In order to rearrange the projection polariscope for experiments in parallel light, we simply remove the three lenses on separate stands (Fig. 71), and the convergent systems of lenses on their special adjustable stand with goniometrical crystal holder, from between the two Nicol prisms, and replace them by two other separately mounted lenses, acting together as an achromatic projecting objective, and a rotatable object stage. The whole arrangement as thus altered for experiments in parallel polarised light is shown in position in Fig. 79. The change is readily made, a gap in the plinth-bed guides near the analysing Nicol enabling it to be effected without removing either of the prisms, the analyser being simply drawn along a few inches nearer the end in order to expose the changing gap. The pair of lenses consists of a plano-convex lens of 5 inches focus and 2¼ inches diameter, and another plano-convex lens of 8½ inches focus and 2 inches aperture, with their convex faces turned towards each other. Together they produce on the screen an excellent image of the object on the stage, and the size of the image can be varied at will by regulating the relative positions of the two lenses with respect to each other and to the object stage. If found more suitable for the particular screen distance available, the 5–inch lens may be replaced by a 6–inch lens also provided as an alternative.

When the analysing Nicol is arranged with its vibration direction parallel to that of the polariser, we obtain bright light on the screen on actuating the electric lantern, and the image of an object on the stage can thus be projected on the screen on a bright ground. But when the analyser is crossed to the polariser, that is, rotated to the position 90° from this parallel position, the two planes of vibration of the Nicols being then at right angles, the screen is quite dark. Before continuing in this dark field our experimental study of quartz, which is obviously a type of the more exceptionally behaving substances owing to its special structure, it will be wise to examine a more ordinary kind of crystalline substance. For this purpose gypsum—better known in optical work as selenite, hydrated sulphate of lime, CaSO₄.2H₂O, crystallising in beautifully transparent and often large crystals belonging to the monoclinic system, a typical one of which has been illustrated in Fig. 9 (page 14), and which we have already referred to in connection with the Mitscherlich experiment described in Chapter VII.—is especially suitable, on account of its clear and colourless transparency, the large size of crystals available, and the brilliancy of the polarisation colours which they afford when adequately thin. A very perfect cleavage being developed parallel to the symmetry plane, the clinopinakoid {010}, such thin films, of even thickness throughout, can be readily prepared.

Such a very thin cleavage plate, about 1½ inches in its longest dimension, is mounted with Canada balsam between a pair of circular glass plates 1⅞ inches in diameter, the standard size of object plates for the projection polariscope; the double plate is then supported in a mahogany frame also of the standard size—4 by 2¼ inches, with clear aperture of 1⅝ inches diameter and supporting rabbet for the plate 1⅞ to 2 inches diameter—on the rotating stage by a pair of spring clips. The Nicols being arranged with their vibration directions parallel, in order to permit light to travel to the screen, and the lenses being arranged properly for a sharply focussed picture of suitable size, the outline of the crystal plate will be seen on the screen, and the whole area of the crystal will either at once appear coloured, or will do so on more or less rotation of the stage carrying the crystal, which rotates the latter in its own plane. The crystal outline is of the character shown in Fig. 80, which also gives the positions of the crystal axes a and c, and a simple stereographic projection of the faces of the crystal, from which the nature of the faces bounding the section-plate will be clear.

On rotating the Nicol analyser the colours change, and appear at their maximum brilliancy when the field is dark and the Nicols crossed. Leaving the analyser crossed to the polariser, and rotating the stage and therefore the crystal, the colours again change, and at certain positions 90° apart during the rotation, marked by the two strong lines in Fig. 80, they disappear altogether, and the crystal becomes dark like the rest of the field, while the positions of maximum brilliancy of colour are found to be situated at the 45°-positions intermediate between these positions of “extinction.” When the quenching occurs the vibration planes of the two rays, travelling by virtue of double refraction through the crystal, are parallel to the planes of vibration of the rays transmitted through the two Nicols, and the fact is a very important one, enabling us to determine the directions of light vibration in the crystal. In the case of our gypsum plate, the cleavage of gypsum being parallel to the unique plane of symmetry of the monoclinic crystal, these two positions are the directions of the two axes of the optical ellipsoid which lie in the symmetry plane, and they correspond to the vibration directions of rays affording the refractive indices α and γ. The direction corresponding to γ is that of the “first median line,” the bisectrix of the acute angle between the optic axes; while α corresponds to the obtuse bisectrix or “second median line.” These directions are clearly marked by the strong lines in Fig. 80. The third axis of the optical ellipsoid is obviously perpendicular to the plate and to the symmetry plane, and corresponds to the intermediate refractive index β. Thus this simple observation of the extinction directions in such a case as gypsum enables us at once to fix completely the orientation of the optical ellipsoid, a fundamental optical determination.

A second thin plate of gypsum may next be examined, similarly prepared and mounted. It is clearly a composite one, being composed of a pair of twins. For when placed on the stage in the dark field of the crossed Nicols, and rotated to the position for maximum brilliancy of colour, it shows different colours in the two halves, as indicated by different shading in Fig. 81. If, however, the analysing Nicol prism be withdrawn from the plinth-bed and removed altogether the crystal appears in its natural colourless condition as a single one, with no indication whatever of any line of division.

Some exceedingly brilliant polarisation effects are afforded by a number of objects exhibited by the author in his lecture at Winnipeg, composed of selenite (gypsum) twins and triplets, some arranged to cross one another like the mica films of Reusch described in the last chapter, but only for a single rotation, three twin strips going to a rotation, at angular distances of 120°; others are arranged in geometrical patterns, and in circles overlapping one another, and the whole series afford the most gorgeous and variegated display of colour imaginable, the colours, moreover, altering either on rotation of the stage or of the analysing Nicol, and thus passing through every tint conceivable.

Having thus demonstrated the usual effect afforded by a doubly refracting crystal plate in parallel polarised light, we may next illustrate two special cases, which will lead us up to the case of quartz once more. The first relates to a crystal belonging to the cubic system, which is theoretically singly refractive or “isotropic”; the second concerns a plate of a uniaxial crystal cut perpendicularly to the optic axis, the unique direction of single refraction of such a crystal. A plate of fluorspar affords a good example of the first case. When placed on the stage of the polariscope it shows no colour at all in polarised light, whatever be the position of the two Nicols with respect to each other, and the field remains dark when they are crossed, the crystal, in fact, behaving just like so much glass.

A word of caution, however, is here necessary, for natural mineral crystals are not infrequently formed under conditions of considerable strain, at high temperatures or under great pressure, as in the case of the diamond for instance. So that we must be careful to choose a normal and well-formed crystal of fluorspar for our experiment. This point may be well illustrated by placing on the stage a thick circular plate of glass, an inch or more in diameter, which has been purposely heated and then suddenly cooled in order to evoke such a condition of strain. Crossing the Nicols so as to obtain the dark field, there is at once produced on the screen a black cross and circular concentric spectrum-coloured rings, resembling with wonderful simulation the interference figure, shown in Fig. 72, Plate XIV., afforded by calcite or other uniaxial crystal in convergent polarised light. Artificial double refraction has been produced in the glass by the strained conditions, in a fashion concentrically symmetrical to the axis of the cylinder, an interference figure being afforded symmetrical about the axis of the cylinder as if it were an optic axis.

The diamond crystallises in the cubic system, in octahedra, hexakis octahedra, or hexakis tetrahedra, and should, therefore, theoretically be without effect on polarised light. Yet it is rare to find a diamond which does not show more or less colour in the dark field, owing to the condition of strain in which it exists. It is notorious that the strain is occasionally so great that a diamond explodes into powder shortly after removal from its enveloping matrix of blue clay. The author, by the great kindness of Sir William Crookes, was enabled to show on the screen, both in a lecture at the Royal Society and in the Evening Discourse to the British Association at Winnipeg, the images of ten magnificent large diamonds, natural, perfectly formed crystals uncut and unspoilt by the lapidary. They were mounted between two circular glass plates of the usual 1⅞ inches diameter, the diamonds being attached by balsam to one of them; each plate was held in a mahogany frame of 1⅝ inches circular aperture, the two frames being then attached face to face to form a single one, an enclosing cell, which could be placed on the rotating stage as an object-slide for the projection polariscope. The appearance of the diamonds on the screen in ordinary light is reproduced in Fig. 82, Plate XVI., as well as is possible without their natural colour, for while several of them are brilliantly colourless, others are tinted, one being a bright green diamond. On producing the dark field by crossing the analysing Nicol with respect to the polariser, the darkness was dispelled by brilliant polarisation colours, at once revealing the diamonds and outlining them clearly against the dark background. On rotating the analyser the colours changed in the usual manner of polarising objects, and bright colours were shown by all the diamonds even when the Nicols were parallel.

It is obvious, then, that both a transparent non-crystalline substance such as glass, and a cubic crystal, must be free from strain in order that it shall exhibit no colour in polarised light and, indeed, no polarisation effects whatever, and behave as an isotropic substance.

The second special case to which attention may be called, that of a plate of an ordinary uniaxial crystal such as calcite, cut perpendicularly to the optic axis, is also obviously subject to the same proviso, that the crystal must be free from strain in order to exhibit the normal phenomena. Such a perfectly normal plate remains quite obscure in the dark field in parallel light, producing neither colour nor interference figure, even on rotation of the object stage with the crystal, in its own plane. For the light traverses the crystal along the optic axis, the axis of single refraction, and the vibrations occur with equal velocity in all directions perpendicular to it. Hence there is no division into two rays, one retarded behind the other on account of less velocity of vibration, and therefore no interference colour.

And now this leads us back to quartz, for this mineral is also uniaxial, and we will investigate in the same manner in parallel polarised light the plates of the mineral cut perpendicularly to the optic axis, which have already been referred to in connection with the experiments concerning the interference figures produced in convergent polarised light. Suppose we take first the large plate of quartz 7.5 mm. thick and over 2 inches in diameter. Placing it on the stage—instead of finding the dark field to be unaffected by the introduction of the plate, and to remain so on rotation of the latter in its own plane, as should theoretically be the case if quartz were a normal uniaxial crystal, and as calcite has been actually shown to do—we observe that it polarises in brilliant colour, the whole hexagonal outline of the plate, clearly focussed on the screen, being filled with an evenly brilliant violet tint, the tint of passage, just as the central part of the interference figure, within the innermost ring, had been coloured in the convergent light experiment with the same plate. The colour changes with the slightest rotation of either of the Nicols, passing into red for one direction of rotation and into blue and green when the Nicol is rotated in the other direction. The tint also alters when the section-plate is rotated about its vertical diameter, by rotating the upper adjustable part of the supporting column of the stage within its outer fixed tubular column; this latter change is equivalent to a thickening of the plate, the light beam having to traverse a longer path through the quartz during such oblique setting of the plate.

This colour is due to the same fact which produced colour in the central part of the interference figure, namely, the optical activity of quartz, the fact that the plane of vibration of a beam of plane polarised light transmitted along the axis of quartz is rotated to the right hand or to the left. The amount of this rotation is precisely equal, although opposite in direction, for the two varieties of quartz, but the rotation varies very considerably for different rays of the spectrum. It also varies directly proportionally to the thickness of the plate. A plate one millimetre thick cut perpendicularly to the axis rotates the plane of polarisation for red hydrogen light (C of the spectrum) to the extent of 17° 19′, for yellow D sodium light 21° 42′, and for greenish-blue F hydrogen light 32° 46′. The rotation is a maximum for plates perpendicular to the axis, and the effect is inappreciable in directions at right angles thereto. It is clearly due to the oppositely spiral winding of the regular-point-system of the crystal structure, round the direction of the optic axis, the trigonal axis of symmetry of the crystal, a structure which we have proved to be characteristic of quartz by the beautiful experiments with the helical piles of mica plates, absolutely reproducing the polarisation effects with quartz, as described in the last chapter.

The opposite optical rotation of the two varieties of quartz can be well shown by constructing a “biquartz.” Two plates of equal thickness, preferably either 7.5 mm. or 3.75 mm., are cut, one from a right-handed and the other from a left-handed crystal, each exactly perpendicular to the optic axis. The two edge-surfaces to be subsequently joined together are also cut, ground and polished as true planes perpendicular to the plate surfaces, and the two plates are then cemented together with Canada balsam by these two prepared edge-surfaces, taking care that the broad plate-surfaces of the two halves are absolutely continuous as if the whole were a single parallel-surfaced plate of quartz. Such a composite plate or “biquartz,” is one of the most useful aids to the study of optical activity, being much used for enhancing the sensitiveness of the determination of the angle of rotation.

When the image of such a 7.5 mm. biquartz, mounted in the usual mahogany frame and placed on the object stage of the projection polariscope, is thrown on the screen—the Nicols being crossed for production of the dark field, and the stage and crystal plate being strictly perpendicular to the parallel beam of polarised light—the whole of the screen covered by the image of the plate appears uniformly coloured with the violet tint of passage. But the moment the analysing Nicol is rotated for a very few degrees, one-half turns red and the other blue and then green. If the Nicol be turned back again to the crossing position with the polariser, and then rotated further in the opposite direction to the former rotation, the appearances on the two sides of the sharply focussed fine line of demarcation between the two halves are inverted, the side which formerly turned red now becoming green, and vice versa. The two varieties of quartz are thus oppositely affected, and it will be obvious that the biquartz is a very delicate test for the exact crossing of a pair of polarising prisms, or for the determination of the mutual extinction of two rectangularly polarised beams of light in general.

A very striking and beautiful mode of exhibiting this opposite and equal rotation of the plane of polarisation by the two varieties of quartz may next be described, an experiment which we owe to Prof. S. P. Thompson. A composite plate of mica is constructed out of 24 sectors of 15° angle each, the whole making up a complete circular plate. They are cemented between two circular glass plates of the usual 1⅞ inch size, with balsam; the sectors are laid down in succession on one of the plates first, side by side, with the edge of every one in turn in close contact with the edge of the next in order, so as to radiate from a common centre. The second glass plate is only cemented after the arrangement has been allowed to set for some days, when there is less risk of disturbing the mounting of the sectors. The latter have all been cut from the same film of mica, which has a thickness corresponding to a retardation of one of the two rays produced by the double refraction of the crystal behind the other equal to one and a half waves. Each sector is so cut that the line bisecting the 15° angle is parallel to the line joining the positions of emergence of the two optic axes of the crystal.

On placing this wheel of mica on the polariscope stage, the Nicols being crossed, the effect shown at b in Fig. 83 is observed on the screen. The four sectors 90° apart, the bisecting lines of which are vertical and horizontal respectively, parallel to the vibration planes of the Nicols, appear as a jet black cross; the sectors next to them appear pale brown, and the next again a still paler delicate shade of sepia, while the central diagonal ones of each quadrant, at 45° to the black cross, are brilliantly white.

On now introducing behind or in front of the stage a right-handed quartz plate one millimetre thick, one of the pair of large ones described in one of the convergent light experiments of the last chapter, the black cross is observed to be deflected one sector to the right, as shown at c in Fig. 83; whereas when the left-handed companion plate is introduced in like manner the cross moves over one sector to the left, as indicated at a in Fig. 83. The two quartz plates are mounted on the same mahogany object frame, a specially long one with two large apertures carrying the quartzes, so that first one and then the other can be placed in or out of position, and when this is done rapidly the movement of the cross from right to left and back again is very marked.

Occasionally a natural biquartz is obtained, on cutting a plate out of a crystal of quartz perpendicularly to the axis. For it is not uncommon to find a crystal which, while apparently a single crystal, is really a twin, the two right and left individuals being joined by an invisible plane of contact, or “plane of composition” as it is called, so beautifully have the two grown together. Figs. 84 and 85 show two kinds of twins of quartz. The former consists of two obviously different individuals, with the little s and x faces indicating right or left-handedness clearly developed in an opposite manner. The crystal shown in Fig. 85, however, appears to be a single individual, yet differs from either a right-handed or a left-handed crystal in showing the s and x faces developed on both right and left solid angles. It is a case of complete interpenetration.

In both cases the plane of twinning is parallel to the optic axis, and to a pair of faces of the hexagonal prism of the second order, perpendicular to a pair of the actual first order prism faces shown by the crystal. They are examples of the well-known “Brazilian twinning” of quartz, so called because many quartz crystals found in Brazil display it.

A natural biquartz of 3.75 millimetres thickness cut from such a crystal as is shown in Fig. 85, the plate having a hexagonal outline just as if the crystal were really a single one, may next be projected on the screen. The Nicols being crossed, the outline of the crystal is seen sharply defined, the whole area of the crystal being coloured a uniform yellow, there being absolutely no trace of any dividing line. But the moment one commences to turn the analysing Nicol different shades, orange and green respectively, begin to develop on the two sides of the line indicating the plane of composition of the twin, the hexagon being divided by a diametral line joining two corners, which have been arranged in mounting the plate in its carrier frame to be above one another, so as to bring the line of composition vertical, as will be clear from Fig. 86. On rotating the analyser further the difference is still more marked, and we have blue on one side and orange red on the other, developing still deeper into red and purple as the analyser approaches the parallel position with respect to the polariser; when this latter position is attained the transition violet tint is developed evenly over the whole plate, and the dividing line has again disappeared.

Another natural biquartz, also shown in the author’s lecture at Winnipeg, introduces us to a new phenomenon. For when the Nicols are crossed we observe a black band down the centre of the plate, marking the line of division of the twins. When the analyser is rotated until it is parallel to the polariser this black band changes to a white one, the sequence of colours on the different sides of the band, that is, in each half of the plate, being the same as just described. The effect with crossed Nicols is more or less simulated in Fig. 87, Plate XVII., which is a reproduction of a direct photograph of the screen picture. The reason for this black band in the dark field, and for the white one in the bright field, is that the two halves of the twin overlap at the centre, the plane of junction of the two individual crystals being oblique to the plate, instead of exactly perpendicular thereto as was the case with the first natural biquartz. We are, in fact, beginning to get the effect of two superposed wedges of quartz.

When the obliquity is greater, or the crystal thicker, a white band appears on each side of the black central one, the Nicols being crossed, and when the thickness is as great as 6 to 7.5 mm. a spectrum band appears on each side of the white one.

That this obliquity of the surface of contact of the two intergrown individuals (not the plane of twinning, which remains parallel to a pair of faces of the hexagonal prism of the second order) is the true explanation can be readily proved by reproducing the effect artificially. A thick double plate of quartz is constructed, as shown in Fig. 88, composed of two halves of respectively right-handed and left-handed quartz, each 6 to 7 millimetres thick, and each of which has had the edge-face of junction ground and polished obliquely at an angle of 30° or so, and oppositely so, instead of perpendicularly to the plates; the two halves are then cemented together in the usual manner for a biquartz, with Canada balsam, in order to make a continuous plate. On placing the plate of this construction possessed by the author on the stage of the projection polariscope, the two halves exhibit on the screen respectively brilliant red and green colour, with a vertical central black band, and on each side of it first a white strip and then a spectrum band, all the bands being parallel to each other, and the whole effect being precisely what was observed with the thickest natural biquartz.

Thus, we have imitated the oblique junction of the twin parts of the second and third biquartzes, and proved that this obliquity is the reason for the phenomena of bands, the black band occupying the centre where the two opposite rotations of the right and left quartz are precisely neutralised. The dark field of the crossed Nicols consequently prevails along this central strip, for the rotatory effect of the first individual crystal on the light passing through it is exactly undone by the subsequent passage of the rays through the other individual. On either side of this neutral strip there is a little preponderance of right-handed quartz on one side, and of left-handed quartz on the other, and the usual effect of a thin plate of quartz is therefore seen, namely, no colour but a little light, while further accretions of thickness of the preponderating variety give all the colours of the spectrum in turn, as with growing thicknesses of ordinary single quartz plates, thus producing the spectrum band.

The black band is also afforded when the plate is cut somewhat obliquely, out of a twin crystal with a junction plane truly perpendicular to the equatorial section, instead of cutting it truly perpendicularly to the axis, the junction plane being then oblique to the plate. The polarisation colours are not so strong, however, unless the plate be made thicker.

This effect of a black band with flanking spectra is very similar to that obtained, due to double refraction and not to optical activity, when two thin wedges of quartz are cemented together to form a parallel plate, one wedge being cut so that the optic axis is parallel to the edge of the wedge, and the other with the optic axis perpendicular to the edge. When such a composite plate of quartz, often known as a Babinet plate from the name of its first constructor, is placed on the stage of the polariscope, and rotated to the 45° position with respect to the planes of vibration of the crossed Nicols, there is observed on the screen a deep black band in the centre parallel to the edge of the wedge, and a number of spectrum bands on each side, separated by white equal interspaces, the rainbow coloured bands showing the orders of Newton’s spectra. The effect, as seen on the screen, is reproduced photographically in black and white in Fig. 89, Plate XVIII.

These experiments lead us naturally to the study of a great variety of quartz twins, involving some of the most beautiful and gorgeously chromatic phenomena which it is possible to produce on the screen with the projection polariscope. They will eventually bring us to the study of amethyst quartz, in which the twinning is repeated so often that the laminations of alternate right and left quartz are sometimes countless, and almost approach molecular dimensions.

The Brazilian twinning of quartz, parallel to a pair of faces of the second order hexagonal prism {11̄20}, often occurs in a very erratic manner, as regards the arrangement of the portions of the composite crystal belonging to the two varieties, the surfaces of contact and character of the interpenetration being frequently very irregular, and often remarkably so. Thus Fig. 90, the upper figure of the coloured frontispiece, gives some faint idea of the appearance presented on the screen by a very beautiful quartz plate, one-half of which is entirely composed of left-handed quartz, giving a rich even rose-red colour when the Nicols are crossed, not very far from the violet transition tint, the plate being nearly 7.5 mm. thick, while the other half consists of an alternation of strips of right and left-handed quartz, joined obliquely to the surface of the plate, the black band and its accompanying white ones and spectrum bands being repeated two or three times before the edge is reached. This is a very instructive case, for it shows in this half of the plate, on a large scale, what occurs in amethyst in a more minutely structural manner, the broad strips, the sections of plates upwards of a quarter of an inch thick, of alternating character becoming in amethyst thin lines, the sections of laminæ or films of microscopic tenuity, their number being correspondingly enormously increased.

It may be interesting to state how this Fig. 90, and the lower Fig. 97 of the frontispiece representing the projection on the screen of benzoic acid in the act of crystallisation, were produced. The pictures on the screen were directly photographed on the latest Lumière autochrome plates, a transparency in the actual natural colours being thus obtained in each case. These transparent colour-photographs were then used as originals wherewith to reproduce the effects on paper by the most recent improved three-colour photographic process.

Two other typical cases of irregular quartz twinning may also with advantage be demonstrated. The first is a plate in which there are repeated 60° V-shaped or 120° wedge-shaped intrusions of one variety into a greater mass of the other variety. The border of the V or 120° wedge is composed of a ribbon, the outer edges of which are spectrum-coloured and the central line of which is formed by the deep black band, which is separated on each side from the spectra by a white strip. Some idea of the beauty of this quartz plate, which was generously lent to the author by Prof. S. P. Thompson, as projected on the screen under crossed Nicols, may be gathered from Fig. 91, Plate XIX., the upper homogeneous part of the plate being coloured a brilliant green, and the lower part red.

The second is an irregular interpenetration of one variety into the other, in repeated V-shapes occupying the lower half of the image of the plate as seen on the screen in the dark field of the projection polariscope, like a range of sharp mountain peaks, the black bands being so rapidly repeated as to be nearly continuous. These darker portions thus appear to form the bulk of the mountains, while the upper untwinned half of the crystal shows a clear and even sky blue; to make the resemblance to a range of Alpine mountains even more complete, the wavy line of demarcation between the twinned and non-twinned portions of the plate is bordered by a white ribbon, of varying width, giving the appearance of a snow-cap to each peak, which shows up clearly against the blue sky. It will be obvious that this quartz plate affords an altogether very beautiful series of phenomena in parallel polarised light on the screen, for the colours change with every movement of the analysing Nicol from the crossed position, the appearance for which has just been described. Fig. 92, Plate XIX., gives only the faintest idea of the beauty of the screen picture afforded by this section-plate. The effect chosen as best for photographic reproduction purposes is one afforded when the analysing Nicol is rotated somewhat away from the crossed position with respect to the polariser.

And now we arrive finally at amethyst quartz, three very beautiful hexagonal plates of which—cut perpendicularly to the optic axis as usual for quartzes intended to display optical activity, from an apparently single hexagonal prism in each case—will be taken as typifying the phenomena exhibited by this especially interesting variety of quartz on the screen in parallel polarised light. The smaller one affords a screen picture, with Nicols not quite crossed, such as is portrayed in Fig. 93, Plate XX. We observe that the area of the hexagon is roughly divisible into six 60°-sectors, and that alternate ones are uniformly coloured, indicating that they belong to wholly right-handed or left-handed quartz; whereas the other alternate sectors are most beautifully marked, as if by line shading parallel or inclined at 30° to the edges of the hexagon, by a considerable number of equally spaced dark or slate coloured bands, close together but separated by white bands, with a trace of spectrum colours along the middle of the latter. If we rotate the analysing Nicol somewhat we can readily find a position, which is not always that of crossed Nicols, for which these parallel bands of laminar twinning are most clearly defined, as shown in the illustration, the colours of the other sectors ever changing during the rotation.

It is obvious that we have here to do with the same phenomenon as was illustrated by the parallel bands shown on the large scale by the section illustrated in Fig. 90 of the coloured frontispiece, the black, white, and spectrum-coloured bands being simply repeated very many more times in the same space, and in alternate sectors of the crystal.

The twinning of amethyst in 60°-sectors is very characteristic of this variety of quartz, and it is an interesting fact that the sectors which show the laminar bands in polarised light often appear purple coloured in ordinary light, the tint from which amethyst derives its name. This is not necessarily or always so however, and the section just described and illustrated in Fig. 93 appears quite colourless throughout on casual inspection in ordinary light, in fact as a clear colourless hexagonal section of ordinary simple quartz; a trace of the amethyst colour becomes, however, apparent on closer examination when held obliquely, in the sectors where the bands become visible in polarised light.

The second plate of amethyst is a magnificent section 9 millimetres thick and 2½ inches in diameter, of which alternate 60°-sectors are deeply amethyst coloured, the tint being a pure violet of about the wave-length of the hydrogen line near G of the spectrum. Moreover, even to the naked eye when the specimen is held in the hand up to the light, in certain positions the laminæ become visible as more deeply shaded violet line markings. On placing it on the stage of the polariscope but with the analysing Nicol removed, so as to observe the natural appearance of the section in white light (for, although polarised by the polarising Nicol, being unanalysed the section exhibits no polarisation effects), these facts become clear to everyone in the room. The violet staining of alternate sectors appears very deep, and traces of lamination in the violet parts are just apparent on close scrutiny, the other alternate sectors appearing colourless and unmarked except by a few flaws almost always present in so large a section-plate of amethyst. The natural appearance of this plate is shown in Fig. 94, Plate XVIII. (facing page 218), as far as is possible photographically, the violet sectors being clearly demarcated.

On replacing the analysing Nicol the colourless sectors are seen to polarise uniformly in brilliant colours, indicating a homogeneous variety of quartz in each, either right or left-handed. Moreover, whenever two of these naturally colourless parts touch each other, which they do as the margin of the plate is approached, an irregular ribbon is produced, composed of the black band in the centre, with first white and then spectrum-coloured flanking strips on each side, the spectra forming the edges of the ribbon. The violet sectors show the laminated twinning, but, owing to the great thickness of this plate, in too complicated (overlapping) a manner to be easily followed, a thinner plate being required to show such fine laminations clearly.

Finally, the third section is such a thinner plate, about 3.5 mm. thick and nearly 1½ inches in diameter. This section of amethyst is probably the most beautiful of all, for it not only shows the laminated twinning to perfection, in three alternate 60°-sectors and in all six in the middle part of the plate, but also these alternate sectors are distinctly violet even to the eye when the specimen is held in the hand against a white background; and the laminations are likewise also clearly visible on holding the section obliquely up to the light. In polarised light, either with crossed or parallel or anyway arranged Nicols, the phenomena on the screen are of the most superb character. The whole of the middle part of the plate appears made up of six sectors, all showing the fine laminar bands parallel to the edges of the second order hexagonal prism {11̄20}, that is, at 30° to the edges of the section, the crystal being a first order hexagonal prism {10̄10}. Some idea of the arrangement will be afforded by Fig. 95, Plate XX. The marginal parts develop into alternately right and left-handed sectors or half-sectors, polarising in different and very brilliant colours, and showing the ribbon bands at every junction. On rotating the analysing Nicol the changes are remarkably beautiful, particularly for the positions of the analyser when the laminar bands take on their deep slate colour, with white and marginally spectral interstrips. The whole phenomena, indeed, afforded by this plate of amethystine quartz, are the most magnificent which the author has ever seen on the screen, in the whole of his crystallographic experiences.

The Brazilian twinning law of quartz, according to which the plane of twinning is parallel to a pair of faces of the second order hexagonal prism {11̄20}, appears capable of explaining all these varieties of right and left-handed twins, the interpenetration of the intimate kind shown in Fig. 85 (page 215) usually resulting in sectorial portions of space being occupied by each kind, the surfaces of junction of oppositely optically active parts being, however, very varied in their distribution and character. Where they happen to be more or less horizontal, a plate cut perpendicularly to the axis to include both kinds would show Airy’s spirals in convergent polarised light, as may readily be demonstrated by such a plate, one of several, in the author’s collection. Where they are oblique, a plate cut at right angles to the axis would, as we have seen experimentally, afford the black, white and spectral ribbon bands in parallel polarised light. Where, however, the mode of interpenetration is still more intimate, we have the rapidly alternating laminæ of the two varieties, right and left-handed, building up the beautiful structure of amethyst in thin layers. A section-plate of such an intimate blending of the two varieties, cut as usual perpendicular to the axis in order that any phenomena of optical activity shall be exhibited at the maximum, affords no indication whatever of optical rotation, the two varieties simply neutralising each other’s effects, and the plate behaves as an ordinary uniaxial crystal, affording in convergent polarised light a black cross like calcite, complete to the centre. In parallel polarised light it shows of course the laminated structure, but the tendency to remain dark under crossed Nicols is shown by the fact that the tints exhibited by the laminations are slates, greys, and even black, when the Nicols are crossed, the delightful other colours only making their appearance when the analysing Nicol is rotated. Thus the simple law of Brazilian twinning is quite capable of explaining the whole of the phenomena exhibited by composite crystals of the two varieties of quartz, and such an explanation is the one accepted by von Groth, in the excellent description of quartz in the last edition of his Physikalische Krystallographie.

An interesting crystal of amethyst very similar to the third of those just described, the one illustrated in Fig. 95, was described by Prof. Judd in the year 1892 to the Mineralogical Society.^[18] The plan of the crystal is given in Fig. 96. The wedges marked x, y, z, are of a pale yellow colour, as are also the three strips, sections of plates, proceeding from the wedges and meeting at the centre o. The wedge y exhibits left-handed polarisation, and the wedge z right-handed. The large wedge x is composite, the part marked x_r being right-handed and that marked x_l left-handed. The surface of junction of the two parts is not perpendicular to the plate, so where the two varieties overlap, the part marked x_rl, a ribbon band is shown in parallel light and Airy’s spirals in convergent polarised light. The yellow parts of the crystal exhibit ordinary rotatory polarisation colours, even tints; but in the remaining sectors of the crystal, the lines of division of which are indicated by the radial lines A, B, C, no trace of circular polarisation is displayed, and the central part, where the lamellæ are very well developed, gives the ordinary calcite-like uniaxial interference figure. The more marginal portions, however, show complicated interference figures, somewhat resembling those of biaxial crystals, owing to irregular distribution of the two varieties of quartz, and probable displacement of the optic axis by distortion.

An ingenious theory of the formation of the lamellæ is put forward by Prof. Judd in the same memoir. He had already shown that quartz is endowed with planes of gliding, parallel to the rhombohedral faces, and suggests that the lamellation is the result of the effect of high pressure and possibly high temperature on the quartz crystal after its formation. The lamellæ appear to be frequently parallel to the rhombohedral terminal faces of the crystal, as if they were indeed glide plane effects. It is quite conceivable that the gliding of layers of molecules, which when permanent usually involves rotation and inversion of the molecules, might result in alternately right and left structural arrangements, and there is considerable evidence that the development of the purple tint occurred subsequently to the growth of the crystal. It is probably due to change in the state of oxidation of the trace of manganese present as a minute impurity in the quartz crystal, and which is concentrated between the lamellæ, just as the yellow tint is due to a slight trace of iron (ferric) oxide. The theory is an interesting one, and throws considerable light on the possible nature of intimate lamellar twinning.

One last experiment may now be referred to, the concluding experiment of the Winnipeg lecture, and which is very reminiscent of the beautiful slate colour of the lamellæ of amethyst. It is the actual crystallisation, projected on the screen, of a thin film of melted benzoic acid, which affords radiating closely packed long and narrow crystals, shooting out on the screen from centres near the margin of the field, very much like the individual crystals of repeatedly twinned quartz in the beautiful amethyst crystal illustrated in Fig. 95. Provided the film of melted benzoic acid be thin enough, the crystals appear on the screen in parallel polarised light, under crossed Nicols, tinted with the same beautiful shades of slate colour as amethyst, the intermediate low-order tint between the black and the grey of Newton’s first order spectrum. Some idea of the appearance on the screen is afforded by Fig. 97, the lower of the two coloured figures in the frontispiece. As in the case of Fig. 90, the screen picture was photographed directly on a Lumière autochrome plate, and the transparency in the actual colours thus obtained was employed as an original wherewith to reproduce the picture on paper by the latest three-colour photographic process.

In carrying out the experiment a few of the flaky crystals of benzoic acid are placed on one of the circular glass object plates of the standard 1⅞-inch size for the projection polariscope; they are covered by a second similar one, and the two plates are then held in a pair of tongs and gently warmed over a small spirit lamp, or miniature Bunsen lamp. As soon as the crystals have fused, and the melted substance is evenly spread as a thin film between the two glass plates, the latter are rapidly transferred to a special mahogany object frame, fitted with a side slide to press the double-plate edge just sufficiently to hold it in position in the frame, which is then at once placed on the rotating stage of the polariscope. The screen appears quite dark at first, the Nicols being crossed, but in a second or two as the slide cools the benzoic acid begins to crystallise out at the sides, brilliant colours and the deep greys being both developed, the former chiefly near the edges of the crystals, rendering the crystallisation wonderfully distinct and beautiful on the black background. Then long needle crystals shoot out from various quarters one after another or simultaneously, in lovely shades of slate or grey tinted with brilliant colours at the margins and tips, the growing point cutting its way along like a sharp brilliantly coloured arrowhead. Eventually an arch is formed of such acicular crystals, radiating simultaneously from many centres, gorgeously coloured in parts, but showing the yet more æsthetic slates and greys in the main. Finally, the whole screen picture fills up with a mass of interlacing yet ever distinct crystals, the last few to crystallise in the centre usually doing so with a burst of especially bright colour, as the thickness increases adequately for the double refraction retardation to reach the more brilliant second order spectrum, a concluding effect which evokes the emphatic delight of even the most phlegmatic philosopher, inured to scenes of beauty in natural phenomena.

The series of experiments with quartz described in this and the previous chapter, culminating with those revealing the alternate repetition of extremely fine layers of right and left-handed quartz in amethyst, will, it is hoped, have illustrated and rendered intelligible the important structural principle of enantiomorphism or mirror-image symmetry. We have only to imagine the layers to become thinner and thinner until we approach ultimately the neighbourhood of the minute dimensions of the chemical molecule, without as yet penetrating within the range of the molecular forces; the two such oppositely constructed and intimately blended structures, built up by atoms arranged oppositely screw-wise, clockwise and anti-clockwise, will now form an ultramicroscopic mixture of the two varieties in equal quantities, that is, in equal molecular proportions.

Such a structure will exhibit the symmetry of the system to which the two individuals belong, but instead of only displaying that of the enantiomorphous class of that system, possessing lower than the full symmetry, as each variety does when crystallised alone, it will now display the full holohedral symmetry of the system. That is, the symmetry is enhanced by this intimate blending of the two complementary enantiomorphous forms, the two together supplying all the possible elements of symmetry of which the system is capable. Moreover, as we have seen in the case of the lamellar portion of the amethyst crystals represented in Figs. 95 and 96, there will now be no sign of optical activity, for the two opposite rotations are equal and destroy each other.

Hence, such a compound crystal shows the holohedral symmetry of the system, and is optically inactive. In such cases we are, in fact, confronted with the phenomenon of pseudo-racemism, as defined in Chapter XI. For we know that the two varieties are still present intact, polarised light revealing them in the case of their grosser development such as is found in amethyst, and the system of symmetry being clearly the same, the forms developed being merely the sum of those of the two individual varieties.

Amethyst thus affords us a gross demonstration of the nature of pseudo-racemism, and as such has proved an exceedingly illuminating study.

We can carry the process further, however, in imagination, until the two differently helical molecules are themselves juxtaposed face to face, right molecule to left molecule. When, however, this occurs, we have entered into that most fascinatingly interesting region, the range of molecular forces, a mysterious sphere of activities of which we are only just beginning to learn something. Within this region of larger activity the two oppositely constructed molecules are often known to combine chemically to produce a molecular compound, just as potassium sulphate molecules, for instance, will combine with those of magnesium sulphate to form the well-known double salt. The double molecule now furnishes the representative point of the space-lattice, in other words, a new space-lattice is now erected, the units of which may be taken to be the representative points of the double molecules. Such a space-lattice will of necessity be of a totally different character to the old one corresponding to the single molecule of either variety (for each variety has the same space-lattice, the points, however, representing differently, enantiomorphously, orientated atomic details). That is to say, we shall have an entirely new kind of crystal produced, in all probability belonging to a different crystal system. It is known as a racemic compound, as described in Chapter XI.

This is exactly what happens in the case of tartaric acid, the two varieties, dextro or right-handed tartaric acid and lævo or left-handed tartaric acid, not forming pseudo-racemic crystals of like but enhanced (holohedral) symmetry, but a truly molecular compound, the well-known inactive racemic acid, in which the phenomenon of “racemism” was first discovered and from which it took its name.

Now a molecular compound is notoriously regarded by chemists as a type of chemical compound of low stability, molecular attraction or affinity not being nearly so powerful as atomic affinity. Hence, under suitable conditions it may be possible to induce the two component varieties to crystallise out separately from the solution of the racemic compound. In the case of racemic acid itself this does not readily happen, but in the cases of certain of its metallic salts, sodium ammonium racemate, for instance, specific conditions are known under which the two varieties of crystals, right and left-handed respectively, may be separately crystallised out from the solution, some of which conditions were referred to in Chapter XI. Racemic acid itself, however, crystallises quite differently to the two tartaric acids, namely, in triclinic prismatic crystals. These are, in fact, absolutely different from the monoclinic crystals of the dextro and lævo varieties of ordinary tartaric acid, for racemic acid takes up also a molecule of water of crystallisation on separating from its aqueous solution. There are certain chemical differences also, due to the chemical union of the two enantiomorphous molecules into a single double molecule, such, for instance, as greater facility of reduction by hydriodic acid to succinic acid.

Thus our experiments with quartz have afforded us the means of acquiring a clear idea of the nature of this most interesting type of crystal structure which involves the principle of mirror-image symmetry. Racemic acid and its similar structures, racemic compounds in general, are known as “externally compensated” structures, the reflective principle here acting externally to the single enantiomorphous molecule. It is but another step, however, to imagine internal compensation of enantiomorphous parts of a molecule, by mirror-image combination of such parts, such as in all probability occurs in the case of the truly inactive fourth variety of tartaric acid, in order to comprehend how the principle enabled the 165 types of homogeneous structure involving this kind of repetition to be arrived at, and thus, together with the 65 regular point-systems already known, to afford us the complete set of 230 types of homogeneous structures possible to crystals.