 9 Grattan's History of Netherlands - 10 Halsted's Life of Richard III. - U Keightley's Outlines of History - 14 " History of England - ib. Elementary do. - - ib. ** History of Greece - ib. " Elementary do. - - ib. *' History of Rome - ib. " Elementary do. - - ib. " Hist, of Roman Empire ib. " Questions on the above Histories, separate - - - ib. ■Laing's KinM of Norway - - 15 M'CuUoch's Dictionary, Historical, Geographical, and Statistical - 20 Mackintosh's History of England - 18 Maunder's Treasury of History and Geography ----- 20 Moore's History of Ireland - - 21 Rome, History of - - - - 25 Russell's Correspondence of the Fourth Duke of Bedford - * 4 Scott's History of Scotland - - 26 Sismondi's History of the Fail of Roman Empire - 27 " History of the Italian Republics ----- 26 Stebbing's History of the Christian Church - - - 28 '* History of Reformation ib. Switzerland, History of - - - 29 Thirlwall's History of Greece - ib. Turner's History of England - 31 JUVENILE BOOKS, INCLUDING MRS. MARCET'S WORKS. Boy's (the) Country Book - - 13 " Own Book - - - 5 Ladies* (the Young) Book - - 32 ANALYTICAL INDEX TO CATALOGUK OF NEW WORKS. Pages Marcet'B Conversations — On the History of England - 18 On Chemistry - - - - ib. On Natural Philosophy - - ib. On Political Economy - - 10 On Vegetable Physiology - ib. For Children - - - - ib. " The Game of Grammar - ib. " Mary's Grammar - - - ib. " John Hopkins's Notions of Political Economy - - ib. " Willy's Holidays - - - ib. " " Stories for Young Children - - ib. " The Seasons - - - - ib. Mairyat's Masterman Ready - - ib. MEDICINE. Bull's Hints to Mothers - - - 5 " Management of Children - ib. Copland's Dictionary of Medicine - 7 Elliotson'6 Human rhysiology - 8 Fxankum On Enlarged Abdomen - 9 Holland's Medical Notes - - 12 Macleod On Rheumatism - - 18 Pereira On Food and Diet - - 23 Reece's Medical Guide - - - 24 MISCELLANEOUS. Bosworth's Anglo-Saxon Dictionary 6 Bray*s Philosophy of Necessity - 5 Cavendish's Debates - - - 6 Clavers'B Forest Life - - - ib. Colton's Lacon - - - - 7 De Morgan On Probabilities - 7 Dendy's Philosoi)hy of Mystery - ib. Duhring's Art of Living - - 8 Good's Book of Nature - - - 9 Graham's English - - - - ib. " Helps to English Grammar ib. Guest's Mabinogion - - - 10 Holland's Progressive Education - 11 Howitt's Rural Life of England - 12 '* Visits to Remarkable Places ib. '* Student-Life of Germany - 13 " Rural and Domestic Life of Germany - - - ib. " Colonisation and Chris- tianity - - - - ib. Jeffrey's (Lord) Contributions to The Edinburgh Review - - 14 Life of a Travelling Physician - 15 Macaulay's CriticsQ ana Historical Essays 18 Milne On the Valuation of Annuities and Assurance on Lives, &c. - 21 Morgan On Assurances, Annuities^ and Reversions - - - - ib. Peter Plymley's Letters - - - 27 Seaward's Narrative of Shipwreck - 26 Smith's (Rev. Sydney) Worits - 27 Taylor's Statesman - - - 29 NATURAL HISTORY IN GENERAL. Callow's Popular Conchology - 6 Gray'sFiguresofMoUuscousAnimals 10 ** Genera of Birds - - - 9 Kirby and Spence's Entomology - 15 Reeve's Conchologia Systematica - 24 Stephens's British Coleoptera - 28 Swainson On the Study of Natural History - - - 28 " Animals - - - - ib. " Quadrupeds - - - ib. " Birds - - - - ib. ** Animals in Menageries - 29 " Fish, AmiJitbians, and Reptiles - - - ib. Insects - - - - ib. " Malacology - - - ib. Habits and Instincts of Animals - - - ib. Taxidermy - - ib. Turton's Shells of theBritishlslands 31 Waterton's Essays on Natural Hist. ib. Westwood's Classification of Insects 32 NOVELS AND WORKS OF FICTION. Blessington's (Lady) Meredith - 21 Doctor (the) 8 Howitt's (Mary) Neighbours - - 12 *' ** Home - - - ib. " " President'sDaughters 13 Ingemann's King Eric and the Outlaws ----- 13 James's Eva St. Clair . - _ 13 " Novels - - - - ib. Marryat's Masterman Ready - - 19 Rambles of the Emperor Ching Tih 6 ONE-VOL. CYCLOP/EDIAS AND DICTIONARIES. Pages Blaine's Encyclopjedia of Rural Sports ------ 4 Brande's Dictionary of Science, Literature, and Art - - - 6 Copland's Dictionary of Medicine - 7 Gwilt's Encyclopsedia of Architec- ture 10 Jolmson's Farmer's Encyclopfedia - 14 Loudon's Encyclopaedia of Trees and Shrubs - - - 16 " EncyclopEedia of Gar- dening - - - ib. *' Encvciopaedia of Agri- culture - • - 17 " EncyclopEedia of Plants- ib. M'CuUoch's Dictionary, Geof^ra- phical, Statistical, and Historical - 20 " Dictionary, Practical, Theoretical, &c. of Commerce - - ib. Murray's Encyclopaedia of Geogra- phy 22 Savage's Dictionary of Printing - 26 Ure's Dictionary of Arts, Manufac- tures, and Mines - - - - 31 POETRY AND THE DRAMA. Aikin's (Dr.) British Poets - - 26 Baillie's New Dramas - - - 3 " Plays of the Passions - ib. Bowdler's Family Shakespeare - 26 Chalenor's Walter Gray - - 6 '* Poetical Remains - 6 L. E. L.'s Poetical Works - - 15 Lighter Hours - - - - 16 Macaulay's Lays of Ancient Rome 18 Milton's L'AUegro and 11 Venseroso 21 Montgomery's Poetical Works - ib Moore's Poetical Works - - ib " Lalla Rnokh, medium 8vo. ib " " " fcp. 8vo. - ib, ** Irish Melodies - - - ib Moral of Flowers - - - - ib Southey's Poetical Works - - 27 " British Poets - - - 26 Spirit of the Woods - - - 27 Thomson's Seasons - - - 30 POLITICAL ECONOMY AND STATISTICS. M'CuUoch's Geographical, Statisti- cal, and Historical Dictionary - 20 " Political Economy - ib. Smith's Wealth of Nations - - 27 Spackman's Statistical Tables - ib. Tooke's History of Prices - - 30 RELIGIOUS AND MORAL WORKS,. ETC. Bellamy's Bible - - . - 4 Bloomneld's Greek Testament - 5 " College and School do. ib. " Greek & English Lexi- con to NewTestament ib. Burder's Oriental Customs - - ib. Burns's Christian Philosophy - 6 Callcott's Scripture Herbal - - ib. Dibdin's Sunday Library - - 28 Doddridge's Family Expositor - 8 Ford's New Devout Communicant 9 " Century of Prayers - - ib. Harcourt's Doctrine of the Deluge 11 Kippis's Collection of Hymns, &c. - U Marriage Gift - - - - 19 O'Sullivan Of the Apostacy pre- dicted bj; St. Paul - 22 Parkes's Domestic Duties - - ib. Pearson's Prayers for Families - 23 Kiddle's Letters from a Godfather - 25 Robinson's Greek&EnglishLexicon to the New Testament ib. Sandford's EnglishFemaleWorthies ib. " Female Improvement - 26 '* On Woman - - - ib. Tate's History of St. Paul - - 29 Tayler's Translation of Don Mel- der -8 Turner's Sacred History - - - 30 Wardlaw's Sermons - - - 31 " On Socinian Controversy ib. White On the Gospel - - - 32 RURAL SPORTS. Bainbridge's Fly-fisher's Guide - 3 Blaine's Dictionary of S|)orts - 4 Hansard's Fishing in Wales - - 11 Hawker's Instructions to Sportsmen ib. Martingale's Sporting Scenes - 19 Ronalds's Fly-fishei's Entomology 25 Thacker's Courser'sHemembrancer 29 " Coursing Rules - - ib. THE SCIENCES IN GENERAL AND MATHEMATICS. Pages Bakewell's Introduction to Geology 3 Brande's Dictionary of Science, Literature, and Art - - - 6 Brewster's Optics - - - - ib. Bischoff On the Heat of the Globe- 4 Conversations on Mineralogy - 7 De la Beche On the Geology of Cornwall, &c. " - ib. Donovan's Chemistry - - - 8 Farey On the Steam Engine - - 8 Fosbroke On the Arts, Manneis, Manufactures, and Institutions of the Greeks and Romans - - 9 Greener's Science of Gunnery - 10 " On the Gun - - - ib. Herschel's Natural Philosophy - 11 " Astronomy - -' - ib. Holland's Manufactures in Metal - 11 Kane's Elements of Chemistry - U Rater and Lardner's Mechanics - ib. Lardner's Cabinet Cyclopxdia - 15 ** Hydrostatics and Pneu- matics- - - - ib. *' Electi'icity & Magnetism ib " Arithmetic - - - ib. '* Geometry - - - ib. ' " Treatise on Heat - - ib. Lectures on Polarised Light - - ib. Lloyd On Light and Vision - - 16 Mackenzie's Physiology of Vision - 18 Marcet's (Mrs.) Conversations on the Sciences, &c. - - 18 — 19 Moseley's Practical Mechanics - 22 '* Engineering&Architecture ib. Narrien's Elements of Geometry - ih. Owen's Lectures on Comp. Anatomy ib. Parnell On Roads - - - 23 Pearson's Practical Astronomy - ib. Phillips's Palaeozoic Fossils of Cornwall, &c. - - ib. " Guide to Geology - - ib. " Treatise on Geology - ib. Introduct. to Mineralogy ib. Poisson's Mechanics - - - ib. Portlock's Report on the Geology of Londonderry - - - - '24 Powell's Natural Philosophy - - ib. Richardson's Geology - - - ib. Roberts's Dictionary of Geology - 25 Wilkinson's Engines of War - - 32 Wood On Railroads - - - ib. TOPOGRAPHY AND GUIDE BOOKS. Adam's Gem of the Peak - - 3 Addison's History of tlie Temple Church - - - 3 " Guide to ditto - - ib. Black's Tourist of England - - 4 Britton's Picture of London - - 6 Guide to all the Watering Places in Great Britain - - - - 10 TRANSACTIONS OF SOCIETIES. Transactions of the Entomological Society - - 30 " Zoological Society ib. " Linneean Society - ib. " Institution of Civil Engineers - ib. " Royal Institute of British Architects ih. Proceedings of the Zoological Society 24 TRAVELS. Allan's Mediterranean - - - 3 China, Last Year in, - _ - 6 De Custine's Russia - - - 7 Laing's Notes of a Traveller - - 15 " Residence in Norway - ib. Tour in Sweden - - ib. Postans's Personal Obser^-ations on Sindh 34 Strong's Greece as a Kingdom - 28 VETERINARY MEDICINE AND AFFAIRS. Field's Veterinary Records - - 9 Morton's Veterinary Medicine - 22 " " Toxicological Chart 21 Percivall's Hippopathology - - 23 " Anatomy of the Horse - ib. Spooner On the Foot and Leg of the Horse - - - 2S " On the Influenza of Horses ib. Thomson's Animal Chemistry - 'J'.) 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