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THE UNIVERSITY OF CALIFORNIA LIBRARY OF THE UNIVERSITY OF
MANUAL
LIBRARV
COLLEGE OF
AGRICULTURE
Berkeley. Cal.
OF
CONTAINING
The Elements of the Science of Minerals and Ms.
FOB THE USE OF
THE PRACTICAL MINERALOGIST AND GEOLOGIST AND FOR INSTRUCTION IN SCHOOLS AND COLLEGES.
BY JAMES D. DANA.
\\
FOURTH EDITION.
REVISED THROUGHOUT AND ENLARGED.
ILLUSTRA TED BY NUMEROUS WOOD-CUTS.
NEW YORK: JOHN WILEY & SONS.
1887.
EARTH'
SCIENCES
LIBRARY
Copyright, 1887. By JOHN WILEY & SONS.
PREFACE.
SCIENCES
LIBRARY
THE preface to the third edition of this work (1878) is as follows:
"This Manual in its present shape is new throughout. In the renovation it has undergone, new illustrations have been introduced, an improved arrangement of the species has been adopted, the table for the determination of minerals has been reconstructed, and the chapter on Rocks has been expanded to a length and fulness that renders it a prominent part of the work. But while modified greatly in all its parts, it is still simple in its methods of presenting the facts in crystallography, and in all other explanations ; and special prom- inence is given, as in former editions, to the more common minerals, with only a brief mention of others. The old practical feature is retained of placing the ores under the prominent metal they contain, and of giving in connection some information as to mines and mining industry.
" The student is referred to the Text-book of Mineralogy, prepared mainly by Mr. E. S. DANA, for a detailed exposition of the subject of crystallography after Naumann's and Miller's systems, and also of optical mineralogy and other physical branches of the science; to the Manual of Determinative Mineralogy and Blowpipe Analysis by Professor GEORGE J. BRUSH, for a thorough work on the use of the blowpipe, and complete- tables for the determination of minerals; and to the author's Descriptive Mineralogy and its Appendixes for a com- prehensive treatise on minerals."
In this, the fourth, edition the general plan and scope of the work remain unchanged. But it has been revised throughout, and brought down to the year 1886 in its descriptions of minerals, and in the in- troduction of the many new species announced during the past eight years. The chapter on Rocks has been rewritten, rearranged, much enlarged, and supplied with new illustrations. The work is greatly indebted, for facts about ores and other useful minerals, to the excel- lent annual report on the "Mineral Resources of the United States," by Mr. Albert Williams, Jr. , published by the United States Geologi- cal Survey. The author would acknowledge also his obligations to Prof. B. J. Harrington, of Montreal, for the revision of the list of localities in Ontario and Quebec.
JAMES D. DANA.
NEW HAVEN, Dec. 15, 1886.
TABLE OF CONTENTS.
MINERALOGY.
PAGE
MINEBALS : General Remarks 1
I. CRYSTALLIZATION OP MINERALS: CRYSTALLOG- RAPHY.
1. General Remarks on Crystallization 4
2. Descriptions of Crystals 8
Explanation of Terms 8
Measurement of Angles ; Goniometers 9
1. SYSTEMS OF CRYSTALLIZATION : Forms and Struc-
ture of Crystals 15
1. Isometric System 18
2. Tetragonal System 31
3. Orthorhombic System 38
4. Monoclinic System 41
5. Triclinic System 45
6. Hexagonal System. 47
A. Hexagonal Section 47
B. Rhombohedral Section 51
7. Distinguishing Characters of the Systems 56
2. TWIN OR COMPOUND CRYSTALS 57
3. PARAMORPHS ; PARAMORPHISM 61
4. PSEUDOMORPHS ; PSEUDOMORPHISM 61
5. CRYSTALLINE AGGREGATES 63
H. PHYSICAL PROPERTIES OF MINERALS.
1. Hardness 67
2. Tenacity 67
Vi TABLE OF CONTENTS.
PAGE
3. Specific Gravity 68
4. Kef raction and Polarization 70
5. Diaphaneity, Lustre, Color 80
6. Electricity and Magnetism 84
7. Taste, Odor 85
in. CHEMICAL PROPERTIES OP MINERALS.
1. Chemical Composition 86
2. Chemical Reactions 92
A. Trials in the Wet Way 92
B. Trials with the Blowpipe 93
IV. DESCRIPTIONS OP MINERALS.
1. Classification 103
2. General Remarks on Ores 104
I. MINERALS CONSISTING OF THE ACIDIC ELEMENTS.
1. Sulphur Group 106
2. Boron Group 109
3. Arsenic Group 110
4. Carbon Group 115
II. MINERALS CONSISTING OF THE BASIC ELEMENTS
WITH OR WITHOUT ACIDIC — THE SILICATES EX- CLUDED.
Gold 122
Silver and its Compounds 129
Platinum, Iridium, Ruthenium 139
Palladium 141
Mercury and its Compounds 142
Copper and its Compounds 145
Lead and its Compounds 160
Zinc and its Compounds 170
Cadmium, Tin 175
Compounds of Titanium 178
Cobalt and Nickel and their Compounds 180
Uranium and its Compounds 186
Iron and its Compounds 188
Manganese and its Compounds 206
TABLE OF CONTENTS. yii
PAGE
Compounds of Aluminium 211
Compounds of Cerium, Yttrium, Erbium, Lanthanum, and
Didymium 221
Compounds of Magnesium 223
Compounds of Calcium 227
- Compounds of Barium and Strontium 240
Compounds of Potassium and Sodium 243
Compounds of Ammonium 249
Compounds of Hydrogen 251
III. SILICA AND SILICATES.
l. SILICA.
Quartz 253
Opal 259
2. SILICATES. General Remarks.- 262
1. Anhydrous Silicates.
1. Bisilicates 263
Pyroxene and Amphibole Group 265
Beryl, etc 274
2. Unisilicates 275
Chrysolite Group 277
Garnet Group 278
Zircon Group 281
Vesuvianite, Epidote, etc 282
Axinite 286
Danburite, lolite 286
Mica Group 287
Scapolite Group 292
Nephelite, Sodalite, Leucite 293
Feldspar Group 296
8. Subsilicates 302
Chondrodite 303
Tourmaline 304
Andalusite, Fibrolite, Cyanite 306
Topaz, Euclase .^7rT. 309
Datolite, Sphene 311
Staurolite. . . . 313
Vlll TABLE OF CONTENTS.
2. Hydrous Silicates.
PAGE
1. General Section 315
Pectolite, Laumontite, Apophyllite 315
Prehnite, Allophane 317
2. Zeolite Section 319
Thomsonite, Natrolite 320
Analcite, Chabazite 322
Harmotome, Stilbite 323
Heulandite 325
8. Margarophyllite Section 326
Talc, Pyrophyllite, Sepiolite 326
Glauconite 329
Serpentine, Deweylite, Saponite 329
Kaolinite, Pinite 332
Hydromica Group 335
Fahlunite 336
Chlorite Group 337
IV. HYDROCARBON COMPOUNDS.
1. Simple Hydrocarbons 842
2. Oxygenated Hydrocarbons 348
3. Asphaltum, Mineral Coals 349
SUPPLEMENT TO DESCRIPTIONS OF SPECIES. Catalogue of American Localities of Minerals 858
V. DETERMINATION OP MINERALS.
General Remarks 405
Synopsis of the Arrangement 410
Table for the Determination of Minerals 413
ON ROCKS.
1. Constituents of Rocks 434
2. Distinctions among Rocks 436
8. The Investigation of Rocka 447
TABLE OF CONTENTS. IX
PAGK
4. Microscopic Characteristics of Rock Constituents 454
5. Descriptions of Rocks 457
I. Calcareous Rocks or Limestones 457
II. Fragmented Rocks, exclusive of Limestones 461
III. Crystalline Rocks, exclusive of Limestones 466
A. Siliceous Rocks, consisting mainly of Silica 468
B. Containing Feldspar, Mica, Leucite, Nephelite,
Sodalite, or other related Alkali-bearing species 469
a. Potash-Feldspar and Mica Series 469
b. Potash -Feldspar and Hornblende or Pyroxene
Series 477
c. Potash-Feldspar and Nephelite Series, Horn-
blendic or not 478
d. Leucite Rocks, with or without Augite 479
e. Soda-Lime-Feldspar and Mica Series 480
/. Soda-Lime-Feldspar and Hornblende or Pyrox- ene Rocks 480
C. Saussurite Rocks 487
D. Rocks without Feldspar 487
1. Garnet, Epidote, and Tourmaline Rocks 487
2. Hornblende, Pyroxene, and Chrysolite Rocks. 488
E. Hydrous Magnesian and Aluminous Rocks 489
6. Durability in Rocks 491
ACADEMY COLLECTION OF MINERALS 495
INDEX.. ,. 497
MINERALOGY.
MINERALS.
MINERALS are the materials of which the earth consists, and plants and animals the living beings over the surface of the mineral-made globe. A few rocks, like limestone and quartzite, consist of a single mineral in more or less pure state; but the most of them are" mixtures of two or more minerals. Through rocks of each kind various other minerals are often distributed, either in a scattered way, or in veins and cavities. Gems are the minerals of jewelry; and ores, those that are important for the metal they con- tain. Water is a mineral, but generally in an impure state from the presence of other minerals in solution. The at- mosphere, and all gaseous materials set free in volcanic and other regions, are mineral in nature, although, because of their invisibility, seldom to be found among the specimens of mineral cabinets. Even fossils are mineral in composi- tion. This is true of coal which has come from buried plant-beds, and amber from the buried resin of ancient trees, as well as of fossil shells and corals.
It is sometimes said that minerals belong to the mineral kingdom, as plants to the vegetable kingdom, and animals to the animal kingdom. Substituting the term inorganic for mineral, the statement is right; for, as there are the two kingdoms of life, so there is in Nature what may be called a kingdom, or grand division, including all species not made through the organizing principle of life. But this inorganic kingdom is not restricted to minerals; it embraces all species made by inorganic forces; those of the earth's crust or surface, and, also, whatever may form un- der the manipulations of the chemist. The laws of com- position and structure, exemplified in the constitution of rocks, are those also of the laboratory. A species made by 1
CH^ RACl'ERS 'OF MINERALS.
art, as we' term it, is not a product of art, but a result solely of the fundamental laws of composition which are at the basis of all material existence; and the chemist only supplies the favorable conditions for the action of those laws. Mineral species are, then, but a very small part of those which make up the inorganic kingdom or division of Nature.
CHAEACTEES OF MINEEALS.
1. Minerals, unlike most rocks, have a definite chemical composition. This composition, as determined by chemi- cal analysis, serves to define and distinguish the species, and indicates their profoundest relations. Owing to differ- ence in composition, minerals exhibit great differences when heated, and when subjected to various chemical rea- gents, and these peculiarities are a means of determining the kind of mineral under examination in any case. The department of the science treating of the composition of minerals and their chemical reactions is termed CHEMICAL MINERALOGY.
2. Each mineral, with few exceptions, has its definite form, by which, when in good specimens, it may be known, and as truly so as a dog or cat. These forms are cubes, prisms, double pyramids, and the like. They are included under plane surfaces arranged in symmetrical order, ac- cording to mathematical law. These forms, in the mineral kingdom, are called crystals. Besides forms, there is also, as in living individuals, a distinctive internal structure for each species. The facts of this branch of the science come under the head of CRYSTALLOGRAPHIC MINERALOGY.
3. Minerals differ in hardness — from the diamond at one end of the scale to soapstone at the other. There is a still lower limit in liquids and gases; but of the hardness or co- hesion in this part of the series the mineralogist has little occasion to take note.
Minerals differ in specific gravity, and this character, like hardness, is a most important means of distinguishing species.
Minerals differ in color, transparency, lustre, and other optical characters.
A few minerals have taste and odor, and when so these characters are noticed in descriptions.
CHARACTERS OF MINERALS. 3
The facts and principles relating to the above characters are embraced in the department of PHYSICAL MINER- ALOGY.
In addition to the above-mentioned branches of the sci- ence of minerals there is also (4) that of DESCRIPTIVE MINERALOGY, under which are included descriptions of the mineral species; and (5) that of DETERMINATIVE MIN- ERALOGY, which gives a systematic review of the methods for determining or distinguishing minerals.
These different branches of the subject are here taken up in the following order: I. Crystallographic Mineralogy; II. Physical Mineralogy; III. Chemical Mineralogy; IV. Descriptive Mineralogy; V. Determinative Mineralogy. On account of the brief manner in which the subjects are treated in this volume, the heads used for the several parts are, (1) The Crystallization of Minerals; (2) Physical Properties of Minerals ; (3) Chemical Properties of Miner- als; (4) Descriptions of Species; (5) Determination of Minerals.
CRYSTALLOGRAPHY.
I. CRYSTALLIZATION OF MINERALS: CRYSTAL- LOGRAPHY.
1. GENERAL REMARKS ON CRYSTALLIZATION.
THE attraction which produces crystals is one of the fundamental properties of matter. It is identical with the cohesion of ordinary solidification; for there are few cases outside of the kingdoms of life in which solidification takes place without some degree of crystallization. Cohesive at- traction is, in fact, the organizing or structure-making principle in inorganic nature, it producing specific forms for each species of matter, as life does for each living spe- cies. A bar of cast-iron is rough and hackly in surface, because of the angular crystalline grains which the iron assumed as solidification took place. A fragment of mar-
CKYSTALS OF SNOW.
ble glistens in the sun, owing to the reflection of light from innumerable crystalline surfaces, every grain in the mass having its crystalline structure. Whe*n the cold of winter settles over the earth in the higher temperate and colder latitudes it is the signal for crystallization over all out-door nature; the air is filled with crystal flakes when it snows; the streams become coated with an aggregation
CRYSTALLOGRAPHY. 5
of crystals called ice; and windows are covered with frost because crystal has been added to crystal in long feathered lines over the glass — Jack Frost's work being the making of crystals. Water cannot solidify without crystallizing, and neither can iron nor lead, nor any mineral material, with perhaps half a dozen exceptions. Crystallization pro- duces masses made of crystalline grains when it cannot make distinct crystals. Granite mountains are mountains of crystals, each particle being crystalline in nature and structure. The lava current, as it cools, becomes a mass of crystalline grains. In fact the earth may be said to have crystal foundations; and if there is not the beauty of external form, there is everywhere the interior, profounder beauty of universal law — the same law of symmetry which, when external circumstances permit, leads to the perfect crystal with regular facets and angles.
Crystals are alone in making known the fact that this law of symmetry is one of the laws of cohesive attraction, and that under it this attraction not only brings the par- ticles of matter into forms of mathematical symmetry, but often develops scores of brilliant facets over their surface
with mathematical exactness of angle, and the simplest of numerical relations in their positions. Crystals teach also the more wonderful >fact that the same species of matter
CRYSTALLOGRAPHY.
may receive, under the action of this attraction, through some yet incomprehensible changes in its condition, a great diversity of forms — from the solid of half a dozen planes £o one of scores. The above figures represent a few of the forms in a common species, pyrite, a compound of iron and sulphur.
8.
10.
Many more figures might be given for this one species, pyrite. The various forms or planes in any such case have, it is true, mutually dependent relations — a fact often ex-
CRYSTALLOGRAPHY. 7
pressed by saying that they have a common fundamental form. But it is none the less a remarkable fact, giving pro- found interest to the subject, that the attraction, while having this degree of unity in any species, still, under each, admits of the multitudinous variations needed to produce so diverse results.
At the time of crystallization the material is usually in a state of fusion, or of gas or vapor, or of solution. In the case of iron the crystallization takes place from a state of fusion, and while the result is ordinarily only a mass of crystalline grains, distinct crystals are sometimes formed in any cavities. If in the cooling of a crucible of melted lead, bismuth, or sulphur the crust be broken soon after it forms, and the liquid part within be turned out, crystals will be found covering the interior. Here, also, is crystalliza- tion from a state of fusion. When frost or snow-flakes form it exemplifies crystallization from a state of vapor. If a saturated solution of alum, made with hot water, be left to cool, crystals of alum after a while will appear, and will become of large size if there is enough of the solution. A solution of common salt, or of sugar, affords crystals in the same way. Again, whenever a mineral is produced through the change or decomposition of another, and at the same time assumes the solid state, it takes at once a crystalline structure, if it does not also develop crys^ tals.
Further, the crystalline texture of a solid mass may often be changed without fusion : e.g., in tempering steel the bar is changed from coarse-grained steel to fine-grained by heating and then cooling it suddenly in cold water, and vice versa, and this is a change in every grain throughout the bar.
Thus the various processes of solidification are processes of crystallization, and the most universal of all facts about minerals is that they are crystalline in texture. A few ex- ceptions have been alluded to, and one example of these is the mineral opal, in which even the microscope detects no evidence of a crystalline condition, except sometimes in minute portions supposed not to be opal. But if we ex- clude coals and resins this mineral stands almost alone. Such facts, therefore, do not affect the conclusion that a knowledge of crystallography is of the highest importance to the mineralogist. It is important because —
8 CKYSTALLOGRAPHY.
1. A study of the crystalline forms and structure of minerals is a convenient means of distinguishing species — the crystals of a species being essentially constant in struc- ture and in angles.
2. The most important optical characters depend on the crystallization, and have to be learned from crystals.
3. The profoundest chemical relations of minerals are often exhibited in the relations of their crystalline forms.
4. Crystallization opens to us Nature at her foundation work, and illustrates its mathematical character.
2. DESCRIPTIONS OF CEYSTALS.
In describing crystals there are two subjects for con- sideration : First, FORM ; and secondly, STEUCTUEE.
A. FOEM. — Under form come up for description, not only the general forms of crystals, but also —
(1) The systems of crystallization, 'that is, the relations of all crystalline forms, and their classification.
(2) The mutual relations of the planes of a crystal as ascertained through their positions and the angles between them.
(3) The distortions of crystals. The perfection of sym- metry exhibited in the figures of crystals, in which all similar planes are represented as having the same size and form, is seldom found in nature, and the true form is often greatly disguised by this means. The facts on this point, and the methods of avoiding wrong conclusions, need to be understood, and these are given beyond. With all such imperfections the angles of crystals remain essentially con- stant. There are irregularities also from other sources.
(4) Twin or compound crystals. With some species twins are more common than regular crystals.
(5) Crystalline aggregates, or combinations of imperfect crystals, or of crystalline grains.
Explanations of Terms.
The following are explanations of a few terms used in connection with this subject:
1. Octahedron. — A solid bounded by eight equal triangles. They are equal equilateral triangles in the regular octahedron (Fig. 2, p. 18) ; equal isosceles triangles in the square octahedron (Fig. 17, p. 33) ; equal inequilateral triangles in the rhom&ic octahedron (Fig. 8, p. 38).
CRYSTALLOGRAPHY. 9
2. Double six-sided pyramids. Double eight-sided pyramids. Double twelve-sided pyramids. — Solids made of two equilateral six-sided, or eight-sided, or twelve-sided, pyramids placed base to base (Fig. 20, p. 33, and 6, 10, pp. 48, 49).
3. Eight prisons. Oblique prisms.— Right prisms are those that are erect, all their sides being at right angles to the base. When inclined, they are calkd oblique prisms.
4. Interfacial angle. — Angle of inclination between two faces or planes.
5. Similar planes. Similar angles. — The lateral faces of a square prism (Fig. 2, p. 15) are equal and have like relations to the axes, and hence they are said to be similar. Solid angles are similar when the plane angles are equal each for each, and the enclosing planes are sev- erally similar in their relations to the axes.
6. Truncated. Bevelled. — An edge of a crystal is said to be trun- cated when it is replaced by a plane equally inclined to the enclosing planes, as in Fig. 13, p. 20 ; and it is bevelled when -replaced by two planes equally inclined severally to the adjoining faces. Only edges that are formed by the meeting of two similar planes can be truncated or bevelled. The angle between the truncating plane and the plane adjoining it on either side always equals 90° plus half the interfacial angle over the truncated edge. When a rectangular edge, or one of 90U, is truncated, this angle is accordingly 135° (= 90° -j- 45D) ; when an edge of 70°, it is 125° (= 90° -f- 35°) ; when an edge of 140°, it is 160° (=90° + 70°).
7. Zone. — A zone of planes includes a series of planes having the edges between them, that is, their mutual intersections, all parallel. Thus in Fig. 14, on page 6, JET at top of figure, i2, i\, H in front, and two planes below, and others on the back of the crystal are in one zone, a vertical zone. Again, in the same figure, H at top, 42, 3|, 22, 42, i2, 42, 22, 3f , and the continuation of this series below and over the back of the crystal lie in another vertical zone. And so in cases in other directions. All planes in the same zone may be viewed as on the circumference of the same circle. The planes of crystals are generally all comprised in a few zones, and the study of the mathematics of crystals is largely the study of zones of planes.
Axes. — Imaginary lines in crystals intersecting one another at their centres. Axes are assumed in order to describe the positions of the planes of crystals. In each system of crystallization there is one verti- cal axis, and in all but hexagonal forms there are two lateral axes.
Diametral sections. — The sections of crystals in which lie any two of the axes. In forms having two lateral axes, there are two vertical diametral sections and one basal.
Diametral prisms. — Prisms whose sides are parallel to the diametral sections.
The angles of crystals are measured by means of instruments called goniometers. These instruments are of two kinds, one the common goniometer, the other, the reflecting goniometer.
10
C R YST A LLOGRAPHY.
The common goniometer depends for its use on the very simple prin- ciple that when two straight lines cross one an- 4: ^p other, as AE, CD, in the annexed figure, the parts
^N\^^-'x' will diverge equally on opposite sides of the point .^-^3\^^ of intersection (O); that is, in mathematical lan- c-"^ \E guage, the angle AOD is equal to the angle COE,
and AO G is equal to DOE.
A common form of the instrument is represented in the figure be- low.
The two arms ab, cd, move on a pivot at o, and their divergence, or the angle they make with one another, is read off on the graduated arc attached. In using it, press up between the edges ao and co the edge of the crystal whose angle is to be measured, and con- tinue thus opening the arms until these edges lie evenly against the faces that include the required angle. To insure accuracy in this respect, hold the instrument and crystal between the eye and the light, and observe that no light passes between the arm and the applied faces of the crystal. The arms may then be secured in position by tighten- ing the screw at <?; the angle will then be measured by the distance on the arc from If to the left or outer edge of the arm cd, this edge being in the line of o, the centre of motion. As the instrument stands in the figure, it reads 45°. The arms have slits at gh, np, by which the parts ao, co, may be shortened so as to make them more convenient for measuring small crystals.
In the best form of the common goniometer the arc is a complete
circle, of larger diameter than in the above figure, and the arms are separate from it. After making the measurement, the arms are laid upon the circle, with the pivot at the centre of motion inserted in a socket at the centre of the circle. The inner edge of one of the arms is then brought to zero on the circle, and the angle is read off as be- fore.
CRYSTALLOGRAPHY. 11
With a little ingenuity the student may construct a goniometer for himself that will answer a good purpose. A semicircle may be de- scribed on mica or a glazed card, and graduated. The arms might also be made of stiff card for temporary use; but mica, bone, or metal is better. The arms should have the edges straight and accurately parallel, and be pivoted together. The instrument may be used like that last described, and will give approximate results, sufficiently near for distinguishing most minerals. The ivory rule accompanying boxes of mathematical instruments, having upon it a scale of sines for measur- ing angles, will answer an excellent purpose, and is as convenient as the arc.
In making such measurements it is important to have in mind the fact that—
1. The sum of the angles about a centre is 360°.
2. In a rhomb, as in a square, the sum of the plane angles is 360°.
In any polygon, the supplements of the angles equal 360°, whatever the number of sides. For example: in a square, the four angles are each 90°, and hence the supplements are 90°, and 4x90=360; again, in a regular hexagon the six angles are each 120, the supplements are 60°, and 6x60=360. So for all polygons, whether regular or irregular. In measuring the angles it is therefore convenient to take down the supplements of the angles. This principle is conveniently applied in the measurement of all the angles of a zone of planes around the crystal ; for the sum of all the supplements should be, as above, 360°, and if this result is not obtained there is error somewhere.
The reflecting goniometer affords a more accurate method of measuring crystals that have lustre, and may be iised with those of minute size. The principle on which this instrument is constructed will be understood from the annexed figure, representing a crystal, whose angle abc is required. The eye, look- ing at the face of the crystal be, observes a reflected image of m, in the direction Pn. On revolving the crystal till ab has the position of be, the same image will be seen again in the same direction Pn. As the crystal is turned, in this revolution, till abd has the present position of be, the angle dbc measures the number of degrees through which it is revolved. But dbc subtracted from 180° equals the angle of the crystal abc. The crystal is there- fore passed, in its revolution, through a number of degrees equal to the supplement of the required angle.
This angle, in the reflecting goniometer of Wollaston, one form of which is represented in the following figure, is measured by attaching the crystal to a graduated circle which revolves with it.
C is the graduated circle. The wheel, m, is attached to the main axis, and moves the graduated circle together with the adjusted crys- tal. The wjieel, n, is connected with an axis which passes through the main axis (which is hollow for the purpose), and moves merely the parts to which the crystal is attached, in order to assist in its adjust- ment. The contrivances for the adjustment of the crystal are at a, b, c, d, k. The screws, c, d, are for the adjustment of the crystal, and the slides, a, b, serve to centre it.
1/5 CRYSTALLOGRAPHY.
To use the instrument, it may be put on a stand or small table, with its base accurately horizontal, and the table placed in front of a win- dow, six to twelve feet off, with the plane of its circle at right angles to the window. A line must then be drawn below the window, near or on the floor, parallel to the bars of the window, and about as far from the eye as from the window-bar.
The crystal is attached to the movable plate & by means of wax, and so arranged that the edge of intersection of the two planes forming the
required angle shall be in a line with the axis of the instrument. This is done by varying its situation on the plate, or by means of the adjacent screws and slides.
When apparently adjusted, the eye must be brought close to the crystal, nearly in contact with it, and on looking into a face, part of the window will be seen reflected, one bar of which must be selected for the trial. If the crystal is correctly adjusted, the selected bar will appear horizontal, and on turning the wheel n, till this bar, as reflected, is observed to approach the dark line below seen in a direct view, it will be found to be parallel to this dark line, and ultimately to coincide with it. The eye for both observations should be held in
CRYSTALLOGKAPHY. 13
precisely the same position. If there is not a perfect coincidence, the adjustment must be altered until this coincidence is obtained. Con- tinue then the revolution of the wheel n, till the same bar is seen by reflection in the next face, and if here there is also a coincidence of the reflected bar with the dark line seen direct, the adjustment is com- plete; if not, alterations must be made, and the first face again tried. In an instrument like the one figured, the circle is usually graduated to twenty or thirty minutes, and, by means of the vernier, minutes and. half minutes are measured. After adjustment, 180° on the arc must be brought opposite 0, on the vernier, v. The coincidence of the bar and dark line is then to be obtained, by turning the wheel n. When obtained, the wheel m should be turned until the same coincidence is observed, by means of the next face of the crystal. If a line on the graduated circle now corresponds with 0 on the vernier, the angle is immediately determined by the number of degrees opposite this line. If no line corresponds with 0, we must observe which line on the vernier coincides with one on the circle. If it is the 18th on the vernier, and the line on the circle next below 0 on the vernier marks 125°, the required angle is 125° 18'; if this latter line marks 125° 20', the required angle is 125° 38'.
In the better instruments other improved methods of arrangement are employed; and in the best, often called Mitscherlich's goniometer, because first devised by him, there are two telescopes, one for passing a ray of light upon the adjusted crystal, having crossed hair-lines in its focus, and the other for viewing it, also with a hair-cross. With such an arrangement, the window-bar and dark line are unnecessary, the hair-crosses serving to fix the position of the crystal, and the telescope that of the eye. If the crystal is perfect in its planes, and the adjust- ment exact, the measurement, with the best instruments, will give the angle within 10".
Other goniometers have only the second of the two telescopes just alluded to, as is the case in the figure on page 12. This telescope gives a fixed position to the eye; and through it is seen a reflection of some distant object, which may be even a chimney-top. For the measure- ment the object, seen reflected in the two planes successively, is brought each time into conjunction with the hair cross. Exact ad- justment is absolutely essential, and with an instrument having the two telescopes, the first step in a measurement cannot be taken without it.
Only small, well-polished crystals can be accurately measured by the reflecting goniometer. If, when using the instrument without tele- scopes, the faces do not reflect distinctly a bar of the window, the flame of a candle or of a gas-burner, placed at some distance from the crystal, may be used by observing the flash from it with the faces in succession as the circle is revolved. A ray of sunlight from a mirror, received on the crystal through a small hole, may be employed in a similar way. But the results of such measurements will be only approximations. With two telescopes and artificial light, and with a cross-slit to let the light pass in place of the cross-hairs of the first of the above mentioned telescopes, this light cross will be reflected from the face of a crystal even when it is not perfect in polish, and quite good results may be obtained.
14 CRYSTALLOGRAPHY.
B. STRUCTURE. — Structure includes cleavage, a charac- teristic of crystals intimately connected with their forms and nature. It is the property, which many crystals have, of admitting of subdivision indefinitely in certain directions, and affording usually even, and frequently polished, sur- faces. The direction is always parallel with the planes of the axes, or with others diagonal to these.
The ease with which cleavage can be obtained varies greatly in different minerals, and in different directions in the same mineral. In a few species, like mica, it readily yields laminae thinner than paper, and in this case the cleavage is said to be eminent. Others, of perfect cleavage, cleave easily, but afford thicker plates, and from this stage there are all grades to that in which cleavage is barely dis- cernible or difficult. The cleavage surfaces vary in lustre from the most brilliant to those that are nearly dull. When cleavage in a mineral is alike in two or more directions, that is, is attainable in these directions with equal facility and affords surfaces of like lustre and character or mark- ing, this is proof that the planes in those directions are similar, or have similar relations to like axes. For ex- ample, equal cleavage in three directions, at right angles to one another, shows that the planes of cleavage correspond to the faces of the cube; so equal cleavage in two directions, in a prismatic mineral, shows that the planes in the two directions are those of a square prism, or else of a rhombic prism; and if they are at right angles to one another, that they are those of the former. This subject is further illus- trated beyond.
In the following pages (1) the Systems of Crystallization and the Forms and Structure of Crystals are first con- sidered; next, (2) Compound or Twin Crystals ; (3) Para- morphs; (4) Pseudomorphs ; and (5) Crystalline Aggre- gates.
SYSTEMS OF CRYSTALLIZATION-.
15
1. SYSTEMS OF CRYSTALLIZATION: FORMS AND STRUCTURE OF CRYSTALS.
The forms of crystals are exceedingly various, while the systems of crystallization, based on their mathematical dis- tinctions, are only six in number. Some of the simplest of the forms under these six systems are the prisms represented in the following figures; and by a study of these forms the
distinctions of the six systems will become apparent. These prisms are all four-sided, excepting the last, which is six- sided. In them the planes of the top and bottom, and any planes that might be made parallel to these, are called the basal planes, and the sides the lateral planes. An imaginary line joining the centres of the bases (c in Figs. 1 to 8) is called the vertical axis, and the diagonals a and 1), drawn in a plane parallel to the base, are the lateral axes.
Fig. 1 represents a cube. It has all its planes- square (like Fig. 9), and all its plane arid solid angles, right angles, and the three axes consequently cross at right angles (or, in other words, make rectangular intersections) and are equal. It is an example under the first of the systems of crystalli- zation, which system, in allusion to the equality of tho axes, is called the Isometric system, from the Greek for equal and measure.
Fig. 2 represents an erect or right square prism having
16 CRYSTALLOGKAPHY.
all its plane angles and solid angles rectangular. The base is square or a tetragon, and consequently the lateral axes are equal and rectangular in their intersections; but, unlike a cube, the vertical axis is unequal to the lateral. There are hence, in the square prism, axes of two kinds making rectangular intersections. The system is hence called, in allusion to the tetragonal base, the Tetragonal system.
Fig. 3 represents an erect or right rectangular prism, in which, also, the -plane angles and solid angles a^e rectangu-
9.
lar. The base is a rectangle (Fig, 10), and consequently the lateral axes, connecting the centres of the opposite lateral faces, are unequal and rectangular in their intersections ; and, at the same time, each is unequal to the vertical. There are hence three unlike axes making rectangular in- tersections ; and the system is called, in allusion to the three unlike axes and in allusion also to its including erect prisms having a rhombic base, the Orthorhombic system, orthos, in Greek, signifying straight or erect.
This rhombic prism is represented in Fig. 4. It has a rhombic base, like Fig. 11 ; the lateral axes connect the centres of the opposite lateral edges ; and hence they cross at right angles and are unequal, as in the rectangular prism. This right rhombic prism is therefore one in system with the right rectangular prism.
Fig. 5 represents another rectangular prism, and Fig. 6 another rhombic prism ; but, unlike Figs. 3 and 4, the prisms are inclined backward, and are therefore oblique prisms. The lateral axes (a, b) are at right angles to one another and unequal, as in the preceding system ; but the vertical axis is inclined to the plane of the lateral axes. It is inclined, however, to only one of the lateral axes, it being at right angles to the other. Hence, of the three angles of axial intersection, two are rectangular, namely, a on b, and c on b, while one is oblique, that is, c (the vertical axis) on a. In allusion to this fact, there being only one oblique angle,
SYSTEMS OF CRYSTALLIZATION. 17
this system is called the Monoclinic system, from the Gree*. for one and inclined.
Fig. 7 represents an oblique prism with a rhomboidal base "(like Fig. 12). The three axes are unequal and the three axial intersections are all oblique. The system is called the Triclinic system, from the Greek for three and inclined.
Fig. 8 represents a six-sided prism, with the sides equal and the base a regular hexagon. The lateral axes are here three in number. They intersect at angles of 60° ; and this is so, whether these lateral axes be lines joining the centres of opposite lateral planes, or of opposite lateral edges, Us a trial will show. The vertical axis is at right angles to the plane of the three lateral axes, inasmuch as the prism is erect or right. The base of the prism being a regular hexagon, the system is called the Hexagonal system.
The systems of crystallization are therefore :
I. The ISOMETRIC system : the three axes rectangular in intersections ; equal.
II. The TETRAGONAL system : the three axes rectangular in intersections ; the two lateral axes equal, and unequal to the vertical.
III. The ORTHORHOMBIC system : the three axes rectan- gular in intersections, and unequal.
IV. The MONO-CLINIC system : only one oblique inclina- tion out of the three made by the intersecting axes ; the three axes unequal.
V. The TRICLINIC system : all the three axes obliquely inclined to one another, and unequal.
VI. The HEXAGONAL system : the vertical axis at right angles to the lateral ; the lateral three in number, and in- tersecting at angles of 60°.
These six systems of crystallization are based on mathe- matical distinctions, and the recognition of them is of great value in the study and description of crystals. Yet these distinctions are often of feeble importance, since they some- times separate species and crystalline forms that are very close in their relations. There are forms under each of the systems that differ but little in angles from some of other systems : for example, square prisms that vary but slightly from the cubic form ; triclinic that are almost iden- tical with monoclinic forms ; hexagonal that are nearly cu- bic. Consequently it is found that the same natural group 2
18
CRYSTALLOGRAPHY.
of minerals may include both orthorhombic and mono- clinic species, as is true of the Hornblende group ; or mono- clinic and triclinic, as is the fact with the Feldspar group,, and so on. It is hence a point to be remembered, when the affinities of species are under consideration, that differ- ence in crystallographic system is far from certain evidence that any species are fundamentally or widely unlike.
I. THE ISOMETRIC SYSTEM.
1, Descriptions of Forms. — The following are figures of some of the forms of crystals under the isometric system:
l.
The first is the cube or hexahedron, already described. Besides the three cubic axes, there are equal diagonals in two other directions ; one set connecting the apices of the diagonally opposite solid angles, four in number (because the number of such angles is eight), and called the octahe- dral axes ; and another set connecting the centres of the diagonally opposite edges, six in number (because the num- ber of edges is twelve), and called the dodecahedral axes.
Fig. 2 represents the octahedron, a solid contained under eight equal triangular faces (whence the name from the Greek eight soldi face), and having the three axes like those in the cube. Its plane angles are 60°; its interfacial angles, that is, the inclination of planes 1 and 1 over an intervening
ISOMETRIC SYSTEM. 19
edge (usually written 1 A 1) = 109° 28' (more exactly 109° 28' 16"); and 1 on 1 over a solid angle, 70° 32'.
Fig. 3 is the dodecahedron, a solid contained under twelve equal rhombic faces (whence the name from the Greek for twelve and face). The position of the cubic axes is shown in the figure. It has fourteen solid angles ; six formed by the meeting of four planes, and eight formed by the meet- ing of three. The interfacial angles (or i on an adjoining i) are»120°; i on * over a four-faced solid angle = 90°.
Fig. 4 is a trapezoliedron, a solid contained under 24 equal trapezoidal faces. There are several different trapezohe- drons among isometric crystalline forms. The one here figured, which is the common one, has the angle over the edge B, 131° 49', and that over the edge C, 146° 27'. A trapezohedron is also called a tetragonal trisoctahedron, the faces being tetragonal or four-sided, and the number of faces being 3 times 8 (tris, octo, in Greek).
Fig. 5 is another trisoctahedron, one having trigonal or three-sided faces, and hence called a trigonal trisoctaUe- dron. Comparing it with the octahedron, Fig. 2, it will be seen that three of its planes correspond to one of the octa- hedron. The same is true also of the trapezohedron.
Fig. 6 is a tetrahexalicdron, that is, a 4 X 6-f aced solid, the faces being 24 in number, and four corresponding to each face of the cube or hexahedron (Fig. 1).-
Fig. 7 is a hexoctahedron, that is, a 6 X 8-faced solid, a pyramid of six planes corresponding to each face in the octahedron, as is apparent on comparison. There are dif- ferent kinds of hexoctahedrons known among crystallized isometric species, as well as of the two preceding forms. In each case the difference is not in number or general ar- rangement of planes, but in the angles between the planes, as explained beyond.
But these simple forms very commonly occur in combina- tion with one another ; a cube with the planes of an octahe- dron and the reverse, or with the planes of any or all of the other kinds above figured, and many others besides. More- over, all stages between the different forms are often repre- sented among the crystals of a species. Thus between the cube and octahedron occur the forms shown in Figs. 8 to 11. Fig. 12 is a cube ; Fig. 8 represents the cube with a plane on each angle, equally inclined to each cubic face; 9, the same, with the planes on the angles more enlarged
20
CRYSTALLOGRAPHY.
the cubic faces reduced in size ; and then 10, the octahe- dron, with the cubic faces quite small; and Fig. 11, the octahedron, the cubic faces having disappeared altogether. This transformation is easily performed by the student with cubes cut out of chalk, clay, or a potato. It shows the fact
8.
that the cubic axes (Fig. 12) connect the apices of the solid angles in the octahedron.
Again, between a cube and a dodecahedron there occur forms like Figs. 13 and 14 ; Fig. 12 being a cube, Fig. 13 the same, with planes truncating the edges, each plane being equally inclined to the adjacent cubic faces, and Fig. 14 an- other, with these planes on the edges large and the cubic faces small ; and then, when the cubic faces disappear by further enlargement of the planes on the edges, the form is a dodecahedron, Fig. 15. The student should prove this transformation by trial with chalk or some other material, and so for other cases mentioned beyond. The surface of such models in chalk may be made hard by a coat of muci- lage or varnish.
Again, between a cube and a trapezohedron there are the forms 17 and 18 ; 16 being the cube ; IjB, cube with three planes placed symmetrically on each angle ; 18, the same with the cubic faces greatly reduced (but also with small octahedral faces), and 19, the trapezohedron, the cubic faces having disappeared.
Again, Fig. 20 represents a cube with three planes on each
ISOMETRIC SYSTEM.
angle, which, if enlarged to the obliteration of the faces of the cube, become the trigonal trisoctahedron, Fig. 21. So
again, Fig. 22 represents a cube with six faces on each angle, which, if enlarged to the same extent as in the last, would X become the hexoctahedron, Fig. 23.
Again, Fig. 25 is a form between the octahedron (Fig. 24)
and dodecahedron (Fig. 26); and Figs. 27 and 28 are forms between the dodecahedron, Fig. 26, and trapezohedron, Fig. 29.
CRYSTALLOGRAPHY.
Again, Fig. 30 is a form between a cube (Fig. 16) and a tetrahexahedron, Fig. 31; Fig. 32, a form between an octa- hedron, Fig. 24, and a tetratiexahedron, Fig. 31; Fig. 33, a
30. 3l!*L 82.
-h-
form between an octahedron and a trigonal trisoctahedron, Fig. 34; Fig. 35, a form between a dodecahedron (planes ?')
33. 34. 35.
and a tetrahexahedron; Fig. 36, a form between the dodeca- hedron and a hexoctahedron, Fig. 37.
Fig. 38 represents a cube with planes of both the octa- hedron and dodecahedron.
2. Positions of planes with reference to the axes. Lettering of figures. — The numbers by which the planes in the above figures, and others of tife work, are lettered, indicate the positions of the planes with reference to the axes, and exhibit the mathematical symmetry and ratios in crystallization. In the figure of the cube (Fig. 1) the three axes are represented; the lateral semi-axis which meets the front planes in the figure is lettered 4; that meeting the side plane to the right b, and the vertical axis c, and the other halves of the same axes respectively -a, -I, -c. By a study of the positions of the planes of the cube and other forms with reference to these axes, the following facts will become apparent.
ISOMETKIC SYSTEM. 23
In the cube (Fig. 1) the front plane touches the extremity of axis a, but is parallel to axes b and c. When one line or plane is parallel to another they do not meet except at an infinite distance, and hence the sign for infinity is used to express parallelism. Employing i, the initial of infinity, as this sign, and writing c, b, a, for the semi-axes so lettered, then the position of this plane of the cube is indicated by the expres- sion ic : ib : la. The top and side-planes of the cube meet one axis and are parallel to the other two, and the same expression answers for each, if only the letters a, b, c, be changed to correspond with their positions. The opposite planes have the same expressions, except that the c, b, a, will refer to the opposite halves of the axes and be -c, -b, -a.
In the dodecahedron, Fig. 15, the right of the two vertical front planes i meets two axes, the axes a and T), at their extremities, and is parallel to the axis c. Hence the position of this plane is expressed by ic : Ib : la. So, all the planes meet two axes similarly and are parallel to the third. The expression answers as well for the planes i in Figs. 13, 14, as for that of the dodecahedron, for the planes have all the same relation to the axes.
In the octahedron, Fig. 11, the face 1 situated to the right above, like all the rest, meets the axes a, b, c, at their extremities; so that the expression -Ic :lb :la answers for all.
Again, in Fig. 17 (p. 21) there are three planes, 2-2, placed symmet- rically on each angle of a cube, and, as has been illustrated, these are the planes of the trapezohedron, Fig. 19. The upper one of the planes 22 in these figures, when extended to meet the axes (as in Fig. 19), intersects the vertical c at its extremity, and the others, a and b, at twice their lengths from the centre. Hence the expression for the plane is Ic : 2b : 2a. So, as will be found, the left-hand plane 2-2 on Fig. 17, will have the expression 2c : Ib : 2a; and the right-hand one, 2c : 2b : la. Further, the same ratio, by a change of the letters for the semi-axes, will answer for all the planes of the trapezohedron.
In Fig. 20 there are other three planes, 2, on each of the angles of a cube, and these are the planes of the trisoctahedron in Fig. 21. The lower one of the three on the upper front solid angle, would meet if extended, the extremities of the axes a and b, while it would meet the vertical axis at twice its length from the centre. The expression 2c : Ib : la indicates, therefore, the position of the plane. So also, Ic : Ib : 2a and Ic : 2b : la represent the positions of 'he other two planes ad- joining; and corresponding expressions may be similarly obtained for all the planes of the trisoctahedron.
Again, in Fig. 30, of the cube with two planes on each edge, and in Fig. 31, of the tetrahexahedron bounded by these same planes, the left of the two planes on the front vertical edge of Fig. 30 (or the corre- sponding plane on Fig. 31) is parallel to the vertical axis; its intersections with the lateral axes, a and b, are at unequal distances from the centre, expressed by the ratio 2b : la. This ratio for the plane adjoining on the right is Ib : 2a. The position of the former is expressed by the ratio ic:2b-: la, and for the other by 'c : Ib : 2a. Thus, for each of the planes of this -tetrahexahedron the ratio between two axes is 1 : 2, while the plane is parallel to the third axis.
Again, in Fig. 22, of the cube with six planes on each solid angle, and in the hexoctahedron in Fig. 23, made up of such planes, each of the planes when extended so that it will meet one axis at once its
24 CRYSTALLOGRAPHY.
length from the centre, will meet the other axes at distances expressed by a constant ratio, and the expression for the lower right one of the six planes will be 3c : f & : la. By a little study, the expressions for the other five adjoining planes can be obtained, and so also those for all the 48 planes of the solid.
In the isometric system the axes, a, b, c, are equal, so that in the general expressions for the planes these letters may be omitted; the expressions for the above-mentioned forms thus become —
Cube (Fig. 1), i : 1 : *. Tetrahexahedron (Fig. 5), i : 1 : 2.
Octahedron (Fig. 2), 1 : 1 : 1. Trigonal trisoctahedron (Fig. 6), Dodecahedron (Fig. 3), 1 : 1 : i. 2:1:1.
Trapezohedron (Fig. 4), 2 : 1 : 2. Hexoctahedron (Fig. 7), 3 : 1 : f .
Looking again at Fig. 17, representing the cube with planes of the trapezobedron, 2 : 1 : 2, it will be perceived that there might be a tra- pezohedron having the ratios H : 1 : 1|, 3:1:3, 4:1:4, 5:1:5, and others; and, in fact, such trapezohedrons occur among crystals. So also, besides the trigonal trisoctahedron 2:1:1 (Fig. 21), there might be, and there in fact is, another corresponding to the expression 3 1:1; and still others are possible. And besides the hexoctahedron
1 : f (Fig. 23), there are others having the ratios 4 : 1 : 2, 4 : 1 :
1 : |, and so on.
In the above ratios, the number for one of the lateral axes is always made a unit, since only a ratio is expressed; omitting this in the ex- pression, the above general ratios become: for the cube, i : i; for the octahedron, 1:1; dodecahedron, 1 : i ; trapezohedron, 2:2; tetra- hexahedron, i : 2 ; trigonal-trisoctahedrou, 2:1; and hexoctahedron, 3 : f . In the lettering of the figures these ratios are put on the planes, but with the second figure, or that referring to the vertical axis, first, Thus the lettering on the hexoctahedron (Fig. 23), is3-|; on the trigonal trisoctahedron (Fig. 21) is 2, the figure 1 being unnecessary; on the tetrahexahedron (Fig. 31), i-2 ; on the trapezohedron (Figs. 4 and 19), 2-2 ; on the dodecahedron (Fig. 15), i ; on the octahedron, 1 ; on the cube, i-i, in place of which H is used, the initial of hexahedron. In the printed page these symbols are written with a hyphen in order to avoid occasional ambiguity, thus 3-f , i-2, 2-2, etc. Similarly, the ratios for all planes, whatever they are, may be written. The numbers are usually small, and never decimal fractions.
The angle between the planes i-2 (or i : 1 : 2) and H, in Fig. 30, page 22, may be easily calculated, and the same for any plane of the series i-n (i : 1 : n). Draw the right-angled triangle, ADC, as in the annexed figure, making the vertical side, .CD, twice that of AC, the base; that is, give them the same ratio as in the axial ratio for the plane. If AC — 1, CD = 2. Then, by trigonometry, making AC the radius, l:E::2:tan DAG ; or 1 : R :: 2 : cot ADC. Whence tan DAG = cot ADC = 2. By add- ing to 90°, the angle of the triangle obtained by working the equation, we have the inclination of the basal plane H, on the plane i-2. So in all cases, whatever the value of n that value equals the tangent of the basal angle of the triangle (or the cotangent of the angle at the vertex), and from this the inclination to the cubic faces is
ISOMETRIC SYSTEM. 25
directly obtained by adding 90°. If n = 1, then the ratio is 1 : 1, as in ACS, and each angle equals 45°, giving 185° for the inclination on either adjoining cubic face.
Again if the angles of inclination have been obtained by measure- ment, the value of n in any case may be found by reversing the above calculation; subtracting 90° from the angle, then the tangent of this angle, or the cotangent of its supplement, will equal n, the tangents varying directly with the value of n.
In the case of planes of the m : 1 : 1 series (including 1:1:1, 2 : 1:1, etc.), the tangents of the angle between a cubic face in the same zone and these planes, less 90°, varies with the value of m. In the case of the plane 1 (or 1 : 1 : 1), the angle between it and the cubic face is 125° 16'. Substracting 90°, we have 35° 16'. Draw a right-angled triangle, OBG, with 35° 16' as its vertex angle. BO has the value of ic, or the semi-axis of the cube. Make DC = 2BG. Then, while the angle OBG has the value of the inclination on the cubic face less 90° for the plane 1 : 1 : 1, ODG has the same for the plane 2:1:1. Now, making 00 the radius, and taking it as unity, BC is the tangent of BOO, or cot OBO. So D0 = 2BG is the tan- gent of DOG, or cot ODG. By lengthening the side CD (= 2BC or 2c) it may be made equal to SBC = 3c, its value in the case of the plane 3:1:1; or to 45(7 = 4c, its value in the case of the plane 4:1:1; or mBO = me for any plane in the series m : 1 : 1 ; and since in all there will be the same relation between the vertical and the tangent of the angle at the base (or the cotangent of the angle at the vertex), it follows that the tangent varies with the value of m. Hence, knowing the value of the angle in the case of the form 1 (1:1: 1), the others are easily calculated from it.
BC being a unit, the actual value of OG is $ V2~, or VJ it being half the diagonal of a square, the sides of which are 1, and from this value the angle 35° 16' might be obtained for the angle OBG.
The above law (that, for a plane of the m : 1 : 1 series, the tangent of its inclination on a cubic face lying in the same zone, less 90°, varies with the value of m, and that it may be calculated for any plane m : 1 : 1 from this inclination in the form 1:1: 1), holds also for planes in the series m : 2 : 1, or m : 3 : 1, or any m : n : 1. That is, given the inclination of 0 on 1 : n : 1, its tangent doubled will be that of 2 : n : 1, or trebled, that of 3 : n : 1, and so on ; or halved, it will be that of the plane £ : n : 1, which expression is essentially the same as 1 : 2n : 2.
These examples show some of the simpler methods of applying ma- thematics in calculations under the isometric system. The values of the axes are not required in them, because a = b = c = l.
3. Hemihedral Crystals. — The forms of crystals described' above are called liololiedral forms, from the Greek for all and face, the number of planes being all that full symmetry requires. The cube has eight similar solid angles — similar, that is, in the enclosing planes and plane angles. Con-
.26
CRYSTALLOGRAPHY.
sequently the law of full symmetry requires that all should have the same planes and the same number of planes ; and this is the general law for all the forms. This is a conse- quence of the equality of the axes and their rectangular in- tersections.
But in some crystalline forms there are only half the number of planes which full symmetry requires. In Fig. 39 a cube is represented with an octahedral plane on half, that is, four, of the solid angles. A solid angle having such
40.
41.
42.
a plane is diagonally opposite to one without it. The same form is represented in Fig. 40. only the cubic faces are the smallest ; and in Fig. 41 the simple form is shown which is made up of the four octahedral planes. It is a tetrahedron or regular three-sided pyramid. If the octahedral faces of Fig. 39 had been on the other four of the solid angles of the cube, the tetrahedron made of those planes would have been that of Fig. 42 instead of Fig. 41.
Other hemihedral forms are represented in Figs. 43 to 45. Fig. 43 is a hemihedral form of the trapezohedron, Fig.
4, p. 18; Fig. 44, hemihedral of the hexoctahedron, Fig. 7, or a hemi-hexoctahedron; and Fig. 45 is a combination of the tetrahedron (plane 1) and hemi-hexoctahedron.
In these forms Figs. 41-44, no face has another parallel to it ; and consequently they are called inclined hemihe- drons.
Fig. 46 represents a cube with the planes of a tetrahexa-
ISOMETRIC SYSTEM.
hedron, as already explained. In fig. 47, the cube has only one of the planes i-2 on each edge, and therefore only twelve in all ; and hence it affords an example of hemihe- drism — a kind that is presented by many crystals of pyrite.
Fig. 48 is the hemihedral form resulting when these twelve
planes i-2 are extended to the obliteration of the cubic
faces ; and Fig. 49 is another, made of the
other twelve of these planes. Again, in Fig.
50, a cube is represented having only three
out of the six planes of Fig. 22, and this is
another example of hemihedrism. These
kinds differ from the inclined hemihedrons
in having opposite, parallel faces, and hence
they are called parallel hemihedrons.
4. Internal Structure of Isometric Crystals, or Cleavage.
— The crystals of many isometric minerals have cleavage, or a greater or less capability of division in directions situated symmetrically with reference to the axes. The cleavage directions are parallel either to the faces of the cube, the octahedron, or the dodecahedron. In galenite (p. 160) there is easy cleavage in three directions parallel to the faces of the cube ; in fluorite (p. 227), in four directions parallel to the faces of the octahedron ; in sphalerite (p. 170)^ in six directions parallel to the faces of the dodecahedron. These cleavages are an important means of distinguishing the species.
The three cubic cleavages are precisely alike in the ease with which cleavage takes place, and in the kinds of surface obtained ; and so is it with the four in the octahedral direc- tions, and the six in the dodecaHedral. Occasionally cleav- ages of two of These systems occur in the same mineral ; that is, for example, parallel both to the faces of the cube and of the octahedron ; but when .so, those of one system are
CRYSTALLOGRAPHY.
much more distinct than those of the other, and cleavage surfaces in the two directions are quite unlike as to smooth- ness and lustre.
5. Irregularities of Isometric Crystals. — A cube has its faces precisely equal, and so it is with each of the forms rep- resented in Figs. SJ to 7, p. 18. This perfect symmetry is almost never found in actual crystals.
51.
52.
53.
H
H
A cubic crystal has generally the form of a square prism (Fig. 51 a stout one, Fig. 52 another long and slender), or a rectangular prism (Fig. 53). In such cases the crystal may still be known to be a cube ; because, if so, the kind of sur-
55. "
;£ace_ and kind of lustre pnjhe six faces will be precisely alike : and if f nere Is cubic_cTeavage it will bejjexactly equal in facility in three "rectangular directions ; or if there is cleavage in four, or six, directions, it will be equal in
ISOMETRIC SYSTEM. 29
degree in the four, or the six, directions, and have mutual inclinations corresponding with the angles of the octahedron or dodecahedron ; and thus the crystal will show that it is isometric in system.
The same shortening or lengthening of the crystal often disguises greatly the octahedron, dodecahedron, and other forms. This is Illustrated in the following figures : Fig. 54 shows the form of the regular octahedron ; 55, an octahe- dron lengthened horizontally ; 56, one shortened parallel to one of the pairs of faces ; 57, one lengthened parallel to another pair, the ultimate result of which obliterates two of the faces, and places an acute solid angle in place of each. The solid is then six-sided, and has rhombic faces whose plane angles are 120° and 60°. The following figures
58.
illustrate corresponding changes in the dodecahedron (Fig. 58). In Fig. 59 the dodecahedron is lengthened vertically, making a square prism with four-sided pyramidal termina- tions. In 60, it is shortened vertically. In 61 the dodeca- hedron is lengthened obliquely in the direction of an octa- hedral axis, and in 62 it is shortened in the same direction, making six-sided prisms with trihedral terminations.
30 CRYSTALLOGRAPHY.
So again in the trapezohedron there are equally deceptive forms arising from elongations and shortenings in the same two directions.
These distortions change the relative sizes of planes,, but not the values of angle_s. In crystals of the several forms" represented in Figs. 54 to 57, the inclinations are the same as in the regular octahedron. There is the same constancy of angle in other distorted crystals.
Occasionally, as in the diamond, the planes of crystals are convex; and then, of course, the angles will differ from the"true angle. It is important, in order to meet the diffi- culties in the way of recognizing isometric crystals, to have clearly in the mind the precise aspect of an equilateral tri- angle, which is the shape of a face of an octahedron; the form of the rhombic face of the dodecahedron; and the form of the trapezoidal face of a trapezohedron. With these distinctly remembered, isometric crystalline forms that are much obscured by distortion, or which show only two or three planes of the whole number, will often be easily recognized.
Crystals in this system, as well as in the others, often have their facesjstrjated., or else_jough withjDoints. This is generally owmgTxTa tendencylhTKe forming crystal to 63 make two different planes at the same time,
or rather an oscillation between the condi- tion necessary for making one plane and that for making another. Fig. 63 represents a cube of pyrite with striated faces. As the faces of a cube are equal, the _striat ions, are alike on all. It will be noted that the stria- tions of adjoining faces are at right angles to one another. The little ridges of the striated surfaces are made up of planes of the pentagonal dodecahedron (Fig. 49, p. 27), and they arise from an oscillation in the crystallizing conditions between that which, if acting alone, would make a cube, and that which would make this hemihedral dodecahedron. Again, in magnetite, oscillations between the octahedron and dodecahedron produce the striations in Fig. 64.
Octahedral crystals of fluorite often occur with the faces
made up of evenly projecting solid angles of a cube, giving
them rough instead of polished planes. This has arisen
from oscillation between octahedral and cubic conditions.
In some cases crystals are filled out only along the diago-
TETRAGONAL SYSTEM. 31
nal planes. Fig. 65 represents a crystal of common salt of this kind, having pyramidal depressions in place of the regular faces. Octahedrons of gold sometimes occur with
65.
MAGNETITE. COMMON SALT.
three-sided pyramidal depressions in place of the octahedral faces. Such forms sometimes result also when crystals are eroded by any cause.
II. TETRAGONAL SYSTEM.
1, Descriptions of Forms. — In this system (1) the axes cross at right angles; (2) the vertical axis is either longer or shorter than the lateral; and (3) the lateral axes are equal.
The following figures represent some of the crystalline forms. They are very often attached by one extremity to the supporting rock and have perfect terminating planes only at the other. Square prisms, with or without pyra- midal terminations, square octahedrons, eight-sided prisms, eight-sided pyramids, and especially combinations of these, are the common forms. Since the lateral axes are equal, the four lateral planes of the square prisms are alike in lustre and surface-markings. For the same reason the symmetry of the crystal is throughout by fours; that is, the number of similar pyramidal planes at the extremity is either four or eight; and they show that they are similar by being exactly alike in inclination to the basal plane as well as alike in lustre.
There are two distinct square prisms. In one (Fig. 10) the axes connect the centres of the lateral faces. In the
32
CRYSTALLOGRAPHY.
other (Fig. 12) they connect the centres of the lateral edges. In Fig. 11 the two prisms are combined; the figure shows that the planes of one truncate the lateral edges of the
1.
IDOCRASE.
APOPHTLLITE. 11. 12.
15.
other, the interfacial angle between adjoining planes being 135°. Figs. 2, 3, 4, 7, are of others having planes of both prisms. In Fig. 13 one prism is represented within the other.
Fig. 14 represents an eight-sided prism, and Fig. 15 a combination of a square prism
!t-*) with an eight-sided prism i-%). Another example of this is shown in Fig. 4, and also in Fig. 9, the planes i-2 in one, and i-3 in the other.
The basal plane in these prisms is an independent plane, because the vertical axis is not equal to the
TETRAGONAL SYSTEM.
33
lateral, and hence it almost always differs in lustre and smoothness from the lateral.
Like the square prisms, the square octahedrons are in two series, one set (Fig. 16) having the lateral or basal edges parallel to the lateral axes, and these axes connecting the centres of opposite basal edges, and the other (Fig. 17) having them diagonal to the axes, these axes connecting the apices of the opposite solid angles, as in the isometric octahedron. There may be, on the same crystal, faces of several octahedrons of these two series, differing in having their planes inclined at different angles to the basal plane.
16. 17. 18. 19.
In Figs. 5 and 7 planes of one of these pyramids terminate the prism, and in Figs. 6 and 8 the planes of two. In Figs. 1 to 3 there are planes of the same octahedron, but com- bined with the basal plane 0; and in Fig. 4 there are planes of two, with 0. In Fig. 9 there are planes of the same octahedron, with planes of a square prism (i-i), and of an eight-sided prism (i-2). In Fig. 18 there is the prism i-i combined with two octahedrons, and the basal plane 0; and in 19 the planes of one octahedron with the prism /. Fig. 20 represents an eight-sided double pyramid, made
21.
of equal planes, equally inclined to the base; and Fig. 21, the same planes on the square prism i-i. The small planes, 3
34 CRYSTALLOGRAPHY.
in pairs, on Fig. 8, are of this kind. In Fig. 22 the small planes 3-3 of Fig. 8 occur alone, without planes of the four- sided pyramids, and therefore make the eight-sided pyra- mid, 3-3.
The solid made of two such eight-sided pyramids placed base to base has the largest number of similar planes possible in the tetragonal system, while the largest number in the isometric system (occurring in the hexoctahedron) is forty- eight.
2, Positions of the planes with reference to the Axes. — Let- tering of planes. In the prism Fig. 10, the lateral planes are parallel to the vertical axis and to one lateral axis, and meet the other lateral axis at its extremity. The expression for it is hence (c standing for the vertical axis and a, b for the lateral) ic : ib : \a, i, as before, standing for in-
finitj^and indicating parallelism. 23. For the prism of Fig. 12, the
prismatic planes meet the two lateral axes at their extremities, and are parallel to the vertical, and hence the expression for them is ic : Ib : la. In the an- nexed figure the two bisecting lines, a -a and b -b, represent the lateral axes; the line st stands for a section of a lateral plane of the first of these prisms, it being
parallel to one lateral axis and meeting the other at its extremity, and ab for that of the second, it meeting the two at their extremities. In the eight-sided prisms (Figs. 14, 15), each of the lateral planes is parallel to the vertical axis, meets one of the lateral axes at its extrem ity, and would meet the other axis if it were prolonged to two or three or more times its length. The line ao, in Fig. 23, has the position of one of the eight planes; it meets the axis b at o, or twice its length from the centre; and hence the expression for it would be ic : 2b : \a, or, since b = a, ic : 2 : 1, which is a general expression for each of the eight planes. Again, ap has the position of one of the eight planes of another such prism; and since Op is three times the length of Ob, the expression for the plane would be ic : 3 : 1. So there may be other eight-sided prisms; and, putting n for any possible ratio, the expres- sion ic : n : 1 is a general one for all eight-sided prisms in the tetra- gonal system.
A plane of the octahedron of Fig. 16 meets one lateral axis at its extremity, and is parallel to the other, and it meets the vertical axis c at its extremity; its expression is consequently (dropping the letters a and b, because these axes are equal) Ic : i : 1. Other octahedrons in the same vertical series may have the vertical axis longer or shorter than axis c; that is, there may be the planes 2c : i : 1, Qc : i : 1, 4c : i : 1, and so on; or {c : i : 1, ic : i : 1, and so on; or, using m for any co- efficient of c, the expression becomes general, me : i : 1. When w = 0 the vertical axis is zero, and the plane is the basal plane 0 of the
TETRAGONAL SYSTEM.
35
prism; and when m = infinity, the plane is ic : i : 1, or the vertical plane of the prism in the same series, i-i, Fig. 10.
The planes of the octahedron of Fig. 17 meet two lateral axes at their extremities, and the vertical at its extremity, and the expression for the plane is hence Ic : 1 : 1. Other octahedrons in this series will have the general expression- we : 1 : 1, in which m may have any value, not a decimal, greater or less than unity, as in the preceding case. When in this series m — infinity, the plane is that of the prism ic : 1 : 1, or that of Fig. 12.
In the case of the double eight-sided pyramid (Figs. 20, 21, 22), the planes meet the two lateral axes at unequal distances from the centre; and also meet the vertical axis. The expression may be 2c : 2 : 1, 4c : 2 : 1, 5c : 3 : 1, and so on; or, giving it a general form, me : n : 1.
In the lettering of the planes on figures of tetragonal crystals, the first number (as in the isometric and all the other systems) is the co- efficient of the vertical axis, and the other is the ratio of the other two, and when this ratio is a unit it is omitted.
The expressions and the lettering for the planes are then as follows:
Expressions. For square prisms ........... j *; * ; { ; \
For eight-sided prisms .......... ic : n : 1
For octahedrons ............ j %'
For double eight-sided pyramids,
me
i : 1 1:1
n : 1
Lettering.
i-n m-i m m-n
24.
The symbols are written without a hyphen on the figures of crystals. On Fig. 14, the plane i-n is that particular i-n in which n = 2, or i-2. In Fig. 21 the planes of the double eight-sided pyramid, m-n, have m — 1 and n = 2 (the expression being 1:2:1), and hence it is let- tered 1-2. In Fig. 8 and in Fig. 22 it is the one in which m = 3 and n = 3 (the expression being 3:3: 1), and hence the lettering 3-3.
The length of the vertical axis c may be calculated as follows, pro- vided the crystal affords the required angles:
Suppose, in the form Fig. 18, the inclination of 0 on plane \-i to have been found to be 130°, or of i-i on the same plane, 140° (one fol- lows from the other, since the sum of the two, as has been explained, is necessarily 270C). Subtracting 90°, we have 40° for the inclination of the plane on the vertical axis c, or 50° for the same on the lateral axis a, or the basal section. In the right-angled triangle, OBC, the angle OBC equals 40°. If OC be taken as a — 1, then BC will be the length of the vertical axis c\ and its value may be obtained by the equation cot 40° = BC, or tan 50° = BC.
On Fig. 18 there is a second octahedral plane, lettered \-it and it might be asked, Why make this plane i-i, instead of I-/? The determination on this point is more or less arbitrary. It is usual to assume that plane as the unit plane in one or the other series of octahedrons (Fig. 16 or Fig. 17) which is of most common occur- rence, 6r that which will give the simplest symbols to the crystalline
36 CRYSTALLOGRAPHY.
forms of a species; or that which will make the vertical axis nearest to unity; or that which corresponds to a cleavage direction.
The value of the vertical axis having been thus determined from 1-&, the same may be determined in like manner for \-i in the same figure (Fig. 18). The result would be a value just half that of BC. Or if there were a plane 2-i, the value obtained would be twice BC, or BD in Fig. 24; the angle ODO-\-9Q° would equal the inclination of 0 on 2-i. So for other planes in the same vertical zone, as 3-i, 4-&, or any plane m-i.
If there were present several planes of the series m-i, and their in- clinations to the basal plane 0 were known, then, after subtracting from the values 90°, the cotangents of the angles obtained, or the tangents of their complements, will equal m in each case; that is, the tangents (or cotangents) will vary directly with the value of m. The logarithm of the tangent for the plane 1-tf, added to the logarithm of 2, will equal the logarithm of the tangent for the plane 2-2, and so on.
The law of the tangents for this vertical zone m-i holds for the planes of all possible vertical zones in the tetragonal system. Further, if the square prism were laid on its side so that one of the lateral planes became the base, and if zones of planes are present on it that are ver- tical with reference to this assumed base, the law of the tangents still holds, with only this difference to be noted, that then one of the late- ral axes is the vertical. It holds also for the orthorhombic system, no matter which of the diametral planes is taken for the base, since all the axial intersections are rectangular. It holds for the monoclinic system for the zone of planes that lies between the axes cand b and that between the axes a and b, since these axes meet at right angles, but not for that between c and a, the angle of intersection here being oblique. It holds for all vertical zones in the hexagonal system, since the basal plane in this system is at right angles to the vertical axis. But it is of no use in the triclinic system, in which all the axial inter- sections are oblique.
The value of the vertical axis c may be calculated also from the in- clination of 0 on 1, or of /on 1. See Fig. 2, and compare it with Fig. 17. If the angle /on 1 equals 140°, then, after subtracting 90°, we have 50° for the basal angle in the triangle OCB, Fig. 24 ; or for half the interfacial angle over a basal edge— edge Z— in Fig. 17. The value of c may then be calculated by means of the formula
c = tan \Z y£,
by substituting 50° for \Z and working the equation. For any octahedron in the series m, the formula is
me = tan \Z v/|
Z being the angle over the basal edge of that octahedron. Ifm = 2, then c = £ (tan \Z y$). Further, m = (tan IZ |/i)-f- c.
The interfacial angle over the terminal edge of any octahedron m may be obtained, if the value of c is known, by the formulas
me = cot 8 cos s = cot iX
X being the desired angle (Fig. 17). The same for any octahedron m-i may be calculated from the formulas
TETRAGONAL SYSTEM. 37
/
me = cot « cos s =cos iYy2
Y being the desired angle (Fig. 16).
For other methods of calculation reference may be made to the " Text-book of Mineralogy," or to some other work treating of mathe- matical crystallography.
3. Hemihedral Forms. — Among the hemihedral forms under the tetragonal system there is a tetrahedron,, called a sphenoid (Fig. 25 or 26), and also forms in which only half of the sixteen planes of the double eight-sided pyramid, or half the eight planes of an eight-sided prism — those alter-
25. 26. 27.
nate in position — are present (Figs. 27, 28). In Fig. 27 the absent planes are those of half the pairs of planes; and in Fig. 28 they include one of each of the pairs, as will be seen on comparing these figures with Fig. 21.
4. Cleavage. — In this system cleavage may occur parallel to the sides of either of the square prisms; parallel to the basal plane; parallel to the faces of a square octahedron; or in two of these directions at the same time. Cleavage parallel to the base and that parallel to a prism are never equal, so that such prisms need not be confounded with distorted cubes.
5. Irregularities in Crystals. — The square prisms are very often rectangular instead of square, and so with the octahedrons. But, as elsewhere among crystals, the angles remain constant. When forms are thus distorted, the four prismatic planes will have like lustre and surface markings, and thus show that the faces are normally equal and tl^e lateral axes therefore equal. If the plane truncating the edge of a prism makes an angle of precisely 135° with the faces of the prism, this is proof that the prism is square, or that the lateral axes are equal, since the angle between a diagonal of a square and one of its sides is 45°, and 135° is the supplement of 45°.
6. Distinctions. — The tetragonal prisms have the base
38
CRYSTALLOGRAPHY.
different in lustre from the sides, and planes on the basal edges different in angle from those on the lateral, and thus they differ from isometric forms. The lateral edges may be truncated, and the new plane will have an angle of 135° with those of the prism, in which they differ from ortho- rhombic forms, while like isometric. The extremities of the prism, if it have any planes besides the basal, will have them in fours or eights, each of the four, or of the eight, inclined to the base at the same angle. When there is any cleavage parallel to the vertical axis, it is alike in two di- rections at right angles with one another. The lateral planes of either square prism are alike in lustre and mark- ings.
III. ORTHORHOMBIC SYSTEM.
1. Descriptions of Forms. — The crystals under the or- thorhombic system vary from rectangular to rhombic prisms and rhombic octahedrons, and include various combinations of such forms. Figs. 1 to 7 are a few of those of the spe- cies barite, and Figs. 8 to 10 of crystals of sulphur.
BAKITE.
SULPHUR.
Fig. 11 represents a rectangular prism (diametral prism), and Fig. 12 a rhombic prism, each with the axes. The axes connect the centres of the opposite planes in the for- mer; but in the latter the lateral axes connect the centres of the opposite edges. Of the two lateral axes the longer is called the macrodiagonal, and the shorter the brachydi-
OETHORHOMB1C SYSTEM.
39
agonal. The vertical section containing the former is the macrodiagonal section, and that containing the latter, the bracJiy diagonal section.
In the rectangular prism, Fig. 11, only opposite planes are alike, because the three axes are unequal. Of these planes, that opposite to the larger lateral axis is called the macfopinacoid, and that opposite the shorter the brachy- pinacoid (from the Greek for long and short,, and a word signifying board or table). Each pair — that is, one of these planes and its opposite — is called a hemiprism.
In the rhombic prism, Fig. 12, the four lateral planes are similar planes. But of the four lateral edges of the
prism two are obtuse and two acute. Fig. 13 represents a combination of the rectangular and rhombic prisms, and illustrates the relations of their planes. Other rhombic
Erisms parallel to the vertical axis occur, differing in inter- icial angles, that is, in the ratio of the lateral axes.
Besides vertical rhombic prisms, there are also horizontal prisms parallel to each lateral axis, a and b. In Fig. 2 the narrow planes in front (lettered %l) are planes of a rhombic prism parallel to the longer of the lateral axes, and those to the right (H) are planes of another parallel to the shorter lateral axis. In Fig. 6 the planes are those of these two horizontal prisms. Such prisms are called also domes, be- cause they have the form of the roof of a house (domus in Latin meaning house). In Fig. 3 these same two domes occur, and also the planes (lettered /) of a vertical rhom- bic prism. Of these domes there may be many, both in the macrodiagonal and the brachydiagonal series, differing in angle (or in ratio of the two. intersected axes). Those parallel to the longer lateral axis, or the macrodiagonal, are called macrodomes ; and those parallel to the shorter, or brachydiagonal, are called bracliydomes.
A rhombic octahedron, lettered i, is shown in Fig. 8; a combination of two, lettered 1 and £, in Fig. 9; and a com-
iO CRYSTALLOGRAPHY.
bination of four, lettered 1, -J, £, -J-, in Fig. 10. This last figure contains also the planes 1, or those of a vertical rhombic prism; the planes 1-f, or those of a dome parallel to the longer lateral axis; the planes l-i, or those of a dome parallel to the shorter lateral axis; the plane 0, or the basal plane; the plane i-i, or the wbrachypinacoid; and also a rhombic octahedron lettered 1-3.
2. Positions of Planes. Lettering of Crystals. — The nota- tion is, in a general way, like that of the tetragonal system, but with dif- ferences made necessary by the inequality of the lateral axes. The let- ters for the three are written c : 5 : a ; 6 being the longer lateral and a the shorter lateral. In place of the square prism of the tetragonal system, i-i, there are the hemiprisms i-l and i-i, or_the macropinacoid and brachy- pinacoid, having the expressions ic : ib : la< and ic : l£: id. The form Jis the rhombic prism, having the expression ic : 15 : Id, correspond- ing to the square prism / in the tetragonal system. The planes i~n or i-ft, are other rhombic vertical prisms, the former corresponding to ic : rnh : \a, the other to ic : \bj na. If n = 2, the plane is lettered either i-2 or i£. The plane l-# has the expression Ic : 15 : M. m-n and m-n comprise all possible rhombic prisms and octahedrons, and cor- respond to the expressions me : rib : la and me : 15 : na. When m = infinity they become i-n and i-n, or expressions for vertical rhombic prisms; when n = infinity they become m-l and m-i, or expressions for macrodomes and brachydomes.
The question which of the three axes should be taken as the verti- cal axis is often decided by reference simply to mathematical con- venience. Sometimes the crystals are prominently prismatic only in one direction, as in topaz, and then the axis in this direction is made the vertical. In many cases a cleavage rhombic prism, when there is one, is made the vertical, but exceptions to this are numerous. There is also no general rule for deciding which octahedron should be taken for the unit octahedron. But however decided, the axial relations for the planes will remain essentially the same. In Fig. 10, bad the plane lettered | been made the plane 1, then the series, instead of being as it is in the figure, 1, i, ^, £, would have been 2, 1, f, f , in which the mutual axial relations are the same.
The relative values of the axes in the orthorhpmbic system may be calculated in the same way as that of the vertical axis in the tetra- gonal system, explained on page 35. The law of the tangents, as stated on page 36, holds for this system.
3. Hemlhedral Forms. — Hemihedral forms are not com- mon in this system. Some of those so considered have been proved to owe the apparent hemihedrism to their being of the monoclinic system, as in the case of datolite and two species of the chondrodite group. In a few kinds, as, for example, calamine, one extremity of a crystal differs
MONOCLINIC SYSTEM. 41
in its planes from the other. Such forms are termed licmi- morphic, from the Greek for half and fonn. They become polar electric when heated, that is, are pyroelectric, show- ing that this hemimorphism i$ connected with polarity in the crystal.
4. Cleavage. — Cleavage may take place in the direction of either of the diametral planes (that is, either face of the rectangular prism) ; but it will be different in facility and in the surface afforded for each. In anhydrite, however, the difference is very small. Cleavage may also occur in the direction of the planes of a rhombic prism, either alone or in connection with cleavage in other directions. It also sometimes occurs, as in sulphur, parallel to the faces of a rhombic octahedron.
5. Irregularities in Crystals. — The crystals almost never correspond in their diametral dimensions with the cal- culated axial dimensions. They are always lengthened, widened, shortened, or narrowed abnormally, but without affecting the angles. Examples of diversity in this kind of distortion are given in Figs. 1 to 7, of barite.
6. Distinctions. — In the orthorhombic system the angle 135° does not occur, because the three axes are unequal. There are pyramids of four similar planes in the system, but never of eight ; and the angles over the terminal edges of the pyramids are never equal as they are in the tetra- gonal system. The rectangular octahedron of the ortho- rhombic system is made up of two horizontal prisms, as shown in Fig. 6, and is therefore not a simple form ; and it differs from the octahedron of the tetragonal system cor- responding to it (Fig. 16, p. 33) in having the angles over the basal edges of two values.
IV. MONOCLINIC SYSTEM.
1. Descriptions of Forms. — In this system the three axes are unequal, as in the orthorhombic system; but one of the axial intersections is oblique, that between the axis a and the vertical axis c. The following examples of its crystalline forms, Figs. 1 to 6, show the effect of this ob- liquity. On account of it the front or back planes above and below the middle in these figures differ, and the ante-
42
CRYSTALLOGRAPHY.
rior and posterior prismatic planes are unequally inclined to a basal plane.
2.
PYROXENE.
HORNBLENDE.
The axes and their relations are illustrated in Figs. 7 and Fio". 7 represents an oblique rectangular prism, and S^an oblique rhombic. The former is the diametral prism, like the rectangular of the orthorhombic system. The axes connect the centres of the opposite faces, and the planes are of three distinct kinds, being parallel to unlike axes and diametral sections. In the latter, as in the rhom- bic prism of the orthorhombic system, the lateral axes con- nect the centres of the opposite sides. Moreover, this rhombic prism may be reduced to the rectangular by the removal of its edges by planes parallel to the lateral axes.
6.
The axis a, or the inclined lateral axis (inclined at an oblique angle to the vertical axis c), is called the clinodiago-
MONOCLINIC SYSTEM.
43
7.
nal ; and the axis b, which is not inclined, the ortliodiago- nal (from the Greek for right, or rectangular). The ver- tical section through the for- mer is called the clinodiago- nal section; it is parallel to the plane i-i (Figs. 1-6). The vertical section through the latter is the orthodiayo- nal section ; it is parallel to planes i-i. Owing to the ob- lique angle between a and c<
planes above a differ in
their relations to the axes from those below, and hence comes the difference in the angle they make with the basal plane.
The halves of a crystal either side of the clinodiagonal section — the vertical section through a and c — are alike in all planes and angles. Another important fact is this : that the plane i-l, or that parallel to the clinodiagonal section, is at right angles not only to 0 and i-i, but to all planes in the zone of 6 and i-i ; that is, in the clinodiagonal zone ; and this is a consequence of the right angle which axis b makes with both axis c and axis a. The plane i-i is called the orthopinacoid, it being parallel to the orthodiagonal ; and the plane i-l, the clinopinacoid, it being parallel to the clinodiagonal.
Vertical rhombic prisms have the same relations to the lateral axes as in the orthorhombic system. Domes, or horizontal rhombic prisms, occur in the orthodiagonal zone, because the vertical axis c and the orthodiagonal b make right angles with one another. In Fig. 6 the planes 1-1, %-i, belong to two such domes. They are called clinodomes, because parallel 'to the clinodiagonal.
In the clinodiagonal zone, on the contrary, the planes above and below the basal plane differ, as already stated, and hence there can be no orthodomes ; they are heiuiortko- domcs. Thus, in Fig. 6, -£-/, 1-i are planes of hemiortho- domes above /-/, and — -J-i is a plane of anolher of different angle below i-i. The plane, and its diagonally opposite, make the hemiorthodome.
The octahedral planes above the plane of the lateral axes also differ from those below. Thus, in Figs. 5 and 6, the planes 1, 1 are, in their inclinations, different planes from
44 CRYSTALLOGRAPHY.
the planes — 1, — 1 ; so in all cases. Thus there can be no monoclinic octahedrons — only hemi- octahedrons. An oblique octahe- dron is made up of two sets of planes ; that is, planes of two hemi- octahedrons. Such an octahedron may be modelled and figured, but it will consist of two sets of planes : one set including the two above the basal section in front and their diagonally opposites behind (Fig. 9), and the other set including the two below the basal sec- tion and their diagonally opposites (Fig. 10).
A hemioctahedron, since it consists of only four planes, is really an obliquely placed rhombic prism, and very fre- quently they are so lengthened as to be actual prisms.
2. Positions of Planes. Lettering of Crystals. — On account of the obliquity of the crystals, the planes above and below the basal section require a distinguishing mark in their lettering, as well as in the mathematical expressions for them. One set is made minus and the other plus. The plus sign is omitted in the lettering. In Fig. 7 there are above the basal section (or above i-i) the planes l-», \-i, 1, \. but below it, —%-i, — 1. The phis planes are those opposite the acute intersection of the basal and orthodiagonal sections, and the minus those opposite the obtuse. No signs are needed for planes of the clinodiagonal section, since they are alike both above and below the basal section.
The distinction of longer and shorter lateral axis is not available in this system, since cither may be the clinodiagonal. The distinction of clinodiagonal and orthodiagonal planes is indicated by a grave accent over the number or letters referring to the clinodiagonal. The lettering for the clinodomes on Fig. 6 is 1-i, 2-1 — the 1 (initial of infi- nite, with the accent) signifying parallelism to the c^'/wdiagonal. The hemioctahedrons, 1, 2, etc., need no such mark, as the expression for them is Ic : 1& : Id, 2c : Ib : Id, the planes having a unit ratio for d and b. But the plane 2-3, in Fig. 5, requires it, its expression being 20 : Ib : 2a; the fact that the last 2 refers to the clinodiagonal is indicated by the accent. If it referred to the orthodiagonal, that is, if the expression for the plane were 2c : 2b : Id, it would be written 2-2 without the accent.
3. Cleavage. — Cleavage may be basal, or parallel to either of the other diametral sections, or parallel to a vertical rhombic prism, or to the planes of a hemioctahedron; or to the planes of a clinodome, or to that of a hemiortho- dome. If occurring in two or more directions in any
TRICLINIC SYSTEM.
45
species it is always different in degree in each different direction, as in all the other systems.
4. Irregularities. — Crystals of this system may be elon- gated abnormally in the direction of either axis, and any diagonal. The hemiorthodomes may be in aspect the bases of prisms, and the hemioctahedrons the sides of prisms. Which plane in the zone of hemiorthodomes should be made the base, and which in the series of hemioctahedrons should be assumed as the fundamental prism determining the direction of the vertical axis, is often decided differ- ently by different crystallographers. Convenience of math- ematical calculation is often the principal point referred to in order to reach a conclusion.
V. TRICLINIC SYSTEM.
1. Descriptions of Forms. — In the triclinic system the three axes are unequal and their three intersections are oblique, and consequently there are never more than two planes of a kind; that is, planes having the same inclina- tions to either diametral section. The following are exam- ples:
1.
AXINITE.
ANORTHITE.
AMBLYGONITls,.
The difference in angle from monoclinic forms is often very small. This is true in the Feldspar family. Fig. 2, of the feldspar called anorthite, is very similar in general form to Fig. 4, of orthoclase, which is monoclinic. This
46
CRYSTALLOG R A PHY.
is still more strikingly seen on comparing Fig. 4 with Fig. 5 representing a crystal of oligoclase, another one of the triclinic feldspars. The planes on the two are the same
4.
ORTHOCLASE.
OLIGOCLASE.
with one exception; but there is this difference, that in orthoclase, as in all monoclinic crystals, the angle between the planes 0 and i-l (the two directions of cleavage) is 90°; and in oligoclase and other triclinic feldspars it is 3° to 6° from 90°, being in oligoclase 93° 50', and in anorthite 94° 10'. This difference in angle involves oblique inter- sections between the axes b and c, and c and a, which are rectangular in monoclinic forms. There is a similarly close relation between the triclinic form of rhodonite and that of pyroxene, and a resemblance also in composition.
The diametral prism in this system is similar to Fig. 7 on page 43, under the monoclinic system, but differs in having the planes all rhomboidal instead of part rectangu- lar. The form corresponding to the oblique rhombic prism of the monoclinic system (Fig. 8, p. 43) also has rhom- boidal instead of rhombic planes; moreover, the two pris- matic planes have unequal inclinations to the vertical dia- metral section, and are therefore dissimilar planes. The prism, consequently, is made of two hemiprisms, and the JDasal plane is another, making in all three hemiprisms.
2. Cleavage, — Cleavage takes place independently in dif- ferent diametral or diagonal directions. In the triclinic feldspars it conforms to the directions in orthoclase, with only the exception arising from the obliquity above ex- plained.
-IT'J^HEXAGONAL SECTION OF HEXAGONAL SYSTEM. 47
VI. HEXAGONAL SYSTEM.
This system is distinguished from the others by the character of its symmetry — the number of planes of a kind around the vertical axis being a multiple of 3. The num- ber of lateral axes is hence 3. It is related to the tetra- gonal system in having the lateral axes at right angles to the vertical and equal, and is hence like it also in the opti- cal characters of its crystals. Its hexagonal prismatic form approaches orthorhombic crystals in the obtuse angle (120°) of the prism, some orthorhombic crystals having an angle of nearly 120°.
Under this system there are two sections:
1. The HEXAGONAL SECTION, in which the number of planes of a kind around each vertical axis above or below the basal section is 6 or 12.
2. The EHOMBOHEDBAL SECTION, in which the number of planes of a kind around each half of the vertical axis, . above or below the basal section, is 3 or 6; and, in addition, the planes above alternate in position with those below. The forms are mathematically hemihedral to the hexago- nal, but not so in their real nature.
I. HEXAGONAL SECTION.
1. Description of Forms. — Figs. 1 to 3 represent some of 1. 2. 3.
12.
MIMETITE.
BERYL.
12
APATITE.
the forms under this section. Figs. 2 and 3 show only one extremity; and such crystals are seldom perfect at both.
48
CRYSTALLOGRAPHY.
All exhibit well the symmetry ~by sixes which characterizes this section of the hexagonal system.
Prisms. Under this system there are two hexagonal prisms and a number of occurring twelve-sided prisms. Fig. 4 represents one of the hexagonal prisms, with its axes — the three lateral connecting the centres of the oppo- site edges. The lateral angles of the prism are 120°. If the lateral edges of this prism are truncated, as in the fig- ure of apatite (Fig. 3), the truncating planes, i-2, are the lateral faces of another similar hexagonal prism, in which, as the relations of the two show, the lateral axes connect the centres of the opposite lateral faces. This prism is represented in Fig. 5.
The lateral edges of the hexagonal prisms occur some- times with two similar planes on each edge, and these planes, when extended to the obliteration of the hexagonal
prism, make a twelve-sided prism. These two planes are seen in Fig. 8, along with the planes 1 of the hexagonal prism, and 1 of a double six-sided pyramid, be- sides the basal plane 0.
Double pyramids. The double pyramids are of three kinds: (1) A series of six-sided, whose planes belong to the same vertical zone with the planes /. The planes of two such pyramids (lettered 1, 2) are shown in Figs. 1 and 2, three of them in Fig. 3 (lettered -J-, 1, 2), and one in Fig. 7, and one such double pyramid, without combination with other planes, in Fig. 6. (2) A series of six-sided double pyramids whose planes are in the same vertical zone with i-2, examples of which occur on Fig. 2 (plane 2-2) and on Fig. 3 (planes 1-2, 2-2, 4-2). The form of
TBTDYMITE.
HEXAGONAL SECTION OF HEXAGONAL SYSTEM.
49
this double pyramid is like that represented in Fig. 6, but the lateral axes connect the centres of the basal edges. The double six-sided pyramid is sometimes called a quartzoid, because it occurs in quartz. (3) Twelve-sided double pyra- mids. Two planes of such a pyramid are shown on a hexa-
9.
gonal prism in Fig. 9, also in Fig. 2 (the planes 3-f ), and the simple form consisting of such planes in Fig. 10 — a form called a lerylloid, as the planes are common in beryl. In Fig. 11 the planes 1 belong to a double six-sided pyra- mid ; and those next below (of which three are lettered W) to a double twelve-sided pyramid.
2. Lettering of Crystals.— The prism of Fig. 5 is lettered «-2, because it is parallel to the vertical axis, and has the ratio of 1 : 2 be- tween two lateral axes. This is shown in the annexed figure, which represents the hexagonal outline of the prism i-2 circumscribing that of the prism /. The plane i- 2 is produced to meet axis a, which it does when a is extended to twice its length; whence the ratio for the axes a, a, is 1 : 2.
The numbers 1, 2, on the double hexagonal pyramids in Fig. 1 indicate the relative lengths of the vertical axis of the two pyramids, they having the same 1 : 1 ratio of the lateral axes; and so in Figs. 2, 3, and others.
The lettering on the pyramids of the other series in Fig. 3, 1-2, 2-2, 42, indicates, by the second figure, that the planes .are in the same vertical zone with the prismatic plane i-2, and by the first figure the relative lengths of the vertical axes.
In the twelve-sided prisms such ratios as £-f , ££» *-f occur. The fraction in any case expresses the ratio of the lateral axes for the par- ticular planes. The double twelve-sided pyramids have the ratios 3-£ 4
50
CRYSTALLOGRAPHY.
APATITE.
(Fig. 2), 4-f, and others. Both in these forms and the twelve sided prisms, the second iigure in, the lettering, expressing the ratio of the lateral axes, has necessarily a value between 1 and 2.
3. Hemihedral Forms. — Fig. 13 represents a crystal of apatite in which there are two sets of planes, o (= 3-f) and
o* (— 4-f) which are hemi- hedral, only half of the full number of each o existing, in- stead of all. This kind of hemi- hedrism consists in the suppres- sion of an alternate half of the planes in each pyramid of the double twelve-sided' pyramid (Fig. 10); and in the suppressed planes of the upper pyramid be- ing here directly over those sup- pressed in the lower pyramid. If the student will shade over half the planes alternately of the two pyramids in Fig. 10, putting the shaded planes above directly over those below, he will understand the nature of the hemihedrism. In some hemihedral forms the suppressed planes of the upper pyramid alternate with those of the lower; but -this kind occurs only in the rhombohedral section of the hexagonal system.
4. Cleavage. — Cleavage is usually basal, or parallel to a six-sided pyramid. Sometimes there are traces of cleavage parallel to the faces of a six-sided pyramid.
5. Irregularities of Crystals. — Distortions sometimes disguise greatly the real forms of hexagonal crystals by enlarging some planes at the expense of others. This is illustrated in Fig. 14, represent- ing the actual form presented by a crystal having the planes shown in Fig. 13. "Whenever in a prism the prismatic angle is exactly 120° or 150°, the form is almost al- ways of the hexagonal system.
RHOMBOHEDRAL SECTION OF HEXAGONAL SYSTEM. 51
2. RHOMBOHEDRAL SECTION".
1. Descriptions of Forms. — The following figures,, 1 to 17, represent rhombohedral crystals, and all are of one mineral, calcite. They show that the planes of either end of the crystal are in threes, or multiples of threes, and that those above are alternate in position with those below. There is
FIGURES OF CRYSTALS OF CALCITE.
one exception to this remark, that of the horizontal or basal plane 0, in Figs. 8, 11, 13. The simple forms include :
1. Rhombohedrons, Figs. 1 to 6. These forms are in- cluded under six equal planes, like the cube, but these planes are rhombic ; and instead of having twelve rectangu- lar edges, they have six obtuse edges and six acute.
2. Scalcnohedrons, Fig. 7. Scalenohedrons are really double six-sided pyramids ; but the six equal faces of each extremity of the crystals are scalene triangles, and are ar- ranged in three pairs ; moreover, the pairs above alternate with the pairs below ; the edges in which the pairs above and below meet — that is, the basal edges — make a zigzag around the crystal.
3. Hexagonal prisms, /, Fig. 8. Regular hexagonal prisms, having the angle between adjoining faces 120°.
A rhombohedron has two of its solid angles made up of
52 CRYSTALLOGRAPHY.
three equal plane angles. When in position the apex of one of these solid angles is directly over that of the other, as in
14.
15.
PIGUKES OP CRYSTALS OP CALCITE.
Figs. 1 to 6, and also in Fig. 18, and the line connecting the apices of these angles (Fig. 18) is called the vertical axis. In this position the rhombohedron has six terminal
18.
edges, three above and three below, and six lateral edges. As these lateral edges are symmetrically situated around the centre of the crystal, the three lines connecting the centres of opposite basal edges will cross at angles of 60°. These lines are the lateral axes of the rhombohedron, and they are at right angles to the vertical axis. It is stated on page 45 that rhombohedral forms are, from a mathematical point of view, Jiemiliedral under the hexagonal system. The rhombohedron, which may be considered a double three- sided pyramid, is hemihedral to the double six-sided pyra- mid. Fig. 19, representing the latter form, has its alternate faces shaded ; suppressing the faces shaded, the form would be that of Fig. 18 ; and suppressing, instead of these, the
RHOMBOHEDRAL SECTION OF HEXAGONAL SYSTEM. 53
the
faces not shaded, the form would be that of another rhom- bohedron, differing only in position. The two are distin- guished as plus and minus rhombohedrons. They are com- bined in Figs. 20, 21, forms of quartz. Ehombohedrons vary greatly in the length of the vertical axis with reference to the lateral. Figs. 1, 2, 3, and 18 represent crystals with the vertical axis short, and Figs. 4, 5, 6 others with a long vertical axis. In the former the. angle over a terminal edge is obtuse or over 90°, and that over a lateral, acute ; and in the latter the reverse is the case, the angle over the terminal edges being less than 90° ; the former are called obtuse rhombohedrons, and the latter acute.
The cube placed on one solid angle, with the diagonal between it and the opposite solid angle vertical, is, in fact, a rhombohedron intermediate between obtuse and acute rhombohedrons, or one of 90° — the edges that are the ter- minal in this position, and those that are the lateral, being alike rectangular edges. Fig. 3 has nearly the form of a cube in this position.
The relation of one series of scalenohedrons to rhombohedron is illustrated in Fig. 22. This figure represents a rhombohedron with the lateral edges bevelled. These bevelling planes are those of a scalenohe- dron, and the outer lines of the same fig- ure show the form of that scalenohedron which is obtained when the bevelment is continued to the obliteration of the rhom- bohedral planes. Fig. 14 represents this scalenohedron with the rhombohedral planes much reduced in size. Other sca- lenohedrons result when the terminal edges are bevelled, and still others from pairs of planes on the angles of a rhombo- hedron.
The scalenohedron is hemihedral to the twelve-sided double pyramid (Fig. 23).
In the hexagonal system the three ver- tical axial planes divide the space about the vertical axis into six sectors (Fig. 12, p. 50). The twelve-sided double pyramid has in each pyramid a pair of faces for each sector; that is, six pairs for each pyramid. If now the three alternate of these pairs in the lower pyra-
54 CRYSTALLOGRAPHY.
mid, and those in the upper pyramid alternate with these (the shaded in Fig. 23), were enlarged to the obliteration of the rest of the- planes, the resulting form would be a scalenohedron — a solid with three pairs of planes to each pyramid instead of six. Such is the mathematical relation of the scalenohedron to the twelve-sided double pyramid. If the faces enlarged were those not shaded in Fig. 23, another scalenohedron would be obtained which would be the minus scalenohedron, if the other were designated the plus.
Fig. 8 shows the relations of a rhombo- hedron to a hexagonal prism. The planes R replace three of the terminal edges at each base of the prism, and those above alternate with those below. The extension of the planes R to the obliteration of those of the prismatic planes, /, and that of the basal plane 0, would produce the rhombohedron of Fig. 1. Figs. 9 and 10 represent the same prism, but with terminations made by the rhombo- hedron of Fig. 2.
By comparing the above figures, and noting that the planes of similar forms are lettered alike, the combinations in the figures will be understood. Fig. 16 is a combination of the planes of the fundamental rhombohedron R, with those of another rhombohedron 4, and of two scalenohedrons I3 and I5. Fig. 17 contains the planes of the rhombohe- dron — J-, with those of the scalenohedron I3, and those of the prism /. These figures, and Figs. 14, 22, have the fundamental rhombohedron revolved 60° from the position in Fig. 1, so that two planes R are in view above instead of the one in that figure.
2. Lettering of Figures.— Figs. 1 to 6, representing rhombo- hedrons of the species calcite, are lettered with numerals, excepting Fig 1. In Fig. 1 the letter R stands for the numeral 1, and the numerals on the others represent the relative lengths of their vertical axes, the lateral being equal. In Fig. 4 the vertical axis is twice that in Fig. 1; in Fig. 6 thirteen times; and in Fig. 15 the planes lettered 16 are those of a rhombohedron whose vertical axis is sixteen times that of Fig. 1. The rhornbohedrons of Figs. 1, 5, 6, and 15 are plus rhombohedrons; that is, they are in the same vertical series; while 2 and 3 are minus rhombohedrons, as explained above. The rhombo- hedron, when its vertical axis is reduced in length to zero, becomes the single basal plane lettered 0 in the series. If, on the contrary, the vertical axis of the rhombohedron is lengthened to infinity, the
RHOMBOHEDRAL SECTION" OF HEXAGONAL SYSTEM. 55
faces of the rhombohedron become those of a six-sided prism. This last will be seen from the relations of the planes R to /on Fig. 8, and from the approximation to a prismatic form in the planes 16 of Fig. 15. For an explanation of the lettering of other planes on rhombo- hedral crystals, reference must be made to the " Text-Book of Miner- alogy."
3. Hemihedrism. Tetartohedrism. — Hemihedrism occurs among rhombohedral forms, similar to that in Fig. 13, page 50, except that the suppressed planes of one pyramid are alternate with those of the other.
One of these is represented in Fig. 24. The planes 6-f are six in number at each extremity, and are so situated that they give a spiral aspect to the crystal. If these planes were only three in number at each extremity, the alternate three of the six, the form would be tetartohedral to the double six-sided pyramid ; that is, there would be one fourth the number of planes that exist in the double twelve- sided pyramid, or 6 planes instead of 24. Such cases of hemihedrism and tetarto- hedrism are common in crystals of quartz, and when existing, the crystals are said to be plagihedral, from the Greek for oblique and/ace. In some crystals the spiral turns to the right and in others to the left, and the two kinds are distinguished as right-handed and left-handed. There are also tetartohedral forms in which one whole pyramid of a scalenohedron, or of a rhom- bohedron, is wanting. For example, in crystals of tourma- line rhombohedral planes, and sometimes scalenohedral, may occur at one extremity of the prism and be absent from the other. This dissimilarity in the two extremities of a crystal of tourmaline is connected with pyro-electric polarity in the mineral. Three-sided prisms, hemihedral to the hexagonal prism, are common in some rhombohedral species, as tourmaline.
4. Cleavage. — Cleavage usually takes place parallel to the faces of a rhombohedron, as in calcite, 35. corundum. Not unfrequently the rhombohe- dral cleavage is wanting, and there is highly
perfect cleavage parallel to the basal plane, as in graphite, brucite.
5. Irregularities of Crystals. — Distortions
occur of the same nature with those under the other
56
CRYSTALLOGRAPHY.
systems. Some examples are given under quartz. Some rhombohedral species, as dolomite, have the opposite faces convex or concave, as in Fig. 25.
Occasional curved crystals occur, as in Fig. 26, repre- senting crystals of quartz, and Fig. 27 of a crystal of chlo-
26.
QUAKTZ.
CHLOKITE.
rite. The feathery crystallizations on windows, called frost, are examples of curved forms under this system.
VII. DISTINGUISHING CHARACTERS OF THE SEVERAL SYSTEMS OF CRYSTALLIZATION.
1. ISOMETRIC SYSTEM. — (1) There may be symmetrical groups of 4 and 8 similar planes about the extremities of each cubic axis; and of 3 or 6 similar planes about the ex- tremities of each octahedral axis> (2) Simple holohedral forms may consist of 6 (cube), 8 (octahedron), 12 (dodeca- hedron), 24 (trapezohedron, trigonal trisoctahedron, and tetrahexahedron), and 48 (hexoctahedron) planes.
2. TETRAGONAL SYSTEM. — (1) Symmetrical groups of 4 and 8 similar planes occur about the extremities of the vertical axis only. (2) Prisms occur paralM only to the vertical axis; and these prisms are either square or eight- sided. (3) The simple holohedral forms may consist of 2 planes (the bases), of 4 planes (square prisms), of 8 planes (eight-sided prisms and square octahedrons), of 16 planes (double eight-sided pyramids).
3. PRTHORHOMBIC SYSTEM. — (1) Symmetrical groups of 4 similar planes may occur about the extremities of either axis, but those of one axis may be referred equally to the others. (2) The prisms are rhombic prisms only, and these may occur parallel to either of the axes, the horizon-
TWIN, OR COMPOUND, CRYSTALS. 57
tal as well as the vertical. (3) Simple holohedral forms may consist of 2 planes (the bases, and each pair of dia- metral planes), of 4 planes (rhombic prisms in the three axial directions), and of 8 planes (the rhombic octahedrons). (4) The forms may be divided into equal halves, symmet- rical in planes, along each of the diametral sections.
4. MONOCLINIC SYSTEM. — (1) No symmetrical groups of similar planes ever occur around the extremities of either axis. (2) The prisms are rhombic prisms, and these can occur parallel only to the vertical axis and the clinodiagonal. (3) The planes occurring in vertical sections above and below the basal section, either in front or behind, are all unlike in inclination to that section, excepting the pris- matic planes in the orthodiagonal zone. (4) Simple forms consist of 2 planes (the bases, the diametral planes, and hemiorthodomes), of 4 planes (rhombic prisms in two direc- tions and hemioctahedrons). (4) The forms may be di- vided into equal and similar halves only along the clinodi- agonal section. No interfacial angle of 90° occurs except between the planes of the clinodiagonal zone and the clinopinacoid.
5. TRICLINIC SYSTEM. — In triclinic crystals there are no groups of similar planes which include more than 2 planes, and hence the simple forms consist of 2 planes only. The forms are not divisible into halves having symmetrical planes. There are no interfacial angles of 90°.
6. HEXAGONAL SYSTEM. — Symmetrical groups of 3, 6, and 12 similar planes may occur about the extremities of the vertical axis. (2) Prisms occur parallel to the vertical axis, and are either six- or twelve-sided (3 in a hemihedral form) and equilateral. (3) Simple holohedral forms may consist of 2 planes (the basal), of 6 planes (hexagonal prism), of 12 planes (twelve-sided prisms and double six-sided pyra- mids), of 24 planes (double twelve-sided pyramids). Simple rhombohedral forms may consist of 2 planes (the basal), of 6 planes (rhombohedrons), and of 12 planes (scalenohedrons).
The distinguishing optical characters are mentioned beyond.
2. TWIN, OR COMPOUND, CRYSTALS.
Compound crystals consist of two or more single crystals, united usually parallel to an axial or diagonal section. A few
58
CRYSTALLOGRAPHY.
are represented in the following figures. Fig. 1 represents a crystal of snow of not unfrequent occurrence. As is evi- dent to the eye, it consists either of six crystals meeting in a point, or of three crystals crossing one another ; and, be- sides, there are numerous minute crystals regularly arranged along the rays. Fig. 2 represents a cross (cruciform) crys-
1.
5.
6.
tal of staurolite, which is similarly compound, but made up of two intersecting crystals. Fig. 3 is a compound crystal of gypsum, and Fig. 4 one of spinel. These will be under- stood from the following figures.
Fig. 5 is a simple crystal of gypsum ; if it be bisected along ab, and the right half be inverted and applied to the other, it will form Fig. 3, which is there- fore a twin crystal in which one half has a reverse position from the other. Fig. 6 is a simple oc- tahedron ; if it be bisected along the plane abcde, and the upper half, after being revolved half way round, be then united to the lower, it will have the form of Fig. 4. Both of these, therefore, are similar twins, in which one of the two com- ponent parts is reversed in position.
Crystals like Figs. 3 and 4 have proceeded from a com- pound nucleus in which one of the two molecules was re- versed ; and those like Fig. 1, from a nucleus of three (or six) molecules. Compound crystals of the kinds above de- scribed thus differ from simple crystals in having been formed from a nucleus of two or more united molecules, instead of from a simple nucleus.
Compound crystals are generally distinguished by their re-entering angles, and often also by the meeting of striae
T\VIX, OR COMPOUND, CRYSTALS.
59
at an angle along a line on -a surface of a crystal, the line indicating the plane of junction of the two crystals.
Compound crystals are called twolings, trillings, foil rlings, according as they consist of two, three, or four united crys- tals. Fig. 1 represents a trilling, and 2, 3, and 4, twolings. In 3 and 4 the combined crystals are simply in contact along the plane of junction ; in 2 they cross one another ; the former are called contact-twins and the latter penetra- tion-twins.
Besides the above, there are also geniculated crystals, as in the annexed figure of a crystal of rutile. The bending has here taken place at equal distances from the centre of the crystal, and it must therefore have been subsequent in time to the commencement of the crystal. The prism began from a simple molecule ; but after attaining a certain length an ab- rupt change of direction took place. The angle of geniculation is constant in the same mineral species, for the same reason that the interfacial angles of planes are fixed ; and it is such that a cross-section directly through the geniculation is parallel to the position of a common secondary plane. In the figure given, the plane of geniculation is parallel to one of the terminal edges. In rutile the geniculated crystals sometimes repeat the bendings at each end until the extremities meet to form a wheel-like twin.
In some species, as albite, the reversion of position on which this kind of twin depends, takes place at so short in- tervals that the crystal consists of 8. parallel plates, each plate often
less than a twentieth of an inch in thickness. A section of such a crystal, made transverse to the plate, is given in Fig. 8 ; without the twinning the section would have been as in Fig. 9. The plates, as the figure shows, make with one another at their edges a re-entering angle (in albite an angle of 172° 48'), and hence a
plane of the albite crystal at right angles to the twinning direction, is covered with a series of ridges and depressions
60
CRYSTALLOGRAPHY.
which are so minute as to be only fine striations, sometimes requiring a magnifying power to distinguish. Such stria- tions in albite are therefore an indication of the compound structure.
This kind of twinning is sometimes called polysynthetic twinning. It occurs in all the triclinic feldspars, and is a means of distinguishing them from orthoclase. Similar twinning occurs also in calcite, and some other species. In "some twin crystals the two component parts of the crystal are not united by an even plane, but run into one another with great irregularity. Oases of this kind occur in the species quartz in twins made up of the forms R and — R (or
— 1). In Fig. 10 the shaded parts of the pyramidal planes are of the form
— 1, and the non-shaded parts of R. Each of the faces is made up partly of R and partly of — 1. The limits of the two are easily seen on holding the crystal up to the light, since the — 1 portion is less well polished than the other. In this crystal, as in other crystals of quartz, the striations of
planes i are owing to oscillations between pyramidal and prismatic planes while the formation of the latter was in progress.
The compound or twinned condition, while often origi- nating in a compound nucleus, and in external molecular influences, may also be produced in many species by pres- sure or a blow.
In this way a simple rhombohedron of calcite may be made a true twin crystal, or a polysynthetic twin. The grains in a white crystalline limestone or marble — the spe- cies calcite or dolomite — are rhombohedral in cleavage, like the ordinary crystals of these minerals; but the cleavage surfaces are usually striated parallel to the longer diameter of the rhombohedral faces, and this striation is due to polysynthetic twinning. It may be always a result of pres- sure at the time of the crystallization of the limestone. The striations common in the triclinic feldspars have been attributed to the same cause.
PARAMORPHS. PSEUDOMORPHS. 61
3. PARAMORPHS. PARAMORPHISM.
Many examples exist in which elements, and compounds that have the same composition essentially, differ in crys- talline form as well as other physical qualities. These are examples of paramorphism. Among the elements, one marked example is carbon, which is isometric in the diamond, but hexagonal in graphite: of extreme hardness, adamantine lustre, and a specific gravity of 3*53 in the former; of extreme softness, a metallic lustre, and a spe- cific gravity of 2*1 in the latter. Such differences may be conceived of as due to differences in molecular condensa- tion. The following are examples among compounds: Calcium carbonate occurs rhombohedral (and G. = 2 '72) in calcite, orthorhombic (and G. =2*93) in* aragonite. Silica is rhombohedral (the hemihedral section of the hex- agonal system) (and G. = 2*65) in quartz; true hexagonal (G. = 2-29} in tridymite; and uncrystallizable in opal (G. = 2-17). Titanium dioxide has an orthorhombic form in brookite, one tetragonal form in rutile, and another tetragonal in octahedrite. In the hornblende group, hornblende and pyroxene are alike in composition and in monoclinic crystallization; but the former has a cleavage angle of 124° 30', .and the latter of 87° 5'. In addition, other species of the group having these two cleavage an- gles, as anthophyllite and enstatite, are orthorhombic in crystallization.
In general one of the forms is less stable under the or- dinary temperature or conditions than the other, because it requires for formation a higher temperature or some other unusual condition. Thus pyroxene is less stable than hornblende; aragonite than calcite, brookite than rutile.
4. PSEUDOMORPHS, PSEUDOMORPHISM.
The crystalline forms under which a species occurs are sometimes those of another species. Quartz often has the crystalline form of calcite, owing to a substitution of silica for the calcium carbonate of the calcite crystal. Serpen- tine has often the form of chrysolite, chondrodite, or some other magnesium mineral, owing to a change in these other magnesium silicates into the hydrous magnesium silicate
CRYSTALLOGRAPHY.
called serpentine.' Such false forms are called ptcudo- morphsy from the Greek pseudos, false, and morpTie, form. The same process that turned the calcite into quartz has converted wood,, shells, and corals into quartz; in other words, made silicified wood, shells, and corals.
The different kinds of pseudomorphism are the following:
1. By substitution: as in the substitution of silica (quartz) for the calcite.
2. By chemical alteration : as in the change to serpen- tine above explained; or the change of iron carbonate (sid- erite) to the hydrous iron oxide (limonite).
3. By impression : as in deposition in a cavity once occu- pied by a crystal; or against the exterior of a crystal.
4. By paramorphism : as when pyroxene becomes changed to hornblende, or aragonite to calcite. In this al- teration of pyroxene, as fast as the outer part becomes changed, it has cleavage parallel to the hornblende prism (/A/= 124° 30"), instead of that of pyroxene (87°
5'), as in the accompanying figure, which in its central part repre- sents a transverse section of a crystal, the centre pyroxene, the outer part hornblende, and in the upper corner a longitudinal section of a similarly altered pyroxene. The cleavage-lines are often an indication of its progress. Such hornblende has been called uralite, because first observed (by H. Rose) Urals; but it is essentially like ordinary
the
in a rock of
hornblende. In the figure the black spots represent grains of magnetite. In many cases no change in composition attends the change; but in others there are some replace- ments by which the elimination of unessential ingredients takes place. Iron is apt to be this removed ingredient, as it is in many of the methods of chemical alteration; and, consequently, while it remains in the crystal it takes an independent form, and usually that of minute grains or crystals of magnetite, or hematite, or menaccanite.
CRYSTALLINE AGGREGATES.
63
5. CRYSTALLINE AGGREGATES.
The crystalline aggregates here included are the simple, not the mixed; that is, they are those consisting of crys- talline individuals of a single species.
The crystalline individuals may be (1) distinct crystals; (2) fibres or columns; (3) scales or lamellae; or (4) grains, either cleavable or not so.
1. Consisting of distinct crystals. — The distinct crystal may be either long or short prismatic, stout or slender to acicular (needle-like), and capillary (hair-like); or they may have any other forms of crystals. They may be ag- gregated (a) in lines; (b) promiscuously with open spaces; (c) over broad surfaces; (d) about centres. The various kinds of aggregates thus made are:
a. Filiform. — Thread-like lines of crystals, the crystals often not well defined.
b. Dendritic. — Arborescent slender spreading branches, somewhat plant-like, made up of more or less distinct crys- tals, as in the frost on windows, and in arborescent forms of native copper, silver, gold, etc.
Fig. 11 represents, much magnified, an arborescent form of magnetite occurring in mica at Pennsbury, in Pennsyl- vania. Arborescent delineations over surfaces of rock are usually called dendrites. They have been formed by crys- tallization from a solution of mineral matter which has entered by some crack and spread between the layers of the rock. They are often black, and consist of oxide of manganese; others, of a brownish color, are made of limonite; others, of a reddish black or black color, of hematite. Moss-like forms also occur, as in moss agate.
c. Reticulated. — Slender ' ^ prismatic crystals promis- cuously crossing, with open spacings.
d. Divergent. — Free crystals radiating from a central point.
64 CRYSTALLOGRAPHY.
e. Drusy. — A surface is drusy when covered with im- planted crystals of small size.
2. Consisting of columnar individuals.
a. Columnar9 when the columnar individuals are stout. I. Fibrous, when they are slender.
c. Parallel fibres, when the fibres are parallel.
d. Radiated) when the columns or fibres radiate from centres.
e. Stellated, when the radiations from a centre are equal around, so as to make star-like or circularly-radiated groups.
/. Globular, when the radiated individuals make globu- lar or hemispherical forms, as in wavellite.
ff. Botryoidalf when the globular forms are in groups, a little like a bunch of grapes. The word is from the Greek for a bunch of grapes.
h. Mammillary, having a surface made up of low and broad prominences. The term is from the Latin mammil- la, a little teat.
i. Coralloidal, when in open-spaced groupings of slender stems, looking like a delicate coral. A result of successive additions at the extremity of a prominence, lengthening it into cylinders, the stems generally having a faintly radi- ated structure.
Specimens of all these varieties of columnar structure, excepting the last, often have a drusy surface, the fibres or columns ending in projecting crystals.
3. Consisting of scales or lamellm.
a. Plumose, having a divergent arrangement of scales, as seen on a surface of fracture; e.g., plumose mica.
b. Lamellar, tabular, consisting of flat lamellar crystal- line individuals, superimposed and adhering.
c. Micaceous, having a thin fissile character, due to the aggregation of scales of a mineral which, like mica, has emi- inent cleavage.
d. Septate, consisting of openly-spaced intersecting tabu- lar individuals; also divided into polygonal portions by reticulating veins or plates. A septarium is a concretion, usually flattened spheroidal in shape, the solid interior of which is intersected by partitions; these partitions are the fillings of cracks in the interior that were due to contraction on drying. Such septate concretions, especially when worn off at surface, often have the appearance of a turtle's back, and are sometimes taken for petrified turtles.
CRYSTALLINE AGGREGATES. 65
4. Consisting of grains. Granular structure. — A mas- sive mineral may be coarsely granular or finely granular, as in varieties of marble, granular quartz, etc. It is termed saccharoidal when evenly granular, like loaf-sugar. It may also be cryptocrystalline, that is, having no distinct grains that can be detected by the unaided eye, as in flint. The term cryptocrystalline is from the Greek for concealed crys- talline. Aphanitic, from the Greek for invisible, has the same signification. The term ceroid is applied when this texture is connected with a waxy lustre, as in some common opal.
Under this section occur also globular, botryoidal, and mmntnillary forms, as a result of" concretionary action in which no distinct columnar interior structure is produced. They are called pisolitic when in masses consisting of grains as large as peas (from the Latin pisum, a pea), and oolitic when the grains are not larger than the roe of a fish, from the Greek for egg.
5. Forms depending on mode of deposition. — Besides the above, there are the following varieties which have come from mode of deposition:
a. Stalactitic, having the form of a cylinder, or cone, hanging from the roofs of cavities or caves. The term stalactite is usually restricted to the cylinders of calcium carbonate hanging from the roofs of caverns; but other minerals are said to have a stalactitic form when resembling these in their general shape and origin. Chalcedony and limonite are often stalactitic. Interiorly the structure may be either granular, radiately fibrous, or concentric.
The waters percolating through the roofs of limestone caverns hold some limestone in solution; and the deposit which each successive drop of water makes, lengthens out the cylinder; and not unf requently they become yards in length, or reach from roof to floor. The stalactites are sometimes hollow cylinders when small, because the drops, which follow one another very slowly, evaporate chiefly at the outer margin of each, the first one thus making a ring, and the following lengthen- ing the ring into the cylinder. The solution is strictly a solution of calcium bicarbonate; as evaporation takes place the excess of carbonic acid goes off and calcium carbonate is deposited.
b. Concentric. — When consisting of lamellae, lapping one over another around a centre, a result of successive concre- tionary aggregations, as in many concretionary forms, most pisolite, part of oolite, some stalactites, etc.
c. Stratified, consisting of layers, as a result of deposi- tion : e.g., some travertine, or tufa.
66 PHYSICAL PROPERTIES OF MINERALS.
d. Banded, straticulate ; color-stratified. Like stratified in origin, but the layers thin and usually indicated only by variations in color or texture; the banding is shown in a transverse section: e.g., agate, much stalagmite, riband jasper, some limestone; it becomes lamellar or slaty when the little layers are separable.
e. Geodes. — When a cavity has been lined by the deposi- tion of mineral matter, but not wholly filled, the enclosing mineral is called a geode. The mineral is often banded, owing to the successive depositions of the material, and frequently has its inner surface set with crystals. Agates are often slices or fragments of geodes.
6. Fracture. — Kinds of fracture in these crystalline ag- gregates depend on the size and form of the particles, their cohesion, and to some extent their having cleavage or not.
Among granular varieties, the influence of cleavage is in all cases very small, and in the finest almost or quite noth- ing. The term hackly is used^for the surface of fracture of a metal, when the grains are coarse, hard, and cleavable, so as to be sharp and jagged to the touch; even, for any surface of fracture when it is nearly or quite flat, or not at all conchoidal; conchoidal, when the mineral, owing to its extremely fine or cryptocrystalline texture, breaks with shallow concavities and convexities over the surface, as in the case of flint. The word conchoidal is from the Latin concha, a shell. These kinds of fracture are not of great importance in mineralogy, since they distinguish varieties of minerals only, and not species.
II. PHYSICAL PROPERTIES OF MINERALS.
THE physical properties referred to in the description and determination of minerals are here treated under the following heads: (1) Hardness; (2) Tenacity; (3) Specific Gravity; (4) Refraction, Polarization; (5) Diaphaneity, Color, Lustre; (6) Electricity and Magnetism; (7) Taste and Odor. All excepting the last are more or less depend- ent on the crystallization, the qualities in each case being alike in crystals in the direction of like or equal axes, and usually unlike in the directions of unlike or unequal axes.
HARDNESS— TENACITY. 67
1. HARDNESS.
The comparative hardness of minerals is easily ascer- tained, and should be the first character attended to by the student in examining a specimen. It is only necessary to draw a file across the specimen, or to make trials of scratch- ing one with another. As standards of comparison the following minerals have been selected, increasing gradually in hardness from talc, which is very soft and easily cut with a knife, to the diamond. This table, called the scale of hardness, is as follows: Q*> ^^^^
1, talc, common foliated variety; 2/nuetf'JeetH-; 3, calcite, transparent variety; 4, fiuorite, crystallized variety; 5, apatite, transparent crystal; 6, or tJwclase, cleavable variety; 7, quartz, transparent variety; 8, topaz, transparent cr}rs- tal; 9, sapphire, cleavable variety; 10, diamond.
If, on drawing a file across a mineral, it is impressed as easily as fluorite, the hardness is said to be 4; if as easily as orthodase, the hardness is said to be 6; if more easily than orthoclase, but with more difficulty than apatite, its hard- ness is described as 5£ or 5 -5.
The file should be run across the mineral three or four times, and care should be taken to make the trial on angles equally blunt, and on parts of the specimen not altered by exposure. Trials should also be made by scratching the specimen under examination with the minerals in the above scale, since sometimes, owing to a loose aggregation of par- ticles, the file wears down the specimen rapidly, although the particles are very hard.
In crystals the hardness is sometimes appreciably different in degree in the direction of different axes. In crystals of mica the hardness is less on the basal plane of the prism, that is, on the cleavage surface, than it is on the sides of the prism. On the contrary, the termination of a crystal of cyanite is harder than the lateral planes. The degree of hardness in different directions may be obtained with great accuracy by means of an instrument called a sclero- meter.
2. TENACITY.
The following rather indefinite terms are used with reference to the qualities of tenacity, malleability, and flexi- bility in minerals:
68 PHYSICAL PROPERTIES OF MINERALS.
1. Brittle. — When a mineral breaks easily, or when parts of the mineral separate in powder on attempting to cut it.
2. Malleable. — When slices may be cut off, and these slices will flatten out under the hammer, as in native gold, silver, copper.
3. Sect He. — When thin slices may be cut off with a knife. All malleable minerals are sectile. Argentite and cerargy- rite are examples of sectile ores of silver. The former cuts nearly like lead, and the latter nearly like wax, which it re- sembles. Minerals are imperfectly sectile when the pieces cut off pulverize easily under a hammer, or barely hold together, as selenite.
4. flexible. — When the mineral will bend, and remain bent after the bending force is removed. Example, talc.
5. Elastic. — When, after being bent, it will spring back to its original position. Example, mica.
A liquid is said to be viscous when on pouring it the drops lengthen and appear ropy.
3. SPECIFIC GRAVITY.
The specific gravity of a mineral (called also its density) is its weight compared with that of some substance taken as a standard. For solids and liquids distilled water, at 60° F., is the standard ordinarily used; and if a mineral weighs twice as much as water, its specific gravity is 2; if three times it is 3. It is then necessary to compare the weight of the mineral with the weight of an equal bulk of water. The process is as follows:
First weigh a fragment of the mineral in the ordinary way, with a delicate balance; next suspend the mineral by a hair, or fibre of silk, or a fine platinum wire, to one of the scales, immerse it, thus suspended, in a glass of distilled water (keeping the scales clear of the water) and weigh it again; subtract the second weight from the first, to ascer- tain the loss by immersion, and divide the first by the dif- ference obtained; the result is the specific gravity. The loss by immersion is equal to the weight of an equal volume of water. The trial should be made on a small fragment; two to five grains are best. The specimen should be free from impurities and from pores or air-bubbles. For exact results the temperature of the water should be noted, and an allowance be made for any variation from the height of
SPECIFIC GRAVITY.
69
thirty inches in the barometer. The observation is usually made with the water at a temperature of 60° F.; 39° -5 F., the temperature of the maximum density of water, is pref- erable.
The accompanying figure represents the spiral balance of Jolly, by which the density is meas- ured by the torsion of a spiral brass wire. On the side of the upright [A) which faces the spiral wire, there is a graduated mirror, and the readings which give the weight of the mineral in and out of water are made by means of an index (at m) connected with the spiral wire; and its exact height, with reference to the graduation, is obtained by noting the coincidence between it and its image as reflected by the gradu- ated mirror. c and dare the pans in which the piece of mineral is placed, first in c, the one out of the water, and then in d, that in the water.
In using the spiral balance the spiral spring is put at any desired height by means of the sliding-rod C. The stand B is raised so that the lower pan, d, shall be in the water, while the other, c, is above it. The position of the index, or signal, m, is then noted, by sighting across it and observing that the index and the image of it in the mirror are in the same horizontal line; let s stand for it. Next put the fragment of the mineral in c, and drop the stand B until the lower pan hangs free in the water, and note the position of m, which we may represent by /; t—s represents the weight in the air. Now place the fragment in the lower pan, and after adjust- ing again the stand B, the position of m is noted as before; call it u. Then t — u — loss of weight in water. From these values the specific gravity is at once obtained.
Another process, and one available for porous as- well as compact minerals, is performed with a light glass bottle, capable of holding exactly a thousand grains (or any known weight) of distilled water. The specimen should be re- duced to a coarse powder. Pour out a few drops of water
PHYSICAL PROPERTIES OF MINERALS.
from the bottle and weigh it; then add the powdered min- eral till the water is again to the brim, and reweigh it; the difference in the two weights, divided by the loss of water poured out, is the specific gravity sought. The weight of the glass bottle itself is here supposed to be balanced by an equivalent weight in the other scale.
Another method consists in the use of a solution of a salt of high specific gravity. The potassium-mercury iodide is one salt so used, and another is the cadmium boro-tungslate. The maximum density of a solution of the former is 3*2; of the latter, 3 '6. By carefully adding water, the solution is reduced in density to that of the mineral, or that in which the mineral in coarse grains will just float; and this den- sity is then determined by weighing a given amount of the solution. The process is used also for the separation of mixed minerals of unequal density. Details of the processes will be found in larger works.
4. REFRACTION AND POLARIZATION.
Light is refracted when it passes from a rarer medium through a denser, as from air through water, or the re- verse. It is polarized, or has its vibrations reduced to vi- brations in a plane, when it passes through a crystal of un- equal crystallographic axes, or a fragment of such a crystal. Amorphous substances (or those totally devoid of traces of crystallization), like glass and opal, and crystallized sub- stances of the isometric system, have single or simple refrac- tion ; while substances crystallized under either of the other systems of crystallization have double refraction.
SIMPLE REFRACTION. — The index of ordinary refraction is obtained by dividing the sine of the angle of incidence of the ray of light by the sine of its angle of refraction. Thus if a ray of light (ah, Fig. 1) strike the sur- face (MN) of the denser material at an angle of 60° from the perpendic- ular (the angle bag), and then passes through it at an angle of 40° from the perpendicular (angle cab), the sine of 60° (ad), divided by the sine of 40° (ae), will be the index of re- fraction. The index of refraction of air being taken as the unit,
REFRACTION AND POLARIZATION. 71
that of water, as experiment has ascertained, is 1-335 ; of fluorite, 1-434; of rock-salt, T557 ; of spinel, 1*764; of garnet, 1'815; of blende, 2^60; of diamond, 2 -439.
Isometric and amorphous substances are said to be isofro- pic, because in them the velocity of light and all light-phe- nomena are alike in all directions.
DOUBLE REFRACTION. POLARIZATION. — Double refrac- tion is illustrated in the annexed figure representing a trans- parent rhombohedron of calcite, with the ray, ab, divided, as it passes through the crystal, into two rays ac and ac'. When such a crystal is placed over a dot the dot appears double, owing to the double refrac- tion. Each of these rays is a polar- ized ray.
Such crystals aro optically either uniaxial or biaxial.
A. Uniaxial. — Uniaxial substances are those of the tetrag- onal and hexagonal systems ; and the vertical axis, about which the parts are arranged symmetrically, is the optic axis. In the direction of this axis refraction is simple, but in all other directions double; and the divergence is greatest in a direction at right angles to the vertical or optic axis.
One of the rays has its vibrations transverse to the axis : it is called the ordinary ray, because it obeys the laws of or- dinary refraction above explained. The other, the extraor- dinary ray, has its vibrations in the direction of the axis, and obeys a different law, because the elasticity of the light- ether in this direction is greater or less than in the trans- verse. If the index of refraction of the extraordinary ray (e) is greater than that of the ordinary (GO), the crystal is said to be positive ; if less, it is negative. Calcite is an example of a negative crystal, ac in Fig. 2 being the extra- ordinary ray ; and quartz is an example of a positive.
Plates of tourmaline made by vertical sections of a transparent crystal transmit the extraordinary ray, while the ordinary ray is absorbed. Hence such plates are con- venient for optical investigations. A simple polariscope made of two tourmaline plates has the form in Fig. 3. The effects are the same whichever tourmaline plate is brought to the eye. The plate away from the eye, or that receiving the light for transmission, is called the polarizer,
PHYSICAL PROPERTIES OF MINERALS.
and the other the analyzer. Light passes freely through the two plates as long as they have the position they had in the crystal, that is, have the vertical axes — the planes of vibration — of the two parallel. But if the axes are crossed, by revolving one plate 90°, no light passes. In a revolu-
tion, light and dark fields alternate every 90°. Crystalline minerals are examined by placing sections of them between the tourmalines.
Calcite, owing to the wide divergence of its refracted rays, is commonly used for polarizing apparatus. In a 4. "nicol prism" of calcite (Fig. 4) the extraor-
dinary ray (ac'} passes through the prism, while the other (ac) is got rid of by reflection from the surface of Canada balsam (mn) along which the two pieces of calcite in the prism are joined.
In a polariscope the two nicols are mounted in tubes, one of which, if the instrument is a vertical one, is placed above, and the other below, a stage arranged for receiving the object for examination. One or both of the nicols, and also the stage, admits of revolution, in order to place the planes of vibration of the nicols in different positions as to one another and as to the specimen centered on the stage; and graduated scales indicate the angle of revolution in nicol and stage. Lenses for magnifying the object are added; and also others, making what is called the condenser, which is placed between the polarizer and the stage.
In the ordinary polariscope, only very low magnifying- powers are used without an ocular, and consequently the field is large so as to be convenient for observations on the light-phenomena. By inserting the condenser the trans-
REFRACTION AND POLARIZATION.
73
74 PHYSICAL PROPERTIES OF MINERALS.
mission of the polarized light in parallel rays is changed to transmission in convergent rays ; and the light-phenomena are changed.
In the polarization-microscope (a figure of which is here introduced) higher powers are used, and also an ocular (eye- piece with lenses). The nicols are at ss (analyzer) and rr (polarizer),; the supporting tube of the analyzer revolves, and rests on a graduated circle ff} with a mark on the edge which is to be set at 0° to put the vibration-planes of the two nicols in a crossed position, and at 90° to make them parallel. The tube of the microscope moves up and down, by the hand, within the outer case pp ; and a fine adjustment is obtained with the screw g, the surface of which is gradu- ated. In the figure the condenser TT is in place, as when required for observations with converging rays (which are made with the ocular removed). The stage revolves and has a lateral movement by screws to aid in centering the object ; and to give further aid, the tube has a slight movment by the screw nn. it is an opening for inserting a plate of quartz (ZZ,) for determining the precise position when an axis of elasticity of the object on the stage coincides with a vibra- tion-plane of a nicol, and for other purposes.
On revolving one of the nicols, the change from the transmission of light to its non- transmission by the analyzer, or the " extinction of the ray," takes place with every 90° of revolution, as with the tourmaline polariscope ; and alike tor parallel and converging light.
If a plate of a uniaxial crystal cut at right angles to the vertical or optic axis is on the stage centered in the field of view, and the nicols are crossed and parallel light • is used,
the field remains dark
6. 7. through the complete
revolution of the stage, as in the case of isometric and isomorphous sub- stances; but if converg- ing light is used in the polariscope, a symmetrical black cross and concentric spectrum-circles are seen when the nicols are crossed (Fig. 6), and a light-cross with the colors reversed (Fig. 7) when they are parallel. The number of spectrum-ringg
REFRACTION AND POLARIZATION. 75
within the field under a given convergence and magnifying- power depends on the refraction and the thickness of the plate under examination. The plate may be so thin that it will have but one color, or none. The tourmaline- polariscope affords the same cross and circles or " interfer- ence-figures/' because the eye is brought so closely to the analyzer in making observations that the light is really converging light.
When the ordinary thin sections mounted on glass are examined in the polarization-microscope,, it is commonly the case, owing to the thinness of the sections, that few if any of the colored rings around the centre of the black cross are in sight. If the sections for examination, instead of being cut parallel to the base of the crystal, or at right angles to the optic axis, are cut a little oblique to it but at right angles still to a vertical axial section, the cross will be symmetrical, but its centre out of the centre of the field; and if cut much oblique to it, its centre may be wholly out of the field, and only one straight black band be visible.
Circular polarization characterizes quartz. The light- vibrations instead of being in a single plane rotate either to the right or left, according as the crystal is right-handed or left-handed (p. 55). Consequently, a plate cut at right angles to the optic or vertical axis has a colored centre to the series of spectrum-circles in all positions of the ana- lyzer; moreover, on revolving the analyzer the color of the centre changes from blue to yellow and red in riff It ^-handed crystals if the revolution is to the right, and in /e/7-handed when the revolution is in the opposite direction.
B. Biaxial. — 1. In orth< rhombic, monoclinic, and tridinic crystals the three crystallographic axes are unequal, and there is unequal elasticity optically in three directions at right angles with one another: a maximum axis (a), a mean (b), and a minimum (c). The elasticity in these directions is inversely as the refraction-indices for the same direc- tions.
There are two directions in which there is no double re- fraction, and these are the directions of the two optic axes. The two are situated in a plane passing through the axes of maximum and minimum elasticity (a and c), and coincide with lines in this plane along which the elasticity equals that of the mean axis. A line bisecting the acute angle of intersection of the two optic axes is called the acute bisec-
70 PHYSICAL PROPERTIES OF MINERALS.
trix, and that for the obtuse angle of intersection, the obtuse bisectrix.
Sections of such crystals cut at right angles to a bisectrix (but best the acute bisectrix, for the angle bisected by the
g obtuse is too divergent
for viewing well the phenomena) show in converging polarized light, when the plate under examination has the line joining the axes coincident with the vibration-plane of either nicol-prism, a black band or an un- symmetrical black cross, similar to that in Fig. 8; if a revolution of 45° is made, the form changes to that in Fig. 9. But the plates under investigation may be so thin or the axis so divergent that the axial centres are not in the field of view.
2. In the Orthorhonibic system the three axes of elasticity coincide in direction with the crystallo^raphic axes. The plane of the two optic axes coincides with one of the three axial sections : which of the three is to be determined by observations on sections cut parallel to each.
In observations made with parallel light on sections cut parallel to the axial planes, extinction of the light takes place whenever the cross-wires in the polarization-micro- scope are parallel with the axes of elasticity (or the crystal- lographic axes) in the section. The extinction, under the orthorhombic system, is hence said to ^parallel extinction.
3. In monoclinic crystals (which have but one plane of symmetry — the clinodiagonal, and one axis — the ortho- diagonal, at right angles to the plane of the other two) one of the axes of elasticity coincides in direction with the or- thodiagonal, and the other two (at right angles with it) lie in the plane of symmetry. Either of the three may be that of maximum (a), mean (b), or minimum (c) elasticity.
The plane of the two optic axes may coincide with either of the three planes passing through the axes of elasticity (one of which planes is that of the clinodiagonal section, and the other two are planes at right angles to the clino- diagonal section passing through the orthodiagonal and one
REFRACTION AND POLARIZATION. 77
other of the axes of elasticity in that section) ; and when situated in the clinodiagonal section they are unsymmetrical in crystallographic relations, but when in either of the other sections they are situated symmetrically either side of the clinodiagonal section.
With reference to observations with parallel light in the polarization-microscope, it is to be noted that — since the plane of the vertical crystallographic axis and axis of elas- ticity makes a right angle with the orthodiagonal, like the planes of vibration of the crossed nicols, but an oblique angle with the clinodiagonal, any section made in the or- thodiagonal zone (or at right angles to the clinodiagonal section) will have extinction parallel) as in the orthprhombic system; but in the case of sections cut in other directions, extinction does not take place when either of the planes or cleavage lines in the clinodiagonal section is brought to parallelism with either vibration-plane of the nicols, and a revolution through an angle — different for different species and positions — has to be made: the amount of this angle is called the extinction-angle as measured from the edge or cleavage-line selected for the measurement. For horn- blende and pyroxene, in which the optic axes lie in the plane of symmetry, the extinction-angle is measured from the cleavage-lines," these being parallel to the vertical axes ; it is 15° for hornblende ; 39° for pyroxene ; Avhile parallel, or 0° (expressed by the symbol || ) for enstatite and hy- persthene which are orthorhombic.
The following figures represent clinodiagonal sections of hornblende and pyroxene, having cc as the vertical axis, and aa as the clinodiagonal, with the angle of extinc- tion marked upon them. A A, BB are the two optic axes, and a, c the two axes of elasticity.
The point of light-extinction is more exactly determin- able if a basal section of calcite is placed between the ocular and analyzer, and the precise moment observed when the distortion of the interference-figures of the calcite ceases. But for microscopic investigations a quartz-plate or a Cal- deron artificial twin of calcite is used. The quartz-plate is inserted above the objective. The nicols being crossed and the analyzer revolved until a particular color, say violet, is obtained, then, on placing the section on the stage, the color will be changed, and will remain different until one of the axes of elasticity in the section corresponds with a vibra-
78
PHYSICAL PROPERTIES OF MINERALS.
tion-plane in the nicols, when it will be violet again. This is the point desired.
4. In the triclinic system, since there is no plane of
HORNBLENDE.
PYROXENE.
symmetry, and the crystallographic axes have no rectangu- lar intersections, the positions of the axes of elasticity and of the optic axes have to be determined by the optical ex- amination of sections cut in different directions, and by the angles of extinction measured from different faces of the crystal or cleavage-lines. Some hints as to the positions of the axes may often be derived from their positions in re- lated monoclinic forms of similar chemical compounds; as, for the triclinic feldspars from the monoclinic, for rhodonite from pyroxene, etc. In the triclinic feldspars the extinc- tion-angle is usually measured from the edge between the two cleavage-planes, or parallel to the shorter diagonal of 0. The angle differs for the different kinds, and is the chief means of microscopical determination.
5. Compound crystals, the isometric excepted, are com- pound in their optical characters as well as form. The component parts have their crystallographic axes in dif- erent positions, and hence also their optical axes ; and as a consequence adjoining spectra have the order of colors reversed or otherwise different. When, in the optical ex- aminations of thin slices, halves or alternate sectors, or alternate bands, differ as to the transmission of light, or as to color, there is evidence of a compound structure. In the polysynthetic twins of albite, labradorite, and other triclinic feldspars, if the slice cuts across the vertical axis,
REFRACTION" AND POLARIZATION.
79
parallel bands of light and darkness, or of color, indicate the multiplicity in the twinning, as the mineral is revolved on the stage. Fig. 12 (from Hawes) shows the number of such bands observed in a slice of labradorite (the frac- turing is a consequence of a movement that took place in
12.
the rock after the mineral had crystallized). Fig. 13 rep- resents the peculiar tessellation in the polysynthetic twin- ning of the feldspar, microcline, arising probably from the fact that the angle between the two cleavage-planes differs but 19' from 90°.
For fuller details as to the methods of making optical investigations, see the Text- book of Mineralogy, or some other large work on the subject.
6. Anomalies in Polarization. — There are some isometric crystals which have the property of polarization. Examples occur in crystals of analcite, leu- cite, alum, boracite, fluorite, and diamond . The facts as to analcite were long since described by Sir David Brewster, and the annexed figure, indicating the arrange- ment of the colors or spectra in a trapezohedral crystal of this spe- cies, is from his paper. In some cases also there are variations from the isometric angles, which seem to point to a tetragonal or other form. Leucite has angles and optical characters that have led to its reference to the tetragonal system. Analogous conditions exist also in tetragonal and hexagonal crystals. The latest view is that all such irregularities are due to a molecular strain within the crystals produced at the time of their formation. It has long been known that
80 PHYSICAL PROPERTIES OF MINERALS.
pressure will cause the development of polarizing proper- ties in many substances; and these are analogous cases, except that the pressure is a strain of molecular origin. Optical characters in many of the species under all the systems of crystallization vary much,, and the above is a prominent source of these variations.
7. Dichroism, Pleochroism. — Crystals, excepting those of the isometric system, when colored, often have different colors by transmitted light, and different degrees of trans- parency in the directions of unequal axes at right angles to one another. In tetragonal and hexagonal crystals there may be different colors in the vertical and lateral directions; and in those under the other systems there may be different colors and transparency in three directions. Crystals of tourmaline when transparent or translucent in a direction transverse to the prism are opaque in a vertical direction, because the ordinary ray is absorbed. Zircon, which in a transverse direction is asparagus-green, is pinkish brown in a vertical, the light being differently absorbed as to its component colors in the two directions. The differ- ence in the colors and transparency may be very slight : it is so in pyroxene and enstatite, while usually strong in hornblende and a hypersthene containing much iron. Epi- dote is an example of a monoclinic mineral with different colors in the three axial directions.
The different colors are best seen by polarized light, and this method may be used with very thin sections. On exam- ining a plate of zircon cut parallel to a face of the vertical square prism, with a single nicol or tourmaline plate, the colors appear alternately as the plate or the nicol is revolved. The nicol should be first set at 0°, so that its vibration- plane coincides with the line 0° to 180° on the stage, and then the plate placed on the stage and the stage revolved; and the color thus obtained compared with that after a revolution of 90°.
5. DIAPHANEITY, LUSTRE, COLOR.
\ n •
1. DIAPHANEITY.
Diaphaneity is the property which many objects possess of transmitting light ; or, in other words, of permitting more or less light to pass through them. This property is
DIAPHANEITY, LUSTRE, COLOR. 81
often called transparency, but transparency is properly one of the degrees of diaphaneity. The following terms are used to express the different degrees of this property:
Transparent — when the outlines of objects, viewed through the mineral, are distinct. Example, glass, crys- tals of quartz.
Subtrarisparent, or semitransparent — when objects are seen but their outlines are indistinct.
Translucent — when light is transmitted, but objects are not seen. Loaf-sugar is a good example; also Carrara marble.
Subtranslucent — when merely the edges transmit light faintly.
When no light is transmitted the mineral is described as opaque.
2. LUSTRE.
The lustre of minerals depends on the nature of their surfaces, which causes more or less light to be reflected. There are different degrees of intensity of lustre, and also different kinds of lustre.
a. The kinds of lustre are six, and are named from some familiar object or class of objects.
1. Metallic — the usual lustre of metals. Imperfect me- tallic lustre is expressed by the term submetallic.
2. Vitreous — the lustre of broken glass. An imperfect vitreous lustre is termed subvitreous. Both the vitreous and subvitreous lustres are common. Quartz possesses the former in an eminent degree ; calcite often the latter. This kind of lustre may be exhibited by minerals of any color.
3. Resinous — lustre of the yellow resins. Example, some opal, zinc blende.
4. Pearly — like pearl. Example, talc, native magnesia, stilbite, etc. When united with submetallic lustre the term metallic-pearly is applied.
5. Greasy — looking as if smeared with oil. Example, elseolite, some quartz.
6. Silky — like silk; it is the result of a fibrous structure. Example, fibrous calcite, fibrous gypsum, and many fibrous minerals, more especially those which in other forms have a pearly lustre.
7. Adamantine — the lustre of the diamond. When sub-
82 PHYSICAL PROPERTIES OF MINERALS.
metallic, it is termed metallic adamantine. Example, some varieties of white lead-ore or cerussite.
b. The degrees of intensity are denominated as follows:
1. Splendent — when the surface reflects light with great brilliancy and gives well-defined images. Example, crys- tals of hematite, cassiterite, some specimens of quartz and pyrite.
2. Shining — when an image is produced, but not a well- defined image. Example, calcite, celestite.
3. Glistening — when there is a general reflection from the surface, but no image. Example, talc.
4. Glimmering — when the reflection is very imperfect, and apparently from points scattered over the surface. Example, flint, chalcedony.
A mineral is said to be dull when there is a total absence of lustre. Example, chalk.
3. COLOR.
1. Kinds of Color. — In distinguishing minerals, both the external color and the color of a surface that has been rubbed or scratched, are observed. The latter is called the streak^ and the powder abraded, the streak-powder.
The colors are either metallic or unmet allic.
The metallic are named after some familiar metal, as copper-red, bronze-yellow, brass-yellow, gold-yellow, steel- gray, lead-gray, iron-gray.
The unmetallic colors used in characterizing minerals are various shades of white, gray, Hack, blue, green, yellow, red, and brown.
There are thus snow-white, reddish-white, greenish- white, milk-white, yellowish- white.
Bluish-gray, smoke-gray, greenish-gray, pearl-gray, ash- gray.
Velvet-black, greenish-black, bluish-black, grayish-black.
Azure-blue, violet-blue, sky-blue, indigo-blue.
Emerald-green, olive-green, oil-green, grass-green, apple- green, blackish-green, pistachio-green (yellowish).
Sulphur-yellow, straw-yellow, wax-yellow, ochre-yellow, honey-yellow, orange-yellow.
Scarlet red, blood-red, flesh-red, brick-red, hyacinth-red, rose-red, cherry-red.
DIAPHANEITY, LUSTRE, COLOR. 83
Hair-brown, reddish-brown, chestnut-brown, yellowish- brown, pinchbeck-brown, wood-brown.
A play of colors : — this expression is used when several prismatic colors appear in rapid succession on turning tjie mineral. The diamond is a striking example ; also pre- cious opal.
Change of colors — when the colors change slowly on turn- ing in different positions, as in labradorite.
Opalescence — when there is a milky or pearly reflection from the interior of a specimen, as in some opals, and in cat's-eye.
Iridescence — when prismatic colors are seen within a crystal; it is the effect of fracture, and is common in quartz.
Tarnish — when the surface colors differ from the inte- rior ; it is the result of exposure. The tarnish is described as irised when it has the hues of the rainbow.
3. Asterism. — Some crystals, especially the hexagonal, when viewed in the direction of the vertical axis, present peculiar reflections in six radial directions. This arises either from peculiarities of texture along the axial portions, or from, some impurities. A remarkable example of it is that of the asteriated sapphire, and the quality adds much to its value as a gem. The six rays are sometimes alter- nately shorter, indicating the rhombohedral character of the crystal.
4. Phosphorescence. — Several minerals give out light either by friction or when gently heated. This property of emitting light is called phosphorescence.
Two pieces of white sugar struck against one another give a feeble light, which may be seen in a dark place. The same effect is obtained on striking together fragments of quartz; and even the passing of a feather rapidly over some specimens of zinc-blende is sufficient to elicit light.
Fluorite is the most convenient mineral for showing phos- phorescence by heat. On powdering it and throwing it on a plate of metal heated nearly to redness, the whole takes on a bright glow. In some varieties the light is emerald- green ; in others, purple, rose, or orange. A massive fluor, from Huntington, Connecticut, shows beautifully the em- erald-green phosphorescence. Some kinds of white marble, treated in the same way, give out a bright yellow light. After being heated for a while the mineral loses its phos- phorescence ; but a few electric shocks will, in many cases, to some degree restore it again.
84 PHYSICAL PROPERTIES OF MINERALS.
6. ELECTRICITY AND MAGNETISM.
ELECTRICITY. — Many minerals become electrified on De- ing rubbed, so that they will attract cotton and other light substances ; and when electrified, some exhibit positive and others negative electricity when brought near a delicately suspended magnetic needle. The diamond, whether pol- ished or not, always exhibits positive electricity, while other gems become negatively electric in the rough state, and positively only in the polished state. Some minerals, thus electrified, retain the power of electric attraction for many hours, as topaz, while others lose it in a few minutes.
Many minerals become electric when heated, and such species are said to be pyroelectric, from the Greek pur, fire, and electric.
A prism of tourmaline, on being heated, becomes polar, opposite electricity being developed in the extremities by the heat. The prisms of tourmaline have different sec- ondary planes at the two extremities.
Several other minerals have this peculiar electric prop- erty, especially boracite and topaz, which, like tourmaline, are Jiemiliedral in their modifications. Boracite crystallizes in cubes, with only the alternate solid angles similarly re- placed (Figs. 39, 40, page 26). Each solid angle, on heat- ing the crystals, becomes an electric pole ; the angles diago- nally opposite are differently modified, and have opposite polarity. Pyroelectricity has been observed also in crystals that are not hemihedral, and in many mineral species. In some cases the number of poles is more than two. In preh- nite crystals a large series occur distributed over the sur- face.
MAGNETISM. — The name Lodestone is given to those specimens of an ore of iron called magnetite which have the power of attraction like a magnet; it is common in many beds of magnetite. When mounted like a horseshoe- magnet, a good lodestone will lift a weight of many pounds. This is the only mineral that has decided magnetic attrac- tion. But several ores containing iron are attracted by the magnet, or, when brought near a magnetic needle, will cause it to vibrate ; and moreover, the metals nickel, cobalt, manganese, palladium, platinum and osmium, have been found to be slightly magnetic.
TASTE AND ODOR. 85
Many iron-bearing minerals become attractable by the magnet after being heated that are not so before heating. This arises from a change of part or all of the iron to the magnetic oxide.
7. TASTE AND ODOR.
Taste belongs only to the soluble minerals. The kinds are —
1. Astringent — the taste of vitriol.
2. Sweetish-astringent — the taste of alum.
3. Saline — taste of common salt.
4. Alkaline — taste of soda.
5. Cooling — taste of saltpetre.
6. Bitter — taste of Epsom salts.
7. Sour — taste of sulphuric acid.
Odor is not given off by minerals in the dry, unchanged state, except in the case of a few gases and soluble minerals. By friction, moistening with the breath, the action of acids, and the blowpipe, odors are sometimes obtained which are thus designated:
1. Alliaceous — the odor of garlic. It is the odor of burn- ing arsenic, and is obtained by friction, and more distinctly by means of the blowpipe, from several arsenical ores.
2. Horse-radish odor — the odor of decaying horse-radish. It is the odor of burning selenium, and is strongly perceived when ores of this metal are heated before the blowpipe.
3. Sulphureous — odor of burning sulphur. Friction will elicit this odor from pyrites, and heat from many sul- phides.
4. Fetid — the odor of rotten eggs or sulphuretted hydro- gen. It is elicited by friction from some varieties of quartz and limestone.
5. Argillaceous — the odor of moistened clay. It is given off by serpentine and some allied minerals when breathed upon. Others, as pyrargillite, afford it when heated.
86
CHEMICAL PROPERTIES OF MINERALS.
III. CHEMICAL PROPERTIES OF MIN- ERALS.
THE chemical properties of minerals are of two kinds: (1} Those relating to the chemical composition of minerals; (2) those depending on their chemical reactions, with or without fluxes, including results obtained by means of the blowpipe.
1. CHEMICAL COMPOSITION.
All the elements made known by chemistry are found in minerals, for the mineral kingdom is the source of what- ever living beings — plants and animals — contain or use. A list of these elements, as at present made out, is contained in the following table, together with the symbol for each used in stating the composition of substances. These sym- bols are abbreviations of the Latin names for the elements. A few of these Latin names differ much from the English, as follows:
Stibium Sb = Antimony
Cuprum Cu = Copper
Ferrum Fe = Iron
Plumbum Pb = Lead Hydrargyrum Hg = Mercury
Kalium K = Potassium
Argeutum Ag = Silver
Natrium Na = Sodium
Stannum Sn = Tin
Wolframium W = Tungsten
TABLE OF THE ELEMENTS.
Aluminium
Antimony
A rsenic
Barium
Beryllium
Bismuth
Boron
Bromine
Cadmium
Caesium
Calcium
Carbon
Cerium
|
M |
27.4 |
Chlorine |
|
Sb |
120 |
Chromium |
|
As |
75 |
Cobalt |
|
Ba< Be Bi |
137 13.8 210 |
Copper Didymium Erbium |
|
B |
11 |
Fluorine |
|
Br |
80 |
Gallium |
|
Cd |
112 |
Gold |
|
Cs |
133 |
Hydrogen |
|
Ca |
40 |
Indium |
|
C |
12 |
Iodine |
|
Ce |
92 |
Iridium |
Cl
Cr
Co
Cu
D
E
F
Ga
Au
H
In
I
Ir
35.5
52
59
63.5
95 166
19
70
197
1
113.4 127 198
CHEMICAL COMPOSITION.
8?
|
Iron |
Fe |
56 |
Selenium |
|
Lanthanum |
La |
139 |
Silver |
|
Lead |
Pb |
207 |
Silicon |
|
Lithium |
Li |
7 |
Sodium |
|
Magnesium |
Mg |
24 |
Strontium |
|
Manganese |
Mn |
55 |
Sulphur |
|
Mercury |
Hg |
200 Tantalum |
|
|
Molybdenum |
Mo |
96 ! Tellurium |
|
|
Nickel |
Hi |
59 1 Thallium |
|
|
Niobium(Columbium)Nb(Cb) 94 |
Thorium |
||
|
Nitrogen |
N |
14 |
Thulium |
|
Osmium |
Os |
199 |
Tin |
|
Oxygen |
O |
16 |
Titanium |
|
Palladium |
Pd |
106 |
Tungsten |
|
Phosphorus |
P |
31 |
Uranium |
|
Platinum , |
Pt |
197 |
Vanadium |
|
Potassium |
K |
39 |
Ytterbium |
|
Rhodium |
Ro |
104 |
Yttrium |
|
Rubidium |
Rb |
85.4 |
Zinc |
|
Ruthenium |
Ru |
104 |
Zirconium |
Se
Ag
Si
Na
Sr
S
Ta
Te
Tl
Th
W
U
V
Yb
Y
Zn
Zr
79.4 108 28 23 87.6 32 182 128 204 231 Tm 170.7 Sn 118 Ti 50 184 240 51.3 173 91 65 90
Germanium is the name of another element.
The combining weights indicate the proportions in which the elements combine. Thus, assuming hydrogen, the lightest of the elements, to be 1, or the unit of the series, the combining weight of oxygen is 16; of iron, 56; of mag- nesium, 24; of sulphur, 32; and so on. When hydrogen and oxygen combine it is in the ratio of 2 pounds of hydro- gen, or else 1 pound of hydrogen, to 16 pounds of oxygen, and two different compounds thus result. When oxygen and magnesium combine it is in the ratio of 16 pounds of oxygen to 24 of magnesium. Oxygen and iron combine in the ratio of 16 of oxygen to 56 of iron; or of 24 of oxygen (1-J- times 16) to 56. Sulphur and oxygen combine in the ratio of 32 of oxygen to 32 of sulphur; or of 48 to 32 of sul- phur. The combining weights are often called the atomic weights.
The following is the manner of using the symbols: For the compound consisting of hydrogen and oxygen in the ratio of 2 to 16, the chemical symbol is H20, meaning 2 of hydrogen to 1 of oxygen. (This compound is water.) For the compound of oxygen and magnesium just referred to, the symbol is MgO; for the two compounds of oxygen and iron, FeO, protoxide of iron; Fe203, sesquioxide of iron, the ratio of 1 to 1£ being expressed by 2 to 3; for the two com- pounds of sulphur and oxygen, S0a and S08,
88 CHEMICAL PROPERTIES OF MINERALS.
Some of the elements so closely resemble one another that their similar compounds are closely alike in crystalli- zation and other qualities, and they are therefore said to be isomorphous.
This is true of iron, magnesium, calcium, and two or three other related elements. In one group of compounds of these bases, the carbonates, the crystalline form for each is rhombohedral, and among them there is a difference of less than two degrees in the angle of the rhombohedron. Besides a carbonate of calcium, a carbonate of magnesium, and a carbonate of iron, there is also a carbonate of calcium and magnesium, in which half of the calcium of the first of these carbonates is replaced by half an atom of magne- sium; and another species in which the base, instead of being all magnesium, is half magnesium and half iron. By half is here meant half in the proportion of their combin- ing weights.
The replacement of one of these elements by the other, and similar replacements among other groups of related elements, run through the whole range of mineral com- pounds. Thus we have sodium replacing potassium, ar- senic replacing phosphorus and antimony, and so on.
In the combinations of oxygen and 'iron, as illustrated above, oxygen is combined with the iron in diiferent pro- portions. FeO contains 1 of Fe (iron) to 1 of 0 (oxygen) and Fe203, or, as it is often written, Fe03, contains f Fe to 1 of 0. As the iron in each of these cases satisfies the oxygen, it is evident that the iron must be in two different states, (1) a protoxide state, and (2) a sesquioxide state. One part of iron in this SQsquioxide state (= |Fe) often replaces in compounds one part of iron in the protoxide state (or IFe), with no greater change of qualities than happens in the replacement of iron by magnesium, or cal- cium,, explained above ; or, avoiding fractions, 3 parts of Fe in the protoxide state replaces 2Fe in the sesquioxide state. Writing Fe for the last 2Fe, the statement becomes 1 of Fe3 replaces 1 of Fe. Aluminium occurs only in the sesquioxide state, and the ordinary symbol of the oxide is Al?03, or A103. But it is closely related to iron in the ses- quioxide state, so that, using the same mode of expression as for iron, 1 of Al replaces 1 of Fe3, or 1 of Mg3, and so on. Similarly, writing R for any metal, 1 of R replaces 1 of E9. Again, in potash (K20), soda (Na30), lithia (LiaO),
CHEMICAL COMPOSITION. 89
water (H20), one of oxygen (0) is combined severally with 2 of K (potassium), of Na (sodium),, of Li (lithium), of hy- drogen ; and hence 2K, 2Na, 2 Li, that is, K2, Na2, Li,, may each replace in compounds ICa, or IMg, etc.
The elements potassium, sodium, lithium, hydrogen, oi which it takes two parts to combine with 1 of oxygen, are called monads. Other elements of the group of monads are rubidium, ccBsium, thallium, silver, and also fluorine, chlorine, bromine, iodine. Still other elements combining by two parts in their oxygen or sulphur compounds, etc., are nitrogen, phosphorus, antimony, boron, niobium, tan- talum, vanadium and gold. For example, for arsenic there are the compounds As2S, As2S3, As203, As205, etc. Another characteristic of these elements of the hydrogen, sodium, chlorine, and arsenic groups is that the number of equiva- lents of the acidic element in the compounds into which they enter is/ with a rare exception, odd, and of the 1, 3, 5, etc., series, and on this account they are called in chemis- try perissads; while the other elements, in whose com- pounds their number is of the 1, 2, 3, etc. (or 2, 4, 6) series, are called artiads. An apparent exception exists under the artiads in the sesquioxides, but this does not alter the general character of the series.
The facts above cited sustain the general statement that Ca3, Mg3, Mn3, Zn3, Fe3, Al, Fe, Mn, have equivalent com- bining values, and hence in minerals often replace one an- other; and so also Ca, Mg, Mn, Zn, Fe, K2, Na2, Li2, H2, may replace one another. Similarly, also, As2, or Sb,, re- places S in some minerals.
With reference to the classification of minerals the ele- ments may be conveniently divided into two groups : (1) the Acidic, and (2) the Basic. The former includes oxy- gen and the elements which were termed the acidifiers and acidifiable elements in the old chemistry. They are those which have been called in mineralogy the mineralizing ele- ments, since they are the elements which are found com- bined with the metals to make them ores, that is, to miner- alize them. The basic are the rest of the elements. The groups overlap somewhat, but this need not be dwelt upon here.
The more important of the acidic elements are the fol- lowing: oxygen, fluorine, chlorine, bromine, iodine, sul- phur, selenium, tellurium, boron, chromium, molybdenum,
90 CHEMICAL PEOPERTIES OF MINERALS.
tungsten, phosphorus, arsenic, antimony, vanadium, nitro- gen, tantalum, niobium, carbon, silicon.
Again, among the conpounds of these elements occurring in the mineral kingdom there are two grand divisions, the binary and the ternary. The binary consist of one or more elements of each of the acidic and basic divisions, and the ternary of one or more elements of each of these two classes, along with oxygen, fluorine, or sulphur as a third. The binary include the sulphides, arsenides, chlorides, fluor- ides, oxides, etc., and the ternary the sulphates, chromates, bor at es,ar senates, phosphates, silicates, carbonates, etc., and also the sulpk-arsenites and sulph-antimonites, in which a basic metal (usually lead, copper, silver) is combined with arsenic or antimony and sulphur.
The following are examples of the symbols of binary and ternary compounds :
1. Binary.
1. Sulphides, Selenides. — Ag2S = silver sulphide; Ag2Se = silver selenide; PbS — lead sulphide; ZnS = zinc sul- phide; FeS? = iron disulphide.
2. Fluorides, Chlorides, etc. — CaF2 — calcium fluoride; AgCl — silver chloride; AgBr = silver bromide; Agl = silver iodide; NaCl = sodium chloride (common salt).
3. Oxides. — AlaO, = 3(A1§ 0) — aluminium sesquioxide; As203 = arsenic trioxide; As20B = arsenic pentoxide; BaO = barium oxide; Be203 = beryllium oxide; B203 = boron trioxide (boracic acid) ; CaO = calcium oxide (lime); CeO = ceria; C0? — carbon dioxide (carbonic acid); Cr03 = chromium trioxide (chromic acid); Cu?0 = copper subox- ide; CuO = copper oxide; DiO = didymia; H20 = hy- drogen oxide (water) ; FeO — iron oxide .; Fe?03 = iron sesquioxide; PbO = lead oxide; LiaO = lithium oxide; MgO = magnesium oxide ; MnO = manganese oxide ; Mn,0s = manganese sesquioxide; MnO, — manganese di- oxide; P20& •= phosphorus pentoxide; K20 — potassium oxide; Si02 — silicon dioxide (silica); Na20 — sodium oxide; SrO = strontium oxide; S02 = sulphur dioxide (sulphurous acid); S03 = sulphur trioxide; Sn02 = tin dioxide ; Tm203 — thulia; V205 = vanadium pentoxide (vanadic acid); W03 = tungsten trioxide (tungstic acid);
CHEMICAL COMPOSITION. 91
5Tb2Os = ytterbia; ZnO = zinc oxide; Zr03 = zirconium dioxide.
The composition of these compounds may be obtained from the table of combining weights, page 86. For exam- ple, with reference to the first of them (AgaS), the table gives for the combining weight of silver (Ag), 108, and for that of sulphur, 32. The elements exist in the compound therefore in the proportion of 216 to 32, and from it the composition of a hundred parts is easily deduced.
If the formula were (Ag2, Pb)S, signifying a silver-and- lead sulphide, and if the silver and lead were in the ratio of 1 to 1, then once the combining weight of silver is taken ; that is, 108, and half the atomic weight of lead, which is 103*5; and the sum of these numbers, with 32 for the sul- phur, expresses the ratio of the three ingredients.
For A1203 we find the combining weight of aluminium 27*4; doubling this for A12 makes 54-8. Again, for oxygen, we find 16; and three times 16 is 48. 54*8 to 48 is there- fore the ratio of aluminium to the oxygen in A1208, from which the percentage proportion may be obtained.
2. Ternary Oxygen Compounds.
Silicates. — Of these compounds there are two prominent groups. In one of these groups the general formula is R03Si, and in the other R204Si. In both of these formu- las, K stands for any basic elements in the protoxide- state, as Ca, Mg, Fe, etc., either alone or in combination. If the basic element is Mg (magnesium) they become Mg08Si, and Mg04Si (sometimes also written MgO -f- Si02 and 2MgO + Si02, this being the old style). In the first of these formulas the combining values of the basic element R and the acidic element or silicon, as measured by their combinations with oxygen, are in the proportion of 1 to 2, for R stands for an element in the protoxide state, while Si stands for silicon, which is in the dioxide state, its oxide being a dioxide; and hence the minerals so constituted are called Bisilicates. In the second of these formulas this ratio is 2 to 2, or 1 to 1, and hence these are called Unisili- cates. The second style of formula (the old style) has the advantage of expressing the bases and acids obtained in an analysis and mentioned in the tables of percentage results
92 CHEMICAL PROPEETIES OF MINERALS.
Multiplying these formulas by 3, they become R309Sis, and (2R3)012Si3; and the same composition is expressed. In this form the substitution of sesquioxide bases for pro- toxide may be indicated: thus, R3ROJ2Si3 signifies that half of the 2R3 is replaced by Al or fee, or some other ele- ment in the sesquioxide state.
There are also some species in which the ratio is 1 to less than 1, and these are called Subsilicates.
The ratio here referred to is the oxygen ratio or the quantivalent ratio.
The other ternary compounds require no special remarks in this place.
2. CHEMICAL REACTIONS. 1. Trials in the wet ivay.
1. Test for Carbonates. — Into a test-tube put a little hy- drochloric acid diluted with one half water, and add a small portion in powder of the mineral. With a carbonate, there will be a brisk effervescence caused by the escape of carbonic dioxide (carbonic acid), when heat is applied, if not before. With calcium carbonate no heat or pulveriza- tion is necessary.
2. Test for Gelatinizing Silica. — Some silicates, as neph- elite and many zeolites, when powdered and treated with strong hydrochloric acid, are decomposed, and deposit the silica in the state of a jelly. The experiment may be per- formed in a test-tube, or small glass flask. Sometimes the evaporation of the liquid nearly to dryness is necessary in order to obtain the jelly. Some silicates do not afford the jelly unless they have been previously ignited before the blowpipe, and some gelatinizing silicates lose the power on ignition.
Test for Soda in some Silicates. — When nephelite is treated with hydrochloric acid the solution deposits, on evaporation, cubes of common salt (sodium chloride); and in this and some other sodium silicates, if the hydrochloric solution is treated with a concentrated solution of uranium acetate, yellow tetrahedrons of sodium uranate are formed.
3. Decomposability -of Minerals by Acids. — To ascertain whether a mineral is decomposable by acids or not, it is very finely powdered and then boiled with strong hydro-
CHEMICAL REACTIONS. 93
chloric acid, or, in case of many metallic minerals, with nit- ric acid. In some cases (as leu cite, scapolite, labradorite, etc.), where no jelly is formed, there is a deposit of silica in a pulverulent state. With the sulphides and nitric acid there is often a deposit of sulphur, which usually floats upon the surface of the fluid as a dark spongy mass; with hydro- chloric acid and some sulphides, sulphuretted hydrogen is given off. Some oxides, and also some sulphates and many phosphates, are soluble entirely without effervescence. But many minerals resist decomposition with nitric acid as well as hydrochloric. It is sometimes difficult to tell whether a mineral is decomposed with the separation of the silica or whether it is unacted upon. In such a case a portion of the clear fluid is neutralized by soda (sodium carbonate), and if anything has been dissolved it will usually be pre- cipitated.
4. Test for Lime in Apatite. — A solution of apatite in hydrochloric acid, if treated with sulphuric acid, deposits gypsum freely.
5. Test for Titanium in Menaccanite. — The pulverized mineral, heated with hydrochloric acid, is slowly dissolved ; the yellow solution, filtered from the undecomposed mineral and boiled with the addition of tin-foil, assumes a beautiful blue or violet color — a result not obtained with hematite, the mineral it most resembles.
6. Test for Fluorine. — Most fluorides (as fluorite, cryolite, etc. ) are decomposed by strong heated sulphuric acid, and give out fluorine which will etch a glass plate in reach of the fumes. The trial may be made in a lead cup, and the glass put over it as a loose cover.
7. Test for Native Iron. — Dilute nitrate of copper de- posits copper on a clean plate of iron.
8. Test for Phosphoric Acid in, Apatite, etc. — A concen- trated nitric-acid solution of ammonium molybdate acts on apatite and deposits yellow octahedrons or dodecahedrons of ammonium phosphomolybdate; and a drop of the solu- tion will produce this result with the apatite of a thin sec- tion prepared for microscopic study.
2. Trials luith the Blowpipe.
The blowpipe, in its simplest form, is merely a bent tube of small size, eight to ten inches long, terminating at one
94 CHEMICAL PROPERTIES OF MINERALS.
end in a minute orifice. It is used to concentrate the flame on a mineral, and this is done by blowing through it while the smaller end is just within the flame.
The annexed figure represents the form commonly em- ployed, except that it often has a trumpet-shaped mouth- piece. It contains an air-chamber (o) to receive the moisture which is condensed in the tube during the blowing; the moisture, unless thus removed, is often blown through the small aperture and interferes with the experiment. The jet, jt, is movable, and it is desirable that it should be made of platinum, in order that it may be cleaned when necessary, either by high heating or by immersion in an acid.
In using the blowpipe it is necessary to breathe and blow at the same time, that the oper- ator may not interrupt the flame in order to take breath. Though seemingly absurd, the neces- sary tact may easily be acquired. Let the stu- dent first breathe a few times through his nos- trils while his cheeks are inflated and his mouth closed. After this practice let him put the blowpipe to his mouth and he will find no diffi- culty in breathing as before while the muscles of the inflated cheeks are throwing the air they contain through the blowpipe. When the air is nearly exhausted the mouth may again be filled through the nose without interrupting the pro- cess of blowing.
The flame of a candle, or a lamp with a large wick, may be used; and when so, it should be bent in the direction the flame is to be blown. But it is far better, when gas can be had, to use a Bunsen's burner.
The flame has the form of a cone, yellow without and blue within. The heat is most intense just beyond the ex- tremity of the blue flame. In some trials it is necessary that the air should not be excluded from the mineral during the experiment, and when this is the case the outer flame is used. The outer is called the oxidizing flame (because oxygen, one of the constituents of the atmosphere, com- bines in many cases with some parts of the assay, or sub- stance under experiment), and the inner the reducing flame. In the latter the carbon and hydrogen of the flame, which are in a high state of ignition, and which are enclosed from
CHEMICAL REACTIONS. 95
the atmosphere by the outer flame, tend to unite with the oxygen of any substance that is inserted in it. Hence sub- stances are reduced in it.
The mineral is supported in the flame either on charcoal ; or by means of steel forceps (as in the annexed figure) with
platinum extremities (ab), opened by pressing on the pins p p\ or on platinum wire or foil.
To ascertain i1c& fusibility of a mineral, the fragment for the platinum forceps should not be larger than the head of a pin, and, if possible, should be thin and oblong, so that the extremity may project beyond the platinum. The fu- sible metals alloy readily with platinum. Hence com- pounds of lead, arsenic, antimony, etc., must be guarded against. These compounds are tested on charcoal. The forceps should not be used with the fluxes, but instead either charcoal or the platinum wire or foil.
The charcoal should be firm and well burnt; that of soft wood is the best. It is employed especially for the reduc- tion of oxides, in which the presence of carbon is often necessary, and also for observing any substances which may pass off and be deposited on the* charcoal around the assay. These coatings are usually oxides of the metals, which are formed by the oxidation of the volatile metals as they issue from the reduction-flame.
The platinum wire is employed in order to observe the action of the fluxes on the mineral, and the colors which the oxides impart to the fluxes when dissolved in them. The wire used is No. 27. This is cut into pieces about three inches long, and the end is bent into a small loop, in which the flux is fused. This makes what is called a bead. When the experiment is complete the beads are removed by uncoiling the loop and drawing the wire through the finger- nails. After use for awhile the end breaks off, because pla- tinum is acted upon by the soda, and then a new loop has to be made. Dilute sulphuric acid will remove any of the flux that may remain upon it after a trial has been made.
Glass tube is employed for various purposes. It should be from a line to a fourth of an inch in bore. It is cut into
9G CHEMICAL PROPERTIES OF MINERALS.
pieces four to six inches long, and used in some cases with both ends open, in others with one end closed. In the closed tube, either heated directly over the Bunsen burner, or with the aid of the blowpipe, volatile substances in the assay are vaporized and condensed in the upper colder part of the tube, where they may be examined by a lens if neces- sary, or by further heating. The odor given off may also be noted; also the acidity of any fumes by inserting a small strip of litmus paper in the mouth of the tube, for acids redden litmus paper. The closed tube is used to observe all the effects that may take place when a substance ds heated out of contact with the air. In the open tube the atmosphere passes through the tube in the heating, and so modifies the result. The assay is placed an inch or an inch and a quarter from the lower end of the tube ; the tube should be held nearly horizontally, to prevent the assay from falling out. The strength of the draught depends upon the inclination of the tube, and in special cases it should be inclined as much as possible.
The most common flaxes are borax (sodium biborate), sail of phosphorus (sodium and ammonium phosphate), and soda (sodium carbonate, either the carbonate or bicarbon- ate of soda of the shops). These substances, when fused and highly heated, are very powerful solvents for metallic oxides. They should be pure preparations. The borax and soda are much the most important. In using the pla- tinum wire, the loop may be highly heated, and then a por- tion of the borax or soda may be taken up by it, and by successive repetitions of this process the requisite amount of the flux may be obtained on the wire. Then, by bringing the melted flux of the loop into contact with one or more grains of the pulverized mineral, the assay is made ready for the trial. With soda and quartz a perfectly clear glob- ule is obtained, cold as well as hot, if the flux is used in the right proportion. Some oxides impart a deep and characteristic color to a bead of borax. In other cases the color obtained is more characteristic when salt of phos- phorus is employed. The color obtained in the outer flame is often different from that which is obtained in the inner flame. The beads are sometimes transparent and some- times opaque. If too much substance is employed the beads will be opaque when it is desired that they should be transparent, and in such cases the experiment should be re-
CHEMICAL REACTIONS. 97
peated with less substance. In many cases pulverized min- eral and the flux,, a little moistened, are mixed together into a ball upon charcoal, especially in the experiments with soda.
In the examination of sulphides, arsenides, antimonides and related ores, the assay should be roasted before using a flux, in order to convert the substance into an oxide. This is done by spreading the substance out on a piece of char- coal and exposing it to a gentle heat in the oxidizing flame. The sulphur, arsenic, antimony, etc. then pass off as ox- ides in the form of vapors, leaving the non-volatile metals behind as oxides. The escaping sulphurous acid gives the ordinary odor of burning sulphur ; arsenous acid, from ar- senic present, the odor of garlic, or an alliaceous odor ; se- lenous acid, from selenium present, the odor of decaying horse-radish ; while antimony fumes are dense white, and have no odor.
The following is the scale of fusibility which has been adopted, beginning with the most fusible :
1. STIBNITE. — Fusible in large pieces in the candle flame.
2. NATROLITE. — Fusible in small splinters in the candle flame.
3. ALMAN DINE, or bright-red GARNET. — Fusible in large pieces with ease in the blowpipe flame.
4. ACTINOLITE. — Fusible in large pieces with difficulty in the blowpipe flame.
5. ORTHOCLASE, or common feldspar. Fusible in small splinters with difficulty in the blowpipe flame.
6. BRONZITE. Scarcely fusible at all.
The color of the flame is an important character in connec- tion with blowpipe trials. When the mineral contains sodium the color of the flame is deep yellow, and this is generally true in spite of the presence of other related ele- ments. When sodium (or soda) is absent, potassium (or potash) gives a pale violet color; calcium (or lime) a pale reddish yellow; lithium, a, deep purple-red, as in lithia- mica; strontium, a bright red, this element being the usu- al source of the red color in pyrotechny; copper, emerald green; phosphates, bluish green; boron, yellowish green; copper chloride, azure-blue. Beads should be examined by daylight only, and should be held in such position that the color is not modified by green trees or other bright objects when examined by transmitted light. Colored flames are 7
98 CHEMICAL PROPERTIES OF MINERALS.
seen to best advantage when some black object is beyond the flame in the line of vision.
It is also to be noted, in the trials, whether the assay heats up quietly or with decrepitation; whether it fuses with effervescence or not, or with intumescence or not; whether it fuses to a bead which is transparent, clouded, or opaque; whether blebby (containing air-bubbles) or not; whether scoria-like or not.
Testing for Water. — The powdered mineral is put at the bottom of a closed glass tube, and after holding the ex- tremity for a moment in the flame of a Bunsen's burner, moisture, if any is present, will have escaped and be found condensed on the inside of the tube, above the heated portion. Litmus or turmeric paper is used to ascertain if the water is acid or alkaline, acids changing the blue of lit- mus paper to red, and alkalies the yellow of turmeric paper to brown.
Testing for an Alkali. — If the fragment of a mineral, heated in the platinum forceps, contains an alkali, it will often, after being highly heated, give an alkaline reaction when placed, after moistening, on turmeric paper, turning it brown. This test is applicable to those salts which, on heating, part with a portion of their acid and are rendered caustic thereby. Such are the carbonates, sulphates, ni- trates, and chlorides of the alkaline metals.
Testing for Alumina or Magnesia. — Cobalt nitrate, in solution, is used to distinguish an infusible and colorless mineral containing aluminium from one containing mag- nesium. A fragment of the mineral is first ignited, and then wet with a drop or two of the cobalt solution and heated again. The aluminium mineral will assume a blue color, and the magnesium mineral a pale red or pink.
Any fusible silicate, when moistened with cobalt nitrate and ignited, will assume a blue color, hence this tost is only decisive in testing infusible substances.
Infusible zinc compounds, when moistened with cobalt nitrate, assume a graen color.
Testing for Lithium. — Some lithium minerals give the bright purple-red flame if simply heated in the platinum forceps. In other cases mix the powdered mineral with one part of fluorite and one of potassium bisulphate. Make the whole into a paste with a little water, and heat it on the platinum wire in the blue flame.
CHEMICAL REACTIONS. 99
Testing for Boron. — When the bright yellow-green of boron is not obtained directly on heating the mineral con- taining it, one part of the powdered mineral should be mixed with one part of powdered fluorite and three of po- tassium bisulphate; and then treated as in the last. The green color appears at the instant of fusion.
Testing for Fluorine. — To detect fluorine in fluorides mix a little of the powdered substance with potassium bi- sulphate, put the mixture in a closed glass tube and fuse gently. The bisulphate gives off half of its sulphuric acid at a high temperature, which acts powerfully on anything it can attack. If a fluoride is present, hydrofluoric acid will be given off, and the walls of the tube will be found roughened and etched when the tube is broken open and cleaned after the experiment. If a silicate containing fluorine be powdered and mined with previously fused salt of phosphorus, and heated in the open tube by blowing the flame into the lower end of the tube, hydrofluoric acid is given off, and the tube is corroded just above the assay.
Silicates. — Nearly all silicates undergo decomposition with salt of phosphorus, setting free the silica, forming a bead which is clear while hot and has a skeleton of silica floating in it. The bead is sometimes clear also when cold.
Iron. — Minerals containing much iron produce a mag- netic globule when highly heated. Usually the reducing flame is required, and sometimes the