PLATE I
Frontispiece

GEM-STONES

GEM-STONES
AND THEIR DISTINCTIVE CHARACTERS

BY
G. F. HERBERT SMITH
M.A., D.Sc.
OF THE BRITISH MUSEUM (NATURAL HISTORY)

WITH MANY DIAGRAMS AND THIRTY-TWO PLATES
OF WHICH THREE ARE IN COLOUR

THIRD EDITION

METHUEN & CO. LTD.
36 ESSEX STREET W.C.
LONDON

First Published March 21st 1910
Second Edition June 1913
Third Edition 1919

PREFACE

IN this edition the opportunity has been taken to correct a few misprints and mistakes that have been discovered in the first, and to alter slightly one or two paragraphs, but otherwise no change has been made.

G. F. H. S.

Wandsworth Common, S.W.

PREFACE TO THE FIRST EDITION

IT has been my endeavour to provide in this book a concise, yet sufficiently complete, account of the physical characters of the mineral species which find service in jewellery, and of the methods available for determining their principal physical constants to enable a reader, even if previously unacquainted with the subject, to have at hand all the information requisite for the sure identification of any cut stone which may be met with. For several reasons I have dealt somewhat more fully with the branches of science closely connected with the properties of crystallized matter than has been customary hitherto in even the most comprehensive books on precious stones. Recent years have witnessed many changes in the jewellery world. Gem-stones are no longer entirely drawn from a few well-marked mineral species, which are, on the whole, easily distinguishable from one another, and it becomes increasingly difficult for even the most experienced eye to recognize a cut stone with unerring certainty. So long as the only confusion lay between precious stones and paste imitations an ordinary file was the solitary piece of apparatus required by the jeweller, but now recourse must be had to more discriminative tests, such as the refractive index or the specific gravity, the determination of which calls for a little knowledge and skill. Concurrently, a keener interest is being taken in the scientific aspect of gem-stones by the public at large, who are attracted to them mainly by æsthetic considerations.

While the treatment has been kept as simple as possible, technical expressions, where necessary, have not been avoided, but their meanings have been explained, and it is hoped that their use will not prove stumbling-blocks to the novice. Unfamiliar words of this kind often give a forbidding air to a new subject, but they are used merely to avoid circumlocution, and not, like the incantations of a wizard, to veil the difficulties in still deeper gloom. For actual practical work the pages on the refractometer and its use and the method of heavy liquids for the determination of specific gravities, and the tables of physical constants at the end of the book, with occasional reference, in case of doubt, to the descriptions of the several species alone are required; other methods—such as the prismatic mode of measuring refractive indices, or the hydrostatic way of finding specific gravities—which find a place in the ordinary curriculum of a physics course are described in their special application to gem-stones, but they are not so suitable for workshop practice. Since the scope of the book is confined mainly to the stones as they appear on the market, little has been said about their geological occurrence; the case of diamond, however, is of exceptional interest and has been more fully treated. The weights stated for the historical diamonds are those usually published, and are probably in many instances far from correct, but they serve to give an idea of the sizes of the stones; the English carat is the unit used, and the numbers must be increased by about 2½ per cent. if the weights be expressed in metric carats. The prices quoted for the various species must only be regarded as approximate, since they may change from year to year, or even day to day, according to the state of trade and the whim of fashion.

The diagram on [Plate II] and most of the crystal drawings were made by me. The remaining drawings are the work of Mr. H. H. Penton. He likewise prepared the coloured drawings of cut stones which appear on the three coloured plates, his models, with two exceptions, being selected from the cut specimens in the Mineral Collection of the British Museum by permission of the Trustees. Unfortunately, the difficulties that still beset the reproduction of pictures in colour have prevented full justice being done to the faithfulness of his brush. I highly appreciate the interest he took in the work, and the care and skill with which it was executed. My thanks are due to the De Beers Consolidated Mines Co. Ltd., and to Sir Henry A. Miers, F.R.S., Principal of the University of London, for the illustrations of the Kimberley and Wesselton diamond mines, and of the methods and apparatus employed in breaking up and concentrating the blue ground; to Messrs. I. J. Asscher & Co. for the use of the photograph of the Cullinan diamond; to Mr. J. H. Steward for the loan of the block of the refractometer; and to Mr. H. W. Atkinson for the illustration of the diamond-sorting machine. My colleague, Mr. W. Campbell Smith, B.A., has most kindly read the proof-sheets, and has been of great assistance in many ways. I hope that, thanks to his invaluable help, the errors in the book which may have escaped notice will prove few in number and unimportant in character. To Mr. Edward Hopkins I owe an especial debt of gratitude for his cheerful readiness to assist me in any way in his power. He read both the manuscript and the proof-sheets, and the information with regard to the commercial and practical side of the subject was very largely supplied by him. He also placed at my service a large number of photographs, some of which—for instance, those illustrating the cutting of stones—he had specially taken for me, and he procured for me the jewellery designs shown on [Plates IV and V].

If this book be found by those engaged in the jewellery trade helpful in their everyday work, and if it wakens in readers generally an appreciation of the variety of beautiful minerals suitable for gems, and an interest in the wondrous qualities of crystallized substances, I shall be more than satisfied.

G. F. H. S.

Wandsworth Common, S.W.

CONTENTS

LIST OF PLATES

GEM-STONES

CHAPTER I

INTRODUCTION

BEAUTY, durability, and rarity: such are the three cardinal virtues of a perfect gem-stone. Stones lacking any of them cannot aspire to a high place in the ranks of precious stones, although it does not necessarily follow that they are of no use for ornamental purposes. The case of pearl, which, though not properly included among gem-stones, being directly produced by living agency, yet holds an honoured place in jewellery, constitutes to some extent an exception, since its incontestable beauty atones for its comparative want of durability.

That a gem-stone should be a delight to the eye is a truism that need not be laboured; for such is its whole raison d’être. The members of the Mineral Kingdom that find service in jewellery may be divided into three groups, according as they are transparent, translucent, or opaque. Of these the first, which is by far the largest and the most important, may itself be further sub-divided into two sections: stones which are devoid of colour, and stones which are tinted. Among the former, diamond reigns supreme, since it alone possesses that marvellous ‘fire,’ oscillating with every movement from heavenly blue to glowing red, which is so highly esteemed and so much besought. Other stones, such as ‘fired’ zircon, white sapphire, white topaz, and rock-crystal, may dazzle with brilliancy of light reflected from the surface or emitted from the interior, but none of them, like diamond, glow with mysterious gleams. No hint of colour, save perhaps a trace of the blue of steel, can be tolerated in stones of this category; above all is a touch of the jaundice hue of yellow abhorred. It taxes all the skill of the lapidary to assure that the disposition of the facets be such as to reveal the full splendour of the stone. A coloured stone, on the other hand, depends for its attractiveness more upon its intrinsic hue than upon the manner of its cutting. The tint must not be too light or too dark in shade: a stone that has barely any colour has little interest, and one which is too dark appears almost opaque and black. The lapidary can to some extent remedy these defects by cutting the former deep and the latter shallow. In certain curious stones—for instance tourmaline—the transparency, and in others—such as ruby, sapphire, and one of the recent additions to the gem world, kunzite—the colour, varies considerably in different directions. The colours that are most admired—the fiery red of ruby, the royal blue of sapphire, the verdant green of emerald, and the golden yellow of topaz—are pure tints, and the absorption spectra corresponding to them are on the whole continuous and often restricted. They therefore retain the purity of their colour even in artificial light, though certain sapphires transmit a relatively larger amount of red, and consequently turn purple at night. Of the small group of translucent stones which pass light, but are not clear enough to be seen through, the most important is opal. It and certain others of the group owe their merit to the same optical effect as that characterizing soap-bubbles, tarnished steel, and so forth, and not to any intrinsic coloration. Another set of stones—moonstone and the star-stones—reflect light from the interior more or less regularly, but not in such a way as to produce a play of colour. The last group, which comprises opaque stones, has a single representative among ordinary gem-stones, namely, turquoise. In this case light is scattered and reflected from layers immediately contiguous to the surface, and the colour is due to the resulting absorption. The apparent darkness of a deep-coloured stone follows from a different cause: the light passing into the stone is wholly absorbed within it, and, since none is emitted, the stone appears black. The claims of turquoise are maintained by the blue variety; there is little demand for stones of a greenish tinge.

It is evidently desirable that any stones used in jewellery should be able to resist the mechanical and chemical actions of everyday life. No one is anxious to replace jewels every few years, and the most valuable stones are expected to endure for all time. The mechanical abrasion is caused by the minute grains of sand that are contained in ordinary dust, and gem-stones should be at least as hard as they—a condition fulfilled by all the principal species with the exception of opal, turquoise, peridot, and demantoid. Since the beauty of the first named does not depend on the brilliancy of its polish, scratches on the surface are not of much importance; further, all four are only slightly softer than sand. It may be noted that the softness of paste stones, apart from any objections that may be felt to the use of imitations, renders them unsuitable for jewellery purposes. The only stones that are likely to be chemically affected in the course of wear are those which are in the slightest degree porous. It is hazardous to immerse turquoises in liquids, even in water, lest the bluish green colour be oxidized to the despised yellowish hue. The risk of damage to opals, moonstones, and star-stones by the penetration of dirt or grease into the interior of the stones is less, but is not wholly negligible. Similar remarks apply with even greater force to pearls. Their charm, which is due to a peculiar surface-play of light, might be destroyed by contamination with grease, ink, or similar matter; they are, moreover, soft. For both reasons their use in rings is much to be deprecated. Nothing can be more unsightly than the dingy appearance of a pearl ring after a few years’ wear.

It cannot be gainsaid that mankind prefers the rare to the beautiful, and what is within reach of all is lightly esteemed. It is for this reason that garnet and moonstone lie under a cloud. Purchasers can readily be found for a ‘Cape-ruby’ or an ‘olivine,’ but not for a garnet; garnets are so common, is the usual remark. Nevertheless, the stones mentioned are really garnets. If science succeeded in manufacturing diamonds at the cost of shillings instead of the pounds that are now asked for Nature’s products—not that such a prospect is at all probable or even feasible—we might expect them to vanish entirely from fashionable jewellery.

A careful study of the showcases of the most extensive jewellery establishment brings to light the fact that, despite the apparent profusion, the number of different species represented is restricted. Diamond, ruby, emerald, sapphire, pearl, opal, turquoise, topaz, amethyst are all that are ordinarily asked for. Yet, as later pages will show, there are many others worthy of consideration; two among them—peridot and tourmaline—are, indeed, slowly becoming known. For the first five of the stones mentioned above, the demand is relatively steady, and varies absolutely only with the purchasing power of the world; but a lesser known stone may suddenly spring into prominence owing to the caprice of fashion or the preference of some great lady or leader of fashion. Not many years ago, for instance, violet was the favourite colour for ladies’ dresses, and consequently amethysts were much worn to match, but with the change of fashion they speedily sank to their former obscurity. Another stone may perhaps figure at some royal wedding; for a brief while it becomes the vogue, and afterwards is seldom seen.

Except that diamond, ruby, emerald, and sapphire, and, we should add, pearl, may indisputably be considered to occupy the first rank, it is impossible to form the gem-stones in any strict order. Every generation sees some change. The value of a stone is after all merely what it will fetch in the open market, and its artistic merits may be a matter of opinion. The familiar aphorism, de gustibus non est disputandum, is a warning not to enlarge upon this point.

PART I—SECTION A
THE CHARACTERS OF GEM-STONES

CHAPTER II

CRYSTALLINE FORM

WITH the single exception of opal, the whole of the principal mineral species used in jewellery are distinguished from glass and similar substances by one fundamental difference: they are crystallized matter, and the atoms composing them are regularly arranged throughout the structure.

The words crystal and glass are employed in science in senses differing considerably from those in popular use. The former of them is derived from the Greek word κρύος, meaning ice, and was at one time used in that sense. For instance, the old fourteenth-century reading of Psalm cxlvii. 17, which appears in the authorized version as “He giveth his ice like morsels,” ran “He sendis his kristall as morcels.” It was also applied to the beautiful, lustrous quartz found among the eternal snows of the Alps, since, on account of their limpidity, these stones were supposed, as Pliny tells us, to consist of water congealed by the extreme cold of those regions; such at the present day is the ordinary meaning of the word. But, when early investigators discovered that a salt solution on evaporation left behind groups of slender glistening prisms, each very similar to the rest, they naturally—though, as we now know, wrongly—regarded them as representing yet another form of congealed water, and applied the same word to such substances. Subsequent research has shown that these salts, as well as mineral substances occurring with natural faces in nature, have in common the fundamental property of regularity of arrangement of the constituent atoms, and science therefore defines by the word crystal a substance in which the structure is uniform throughout, and all the similar atoms composing it are arranged with regard to the structure in a similar way.

The other word is yet more familiar; it denotes the transparent, lustrous, hard, and brittle substance produced by the fusion of sand with soda or potash or both which fills our windows and serves a variety of useful purposes. Research has shown that glass, though apparently so uniform in character, has in reality no regularity of molecular arrangement. It is, in fact, a kind of mosaic of atoms, huddled together anyhow, but so irregular is its irregularity that it simulates perfect regularity. Science uses the word glass in this widened meaning. Two substances may, as a matter of fact, have the same chemical composition, and one be a crystal and the other a glass. For example, quartz, if heated to a high temperature, may be fused and converted into a glass. The difference in the two types of structure may be illustrated by a comparison between a regiment of soldiers drawn up on parade and an ordinary crowd of people.

The crystalline form is a visible sign of the molecular arrangement, and is intimately associated with the directional physical properties, such as the optical characters, cleavage, etc. A study of it is not only of interest in itself, but also of great importance to the lapidary who wishes to cut a stone to the best advantage, and it is, moreover, of service in distinguishing stones when in the rough state.

Fig. 1.—Cubo-Octahedra.

The development of natural faces on a crystal is far from being haphazard, but is governed by the condition that the angles between similar faces, whether on the same crystal or on different crystals, are equal, however varying may be the shapes and the relative sizes of the faces (Fig. 1), and by the tendency of the faces bounding the crystal to fall into series with parallel edges, such series being termed zones. Each species has a characteristic type of crystallization, which may be referred to one of the following six systems:—

1. Cubic.—Crystals in this system can be referred to three edges, which are mutually at right angles, and in which the directional characters are identical in value. These principal edges are known as axes. Some typical forms are the cube (Fig. 2), characteristic of fluor; the octahedron (Fig. 3), characteristic of diamond and spinel; the dodecahedron (Fig. 4), characteristic of garnet; and the triakisoctahedron, or three-faced octahedron (Fig. 5).

Fig. 2.—Cube.

Fig. 3.—Octahedron.

Fig. 4.—Dodecahedron.

All crystals belonging to this system are singly refractive.

2. Tetragonal.—Such crystals can be referred to three axes, which are mutually at right angles, but in only two of them are the directional characters identical. A typical form is a four-sided prism, mm, of square section, terminated by four triangular faces, p (Fig. 6), the usual shape of crystals of zircon and idocrase.

Fig. 5.—Triakisoctahedron, or
Three-faced Octahedron.

Fig. 6.—Tetragonal Crystal.

Crystals belonging to this system are doubly refractive and uniaxial, i.e. they have one direction of single refraction (cf. [p. 45]), which is parallel to the unequal edge of the three mentioned above.

Fig. 7.—Two alternative sets of Axes in the Hexagonal System.

3. Hexagonal.—Such crystals can be referred alternatively either to a set of three axes, X, Y, Z (Fig. 7), which lie in a plane perpendicular to a fourth, H, and are mutually inclined at angles of 60°, or to a set of three, a, b, c, which are not at right angles as in the cubic system, but in which the directional characters are identical. The fourth axis in the first arrangement is equally inclined to each in the second set of axes. Many important species crystallize in this system—corundum (sapphire, ruby), beryl (emerald, aquamarine), tourmaline, quartz, and phenakite. The crystals usually display a six-sided prism, terminated by a single face, c, perpendicular to the edge of the prism m (Fig. 8), e.g. emerald, or by six or twelve inclined faces, p (Fig. 9), e.g. quartz, crystals of which are so constant in form as to be the most familiar in the Mineral Kingdom. Tourmaline crystals (Fig. 10) are peculiar because of the fact that often one end is obviously to the eye flatter than the other.

Figs. 8–10.—Hexagonal Crystals.

Crystals belonging to this system are also doubly refractive and uniaxial, the direction of single refraction being parallel to the fourth axis mentioned above, and therefore also parallel to the prism edge. Hence deeply coloured tourmaline, which strongly absorbs the ordinary ray, must be cut with the table-facet parallel to the edge of the prism.

Fig. 11.—Relation of the two directions
of single Refraction to the Axes in an Orthorhombic Crystal.

4. Orthorhombic.—Such crystals can be referred to three axes, which are mutually at right angles, but in which each of the directional characters are different. The crystals are usually prismatic in shape, one of the axes being parallel to the prism edge. Topaz, peridot, and chrysoberyl are the most important species crystallizing in this system.

Crystals belonging to this system are doubly refractive and biaxial, i.e. they have two directions of single refraction (cf. p. 45). The three axes a, b, c (Fig. 11) are parallel respectively to the two bisectrices of the directions of single refraction, and the direction perpendicular to the plane containing those directions.

5. Monoclinic.—Such crystals can be referred to three axes, one of which is at right angles to the other two, which are, however, themselves not at right angles. Spodumene (kunzite) and some moonstone crystallize in this system.

Crystals belonging to this system are doubly refractive and biaxial, but in this case the first axis alone is parallel to one of the principal optical directions.

6. Triclinic.—Such crystals have no edges at right angles, and the optical characters are not immediately related to the crystalline form. Some moonstone crystallizes in this system.

Fig. 12.—Twinned
Octahedron.

Crystals are often not single separate individuals. For instance, diamond and spinel are found in flat triangular crystals with their girdles cleft at the corners (Fig. 12). Each of such crystals is really composed of portions of two similar octahedra, which are placed together in such a way that each is a reflection of the other. Such composite crystals are called twins or macles. Sometimes the twinning is repeated, and the individuals may be so minute as to call for a microscope for their perception.

A composite structure may also result from the conjunction of numberless minute individuals without any definite orientation, as in the case of chalcedony and agate. So by supposing the individuals to become infinitesimally small, we pass to a glass-like substance.

It is often a peculiarity of crystals of a species to display a typical combination of natural faces. Such a combination is known as the habit of the species, and is often of service for the purpose of identifying stones before they are cut. Thus, a habit of diamond and spinel is an octahedron, often twinned, of garnet a dodecahedron, of emerald a flat-ended hexagonal prism, and so on.

It is one of the most interesting and remarkable features connected with crystallization that the composition and the physical characters—for instance, the refractive indices and specific gravity—may, without any serious disturbance of the molecular arrangement, vary considerably owing to the more or less complete replacement of one element by another closely allied to it. That is the cause of the range of the physical characters which has been observed in such species as tourmaline, peridot, spinel, etc. The principal replacements in the case of the gem-stones are ferric oxide, Fe₂O₃, by alumina, Al₂O₃, and ferrous oxide, FeO, by magnesia, MgO.

A list of the principal gem-stones, arranged by their chemical composition, is given in [Table I] at the end of the book.

CHAPTER III

REFLECTION, REFRACTION, AND DISPERSION

IT is obvious that, since a stone suitable for ornamental use must appeal to the eye, its most important characters are those which depend upon light; indeed, the whole art of the lapidary consists in shaping it in such a way as to show these qualities to the best advantage. To understand why certain forms are given to a cut stone, it is essential for us to ascertain what becomes of the light which falls upon the surface of the stone; further, we shall find that the action of a stone upon light is of very great help in distinguishing the different species of gem-stones. The phenomena displayed by light which impinges upon the surface separating two media[1] are very similar in character, whatever be the nature of the media.

Ordinary experience with a plane mirror tells us that, when light is returned, or reflected, as it is usually termed, from a plane or flat surface, there is no alteration in the size of objects viewed in this way, but that the right and the left hands are interchanged: our right hand becomes the left hand in our reflection in the mirror. We notice, further, that our reflection is apparently just as far distant from the mirror on the farther side as we are on this side. In Fig. 13 MM´ is a section of the mirror, and O´ is the image of the hand O as seen in the mirror. Light from O reaches the eye E by way of m, but it appears to come from O´. Since OO´ is perpendicular to the mirror, and O and O´ lie at equal distances from it, it follows from elementary geometry that the angle i´, which the reflected ray makes with mn, the normal to the mirror, is equal to i, the angle which the incident ray makes with the same direction.

Fig. 13.—Reflection at a Plane Mirror.

Again, everyday experience tells us that the case is less simple when light actually crosses the bounding surface and passes into the other medium. Thus, if we look down into a bath filled with water, the bottom of the bath appears to have been raised up, and a stick plunged into the water seems to be bent just at the surface, except in the particular case when it is perfectly upright. Since the stick itself has not been bent, light evidently suffers some change in direction as it passes into the water or emerges therefrom. The passage of light from one medium to another was studied by Snell in the seventeenth century, and he enunciated the following laws:—

1. The refracted ray lies in the plane containing the incident ray and the normal to the plane surface separating the two media.

It will be noticed that the reflected ray obeys this law also.

2. The angle r, which the refracted ray makes with the normal, is related to the angle i, which the incident ray makes with the same direction, by the equation

n sin i = n´ sin r, (a)

where n and n´ are constants for the two media which are known as the indices of refraction, or the refractive indices.

This simple trigonometrical relation may be expressed in geometrical language. Suppose we cut a plane section through the two media at right angles to the bounding plane, which then appears as a straight line, SOS´ (Fig. 14), and suppose that IO represents the direction of the incident ray; then Snell’s first law tells us that the refracted ray OR will also lie in this plane. Draw the normal NON´, and with centre O and any radius describe a circle intersecting the incident and refracted rays in the points a and b respectively; let drop perpendiculars ac and bd on to the normal NON´. Then we have n.ac = n´.bd, whence we see that if n be greater than n´, ac is less than bd, and therefore when light passes from one medium into another which is less optically dense, in its passage across the boundary it is bent, or refracted, away from the normal.

Fig. 14.—Refraction across a Plane Surface.

We see, then, that when light falls on the boundary of two different media, some is reflected in the first and some is refracted into the second medium. The relative amounts of light reflected and refracted depend on the angle of incidence and the refractive indices of the media. We shall return to this point when we come to consider the lustre of stones.

We will proceed to consider the course of rays at different angles of incidence when light passes out from a medium into one less dense—for instance, from water into air. Corresponding to light with a small angle of incidence such as I₁O (Fig. 15), some of it is reflected in the direction OI´₁ and the remainder is refracted out in the direction OR₁. Similarly, for the ray I₂O some is reflected along OI´₂ and some refracted along OR₂. Since, in the case we have taken, the angle of refraction is greater than the angle of incidence, the refracted ray corresponding to some incident, ray I_cO will graze the bounding surface, and corresponding to a ray beyond it, such as I₃O, which has a still greater angle of incidence, there is no refracted ray, and all the light is wholly or totally reflected within the dense medium. The critical angle I_cON, which is called the angle of total-reflection, is very simply related to the refractive indices of the two media; for, since r is now a right angle, sin r = 1, and equation (a) becomes

n sin i = n´ (b)

Hence, if the angle of total-reflection is measured and one of the indices is known, the other can easily be calculated.

Fig. 15.—Total-Reflection.

The phenomenon of total-reflection may be appreciated if we hold a glass of water above our head, and view the light of a lamp on a table reflected from the under surface of the water. This reflection is incomparably more brilliant than that given by the upper surface.

The refractive index of air is taken as unity; strictly, it is that of a vacuum, but the difference is too small to be appreciated even in very delicate work. Every substance has different indices for light of different colour, and it is customary to take as the standard the yellow light of a sodium flame. This happens to be the colour to which our eyes are most sensitive, and a flame of this kind is easily prepared by volatilizing a little bicarbonate of soda in the flame of a bunsen burner. A survey of [Table III] at the end of the book shows clearly how valuable a measurement of the refractive index is for determining the species to which a cut stone belongs. The values found for different specimens of the species do in cases vary considerably owing to the great latitude possible in the chemical constitution due to the isomorphous replacement of one element by another. Some variation in the index may even occur in different directions within the same stone; it results from the remarkable property of splitting up a beam of light into two beams, which is possessed by many crystallized substances. This forms the subject of a later chapter.

Upon the fact that the refractive index of a substance varies for light of different colours depends such familiar phenomena as the splendour of the rainbow and the ‘fire’ of the diamond. When white light is refracted into a stone it no longer remains white, but is split up into a spectrum. Except in certain anomalous substances the refractive index increases progressively as the wave-length of the light decreases, and consequently a normal spectrum is violet at one end and passes through green and yellow to red at the other end. The width of the spectrum, which may be measured by the difference between the refractive indices for the extreme red and violet rays, also varies, though on the whole it increases with the refractive index. It is the dispersion, as this difference is termed, that determines the ‘fire’—a character of the utmost importance in colourless transparent stones, which, but for it, would be lacking in interest. Diamond excels all colourless stones in this respect, although it is closely followed by zircon, the colour of which has been driven off by heating; it is, however, surpassed by two coloured species: sphene, which is seldom seen in jewellery, and demantoid, the green garnet from the Urals, which often passes under the misnomer ‘olivine.’ The dispersion of the more prominent species for the B and G lines of the solar spectrum is given in [Table IV] at the end of the book.

We will now proceed to discuss methods that may be used for the measurement of the refractive indices of cut stones.

CHAPTER IV

MEASUREMENT OF REFRACTIVE INDICES

THE methods available for the measurement of refractive indices are of two kinds, and make use of two different principles. The first, which is based upon the very simple relation found in the last chapter to subsist at total-reflection, can be used with ease and celerity, and is best suited for discriminative purposes; but it is restricted in its application. The second, which depends on the measurement of the angle between two facets and the minimum deviation experienced by a ray of light when traversing a prism formed by them, is more involved, entails the use of more elaborate apparatus, and takes considerable time, but it is less restricted in its application.

(1) The Method of Total-Reflection

We see from equation b ([p. 18]), connecting the angle of total-reflection with the refractive indices of the adjacent media, that, if the denser medium be constant, the indices of all less dense media may be easily determined from a measurement of the corresponding critical angle. In all refractometers the constant medium is a glass with a high refractive index. Some instruments have rotatory parts, by means of which this angle is actually measured. Such instruments give very good results, but suffer from the disadvantages of being neither portable nor convenient to handle, and of not giving a result without some computation.

Fig. 16.—Refractometer (actual size).

For use in the identification of cut stones, a refractometer with a fixed scale, such as that (Fig. 16) devised by the author, is far more convenient. In order to facilitate the observations, a totally reflecting prism has been inserted between the two lenses of the eyepiece. The eyepiece may be adjusted to suit the individual eyesight; but for observers with exceptionally long sight an adapter is provided, which permits the eyepiece being drawn out to the requisite extent. The refractometer must be held in the manner illustrated in Fig. 17, so that the light from a window or other source of illumination enters the instrument by the lenticular opening underneath. Good, even illumination of the field may also very simply be secured by reflecting light into the instrument from a sheet of white paper laid on a table. On looking down the eyepiece we see a scale (Fig. 18), the eyepiece being, if necessary, focused until the divisions of the scale are clearly and distinctly seen. Suppose, for experiment, we smear a little vaseline or similar fatty substance on the plane surface of the dense glass, which just projects beyond the level of the brass plate embracing it. The field of view is now no longer uniformly illuminated, but is divided into two parts (Fig. 19): a dark portion above, which terminates in a curved edge, apparently green in colour, and a bright portion underneath, which is composed of totally reflected light. If we tilt the instrument downwards so that light enters the instrument from above through the vaseline we find that the portions of the field are reversed, the dark portion being underneath and terminated by a red edge. It is possible so to arrange the illumination that the two portions are evenly lighted, and the common edge becomes almost invisible. It is therefore essential for obtaining satisfactory results that the plate and the dense glass be shielded from the light by the disengaged hand. The shadow-edge is curved, and is, indeed, an arc of a circle, because spherical surfaces are used in the optical arrangements of the refractometer; by the substitution of cylindrical surfaces it becomes straight, but sufficient advantage is not secured thereby to compensate for the greatly increased complexity of the construction. The shadow-edge is coloured, because the relative dispersion, ^{n_v − n_r} /_n (n_v and n_r being the refractive indices for the extreme violet and red rays respectively), of the vaseline differs from that of the dense glass. The dispersion of the glass is very high, and exceeds that of any stone for which it can be used. Certain oils have, however, nearly the same relative dispersion, and the edges corresponding to them are consequently almost colourless. A careful eye will perceive that the coloured shadow-edge is in reality a spectrum, of which the violet end lies in the dark portion of the field and the red edge merges into the bright portion. The yellow colour of a sodium flame, which, as has already been stated, is selected as the standard for the measurement of refractive indices, lies between the green and the red, and the part of the spectrum to be noted is at the bottom of the green, and practically, therefore, at the bottom of the shadow, because the yellow and red are almost lost in the brightness of the lower portion of the field. If a sodium flame be used as the source of illumination, the shadow-edge becomes a sharply defined line. The scale is so graduated and arranged that the reading where this line crosses the scale gives the corresponding refractive index, the reading, since the line is curved, being taken in the middle of the field on the right-hand side of the scale. The refractometer therefore gives at once, without any intermediate calculation, a value of the refractive index to the second place of decimals, and a skilled observer may, by estimating the tenths of the intervals between successive divisions, arrive at the third place; to facilitate this estimation the semi-divisions beyond 1·650 have been inserted. The range extends nearly to 1·800; for any substance with a higher refractive index the field is dark as far as the limit at the bottom.

Fig. 17.—Method of Using the Refractometer.

Fig. 18.—Scale of the Refractometer.

Fig. 19.—Shadow-edge given by a singly refractive Substance.

A fat, or a liquid, wets the glass, i.e. comes into intimate contact with it, but if a solid substance be tested in the same way, a film of air would intervene and entirely prevent an observation. To displace it, a drop of some liquid which is more highly refractive than the substance under test must first be applied to the plane surface of the dense glass. The most convenient liquid for the purpose is methylene iodide, CH₂I₂, which, when pure, has at ordinary room temperatures a refractive index of 1·742. It is almost colourless when fresh, but turns reddish brown on exposure to light. If desired, it may be cleared in the manner described below (p. 66), but the film of liquid actually used is so thin that this precaution is scarcely necessary. If we test a piece of ordinary glass—one of the slips used by microscopists for covering thin sections is very convenient for the purpose—first applying a drop of methylene iodide to the plane surface of the dense glass of the refractometer (Fig. 20), we notice a coloured shadow-edge corresponding to the glass-slip at about 1·530 and another, almost colourless, at 1·742, which corresponds to the liquid. If the solid substance which is tested is more highly refractive than methylene iodide, only the latter of the shadow-edges is visible, and we must utilize some more refractive liquid. We can, however, raise the refractive index of methylene iodide by dissolving sulphur[2] in it; the refractive index of the saturated liquid lies well beyond 1·800 and the shadow-edge corresponding to it, therefore, does not come within the range of the refractometer. The pure and the saturated liquids can be procured with the instrument, the bottles containing them being japanned on the outside to exclude light and fitted with dipping-stoppers, by means of which a drop of the liquid required is easily transferred to the surface of the glass of the instrument. So long as the liquid is more highly refractive than the stone, or whatever may be the substance under examination, its precise refractive index is of no consequence. The facet used in the test must be flat, and must be pressed firmly on the instrument, so that it is truly parallel to the plane surface of the dense glass; for good results, moreover, it must be bright.

Fig. 20.—Faceted Stone in Position on the Refractometer.

Fig. 21.—Shadow-edges given by a doubly refractive substance.

We have so far assumed that the substance which we are testing is simple and gives a single shadow-edge; but, as may be seen from Table V, many of the gem-stones are doubly refractive, and such will, in general, show in the field of the refractometer two distinct shadow-edges more or less widely separated. Suppose, for example, we study the effect produced by a peridot, which displays the phenomenon to a marked degree. If we revolve the stone so that the facet under observation remains parallel to the plane surface of the dense glass of the refractometer and in contact with it, we notice that both the shadow-edges in general move up or down the scale. In particular cases, depending upon the relation of the position of the facet selected to the crystalline symmetry, one or both of them may remain fixed, or one may even move across the other. But whatever facet of the stone be used for the test, and however variable be the movements of the shadow-edges, the highest and lowest readings obtainable remain the same; they are the principal indices of refraction, such as are stated in Table III at the end of the book, and their difference measures the maximum amount of double refraction possessed by the stone. The procedure is therefore simplicity itself; we have merely to revolve the stone on the instrument, usually through not more than a right angle, and note the greatest and least readings. It will be noticed that the shadow-edges cross the scale symmetrically in the critical and skewwise in intermediate positions. Fig. 21 represents the effect when the facet is such as to give simultaneously the two readings required. The shadow-edges a and b, which are coloured in white light, correspond to the least and greatest respectively of the principal refractive indices, while the third shadow-edge, which is very faint, corresponds to the liquid used—methylene iodide. It is possible, as we shall see in a later chapter, to learn from the motion, if any, of the shadow-edges something as to the character of the double refraction. Since, however, each shadow-edge is spectral in white light, they will not be distinctly separate unless the double refraction exceeds the relative dispersion. Topaz, for instance, appears in white light to yield only a single shadow-edge, and may thus easily be distinguished from tourmaline, in which the double refraction is large enough for the separation of the two shadow-edges to be clearly discerned. In sodium light, however, no difficulty is experienced in distinguishing both the shadow-edges given by substances with small amount of double refraction, such as chrysoberyl, quartz, and topaz, and a skilled observer may detect the separation in the extreme instances of apatite, idocrase, and beryl. The shadow-edge corresponding to the greater refractive index is always less distinct, because it lies in the bright portion of the field. If the stone or its facet be small, it must be moved on the plane surface of the dense glass until the greatest possible distinctness is imparted to the edge or edges. If it be moved towards the observer from the further end, a misty shadow appears to move down the scale until the correct position is reached, when the edges spring into view.

Any facet of a stone may be utilized so long as it is flat, but the table-facet is the most convenient, because it is usually the largest, and it is available even when the stone is mounted. That the stone need not be removed from its setting is one of the great advantages of this method. The smaller the stone the more difficult it is to manipulate; caution especially must be exercised that it be not tilted, not only because the shadow-edge would be shifted from its true position and an erroneous value of the refractive index obtained, but also because a corner or edge of the stone would inevitably scratch the glass of the instrument, which is far softer than the hard gem-stones. Methylene iodide will in time attack and stain the glass, and must therefore be wiped off the instrument immediately after use.

(2) The Method of Minimum Deviation

If the stone be too highly refractive for a measurement of its refractive index to be possible with the refractometer just described, and it is desired to determine this constant, recourse must be had to the prismatic method, for which purpose an instrument known as a goniometer[3] is required. Two angles must be measured; one the interior angle included between a suitable pair of facets, and the other the minimum amount of the deviation produced by the pair upon a beam of light traversing them.

Fig. 22.—Path at Minimum Deviation of a Ray
traversing a Prism formed of two Facets of a
Cut Stone.

Fig. 22 represents a section of a step-cut stone perpendicular to a series of facets with parallel edges; t is the table, and a, b, c, are facets on the culet side. The path of light traversing the prism formed by the pair of facets, t and b, is indicated. Suppose that A is the interior angle of the prism, i the angle of incidence of light at the first facet and i´ the angle of emergence at the second facet, and r and r´ the angles inside the stone at the two facets respectively. Then at the first facet light has been bent through an angle i - r, and again at the second facet through an angle i´ - r´; the angle of deviation, D, is therefore given by

D = i + i´ - (r + r´).

We have further that

r + r´ = A,

whence it follows that

A + D = i + i´.

If the stone be mounted on the goniometer and adjusted so that the edge of the prism is parallel to the axis of rotation of the instrument and if light from the collimator fall upon the table-facet and the telescope be turned to the proper position to receive the emergent beam, a spectral image of the object-slit, or in the case of a doubly refractive stone in general, two spectral images, will be seen in white light; in the light of a sodium flame the images will be sharp and distinct. Suppose that we rotate the stone in the direction of diminishing deviation and simultaneously the telescope so as to retain an image in the field of view, we find that the image moves up to and then away from a certain position, at which, therefore, the deviation is a minimum. The image moves in the same direction from this position whichever way the stone be rotated. The question then arises what are the angles of incidence and refraction under these special conditions. It is clear that a path of light is reversible; that is to say, if a beam of light traverses the prism from the facet t to the facet b it can take precisely the same path from the facet b to the facet t. Hence we should be led to expect that, since experiment teaches us that there is only one position of minimum deviation corresponding to the same pair of facets, the angles at the two facets must be equal, i.e. i = i´, and r = r´. It is, indeed, not difficult to prove by either geometrical or analytical methods that such is the case.

Therefore at minimum deviation r = ^A/₂ and i = ^{A + D}/₂ and, since sin i = n sin r, where n is the refractive index of the stone, we have the simple relation—

n = ^{sin A + D/₂} / _{sin ^A/2}

This relation is strictly true only when the direction of minimum deviation is one of crystalline symmetry in the stone, and holds therefore in general for all singly refractive stones, and for the ordinary ray of a uniaxial stone; but the values thus obtained even in the case of biaxial stones are approximate enough for discriminative purposes. If then the stone be singly refractive, the result is the index required; if it be uniaxial, one value is the ordinary index and the other image gives a value lying between the ordinary and the extraordinary indices; if it be biaxial, the values given by the two images may lie anywhere between the greatest and the least refractive indices. The angle A must not be too large; otherwise the light will not emerge at the second facet, but will be totally reflected inside the stone: on the other hand, it must not be too small, because any error in its determination would then seriously affect the accuracy of the value derived for the refractive index. Although the monochromatic light of a sodium flame is essential for precise work, a sufficiently approximate value for discriminative purposes is obtained by noting the position of the yellow portion of the spectral image given in white light.

In the case of a stone such as that depicted in Fig. 22 images are given by other pairs of facets, for instance ta and tc, unless the angle included by the former is too large. There might therefore be some doubt, to which pair some particular image corresponded; but no confusion can arise if the following procedure be adopted.

Fig. 23.—Course of Observations in the Method of Minimum Deviation.

The table, or some easily recognizable facet, is selected as the facet at which light enters the stone. The telescope is first placed in the position in which it is directly opposite the collimator (T₀ in Fig. 23), and clamped. The scale is turned until it reads exactly zero, 0° or 360°, and clamped. The telescope is released and revolved in the direction of increasing readings of the scale to the position of minimum deviation, T. The reading of the scale gives at once the angle of minimum deviation, D. The holder carrying the stone is now clamped to the scale, and the telescope is turned to the position, T₁,in which the image given by reflection from the table facet is in the centre of the field of view; the reading of the scale is taken. The telescope is clamped, and the scale is released and rotated until it reads the angle already found for D. If no mistake has been made, the reflected image from the second facet is now in the field of view. It will probably not be quite central, as theoretically it should be, because the stone may not have been originally quite in the position of minimum deviation, a comparatively large rotation of the stone producing no apparent change in the position of the refracted image at minimum deviation, and further, because, as has already been stated, the method is not strictly true for biaxial stones. The difference in readings, however, should not exceed 2°. The reading, S, of the scale is now taken, and it together with 180° subtracted from the reading for the first facet, and the value of A, the interior angle between the two facets, obtained.

Let us take an example.

The readings S and T are very nearly the same, and therefore we may be sure that no mistake has been made in the selection of the facets.

In place of logarithm-tables we may make use of the diagram on [Plate II]. The radial lines correspond to the angles of minimum deviation and the skew lines to the prism angles, and the distance along the radial lines gives the refractive index. We run our eye along the line for the observed angle of minimum deviation and note where it meets the curve for the observed prism angle; the refractive index corresponding to the point of intersection is at once read off.

This method has several obvious disadvantages: it requires the use of an expensive and elaborate instrument, an observation takes considerable time, and the values of the principal refractive indices cannot in general be immediately determined.

[Table III] at the end of the book gives the refractive indices of the gem-stones.

PLATE II

REFRACTIVE INDEX DIAGRAM

CHAPTER V

LUSTRE AND SHEEN

IT has been already stated that whenever light in one medium falls upon the surface separating it from another medium some of the light is reflected within the first, while the remainder passes out into the second medium, except when the first is of lower refractivity than the second and light falls at an angle greater than that of total-reflection. Similarly, when light impinges upon a cut stone some of it is reflected and the remainder passes into the stone. What is the relative amount of reflected light depends upon the nature of the stone—its refractivity and hardness—and determines its lustre; the greater the amount the more lustrous will the stone appear. There are different kinds of lustre, and the intensity of each depends on the polish of the surface. From a dull, i.e. an uneven, surface the reflected light is scattered, and there are no brilliant reflections. All gem-stones take a good polish, and have therefore, so long as the surface retains its polish, considerable brilliancy; turquoise, on account of its softness, is always comparatively dull.

The different kinds of lustre are—

1. Adamantine, characteristic of diamond.
2. Vitreous, as seen on the surface of fractured glass.
3. Resinous, as shown by resins.

Zircon and demantoid, the green garnet called by jewellers “olivine,” alone among gem-stones have a lustre approaching that of diamond. The remainder all have a vitreous lustre, though varying in degree, the harder and the more refractive species being on the whole the more lustrous.

Some stones—for instance, a cinnamon garnet—appear to have a certain greasiness in the lustre, which is caused by stray reflections from inclusions or other breaks in the homogeneity of the interior. A pearly lustre, which arises from cleavage cracks and is typically displayed by the cleavage face of topaz, would be seen in a cut stone only when flawed.

Certain corundums when viewed in the direction of the crystallographical axis display six narrow lines of light radiating at angles of 60° from a centre in a manner suggestive of the conventional representations of stars. Such stones are consequently known as asterias, or more usually star-stones—star-rubies or star-sapphires, as the case may be, and the phenomenon is called asterism. These stones have not a homogeneous structure, but contain tube-like cavities regularly arranged at angles of 60° in planes at right angles to the crystallographical axis. The effect is best produced when the stones are cut en cabochon perpendicular to that axis.

Chatoyancy is a somewhat similar phenomenon, but in this case the fibres or cavities are parallel to a single direction, and a single broadish band is displayed at right angles to it. Cat’s-eyes, as these stones are termed, are cut en cabochon parallel to the fibres. The true cat’s-eye ([Plate XXIX], Fig. 1) is a variety of chrysoberyl, but the term is also often applied to quartz showing a similar appearance. The latter is really a fibrous mineral, such as asbestos, which has become converted into silica. The beautiful tiger’s-eye from South Africa is a silicified crocidolite, the original blue colour of which has been altered by oxidation to golden brown. Recently tourmalines have been discovered which are sufficiently fibrous in structure to display an effective chatoyancy.

The milky sheen of moonstone ([Plate XXIX], Fig. 4) owes its effect to reflections from twin lamellæ. The wonderful iridescence which is the glory of opal, and is therefore termed opalescence, arises from a structure which is peculiar to that species. Opal is a solidified jelly; on cooling it has become riddled with extremely thin cracks, which were subsequently filled with similar material of slightly different refractivity, and thus it consists of a series of films. At the surface of each film interference of light takes place just as at the surface of a soap-bubble, and the more evenly the films are spaced apart the more uniform is the colour displayed, the actual tint depending upon the thickness of the films traversed by the light giving rise to the phenomenon.

CHAPTER VI

DOUBLE REFRACTION

THE optical phenomenon presented by many gem-stones is complicated by their property of splitting up a beam of light into two with, in general, differing characters. In this chapter we shall discuss the nature of double refraction, as it is termed, and methods for its detection. The phenomenon is not one that comes within the purview of everyday experience.

So long ago as 1669 a Danish physician, by name Bartholinus, noticed that a plate of the transparent mineral which at that time had recently been brought over from Iceland, and was therefore called “Iceland-spar,” possessed the remarkable property of giving a double image of objects close to it when viewed through it. Subsequent investigation has shown that much crystallized matter is doubly refractive, but in calcite—to use the scientific name for the species which includes Iceland-spar—alone among common minerals is the phenomenon so conspicuous as to be obvious to the unaided eye. The apparent separation of the pair of images given by a plate cut or cleaved in any direction depends upon its thickness. The large mass, upwards of two feet (60 cm.) in thickness, which is exhibited at the far end of the Mineral Gallery of the British Museum (Natural History), displays the separation to a degree that is probably unique.

Fig. 24.—Apparent doubling of the Edges of a Peridot when viewed through the Table-Facet.

Although none of the gem-stones can emulate calcite in this character, yet the double refraction of certain of them is large enough to be detected without much difficulty. In the case of faceted stones the opposite edges should be viewed through the table-facet, and any signs of doubling noted. The double refraction of sphene is so large, viz. 0·08, that the doubling of the edges is evident to the unaided eye. In peridot (Fig. 24), zircon (b), and epidote the apparent separation of the edges is easily discerned with the assistance of an ordinary lens. A keen eye can detect the phenomenon even in the case of such substances as quartz with small double refraction. It must, however, be remembered that in all such stones the refraction is single in certain directions, and the amount of double refraction varies therefore with the direction from nil to the maximum possessed by the stone. Experiment with a plate of Iceland-spar shows that the rays transmitted by it have properties differing from those of ordinary light. On superposing a second plate we notice that there are now two pairs of images, which are in general no longer of equal brightness, as was the case before. If the second plate be rotated with respect to the first, two images, one of each pair, disappear, and then the other two, the plate having turned through a right angle between the two positions of extinction; midway between these positions the images are all equally bright. This variation of intensity implies that each of the rays emerging from the first plate has acquired a one-sided character, or, as it is usually expressed, has become plane-polarized, or, shortly, polarized.

Fig. 25.—Wave-Motion.

Before the discovery of the phenomenon of double refraction the foundation of the modern theory of light had been laid by the genius of Huygens. According to this theory light is the result of a wave-motion (Fig. 25) in the ether, a medium that pervades the whole of space whether occupied by matter or not, and transmits the wave-motion at a rate varying with the matter with which it happens to coincide. Such a medium has been assumed because it explains satisfactorily all the phenomena of light, but it by no means follows that it has a concrete existence. Indeed, if it has, it is so tenuous as to be imperceptible to the most delicate experiments. The wave-motion is similar to that observed on the surface of still water when disturbed by a stone flung into it. The waves spread out from the source of disturbance; but, although the waves seem to advance, the actual particles of water merely move up and down, and have no motion at all in the direction in which the waves are moving. If we imagine similar motion to take place in any plane and not only the horizontal, we form some idea of the nature of ordinary light. But after passing through a plate of Iceland-spar, light no longer vibrates in all directions, but in each beam the vibrations are parallel to a particular plane, the two planes being at right angles. The exact relation of the direction of the vibrations to the plane of polarization is uncertain, although it undoubtedly lies in the plane containing the direction of the ray of light and the perpendicular to the plane of polarization. The waves for different colours differ in their length, i.e. in the distance, 2 bb (Fig. 25), from crest to crest, while the velocity, which remains the same for the same medium, is proportional to the wave-length. The intensity of the light varies as the square of the amplitude of the wave, i.e. the height, ab, of the crest from the mean level.

Various methods have been proposed for obtaining polarized light. Thus Seebeck found in 1813 that a plate of brown tourmaline cut parallel to the crystallographic axis and of sufficient thickness (cf. [p. 11]) transmits only one ray, the other being entirely absorbed within the plate. Another method was to employ a glass plate to reflect light at a certain critical angle. The most efficient method, and that in general use at the present day, is due to the invention of Nicol. A rhomb of Iceland-spar (Fig. 26), of suitable length, is sliced along the longer diagonal, dd, and the halves are cemented together by means of canada balsam. One ray, ioo, is totally reflected at the surface separating the mineral and the cement, and does not penetrate into the other half; while the other ray, iee, is transmitted with almost undiminished intensity. Such a rhomb is called a Nicol’s prism after its inventor, or briefly, a nicol.

Fig. 26.—Nicol’s Prism.

If one nicol be placed above another and their corresponding principal planes be at right angles no light is transmitted through the pair. In the polarizing microscope one such nicol, called the polarizer, is placed below the stage, and the other, called the analyser, is either inserted in the body of the microscope or placed above the eyepiece, and the pair are usually set in the crossed position so that the field of the microscope is dark. If a piece of glass or a fragment of some singly refractive substance be placed on the stage the field still remains dark; but in case of a doubly refractive stone the field is no longer dark except in certain positions of the stone. On rotation of the plate, or, if possible, of the nicols together, the field passes from darkness to maximum brightness four times in a complete revolution, the relative angular intervals between these positions being right angles. These positions of darkness are known as the positions of extinction, and the plate is said to extinguish in them. This test is exceedingly delicate and reveals the double refraction even when the greatest difference in the refractive indices is too small to be measured directly.

Doubly refractive substances are of two kinds: uniaxial, in which there is one direction of single refraction, and biaxial, in which there are two such directions. In the case of the former the direction of one, the ordinary ray, is precisely the same as if the refraction were single, but the refractive index of the other ray varies from that of the ordinary ray to a second limiting value, the extraordinary refractive index, which may be either greater or less. If the extraordinary is greater than the ordinary refractive index the double refraction is said to be positive; if less, to be negative. A biaxial substance is more complex. It possesses three principal directions, viz., the bisectrices of the directions of single refraction and the perpendicular to the plane containing them. The first two correspond to the greatest and least, and the last to the mean of the principal indices of refraction. If the acute bisectrix corresponds to the least refractive index, the double refraction is said to be positive, and if to the greatest, negative. The relation of the directions of single refraction, s, to the three principal directions, a, b, c, is illustrated in Fig. 27 for the case of topaz, a positive mineral. The refractive indices of the rays traversing one of the principal directions have the values corresponding to the other two. In the direction a we should measure the greatest and the mean of the principal refractive indices, in the direction b the greatest and the least, and in the direction c the mean and the least. The maximum amount of double refraction is therefore in the direction b.

Fig. 27.—Relation of the two
Directions of single Refraction to
the principal Optical Directions
in a Biaxial Crystal.

In the examination of a faceted stone, of the most usual shape, the simplest method is to lay the large facet, called the table, on a glass slip and view the stone through the small parallel facet, the culet. Should the latter not exist, it may frequently happen that owing to internal reflection no light emerges through the steeply inclined facets. This difficulty is easily overcome by immersing the stone in some highly refracting oil. A glass plate held by hand over the stone with a drop of the oil between it and the plate serves the purpose, and is perhaps a more convenient method. A stone which does not possess a pair of parallel facets should be viewed through any pair which are nearly parallel.

We have stated that a plate of glass has no effect on the field. Suppose, however, it were viewed when placed between the jaws of a tightened vice and thus thrown into a state of strain, it would then show double refraction, the amount of which would depend on the strain. Natural singly refractive substances frequently show phenomena of a similar kind. Thus diamond sometimes contains a drop of liquid carbonic acid, and the strain is revealed by the coloured rings surrounding the cavity which are seen when the stone is viewed between crossed nicols. Double refraction is also common in diamond even when there is no included matter to explain it, and is caused by the state of strain into which the mineral is thrown on release from the enormous pressure under which it was formed. Other minerals which display these so-called optical anomalies, such as fluor and garnet, are not really quite singly refractive at ordinary temperatures; each crystal is composed of several double refractive individuals. But all such phenomena cannot be confused with the characters of minerals which extinguish in the ordinary way, since the stone will extinguish in small patches and these will not be dark all at the same time; further, the double refraction is small, and on revolving the stone between crossed nicols the extinction is not sharp. Paste stones are sometimes in a state of strain, and display slight, but general, double refraction. Hence the existence of double refraction does not necessarily prove that the stone is real and not an imitation. Stones may be composed of two or more individuals which are related to each other by twinning, in which case each individual would in general extinguish separately. Such individuals would be larger and would extinguish more sharply than the patches of an anomalous stone.

Fig. 28.—Interference of Light.

An examination in convergent light is sometimes of service. An auxiliary lens is placed over the condenser so as to converge the light on to the stone. Light now traverses the stone in different directions; the more oblique the direction the greater the distance traversed in the stone. If it be doubly refractive, in any given direction there will be in general two rays with differing refractive indices and the resulting effect is akin to the well-known phenomenon of Newton’s rings, and is an instance of what is termed interference. It may be mentioned that the interference of light (Fig. 28) explains such common phenomena as the colours of a soap-bubble, the hues of tarnished steel, the tints of a layer of oil floating on water, and so on. Light, after diverging from the stone, comes to focus a little beneath the plane in which the image of the stone is formed. An auxiliary lens must, therefore, be inserted to bring the focal planes together, so that the interference picture may be viewed by means of the same eyepiece.

If a uniaxial crystal be examined along the crystallographic axis in convergent light an interference picture will be seen of the kind illustrated on [Plate III]. The arms of a black cross meet in the centre of the field, which is surrounded by a series of circular rings, coloured in white light. Rotation of the stone about the axis produces no change in the picture.

PLATE III

1. UNIAXIAL

2. UNIAXIAL
(Circular Polarization)

3. BIAXIAL
(Crossed Brushes)

4. BIAXIAL
(Hyperbolic Brushes)

INTERFERENCE FIGURES

A biaxial substance possesses two directions (the optic axes) along which a single beam is transmitted. If such a stone be examined along the line bisecting the acute angle between the optic axes (the acute bisectrix) an interference picture[4] will be seen which in particular positions of the stone with respect to the crossed nicols takes the forms illustrated on [Plate III]. As before, there is a series of rings which are coloured in white light; they, however, are no longer circles but consist of curves known as lemniscates, of which the figure of 8 is a special form. Instead of an unchangeable cross there are a pair of black “brushes” which in one position of the stone are hyperbolæ, and in that at right angles become a cross. On rotating the stone we find that the rings move with it and are unaltered in form, whereas the brushes revolve about two points, called the “eyes,” where the optic axes emerge. If the observation were made along the obtuse bisectrix the angle between the optic axes would probably be too large for the brushes to come into the field, and the rings might not be visible in white light, though they would appear in monochromatic light. In the case of a substance like sphene the figure is not so simple, because the positions of the optic axes vary greatly for the different colours and the result is exceedingly complex; in monochromatic light, however, the usual figure is visible.

It would probably not be possible in the case of a faceted stone to find a pair of faces perpendicular to the required direction. Nevertheless, so long as a portion of the figures described is in the field of view, the character of the double refraction, whether uniaxial or biaxial, may readily be determined.

There is yet another remarkable phenomenon which must not be passed over. Certain substances, of which quartz is a conspicuous example and in this respect unique among the gem-stones, possess the remarkable property of rotating the plane of polarization of a ray of light which is transmitted parallel to the optic axis. If a plate of quartz be cut at right angles to the axis and placed between crossed nicols in white light, the field will be coloured, the hue changing on rotation of one nicol with respect to the other. Examination in monochromatic light shows that the field will become dark after a certain rotation of the one nicol with respect to the other, the amount of which depends on the thickness of the plate. If the plate be viewed in convergent light, an interference picture is seen as illustrated on [Plate III], which is similar to, and yet differs in some important particulars from the ordinary interference picture of a uniaxial stone. The cross does not penetrate beyond the innermost ring and the centre of the field is coloured in white light. If a stone shows such a picture, it may be safely assumed to be quartz. It is interesting to note that minerals which possess this property have a spiral arrangement of the constituent atoms.

It has already been remarked ([p. 28]) that if a faceted doubly refractive stone be rotated with one facet always in contact with the dense glass of the refractometer the pair of shadow-edges that are visible in the field move up or down the scale in general from or to maximum and minimum positions. The manner in which this movement takes place depends upon the character of the double refraction and the position of the facet under observation with regard to the optical symmetry of the stone. In the case of a uniaxial stone, if the facet be perpendicular to the crystallographic axis, i.e. the direction of single refraction, neither of the shadow-edges will move. If the facet be parallel to that direction, one shadow-edge will move up and coincide with the other, which remains invariable in position, and away from it to a second critical position; the latter gives the value of the extraordinary refractive index, and the invariable shadow-edge corresponds to the ordinary refractive index. This phenomenon is displayed by the table-facet of most tourmalines, because for reasons given above ([p. 11]) they are as a rule cut parallel to the crystallographic axis. In the case of facets in intermediate positions, the shadow-edge corresponding to the extraordinary refractive index moves, but not to coincidence with the invariable shadow-edge. The case of a biaxial stone is more complex. If the facet be perpendicular to one of the principal directions one shadow-edge remains invariable in position, corresponding to one of the principal refractive indices, whilst the other moves between the critical values corresponding to the remaining two of the principal refractive indices. In the interesting case in which the facet is parallel to the two directions of single refraction, the second shadow-edge moves across the one which is invariable in position. In intermediate positions of the facet both shadow-edges move, and give therefore critical values. Of the intermediate pair, i.e. the lower maximum and the higher minimum, one corresponds to the mean principal refractive index, and the other depends upon the relation of the facet to the optical symmetry. If it is desired to distinguish between them, observations must be made on a second facet; but for discriminative purposes such exactitude is unnecessary, since the least and the greatest refractive indices are all that are required.

The character of the refraction of gem-stones is given in Table V at the end of the book.

CHAPTER VII

ABSORPTION EFFECTS: COLOUR, DICHROISM, ETC.

WHEN white light passes through a cut stone, colour effects result which arise from a variety of causes. The most obvious is the fundamental colour of the stone, which is due to its selective absorption of the light passing through it, and would characterize it before it was cut. Intermingled with the colour in a transparent stone is the dispersive effect known as ‘fire,’ which has already been discussed ([p. 20]). In many instances the want of homogeneity is responsible for some peculiar effects such as opalescence, chatoyancy, and asterism. These phenomena will now be considered in fuller detail.

Colour

All substances absorb light to some extent. If the action is slight and affects equally the whole of the visible spectrum, the stone appears white or colourless. Usually some portion is more strongly absorbed than the rest, and the stone seems to be coloured. What is the precise tint depends not only upon the portions transmitted through the stone, but also upon their relative intensities. The eye, unlike the ear, has not the power of analysis and it cannot of itself determine how a composite colour has been made up. Indeed, so far as it is concerned, any colour may be exactly matched by compounding in certain proportions three simple primary colours—red, yellow, and violet. Alexandrite, a variety of chrysoberyl, is a curious and instructive case. The balance in the spectrum of light transmitted through it is such that, whereas in daylight such stones appear green, in artificial light, especially in gas-light, they are a pronounced raspberry-red ([Plate XXVII], Figs. 11, 13). The phenomenon is intensified by the strong dichroism characteristic of this species.

The colour is the least reliable character that may be employed for the identification of a stone, since it varies considerably in the same species, and often results from the admixture of some metallic oxide, which has no essential part in the chemical composition and is present in such minute quantities as to be almost imperceptible by analysis. Who would, for instance, imagine from their appearance that stones so markedly diverse in hue as ruby and sapphire were really varieties of the same species, corundum? Again, quartz, in spite of the simplicity of its composition, displays extreme differences of tint. Nevertheless, certain varieties do possess a distinctive colour, emerald being the most striking example, and in other cases the trained eye can appreciate certain characteristic subtleties of shade. At any rate, the colour is the most obvious of the physical characters, and serves to provide a rough division of the species, and accordingly in Table II at the end of the book the gem-stones are arranged by their usual tints.

Dichroism

The two rays into which a doubly refractive stone splits up a ray of light are often differently absorbed by it, and in consequence appear on emergence differently coloured; such stones are said to be dichroic. The most striking instance is a deep-brown tourmaline, which, except in very thin sections, is quite opaque to the ordinary ray. The light transmitted by a plate cut parallel to the crystallographic axis is therefore plane-polarized; before the invention by Nicol of the prism of Iceland-spar known by his name this was the ordinary method of obtaining light of this character (cf. p. 43). Again, in the case of kunzite and cordierite the difference in colour is so marked as to be obvious to the unaided eye; but where the contrast is less pronounced we require the use of an instrument called a dichroscope, which enables the twin colours to be seen side by side.

Fig. 29.—Dichroscope (actual size).

Fig. 30.—Field of the Dichroscope.

Fig. 29 illustrates in section the construction of a dichroscope. The instrument consists essentially of a rhomb of Iceland-spar, S, of such a length as to give two contiguous images (Fig. 30) of a square hole, H, in one end of the tube containing it. In some instruments the terminal faces of the rhomb are ground at right angles to its length, but usually, as in that depicted, prisms of glass, G, are cemented on to the two ends. A cap C, with a slightly larger hole, which is circular in shape, fits on the end of the tube, and can be moved up and down it and revolved round it, as desired. The stone, R, to be tested may be directly attached to it by means of some kind of wax or cement in such a way that light which has traversed it passes into the window, H, of the instrument; the cap at the same time permits of the rotation of the stone about the axis of the main tube of the instrument. The dichroscope shown in the figure has a still more convenient arrangement: it is provided with an additional attachment, A, by means of which the stone can be turned about an axis at right angles to the length of the tube, and thus examined in different directions. At the other end of the main tube is placed a lens, L, of low power for viewing the twin images: the short tube containing it can be pushed in and out for focusing purposes. Many makers now place the rhomb close to the lens, L, and thereby require a much smaller piece of spar; material suitable for optical purposes is fast growing scarce.

Suppose that a plate of tourmaline cut parallel to its crystallographic axis is fastened to the cap and the latter rotated. We should notice, on looking through the instrument, that in the course of a complete revolution there are two positions, orientated at right angles to one another, in which the tints of the two images are identical, the positions of greatest contrast of tint being midway between. If we examine a uniaxial stone in a direction at right angles to its optic axis we obtain the colours corresponding to the ordinary and the extraordinary rays. In any direction less inclined to the axis we still have the colour for the ordinary ray, but the other colour is intermediate in tint between it and that for the extraordinary ray. The phenomenon presented by a biaxial stone is more complex. There are three principal colours which are visible in differing pairs in the three principal optical directions; in other directions the tints seen are intermediate between the principal colours. Since biaxial stones have three principal colours, they are sometimes said to be trichroic or pleochroic, but in any single direction they have two twin colours and show dichroism. No difference at all will be shown in directions in which a stone is singly refractive, and it is therefore always advisable to examine a stone in more than one direction lest the first happens to be one of single refraction. For determinative purposes it is not necessary to note the exact shades of tint of the twin colours, because they vary with the inherent colour of the stone, and are therefore not constant for the same species; we need only observe, when the stone is tested with the dichroscope, whether there is any variation of colour, and, if so, its strength. Dichroism is a result of double refraction, and cannot exist in a singly refractive stone. The converse, however, is not true and it by no means follows that, because no dichroism can be detected in a stone, it is singly refractive. A colourless stone, for instance, cannot possibly be dichroic, and many coloured, doubly refractive stones—for example, zircon—exhibit no dichroism, or so little that it is imperceptible. The character is always the better displayed, the deeper the inherent colour of the stone. The deep-green alexandrite, for instance, is far more dichroic than the lighter coloured varieties of chrysoberyl.

If the stone is attached to the cap of the instrument, the table should be turned towards it so as to assure that the light passing into the instrument has actually traversed the stone. If little light enters through the opposite coign, a drop of oil placed thereon will overcome the difficulty (cf. [p. 46]). It is also necessary, for reasons mentioned above, to examine the stone in directions as far as possible across the girdle also. A convenient, though not strictly accurate, method is to lay the stone with the table facet on a table and examine the light which has entered the stone and been reflected at that facet. The stone may easily be rotated on the table, and observations thus made in different directions in the stone. Care must be exercised in the case of a faceted stone not to mistake the alteration in colour due to dispersion for a dichroic effect, and the stone must be placed close to the instrument during an observation, because otherwise the twin rays traversing the instrument may have taken sensibly different directions in the stone.

Dichroism is an effective test in the case of ruby; its twin colours—purplish and yellowish red—are in marked contrast, and readily distinguish it from other red stones. Again, one of the twin colours of sapphire is distinctly more yellowish than the other; the blue spinel, of which a good many have been manufactured during recent years, is singly refractive, and, of course, shows no difference of tint in the dichroscope.

[Table VI] at the end of the book gives the strength of the dichroism of the gem-stones.

Absorption Spectra

A study of the chromatic character of the light transmitted by a coloured stone is of no little interest. As was stated above, the eye has not the power of analysing light, and to resolve the transmitted rays into their component parts an instrument known as a spectroscope is needed. The small ‘direct-vision’ type has ample dispersion for this purpose. It is advantageous to employ by preference the diffraction rather than the prism form, because in the former the intervals in the resulting spectrum corresponding to equal differences of wave-length are the same, whereas in the latter they diminish as the wave-length increases and accordingly the red end of the spectrum is relatively cramped.

The absorptive properties of all doubly refractive coloured substances vary more or less with the direction in which light traverses them according to the amount of dichroism that they possess, but the variation is not very noticeable unless the stone is highly dichroic. If the light transmitted by a deep-coloured ruby be examined with a spectroscope it will be found that the whole of the green portion of the spectrum is obliterated (Fig. 31), while in the case of a sapphire only a small portion of the red end of the spectrum is absorbed. Alexandrite affords especial interest. In the spectrum of the light transmitted by it, the violet and the yellow are more or less strongly absorbed, depending upon the direction in which the rays have passed through the stone (Fig. 31), and the transmitted light is mainly composed of two portions—red and green. The apparent colour of the stone depends, therefore, upon which of the two predominates. In daylight the resultant colour is green flecked with red and orange, the three principal absorptive tints (cf. [p. 235]), but in artificial light, which is relatively stronger in the red portion of the spectrum, the resultant colour is a raspberry-red, and there is less apparent difference in the absorptive tints (cf. [Plate XXVII], Figs. 11, 13).

Fig. 31.—Absorption Spectra.

In all the spectra just considered, and in all like them, the portions that are absorbed are wide, the passage from blackness to colour is gradual, and the edges deliminating them are blurred. In the spectra of certain zircons and in almandine garnet the absorbed portions, or bands as they are called, are narrow, and, moreover, the transition from blackness to colour is sharp and abrupt; such stones are therefore said to display absorption-bands. Church in 1866 was the first to notice the bands shown by zircon (Fig. 31). Sorby thought they portended the existence of a new element, to which he gave the name jargonium, but subsequently discovered that they were caused by the presence of a minute trace of uranium. A yellowish-green zircon shows the phenomenon best, and it has all the bands shown in the figure. The spectrum varies slightly but almost imperceptibly with the direction in the stone. Others show the bands in the yellow and green, while others show only those in the red, and some only one of them. The bands are not confined to stones of any particular colour, or amount of double refraction. Again, many zircons show no bands at all, so that their absence by no means precludes the stone from being a zircon.

Almandine is characterized by a different spectrum (Fig. 31). The band in the yellow is the most conspicuous, and is no doubt responsible for the purple hue of a typical almandine. The spectrum varies in strength in different stones. Rhodolite ([p. 214]), a garnet lying between almandine and pyrope, displays the same bands, and indications of them may be detected in the spectra of pyropes of high refraction.

PLATE IV

JEWELLERY DESIGNS

CHAPTER VIII

SPECIFIC GRAVITY

IT is one of our earliest experiences that different substances of the same size have often markedly different weights; thus, there is a great difference between wood and iron, and still greater between wood and lead. It is usual to say that iron is heavier than wood, but the statement is misleading, because it would be possible by selecting a large enough piece of wood to find one at least as heavy as a particular piece of iron. We have, in fact, to compare equal volumes of the two substances, and all ambiguity is removed if we speak of relative density or specific gravity—the former term being usually applied to liquids and the latter to solids—instead of weight or heaviness. The density of water at 4° C. is taken as unity, that being the temperature at which it is highest; at other temperatures it is somewhat lower, as will be seen from [Table IX] given at the end of the book. The direct determination of the volume of an irregular solid presents almost insuperable difficulty; but, fortunately, for finding the specific gravity it is quite unnecessary to know the volume, as will be shown when we proceed to consider the methods in use.

The specific gravity of a stone is a character which is within narrow limits constant for each species, and is therefore very useful for discriminative purposes. It can be determined whatever be the shape of the stone, and it is immaterial whether it be transparent or not; but, on the other hand, the stone must be unmounted and free from the setting.

The methods for the determination of the specific gravity are of two kinds: in the first a liquid is found of the same, or nearly the same, density as the stone, and in the second weighings are made and the use of an accurate balance is required.

(1) Heavy Liquids

Experiment tells us that a solid substance floats in a liquid denser than itself, sinks in one less dense, and remains suspended at any level in one of precisely the same density. If the stone be only slightly less dense than the liquid, it will rise to the surface; if it be just as slightly denser, it will as surely sink to the bottom, a physical fact which has added so much to the difficulty and danger of submarine manœuvring. If then we can find a liquid denser than the stone to be tested, and place the latter in it, the stone will float on the surface. If we take a liquid which is less dense than the stone and capable of mixing with the heavier liquid, and add it to the latter, drop by drop, gently stirring so as to assure that the density of the combination is uniformly the same throughout, a stage is finally reached when the stone begins to move downwards. It has now very nearly the density of the liquid, and, if we find by some means this density, we know simultaneously the specific gravity of the stone.

Various devices and methods are available for ascertaining the density of liquids—for instance, Westphal’s balance; but, apart from the inconvenience attending such a determination, the density of all liquids is somewhat seriously affected by changes in the temperature, and it is therefore better to make direct comparison with fragments of substances of known specific gravity, which are termed indicators. If of two fragments differing slightly in specific gravity one floats on the surface of a uniform column of liquid and the other lies at the bottom of the tube containing the liquid, we may be certain that the density of the liquid is intermediate between the two specific gravities. Such a precaution is necessary because, if the liquid be a mixture of two distinct liquids, the density would tend to increase owing to the greater volatility of the lighter of them, and in any case the density is affected by change of temperature. The specific gravity of stones is not much altered by variation in the temperature.

A more convenient variation of this method is to form a diffusion column, so that the density increases progressively with the depth. If the stone under test floats at a certain level in such a column intermediate between two fragments of known specific gravity, its specific gravity may be found by elementary interpolation. To form a column of this kind the lighter liquid should be poured on to the top of the heavier. Natural diffusion gives the most perfect column, but, being a lengthy process, it may conveniently be quickened by gently shaking the tube, and the column thus formed gives results sufficiently accurate for discriminative purposes.

By far the most convenient liquid for ordinary use is methylene iodide, which has already been recommended for its high refraction. It has, when pure, a density at ordinary room-temperatures of 3·324, and it is miscible in all proportions with benzol, whose density is O·88, or toluol, another hydrocarbon which is somewhat less volatile than benzol, and whose density is about the same, namely, 0·86. When fresh, methylene iodide has only a slight tinge of yellow, but it rapidly darkens on exposure to light owing to the liberation of iodine which is in a colloidal form and cannot be removed by filtration. The liquid may, however, be easily cleared by shaking it up with any substance with which the iodine combines to form an iodide removable by filtration. Copper filings answer the purpose well, though rather slow in action; mercury may also be used, but is not very satisfactory, because a small amount may be dissolved and afterwards be precipitated on to the stone under test, carrying it down to the bottom of the tube. Caustic potash (potassium hydroxide) is also recommended; in this case the operation should preferably be carried out in a special apparatus which permits the clear liquid to be drawn off underneath, because water separates out and floats on the surface. In Fig. 32 three cut stones, a quartz (a), a beryl (b), and a tourmaline (c) are shown floating in a diffusion column of methylene iodide and benzol. Although the beryl is only slightly denser than the quartz, it floats at a perceptibly lower level. These three species are occasionally found as yellow stones of very similar tint.

Fig. 32.—Stones of different
Specific Gravities floating
in a Diffusion Column of
heavy Liquid.

Various other liquids have been used or proposed for the same purpose, of which two may be mentioned. The first of them is a saturated solution of potassium iodide and mercuric iodide in water, which is known after the discoverer as Sonstadt’s solution. It is a clear mobile liquid with an amber colour, having at 12° C. a density of 3·085; it may be mixed with water to any extent, and is easily concentrated by heating; moreover, it is durable and not subject to alteration of any kind; on the other hand, it is highly poisonous and cauterizes the skin, not being checked by albumen; it also destroys brass-ware by amalgamating the metal. The second is Klein’s solution, a clear yellow liquid which has at 15° C. a density of 3·28. It consists of the boro-tungstate of cadmium, of which the formula is 9WO₃.B₂O₃.2CdO.2H₂O + 16Aq, dissolved in water, with which it may be diluted. If the salt be heated, it fuses at 75° C. in its own water of crystallization to a yellow liquid, very mobile, with a density of 3·55. Klein’s solution is harmless, but it cannot compare for convenience of manipulation with methylene iodide.

The most convenient procedure is to have at hand three glass tubes, fitted with stoppers or corks, to contain liquids of different densities—

(a) Methylene iodide reduced to 2·7; using as indicators orthoclase 2·55, quartz 2·66, and beryl 2·74.

(b) Methylene iodide reduced to 3·1; indicators, beryl 2·74 and tourmaline 3·10.

(c) Methylene iodide, undiluted, 3·32.

The pure liquid in the last tube should on no account be diluted; but the density of the other two liquids may be varied slightly, either by adding benzol in order to lower it, or by allowing benzol, which has far greater volatility than methylene iodide, to evaporate, or by adding methylene iodide, in order to increase it. The density of the liquids may be ascertained approximately from the indicators.

A glance at the table of specific gravities shows that as regards the gem-stones methylene iodide is restricted in its application, since it can be used to test only moonstone, quartz, beryl, tourmaline, and spodumene; opal and turquoise, being amorphous and more or less porous, should not be immersed in liquids, lest the appearance of the stone be irretrievably injured. Methylene iodide readily serves to distinguish the yellow quartz from the true topaz, with which jewellers often confuse it, the latter stone sinking in the liquid; again aquamarine floats, but the blue topaz, which is often very similar to it, sinks in methylene iodide.

By saturating methylene iodide with iodine and iodoform, we have a liquid (d) of density 3·6; a fragment of topaz, 3·55, may be used to indicate whether the liquid has the requisite density. Unfortunately this saturated solution is so dark as to be almost opaque, and is, moreover, very viscous. Its principal use is to distinguish diamond, 3·535, from the brilliant colourless zircon, with which, apart from a test for hardness, it may easily be confused. It is easy to see whether the stone floats, as it would do if a diamond. To recover a stone which has sunk, the only course is to pour off the liquid into another tube, because it is far too dark for the position of the stone to be seen.

It is possible to employ a similar method for still denser stones by having recourse to Retgers’s salt, silver-thallium nitrate. This double salt is solid at ordinary room-temperatures, but has the remarkable property of melting at a temperature, 75° C., which is well below the point of fusion of either of its constituents, to a clear, mobile yellow liquid, which is miscible in any proportion with water, and has, when pure, a density of 4·6. The salt may be purchased, or it may be prepared by mixing 100 grams of thallium nitrate and 64 grams of silver nitrate, or similar proportions, in a little water, and heating the whole over a water-bath, keeping it constantly stirred with a glass rod until it is liquefied. The two salts must be mixed in the correct proportions, because otherwise the mixture might form other double salts, which do not melt at so low a temperature. A glance at the table of specific gravities shows that Retgers’s salt may be used for all the gem-stones with the single exception of zircon (b). There are, however, some objections to its use. It is expensive, and, unless kept constantly melted, it is not immediately available. It darkens on exposure to strong sunlight like all silver salts, stains the skin a peculiar shade of purple which is with difficulty removed, and in fact only by abrasion of the skin, and, like all thallium compounds, is highly poisonous.

It is convenient to have three tubes, fitted as before with stoppers or corks, to contain the following liquids, when heated:—

(e) Silver-thallium nitrate, reduced to 3·5; using as indicators, peridot or idocrase 3·40 and topaz 3·53.

(f) Silver-thallium nitrate, reduced to 4·0; indicators, topaz 3·53 and sapphire 4·03.

(g) Silver-thallium nitrate, undiluted, 4·6.

The tubes must be heated in some form of water-bath; an ordinary glass beaker serves the purpose satisfactorily. The pure salt should never be diluted; but the density of the contents of tubes (e) and (f) may be varied at will, water being added in order to lower the density, and concentration by means of evaporation or addition of the nitrate being employed in order to increase it. To avoid the discoloration of the skin, rubber finger-stalls may be used, and the stones should not be handled until after they have been washed in warm water. The staining may be minimized if the hands be well washed in hot water before being exposed to sunlight. It is advisable to warm the stone to be tested in a tube containing water beforehand lest the sudden heating develop cracks. A piece of platinum, or, failing that, copper wire is of service for removing stones from the tubes; a glass rod, spoon-shaped at one end, does equally well. It must be noted that although Retgers’s salt is absolutely harmless to the ordinary gem-stones—with the exception of opal and turquoise, which, as has already been stated, being to some extent porous, should not be immersed in liquids—it attacks certain substances, for instance, sulphides and cannot be applied indiscriminately to minerals.

The procedure described above is intended only as a suggestion; the method may be varied to any extent at will, depending upon the particular requirements. If such tests are made only occasionally, a smaller number of tubes may be used. Thus one tube may be substituted for the two marked a and b, the liquid contained in it being diluted as required, and a series of indicators may be kept apart in small glass tubes. On the other hand, any one having constantly to test stones might increase the number of tubes with advantage, and might find it useful to have at hand fragments of all the principal species in order to make direct comparison.

(2) Direct Weighing

The balance which is necessary in both the methods described under this head should be capable of giving results accurate to milligrams, i.e. the thousandth part of a gram, and consistent with that restriction the beam may be as short as possible so as to give rapid swings and thus shorten the time taken in the observations. A good assay balance answers the purpose admirably. Of course, it is never necessary to wait till the balance has come to rest. The mean of the extreme readings of the pointer attached to the beam will give the position in which it would ultimately come to rest. Thus, if the pointer just touches the eighth division on the right-hand side and the second on the other, the mean position is the third division on the right-hand side (½(8 − 2) = 3). Instead of the ordinary form of chemical balance, Westphal’s form or Joly’s spring-balance may be employed. Weighings are made more quickly, but are not so accurate.

In refined physical work the practice known as double-weighing is employed to obviate any slight error there may be in the suspension of the balance. A counterpoise which is heavier than anything to be weighed is placed in one pan, and weighed. The counterpoise is retained in its pan throughout the whole course of the weighings. Any substance whose weight is to be found is placed in the other pan, and weights added till the balance swings truly again. The difference between the two sets of weights evidently gives the weight of the substance. Balances, however, are so accurately constructed that for testing purposes such refined precautions are not really necessary.

It is immaterial in what notation the weighings are made, so long as the same is used throughout, but the metric system of weights, which is in universal use in scientific work, should preferably be employed. Jewellers, however, use carat weights, and a subdivision to the base 2 instead of decimals, the fractions being ½, ¼, ⅛, ¹/₁₆, ¹/₃₂, ¹/₆₄. If these weights be employed, it will be necessary to convert these fractions into decimals, and write ½ = ·500, ¼ ·250, ⅛ = ·125, ¹/₁₆ = ·062, ¹/₃₂ = ·031, ¹/₆₄ = ·016.

(a) Hydrostatic Weighing

The principle of this method is very simple. The stone, the specific gravity of which is required, is first weighed in air and then when immersed in water. If W and W´ be these weights respectively, then W − W´ is evidently the weight of the water displaced by the stone and having therefore the same volume as it, and the specific gravity is therefore equal to ^W/_{W − W^r}.

If the method of double-weighing had been adopted, the formula would be slightly altered. Thus, suppose that c corresponds to the counterpoise, w and w´ to the stone weighed in air and water respectively; then we have W = c − w and W´ = c − w´, and therefore the specific gravity is equal to ^{c − w}/_{w´ − w}.

Fig. 33.—Hydrostatic Balance.

Some precautions are necessary in practice to assure an accurate result. A balance intended for specific gravity work is provided with an auxiliary pan (Fig. 33), which hangs high enough up to permit of the stone being suspended underneath. The weight of anything used for the suspension must, of course, be determined and subtracted from the weight found for the stone, both when in air and when in water. A piece of fine silk is generally used for suspending the stone in water, but it should be avoided, because the water tends to creep up it and the error thus introduced affects the first place of decimals in the case of a one-carat stone, the value being too high. A piece of brass wire shaped into a cage is much to be preferred. If the same cage be habitually used, its weight in air and when immersed in water to the customary extent in such determinations should be found once for all.

Care must also be taken to remove all air-bubbles which cling to the stone or the cage; their presence would tend to make the value too low. The surface tension of water which makes it cling to the wire prevents the balance swinging freely, and renders it difficult to obtain a weighing correct to a milligram when the wire dips into water. This difficulty may be overcome by substituting a liquid such as toluol, which has a much smaller surface tension.

As has been stated above, the density of water at 4° C. is taken as unity, and it is therefore necessary to multiply the values obtained by the density of the liquid, whatever it be, at the temperature of the observation. In Table IX, at the end of the book, are given the densities of water and toluol at ordinary room-temperatures. It will be noticed that a correct reading of the temperature is far more important in the case of toluol.

Example of a Hydrostatic Determination of Specific Gravity—

Weight of stone in air = 1·471 gram

Weight of stone in water = 1·067 „

Specific gravity = ^1·471/_{1·471 − 1·067} = ^1·471/_0·404.

Allowing for the density of water at the temperature of the room, which was 16° C., the specific gravity is 3·637. Had no such allowance been made, the result would have been four units too high in the third place of decimals. For discriminative purposes, however, such refinement is unnecessary.

(b) Pycnometer, or Specific Gravity Bottle

The specific gravity bottle is merely one with a fairly long neck on which a horizontal mark has been scratched, and which is closed by a ground glass stopper. The pycnometer is a refined variety of the specific gravity bottle. It has two openings: the larger is intended for the insertion of the stone and the water, and is closed by a stopper through which a thermometer passes, while the other, which is exceedingly narrow, is closed by a stopper fitting on the outside, and is graduated to facilitate the determination of the height of the water in it.

The stone is weighed as in the previous method. The bottle is then weighed, and filled with water up to the mark and weighed again. The stone is now introduced into the bottle, and the surplus water removed with blotting-paper or otherwise until it is at the same level as before, and the bottle with its contents is weighed. Let W be the weight of the stone, w the weight of the bottle, W´ the weight of the bottle and the water contained in it, and W″ the weight of the bottle when containing the stone and the water. Then W´ − w is the weight of the water filling the bottle up to the mark, and W″ − w − W is the reduced weight of water after the stone has been inserted; the difference, W + W´ − W″, is the weight of the water displaced. The specific gravity is therefore ^W/_{W + W´ − W″}. As in the previous method, this value must be multiplied by the density of the liquid at the temperature of the experiment. If the method of double-weighing be adopted, the formula will be slightly modified.

Of the above methods, that of heavy liquids, as it is usually termed, is by far the quickest and the most convenient for stones of ordinary size, the specific gravity of which is less than the density of pure methylene iodide, namely, 3·324, and by its aid a value may be obtained which is accurate to the second place of decimals, a result quite sufficient for a discriminative test. The method is applicable no matter how small the stone may be, and, indeed, for very small stones it is the only trustworthy method; for large stones it is inconvenient, not only because of the large quantity of liquid required, but also on account of the difficulty in estimating with sufficient certainty the position of the centre of gravity of the stone. A negative determination may be of value, especially if attention be paid to the rate at which the stone falls through the liquid; the denser the stone the faster it will sink, but the rate depends also upon the shape of the stone. Retgers’s salt is less convenient because of the delay involved in warming it and of the almost inevitable staining of the hands, but its use presents no difficulty whatever.

Hydrostatic weighing is always available, unless the stone be very small, but the necessary weighings occupy considerable time, and care must be taken that no error creeps into the computation, simple though it be. Even if everything is at hand, a determination is scarcely possible under a quarter of an hour.

The third method, which takes even longer, is intended primarily for powdered substances, and is not recommended for cut stones, unless there happen to be a number of tiny ones which are known to be exactly of the same kind.

The specific gravities of the gem-stones are given in [Table VII] at the end of the book.

CHAPTER IX

HARDNESS AND CLEAVABILITY

EVERY possessor of a diamond ring is aware that diamond easily scratches window-glass. If other stones were tried, it would be found that they also scratched glass, but not so readily, and, if the experiment were extended, it would be found that topaz scratches quartz, but is scratched by corundum, which in its turn yields to the all-powerful diamond. There is therefore considerable variation in the capacity of precious stones to resist abrasion, or, as it is usually termed, in their hardness. To simplify the mode of expressing this character the mineralogist Mohs about a century ago devised the following arbitrary scale, which is still in general use.

Mohs’s Scale of Hardness

1. Talc
2. Gypsum
3. Calcite
4. Fluor
5. Apatite
6. Orthoclase
7. Quartz
8. Topaz
9. Corundum
10. Diamond

A finger-nail scratches gypsum and softer substances. Ordinary window-glass is slightly softer than orthoclase, and a steel knife is slightly harder; a hardened file approaches quartz in hardness, and easily scratches glass.

By saying that a stone has hardness 7 we merely mean that it will not scratch quartz, and quartz will not scratch it. The numbers indicate an order, and have no quantitative significance whatever. This is an important point about which mistakes are often made. We must not, for instance, suppose that diamond has twice the hardness of apatite. As a matter of fact, the interval between diamond and corundum is immensely greater than that between the latter and talc, the softest of mineral substances. Intermediate degrees of hardness are expressed by fractions. The number 8½ for chrysoberyl means that it scratches topaz as easily as it itself is scratched by corundum. Pyrope garnet is slightly harder than quartz, and its hardness is said therefore to be 7¼.