. CRYSTALLOGRAPHY AN ELEMENTARY MANUAL FOR THE LABORATORY BY M. EDWARD WADSWOKTH, A. M., PH. D., F. G. S., Dean of the School of Mines and Professor of Mining Geology in the University of Pittsburgh ; Late President of the Michigan College of Mines and Dean of the School of Mines and Metallurgy in the Pennsylvania State College. WITH 6 TABLES,, 29 PLATES. .AN QJB12 FIGURES PHILADELPHIA : JOHN JOSEPH McVEY 1909 COPYRIGHT, 1909, JOHN JOS. McVEY So tbc jflfcemotB of JOSIAH DWIGHT WHITNEY, LL. D. STATE GEOLOGIST OF CALIFORNIA AND STURGIS-HOOPER PROFESSOR OF GEOLOGY IN HARVARD UNIVERSITY. LINGUIST, CHEMIST, MINERALOGIST, GEOLOGIST, AND MINING GEOLOGIST. ONE OF GOD'S NOBLEST WORKS, AN HONEST MAN. 331235 INTRODUCTION CRYSTALLOGRAPHY can be studied from two different view-points : one as a mathematical science with its applications both in the instrumental determination of crystal angles and in their mapping or projection ; the other chiefly as an observational study with the appli- cation of some simple rules that will enable the pros- pector and laboratory student to determine the crys- talline form with sufficient accuracy for practical purposes in the field or laboratory. It is the intention here simply to devote our time to the latter practical purpose, which is all that the average engineering or science student, who is not making a specialty of Crystallography and Mineralogy, has time to accom- plish. In the study of this subject I worked out a course of brief lectures in 1873, and used them in laboratory work at Harvard University. Subsequently, in 1876 and in later years, they were given in connection with my lectures upon Mineralogy in that institution. These lectures form the nucleus of this little work. With but little modification they were given after- (v) yi INTRODUCTION. wards at Colby University, 1885-1887; and at the Michigan College of Mines (formerly the Michigan Mining School), from 1887 for a number of years, until I turned the work over to my assistant, Dr. H. B. Patton, placing my lecture notes in his hands. The principal and essential features of these lecture notes were the rules for the determination of the forms by the relation of the planes to the crystallographic axes. They were originally worked out by me in 1873, and I have never seen them in print anywhere, except when Dr. Patton in 1893 published the lecture notes he had used at the Michigan College of Mines. A second enlarged edition of his book was published by Dr. Patton in 1896, and a third in 1905. Un- fortunately, Dr. Patton failed to acknowledge the source whence those rules were obtained. It has been my intention for over thirty years to elaborate and publish my notes for the use of my students, but as my time has been fully occupied in other work, principally in development work and in executive duties, as well as in original investigation, very little time has been available in which to prepare my notes for publication. Even now, on account of the present demands upon my time, but little elabora- tion can be made. These notes are published now primarily for use in my own classes, containing over one hundred students in Mineralogy. It is hoped, INTRODUCTION. v however, that they will be useful to other teachers, who, under similar circumstances, are required to give instruction in Crystallography, Mineralogy, and kin- dred sciences, as a means to an end, and not as subjects to be studied purely for themselves. Such a practical purpose cornes naturally as the result of the present tendency of industrial education. It is now required that the fundamental sciences be reduced to the mini- mum, in order that in four years the student may re- ceive not only his general culture and intellectual fur- nishing, but that he may also obtain the maximum amount of training in the practical application of the sciences to his future engineering or technical occupa- tion. My notes have been presented in the form of lectures in THE PENNSYLVANIA STATE COLLEGE since 1901, and until recently I have followed the more common cus- tom of starting with the Isometric System; but exper- ience has led me to believe it is best to develop the work in the reverse order, beginning with the Tri- clinic System. While the original notes form the essential basis of this work, there will be this differ- ence : the original notes for lecture purposes formed simply a skeleton, and any additional explanations were given orally by the instructor. In the case of this book the necessary explanatory matter has been added to a considerable extent. INTRODUCTION. Instruction in Crystallography presupposes the use of a collection of natural crystals and of crystal models, as well as personal instruction in the laboratory. In case such collections can not be had, models can be cut out of soft wood like cedar, or out of chalk. They can be made also from putty or clay and dried. Per- ishable ones can be cut out of potatoes or turnips or some other suitable vegetable. The glass, paper and wooden models for sale by Dr. F. Krantz, Bonn-am-Rhein, Germany, and other Ger- man dealers, are excellent, and every laboratory should be well stocked with them. Smaller collec- tions are for sale by the Foote Mineral Company, Philadelphia ; Otto Kuntze, Iowa City, Iowa ; and Ward's Natural Science Establishment, Rochester, N. Y. The larger foreign collections can be imported by the above-mentioned firms, as well as by others, for the institutions or individuals desiring them. Natural Crystals can be obtained from the above firms or from any other dealers in minerals. The methods of instruction I have employed in Crystallography and Mineralogy were detailed in a paper read before the Society of Naturalists in 1883, and published in the Popular Science Monthly during the following year (pages 454-459). After a long ex- perience with these methods it appears that the best results have been obtained by first going over care- INTRODUCTION. IX fully one crystal system and studying a selected set of models in that system. After the pupil has familiar- ized himself with the general characters and forms in that system, he has been given a large collection of unlabeled models of that system. After working them out, he has then been given an individual recitation upon these forms, his errors have been corrected, and all points of obscurity have been explained to him. The same method has then been followed with an- other system, and so on, until the entire six systems, including their twin forms, are understood, so far as the crystal models are concerned. The student has then been assigned drawers con- taining models of every system mixed together, so that he will learn to distinguish the forms of one system from those of another. After this he has been as- signed natural crystals belonging to each system for his personal study, following the same method as with the models ; and then he has been handed a mixed set of natural crystals of every system. The method will naturally have to be varied in each case according to the number of crystals or models each instructor has at his disposal. There seems to be no way of teaching the student to know the things he is studying except the labora- tory or field method, as mere theory is of but little avail in the practice of the engineer or mining X INTRODUCTION. geologist, when he needs to know what is the mineral he has found. The student who wishes to carry the study of Crys- tallography further will find help in the excellent chapter upon this subject in Brush and Penfield's " Manual of Determinative Mineralogy and Blowpipe Analysis," John Wiley & Sons, New York, or in the following valuable works : Bauerman, " Systematic Mineralogy," Longmans, Green & Co., London, 1881. Dana, "Text Book of Mineralogy," 3rd Ed., John Wiley & Sons, New York, 1898. Gurney, "Crystallography," Society for Promoting Chris- tian Knowledge, London. No date. Hilton, "Mathematical Crystallography," Clarendon Press, Oxford, 1903. Kraus, " Essentials of Crystallography," Ann Arbor, 1906. Lewie, "Treatise on Crystallography," University Press, Cambridge, England, 1899. Miers, "Mineralogy," Macmillan & Co., London, 1902. Miller, "A Tract on Crystallography," Deighton, Bell & Co., Cambridge, England, 1863. Milne, ' ' Notes on Crystallography and Crystallo-physics, ' ' Trfibner & Co., London, 1879. Moses, "The Characters of Crystals," D. Van Nostrand Co., New York, 1899. Moses and Parsons, "Elements of Mineralogy, Crystal- lography and Blowpipe Analysis," 2nd Ed., D. Van Nostrand Co., New York, 1904. INTRODUCTION. xi Patton, "Lecture Notes on Crystallography," 3rd Ed., D. Van Nostrand Co.., New York, 1905. Story-Mask elyne, "Crystallography," Clarendon Press, Oxford, 1895. Williams, " Elements of Crystallography," Henry Holt & Co., New York, 1890. Woodward, "Crystallography for Beginners," Simpkin, Marshall, Hamilton, Kent & Co., London, 1896. In the German and the French, among the more recent works, , the attention of the student may be called to the following : Bauer, "Lehrbuch der Mineralogie," 2 A., 1904. Bravais, " Etudes crystallographiques," 1866. Brezina, " Methodik der Krystallbestimmung," 1883. Bruhns, "Elemente der Krystallographie," 1902. Des Cloizeaux, " Legons de cristallographie," 1861. Frankenheim, " Zur Krystallkunde," 1869. Friedel, "Cours de Mineralogie," 1893. Goldschmidt, ' * Krystallographische Projection sbilder," 1887. Goldschmidt, " Index 'der Krystallformen der Mineral- ien," 1886-1891. Groth, u Physikalische Krystallographie," 1905. Hecht, "Anleitung zur Krystallberechnung," 1893. Heinrich, " Lehrbuch der Krystallberechnung, " 1886. Hochstetter and Bisching, "Leitfaden der beschreibenden Krystallographie," 1868. Xii INTRODUCTION. Joerres, "Eine Abhandlung tiber Krystallographie," von W. H. Miller, 1864. Karsten, " Lehrbueh der Krystallographie," 1861. Klein, "Einleitung in die Krystallberechnung," 1876. Klockmann, " Lehrbuch der Mineralogie," 4 A., 1907. Knop, "System der Anorganographie," 1876. Kobell, "Zur Berechnung der Krystallformen," 1867. Kopp, "Einleitung in die Krystallographie, mit einem Atlas," 1862. Krefei, " Eleraente der mathematischen Krystallog- raphie," 1887. Lang, " Lehrbuch der Krystallographie," 1866. Lapparent, "Cours de Mineralogie," 3rd Ed., 1899. Liebisch, u Geometrische Krystallographie," 1881. Liebisch, " Physikalische Krystallographie," 1891. Liebisch, " Grundriss der physikalischen Krystallog- raphie," 1896. Linck, "Grundriss der Krystallographie," 1896. Lion, " Trait6 616mentaire cristallographie g6ometrique," 1891. Mallard, "Trait6 der cristallographie," 1879. Martius-Matzdorff, "Die Elemente der Krystallogra- phie," 1871. Naumann-Zirkel, "Elemente der Mineralogie," 14 A., 1901. Nies, " Allgemeine Krystallbeschreibung," 1895. Quenstedt, " Grundriss der bestimmenden und rechnenden Krystallographie," 1873. Renard et Stoeber, " Notions de Mineralogie, 1900. INTRODUCTION. Xlll Rose-Sadebeck, " Elemente der Krystallographie, ' ' Band L, 1873. Sadebeck, "Angewandte Krystallographie," 1876. Schoenflies, " Krystallsysteme und Krystallstructur," 1891. Scbrauf, " Lebrbuch der Krystallographie," 1866. Sohncke, " Entwicklung einer Theorie der Krystall- structur," 1879. Sommerfeldt, u Geometrische Kristallograpbie," 1006. Sommerfeldt, " Physikalische Kristallograpbie," 1907. Soret, " Elements de crystallographie physique," 1893. Tschermak, "Lebrbuch der Wineralogie," 6 A., 1905. Twrdy, "Methodischer Lehrgang der Kristallographie," 1900. Viola, "Grundzuege der Kristallograpbie," 1904. WebBky, "Anwendung der Linearprojection zur Berech- nung der Krystalle," 1886. Werner, " Leitfaden zum Studium der Krystallographie," 1867. VViilfing, " Tabellarische Uebereicht der einfachen For- men 32 krystallographischen Symmetriegruppen," 1895. WyroubofT, " Manuel pratique de cristallographie," 1888. To many of the older works, especially those of Miller and Naumann, every student of Crystallography needs to refer, as well as to the writings of James D. Dana. The author has been indebted greatly not only to them, but also to very many of the works cited above, and to the lectures and writings of Cooke. xiv INTRODUCTION. Obviously the training in Crystallography, as in every other subject, should not proceed by making the principles obscure, but rather by having them clearly and easily understood. The student should obtain his knowledge of the subject and his mental discipline by applying these principles in actual prac- tice. In the practical application he should be thor- oughly questioned to see that he has not only mastered the principles but can readily and understandingly apply them in the laboratory and field. The text in " Language Studies " and the examples in Mathematics furnish laboratory practice for students in those subjects, but in " Nature Studies " the objects must be supplied and worked over in the laboratory or field ; otherwise the pupil better be employed in learning one of Webster's orations, instead of mem- orizing words that he knows nothing about. Recita- tion in " Science Study " without laboratory or field training amounts to mere declamation, whether the teaching is given in the primary school or in the col- lege or university. To repeat : the study of Crystallography with models and natural crystals can be made pleasant and inter- esting, but without them the study is in the nature of a farce unless pursued purely as a branch of Mathe- matics. Similar methods to those mentioned for Crystallography I have employed with excellent re- INTRODUCTION. XV suits in Mineralogy and Petrography ; and by my direction they were used with similar satisfactory results in the study of Zoology and Paleontology, taught by my assistant, now Professor, A. E. Seaman, at the Michigan College of Mines. These principles seem capable of a much more extended use in scien- tific, technical, and practical education. It is my expectation to publish similar lecture notes on Min- eralogy and Petrography. In a subject so thoroughly worked over as Crystal- lography has been, nothing original can be expected in so elementary a text as this, except possibly in its effort to lessen the student's labor and thus save him time. If it can enable engineering and scientific students to grasp readily as much of the principles of Crystallography as they need for their subsequent Mineralogical work, its purpose will have been accom- plished. The first nine chapters are intended to be used for laboratory work and for recitation, and the last three for reference and illustration. In trying to make matters clear to a student one is apt to forget that the pupil has not the same familiar- ity with the various steps in the process as has the writer. This book is an attempt to smooth the way for the pupil as far as practicable. The author will be very glad to receive the sug- gestions of other teachers of this subject, and will be XVI INTRODUCTION. sincerely grateful to anyone who will point out to him such parts of his book as are not entirely clear or accurate. M. EDWARD WADSWORTH. THE PENNSYLVANIA STATE COLLEGE, State College, Pa., August 12, 1909. TABLE OF CONTENTS PAGE INTRODUCTION v-xvi Origin of these Notes v-vii Rules for Determining Forms vi Need of Laboratory Collections viii Methods of Instruction viii, ix, xiv, xv Literature x-xiii Application of Principles xv, xv CHAPTER I PRELIMINARIES 1-8 Natural World - 1 Mineral Kingdom or Mineralogy 1 Vegetable Kingdom or Botany ^ > Biology 1 Animal Kingdom or Zoology J Mineralogy 1, 2 Mineral Chemistry . 2 Optical Mineralogy 2 Crystallography 2 Minerals and Crystals 3-6 Distortion of Forms . , . 3 Uniformity of Inclination of Faces 3 Locating Points 3-6 Axes 6 Nomenclature 6 Octants 7 (l) TABLE OF CONTENTS. PAGE Crystal lographic Systems 7, 8 Triclinic 7 Monoclinic 7 Orthorhombic 7 Tetragonal 7 Isometric 7 Hexagonal 8 CHAPTER II THE TRICLINIC SYSTEM 9-39 Its Axes and Angles 9 Nomenclature 10 Relation of Planes to the Axes 10 Vertical Axis 10 Lateral Axes 10 Brachy-Axis , . 10 Macro-Axis 10 Pinacoids 11 Vertical Pinacoids or Basal Pinacoids 11 Brachy-Pinacoids 11, 12 Macro-Pinacoids 12 Domes and Prisms 12 Brachy-Domes , . . . 12 Macro-Domes 12 Vertical Domes or Prisms 12 Pyramids or Octahedrons 12, 13 Axial Models . . 13 Similar Axes, Planes, Edges, and Angles 13, 14 Symmetry 14-19 Illustration of the Term 14-17 Plane of Symmetry 15-18 Axes of Symmetry 18,19 Binary Symmetry 18 (2) TABLE OF CONTENTS. PAGE Trigonal Symmetry 18, 19 Tetragonal Symmetry 18 Hexagonal Symmetry 18 Centre of Symmetry 19 Distinguishing Characteristics of the Triclinic Crystals 19-21 Distinction from other Systems 19-21 Obliquity of Planes and Edges 20,21 Wedge-shaped Forms 20, 21 Position of Axes 21 Rules for naming Triclinic Planes 21, 22 Pinacoids 21 Domes and Prisms 21, 22 Pyramids or Octahedrons , 22 Forms 22-28 Holohedral Forms 23 Hemihedral Forms . 24, 25 Tetartohedral Forms 25 Simple and Compound Crystals 25-28 Dominant Forms 26 Subordinate Forms 26 Modification 26-28 Replacement 26-28 Truncation 27 Bevelment 27, 28 Beading Crystallographic Drawings 28-34 Notation of Weiss 28-32 u " Naumann 32, 33 " u J. D. Dana 32, 33 u Miller 32-34 "Levy 29 Axial Notation 29-34 Parameters . . 31-33 Indices 32-34 (3) TABLE OF CONTENTS. PAGE Positive and Negative Symbols 33, 34 Comparative Table of Triclinic Notations 35 Table I Hemihedral and Tetartohedral Notations 36-38 Directions for Studying Triclinic Crystals 38, 39 CHAPTER III MONOCLINIC SYSTEM 40-49 Its Axes and Angles 40 Symmetry 40,41 Plane of Symmetry 40 Axis of Binary Symmetry ....... 41 Centre of Symmetry 41 Nomenclature 41-43 Axes 41,42 Vertical Axis 4 " 41 Lateral Axes 41, 42 Ortho-Axis 42 Clino-Axis .... ..... -..;. . /. 42 Pinacoids 42, 43 Vertical Pinacoids or Basal Pinacoids 42 Clino-Pinacoids 43 Ortho-Pinacoids 43 Domes and Prisms 43 Clino-Domes 43 Ortho-Domes 43 Vertical Domes or Prisms 43 Pyramids or Octahedrons 43 Relation of Planes to Axes ...;*-.. ... 43 Distinguishing Characteristics of the Monoclinic Crystals ... 44 Rules for naming Monoclinic Planes 44, 45 Pinacoids 44 (4) TABLE OF CONTENTS. PAGE Domes and Prisms 44 Pyramids 01 Octahedrons 45 Forms 45, 46 Holohedral Forms 45 Hemihedral Forms 45 Hemimorphic Forms 45, 46 Clinohedral or Pseudo-hemimorphic Forms 46 Compound Forms 46 Reading Drawings of Monoclinic Crystals 46-48 Comparative Table of Monoclinic Notations 48 Table II 48 Directions for studying Monoclinic Crystals 49 CHAPTER IV ORTHOBHOMBIC SYSTEM 50-59 Its Axes and Angles .... , 50 Nomenclature 50, 5l Axes . . 7 . , V . . . 50 Vertical Axis . 50 Lateral Axes 50 Brachy-Axis 50 Macro-Axis 50 Pinacoids 50 Vertical Pinacoids or Basal Pinacoids 50 Brachy-Pinacoids 50 Macro-Pinacoids 50 Domes and Prisms 50,51 Brachy-Domes 50, 51 Macro-Domes 50, 51 Vertical Domes or Prisms 50, 51 Pyramids or Octahedrons 51 Relation of Planes to Axes 51 Symmetry 51, 52 (5) TABLE OF CONTENTS. PAGE Distinguishing Characteristics of the Orthorhombic Crystals. 53, 54 Kules for Naming Orthorhombic Planes 54 Pinacoids 54 Domes and Prisms 54 Pyramids or Octahedrons : . 54 Forms 54-57 Holohedral Forms 54, 55 Symmetry 55 Hemihedral Forms 55, 56 Sphenoids .... 55, 56 Symmetry 55 Hemimorphic Forms 56 Symmetry 56 Compound Forms 57 Holohedral Forms . 57 Hemihedral Forms 57 Hemimorphic Forms 57 Beading Drawings of Orthorhombic Crystals 57,58 Comparative Table of Orthorhombic Notations 58 Table III 58 Directions for Studying Orthorhombic Crystals 59 CHAPTEK V TETRAGONAL SYSTEM 60-72 Its Axes and Angles 60 Nomenclature 60-62 Axes 60 Vertical Axis 60 Lateral Axes 60 Pinacoids 60 Vertical or Basal Pinacoids i' . . . 60 Prisms , . . 61 Primary Prisms or Prisms of the First Order 61 (6) TABLE OF CONTENTS. PAGE Secondary Prisms or Prisms of the Second Order ... 61 Ditetragonal or Dioctahedral Prisms 61 Pyramids or Octahedrons . 61 , 62 Primary Pyramids or Pyramids of the First Order . . 61 Secondary Pyramids or Pyramids of the Second Order. 61, 62 Ditetragonal Pyramids or Dioctahedrons or Zirconoids. 62 Kelation of Planes to Axes 62 Distinguishing Characteristics of Tetragonal Crystals 62 Kules for Naming Tetragonal Planes 62, 63 Pinacoids 62, 63 Domes and Prisms 63 Pyramids or Octahedrons 63 Forms 63-69 Holohedral Forms 63-65 Symmetry 64 Relations and Numbers of Prisms and Pyramids ... 65 Hemihedral Forms . ._ ........ 65-69 Sphenoidal Group 65-67 Sphenoids 65-67 Tetragonal Scalenohedrons . . . . 66,67 Symmetry ....... 67 Pyramidal Group 67-69 Tertiary Prisms or Prisms of the Third Order . . 67 Tertiary Pyramids or Pyramids of the Third Order 67, 68 Symmetry 68 Tetragonal Trapezohedrons 69 Right-Handed or Positive . . . . ....... 69 Left-Handed or Negative 69 Symmetry 69 Compound Forms 69 Reading Drawings of Tetragonal Crystals 69, 70 Comparative Table of Tetragonal Notation 71 (7) TABLE OF CONTENTS. PAGE TablelV 71 Directions for Studying Tetragonal Crystals 72 CHAPTER VI HEXAGONAL SYSTEM 73-121 Its Axes and Angles 73 Relations of the Hexagonal and Tetragonal Systems . . . 73, 74 Symmetries of both Systems 74 Divisions of the Hexagonal System 74 Hexagonal Division 74 Rhombohedral (Trigonal) Division 74 Miller-Bravais Indices 75 Modernized Weiss Parameters 75 Nomenclature 75 Relations of Planes to Axes 75 Distinguishing Characteristics of Hexagonal Crystals ... 76 Principal Forms of the Hexagonal System ... .... 76-80 Holohedral Forms 80-85 Basal Pinacoid 80 Primary Hexagonal Prism 80, 81 Secondary Hexagonal Prism 81 Dihexagonal Prism 81 Primary Hexagonal Pyramid 81 Secondary Hexagonal Pyramid 82 Dihexagonal Pyramid 82 Relations of the Primary and Secondary Hexagonal Prisms and Pyramids 82-85 Parameters of the Secondary Prisms and Pyramids .... 82-84 Symmetry of the Holohedral Forms 84, 85 Hemihedral Forms 85-96 Rhombohedral Group 85-91 Primary Rhombohedron 85-88 (8) TABLE OF CONTENTS. PAGE Positive Rhombohedron 85 Negative Khombohedron ;"... 85, 86 Terminal Edges 86 Lateral Edges ..-.; >,> 86 Solid Angles . . . , . ^ 86 Acute Rhombohedron 87 Obtuse Rhombohedron 87 Principal Rhombohedron 87 Subordinate Rhombohedron 87 Rhombohedral Truncation . 87, 88 Hexagonal Scalenohedron 88-90 Positive Scalenohedron 88-90 Negative Scalenohedron 88-90 Distinction between the Hexagonal and Tetragonal Scalenohedrons 89 Lateral Edges 89 " Saw Teeth" 89 Distinction between Positive and Negative Scalenohe- drons 89,90 Inscribed Rhombohedrons or Rhombohedrons of the Middle Edges 90 Relation of the Rhombohedron and the Scalenohedron. 90 Number of Scalenohedrons 90 Symmetry of the Rhombohedral Group 90, 91 Pyramidal Group 91-93 Tertiary Hexagonal Prism 91,92 Relation of the Tertiary to the Primary and Secondary Hexagonal Prisms 91 Positive or Right-handed Prism . . . 92 Negative or Left-handed Prism . 92 Symbols for these Forms 92 Tertiary Hexagonal Pyramid . . - . . . 92, 93 (9) TABLE OF CONTENTS. PAGE Positive or Right-handed Pyramid 92 Negative or Left-handed Pyramid 92 Relation of the Tertiary to the Primary and Secondary QQ Hexagonal Pyramids Symmetry of the Pyramidal Group 9 Hexagonal Trapezohedral Group 93-95 Positive or Eight-handed Hexagonal Trapezohedron ... 94 Negative or Left-handed Hexagonal Trapezohedron .... 94 Symmetry of the Trapezohedral Group 04 Distinction from the Scalenohedron 94 Distinction of the Right-handed from the Left-handed . . . 94, 95 Trigonal Group 95, 96 Ditrigonal Pyramid 95 Positive 95 Negative 95 Symmetry 96 Tetartohedral Forms 96-102 Rhombohedral Group 96-98 Secondary Rhombohedron 96, 97 Relation to the Primary Rhombohedrons 97 Positive and Negative 97 Right-handed and Left-handed 97 Tertiary Rhombohedron 97 Relation to the Primary and Secondary Rhombohe- drons 97, 98 Symmetry of the Secondary and Tertiary Rhombohe- drons 98 Trapezohedral Group 98-100 Secondary Trigonal Prism 99 Positive or Right-handed 99 Negative or Left-handed 99 Ditrigonal Prism 99 (10) TABLE OF CONTENTS. PAGE Positive or Eight-handed 99 Negative or Left-handed . . . . 99 Secondary Trigonal Pyramid 99, 100 Positive or Right-handed 99 Negative or Left-handed 99 Trigonal Trapezohedron 100 Negative Eight- or Left-handed 100 Positive Eight- or Left-handed 100 Symmetry of the Trapezohedral Group 100 Trigonal Group . - . -- 101,102 Primary Trigonal Prism ' 101 Positive 101 Negative 101 Tertiary Trigonal Prism 101,102 Positive Eight- or Left-handed 101,102 Negative Eight- or Left-handed 102 Primary Trigonal Pyramid 102 Positive . . . . 102 Negative... . . < 102 Tertiary Trigonal Pyramid 102 Positive Eight- or Left-handed . 102 Negative Eight- or Left-handed 102 Symmetry .... . v , ...... v 102 Hemimorphic Forms 102-104 lodyriteType .102,103 Symmetry 103 Nephelite Type 103 Symmetry 103 Tourmaline Type . .."..,.,. . : . 103 Symmetry . ... / .. . 103 Sodium Periodate Type . . . ...... 103, 104 Symmetry 104 (ID TABLE OF CONTENTS. PAGE Compound Forms 104 Rules for Naming Hexagonal Planes 104-109 Pinacoids 104 Prisms 104-106 Pyramids 106-108 Rhombohedrons 106-108 Scalenohedrons 107 Trapezohedrons 107, 108 Hemimorphic Forms 108, 109 Reading Drawings of Hexagonal Crystals 109-113 Lettering Semi-axes 109 Parameters or Indices 110, 111 Miller-Bravais Notation 110-112 Weiss Notation Ill Naumann Notation 111-113 Dana Notation 112 Notation of Ehombohedron and Scalenohedron 112 Notation of Hemimorphic Forms 112,113 Hexagonal Forms and Notations 114-120 Table V 114-120 Directions for Studying Hexagonal Crystals 121 CHAPTER VIJ ISOMETRIC SYSTEM 122-147 Axes 122 Nomenclature 122, 123 Semi-Axes 122 Distinguishing Characteristics of the Isometric Crystals . . 123 Forms of the Isometric System 123-125 Holohedral Forms . . . . 125-131 Hexahedron alias Cube . . . , 126 Dodecahedron .... 126 127 (12) TABLE OF CONTENTS. PAGE Tetrakis Hexahedron . . 127 Octahedron 127, 128 Trigonal Triakis Octahedron . . ' 128, 129 Tetragonal Triakis Octahedron L . . . 129 Hexakis Octahedron 130 Symmetry 130, 131 Cubic Axes . 131 Octahedral Axes 131 Dodecahedral Axes . . ..?..,. 131 Hemihedral Forms .131-139 Oblique Hemihedral Forms -..'>,*. 131-135 Tetrahedron 132 Positive 132 Negative. .-. , 132 Tetragonal Triakis Tetrahedron . . . * . . . . . 132, 133 Positive 133 Negative 133 Trigonal Triakis Tetrahedron 133, 134 Hexakis Tetrahedron -. * . . . . .134,135 Positive 135 Negative 135 Symmetry 135 Parallel Hemihedral Forms 135-138 Pentagonal Dodecahedron 135-137 Positive 136, 137 Negative. . . ...... .. . -> : ... % . . .136,137 Dyakis Dodecahedron 137,138 Positive 137 Negative 137 Symmetry . - 138 Gyroidal Hemihedral Forms 138, 139 Pentagonal Icositetrahedron 138, 139 (13) TABLE OF CONTENTS. PAGE Eight-handed 138, 139 Left-handed 138, 139 Symmetry 139 Tetartohedral Forms 140, 141 Tetrahedral Pentagonal Dodecahedron = 140, 141 Positive Eight- or Left-handed 140, 141 Negative Eight- or Left-handed 140, 141 Symmetry 141 Compound Forms 141,142 Holohedral Compound Forms 141 Oblique Hemihedral Compound Forms 141 Parallel Hemihedral Compound Forms 141 Gyroidal Hemihedral Compound Forms 142 Tetartohedral Compound Forms . 142 Eules for Naming Isometric Planes 142-144 Cube 142 Dodecahedron 143 Tetrakis Hexahedron 143 Pentagonal Dodecahedron 143 Octahedron 143 Tetrahedron 143 Trigonal Triakis Octahedron 143 Tetragonal Triakis Tetrahedron 143 Tetragonal Triakis Octahedron 144 Trigonal Triakis Tetrahedron 144 Hexakis Octahedron 144 Hexakis Tetrahedron 204 Pentagonal Icositetrahedron 144 Dyakis Dodecahedron ... 144 Tetragonal Pentagonal Dodecahedron 144 Eeading Drawings of Isometric Crystals 145 Isometric Forms and Notations 146, 147 (14) TABLE OF CONTENTS. PAGE Table VI . 146, 147 Directions for Studying Isometric Crystals 147 CHAPTER VIII MINERAL AGGREGATES, PARALLEL GROWTHS, AND TWINS . 148-154 Crystalline 148 Amorphous 148 Pseudomorphs 148 Compound Minerals or Crystals .... 149, 150 Mineral Aggregate 149 Parallel Growths or Groups 149 Twins 149, 153 Reentrant Angles 150, 151 Striations 150, 151 Oscillatory Combination 151 Polysynthetic Twinning 151, 153 Contact Twinning 152, 153 Composition Plane 152 Twinning Axis 152 Cyclic Twins 153 Penetration Twinning 4 ..... 153 Mimicry . 153, 154 CHAPTER IX CLEAVAGE 155-160 Nomenclature 155, 156 Notation 156 Triclinic Cleavages 156 Monoclinic Cleavages 157 Orthorhombic Cleavages 157 Tetragonal Cleavages 157, 158 Hexagonal Cleavages 158 Isometric Cleavages 159 (15) TABLE OF CONTENTS. PAGE Partings 159, 160 Nomenclature 159 Parting Structure 159 Cleavage Structure 159 Mineral Parting 160 Parallel Kock Jointing 160 Mineral Cleavage 160 Eock or Slaty Cleavage 160 CHAPTER X CRYSTALLOGRAPHIC SYMMETRY 161-166 Symmetry Drawings 161,162 Notation 161, 162 Triclinic Symmetry 162 Monoclinic Symmetry 162 Holohedral Symmetry 162 Clinohedral or Hemihedral Symmetry 162 Orthorhombic Symmetry 162, 163 Holohedral Symmetry 162 Hemihedral Symmetry 162, 163 Hemimorphic Symmetry 163 Tetragonal Symmetry 163 Holohedral Symmetry 163 Sphenoidal Symmetry 163 Pyramidal Symmetry 163 Trapezohedral Symmetry J63 Hexagonal Symmetry 163-165 Holohedral Symmetry 163 Hemihedral Symmetry 164 Rhombohedral Symmetry 164 Pyramidal Symmetry 164 Trapezohedral Symmetry 164 (16) TABLE OF CONTENTS. PAGE Trigonal Symmetry 164 Tetartohedral Symmetry 164, 165 Rhombohedral Symmetry 164 Trapezohedral Symmetry 165 Trigonal Symmetry 164, 165 Hemimorphic Symmetry 165 lodyrite Symmetry 165 Nephelite Symmetry 165 Tourmaline Symmetry 165 Sodium Periodate Symmetry 165 Isometric Symmetry 165, 166 Holohedral Symmetry 165 Hemihedral Symmetry 165, 166 Oblique Hemihedral Symmetry 165 Parallel Hemihedral Symmetry 166 Gyroidal Hemihedral Symmetry 166 Tetartohedral Symmetry 166 CHAPTER XI THE THIRTY-TWO CLASSES OF CRYSTALS 167-186 Triclinic System V ,. . . 167-169 1. Asymmetric or Hemihedral Class 167, 168 2. Pinacoidal or Holohedral Class . r 168, 169 Monoclinic System 169, 170 3. Sphenoidal or Hemimorphic Class 169 4. Domatic or Hemihedral Class . 'I . . ..._ 169,170 5. Prismatic or Holohedral Class _ 170 Orthorhombic System ..;......... 170-172 6. Bisphenoidal or Hemihedral Class 170, 171 7. Pyramidal or Hemimorphic Class . . '. . ..... 171 8. Bipyramidal or Holohedral Class 171,172 Tetragonal System 172-176 9. Bisphenoidal Tetartohedral Class 172 (17) TABLE OF CONTENTS. PAGE 10. Pyramidal Class 172,173 11. Scalenohedral or Sphenoidal Class 173,174 12. Trapezohedral Class 174 13. Bipyramidal Class 174, 175 14. Ditetragonal Pyramidal Class 175 15. Ditetragonal Bipyramidal Class 175, 176 Hexagonal System 176-183 TRIGONAL DIVISION . 176-180 16. Trigonal Pyramidal or Ogdohedral Class 176, 177 17. Khombohedral Class 177 18. Trigonal Trapezohedral Class 177, 178 19. Trigonal Bipyramidal Class 178 20. Ditrigonal Pyramidal Class 178, 179 21. Ditrigonal Scalenohedral Class 179 22. Ditrigonal Bipyramidal Class . 179, 180 HEXAGONAL DIVISION 180-183 23. Hexagonal Pyramidal Class 180, 181 24. Hexagonal Trapezohedral Class 181 25. Hexagonal Bipyramidal Class 181,182 26. Dihexagonal Pyramidal Class 182 27. Dihexagonal Bipyramidal Class 182, 183 Isometric System 183-186 28. Tetrahedral Pentagonal Dodecahedral Class - . . 183. 184 29. Pentagonal Icositetrahedral Class 184 30. Dyakis Dodecahedral or Parallel Hemihedral Class. 184,185 31. Hexakis Tetrahedral or Oblique Hemihedral Class. 185,186 32. Hexakis Octahedral or Holohedral Class .... 186 CHAPTER XII CRYSTALLOGRAPHIC NOMENCLATURE 187-202 Similarity of Personal and Crystallographic Nomenclature. 187-189 The Families of the Prism Tribe ....''. / 189-193 (18) TABLE OF CONTENTS. PAGE The Family of Triclinic Prisms 189, 190 The Family of Monoclinic Prisms 190 The Family of Orthorhombic Prisms 190, 191 The Family of Tetragonal Prisms 191 The Family of Hexagonal Prisms 191-193 The Families of the Pyramid Tribe 193-199 The Family of Triclinic Pyramids . 193 The Family of Monoclinic Pyramids 193 The Family of Orthorhombic Pyramids 194 The Family of Tetragonal Pyramids 194-196 The Family of Hexagonal Pyramids 196-199 The Families of the Pinacoid Tribe 199.200 The Families of the Isometric Tribe 200-202 Description of the Plates .203-261 Plate I, Figs. 1-11 ... 203 Plate II, Figs. 12-34 . . 1''. . . . 204,205 Plate III, Figs. 35-55 .... . . . . . '. . . . .206,207 Plate IV, Figs. 56-85 ...>-.." '. . .207-210 Plate V, Figs. 86-112 .211-213 Plate VI, Figs. 113-144 / -. i ' 213-215 Plate VII, Figs. 145-169 216-218 Plate VIII, Figs. 170-198 .... . 218-220 Plate IX, Figs. 199-220 ...... .221-223 Plate X, Figs. 221-245 223-226 Plate XI, Figs. 246-269 226-229 Plate XII, Figs. 270-297 . . . . .229-232 Plate XIII, Figs. 298-319 . . . *, . . . ... ,.V_. . 232-234 Plate XIV, Figs. 320-339 ...... ....'.. 235,236 Plate XV, Figs. 340-365 236-238 Plate XVI, Figs. 366-385 238-240 Plate XVII, Figs. 386-415 240-243 Plate XVIII, Figs. 416-445 244-246 (19) TABLE OF CONTENTS. PAGE Plate XIX, Figs. 446-472 247,248 Plate XX, Figs. 473-500 248-250 Plate XXI, Figs. 501-524 250-253 Plate XXII, Figs. 525-548 253-255 Plate XXIII, Figs. 549-580 255-258 Plate XXIV, Figs. 581-595 258-260 Plate XXV, Figs. 596-612 260,261 Triclinic Forms 203, 205, 206, 247, 249, 258, 261 Monoclinic Forms 203, 208-211, 248-250, 255, 258, 261 Orthorhombic Forms . 203, 204, 211-216, 247, 250, 252, 256-259 Tetragonal Forms, 203, 205, 206, 216-221, 224, 225, 251, 253, 259, 261 Hexagonal Forms . . . 203-207, 215, 221-235, 249-255, 259, 260 Isometric Forms. . . .203,204,207,208,251,236-248,253-261 Errata 262,263 Index , 265-299 (20) NOTES ON CRYSTALLOGRAPHY CHAPTER I PRELIMINARIES ALL students of the sciences know that the natural objects of this earth are divided into 'three kingdoms : Animal, Vegetable, and Mineral The first comprises all animals ; the second includes every plant ; and the third all other materials such as minerals and min- eral aggregates, or rocks, water, air, etc. The Animal and Vegetable Kingdoms can be united under one head called the Organic World, and the Mineral Kingdom can be called the Inorganic World. Our knowledge of these kingdoms has also its three- fold classification : Zoology comprises our knowledge of the various forms of animal life ; Botany relates to plant life; and Mineralogy, in its broadest sense, can be held to cover our knowledge of the inorganic world. Botany and Zoology together are united under the broader term Biology, or the " Science of Life ". The inquiring student will find, however, that in 2 *; ^'OTES'.pW p&YSf ALLOGRAPHY. its mcV$:<^^ii -'tfceegtanceHhe term Mineralogy is not used in its broadest or most universal sense, but is rather employed to comprise our knowledge of the simple minerals, when that term is used with a re- stricted meaning. If this limitation is applied, a Mineral may be defined as an inorganic body which has a more or less definite chemical composition and internal structure, and which, as a rule, tends to have a definite shape or form. Mineral Chemistry is the name of the science that relates to the chemical com- position of the minerals ; Optical Mineralogy is the name of the science which relates to the internal structure of minerals as shown by their effects upon light. The form that a mineral tends to assume is known as a Crystal, see Fig. 10, and our knowledge of these forms is named Crystallography, or the Science of Crystals. As our present purpose is to enable a man to de- termine his minerals in the field and laboratory in the quickest and shortest way consistent with a fair de- gree of accuracy, it would not be necessary to devote time to Crystallography, if it were not that each min- eral tends to have a more or less distinctive form or forms; and these forms, when sufficiently perfect for use, furnish us with the best, quickest, and surest means of determining a mineral. In many cases a mere glance is sufficient. PRELIMINARIES. 3 A Mineral, when it shows its crystallographic form, is seen to be bound by faces or planes; hence a Crystal can be defined as a body bounded by plane surfaces. See Fig. 9. Although theoretically the planes of a crystal are perfect and of equal size, yet in point of fact this is not generally true : first, because of the interference with one another of the adjacent crystals ; and secondly, because of the necessity that each one should be im- planted or should rest on something during its process of growth. By these and other causes the natural development of the planes of the crystal is hindered, and their outlines are distorted ; some of the planes may even be totally suppressed. Thus the crystal planes are by no means constant in outline, size, or area, but they are closely, if not entirely, constant in their inclination to one another that is, in the angles that each plane forms with those adjacent to it. See Figs. 12-27. The variations of these angles are so slight that rarely can they be detected except through accurate instrumental work. The ordinary work of a prospector or a student, who does not desire to be a professional Mineralogist, but rather to be able to de- termine his minerals in the shortest way consistent with a fair degree of accuracy, is such, that for all practical purposes the angles of any mineral species may be considered to be always identical. Our method of locating a point upon a crystal may 4 NOTES ON CRYSTALLOGRAPHY. be compared with the method commonly used in locat- ing any point upon the earth's surface. In the latter the exact distance from a certain datum or reference point is determined, and the precise compass direction obtained. Thus one uses the distance measured along a certain line and the angle which that line makes with the meridian of that datum point. This is accur- ate enough for most local purposes and becomes more exact as one approaches the sea level. At the sea level one may also measure a distance east from a given point, say six miles, and then due north to the place to be located at a distance, say, of eight miles. It could then be stated that the point sought lay eight miles north and six miles east of the datum or refer- ence locality. In case, however, the point to be located is not on the sea level, but on high land or a moun- tain, we would say that the locality under considera- tion was X miles south of the datum or given point A, Z miles west of it, and Y feet high above the sea level. This gives the exact position of the point which is to be located on the mountain. From this illustra- tion one can see how points or bodies are located in space with reference to a chosen point by means of three lines at right angles to one another, or by means of the same or a greater number of lines placed at oblique angles or partially at right angles to one an- other. PRELIMINARIES. 5 This system of determining points can also be used for locating a plane or any other object in space, such as a star or the plane of a crystal. Our entire mathematical conception of Crystallog- raphy is based on finding the location of the crystal planes and the angles they form with one another with reference to a single datum point. Our purpose in this work is not to discuss the subject mathemati- cally, but merely to use such mathematical or space conceptions as will give us an idea of the relative posi- tion of different planes to the chosen datum point. Returning to our idea of referring the location of any point to three or more lines and the angles that they make with one another, we find that there are practically six different methods or systems needed for the purpose of locating the different actual sets of planes found in nature upon the various minerals. To apply these principles, first, select a certain datum point which is the point forming the theoretical or geometrical centre of the crystals. This centre is not the actual centre of gravity of most crystals, but the geometrical centre that would exist if the crystal were absolutely perfect, or if we conceive the planes so placed as to make it absolutely faultless. While this conception may appear difficult of attainment, yet with a little attention and thought it will be found very easy and simple. Secondly, from the above 6 NOTES ON CRYSTALLOGRAPHY. chosen point draw lines of indefinite length, which form any angles whatsoever with one another, and we shall, by means of the datum point and of the three or four lines chosen and their angles of intersection, obtain data that will enable us to name the crystal- lographic forms. The above lines or directions are called Axes. The process of learning to name the forms is simple and easy if one employs care and judgment about it ; and this naming is all that is required in ordinary field and laboratory work. The mathematical de- scription, calculation and correct drawing of the crys- tallographic forms is another and much more difficult matter, requiring a thorough knowledge of the prin- ciples of Spherical Trigonometry or Analytic Geom- etry of Three Dimensions and practice in Projection Drawing. The recognition of the crystal forms will require on the part of a good student with a suitable supply of crystal models and natural crystals from 15 to 25 hours of study and laboratory practice, while the mathematical work will demand months and perhaps even years of time. Our purpose in these pages is simply to enable the student to study and name the forms and to under- stand the ordinary use of the so-called crystallographic nomenclature, or the figures and letters commonly written on or about a crystal or mineral form, as drawn and given in our mineralogical books and papers. PRELIMINARIES. 7 In representing our three axes in a drawing (Fig. 7), we readily see that if three planes be drawn through the intersection of the lines at the point A, and extend- ing along these lines, as shown in Fig. 7, the space is then divided into eight parts or Octants ; for instance, the part formed by the planes meeting in the points ABCDEFHisan octant. In an octant the angles and axial distances may all be equal, or they may all be unequal, or there may be every possible variation between these limits. In arranging our systems we start with all the angles in each octant unequal and all the axes un- equal. In varying from this we change in each octant first the angles, leaving the axes unequal ; then we vary the axes, leaving the angles equal. Our varia- tions of angles and axes then are as follows : 1. Triclinic System. All angles are oblique and both angles and axes unequal. See Fig. 1. 2. Monoclinic System. One of the angles is oblique and two are right angles, but all the axes are of un- equal length. See Fig. 2. 3. Orthorhombic System. All three angles are right angles, but all the axes remain unequal. See Fig. 3. 4. Tetragonal System. All the angles are right angles, but two axes are equal and one is unequal to the other two. See Fig. 4. 5. Isometric System. All three angles are equal, and the three axes are equal. See Fig. 5. 8 NOTES ON CRYSTALLOGRAPHY. 6. Hexagonal System. In the sixth case we de- part, as a matter of convenience, from the three axes and use four. Three of the four axes are placed hori- zontally and form angles of sixty degrees with one another. The fourth axis is placed vertically and forms right angles with the horizontal axes. See Fig. 6. CHAPTER II THE TRICLINIC SYSTEM THIS system derives its name from the Greek Tris, "thrice," and Klino, "to slope, slant, or incline against," the term referring to the three-fold inclina- tion of the axes to one another. In this system the planes are arranged about a given point or theoretical centre, from which the axes radiate, all forming dif- ferent oblique angles with one another in the same octant. See Fig. 1. Practically the distance along the lines and the angles between the lines are all un- equal. The axes in Crystallography are, however, no more real things than are the poles of the earth, its axis, equator, meridians, or parallels. The axes are simply chosen directions or imaginary lines that will enable us to describe the crystal in the shortest and most convenient manner. It must, however, be re- membered that the selection of the axes or directions in this system is an arbitrary thing ; for no matter what directions may be chosen, still others remain available. (9) 10 NOTES ON CRYSTALLOGRAPHY. NOMENCLATURE Having selected our axes and their directions, we may next define some of the terms that we must use if we desire to be. in accord with other writers upon this subject. If we commence with any one plane upon the crystal, that plane must cut all three of these axes at some distance, or be parallel to one or two of them. In accordance with geometrical usage a plane parallel to a line is said to cut that line at infinity, a distance which, according to mathematical custom, is designated by the figure 8 laid upon its side or hori- zontally ( oo ), or by an i, the initial of infinity. In the Triclinic System, when we are studying a crystal or model, the form is so placed that one axis is more nearly vertical than the other two. Hence we speak of the first as the Vertical Axis, although such language is rarely accurate. See Y, Fig. 1. The other two axes are called Lateral Axes. See X and Z, Fig. 1. Since in this system all the axes are of unequal length it is necessary to distinguish one lateral axis from the other. This is done by calling the shorter axis the Brachy-Axis or Brachy -Diagonal (Greek, Brachys, " short "), (see X, Fig. 1), and the longer axis the Macro-Axis or Macro -Diagonal (Greek, Makros, "long"), see Z, Fig. 1. THE TRICLINIC SYSTEM. 11 PINACOIDS In naming any plane of a crystal in this system, we observe which one of the three possible relations it may hold to the three chosen axes : 1. The plane may intersect all three axes. 2. It may cut two axes and be parallel to the third axis. 3. It may intersect one axis and be parallel to the other two. In the last case it is evident that but six such planes can exist in this system, each one cutting each end of the three axes. These planes are called Finacoids, from the Greek, Pinax, " a plank or board," and Eidos, " shape or form " which in composition takes the form of old and is translated " resembling, or like, or in the form of." The name refers to the position of each of these planes on the sides or ends of the crystal, just as a slice form- ing a plank or board may be taken from the side or sides of a mill log by a saw. See 010, Figs. 8-10. The simplest method of designating the pinacoids is to name them from the axis that each one cuts ; but practice has partially varied that system, so that our nomenclature is as follows : 1. If a pinacoid cuts the vertical axis it is called a Vertical Pinacoid ; or more commonly, since the crys- tals, when studied, are placed or allowed to rest on one vertical pinacoid, it is usually named a Basal Pinacoid or Basal Plane. See 001, Fig. 33. 2. In case a pinacoid intersects one lateral axis and 12 NOTES ON CRYSTALLOGRAPHY. thus is parallel to the other one and the vertical axis, it is named from the lateral axis to which it is parallel. If parallel to the brachy-axis, it is a Brachy-Pinacoid, (see 010, Figs. 8-10 and 31-35); if parallel to the macro-axis, it is a Macro-Pinacoid- See 100, Figs. 32-35. DOMES AND PRISMS If the plane cuts two axes but is parallel to the third axis, it is a Dome or Prism Plane. The term dome is derived from the Latin word domus, "a house." This term is employed because, when two dome planes meet, they form an angle with each other similar to that of the " pitch roof" of a house. See 110 L 111, Figs. 9 and 10. The domes or dome planes are named from the axis to which they are parallel ; as, for ex- ample, a Brachy-Dome is so named when it lies par- allel to the brachy-axis, (see 021, Fig. 30, and 101 and 102, Fig. 34) ; and a Macro-Dome Plane is so called when the plane is parallel to the macro-axis. Thus we may call a dome, like a house set on end, parallel to the vertical axis, a Vertical Dome ; but it is custom- ary to name the vertical dome planes Prismatic Planes, and to confine the term dome planes to those planes parallel to one of the lateral axes. See 110, Figs. 29-35. PYRAMIDS OR OCTAHEDRONS Having disposed of the problem of naming two out THE TRICLINIC SYSTEM. 13 of the three possible series of planes in this system, we now come to the third or last series, or the Pyramids. To repeat, in the first possible case the planes might intersect one axis and be parallel to the other two, giving rise to the Pinacoidal Planes; in the second possible series, the planes might intersect two axes and be parallel to the third, giving rise to our Dome or Prism Planes ; and in this third or last case, the planes may cut all three axes, forming Pyramidal Planes. See 111, Figs. 28-32, 34, and 35. These cases cover all possible arrangements of planes about the axes of the Triclinic System. AXIAL MODELS Models of the different axial systems will be found useful if not indispensable for the proper understand- ing of the systems. These can be made by having wires suitably cut, and soldered together at the proper angles ; or we may thrust wires through cork, making as before the different systems. Then, by using a piece of cardboard or better a glass plate as a crystal plane we can see the relative position of the planes and the points where they proportionately cut the axes, or intersect their prolongation. SIMILAR AXES, PLANES, EDGES, AND ANGLES In any system of axes, one axis or semi-axis is con- sidered similar to another when it has the same length 14 NOTES ON CRYSTALLOGRAPHY. and the same inclination to the other axis or semi-axis. For example, we may note that in the Triclinic Sys- tem none of the semi-axes are similar ; but that in the Isometric System all the axes and semi-axes are similar. See Figs. 1-6. Planes are said to be similar when the distance from the centre to the points at which they cut similar semi-axes are equal. See planes 111, 111, 111 and 111, Figs. 12, 15, 17, and 18. One edge is said to be similar to another edge when both are formed by the intersection of two similar planes. See the octahedral edges in Fig. 12. A solid or crystal angle is said to be similar to an- other crystal angle when both are formed by the same number of similar planes. See the octahedral solid angles in Fig. 1 2. j SYMMETRY The question naturally arising first in the mind of any student is how he can ascertain whether the crys- tal or crystal model belongs to the Triclinic System or not. In order to make this fairly easy, attention is called here to symmetry. The meaning of symmetry as here used may be illustrated by reference to a well- proportioned or symmetrical man. In this case his right hand is similar to his left hand, and his right ear, eye, arm, leg, and foot will also be similar when THE TRICLINIC SYSTEM. 15 each is compared with the corresponding member on the left side of the body. The same illustration can be carried out if we take certain undivided parts of the body, as for instance, the nose. A plane exactly cutting the nose from top to bottom into two equal parts would have the right nostril similar to the left, i. e., the right half of the nose would be similar to the left half. A like division of the mouth and tongue would show that the two parts of each are similar. If we undertake to divide the body of a man into two equal parts so that each half shall be symmetrical with the other half, a little observation and thought will show us that there is only one position in which such a plane can be passed directly through the body ; e. g., from the head to the feet, separating the skull, nose, mouth, thorax, etc., into two equal and symmetrical parts. The same thing can be done with many other animals, like the dog or cat. The symmetry in such cases is said to be bilateral, and the plane that will divide the object into two symmetrical halves is called a Plane of Symmetry. See plane ABCD, Fig. 9. In the majority of the lower orders of animals and plants more than one plane sometimes several, some- times many can be found that will divide the object into two equal and symmetrical parts. So, too, in our crystals, the number of planes of symmetry may vary in the different systems from none to nine ; and 16 NOTES ON CRYSTALLOGRAPHY. in some cases they are extremely important as dis- tinguishing characteristics of the systems. Symmetry does not exist in the abnormal and distorted forms of man or of other animals or of minerals, although the normal forms may show perfect or approximately per- fect symmetry. It is a common mistake for a student to suppose that symmetry implies that qne of the symmetrical halves can exactly replace the other half. This is not a requirement of symmetry.. The left half of a man can not be put in the position of the right half and fill its place ; the necessary requirement is that the oppo- site halves shall have the same members and be simi- lar in form. In crystals it is requisite that the planes, edges, and angles should be similar for each half. Again, it is necessary that the two halves be sym- metrical when looked at from any position, so that the plane of symmetry, if prolonged, would bisect the nose, eyes, and mouth of the observer ; yet there is no more common mistake on the part of the inexperienced student than to think that a crystal is symmetrical, if after bisecting it with a plane of symmetry, he can turn one half into some other position so that it will then stand symmetrical with the other half. The symmetry must show without any turning or twisting of the crystal. Certainly no one would ever think of making the two halves of a man symmetrical by turn- THE TRICLINIC SYSTEM. 17 ing one-half partly around ; and, while not as obvious to the observer, it is equally absurd to turn one-half of the crystal partly around to make it symmetrical with the other half. If ordinary observation will not determine for the student a plane of symmetry, he can ascertain whether or not any chosen plane is a plane of symmetry by holding the crystal or model in front of a mirror, with the supposed plane of symmetry exactly parallel to the face of the mirror. If then the reflection of the side of the crystal or model shown in the mirror is exactly like the side of the crystal next to the observer or farthest from the mirror, the plane in question is a plane of symmetry. If we examine Figs. 811, we can see what a plane of symmetry means in those forms. In Figs. 8 and 9 the plane of symmetry is the plane formed by the rhomboid A B C D. In these figures it can be seen that this plane so divides the crystals that the planes e, f and P on one side are exactly matched by sim- ilar planes on the other side of the crystal. In Fig. 10 the six-sided plane A B C D H is the plane of symmetry, and it divides the crystal into two similar halves, in which the right-hand plane / matches the left-hand plane /, and so on. In the case of Fig. 11 the plane of symmetry is the rhomboid A B C D, which divides the plane r into two equal parts, and ' 2 18 NOTES ON CRYSTALLOGRAPHY. has the right side planes, I and ^/matched by similar planes on the left side. Symmetry shows itself not only in planes of sym- metry but also in Axes and in Centres of Symmetry. When any direction is selected as an axis and the crystal or model is revolved about that axis, if similar planes or angles show from tyne to time in the same position on the form during such revolutions, the selected direction is called an Axis of Symmetry. If the crystals represented by Figs. 3640 are re- volved about the vertical axis, it will be noticed that in each case similar planes are presented six times to the observer. Because the same faces recur six times during one complete revolution, such an axis of sym- metry is called an Axis of Hexagonal Symmetry (Greek, Hex, " six " and Gonos, " angle "). In the case of Figs. 8-11, a like revolution of the crystals, which they represent, about their vertical axis shows the recurrence of similar faces in but two posi- tions ; hence this symmetry is called an Axis of Binary Symmetry (Latin, Binarius, " consisting of two "). In Figs. 41-44, a similar revolution of the crystals, which they represent, would show four positions in which similar faces present themselves. This axis of symmetry is then an Axis of Tetragonal Symmetry (Greek, Tetra, "four"). Figs. 45-50 show, when the crystals they represent THE TRICLINIC SYSTEM. 19 are revolved about the vertical axis, an Axis of Trig- onal Symmetry (Greek, Tris, " thrice "). Crystals can have only Axes of Binary, Trigonal, Tetragonal, and Hexagonal Symmetry. When each face, angle, and edge of a crystal or crystal model has a similar face, angle, or edge re- peated exactly on the opposite side of the crystal or model, the theoretical central point or axial centre of the crystal or model is a Centre of Symmetry. Or, in other words, whenever one-half of the crystal or model has every plane, angle, and edge repeated by a similar plane, angle, or edge on the opposite half, the centre of that form is a Centre of Symmetry. Thus Centres of Symmetry are shown in Figs. 28-35, as the centre of each crystal has on one side a face matched by a plane on the other side ; the same fact can be noted concerning all the other faces, angles, and edges on the crystals which these figures represent. DISTINGUISHING CHARACTERISTICS OF THE TRICLINIC CRYSTALS It is hardly scientific to define anything by stating what it has not, but in many cases this method of de- scription is the simplest. So here we may say that the Triclinic System is characterized by the fact that it has no plane of symmetry ; that is, we can find, in crystals belonging to this system, no plane that will 20 NOTES ON CRYSTALLOGRAPHY. divide the crystals into two equal and symmetrical parts. See Figs. 28-35. The absence of any plane of symmetry, while char- acteristic of the Triclinic System, is not an absolute proof of it, since some of the forms in the other sys- tems have also no plane of symmetry. These forms are so extremely rare in the case of minerals that they will occasion no trouble in the field, and it is only in the case of crystal models or in artificial crystals that any difficulty will occur. All difficulties, however, will disappear if we re- member that in the case of the other five systems all the forms that have no plane of symmetry do have one or more axes of symmetry, while all the Triclinic forms are destitute of any axis of symmetry as well as of any planes of symmetry. They can only have a centre of symmetry. Again, if a Triclinic crystal is placed on its basal plane, it can readily be seen that the side planes form oblique angles with the basal plane. In fact, the obliquity of the planes to one another or the twisting of the forms, as if a box were taken by its corners and twisted out of shape, can usually be seen in whatever position the crystals are placed. From the obliquity of the angles the crystals of the Triclinic System are quite apt to have wedge-shaped forms, although the wedges are twisted or skewed, and THE TRICLINIC SYSTEM. 21 not straight, as are the wedge-shaped forms in the other systems. See Figs. 28-35. From the above characters : 1. Determine whether or not the crystal model be- longs to the Triclinic System. 2. Determine where the three axes are to be placed. They must be so located as to fulfill the requirements of this system ; that is, they must be of equal length and form oblique angles with one another. If these conditions are fulfilled, then it is best to locate each axis parallel to some plane or edge : the planes or edges chosen must hold the same relation to one another ; i. e., they must form oblique angles and be of unequal length. As a rule place the axes so as to have first, as many pinacoidal planes as possible, and next as many prism or dome planes as possible, but with the fewest possible pyramidal planes. RULES FOR NAMING TRICLINIC PLANES I. If any plane cuts one axis and is parallel to the other two, it is a Pinacoid. If it cuts the vertical axis, it is a Basal or Vertical Pinacoid, or a Basal Plane ; if it intersects the brachy-axis, it is a Macro -Pinacoid ; if it cuts the macro-axis, it is a Brachy-Pinacoid. II. If any plane cuts two axes and is parallel to the third axis, it is a Dome or Prism Plane, and is named from the axis to which it is parallel : if it is parallel to 22 NOTES ON CRYSTALLOGRAPHY. the vertical axis, it is a Prism or a Vertical- Dome Plane ; if it is parallel to the brachy-axis, it is a Brachy-Dome Plane ; if it is parallel to the macro-axis, it is a Macro-Dome Plane. III. If a plane cut all three axes, it is a Pyramidal or Octahedral Plane. FORMS The term Form is employed in Crystallography to indicate the union of similar planes about crystallog- raphic axes. These planes may or may not inclose space. In the case of eight similar planes forming an octahedron, space is inclosed between the planes. Four similar dome planes, arranged parallel to the same axis, inclose space in the same way that a stove-pipe does, but the ends are open, and space can only be actually inclosed by the addition of two pinacoids, one at each end. In like manner, two pinacoids in the Tetragonal or Hexagonal Systems make a form, but they do not inclose space. From the above, we can see that in Crystallography the term form frequently has a significance somewhat different from its ordinary meaning. In Crystallography we have complete forms, half forms, and quarter forms ; and to enable us better to understand the meaning of forms in Crystallography, it is necessary to define these three kinds of forms. THE TRICLINIC SYSTEM. 23 1. Holohedral Forms occur when we have a union of all the similar possible planes that can be arranged about the axes of any crystallographic system. See Fig. 12. The name comes from the combination of two Greek words, Holos, " whole, perfect or complete," and Hedra, " a seat of any kind like a chair, stool or bench, or a foundation or base." This makes a somewhat far- fetched translation, as the implication is that the seats or places are all filled, which in Crystallography is said to mean a form with all possible faces. When crystals have the entire number of similar possible faces, it is customary to call them Holohedral Forms ; and it should be noted that these forms possess all the symmetry possible in any given crystallographic sys- tem ; i. e.j they have all the planes, axes, and centres of symmetry possible in that system. Such crystals are said to have the highest symmetry. It should be noted that the highest symmetry in the Isometric System comprises nine planes of symmetry, three axes of tetragonal symmetry, four axes of trigonal sym- metry, six axes of binary symmetry, and a centre of symmetry. See Figs. 12, 15, and 17. Again, the highest symmetry of the Orthorhombic System is expressed by three planes of symmetry, three axes of binary symmetry, and a centre of symmetry. See Fig. 51. Further, the Triclinic System has no plane or axis of 24 NOTES ON CRYSTALLOGRAPHY. symmetry, but only a centre of symmetry. See Figs. 28-35. When the subject of Crystallography is devel- oped from the Isometric System and ends with the Tri- clinic, it begins with the highest possible symmetry and complexity, descending towards the lower and simpler forms. On the other hand, if the development begins with the Triclinic System, it commences with the simplest forms, or lowest symmetry, and ascends towards the highest and most complex forms. 2. Hemihedral Forms occur when we have a union of one-half of all the similar possible planes that can be arranged about the axes of any crystallographic system. Hence all such forms are called hemi-forms, from the Greek, Hemisys, " the half," which is ordi- narily contracted in compound words to Hemi or " half." In the Hemihedral Forms the symmetry is lower than in the Holohedral Forms ; i. e., there are fewer planes or axes of symmetry than in the Holohedral Forms. For example, one set of Hemihedral Forms in the Isometric System has three planes of symmetry, four axes of trigonal symmetry, three axes of binary symmetry, and a centre of symmetry. See Figs. 52 and 53. In the Triclinic System it should be noticed that at the most only two planes in any case are alike, i. e., have similar indices. So in the case of the Prisms THE TRICLINIC SYSTEM. 25 and Domes, instead of four similar sides, there exist only two, or one-half of the completed form ; hence these forms are called Henri-Prisms and Hemi-Domes. 3. Tetartohedral Forms occur when we have a union of one-fourth of all the similar possible planes that can be arranged about the axes of any crystallographic system. These forms are called Tetartohedral Forms, from the Greek, Tetartos, "the fourth part of any thing." In the Triclinic System the Pyramids or Octahedrons have only one quarter of the faces neces- sary to make a complete form ; hence, instead of call- ing the faces Pyramids, it is correct to speak of them as Tetarto-Pyramids. See Figs. 28-32 and 111, Figs. 34 and 35. The Tetartohedral Forms have a low order of symmetry, as shown in the planes, axes, or centres of symmetry ; for example, in the Hexagonal System a tetartohedral form known as the Trigonal Trapezo- hedron has neither plane nor centre of symmetry, but has one axis of trigonal and three axes of binary sym- metry. See Figs. 54 and 55. SIMPLE AND COMPOUND CRYSTALS A crystal is said to be simple when it is made up of the planes of one form only. See Figs. 7, 12, and 52-55 ; but it is called compound when it is com- posed of the planes of two or more different forms. 26 NOTES ON CRYSTALLOGRAPHY. See Figs. 8-11, 15-18, and 28-51. Compound crys- tals comprise a large majority of crystals. Simple crystals are found in the Hexagonal and Isometric Systems more often than in any of the others ; while the Triclinic and Monoclinic crystals are all com- pound, for no single form in these systems can inclose space. See Figs. 28 and 35. In describing these forms we require some special terms. Occasionally the planes of the several forms that make the compound crystals are all equally de- veloped ; but in most cases the planes of one form are more conspicuous than are those of the others. The chief form is called the Dominant Form and second- ary ones are called Subordinate Forms. See Fig. 17. In describing a crystal or model, it is usual to select the most conspicuous form as the Dominant Form, and then to state that it is modified by such and such Subordinate Forms, naming the secondary forms one after the other, in the order of their prominence. For example, in Fig. 17 we say that the dominant form is an octahedron (111) modified, first, by the planes of a cube, (100), and, secondly, by the planes of a dodeca- hedron, (110). In the union of the various forms that make up the completed crystal, the planes of one form take the place of the edges or solid angles of another form. In such a case we use the term Replace to indicate the re- THE TRICLINIC SYSTEM. 27 lation of the two forms. For example, in Fig. 17 the dominant form is an octahedron (111), the solid angles of which are replaced by the planes of a cube (100), and the edges of which are replaced by the planes of a do- decahedron (110). In the above example the dodeca- hedral planes, (110), make, on each of their sides, equal angles with the octahedral planes (111); in such cases we commonly say that the edge of the octahedron (111) has been truncated. In like manner, the cube plane (100) is equally inclined to the four adjacent faces of the octa- hedron (111). In this case we usually say that the solid angles of the octahedron (111) have been truncated by the planes of a cube (100). From this we may define Truncation of an edge as the Replacement of that edge by a plane equally inclined to the adjacent similar planes. The Truncation of a solid angle is the Replace- ment of that angle by a plane equally inclined to the adjacent similar planes. Figs. 56-58 show a form of replacement that is commonly distinguished by the special term Bevelment. In this we can see that the two repla-cing planes are unequally inclined on oppo- site sides to the two planes forming the replaced edge, but that the intersections of all the planes are parallel. In Fig. 58 the replaced edge was formed by the meeting of the two planes, a and d. This edge is now replaced by the planes b (310) and c (130). The plane 6, for in- stance, inclines on the plane a (100) at the same angle 28 NOTES ON CRYSTALLOGRAPHY. that the plane c does on the cube face d (010). Again, the plane b inclines to the cube face d at a different angle from its inclination upon the cube face a. The plane c, in like manner, inclines on the cube face a at a different angle from that which it makes on c. These opposite inclinations are equal in the two planes. If this were not so, the intersections could not be parallel. We say then that an edge is Bevelled when it is replaced by two planes which are unequally inclined on oppo- site sides to the two planes forming the replaced edge, but which have all their intersections parallel. It needs to be noted that in studying a crystal com- posed of several forms, no attention is to be paid to the shape or size of the replacing planes. Their in- clinations to the axes are the only points with which we are concerned. READING CRYSTALLOGRAPHIC DRAWINGS In order to express the relations of the different planes to one another upon a crystal and to enable one crystallographer to understand the work of an- other, without his writing out long and tedious de- scriptions, several systems of crystallographic short- hand have been proposed. Of these systems, the one that formerly prevailed amongst English-speaking people is the German system of Weiss, which was subsequently modified by Naumann, and later by THE TRICLINIC SYSTEM. 29 J. D. Dana, whose symbols are the simplest of the three. The present prevailing system of notation, or at least the one that will in time receive almost if not quite universal adoption, is the Whewell-Grassmann- Miller system as modified by Bravais. For the ele- mentary conception of crystals the crystallographic system of Naumann is more easily understood by the student and is better from the observational stand- point ; but for the work of the crystallographer the Miller notation or the Miller-Bravais system lends itself to easier calculations, and is superior from the the mathematical view-point. The French have generally employed the Haiiy notation as modified by Le>y and Des Cloizeaux, but for our purpose attention will be given only to the notations of Weiss, Naumann, Dana arid Miller- Bravais. These notations have been modified by some later cry stall ographers, notably Groth. It is now time to turn our attention to crystallo- graphic symbols. The first to be considered are those belonging to the axial notations. See Fig. 1. In this system, where the three axes are all of different lengths, the shorter lateral semi-axis is designated by the italic letter a, over which the printer's breve or short vowel mark ( ) is placed to indicate that it is the shorter lateral semi-axis or brachy-semi-axis. In a similar manner the longer of the lateral semi-axes is 30 NOTES ON CRYSTALLOGRAPHY. designated by the italic letter b, over which the macron or printer's long vowel mark (-) is placed to indicate that this is the longer lateral semi-axis or macro- semi-axis. The vertical semi-axis is designated by the italic letter c, over which is erected a short vertical mark or perpendicular ( ) to indicate that this refers to the vertical semi-axis. A plane, in crystallographic notation, is always designated by the distance from the centre to the point at which it intersects each axis. The beginner may think this a very difficult procedure, but in prac- tice it is simple enough ; for we deal only with the relative distances and have nothing at all to do with the absolute distances. If the axes are different, as they are in this system, we assume a unit of distance on each axis : the unit is not an inch or any other standard measure of length, but implies that if one plane cut the axis at unity or 1, another plane may also intersect this axis at f , j, 2, 3, 4, or any number of times that unit of distance. If we had hundreds of crystal planes parallel to one another, they could all then be reduced to our unit of distance and thus considered as one. It is only when the planes vary in their intercepts upon the axes that they are considered as separate planes. If in any crystal a plane is selected as the standard, it will be THE TRICLINIC SYSTEM. 31 found that all other planes intercept the axes either with the same unit of distance or at some simple mul- tiple or fraction of it, like J, J, J, }, f, |, f, 2, 3, 4, 5, 6, 7, 8, 9, and so on. The intercepts of a plane upon the axes are known as the Parameters ; or we may define the parameters as the relative distances from the chosen centre of the crystal to the point at which a plane intersects the the imaginary axes. The important thing about a crystal plane is its inclination to the axes. This in- clination varies only when the parameters vary ; for if the parameters of one plane are written 1 a : 3 b : 2 c and those of another plane written 4 a : 12 b : 8 c, it becomes at once apparent that if we divide the second set of parameters by 4, they reduce to the same form as the first, and that therefore the inclinations of the two planes are identical and the planes are both the same. From this it follows that the parameters should always be reduced to their lowest terms or have no common divisor. It may further be noticed that the sizes of the planes have no significance in Crystal- lography. To return to our laws for the nomenclature of planes in the Triclinic System : by noting the position where the Vertical Pinacoid or Basal Plane cuts each axis, and by writing the axes with the parameter figures, we can see at once that the parameters of this plane will 32 NOTES ON CRYSTALLOGRAPHY. be as follows : oo a : co 6 : 1 c. Now the figure 1 be- fore the c is superfluous, and the parameters can be written thus : oo a : oo b : c. These symbols may be translated as follows : the plane in question cuts both lateral axes at infinity or is parallel to them, while it intersects the vertical axis at the unit of distance. Such a plane can only be a Vertical Pinacoid or Basal Plane. When the parameters are written as above, the notation is known as the Weiss system. Naumann abbreviated this form by writing the capital letter P and placing zero before it, as follows : P. Dana further abbreviated by writing this plane as or c. Miller employs the reciprocals of the Weiss param- eters, calling them Indices; e. g., in the above, the reciprocals are ^ : < : -J- = : : 1 ; or, as it is the custom to write the indices in the Miller system with- out colons, the indices are written as follows : 1. In every case in the Miller system where any of the reciprocals are in the form of fractions, all the indices are multiplied by the smallest number that will re- duce all these fractions to whole numbers. From this it follows that all the Miller indices are whole num- bers, generally ranging from to 6. In following out the above notations our symbols for the Brachy- Pinacoid would be in the Weiss method : oo a : b : co c, modified by Naumann to QO P co , or oo P GO , and by Dana to i-i, or a. Miller's indices would be 1 0. THE TRICLINIC SYSTEM. 33 In the case of a prismatic plane the Weiss notation would be a : b : oo c, or a : -b : GO c, according as the plane cuts the axis b (Fig. 1) on the right or the left side. Naumann's modifications are as follows : oo P for the first, and oo 'P for the second. Both of these Dana abbreviates as I' or m, and v /6r M.* In marking the directions on the axes, parameters taken on the lateral axes to the front and to the right side are considered positive, but those measured to- wards the back and to the left side are called negative. The direction taken on the vertical axis above the lateral axes is called positive, while that below is called negative. See Fig. 1. The positive sign (+) is not usually given, for it is understood that unless the negative ( ) sign is written, all the parameters are positive. In order to indicate the different positions relative to the axes, Naumann used the accent mark placed to the right or left above and to the right or left below, as follows : P, 'P, P,, ,P. See Fig. 28. Some employ the accent mark not about the P, but in the same relative position about the let- ters or infinity sign accompanying the P; as raP oo ', or /f mP oo . * Besides using the symbols of Naumann, Dana, or Miller to desig- nate the planes upon a crystal, it is not uncommon to select letters with or without any system. In such instances the text is expected to ex- plain the notation in each case. Figs. 28-35 illustrate some of the methods of notation in the Triclinic System. 3 34 NOTES ON CRYSTALLOGRAPHY. In the Miller notation as now employed the a semi- axis is always given first, the b semi-axis second, and the c semi-axis third, using for the indices either known integers, or else employing in their places the letters h for the a semi-axis, k for the b semi-axis, and I for the c semi-axis. But whenever either the h, k, or I become equal in value to one of the others, then the same letter is used in both cases ; as, h h I, or h k k. When all three letters have the same values, the indices reduce instantly from h h h to 1 1 1. When- ever the direction is taken negatively in the Miller indices, the negative sign is written above the letter, as h. If the student now understands the Weiss system of notation derived from the intercepts of each plane upon each axis, it is hoped that Figs. 28-35 and the following table adapted from the works of Bauerman, J. D. and E. S. Dana, Groth, Liebisch, Mallard, and others, will make the notations intelligible to him. THE TRICLINIC SYSTEM. 35 TABLE I TRICLINIC FORMS AND NOTATIONS Form. Weiss. Naumann. Dana. Miller. Basal-Pinacoids. ooa 006 : c OP O or c 001 Brachy-Pinacoids. ooa 6 : ooc ooPoo i-l or 6 010 Macro-Pi nacoids. * 006 : ooc ooPoo i-5 or a 100 a b : ooc 00 P' J 7 orm 110 a 6 : ooc 00 'P '/or Jf no Hemi-Prisms. a a nb : ooc nb : oo c ooP'n oo 'Pn i-n' MO na 6 : ooc ooP'n i-n MO na b : ooc oo 'Pn i-n MO Hemi-Brachy- ooa 6 : me m/P'oo m-! 05W Domes. ooa 6 : me m'P/oo m-l 0& Hemi-Macro- a 006 : me m'P'oo 'm-t 7 mi Domes. a 006 : me m^/oo / m-* / m a b:e P' 1 in a b':c 'P 1 in a 6:c' P* 1 nf a &':c' /P 1 in a b : me mP' m' hhl a b: me m/P ,m hhl a b : me mP/ m x Jhl Tetarto-Pyramids. a b : me m'P 'm hhl a nb : me mP'n m-n f hkl a nb : me m/Pn /m-n hkl -a nb : me mP/n m-n x ~hkl a nb : me m/Pn 'm-n hkl na b : me mP'n m-n' hkl na b : me m/Pn /m-n hkl na b : me mP,n m-n/ hkl na b : me m'Pn 'm-n hkl 36 NOTES ON CRYSTALLOGRAPHY. HEMIHEDRAL AND TETARTOHEDRAL NOTATIONS The previous account of the notations particularly applies to the holohedral forms. The majority of crystallographers, however, indicate the hemihedral forms by writing J in connection with the symbols, w'P'oo thus : \ (a : oo b : me), or -^ , etc. For the tetar- tohedral forms the J is written in the same way : mP J (a : b: me), or -7 Sometimes the forms are con- sidered " positive and negative, or right-handed and left-handed. These conditions are indicated by writ- ing -f or , or before the symbols, or by writing r or I for right or left before or after the symbols. More use is made of this method of writing the symbols of the hemi- and tetarto-hedral forms in the Isometric and Hexagonal Systems than in any of the others. Very few writers, however, employ any method of notation to distinguish the half or quarter forms in the Triclinic System. In that system all the prisms and domes are hemihedral and all the pyra- mids are tetartohedral forms ; hence it follows that any plane, whose symbol indicates that it is a dome or prism in this system, must belong to the half forms. In like manner, if the symbol of any face denotes that it is pyramidal, it must belong to the quarter forms. Therefore, it is considered that any special distinctive half or quarter form marks are unnecessary. THE TRICLINIC SYSTEM. 37 A few writers distinguish the partial forms in the Monoclinic System, but the majority do not use any of the characteristic fractions. These fractions are used chiefly in the other four systems, of which the Hexa- gonal and Isometric Systems, as before indicated, afford the majority of examples. In the Miller System of notation the symbols, like h k I, stand for individual faces. Sometimes these are placed in ( ), as (h k I), When they are united to make a. form, the symbols of the plane have a brace { \ written before and after them, as {h k l\. The hemihedral and tetartohedral forms are indi- cated by writing some letter of the Greek alphabet before the symbol of the face or form ; e. g.. K for hemi- hedral inclined faces and * for hemihedral parallel faces ; { 1 1 1 } and * { h k o }. The more recent crystallographers have largely dis- carded the use of the terms holohedral, hemihedral, and tetartohedral, and prefer to consider that the six crys- tallographic systems are divided into thirty-two groups distinguished by their differences in symmetry. It is here preferred to retain the use of the above terms, because it is thought that, for the present at least, they offer the fewest difficulties to the student who studies crystallography simply as an aid in the practical field determination of minerals. Since the parameters of a plane belonging to a half 38 NOTES ON CRYSTALLOGRAPHY. or quarter form are exactly the same as they are when this plane is a constituent part of a holohedral form, there is in our common determinative work no inher- ent need of distinguishing the planes of the different partial forms from the entire forms. They have to be distinguished when drawings are to be made, or when an exact idea of the form of the crystal is to be conveyed. For much of the determin- ative work the special separation into holohedral, or hemihedral, or tetartohedral forms is not required. Circumstances and particular conditions will deter- mine when the special separation is desirable. DIRECTIONS FOR STUDYING TRICLINIC CRYSTALS 1. Prove that the crystal or model is triclinic. 2. Locate the axes as previously directed. 3. Note the dominant and modifying forms. 4. In giving the forms say that the dominant form is (naming the form); modified by (naming the next important subordinate form); and so on, until all the forms have been given. 5. Select and name the pinacoids by the rule. 6. Select and name the dome and prism planes by the rule. 7. Select and name the pyramidal or octahedral planes by the rule. In naming the above planes, give, first, all those on the dominant form, and, secondly, all THE TRICLINIC SYSTEM. 39 the faces on each secondary form in order of the pre- cedence of those forms. 8. In naming the forms state whether they are holo- hedral, hemihedral, or tetartohedral. To do this re- member that if all the similar planes of any form are present, that form is holohedral ; if one-half of all the similar planes are present, the form is hemihedral; and if only one-fourth of all the similar planes are present the form is tetartohedral. 9. Locate the planes, axes, and centres of symmetry, if there are any. 10. It is to be noted that a crystal form may have as many domes or prisms and octahedrons as there are different positions in which planes making these forms can intersect the axes without becoming parallel to any other plane ; but in practice it is found that usually there are but few forms of any special class (pyramid, or dome, or prism) united in the same com- pound form. CHAPTER III THE MONOCLINIC SYSTEM THIS system derives its name from the Greek word Monos, "one" and Klino, " to incline or lean against," from the inclination of one axis to the other two. In this system the axes are three in number and are un- equal in length ; because it is found that the simplest variation from the Triclinic System is to require that two of the axes be at right angles to each other, but form oblique angles with the other one. SYMMETRY Before we enter upon a fuller discussion of these forms, it is best to look at the plane of symmetry in the Monoclinic System. In this system an examina- tion of the crystals shows that there is one direction, and only one, in which, if a plane be passed through the crystal, it \fill make a division into two equal and symmetrical halves. This single plane of symmetry occurs only in the Monoclinic System, with but three exceptions in other systems. See Figs. 198 and 199. The exceptions can be distinguished by the fact that (40) THE MONOCLINIC SYSTEM. 41 the Monoclinic System has in the normal forms an axis of binary symmetry only, while the three excep- tions have, respectively, axes of trigonal, tetragonal, and hexagonal symmetry. It should be particularly noted that the axis of binary symmetry in the Mono- clinic System is perpendicular to the plane of sym- metry. In this system the normal forms have a centre of symmetry. See Figs. 8-11 and 59-86. NOMENCLATURE In the Monoclinic System it is customary to locate the plane of symmetry first and the axis of symmetry next. As a rule, a Monoclinic crystal placed on end will rest on one of two parallel planes or edges, and the shortest line joining them will be the vertical axis. See Figs. 9-11, 60, 64, 71, 78, and 83. Having ascertained the plane and the axis of sym- metry, place the crystal on its base or basal edge, and consider an axis to lie in that plane of symmetry, and to be drawn from the base parallel to the side planes and edges. As before stated, this axis is called the Vertical Axis. See c, Figs. 2, 60, and 64. Of the other two axes one must be coincident with the axis of binary symmetry and therefore perpendicular to the plane of symmetry. The other axis must lie in the plane of symmetry and must be drawn, as a rule, 42 NOTES ON CRYSTALLOGRAPHY. parallel " to the base or basal edge. Both these axes are called Lateral Axes. The one that is perpendicu- lar to the plane of symmetry is named the Ortho-Axis (see ~b, Figs. 2, 60, and 64) or the Ortho -Diagonal (Greek, Orthos, " in a straight or right line ") ; while the other lateral axis, or the one lying in the plane of symmetry, is called the Clino-Axis (see d, Figs. 2, 60, and 64), or Clino -Diagonal (Greek, Klino, " to incline, or to make a slope or slant, or to lean against"). From these meanings the Ortho-Axis is often called the Straight Axis and the Clino-Axis the Inclined or Oblique Axis. In this case, as in the preceding one, planes may in- tersect only one axis, or cut two axes, or intersect all three, giving us as before Pinacoids, Domes or Prisms, and Pyramids or Octahedrons. In the naming of pinacoids in the Monoclinic Sys- tem, their relations to the axes are used, as in the Tri- clinic System. As the Monoclinic lateral axes have different names from the Triclinic lateral axes, the nomenclature will, in that respect, vary in the two systems. From this it follows : 1. If a pinacoid cuts the vertical axis and is par- allel to the two lateral axes, it is a Vertical Pinacoid ; but it is generally called a Basal Plane, or a Basal Pinacoid. See 001, Figs. 59-63, 65-70, and 73-77. On the other hand, the lateral pinacoids are named THE MQNOCLINIC SYSTEM. 43 from the lateral axis to which they are parallel ; as, for example, if a pinacoid intersects the ortho-axis and is parallel to the clino-axis, it is a Clino -Pinacoid (see 010, Figs. 61, 67-72, 74, 75, 77, and 81-86); if it cuts the clino-axis and is parallel to the ortho-axis, it is designated as an Ortho-Pinacoid (see 100, Figs. 59, 61, 62, 65, 68, 71, 72, 78, and 83). 2. The dome or prism planes are named from the axis to which they are parallel. Thus they are called Clino-Dome Planes if they are parallel to the clino- axis (see Oil, Figs. 65, 70, 75, and 84) ; but they are named Ortho-Dome Planes if they are parallel to the ortho-axis (see 401, 102, Fig. 69 ; and 101, Figs. 65, 66, 70, and 79) ; and they are called Vertical Dome Planes, or more commonly Prism Planes, if they are parallel to the vertical axis (see 110, Figs. 59, 60, 62, 63, 65-72, 74-77, and 82-86). 3. If a plane cuts all three axis, it is a Pyramidal or Octahedral Plane. See 111, Figs. 64, 68, 69, 71, 72, 77-83, 85, and 86. RELATION OF PLANES TO THE AXES To enable one to name the crystal planes in the easiest way, it is best, as a rule, to locate the axes parallel to the largest number of planes possible ; i. e., to make as many pinacoids, domes, and prisms as pos- sible, and as few pyramids or octahedrons as possible. 44 NOTES ON CRYSTALLOGRAPHY. DISTINGUISHING CHARACTERISTICS OF THE MONOCLINIC CRYSTALS See whether or not the form belongs in the Mono- clinic System, determining this, first, by the presence of one plane of symmetry and one binary axis of sym- metry only, and next, by the fact that the edges and planes at the ends of the crystals make oblique angles with the edges and planes on the sides, so that when a model or perfect crystal is set on end, with an end plane or edge parallel to the table, it leans backwards, forming oblique angles with the table, but without any sidewise twist, as is the case with the Triclinic Crystals. See Figs. 28-35 for Triclinic Crystals, and Figs. 8-11, and 59-86 for Monoclinic Crystals. RULES FOR NAMING MONOCLINIC PLANES I. If a plane cuts one axis and is parallel to the other two, it is a Pinacoid. If it cuts the vertical axis, it is a Basal or Vertical Pinacoid, or a Basal Plane ; if it intersects the ortho-axis, it is a Clino-Pinacoid ; if it cuts the clino-axis, it is an Ortho-Pinacoid. II. If a plane cuts two axes and is parallel to the third axis, it is a Dome or Prism Plane, and is named from the axis to which it is parallel ; if it is parallel to the vertical axis, it is a Prism or Vertical Dome Plane ; if parallel to the clino-axis, it is a Clino-Dome Plane ; if parallel to the ortho-axis, it is an Ortho-Pome Plane, THE MONOCLINIC SYSTEM. 45 III. If a plane cuts three axes, it is a Pyramidal or Octahedral plane. HOLOHEDRAL FORMS The Holohedral Forms in this system are the prisms (vertical domes) and the clino-domes. HEMIHEDRAL FORMS The Hemihedral Forms in this system are the ortho- domes and pyramids or octahedrons; hence, all are properly called Hemi-Ortho-Domes and Hemi-Pyra- mids or Hemi- Octahedrons. They can be distinguished by their conformity to the laws for dome and pyramidal planes, and by the fact that they modify only one-half the similar planes upon the crystal. See Figs. 62, 63, 65 72, 75-77, and 79-86. HEMIMORPHISM The term Hemimorphism is employed to describe crystals whose opposite ends are unlike, i. e., composed of different half-forms or of unlike planes (Greek, Morphe, "form" or " shape"). A requirement of true Hemimorphism is that these dissimilar planes or half- forms shall be at opposite ends of an axis of symmetry, which must also be a crystallographic axis. See Figs. 87 and 88. No true hemimorphic forms occur amongst the minerals crystallizing in the Monoclinic System ; but 46 NOTES ON CRYSTALLOGRAPHY. there is one pseudo-hemimorphic form that needs to be considered here. It is the rare mineral clinohe- drite (''inclined planes"), which is placed by itself in the Clinohedral Group. ' While this form resembles a hemimorphic form, it fails to be so classed because it lacks the essential characteristic of the hemimorphic forms, an axis of symmetry. This pseudo-hemimor- phic form has neither axis nor centre of symmetry, but it does have a plane of symmetry. COMPOUND FORMS The compound forms of this system are compara- tively simple, consisting of prisms, domes, and pina- coids ; sometimes with hemi-pyramids, but more usu- ally without them in the commoner forms. It is to be remembered that the holohedral and hemihedral forms are to be distinguished by the presence of all the possible similar planes for the holohedral forms, and by the presence of half the number of possible similar planes for the hemihedral forms. See Figs. 8-11, 59-86. READING DRAWINGS OF MONOCLINIC CRYSTALS In this system the letters used to designate the axes are the same as those employed in the Triclinic Sys- tem ; but for one of the lateral axes, the clino-axis, the distinguishing mark is the grave accent over the semi- axis letter, thus d. Some authors, notably the Danas, THE MONOCLINIC SYSTEM. 47 change the mark over the ortho-semi-axis letter 6 ; e. g., instead of writing 6, they write b, using the sign _L- to indicate the straight or ortho-axis or the perpendicular axis. Our axial letters and signs are then as follows : Clino-Semi-Axis, d. Ortho-Semi-Axis, b or b. Vertical Semi-Axis, c. Practically, then, the notation in the Monoclinic System will be similar to that of the Tri clinic System, the variations being due to the different positions of the axes. The positive and negative signs for the parameters and indices are used as in the Triclinic System. See Figs. 2, 60, and 64. Thus, in the Weiss notation, the symbols of the Vertical Pinacoid or Basal Plane are oo d : oo 6 : c. This is abbreviated in the Naumann system as P; in Dana's as 0; and in Miller's as 1. See Fig. 61. In the Naumann symbols the clino-axis or ortho- axis is marked either by this P x or by P; some, how- ever, place the axial mark over the letters or the infinity symbol that accompanies the P, as oo Pn or oo P n, while others omit the marks. Table II, giving the Weiss, Naumann, Dana and Miller symbols, it is hoped, will make the different systems of symbols suf- ficiently clear to the student, especially if he will study Figs. 8-11 and 59-86. 48 NOTES ON CRYSTALLOGRAPHY. As previously stated, only a very few crystallo- graphers distinguish by symbols the hemihedral forms in the Monoclinic System, which has no tetartohedral forms amongst the minerals. TABLE II MONOCLINIC FORMS AND NOTATIONS Form. Weiss. Naumann. Dana. Miller. Basal Pinacoids. cca 006 :c OP O or c 001 Clino-Pinacoids. ooa 6 : QOC QOPOO i-i or b 010 Ortho-Pinacoids. a oo 6 : oo c GOPOO i-i or a 100 a 6 : ooc OOP lor m 110 Prisms. na 6 : coc oo Pn i-n hkO a nb : oo c voPn i-n hldb Clinodomes. cca b : me mPoo m-\ w Hemi- Orthodomes. a a 006 : me oo b :-mc -raPoo mP(x> -m-i m-i mi JiQl a b:-c P 1 ni a b:c -P -1 111 a b :-mc mP m ~hhl Hemi-Pyramids. a na b : me b :-mc -mP mPn -m m-n hhl ~hkl na b : me -mPn -m-n hkl a nb :-mc mPn m-n ~hkl a nb : me -mPn -m-n hkl THE MONOCLINIC SYSTEM. 49 DIRECTIONS FOR STUDYING MONOCLINIC CRYSTALS 1. Prove that the crystal or model is Monoclinic. 2. Determine the plane and the axis of symmetry ; remembering that a single extremely rare pseudo- hem imorphic (clinohedral) form alone, amongst the Monoclinic minerals, has no axis of symmetry. 3. Locate the axes, as previously directed. 4. Note the dominant and modifying forms in the order of their importance. 5. Select and name the planes of each form in the following order : pinacoids, prisms, domes, and pyra- mids. 6. Distinguish the holohedral, hemihedral, and pseudo-hemimorphic or clinohedral forms. 4 CHAPTER IV THE ORTHORHOMBIC SYSTEM THIS system derives its name from the Greek, Orthos, " straight " or " right/' and Ehombos, " a rhomb," because its similar planes commonly form right rhombs. Continuing to vary the axes and angles, we note that this system must have all its axial angles right angles, while the axes still remain of unequal length. NOMENCLATURE Since the axes are of unequal length, it is necessary to distinguish each semi-axis by distinctive names and letters. This is done by using the same nomenclature as in the Triclinic System : Brachy-Semi-Axis, a ; Macro-Semi-Axis, 1 ; and Vertical Semi- Axis, c, re- spectively. See Fig. 3. As before, the planes may intersect one axis and be parallel to the other two, forming Pinacoidal Planes (see 100, 001, and 010, Figs. 87-94, 97, 101-104, 108, 109, 118, 120-122, 125-129, and 131-135) ; or they may cut two axes and be parallel to the third axis, making Dome and Prism Planes (see 110, 101, Oil, (50) THE ORTHORHOMBIC SYSTEM. Si 120, 210, 012, and 021, Figs. 87-104, 113, 115, 117- 121, and 123-135) ; or they may intersect all three axes, forming Pyramidal or Octahedral Planes (see 111, Figs. 87, 88, 91, 92, 96, 97, 105-129 and 131- 135). In naming the above planes we proceed as we did in the Triclinic System, using the same nomenclature. The student is referred to that system for the method. RELATION OF PLANES TO AXES In this system, as in the preceding systems, we place the axes, as a rule, so that they are parallel to the greatest number of planes possible ; i. e., to make as many pinacoids and as many domes and prisms as possible, and as few pyramids as possible. SYMMETRY In this system the normal forms have three planes of symmetry coinciding in direction with the three axes of the system, and therefore at right angles to one another. See Figs. 3, 7, 51, and 87-135. The normal orthorhombic forms further have three axes of binary symmetry which are coincident with the three unequal crystal axes. In the Isometric System the Pyritohedron or Penta- gonal Dodecahedron (see Figs. 52 and 53), and the Diploid or Dyakis-Dodecahedron (see Figs. 136 and 137), have also three planes of symmetry only, which 52 ttOTES ON CRYSTALLOGRAPHY. are at right angles to one another. These forms need not be mistaken for Orthorhombic crystals, since they are of equal dimensions along each plane of symmetry, while in the Orthorhombic forms the dimensions are unequal. The above Isometric forms also have three axes of binary symmetry that are coincident with the equal crystal axes, and they further have four axes of trigonal symmetry. In the Hexagonal System the rhombohedral (see (Figs. 138 and 139), and scalenohedral (see Figs. 140 and 141) forms have also three planes of symmetry, but these form angles of 60 with one another, and all extend in the same direction ; i. e., they lie in the plane of the vertical axis, instead of forming right angles with one another, as in the Orthorhombic System. The Rhombohedron and Scalenohedron also have three axes of binary symmetry, but they all lie in the plane of the lateral axes. They also have a vertical axis of trigonal symmetry coincident with the vertical crystal axis. Further, the three lateral dimensions of the Hexagonal crystals are the same, but all the dimensions are unequal in the Orthorhombic forms ; while the similar parts are three or some multiple of three in the Hexagonal System, and but two or four or some multiple of four in the Orthorhombic System. THE ORTHORHOMBIC SYSTEM. 53 DISTINGUISHING CHARACTERISTICS OF THE ORTHO- RHOMBIC CRYSTALS 1. Determine whether or not the crystal or crystal model belongs to the Orthorhombic System. This can easily be done by noting the three unequal dimensions of the crystal ; by observing that these dimensions form right angles with one another ; by noticing the presence in the normal forms of but three planes of symmetry arranged at right angles with one another and parallel to the three unequal directions shown on the crystal ; by noting that the three axes Of binary symmetry lie in the three planes of symmetry and coincide with the three crystal axes ; and by observing that the similar parts at the ends, or on the sides of the crystal, are in twos or fours, but never in threes or any multiple of three. 2. Having determined that the crystal is ortho- rhombic, place it generally with its thinnest direction in a vertical position. In many cases this gives a basal plane or pinacoid for it to rest upon. Call the direction perpendicular to the table the vertical axis ; then imagine the planes of the ends prolonged until they meet or intersect. Consider then the longer of the two lateral directions thus formed the macro-axis, and the shorter will be the brachy-axis. It often happens that if we imagine the crystal planes to be prolonged until they meet one another, the apparently 54 NOTES ON CRYSTALLOGRAPHY. shortest length of the crystal is the longest dimension. If the axes are properly selected in the normal forms, they will lie in the three planes of symmetry and will coincide with the three axes of binary symmetry. RULES FOR NAMING ORTHORHOMBIC PLANES I. A plane which intersects one axis and is parallel to the other two is a Pinacoidal Plane. If it cuts the vertical axis, it is called a Basal Pinacoid or Basal Plane. If it intersects the brachy-axis, it is an Ortho- Pinacoid. If it cuts the ortho-axis, it is a Brachy- Pinacoid. II. If the plane intersects two axes and is parallel to the third axis, it is a Dome or Prism Plane. If this plane is parallel to the vertical axis, it is known as a Vertical Dome Plane, or more usually as a Prism Plane; if parallel to the clino-axis, it is a Clino- Dome Plane ; if parallel to the ortho-axis, it is an Ortho-Dome Plane. III. If the plane intersects all three axes, it is a Pyramidal or Octahedral Plane. IV. In case the form has only half the full num- ber of faces, give to that form the name of the hemi- hedral form that has the same parameters. HOLOHEDRAL FORMS Most of the common crystals of the Orthorhombic System are composed of holohedral forms. These THE ORTHORHOMBIC SYSTEM. 55 forms have, as previously stated, three planes of sym- metry and three axes of binary symmetry. HEMIHEDRAL FORMS The hemi-domes and hemi-prisms are not very com- mon in this system, and when they do occur they can be recognized by their modification of only one-half the similar parts of the dominant form. The more commonly-occurring forms are hemi- pyramids, which produce wedge-shaped forms called Sphenoids (Greek, Sphen, " a wedge "). For purposes of distinction these forms are often called Orthorhom- bic Sphenoids. They are characterized by their wedge- or axe-shaped edges; arid are distinguished from the wedge-shaped forms in the other systems by their three unequal dimensions, by the fact that their faces are scalene triangles, by the possession of three axes of binary symmetry, and by their lack of any plane or centre of symmetry. See Figs. 88 and 142- 150. Figs. 88, 149, and 150 show how a sphenoid modifies the opposite ends of a crystal, producing a form that might be mistaken for a hemimorphic one. The formation of the Sphenoids can be easily under- stood if we will take a simple pyramid and consider one-half of its planes obliterated (i. e., alternate planes), and enlarge the other four alternate planes until they meet and make a complete form. Fig. 235 shows by 56 NOTES ON CRYSTALLOGRAPHY. its blackened planes the faces to be obliterated. See Figs. 145 and 146. We can illustrate this for our- selves by pasting sheets of paper to the alternate faces of a model of a pyramid, and trimming the sheets until they join at their edges, making a completed form. It is illustrated better by the glass models made in Germany, which show paper pyramids on the inside of the models with the alternate faces carried out in glass, until they meet, making glass sphenoids. The above method of derivation of the sphenoid shows that another sphenoid can be formed if we carry out the planes which we before considered suppressed and then look upon the others as obliterated. We may designate these two sphenoids as positive and nega- tive ; or as they are related to each other as the right hand is to the left hand, it is usual to call the positive sphenoids right-handed and the negative ones left- handed. HEMIMORPHIC FORMS Fig. 87 represents a hemirnorphic form of this sys- tem and shows distinctly the different planes modify- ing the opposite ends of the crystal. In this system the hemimorphic forms have two dis- similar planes of symmetry and one axis of binary symmetry, but they are destitute of a centre of sym- metry. THE ORTHORHOMBIC SYSTEM. 57 COMPOUND FORMS The more usual compound forms in the Orthorhom- bic System are composed of pinacoids, prisms, and domes, sometimes without pyramids, but oftener with them, The holohedral forms are the most common, but these forms are not infrequently associated with hemihedral or hemimorphic forms. The heinihedral forms can be distinguished readily by the fact that they have half the number of possible similar planes. The hemimorphic forms can be determined by the fact that the planes at the opposite ends of a crystal axis (which is also an axis of symmetry) are dissimilar. See Figs. 87 135. READING DRAWINGS OF ORTHORHOMBIC CRYSTALS As previously mentioned the notation for the axes of the Orthorhombic System is as follows : Brachy-Semi-Axis, a. Macro-Semi-Axis, b. Vertical Semi-Axis, c. See Fig. 3. These symbols are considered positive or negative under the same rules as those given under the Tri- clinic System. The notations in this system will then be almost identical with those of the Triclinic System. This fact leads to the belief that the Orthorhombic notations will not offer any difficulties to the student who has mastered the Triclinic notations. 58 NOTES ON CRYSTALLOGRAPHY. The methods employed for distinguishing the right or positive sphenoids from the left or negative ones are shown sufficiently well in Table III, so that the stu- dent should have no difficulty in understanding the notations, TABLE III ORTHORHOMBIC FORMS AND NOTATIONS Forms. Weiss. Naumann. Dana. Miller. Basal Pinacoids. GO a GO b i c OP Oorc 001 Brachy- Pinacoids. ooa b '. coc coPcc i-i or & 010 Macro- Pinacoids. a 006 : coc coPco i-i or a 100 a b : ooc ccP Jor w 110 Prisms. na 6: coc coPn i-n hkO a nb : coc coPn i-n hkO Brachy- Domes. oo a 6 : me wPco m-l Okl Macro- Domes. a co 6 : we wPco m-i hQl a 6 : c p 1 111 Pyramids. a 6 : me na b: me wP mPn w w-n hhl hkl a nb : me mPn m-n hkl +orri( d : b : me) + orr^ -f- or r K\hhl\ or Z ( a : b : me) ~2" or Z m K \hhl\ Sphenoids. +orr lf(na : b :mc) J- nr v WiP 11 _j_ nj.^.^-^ K\hkl\ 2 2 or 1$ (na : b : me) 7 wPn or j| m-n K\hkll 2 2 + or r l(a-nb' we) + r wPn 4. r m-n + _ - - Z 2 I 2 K\hkl\ THE ORTHORHOMBIC SYSTEM. 59 DIRECTIONS FOR STUDYING ORTHORHOMBIC CRYSTALS 1. Prove that the crystal or model is orthorhombic. 2. Locate the axes, as previously directed. 3. Note the dominant and modifying forms in the order of their importance. 4. Select and name the planes of each form in the following order : pinacoids, prisms, domes, and pyra- mids. 5. Distinguish the holohedral, heniihedral, and hemimorphic forms, designating the sphenoids as such. 6. Locate the planes, axes, and centres of symmetry. CHAPTER V THE TETRAGONAL SYSTEM In the next variation that leads to the formation of another system all the angles are right angles, but two of the axes are equal, and the third one is unequal in length to the other two. The only requirement is that this third axis must be either longer or shorter than the other two and must be perpendicular to them. This variable axis is always selected as the Vertical Axis. The other two axes, also lying so as to make right angles with each other, as well as with the Vertical Axis, are called Lateral Axes. See Figs. 4 and 162. NOMENCLATURE In this system the nomenclature differs somewhat from that followed in the three preceding systems, be- coming more complicated. I. If a plane cuts the vertical axis and is parallel to the lateral axes, it is called a Basal Pinacoid or Basal Plane. See Figs. 147-149. There can be but two such planes on any crystal. (60) THE TETRAGONAL SYSTEM. 61 II. Of lateral planes parallel to the vertical axis three cases may occur : 1. The plane may cut both lateral axes equally, giv- ing rise to a Primary or Direct Prism Plane, frequently called a Prismatic Plane of the First Order. See 110, Figs. 147, 150, and 157. 2. If the before-mentioned plane cuts only one lateral axis and is parallel to the other, it is known as a Secondary or Inverse Prism Plane, or as a Prismatic Plane of the Second Order. See 100 and 010, Figs. 152, 153, and 156-159, 174, 183, 188, and 190. 3. If the aforesaid plane cuts the two lateral axes at unequal distances, it is called a Ditetragonal Prism Plane. See h k 0, Figs. 160, 161, and 189 ; and 320, Fig. 190. III. Again, if a plane cuts the vertical axis and in- tersects one or both lateral axes, it is called a Pyramidal or Octahedral Plane. Of Pyramidal Planes there may also be three cases : 1. If the plane in question cuts both lateral axes equally, it is known as a Primary or Direct Pyramidal or Octahedral Plane, or as a Pyramidal Plane of the First Order. See 111, Figs. 154, 155, 157, 159, 162, 164, 166-183, and 185-191. 2. If it cuts only one lateral axis and is parallel to the other, it is known as a Secondary or Inverse Pyra- midal Plane, or as a Pyramidal Plane of the Second 62 NOTES ON CRYSTALLOGRAPHY. Order. See 101, Oil, and h Z, Figs. 156, 163, 165, and 175-182. 3. If it cuts both lateral axes at unequal distances, it is called a Ditetragonal Pyramidal Plane, or a Zir- conoidal Plane, or a Dioctahedral Plane. See h k I, Figs. 160 and 184-186; 313, Figs. 187 and 188; and 321, Fig. 191. RELATIONS OF THE PLANES TO THE AXES As in the preceding system, the axes are to be located so as to have upon the crystal as many pina- coids and prisms as possible, with the fewest possible pyramids. DISTINGUISHING CHARACTERISTICS OF TETRAGONAL CRYSTALS Crystals that belong in this system are generally distinguished by the possession of two equal exten- sions and one unequal ; by the fact that the opposite ends of the unequal extension are similar ; and by the further fact that the planes at the ends of the unequal extension are commonly in twos, fours, or eights ; or that the vertical axis (the axis of unequal extension) is coincident with an axis of binary or tetragonal symmetry. RULES FOR NAMING TETRAGONAL PLANES I. Any plane parallel to both the lateral axes is a THE TETRAGONAL SYSTEM. 63 Pinacoid, and is called a Basal Pinacoid or a Basal Plane. II. Any plane which cuts one or more lateral axes and is parallel to the vertical axis is a Prismatic Plane. If it intersects both lateral axes equally, it is a Primary or Direct Prismatic Plane, or a Prismatic Plane of the First Order ; if it intersects one lateral axis but is parallel to the other, it is a Secondary or Inverse Prismatic Plane, or a Prismatic Plane of the Second Order ; but if it cuts the lateral axes unequally, it is a Ditetragonal or Dioctahedral Prismatic Plane. III. If the plane cuts all three axes, it is a Pyra- midal or Octahedral Plane. If it cuts the two lateral axes equally, it is a Primary or Direct Pyramidal or Direct Octahedral Plane, or a Pyramidal Plane of the First Order. If it intersects one lateral axis and is parallel to the other, it is a Secondary or Inverse Pyramidal or Inverse Octahedral Plane, or a Pyra- midal Plane of the Second Order. If it cuts the two lateral axes unequally, it is a Ditetragonal Pyramidal Plane, or a Zirconoidal Plane, or a Dioctahedral Plane. IV. In case there are present only one-half as many faces as the complete form should have, give to the partial form the name that belongs to the hemihedral form having the same parameters. HOLOHEDRAL FORMS The majority of forms in this system are holohedral. 64 ^OTES ON CRYSTALLOGRAPHY. They are distinguished by the possession of five planes, five axes, and one centre of symmetry. Of the axes of symmetry, one is an axis of tetragonal symmetry and the four others are axes of binary sym- metry. Of the planes of symmetry one is passed midway be- tween the opposite ends of the unequal extension, par- allel to the lateral axes and bisecting the vertical axis. Two of the other planes of symmetry pass through the vertical axis and the two lateral ones. Two more planes of symmetry pass through the vertical axis in such a way as to form an angle of 45 with each of the lateral axes. The axis of tetragonal symmetry joins the opposite ends of the unequal extension, and is coincident with the vertical axis. Of the axes of binary symmetry, two are coincident with the lateral axes. The other two lie in the plane of the lateral axes, but form angles of 45 with them. In the simple forms the Primary and Secondary Tetragonal Prisms are identical in appearance, and we can call such simple forms Primary or Secondary, as we chose. It is customary, however, to call such simple forms Primary, and place the lateral axes accordingly. When the forms are compound, then the position of the axes of the selected dominant form determines whether the subordinate prisms are Pri- mary or Secondary. THE TETRAGONAL SYSTEM. 65 The above can be said also for the Primary and Secondary Pyramids. It is obvious that there can be as many Primary and Secondary Pyramids upon a single crystal as there can be different positions on the vertical axis at which planes can cut that axis or we might say, theoretically, an infinite number ; yet we find practic- ally only one, two, or three, or, at most, a very few pyramids. HEMIHEDRAL FORMS The hemihedral forms of the Tetragonal System that are important to Mineralogists can conveniently be divided into two groups, the Sphenoidal and the Pyramidal ; but for crystallographic reasons, attention needs to be called also to the Trapezohedral Group. I. The Sphenoidal Group is characterized by the wedge-shape of its forms, by the equality of two of their dimensions, and by the inequality of the third dimension compared with the two others. Attention is called to two special forms in this group, the Sphenoid and the Tetragonal Scaleno- hedron. 1. The Sphenoid in this system is similar to that in the Orthorhombic System, except that two of the dimensions of the former are equal, while all three of the latter are unequal. The sphenoids are further distinguished by the fact that their four faces are 5 66 NOTES ON CRYSTALLOGRAPHY. composed of isosceles triangles, while those of the Orthorhombic sphenoids are composed of scalene tri- angles. See Figs. 192-195. As in the Orthorhombic System, we can consider these forms to have been produced by the obliteration of four alternate planes of the tetragonal or square pyramid, and by the prolongation of the other four alternate planes until they meet and make a complete form. See Fig. 236, whose blackened planes indicate the faces suppressed. For the purpose of distinction these sphenoids are often called Tetragonal Sphenoids. See Fig. 194. 2. The Tetragonal Scalenohedron can be considered to have been formed by the suppression of four alter- nate pairs of planes in the ditetragonal pyramid, and by the extension of the other four alternate pairs of planes, until they meet and make a complete form. See Fig. 237, in which the blackened planes indicate the planes suppressed. The resulting form has eight faces composed of scalene triangles, but the cutting edge of the wedge is broken, and is composed of two straight lines meeting at an angle. See Figs. 196 and 197. In the sphenoids the cutting edge is formed by a single straight line. See Figs. 192-194. 3. The symmetry in the Sphenoid and in the Tetra- gonal Scalenohedron is lower than that of the holohe- dral forms. In the Sphenoidal Group there are two THE TETRAGONAL SYSTEM. 67 vertical planes of symmetry that form angles of 45 with the lateral axes. There are also three axes of binary symmetry coincident with the three crystallo- graphic axes. There is no centre of symmetry. See Figs. 192-197. II. The Pyramidal Group comprises only two dis- tinct forms of importance in our work : the Henri- Di- tetragonal Prisms, or Tertiary Prisms, or Prisms of the Third Order; and the Hemi-Ditetragonal Pyramids, or Tertiary Pyramids, or Pyramids of the Third Order. 1. The Hemi-Ditetragonal or Tertiary Prism or Prism of the Third Order can be regarded as formed by the suppression of each alternate face of the di- tetragonal prism and by the extension of the other four faces until they meet, forming a four-faced prism. This prism is found as a modifying form only. See Fig. 238, in which the shaded faces indicate the oblit- erated planes. 2. The Hemi-Ditetragonal or Tertiary Pyramid or Pyramid of the Third Order can be considered as formed by the suppression of alternate planes on the upper half of the ditetragonal pyramid, and a like suppression of the similar planes directly below. Then the set of eight corresponding faces are extended until they meet, completing the form and developing an eight-sided pyramid similar to the primary and sec- ondary pyramids or to those of the first and second 68 NOTES ON CRYSTALLOGRAPHY. order. See Fig. 239, whose shaded planes indicate the faces suppressed. Both of the above forms can be distinguished by de- termining the parameters of the planes, and observing that the number of planes is one-half those required by the corresponding holohedral form. The Tertiary Pyramid or Pyramid of the Third Order, like the Tertiary Prism or Prism of the Third Order, never occurs except as a modifying form. If either of the above forms occurred alone as a simple form, it would be identical with a Primary or Secondary Prism or Pyramid. The different position of the lateral axes is the only distinguishing feature, and this can be ob- served only in compound forms. See Figs. 198 and 199. Fig. 198 shows a cross-section of the primary prism or primary pyramid inscribed in a cross-section of a tertiary prism or pyramid. This figure illustrates the different positions of the lateral axes for the different prisms and pyramids when in compound forms, as shown in Fig. 199. 3. The symmetry of the Pyramidal Group is still lower than that of the Sphenoidal Group. The former has one plane of symmetry, a single axis of tetragonal symmetry, and a centre of symmetry. The plane of symmetry lies in the plane of the lateral axes and bisects the vertical axis. The axis of tetragonal sym- THE TETRAGONAL SYSTEM. 69 raetry is coincident with the vertical axis and there- fore is perpendicular to the plane of symmetry. III. The Trapezohedral Group or the Tetragonal Trapezohedrons are discussed here to some extent because they are common in the larger sets of crystal models. These forms are not known to occur in any natural minerals, but only in artificial crys- tallizations. They can be considered to be formed by the extension of the alternate planes of the dite- tragonal pyramid above and below, until they meet, (see Fig. 184). This gives rise to two forms called respectively Right-handed (r) and Left-handed (Q, or Positive and Negative. See Figs. 200 and 201. The Trapezohedrons have four axes of binary sym- metry lying in the plane of the lateral axes, and have one axis of tetragonal symmetry that coincides with the vertical axis. COMPOUND FORMS The common forms of the Tetragonal System are holohedral ones, which are sometimes combined with hemihedral forms. See Fig. 240. Of the hemihedral forms the sphenoids alone occur in crystals separated from other forms. See Figs. 192-194, 196, and 197. READING DRAWINGS OF TETRAGONAL CRYSTALS Since the lengths of the two lateral axes are the same, one letter will suffice to designate both semi- 70 NOTES ON CRYSTALLOGRAPHY. lateral axes, a. For the vertical semi-axis the usual symbol is employed, c. The symbols of a simple prism in this system are, in the Weiss notation, a : a : oo c, or as it is very commonly written a : a : oo c, with the omission of the vertical mark. Naumann's notation for this prism is oo P, Dana's, I or m, and Mil- ler's, 110. The various notations are correlated for the forms in Table IV and, so far as may be, on the Figs. 41-44 and 151-201. THE TETRAGONAL SYSTEM. 71 TABLE IV TETRAGONAL FORMS AND NOTATIONS Forms. Weiss. Naumann. Dana. Miller. Basal Pinacoids. oca : aoa : c OP Oor c 001 Primary Prisms. a : a : ooc ooP Jor m 110 Secondary Prisms. a : QO a : oo c 00 P 00 i-i or a 100 Ditetragonal Prisms. a: na : QOC oo Pn i-n hlcQ Primary Pyramids. a : a : c a : a : me P mP 1 m 111 hhl Secondary Pyramids. a : ooa : c a : QO a : me Poo mPoo l- m-i 101 hQl Ditetragonal Pyramids. a : na : me mPn m-n hkl Tetragonal Sphenoids. i(a : a : me) Ka a " wic) mP 2 mP m ~2 m K\hhl} K {hhl\ 2 ~ 2 Tetragonal Scalenohedrons. i(a : na : me) (a : na : me) mPn 2~ mPn 2 (m-n) 2 (m-n) "~2~ K\hkl\ *\h&} fooPn"] i-n 1 I 1 f\ I Tertiary Prisms. [a : na : oo c] L 2 J TooPnl 2 i-n Tr^/iAcOf TTJ/lfcOf L 2 J 2 Tertiary Pyramids. i[a : na : me] i[a : na : me] rmPnl L 2 J frnPn-] [m-n] ~2~ [m-n] K{hkl\ K\hkl} L 2 J 2 mPn . m-n 1 1.7 ll Tetragonal Trapezohedrons. i(a : na : mc)r i(a : na : me) I 2 mPn 7 ~~2~" "2 r m-7i j ~~ 2 T\hkl\ r{hkl\ 72 NOTES ON CRYSTALLOGRAPHY. DIRECTIONS FOR STUDYING TETRAGONAL CRYSTALS 1. Prove that the crystal or model is Tetragonal. 2. Locate the axes, as previously directed. 3. Note the dominant and modifying forms in the order of their importance. 4. Select and name the planes of each form in the following order : pinacoids, prisms, domes, and pyra- mids. 5. Distinguish the holohedral and hemihedral forms, naming the sphenoids, scalenohedrons, tertiary prisms and pyramids, and the trapezohedrons when they occur. 6. Locate the planes, axes, and centres of symmetry. CHAPTER VI THE HEXAGONAL SYSTEM IN this system it is found best, as a matter of prac- tical convenience, to depart from the custom followed in the other systems of using three axes, and to em- ploy four. Of these four, three are taken as Lateral Axes, and are so placed that they form angles of 60 with one another. The fourth axis, like the Tetra- gonal vertical axis, is either longer or shorter than the lateral axes, and is perpendicular to them. This axis is called, as in the other systems, the Vertical Axis. See Fig. 6. The Hexagonal System is considered in connection with the Tetragonal System, because it has one dimen- sion that is either longer or shorter than its other dimensions, which are equal to one another ; also because the end planes of the longer or shorter direc- tion are similar to one another, but are unlike the planes on the sides. The most obvious difference in the forms is that the Tetragonal System has its parts in twos, fours, or eights (see Figs. 41-44 and 154-201), while the Hexagonal System has its parts in threes, (73) 74 NOTES ON CRYSTALLOGRAPHY. sixes, or some multiple of three. See Figs. 36-40, 45-50, 54, 55, 138-141, 202-234, and 240-324. The symmetries of the holohedral forms in the two systems are similar, as the Tetragonal System has one horizontal and four vertical planes of symmetry (see Figs. 41-44, 155, 157-159, and 161-191), while the Hexagonal System has one horizontal and six vertical planes of symmetry (see Figs. 36-40, 203-208, 254- 267, 315-319, and 321-323). Some crystallographers, e. g., Miller and Schrauf, employ three axes for this system, while others, e. g., Groth, separate the Hexagonal System into two parts ; one part retains the old name of the Hexagonal Sys- tem and has, like it, four axes, while the other part is designated as the Rhombohedral or Trigonal System and has only three axes. Liebisch uses the four axes for the complete system and divides it into two grand divisions according to the grade of the axis of symmetry which is coincident with the vertical axis. When the vertical axis is co- incident with an axis of hexagonal symmetry, the forms are placed in the Hexagonal Division. When the vertical axis is coincident with an axis of trigonal symmetry, the forms are placed in the Rhombohedral (Trigonal) Division. The same divisions are made by the Danas and by Moses. For the semi-axis in the Hexagonal System we use THE HEXAGONAL SYSTEM. 75 in the Miller-Bravais notation the following indices (see Fig. 6): h for the a l semi-axis ; h for the -a l ; k for the a 2 ; k for the -a 2 ; i for the a 3 ; I for the -a 3 ; I for the c 1 ; and Z for the -c. To repeat, the Miller-Bravais Indices, then, are hkll, and the modernized Weiss Parameters are a l :a 2 :-a s : c, or, in a more general form, na l :pa 2 :-a & :mc. It is, however, customary to omit the subscript figures, since the lateral semi-axes are all equal, and to write the notations as follows : na : pa : -a : me. The vertical mark is often omitted over the c, as it is in the Tetra- gonal System. NOMENCLATURE Owing to the employment of the four axes and to the diverse grades of symmetry, or to the numerous and important partial forms, the nomenclature in this system is more complicated than in the Tetragonal or even in the Isometric System. To a considerable extent the forms have names similar to those of the Tetragonal System. RELATIONS OF PLANES TO AXES As in the preceding system, the axes are placed so as to have as many pinacoidal and prismatic planes as possible, with the fewest possible pyramidal planes. This rule extends to all the partial as well as to the holohedral forms. 76 NOTES ON CRYSTALLOGRAPHY. DISTINGUISHING CHARACTERISTICS OF HEXAGONAL CRYSTALS The crystals of this system are generally distin- guished by the possession of three equal extensions and one unequal ; by the fact that the opposite ends of the unequal extension are similar ; and by the fur- ther fact that the planes at the ends of the unequal extension are commonly in threes or sixes or some multiple of three ; or, as previously stated, the vertical axis (the axis of unequal extension) is coincident with an axis of hexagonal or trigonal symmetry. See Figs. 36-40, 45-50, 54, 55, 138-141, 202-234, and 241-324. PRINCIPAL FORMS 0F THE HEXAGONAL SYSTEM As a matter of convenience there is given below a summary of the principal forms of this system, or those which are described more fully later in the text. I. Holohedral Forms : 1. Basal Pinacoid. 2. Primary Hexagonal Prism. 3. Secondary Hexagonal Prism. 4. Dihexagonal Prism. 5. Primary Hexagonal Pyramid. 6. Secondary Hexagonal Pyramid. 7. Dihexagonal Pyramid. THE HEXAGONAL SYSTEM. II. Hemihedral Forms: A. Rhombohedral Group : 1. Primary Rhombohedron : a. Positive. b. Negative. 2, Hexagonal Scalenohedron : a. Positive. b. Negative. B. Pyramidal Group : 1. Tertiary Hexagonal Prism : a. Positive or Right-handed. b. Negative or Left-handed. 2. Tertiary Hexagonal Pyramid : a. Positive or Right-handed. b. Negative or Left-handed. C. Trapezohedral Group : 1. Hexagonal Trapezohedron : a. Positive or Right-handed. b. Negative or Left-handed. D. Trigonal Group : 1. Ditrigonal Pyramid: a. Positive. b. Negative. III. Tetartohedral Forms : A. Rhombohedral Group : 1. Secondary Rhombohedron : a. Positive : 77 78 NOTES ON CRYSTALLOGRAPHY. u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 2. Tertiary Rhombohedron : a. Positive : u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. B. Trapezohedral Group : 1. Secondary Trigonal Prism : a. Positive or Right-handed. b. Negative or Left-handed. 2. Ditrigonal Prism : a. Positive or Right-handed. b. Negative or Left-handed. 3. Secondary Trigonal Pyramid : a. Positive : u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 4. Trigonal Trapezohedron : THE HEXAGONAL SYSTEM. 79 a. Positive : u. Right-handed. w. .Left-handed. b. Negative : x. Right-handed. z. Left-handed. 0. Trigonal Group : 1. Primary Trigonal Prism : a. Positive. b. Negative. 2. Tertiary Trigonal Prism : a. Positive: u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 3. Primary Trigonal Pyramid : a. Positive. b. Negative. 4. Tertiary Trigonal Pyramid : a. Positive : u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 80 NOTES ON CRYSTALLOGRAPHY. IV. Hemimorphic Forms : 1. lodyrite Type. 2. Nephelite Type. 3. Tourmaline Type. 4. Sodium-Periodate Type. I. HOLOHEDRAL FORMS In one prominent respect the Hexagonal System differs from the preceding systems : in the Hexagonal System the holohedral forms are less common and important than are the hemihedral forms. Following as closely as practicable the nomenclature of the Tetragonal System, we find that the holohedral planes and their names are related to the axes as follows : 1. If the plane is parallel to the lateral axes, it is a Pinacoid, commonly called a Basal Pinacoid or a Basal Plane. Its symbol is P or 0001. There can be but two such planes on a crystal, the same as in the Tet- ragonal System. See P or 0001, Figs. 37-39, 205- 207, 215, 216, 220, 221, 242, 246-248, 263, 269, 272, 275, 289, and 315-323. 2. A plane parallel to the vertical axis and to one of the lateral axes, and cutting the other two lateral axes at equal distances from the centre of the crystal, is known as a plane belonging to a Primary Hexag- onal Prism or a Hexagonal Prism of the First Order. In this form the angles of the lateral edges are all THE HEXAGONAL SYSTEM. 81 equal. See oo P or 1010, Figs. 36-38, 40, 49, 202, 205, 212-214, 217, 219, 254, 255, 283, 298, 302-304, 307- 319, and 321-323. If a plane is parallel to the verti- cal axis, cuts one lateral axis at some unit of distance, and intersects the other two lateral axes at twice that unit of distance, it is said to be a plane belonging to a Secondary Hexagonal Prism or a Hexagonal Prism of the Second Order. As in the Primary Prism, the angles of the lateral edges are all equal. See oo P 2 or 1120, Figs. 46, 50, 206, 212, 215, 216, 220, 278- 280, 299, 318-320, 322, and 323. If the plane is parallel to the vertical axis, but cuts all three lateral axes at unequal distances, then the plane is said to belong to a Dihexagonal Prism. In this form the alternate angles of the lateral edges are unequal. See Figs. 207, 219, 242, 246, and 257. 3. If a plane cuts the vertical axis, is parallel to one lateral axis, and intersects the other two at equal dis- tances, the plane belongs to a Primary Hexagonal Pyramid or a Hexagonal Pyramid of the First Order. In this form the lateral edges are straight and equal, while the edges running to the apices form equal angles. See htihl, 1011, raP, and P, Figs. 36-39, 47, 202, 203, 212-214, 217-219, 254-266, 315, 316, 318, 319, and 321-323. If the plane cuts the vertical axis and intersects one lateral axis at a chosen unit of dis- tance, and the other two lateral axes at twice that unit 6 82 NOTES ON CRYSTALLOGRAPHY. of distance, it is a plane belonging to a Secondary Hexagonal Pyramid or a Hexagonal Pyramid of the Second Order. The edges and angles are the same as in the Primary Pyramid. See P2, 2P2, raP2, hhZhl, and 1122, Figs. 37, 40, 204, 209, 212, 243, 249, 255, 258, 261, 267, 276, 306, 308, 317, 319, and 321- 323. If the plane cuts the vertical axis and intersects all the lateral axes at unequal distances, it belongs to a Dihexagonal Pyramid. The lateral edges are hori- zontal and equal, but the alternate angles formed by the edges running to the apices are unequal. See htel, mPn, 2133, and 3Pf, Figs. 40, 208, 219, 229, 234, 241, 259, 262, 266, and 321. 4. The above statements apply to the holohedral forms. In case the plane is found to belong to a partial form, then the special name of the partial form having the same parameters should be used. The Primary Hexagonal Prism and Pyramid pos- sess cross-sections as shown in Fig. 202, which indi- cates the relation of the lateral axes to the planes. When the Secondary Hexagonal Prism or Pyramid is in a simple form, its appearance is identical with that of the Primary Hexagonal Prism or Pyramid. We may call these simple forms either Primary or Secondary, as we prefer, although it is customary always to call the simple forms Primary, as in the case of the Tetragonal System. See Figs. 36-40, 202- THE HEXAGONAL SYSTEM. 83 206, 212, 218, 243, 249, 254, 264, 268, 315-318, and 323. When the forms are compound, then the position of the axes of the dominant form determines whether the subordinate forms are Primary or Secondary. See Figs. 36-40, 254-267, and 308-323. As in the Tetragonal System, we can have as many Primary and Secondary Pyramids as we can have dif- ferent points on the vertical axis. That is, we can have, theoretically, an indefinite number ; practically we find but few on any crystal. See Figs. 36-40, 254-267, and 308-323. A student naturally desires to know why, in the case of the Secondary Prisms and Pyramids, we state that the planes cut two lateral axes at twice the unit of distance at which it cuts the other one. The reason is shown by a simple trigonometric opera- tion. See Fig. 209. From Geometry we know that the side of a regular hexagon inscribed in a circle is equal to the radius of that circle. This makes the side (d) of the hexagon and the two radii (b and g) equal. Since, then, the triangle formed by the sides b, d, and s is an equilateral one, it follows according to Geometry that the angles are all equal. The sides b and d of the triangle are the semi-axes in a section of a primary hexagonal prism or pyramid. See Fig. 202. There- fore the angle b p d is an angle of 60, and hence the 84 NOTES ON CRYSTALLOGRAPHY. other two angles of the triangle are angles of 60. From Trigonometry we learn that u r is the tangent of the angle b p d or 60. Trigonometry also teaches us that Tan. 60 = 1/3. From Geometry we know that (pr) 2 = b 2 + (ur) 2 . Now b is the shorter axis or the smaller parameter of the secondary prism or pyramid ; therefore, in Crystallography it is unity or 1 ; while u r is the tangent of 60 or 1/3. Hence by substituting these numbers our equation reads : (pr) 2 = 1 2 -f (1/3) 2 , or pr = 1/1 + 3 =1/4 = 2. Now the 2 thus obtained is one of the longer parameters of the secondary prism or pyramid. From inspection of Fig. 209 it can be seen that both the longer parameters are the same ; hence it follows that in the Weiss notation the para- meters of a secondary prism would be 2a : a : 2a : oo c, and those of a secondary pyramid would be 2a : a : 2a : me. The holohedral forms possess six vertical planes of symmetry : three are coincident with the vertical axis and the three lateral axes ; the other three coin- cide with the vertical axis, but bisect the angles between the lateral axes. Further, there is one hori- zontal plane of symmetry which bisects the vertical axis and lies in the plane of the lateral axes. Again, the holohedral forms have six horizontal axes of binary symmetry : three that bisect the angles between the lateral axes, and three that are coincident THE HEXAGONAL SYSTEM. 85 with those crystal axes. These forms have also a vertical axis of hexagonal symmetry which is coinci- dent with the vertical crystal axis, as well as a centre of symmetry. II. HEMIHEDRAL FORMS A. Rhombohedral Group. The distinctive forms in this group are two : 1. The Rhombohedron. 2. The Scalenohedron. 1. The Rhombohedron as a hemihedral form can be considered to be produced by the suppression of the alternate upper and lower planes of the primary hex- agonal pyramid and by the extension of the other al- ternate planes until they meet one another so as to produce a complete form. See Figs. 218 and 233. In Fig. 218, if the shaded planes are the ones considered suppressed, the rhombohedron produced by the exten- sion of the non-shaded planes until they meet is called a Positive Rhombohedron. See Fig. 139. A rhombohedron is called Positive when one of its three upper rhombs stands face to face with the ob- server. When the shaded parts of the primary hexagonal pyramid (Fig. 218) are the parts carried out until they meet, and the non-shaded parts are the parts obliter- ated, then the rhombohedron produced is known as a Negative Rhombohedron. See Fig. 138. 86 NOTES ON CRYSTALLOGRAPHY. A rhombohedron is called Negative when one of the three upper edges is turned directly towards the ob- server ; or in other words, when this edge lies in the plane of symmetry bisecting the observer. Besides the six equal and similar rhombs that bound the rhombohedron, it possesses two kinds of edges and two kinds of solid angles. There are six similar Terminal Edges, three above and three below, which are marked in Figs. 138 and 139 by the letter A. The junction of each set of three terminal edges marks each end of the vertical axis. Again, there are six equal and similar Lateral Edges, which run zigzag about the crystal and which are designated by the letter B, in the same figures. At each end of the vertical axis there is a solid angle formed by three equal plane angles. These two solid angles are designated on the figures by the letter C. Further, the rhombohedrons have six lateral solid angles, designated by the letter D. While these lateral angles are similar, they are not formed by the inter- section of equal plane angles, but by either two obtuse angles and one acute angle, or by one obtuse angle and two acute angles. The angles measured over the lateral edges are all alike, but are different from the angles measured over the terminal edges. If the angle obtained by measuring over a terminal edge is added to the angle obtained by measuring over a lateral edge, THE HEXAGONAL SYSTEM. 87 the sum of the two is 180 ; or one is as much greater than a right angle as the other is less. Hence it is customary to place the rhombohedrons in two sections, Acute and Obtuse. An Acute Rhombohedron is one whose equal angles measured over the terminal edges are each less than 90. See Fig. 222. An Obtuse Rhombohedron is one whose equal angles measured over the terminal edges are each greater than 90. See Fig. 223. It often happens that, upon a crystal, several different rhombohedrons occur, which have the same intercepts upon the lateral axes, but have different intercepts upon the vertical axis. In such a case one is selected as the Principal or Fundamental Rhombo- hedron, while the others are considered as Subordinate Rhombohedrons. See Figs. 45, 224-228, 270, 271, 275-277, 280, and 307-314. Having selected the principal rhombohedron, we find that all rhombohedrons which have the same lateral parameters, but which have larger intercepts on the vertical axis, are acute rhombohedrons, but that if they have smaller intercepts on the vertical axis, they are obtuse rhombohedrons. See Figs. 224-227, 275-277, 280, and 286. It is found that these rhombohedrons have this rela- tion to one another : A positive rhombohedron will 88 NOTES ON CRYSTALLOGRAPHY. truncate the terminal edges of the negative rhombo- hedron that has twice its parameter on the vertical axis. Again, a negative rhombohedron will truncate the terminal edges of the positive rhombohedron that has twice its parameter on'the vertical axis. See Figs. 45, 225, and 228. The vertical axis, as before stated, joins the trihedral solid angles, while the three lateral axes join the cen- tres of the opposite lateral zigzag edges. The rhombohedrons thus far described are often designated as Primary Rhombohedrons or as Rhombo- hedrons of the First Order. 2. The Hexagonal Scalenohedron as a hemihedral form of the Hexagonal System is regarded as being formed by the suppression of alternate pairs of adja- cent planes above and alternate pairs of adjacent planes below ; and by the extension of the remaining pairs of planes of the dihexagonal pyramid until they meet and form a complete figure. This is illustrated in Fig. 229, in which the extended faces are shaded. See also Fig. 232, in which we have the scalenohedral faces extended to complete the form. The pyramidal faces used are marked -J-, and the suppressed faces marked . The result of extending the shaded faces in Fig. 229 is to produce a form bounded by twelve sim- ilar Scalene triangles ; hence its name. See Fig. 140. If we also extend the non-shaded pairs of planes THE HEXAGONAL SYSTEM. 89 and suppress the others, we obtain a similar form as shown in Fig. 141. The first form is called Positive, and the second Negative. The Hexagonal Scalenohedron is called Hexagonal to distinguish it from the Tetragonal Scalenohedron ; but as the latter is so rare and is never found except in combination, it is customary to speak of the hexa- gonal form as the Scalenohedron, and when mentioning the tetragonal form, to designate it always as the Tetragonal Scalenohedron. See Figs. 196 and 197. The Hexagonal Scalenohedron has six lateral edges above and six lateral edges below ; and their terminal junctions mark the two ends of the vertical axis. The angles measured over the lateral edges are of two kinds alternately acute and obtuse. The acute angles above are over the obtuse angles below ; and the ob- tuse angles above are over the acute angles below. See Figs. 140, 141, 230-232, 244, 245, 252, 253, and 287- 305. The Scalenohedron has six equal lateral edges that zigzag about the crystal ; while the saw teeth produced have equal sides, and are bisected by the lateral edges forming the obtuse angles. See Figs. 140, 141, 232, 244, 245, 252, and 253. The selection of the Positive and Negative forms is an arbitrary matter, although much depends upon the other forms with which they are combined. 90 NOTES ON CRYSTALLOGRAPHY. It is customary to consider a scalenohedron positive when it is so placed that the terminal edge next the observer is obtuse, and when the saw tooth, bisected by the terminal edge, has its point downwards. See Figs. 140 and 253. When the terminal edge next to the observer is acute and the point of the saw tooth is turned upwards, the scalenohedron is negative. See Figs. 141 and 252. It can be seen that the zigzag edges of the rhombo- hedron correspond to the zigzag edges of the scaleno- hedron ; therefore, a rhombohedron can be inscribed in any scalenohedron which has a longer vertical axis than has the rhombohedron. The rhombohedron thus inscribed is known as the Inscribed Rhombo- hedron or the Rhombohedron of the Middle Edges. See Fig. 231. The vertical axis of the scalenohedron is the pro- longed vertical axis of the inscribed rhombohedron. Hence there may be an indefinite number of scaleno- hedrons for every inscribed rhombohedron ; but in practice, it is found that the vertical semi-axis of the scalenohedron is always some simple multiple of the inscribed rhombohedron. The Rhombohedral Group has three vertical planes of symmetry, which bisect the angles made by the lateral axes and coincide with the vertical axis. The group has also three horizontal axes of binary sym- THE HEXAGONAL SYSTEM. 91 metry, which are coincident with the lateral axes. It has also one vertical axis of trigonal symmetry, which coincides with the vertical crystal axis ; and a centre of symmetry. B. The Pyramidal Group : 1. Tertiary Hexagonal Prism : a. Positive or Right-handed. b. Negative or Left-handed. 2. Tertiary Hexagonal Pyramid : a. Positive or Right-handed. b. Negative or Left-handed. 1. The Tertiary Hexagonal Prism or Prism of the Third Order, taken as a hemihedral form, can be con- sidered to be produced by the suppression of each alter- nate plane of the dihexagonal prism and by the ex- tension of the sides of the remaining alternate planes until they meet. See Figs. 213, 219, and 242. The form thus produced is identical in appearance with the Primary and Secondary Hexagonal Prisms, and it dif- fers only in the positions of the lateral axes. A hex- agonal prism will be considered a Tertiary Hexagonal Prism, only when its relation to the other forms and to the selected lateral axes shows that it cuts all three lateral axes unequally. This fact can readily be seen when a Tertiary Hexagonal Prism is united as a sub- ordinate form with a dominant Primary or Secondary Prism, especially if there are a number of other sub- ordinate forms. 92 NOTES ON CRYSTALLOGRAPHY. By alternating the planes that we consider sup- pressed and those that we regard as extended, two prisms can be obtained which are called Positive or Right-handed and Negative or Left-handed. In the above cases, when the positive or negative sign is employed, the sign for the right-handed or left- handed forms is omitted. So, when the r or I is used, the positive or negative sign is dropped. This is the custom in all cases where the positive or negative, or right-handed or left-handed, symbols are employed. -. In giving the signs on the figures in this book, es- pecially when they are first used, both the positive and the right-handed, or the negative and the left-handed signs are given in order to impress upon the student the idea that either sign can be used with the Naumaim symbols. 2. The Tertiary Hexagonal Pyramid can be re- garded as formed from the di hexagonal pyramid by the extension of an alternate plane above and its ad- jacent plane immediately below, (these planes stand base to base), and by the suppression of like alternate pairs of planes. See Fig. 234. The two planes in each case would, if made parallel to the vertical axis, unite into one plane coincident with a prism plane. Two sets of tertiary pyramids can thus be formed : Positive or Right-handed and Negative or Left-handed. THE HEXAGONAL SYSTEM. 93 The relation of the Tertiary Pyramid to the Primary and the Secondary Pyramids is the same as previously stated for the three prisms. It follows from what has been previously said that neither the Tertiary Prism nor the Tertiary Pyramid can occur except in combination with other hexagonal forms. The Tertiary Hexagonal Prisms and Pyramids have an axis of hexagonal symmetry that is coincident with the vertical axis. They a'lso possess a plane of sym- metry that is coincident with the plane of the lateral axes ; and a centre of symmetry. C. Trapezohedral Group : 1. Hexagonal Trapezohedron : a. Positive or Right-handed. b. Negative or Left-handed. The Hexagonal Trapezohedral Group does not oc- cur among minerals, but is met with in artificial crys- tals and in crystal models. The forms of this group can be considered to be produced by the suppression of the alternate upper and lower planes of the dihexagonal pyramid and by the extension of the other alternate planes until they meet. See Fig. 241. The form produced is a twelve- faced figure with unequal zigzag edges. By extend- ing the planes previously suppressed and by obliterat- ing the planes previously extended, another form is 04 NOTES ON CRYSTALLOGRAPHY. produced, which is similar to the preceding form, just as a man's left hand is similar to his right hand. The first form is called the Positive or Right-handed Hexagonal Trapezohedron (see Fig. 210); and the sec- ond form is named the Negative or Left-handed- Hex- agonal Trapezohedron. See Fig. 211. The Hexagonal Trapezohedrons have no plane of symmetry, but they have six horizontal axes of binary symmetry, (see p. 84), while the vertical crystal axis is an axis of hexagonal symmetry. The Hexagonal Trapezohedron can be distinguished from other forms by the fact that its planes are in sixes ; by the fact that all the angles formed by the edges which meet at the apices are equal; and by the further fact that the saw-teeth of its zigzag lateral edges have sides of unequal length, while in the Hex- agonal Scalenohedron the zigzag edges have the sides of the saw-teeth equal. Further, because the alternate zigzag edges in the Hexagonal Trapezohedron are un- equal, it happens that the edge angles below are not directly beneath the planes above, as they are in the Hexagonal Scalenohedron, but are thrown to one side or the other. Again, the faces of the Hexagonal Trapezohedron are Trapeziums, while those of the Hex- agonal Scalenohedron are Scalene Triangles. See Figs. 140, 141, 210, 211, 252, and 253. The right-handed Hexagonal Trapezohedrons can THE HEXAGONAL SYSTEM. 95 be distinguished from the left-handed ones in the following manner : place the form so that one of the edges running to the apex will be directly in front of the observer and coincident with the plane of sym- metry passing between his eyes. If the shorter side of the zigzag edge immediately in front inclines to the right-hand, the trapezohedron is right-handed ; but if the shorter side is inclined towards the left-hand, the trapezohedron is left-handed. See Figs. 210 and 211. D. Trigonal Group : 1. Ditrigonal Pyramid : a. Positive. b. Negative. Of the Trigonal Group the only form to which at- tention is called here is the Ditrigonal Pyramid, since the other Trigonal forms are taken up elsewhere. This form as a hemihedral form is considered to be produced by suppressing the alternate pairs of planes above and below of the dihexagonal pyramid, the pairs of planes standing base to base ; and by extending the corresponding pairs of planes above and below, until the form is completed. See Fig. 326, in which the shaded pairs of planes denote the faces suppressed, while the non-shaded ones are the pairs of planes extended. Fig. 325 shows the resulting form. By varying the planes to be suppressed both Positive and Negative forms are produced. 96 NOTES ON CRYSTALLOGRAPHY. These forms possess four planes of symmetry : one is horizontal and coincident with the plane of the lat- eral axes; the other three are vertical and bisect the angles between the lateral axes, as also do the three axes of binary symmetry. The vertical axis is an axis of trigonal symmetry. No minerals have been found in the forms of this group. III. TETARTOHEDRAL FORMS A, Rhombohedral Group : 1. Secondary Khombohedron : a. Positive : u. Right-handed, w. Left-handed. b. Negative : x. Eight-handed. z. Left-handed. 2. Tertiary Rhombohedron : a. Positive : u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 1. The Secondary Rhombohedron or Rhombohedron of the Second Order can be regarded as obtained by the suppression of the alternate upper and lower faces of the secondary pyramid and the extension of the others. See Fig. 243. The Secondary Rhombohedron THE HEXAGONAL SYSTEM. 97 differs in no way from the Primary Rhombohedron except in the position of the axes. Two of its lateral indices are equal, while the third is twice as great as the others. The Secondary Rhombohedron never oc- curs alone, but is always found in combination with other forms, the positions of whose axes will indicate the nature of the associated rhombohedrons. By alternation of the planes to be extended and those to be suppressed two Secondary Rhombohedrons are obtained : Positive and Negative, either of which may be Right-handed or Left-handed. 2. The Tertiary Rhombohedron or Rhombohedron of the Third Order can be considered to be formed by the suppression of the alternate upper and lower planes of the hexagonal scalenohedron, and by the ex- tension of the other alternate planes until they make a completed form. Each scalenohedron will produce two forms, and since there are two hexagonal scaleno- hedrons, we shall have four Tertiary Rhombohedrons. See Figs. 244 and 245. The Tertiary Rhombohedron differs in no respect from the Primary or the Secondary Rhombohedron except in the position of its axes ; but as it is always found in combination with other forms, the position of the axes of the latter will tell whether a given rhom- bohedral plane belongs to a Primary, Secondary, or Tertiary Rhombohedron. Of the lateral indices of the 7 98 NOTES ON CRYSTALLOGRAPHY. Tertiary Rhombohedron, one is unity, one twice, and one three times as great. On account of the difference in the position of their axes the Secondary and the Tertiary Rhombohedrons have a lower order of symmetry than has the Primary Rhombohedron. The first two have no planes of symmetry, but do have a centre of symmetry and an axis of trigonal symmetry that is coincident with the vertical axis of the crystal. B. Trapezohedral Group : 1. Secondary Trigonal Prism : a. Positive or Right-handed. b. Negative or Left-handed. 2. Ditrigonal Prism : a. Positive or Right-handed. b. Negative or Left-handed. 3. Secondary Trigonal Pyramid : a. Positive : u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 4. Trigonal Trapezohedron : a. Positive : u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. THE HEXAGONAL SYSTEM. 99 1. The Secondary Trigonal Prism or Trigonal Prism of the Second Order can be considered to have been produced by the suppression of each alternate plane of the secondary hexagonal prism and the ex- tension of the other three faces until they meet. Figure 220, by its shading, shows the planes that are supposed to be suppressed on this form, while the non-shaded planes are those supposed to be extended. Figure 221 is a representation of the form produced. By imagining the preceding shaded planes of the secondary hexagonal prism extended and the non- shaded ones suppressed, another Secondary Trigonal Prism will be produced. One prism can then be called the Positive or Right-handed and the other the Neg- ative or Left-handed. 2. The Ditrigonal Prism can be looked upon as pro- duced by the extension of alternate pairs of planes of the dihexagonal prism and by the suppression of the other alternate pairs of planes. As before, by inter- changing the planes to be extended, two forms are pro- duced : The Positive or Right-handed and the Negative or Left-handed. See Figs. 219, 230, and 246-248. 3. The Secondary Trigonal Pyramid is regarded as formed from the secondary hexagonal pyramid by ex- tending the three alternate planes above and also the three alternate planes below, whose bases are coinci- dent with the bases of the extended planes above. The 100 NOTES ON CRYSTALLOGRAPHY. other alternate planes are suppressed. See Fig. 249, in which the shaded planes are the ones that are here considered suppressed. By extending the planes previously considered sup- pressed and by obliterating the others, another com- panion form is produced, giving us Positive or Right- handed and Negative or Left-handed Trigonal Pyra- mids. See Figs. 250 and 251. 4. The Trigonal Trapezohedron can be looked upon as being formed by the extension, in the scalenohe- dron, of every other plane above and of the planes immediately below (i. e., the alternate upper and lower planes whose bases join), and by the suppression of the other six planes. See Figs. 252 and 253. By alternating the planes extended and those sup- pressed, two forms can be produced for the positive and two for the negative scalenohedron, or four in all. These are designated as Positive Right- or Left-handed, and Negative Right- or Left-handed. See Figs. 54 and 55. The Trigonal Trapezohedrons are always found in combination with other forms, and never occur isolated in nature. See 'J, Figs. 308-312. The group possesses three axes of binary symmetry coin- cident with the lateral axes, and an axis of trigonal symmetry coincident with the vertical axis, but it has neither plane nor centre of symmetry. THE HEXAGONAL SYSTEM.' 101 C. Trigonal Group : 1. Primary Trigonal Prism : a. Positive. s b. Negative. 2. Tertiary Trigonal Prism : a. Positive : u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 3. Primary Trigonal Pyramid : a. Positive. b. Negative. 4. Tertiary Trigonal Pyramid : a. Positive: u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. z. Left-handed. 1. The Primary Trigonal Prism can be considered to be produced by proceeding with the primary hexa- gonal prism as was done with the secondary hexagonal prism to form the secondary trigonal prism. See page 99. Two forms result Positive and Negative. 2. The Tertiary Trigonal Prism can be considered to be formed by extending every fourth plane of the dihexagonal prism until they meet, and by suppressing the other three-fourths. By varying the planes ex- tended, four forms can be produced : Positive Right- 102 NWES ON CRYSTALLOGRAPHY. and Left-handed, and Negative Right- and Left- handed. 3. The Primary Trigonal Pyramid as a tetartohe- dral form is considered to be produced from the primary hexagonal pyramid in the same way in which the secondary trigonal pyramid was made. See page 99. Two forms result, Positive and Negative-. 4. The Tertiary Trigonal Pyramid as a tetartohe- dral form can be regarded as produced by extending every fourth upper and lower plane (arranged base to base) of the dihexagonal pyramid and suppressing the other three-fourths. By varying the planes to be extended, four forms result : Positive Right- and Left- handed, and Negative Right- and Left-handed. These trigonal forms have one horizontal plane of symmetry coincident with the plane of the lateral axes, and an axis of trigonal symmetry coincident with the vertical axis, but are destitute of any centre of symmetry. HEMIMORPHIC FORMS. 1. The lodyrite Type is shown in Figs. 214-216. Fig. 214 is terminated at one end by a hexagonal pyramid (1011), and has .upon the other end a hexa- gonal prism (lOlO), and a basal pinacoid (OOOl). Figures 215 and 216 have one end terminated by a basal pinacoid (0001) and a pyramid (4041), and the other end terminated by pyramids (see Fig. 215, 4045 THE HEXAGONAL SYSTEM. 103 and 9-9O8-20),* or by a pyramid (see Fig. 216, 4045). A prism (1120) lies between the terminal pyramids. The lodyrite Type has six vertical planes of sym- metry, and a vertical axis of hexagonal symmetry coincident with the vertical axis. 2. The Nephelite Type may be distinguished by the fact that the terminations at opposite ends of the verti- cal axis are composed of different hexagonal pyramids, or by the fact that the crystal is formed by half of a hexagonal pyramid resting on its basal pinacoid. Figure 217 illustrates well one of the first set of forms. This type has an axis of hexagonal symmetry. 3. The Tourmaline Type is most commonly repre- sented by prisms, terminated at each end by diverse rhombohedrons. These forms have three vertical planes of symmetry that bisect the lateral axial angles, and an axis of trigonal symmetry that is coincident with the vertical crystal axis. See Fig. 324. 4. The Sodium Periodate Type is formed by taking the upper or lower part of a trigonal pyramid and terminating it by a basal pinacoid, as shown by Fig. *When, as occasionally happens, the Miller-Bravais indices are so large that a single index contains two figures, it is customary to avoid mistakes in the indices by separating each index by a point at the tipper part of the line. See above and 11-2-T3-3 and 14'14-28'3. Others use the points below, e. g., 10.5.6, 9.8.17.1, and 7.4.11.6. Others em- ploy commas, e. g., 6,4,10,4; 16.0,16,1; and 9,9,18,20. Still others omit all points of separation. 104 NOTES ON CRYSTALLOGRAPHY. 327. These forms have one vertical axis of trigonal symmetry coincident with the vertical crystallographic axis. COMPOUND FORMS. The compound forms of the Hexagonal system are numerous and varied. Of these the combinations of the hemihedral and tetartohedral forms are more common and important than are the compound holo- hedral forms. The student should take especial care in deciding which is the principal form and in determining the positions of its axes, since upon them depends the ease or difficulty in naming the subordinate forms. References to the figures of hexagonal crystals given in this book will show that the majority of them are compound, and that some are more or less compli- cated. See Figs. 36-40, 45-50, 54, 55, 138-141, 202- 234, and 241-327. RULES FOR NAMING HEXAGONAL PLANES. I. A plane parallel to all the lateral axes is a Basal Pinacoid or a Basal Plane. II. A plane which is parallel to the vertical axis and one of the lateral axes, but which cuts the other two lateral axes equally, is a plane belonging to a Primary Prism: a. If the number of similar planes is six, each plane belongs to a Primary Hexagonal Prism or Hexagonal Prism of the First Order. THE HEXAGONAL SYSTEM. 105 b. If the number of similar planes is three, each plane belongs to a Primary Trigonal Prism or Trigonal Prism of the First Order. III. If a plane is parallel to the vertical axis and cuts one lateral axis at some distance, and the other two lateral axes at twice that distance, the plane be- longs to a Secondary Prism : a. If the number of similar planes is six, each plane belongs to a Secondary Hexagonal Prism or Hexagonal Prism of the Second Order. b. If the number of similar planes is three, each plane belongs to a Secondary Trigonal Prism or Tri- gonal Prism of the Second Order. IV. If the plane is parallel to the vertical axis and intersects all three lateral axes at unequal distances, the plane belongs to a Dihexagonal Prism or to one of its partial forms : a. If the number of similar planes is twelve, then each plane belongs to a Dihexagonal Prism. b. If the number of similar planes is six, each plane belongs to a Tertiary Hexagonal Prism or Hexagonal Prism of the Third Order, provided its lateral angles are equal ; but if the lateral angles are alternately unequal,* then each plane belongs to a Ditrigonal Prism. * In this case three of the alternate angles are equal to one another, while the three other alternate angles are unequal to the first three, but they are all equal to one another. 106 NOTES ON CRYSTALLOGRAPHY. c. If the number of similar planes is three, then each plane belongs to a Tertiary Trigonal Prism or Trigonal Prism of the Third Order. V. If a plane intersects the vertical axis, is parallel to one lateral axis, and cuts the other two lateral axes at, equal distances, it belongs to a Primary Pyramid or to some one of its partial forms : a. If the number of similar planes at each end is six, then each plane belongs to a Primary Hexagonal Pyramid or Hexagonal Pyramid of the First Order. b. When the number of similar planes at each end is three, and the figure is placed with the vertical axis perpendicular, if the faces are rhombohedral and the lateral edges inclined to the horizon, then each plane belongs to a Rhombohedron, but if the faces are trian- gular and the lateral edges horizontal, then each plane belongs to a Primary Trigonal Pyramid or Trigonal Pyramid of the First Order. VI. If a plane cuts the vertical axis and intersects one lateral axis at a unit of distance, cutting the other two at twice that distance, it is a plane belonging to a Secondary Pyramid or to some of its partial forms : a. If the number of similar planes at each end is six, then each plane belongs to a Secondary Hexagonal Pyramid or Hexagonal Pyramid of the Second Order. b. When the number of similar planes at each end is three, and the figure is placed with the vertical axis THE HEXAGONAL SYSTEM. 107 perpendicular, if the faces are rhombohedral and the lateral edges inclined to the horizon, then each plane belongs to a Secondary Rhombohedron, but if the faces are triangular and the lateral edges horizontal, then each plane belongs to a Secondary Trigonal Pyramid or Trigonal Pyramid of the Second Order. VII. If a plane cuts the vertical axis and intersects all the lateral axes at unequal distances, the plane be- longs to a Dihexagonal Pyramid or to some one of its partial forms : a. If the number of similar planes at each end of the crystal is twelve, then each plane belongs to a Dihexag- onal Pyramid. b. If the number of similar planes at each end of the crystal is six, then each plane belongs to one of the four following hemihedral or half forms : (1) If the alternate terminal angles are unequal (three and three) and the lateral edges are zigzag and equal, then each plane belongs to a Scalenohedron ; (2) if the terminal angles are all equal and the edges horizontal, then each plane belongs to the Tertiary Hexagonal Pyramid; (3) if the terminal angles are equal and the lateral edges zigzag and unequal, each plane belongs to a Hexagonal Trapezohedron ; (4) if the alternate termi- nal angles are unequal (three and three) and the lateral edges horizontal, each plane belongs to the Ditrigonal Pyramid. 108 NOTES ON CRYSTALLOGRAPHY. c. If the number of similar planes at each end of the crystal is three, then each plane may belong to one of the three following tetartohedral or quarter forms : (1) If the faces are rhombohedral and the edges oblique to the horizontal plane, each face belongs to a Tertiary Rhombohedron or Rhombohedron of the Third Order ; (2) if the faces are trapeziums with unequal lateral zigzag edges, each face belongs to a Trigonal Trapezo- hedron ; (3) if the terminal angles are all equal, and if the faces, triangles, and the lateral edges are hori- zontal, then each face belongs to the Tertiary Trigonal Pyramid or Trigonal Pyramid of the Third Order.* VIII. If the opposite ends of the crystal are unlike, the forms are Hemimorphic a. If the form is composed of a hemi-dihexagonal pyramid and a basal plane, or of hemi-dihexagonal and primary or secondary pyramids and prisms with a basal plane, then the form belongs to the lodyrite Type. * The statements that the lateral edges are oblique or horizontal, and that the planes are triangles, etc., refer to a complete single form. In the case of compound forms the various planes so modify one another that the positions of the lateral edges and the shapes of the planes are much varied. In such cases the student will need to refer to the text for the relative positions of the planes in each case, or to reconstruct the complete form for each set of similar planes when handling com- plicated compound forms, until he has had sufficiently extended prac- tice in this work to enable him to recognize readily the forms from the positions of their planes. THE HEXAGONAL SYSTEM. 109 b. If the form is composed of hexagonal pyramids and prisms with or without one or two basal planes, then the form belongs to the Nephelite Type. c. If the form consists of a hemi-hexagonal or ditri- gonal pyramid terminated by a basal plane, or of hexagonal prisms terminated by hemi-hexagonal pyramids and by basal planes, or of hexagonal, ditri- gonal, and trigonal prisms terminated by hemi-rhorn- bohedrons, and with or without hemi-hexagonal pyra- mids, the form belongs to the Tourmaline Type. d. If the form consists of a hemi-trigonal pyramid or pyramids with or without trigonal prisms, and terminated on the base by a pinacoid, the form belongs to the Sodium-Periodate Type.* READING DRAWINGS OF HEXAGONAL CRYSTALS. The four axes of the Hexagonal system render the crystallographic shorthand in that system more com- plicated than in the preceding systems. The lettering of the semi-axes is shown in Fig. 6 and noted on page 75. In the preceding systems the front semi-axis and the right semi-axis are considered as positive, while those semi-axes extending to the rear * To distinguish between these hemimorphic types is not easy, and the rules above given are far from accurate, especially in the case of the first three types. Frequent reference will have to be made to the text ; to the centres, axes and planes of symmetry ; to the positions of the crystallographic axes, and to the figures given in the plates. 110 NOTES ON CRYSTALLOGRAPHY. and to the left are considered negative. Further, the parameter or index of the semi-axis extending forwards or backwards is read first, and that belonging to the semi-axis extending to the right or left, as the case may be, is read secondly. In the Hexagonal system the method of reading the lateral semi-axes is changed. Commencing with the semi-axis in front and consider- ing that as positive, we call the next semi-axis to the right negative. Continuing to read the parameters or indices of the lateral semi-axes from the right around to the rear and to the left of the vertical axis, we desig- nate the third lateral semi-axis as positive, the fourth negative, the fifth positive, and the sixth negative; or the signs of the axes alternate as we read around the vertical axis either from right to left or left to right. In reading the parameters or indices, it is the ap- proved modern method to read first the parameter belonging to the lateral semi-axis in the front or in the rear ; secondly, that of the third lateral semi-axis to the right or the left, and thirdly, that of the second lateral semi-axis. As in the other systems, the vertical semi-axis is given last, and is called positive when above the lateral axes and negative when below them. It should be observed, then, that at least one of the lateral parameters or indices of any plane or form in the Hexagonal system is always negative (see page 75), while some of the others may be. In the Miller- THE HEXAGONAL SYSTEM. Ill Bravais notation the majority of crystallographers use i for the second lateral semi-axis, i. e., for the axis that lies to the right of the lateral semi-axis in the front. It should further be observed that in this notation the amount of the lateral negative integer or integers is exactly equal to the amount of the lateral positive in- teger or integers. As before, the hemihedral forms are distinguished, in the Weiss notation, by writing J before the symbols of the form or plane, or, in the Naumann notation, by writing 2 as the denominator of a fraction, whose numerator is the symbol of the corresponding holohe- dral form. In the same way the tetartohedral planes and forms are designated by writing J before the Weiss symbol, or, in the Naumann notation, by using 4 as the denominator and the symbol of the holohedral form as the numerator in each case. In the Miller-Bravais notation the hemihedral planes and forms are indicated by some Greek letter written before the indices, while those which are tetartohedral are designated by any two Greek letters placed before the symbols. Further, when the hemihedral, or selected tetartohedral forms can be easily known as such by the context or by the figure, the Greek letters are often omitted before the symbols. Most of these symbols are quite easily understood 112 NOTES ON CRYSTALLOGRAPHY. when they are compared with those of preceding systems as shown in the various tables. The symbols or crystallographic shorthand employed in the cases of the rhombohedrons and scalenohedrons in the Naumann system require special mention. Ac- cording to the method of derivation of the funda- mental primary rhombohedron (see page 85), its sym- p bol in the usual form would be-, but in the Naumann system this is usually abbreviated as R. In the cases of the subordinate primary rhombohedrons the usual symbol would be , but this is abbreviated as mR, in which the m may be J, &, f, f , 1, 7, i, 3, 4, -, 6, 7, and so on. The more obvious symbols for the scalenohedrons are - for the principal forms, and ^? for the subordinate forms, but these are commonly written as Rn and mRn in the Naumann system. Dana further abbreviates these as m n . Since the rhombohedrons and scalenohedrons are much more common than are the holohedral forms, it is a matter of convenience to dispense with the frac- tional symbols in the former. In the hemimorphic forms, since the opposite ends of the crystals are unlike, the letter o is employed to THE HEXAGONAL SYSTEM. 113 designate the forms that are over or upon the upper portion of the crystals, and the letter u is used to indi- cate those on the under or lower part of the crystal. The employment of the initial o for over and u for under conduces not only to convenience in the use of other texts but also to uniformity, since the German crystallographers employ the same letters : o for ober and u for unter. In the same way, crystallographers use r for right (rechts) or right-handed and I for left (links) or left- handed in connection with the symbols of right-handed or left-handed forms. 8 114 NOTES ON CRYSTALLOGRAPHY. "3 M llcr-Brav | 'i "2 r i* ,^ "^ IfCc || i'l ,^'2 53 h h I IN C f* c 1-1 e c CI * t* **A 1 1 1 1 .5 -'.5l- j *_ at O O 1 i i 'IS i2 ,2" 2 S ;2 -fS J i i i i & fe fc ^ U Se fe fe S5 Se S5 \ (5 r~^ i i i 1 2 \s *. i. A <** -N CO ^ <|Tt"|<* ^ "^ e ?|'^ ?|^ ? T* ? ^ ** ^. | | | | 1 1 1 d a 8 r^Hn^H 5- "-a t p,^ ^ y^^ es S 2 . Si S g| R C R K *s ^S ^S f ft, ^w^H ^ c* ^^U-R, *a, ^ s Is 8 ^ 8 i 8 8 8 8> 8 8 1 1 *. ^ ?* 1^,,^ |^ f^ s 1 w O O 8 8 8 8 8888 | T * If ? f T f Ts e e I 1 1 i S &< ^s e e 8 8 s s Sri* i ii e e e e e e S 8 e a e C R s: M r ^ sT % fXi ^CH ^ o, ^ft^L ^a^ Tt< 8 8 s s g 5 S S 1 1 ? ?~ ~* J* r-^ 8 8 ^ -^ 1 1 1 i 1 I | f f f f f f f T T f i S2, Al 8 8 ^ s e 8 e e ^ a, sx A 6 6 8 8 8 8 8 8 8 53 5= C'B 5 ii fc w ll THE HEXAGONAL SYSTEM. 117 1 * _*_ -A_ ii ? ^ - ^ % i i 1 1 3 ^ 1 1 !i > I** < a T T Si id * b b fc b b oj C n 1 t~ %H J 1"** * ?~ ? s 5,7 (. * K M fi O fiS ,; jz; PS ~* * "* * % o s I 1 fill O O s s 1 f ? T If 88 8 r . .. s Sii & a a a a a a t a" 8 8 s e 3388 8 8 s= s s s s s 1 ^ ^ H * 7 HM i 6 6 a S OS f^ f i 1 1 2 S & <~i 5 Is H g ss R O) P a K? B &~ B* H I 1 THE HEXAGONAL SYSTEM. 119 .2 1 c 1 i fc N fc fe |'| i | 1 i t I E2E'" |r i ii_ii i'-^- O S C> 2 c c gl Sl^ gl 5 2 Nuumann. C C 2 3 | (C "M SC C > 'HH THE HEXAGONAL SYSTEM. 121 DIRECTIONS FOR STUDYING HEXAGONAL CRYSTALS 1. Prove that the crystal or model is hexagonal. 2. Locate the axes so as to make the forms as few and simple as possible, and place the crystal with the vertical axis erect. 3. Determine whether the vertical axis is coincident with an axis of hexagonal or trigonal symmetry. This will separate the forms into two divisions : the Hexagonal and the Rhombohedral or Trigonal. a. The Hexagonal Division comprises the Holo- hedral Forms, the Pyramidal Group, the Hexagonal Trapezohedrons, and the lodyrite and Nephelite Types. b. The Trigonal Division comprises the Rhombo- hedral Group, the Ditrigonal Pyramids, the Tetarto- hedral Forms, and the Tourmaline and Sodium- Periodate Types. 4. Note the dominant and modifying forms in the order of their importance. 5. Select and name the planes belonging to each form. 6. Distinguish the holohedral, hernihedral, tetarto- hedral and hemimorphic forms, giving to each its appropriate name. 7. Locate the planes, the remaining axes, and the centers of symmetry. CHAPTER VII ISOMETRIC SYSTEM THIS system derives its name from the Greek Isos, " equally distributed," and Metron, " measure or pro- portion," because along its axes its measurements are equal and the holohedral forms are equally propor- tioned. In this s} T stem, then, the three axes are of equal length and the angles are all right angles, con- sequently there can be no dominant unequal direction or directions. See Fig. 5. NOMENCLATURE Since the axes are all equal, the semi-axes can each be represented by a; and since any one of them can be selected as a vertical semi-axis and the others as lateral semi-axes, the a is in many cases omitted, the parameters only being written. As in the other systems having three axes, a plane may intersect one, or two, or three axes ; and to locate the axes in any Isometric form they must be so placed that their directions will form right angles with one another and that their lengths will be equal. The nomenclature in this system is somewhat ex- (122) THE ISOMETRIC SYSTEM. 123 tensive and complicated, although not so difficult as is that of the Hexagonal System. DISTINGUISHING CHARACTERISTICS OF THE ISOMETRIC CRYSTALS The Isometric crystals are distinguished by the possession of three equal dimensions at right angles to one another, and by the further fact that these direc- tions are always, not only crystallographic axes, but also axes of symmetry. These axes of symmetry are either tetragonal or binary. In the Holohedral forms and in the Pentagonal Icosi tetrahedrons the crystal- lographic axes are axes of tetragonal symmetry; but in the Hemihedral and Tetartohedral forms the crys- tallographic axes are axes of binary symmetry. This equality of dimensions gives to all the Isometric forms, especially the holohedral ones, an appearance of having been inscribed in a sphere. See Figs. 12, 15, 17, 52, 53, 56-58 and 328-445. FORMS OF THE ISOMETRIC SYSTEM I. Holohedral Forms: 1. Hexahedron or Cube. 2. Dodecahedron or Rhombic Dodecahe- dron. 3. Tetrakis Hexahedron or Tetrahexahe- dron. 4. Octahedron. 124 NOTES ON CRYSTALLOGRAPHY. 5. Trigonal Triakis Octahedron, or Triakis Octahedron, or Pyramid Octahedron, or Trisoctahedron. 6. Tetragonal Triakis Octahedron, or Icositetrahedron, or Trapezohedron. 7. Hexakis Octahedron or Hexoctahedron. II. Hemihedral Forms : A. Oblique Hemihedral Forms : 1. Tetrahedron : a. Positive. b. Negative. 2. Tetragonal Triakis Tetrahedron, or Tet- ragonal Tristetrahedron, or Deltoid Dodecahedron, or Tristetrahedron : a. Positive. b. Negative. 3. Trigonal Triakis Tetrahedron, Triakis Tetrahedron, or Trigonal Tristetra- hedron, Pyramid Tetrahedron, or Trigon-Dodecahedron : a. Positive. b. Negative. 4. Hexakis Tetrahedron or Hextetrahe- dron : a. Positive. b. Negative. THE ISOMETRIC SYSTEM. 125 B. Parallel Hemihedral Forms : 1. Pentagonal Dodecahedron or Pyrito- hedron : a. Positive. b. Negative. 2. Dyakis Dodecahedron or Diploid : a. Positive. b. Negative. C. Gyroidal or Plagihedral Hemihedral Forms : 1. Pentagonal Icositetrahedron or Gyroid : a. Right r handed. b. Left-handed. III. Tetartohedral Forms : 1. Tetrahedral Petagonal Dodecahedron : a. Positive. u. Right-handed. w. Left-handed. b. Negative. x. Right-handed. z. Left-handed. I. HOLOHEDRAL FORMS Given three equal axes at right angles to one an- other, it is our first task to see how many complete forms can be produced by arranging all the planes we can in all possible positions about these axes. 1. Let the plane intersect one axis and be parallel 126 NOTES ON CRYSTALLOGRAPHY. to the other two, so that its symbol will be 1 : oo : oo . If we take our model of the Isometric axes (see Fig. 5) and place our glass plate or piece of cardboard upon it so that it will intersect one axis and be parallel to the other two, we find that there are just six positions in which the plane can be so put as to fulfil these re- quirements; one at each end of the semi-axes. If, then, planes be placed in these positions and be so cut that their edges will exactly join and make a complete form, we shall have a figure of six equal sides, which are all at right angles to one another, or a form that is called a Hexahedron (Greek, Hex and Hedra, which are defined on pages 18 and 33). We are all familiar with this form under its common nickname, the Cube. See Figs. 328, 336 and 387. 2. The next possible variation is when the planes cut two axes equally and are parallel to the third axis ; its symbol is 1 : 1 : oo. By placing the trial plate about the axes in all the different positions in which it will fulfil the necessary requirements, one can ascertain that there are just twelve different posi. tions in which the plane can be placed. These posi- tions are such that the plane can join the ends of two of the semi-axes and still be parallel to the third axis. If enough planes are placed in these positions and extended until they meet, a twelve-sided figure or Dodecahedron will be produced. This is sometimes THE ISOMETRIC SYSTEM. 127 called the Rhombic Dodecahedron, to distinguish it from the other Dodecahedrons. The name comes from the Greek, Dodeka, " twelve," and Hedra, see page 23. See Fig. 329. 3. The next variation in the position of our plane will be to have it cut two of the axes unequally and still remain parallel to the third axis ; its symbol is 1 : m : oo. By placing our plate in all the different positions in which it can be located about the Iso- metric axes and still fulfil the above requirements, we ascertain that there are twenty-four such positions. If we put these twenty-four planes about the axes so that each face will cut one axis at unity and the next at some greater distance, m, and will be parallel to the third axis, then we find that each Hexahedron or Cube face has been replaced by a pyramid formed by four triangles (6X4=24). From this combination we obtain the name Tetrakis Hexahedron, which is derived from the Greek Tetrakis, " four times," combined with Hexahedron, the deriva- tion of which has already been explained (see p. 126). The faces, then, are four triangles taken six times, or twenty-four triangles. See Fig. 330. 4. The next most simple variation is to place the plane so as to cut all three axes equally ; its symbol is 1 : 1 : 1. In this case it will be found that there are eight 128 NOTES ON CRYSTALLOGRAPHY. positions in which the plane can be located upon the axes in such a manner as to fulfil the requirements above given. The placing of eight planes so as to intersect all the axes equally, and their extension until they join and make a complete form, will give rise to the figure known as the Octahedron or Regular Octa- hedron, whose faces are composed of eight equilateral triangles, and whose name comes from the Greek, Okto, " eight," and Hedra, see page 23. See Figs. 12, 338, 339. 5. The next variation is to have the plane cut two axes equally, and the third axis at some greater dis- tance, ra. The symbol is 1 : 1 : m. By arranging our plate in as many positions as pos- sible about the axes, and still making it agree with the above variation, we shall find that for each octa- hedral face there are three positions that answer, or twenty-four planes. If these twenty-four planes are put in position and extended until they all meet to form a complete whole, it is found that all the faces are triangles. Thus it is seen that the form is com- posed of three triangles multiplied by the complete number of octahedral faces (8), or twenty-four triangles. Hence the name Trigonal Triakis Octahedron, mean- ing a form whose faces are made by eight times three triangles. This is taken from the Greek Triakis, thrice; see also pages 19, 23, and 128. The name is THE ISOMETRIC SYSTEM. 129 often abbreviated as the Trisoctahedron ; again, the form is occasionally denominated the Pyramid Octa- hedron, because each octahedral face is replaced by a triangular pyramid whose faces are triangles. See Fig. 331. 6. The next variation is to have the plane cut one axis at unity and the other axes at a greater distance, which shall be equal for both these axes. The symbol is 1 : m : m. If we place the plate upon the axes so as to find how many different positions there are in which it can be put and still fulfil the above requirements, it will be seen that there are twenty-four. If we place twenty-four planes in these positions and extend them so that they will meet and make a complete figure, it will be seen that the complete figure is composed of twenty-four tetragons ; i. e., three tetragons replacing each octahedral face. See Figs. 332 and 333. The name Tetragonal Triakis Octahedron is derived from the Greek, see pages 18, 23 and 128. Other names given to it are the Trapezohedron, because each face is a trapezium ; Leucitohedron or Leucitoid, be- cause the mineral Leucite crystallizes in this form ; and Icositetrahedron from the Greek Eikosi, " twenty," Tetra (in composition) see page 18, and Hedra, see page 23. 7. The next and last possible variation is when the 9 130 NOTES ON CRYSTALLOGRAPHY. plane cuts all three axes at unequal distances; its symbol is 1 : m : n. Placing the plate upon the axes so that it will cut all three unequally, we find that there are forty-eight positions in which the above requirements will be fulfilled, or six for every octahedral face ; hence the name Hexakis Octahedron, which is often shortened to Hexoctahedron, from the Greek Hexakis "six times," the entire name signifying " six times eight faces," or the " forty-eight-faced form." It is often nicknamed the Adamantoid because the Diamond (Greek Adamas, " adamant ") crystallizes in this form. See Figs. 334 and 335. The holohedral forms have nine planes of symmetry. Three of these form right angles with one another and are coincident with the planes of the crystallographic axes. The other six planes of symmetry unite the diagonally opposite edges of the cube and, in the center, are coincident with one axis and make angles of 45 with the other two. Since, in the other holo- hedral forms, they of necessity occupy the same posi- tion that they do in the cube, they can be easily located by comparing the other forms with a cube. There are also three axes of tetragonal symmetry that coincide with the crystallographic axes (cubic axes) ; four axes of trigonal symmetry (octahedral axes) that join the diagonally opposite corners of the cube ; and THE ISOMETRIC SYSTEM. 131 lastly, six axes of binary symmetry that join the centres of the diagonally opposite edges of the cube (dodecahe- dral axes). It can be seen that the axes of tetragonal symmetry lie in the chief planes of symmetry, bisect- ing them ; and that the axes of binary symmetry lie in the other six planes of symmetry, bisecting them. There is also a center of symmetry. As a matter of convenience, the above axes of sym- metry are also considered as crystal lographic axes and are used in descriptions and in calculations. 1. The three crystallographic axes proper of this system are called Cubic because they are perpendicu- lar to the faces of the cube. See a, a, Fig. 336. 2. The four axes that join the diagonally opposite corners of the cube are designated as Octahedral be- cause they are perpendicular to the faces of the octa- hedron. See b, 6, Fig. 336. 3. The six axes that join the centers of diagonally opposite corners of the cube are called Dodecahedral because they are perpendicular to the faces of the do- decahedron. See c, c, Fig. 337. II. HEMIHEDRAL FORMS. A. Oblique Hemihedral Forms : These forms are called oblique because the faces are not parallel to one another, but are always so arranged that they form oblique angles with each other. See Figs. 338-353. 132 NOTES ON CRYSTALLOGRAPHY. 1. The Tetrahedron can be regarded as produced by extending, until they meet, the alternate upper and lower planes of the octahedron, and by suppressing the other alternate planes. This operation causes the apices of the octahedron to be prolonged into an edge, and yields a four-faced wedge-shaped figure formed of equilateral triangles, and named Tetrahedron, from the two Greek words Tetra and Hedra, which have previously been defined (see pages 18 and 23). Its symbol in the Weiss notation is J (1 :' 1 : 1), the paren- theses being used to denote Oblique Hemihedral Forms. See Figs. 338 and 339. If the planes that were considered suppressed are extended and those formerly extended are suppressed, another form results, composed of the other half of the octahedron. Singly, one tetrahedron differs in no way from the other, except in its position. In combina- tion, the planes of one modify the solid angles of the other, and they are distinguished from each other as Positive and Negative. See Figs. 340 and 341. If the tetrahedron is so placed that one edge is hori- zontal and parallel to the observer, then the form can be called Positive. If another tetrahedron is so placed that its horizontal edge is pointing towards the observer, the form is Negative. 2. The Tetragonal Triakis Tetrahedron may be considered as formed by the extension of the alternate THE ISOMETRIC SYSTEM. 133 upper and lower sets of three triangular faces, which occupy, in the trigonal triakis octahedron, the posi- tions of the alternate faces of the octahedron, and by the suppression of the other alternate sets of three planes. When the faces thus extended are carried out so as to make a complete form, it will be found that each face is not a triangle, as in its original form, but is now a tetragon. See Figs. 342-345. The completed form is called Tetragonal Triakis Tetrahedron, i. e., four times three tetragonal faces, a name derived from the Greek, see pages 18, 128, and 132. This is often abbreviated as the Tristetrahedron. Its symbol is J (1:1: m). There are two forms to be produced by varying the sets of faces that are to be extended or to be suppressed, or the Positive and Negative. The tetrahedral edge, instead of being straight, is broken and formed by two lines. If this broken edge is placed parallel to the observer, the form can be called Positive : but if it is directed towards the observer, it is considered as Negative. See Figs. 344 and 845. 3. The Trigonal Triakis Tetrahedron may be con- sidered as produced by the extension of the alternate upper and lower sets of three tetragons that occupy the place of the octohedral faces in the tetragonal triakis octahedron, and by the suppression of the other alternate sets. When the extended faces are carried 134 NOTES ON CRYSTALLOGRAPHY. out so as to meet, the original tetragons become triangles, and the figure is composed of four times three triangular faces. See Figs. 346-349. The name Trigonal Triakis Tetrahedron is derived from the Greek, see pages 19, 128, and 132. Its symbol is J (1: m: m). As before, there are two forms, Posi- tive and Negative. The tetrahedral edge in this form is a straight line. If this be placed parallel to s the observer, then the form can be considered Positive but if this edge is directed towards the observer, the form is Negative. See Figs. 348, 349. The name is often abbreviated as the Trigonal Tristetrahedron. The student should always remember that the hemi- hedral form of the Trigonal Triakis Octahedron is the Tetragonal Triakis Tetrahedron, and that of the Tetragonal Triakis Octahedron is the Trigonal Triakis Tetrahedron. See Figs. 344 and 348. 4. The Hexakis Tetrahedron, or, as abbreviated, the Hextetrahedron, can be considered to be derived from the extension of the upper and lower alternate sets of six triangles that occupy the position of the octahedral faces in the hexakis octahedron, and by the suppression of the other sets of alternate faces. See Figs. 350 and 351. This procedure leads to the production of six triangles in the position of each tetrahedral face, or four times six, a fact which gives to the form its name Hexakis Tetrahedron (from the Greek, see pages 130 THE ISOMETRIC SYSTEM. 135 and 132). This form may be either Positive or Nega- tive. Its tetrahedral edge is formed by two broken lines. If the form is so placed that its upper tetra- hedral edge runs parallel to the observer, the form is Positive ; but if this edge is directed towards the ob- server, it is Negative. Its symbol is J(l : m : ri). See Figs. 352 and 353. The Oblique Hemihedral forms have six planes of symmetry which lie parallel to the faces of the dodeca- hedron ; i. e., each one lies parallel to one tetrahedral edge, and is perpendicular to and bisects the opposite tetrahedral edge. These forms have four axes of trigonal symmetry that extend perpendicularly from each solid tetrahedral angle to the opposite tetrahedral face in the tetra- hedron (octahedral axes) ; and which of course occupy the same positions in the other oblique hemihedral forms. They also have three axes of binary sym- metry coincident with the crystallographic axes, but have no center of symmetry. B. Parallel Hemihedral Forms. These forms are called parallel, because every plane has an opposite plane that is parallel to it. See Figs. 52, 53, 136, 137 and 356-359. The Pentagonal Dodecahedron may be considered to be formed from the tetrakis hexahedron by the ex- 136 NOTES ON CRYSTALLOGRAPHY. tension of one pair of planes touching at their apices, in each set of four triangles which replace the faces of the hexahedron, and by the suppression of the other pair. If we do this for each replaced hexahedral face, taking care to alternate the pairs so that no two extended or two suppressed planes join base to base, a twelve-faced figure results, whose face is a pentagon or has five sides ; four of these are equal, while the fifth is bisected by the termination of a crystallo- graphic axis, and is of unequal length as compared with the other four sides. See Figs. 354-359. As the form is composed of twelve pentagons, it is called the Pentagonal Dodecahedron (from the Greek, pente, "five," compounded with other Greek words that have been defined on pages 18 and 127). It is also commonly nicknamed Pyritohedron, which may be freely translated as the Pyrite-faced-figure, because the mineral Pyrite often crystallizes in this form. The symbol is J[l : m : oo ]; the brackets are used to distinguish parallel-faced forms in the Weiss system. By extending the planes previously suppressed, and by suppressing those previously extended, another Pentagonal Dodecahedron results, which in no way differs from the preceding, except in the position of its axes. The first is known as Positive and the second as Negative. If the forms are so placed that one crystallographic axis is perpendicular, and if the edge THE ISOMETRIC SYSTEM. 137 bisected by that axis is parallel to the observer, the form in question is Positive ; but if it is directed to- wards the observer, then it is Negative. Again if the axis is horizontal and directed towards the observer, and if the edge nearest him is perpendicular, the crystal is positive ; but if that edge is horizontal, the form is negative. See Figs. 52, 53, 356 and 357. 2. The Dyakis Dodecahedron can be considered to be formed by extending each set of two planes of the hexakis octahedron which answer to each plane of the Tetrakis Hexahedron that was extended or suppressed to form the Pentagonal Dodecahedron. If, then, each set of planes be extended or suppressed as was done in the preceding case, two forms result, Positive and Negative, each made up of twenty-four faces that are trapeziums. See Figs. 136, 137 and 360-364. If a Dyakis Dodecahedron be placed with an axis vertical and if the broken edge that answers to the edge of the Pentagonal Dodecahedron runs parallel to the ob- server, then the form is Positive ; but if it extends to- wards the observer, then the form is considered to be Negative. See Figs. 136, 137 and 362-364. The name Dyakis Dodecahedron or Didodecahedron is de- rived from the Greek, Dyakis, or Dis, " twice or double," united with other Greek words that have been given on pages 23 and 127, meaning a double dodecahedron or twenty-four-faced figure. It is often 138 NOTES ON CRYSTALLOGRAPHY. nicknamed the Diploid (from the Greek Diplos, " two- fold or double" and oid, see page 11). Haidenger, who gave the form this name, states, in substance, that he does so because of the peculiar arrangement of its surface into three pairs of double twin planes (3x2x2x2= 24). Its symbol is [1 : m : n\ . The Parallel Hemihedral forms possess three planes of symmetry forming right angles with one another, and coinciding with the planes of the crystallographic axes. These forms also have four axes of trigonal symmetry that join the diagonally opposite triedral solid angles in the Dyakis Dodecahedron (octahedral axes) and also the triedral solid angles that occupy the same position in the Pentagonal Dodecahedron. The three crystallographic axes (cubic axes) are here axes of binary symmetry. There is also a center of symmetry. C. Gyroidal Plagiohedral or Hemihedral Forms. 1. The Pentagonal Icositetrahedron may be con- sidered to be formed by the extension of the alternate planes of the hexakis octahedron until they meet and by the suppression of the other set of alternate planes. By reversing this process another twenty-four-faced figure will result. Thus there are two forms known as Right-handed and Left-handed. See Figs. 365- 367. THE ISOMETRIC SYSTEM. 139 These two forms can be distinguished by placing one axis perpendicular to the observer and one point- ing directly towards him. Let him look at the edge that begins at the top of the vertical axis and runs most nearly parallel with the axis pointing towards him. If that edge inclines towards the right of the axis the form is Right-handed, but if it inclines to the left of the axis it is Left-handed. In the case of many figures and also in some models the forms are inter- changed. The faces of these forms are all similar irregular pentagons, and the forms are called Icositetrahedrons (see page 129). This is also nicknamed the Gyroid (from the Greek Gyros, " round, bent, curved or arched "), because the planes are arranged in an irregular circular order about the crystal. The Pentagonal Icositetrahedrons have neither planes nor center of symmetry. They do have three axes of tetragonal symmetry coincident with the crystal- lographic (cubic) axes, four axes of trigonal symmetry coincident with the octahedral axes, and six axes of binary symmetry coincident with the dodecahedral axes, or they have all the axial symmetry of the holohedral forms. 140 NOTES ON CRYSTALLOGRAPHY. III. TETARTOHEDRAL FORMS. 1. The Tetrahedral Pentagonal Dodecahedron, or the Tetartoid, may be considered to be formed by the extension of every set of three alternate planes amongst every set of six that replaced the tetrahedral faces in the hexakis tetrahedron, and by the suppression of the other sets of three. By doing this one obtains a twelve-faced figure of a tetrahedral form with three irregular pentagonal faces replacing each tetrahedral face. By the alteration of the extended and sup- pressed faces, two forms, Right-handed and Left- handed, result from each hexakis tetrahedron. Since there are two hexakis tetrahedrons, or a positive and a negative form, there will be four of these tetarto- hedral forms : a. Positive: u. Right-handed. w. Left-handed. b. Negative : x. Right-handed. 2. Left-handed. Let the student place the Tetrahedral Pentagonal Dodecahedron with the broken line (composed of three zigzag lines, and corresponding to the edge of a tetra- hedron) approximately horizontal and parallel to him- self. If, then, the upper right-hand plane of the three THE ISOMETRIC SYSTEM. 141 next to him lie with its longest direction nearly hori- zontal, the crystal is Positive ; but if the same plane has its longest direction standing nearly vertical, the crystal is Negative. See Figs. 369 and 370. The Tetrahedral Pentagonal Dodecahedrons have neither planes of symmetry nor any center of symmetry. They have four axes of trigonal symmetry that join the acute triedral solid angles with the opposite obtuse triedral solid angles ; or, in other words, they are perpendicular to the faces of a tetrahedron. The crystallographic (cubic) axes are coincident with three axes of binary symmetry. COMPOUND FORMS. Single forms are common in the Isometric system, but the union of two or more forms in a single crystal is the more general rule, as it is in the other systems, and they are associated as follows: 1. The Holohedral Forms can all combine with one another. See Figs. 15, 17, 56-58, and 371-400. 2. The Oblique Hemihedral Forms can combine with one another and with the Cube, Dodecahedron, and Tetrakis Hexahedron, but are never united with the Parallel Hemihedral Forms. See Figs. 401-423. 3. The Parallel Hemihedral Forms can combine with one another and with the Cube, Dodecahedron, Trigonal Triakis Octahedron, and Tetragonal Triakis Octahedron. See Figs. 424-445. 142 NOTES ON CRYSTALLOGRAPHY. 4. The Pentagonal Icositetrahedrons or Gyroids can combine with each other or with the Cube, Dodecahe- dron, TetmUs Hexahedron, Octahedron, Trigonal Triakis Octahedron, and Tetragonal Triakis Octahedron. 5. The Tetrahedral Pentagonal Dodecahedrons can combine with one another and with the Cube, Dode- cahedron, Pentagonal Dodecahedron, Tetrahedron, Tetra- gonal Triakis Tetrahedron and Trigonal Triakis Tetra- hedron. RULES FOR NAMING JSOMETRIC PLANES. In this system the distinction of the planes of one form from those of another is accomplished most easily by the use of the parameters. If the student has located the axes correctly and determined the parameters of a plane, and if he remembers the name of the form that has these parameters, he can at once designate the form to which the plane belongs. He need pay no attention to the size or shape of the plane ; for its relation to the axes and the number of similar planes making the complete form are the only points with which he is concerned. If he understands the above statement, he can name any plane in this system by the following rules : I. If the plane cuts one axis at unity and is parallel to the other two, that is, if its symbol is 1 : oo : oo, the plane belongs to a Cube. THE ISOMETRIC SYSTEM. 143 II. If the plane cuts two axes at unity and is par- allel to the other one, that is, if its S3 r mbol is 1 : 1 : , the plane belongs to a Dodecahedron. III. If the plane intersects two of the axes un- equally and is parallel to the third axis, that is, if its symbol is 1 : m : oo, the plane belongs to one of two forms : a. If the form has the complete number of planes (24), then the plane belongs to a Tetrakis Hexahedron. b. If the form has one-half the complete number of planes (12), then the plane belongs to a Pentagonal Dodecahedron. IV. If the plane cuts all three axes at unity, that is, if its symbol is 1 : 1 : 1, it may belong to one of two forms : a. If the form has the complete number of planes (8), then the plane belongs to an Octahedron. b. If the form has half the complete number of planes (4), then it belongs to a Tetrahedron. V. If the plane intersects two axes at unity and the third axis at a greater distance, that is, if its symbol is 1 : 1 : m, it belongs to one of two forms : a. If the form has the complete number of planes (24), then the plane belongs to a Trigonal Triakis Oc- tahedron. b. If the form has one-half the complete number of planes (12), then the plane belongs to a Tetragonal Triakis Tetrahedron. 144 NOTES ON CRYSTALLOGRAPHY. VI. If the plane cuts one axis at unity and inter- sects the other two axes at a distance which is greater than unity, but which is equal for both axes, that is, if its symbol is 1 : ra : m, the plane may belong to one of two forms : a. If the form has the complete number of planes (24), then the plane belongs to a Tetragonal Triakis Octahedron. b. If the form has half the complete number of planes (12), then the plane belongs to a Trigonal Triakis Tetrahedron. VII. If the plane cuts all three axes unequally, that is, if its symbol is 1 : m : n, the plane may belong to one of four forms : a. If the form has the complete number of faces (48), then the plane belongs to a Hexakis Octahedron. b. If the form has half the complete number of planes (24), it may belong to one of two forms : 1. If the opposite planes form oblique angles with each other, the planes belong to a Pentagonal Icosi- tetrahedron or Gyroid. 2. If the opposite sides are parallel, the planes be- long to a Dyakis Dodecahedron or Diploid. c. If the form has one-fourth the complete number of planes (12), the planes belong to a Tetragonal Pentagonal Dodecahedron. THE ISOMETRIC SYSTEM. 145 READING DRAWINGS OF ISOMETRIC CRYSTALS Since in this system all the semi-axes or parameters are equal, a is the symbol used to designate each semi-axis, and any plane cutting all the axes equally would have as its symbol la: la: la; but there is apparently no advantage in keeping the a, and our symbol can as well be written 1:1:1. As a matter of convenience, the a is dropped in this text, but it is retained in most crystallographies in which the Weiss notation is used. The a can readily be supplied in the notation if one desires to employ the more com- mon form of the Weiss symbols. The other symbols follow so closely those which have been given in the other systems that the stud,ent should have no difficulty in understanding them. As stated on pages 37 and 111, Greek letters are used to designate the various partial forms in the Miller notation. In the following table, is used to designate in that notation the oblique Hernihedral forms ; T, to indicate the Parallel Hemihedral forms ; y, to mark the Pentagonal Icositetrahedrons ; and *cny to point out the Tetartohedral forms. While italic letters are used in crystallographic symbols in most cases, in some publications, particu- larly in a few recent text-books, the common type is employed. 10 146 NOTES ON CRYSTALLOGRAPHY. TABLE VI ISOMETRIC FORMS AND NOTATIONS Forms. Weiss. Naumann. Dana. Miller. Hexahedron or Cube. 1 : oo : oo ooOoo t-i or a 100 Dodeca- hedron 1 : l:oo OnO i or cZ 110 Tetrakis Hex- ahedron. 1 : m : QO oo Om i-m hkQ Octahedron. 1: 1:1 1 or o 111 Trigonal Tri- akis Octa- hedron. 1: l:m mO m hhl Tetragonal Triakis Oc- tahedron. 1 : m : m mOm m-ra hll Hexakis Octahedron. 1 : :m : n m On m-7i hkl Tetrahedrons. i(l: 1:1) 2 O Kl) K i HI } i(l: 1:1) 2 -i(D M11U raO Tetragonal Triakis Tet- rahedrons. -;;::! IT _mO 2 Km) -{ /i/iZ }- ! WiZ } 7?i Om Trigonal Tri- akis Tetra- i(l : m : ?n) mOm i(m-n) *f**f hedrons. HI : TO j m) "T" i(m-n) Hdfi mOn Hexakis Tet- T( I : TO : 71) 2 ^(m 71) ^ /i^z } rahedrons. 1(1 : m : ?0 mOn 1 /* \ ^(m-?0 '&*. 2 Pentagonal Dodecahe- !::.) Too 0771-1 J(i-m) 7T <{ AfcO }- L 2 J drons. -i(l:m:co) Too Om~] IT" J i(i-Wl) Tr^khO}- THE ISOMETRIC SYSTEM. TABLE VI Concluded 147 Forms. Weiss. Naumann. Dana. Miller. Dyakis Dodecahe- drons. i 1 : m : n 1 : m : n rr)lOu~| L~2~ J rmOn~| L~2~ J ^ (m-n) HM> Pentagonal Icositetra- hedrons. $(} : m : n)r ^T" **"* rUfcU y^Zfc^}- i(l :m:n)r mOn r K-)r ^wj Tetrahedral Pentagonal Dodecahe- drons. i(l :m :n)r "4~ "~4~ K-)i /CTT^j lkh\ -4(1: :m:)l "~4~ -(im-)( KIT ^ ^ -^ 5. Hemibrachydomatic Cleavage < ! .' w ' I fp f oo, ]_i/ ? oil. ( 'P oc> 'l-i', 101. 6. Hemimacrodomatic Cleavage \ - I /^/ <*> X 1 " 1 /' 101 - The two last cleavages are commonly grouped as Hemidomatic. CLEAVAGE. 157 MONOCLINIC CLEAVAGE In the Monoclinic System the most common cleav- ages are Pinacoidal and Prismatic. The chief cleav- ages and their symbols are as follows : 1. Basal Cleavage, P. or c, 001. 2. Clinopinacoidal Cleavage, oo P oo, i-i\ or b, 010. 3. Orthopinacoidal Cleavage, oo P 65, i-l or a, 100. 4. Prismatic Cleavage, oc P, I or m, 110. 5. Clinodomatic Cleavage, P co , 1-i, Oil. 6 Hemiorthodomatic Cleavage, \ I -Poo ,1-1,101. 7. Hemipyramidal Cleavage, < ' v i , 1, JLJ..L. ORTHORHOMBIC CLEAVAGE In the Orthorhombic system the most common cleavages are Pinacoidal and Prismatic. The symbols and most cleavages in this system are : 1. Basal Cleavage, OP, or c, 001. 2. Brachypinacoidal Cleavage, oo P oo , i-1 or b, 010. 3. Macropinacoidal Cleavage, oo P GO , i-i or a, 100. 4. Prismatic Cleavage, oo P, I or m, 110. 5. Brachydomatic Cleavage, Poo , 1-T, Oil. 6. Macrodomatic Cleavage, Poo, 1-T, 101. TETRAGONAL CLEAVAGE In the Tetragonal system the common cleavages 158 NOTES ON CRYSTALLOGRAPHY. are Pinacoidal and Prismatic, with the more rarely occurring Pyramidal. Their symbols are as follows : 1. Basal Cleavage, OP, or c, 001. 2. Primary Prismatic Cleavage, oo P, I or m, 110." 3. Secondary Prismatic Cleavage, oo P oo , i-i or a, 100. 4. Primary Pyramidal Cleavage, P, 1, 111. 5. Secondary Pyramidal Cleavage, 2 Poo , 2-^, 201. The second and third cleavages are usually united under the general name Prismatic ; the fourth and fifth are commonly united under the general term Pyramidal. HEXAGONAL CLEAVAGE In the Hexagonal System the more common cleav- ages are Pinacoidal, Prismatic, and Rhombohedral. The chief cleavages with their symbols are as follows : 1. Basal Cleavage, P, or c, 0001. 2. Primary Prismatic Cleavage, oo P, /or m, 1010. 3. Secondary Prismatic Cleavage, oo P 2, i-2 or a, 1120. 4. Primary Pyramidal Cleavage, P, 1, 1011. 5. Secondary Pyramidal Cleavage, P 2, 1-2, 1122. 6. Rhombohedral Cleavage, R, 1, * { 1011 J> or 1011. As in the Tetragonal System, the second and third cleavages are united under the general term Prismatic, and the fourth and fifth cleavages are coupled together as Pyramidal. CLEAVAGE. 159 ISOMETRIC CLEAVAGE . In the Isometric System the cleavages are Cubic, Dodecahedral, and Octahedral. Their symbols are as follows : Cubic Cleavage, oo oo , i-i or a, 100. Dodecahedral Cleavage, oo 0, i or c, 110. Octahedral Cleavage, 0, 1 or o, 111. PARTINGS In nature crystals are often subjected to pressure that gives rise to a platy structure. The plates thus produced are usually taken for cleavage laminae. Since these Parting Planes are parallel to crystal- lographic planes, the same symbols are given to them as to those of the cleavage planes ; that is, the symbol is that of the crystallographic plane to which the Part- ing is parallel. Since the parting planes have been produced by pressure and the consequent slipping of the mineral particles on one another, a parting structure can be dis- tinguished from true cleavage structure by the fact that the portion of the mineral lying between two adjacent planes of parting shows no tendency to split parallel to those planes. In the mineral cleavage there is a tendency on the part of the mineral to split indefinitely along planes parallel to the obvious cleavage planes. There is thus, on the one* hand, a resemblance be- 160 NOTES ON CRYSTALLOGRAPHY. tween mineral parting and parallel rock jointing ; and, on the other hand, a similar resemblance between mineral cleavage and rock or slaty cleavage. The part between any two cleavage planes in a rock or mineral tends to split indefinitely parallel to those planes; but in the case of rock jointing or mineral part- ing there is no tendency for the rock or mineral between two adjacent planes to split parallel to those planes. To a certain degree the resemblance extends to the origin of each ; as both parallel rock jointing and min- eral parting appear to be largely due to pressure and torsion, and are produced subsequently to the forma- tion of the rock or mineral. On the other hand min- eral cleavage is probably due to the molecular structure of the crystal or to its mode of chemical formation, and is congenital or was produced in the crystal when it was formed ; while rock or slaty cleavage seems to be caused in nature by pressure and chemical action combined, and is produced subsequently to the deposi- tion of the rock. CHAPTER X CRYSTALLOGRAPHIC SYMMETRY THE symmetry of the different crystal groups can be conveniently represented by the method employed by Gadolin * in 1867. This method projects the crys- tal as a sphere whose center is the point of intersection of the crystallographic axes. The positions of the planes of symmetry are shown by the circle and curved lines drawn within the circle. If this circle or these lines are drawn as full lines, each one indicates a plane of symmetry ; if they are shown as dotted or broken lines, the plane of symmetry is wanting. See Figs. 581-612. The crystallographic axes are indicated by straight lines marked at the extremities by arrow feathers. If these axes are drawn as continuous black lines, each axis is an axis of symmetry ; if the axial lines are formed by dots or dashes, making a broken line, then each axis. is not an axis of symmetry. See Figs. 581- * Abhandlung iiber die Herleitung aller Krystallographischer Sys- tems mit ihren Unterabtheilungen aus einem einzigen Prinzipe von Axel Gadolin (1867), Leipzig, 1896. 11 (161) 162 NOTES ON CRYSTALLOGRAPHY. 612. An axis of binary symmetry is indicated by a black spindle-shaped figure (Fig. 587); one of trigonal symmetry by a black triangle (Fig. 592); one of tetra- gonal symmetry by a black quadrilateral (Fig. 589), and one of hexagonal symmetry by a blaek hexagon (Fig. 593). The center of symmetry is designated in this book by a small circle inclosing the centers of the figures and the central symbols of the axes of sym- metry, if there are any. A. TRICLINIC SYSTEM This system has a center of symmetry, but it has neither plane nor axis of symmetry. See pages 19, 20 ; Fig. 581. B. MONOCLINIC SYSTEM I. The Holohedral Forms have a plane of symmetry, an cms of binary symmetry, and a center of symmetry. See pages 40, 41 ; Fig. 582. II. The Clinohedral or Hemihedral Forms have a plane of symmetry but they have neither axis nor center of symmetry. See pages 45, 46 ; Fig. 583. C. ORTHORHOMBIC SYSTEM I. The Holohedral Forms have three planes of sym- metry, three axes of binary symmetry, and a center of symmetry. See pages 51, 52 ; Fig. 584. II. The Hemihedral Forms have three axes of binary CRYSTALLOGRAPHIC SYMMETRY. 163 symmetry, but they have neither plane nor center of symmetry. See page 55 ; Fig. 585. III. The Hemimorphic Forms have two planes of symmetry and one axis of binary symmetry, but they have no center of symmetry. See page 56 ; Fig. 586. D. TETRAGONAL SYSTEM I. The Holohedral Forms have five planes of sym- metry, one axis of tetragonal symmetry, four axes of binary symmetry, and a center of symmetry. See page 64 ; Fig. 587. II. The three divisions of the Hemihedral Forms have different symmetries, as follows : 1. The Sphenoidal Group has two planes of symmetry and three axes of binary symmetry, but it has no center of symmetry. See pages 66, 67 ; Fig. 588. 2. The Pyramidal Group has one plane of symmetry, one axis of tetragonal symmetry, and a center of symmetry. See pages 68, 69 ; Fig. 589. 3. The Trapezohedral Group has one axis of tetra- gonal symmetry and four axes of binary symmetry, but it has neither plane nor center of symmetry. See page 69 ; Fig. 590. E. HEXAGONAL SYSTEM I. The Holohedral Forms have seven planes of sym- metry, one axis of hexagonal symmetry, six axes of binary symmetry, and a center of symmetry. See pages 84, 85 ; Fig. 591. 164 NOTES ON CRYSTALLOGRAPHY. II. The four divisions of the Hemihedral Forms differ in symmetry, as follows : 1. The Rhombohedral Group has three planes of sym- metry, one axis of trigonal symmetry, three axes of binary symmetry, and a center of symmetry. See pages 90, 91 ; Fig. 592. 2. The Pyramidal Group has one plane of symmetry, one axis of hexagonal symmetry, and a center of symmetry. See page 93 ; Fig. 593. 3. The Trapezohedral Group has one axis of hex- agonal symmetry and six axes of binary symmetry, but it has neither plane nor center of symmetry. See page 94 ; Fig. 594. 4. The Trigonal Group has four planes of symmetry, one axis of trigonal symmetry, three axes of binary sym- metry, and a center of symmetry. See page 96 ; Fig. 595. III. The three divisions of the Tetartohedral Forms possess symmetry as follows : 1. The Rhombohedral Group has an axis of trigonal symmetry and a center of symmetry, but it has no plane of symmetry. See page 98 ; Fig. 596. 2. The Trapezohedral Group has an axis of trigonal symmetry and three axes of binary symmetry, but it has neither plane nor center of symmetry. See pages 98- 100 ; Fig. 597. 3. The Trigonal Group has one plane of symmetry CRYSTALLOGRAPHIC SYMMETRY. 165 and one axis of trigonal symmetry, but it has no center of symmetry. See pages 101, 102 ; Fig. 598. IV. The four divisions of the Hemimorphic Forms show diverse symmetries, as follows : 1. The lodyrite Type has six planes of symmetry and an axis of hexagonal symmetry, but it has no center of symmetry. See pages 102, 103 ; Fig. 599. 2- The Nephelite Type has an axis of hexagonal sym- metry, but it has neither plane nor center of symmetry. See page 103 ; Fig. 600. 3. The Tourmaline Type has three planes of sym- metry and an axis of trigonal symmetry, but it has no center of symmetry. See page 103 ; Fig. 601. 4. The Sodium Periodate Type has an axis of tri- gonal symmetry, but it has neither plane nor center of symmetry. See pages 103, 104 ; Fig. 602. F. ISOMETRIC SYSTEM I. The Holohedral Forms have nine planes of sym- metry, three axes of tetragonal symmetry, four axes of trigonal symmetry, six axes of binary symmetry, and a center of symmetry. See pages 125-131 ; Fig. 603. II. The three divisions of the Hemihedral Forms show symmetry as follows : 1. The Oblique Hemihedral Forms have six planes of symmetry, four axes of trigonal symmetry, and three axes of binary symmetry, but they have no center of sym- metry. See pages 131-135 ; Fig. 604. 166 NOTES ON CRYSTALLOGRAPHY. 2. The Parallel Hemihedral Forms have three planes of symmetry, four axes of trigonal symmetry, three axes of binary symmetry, and a center of symmetry. See pages 135-138 ; Fig. 605. 3. The Gyroidal Hemihedral Forms have three axes of tetragonal symmetry, four axes of trigonal symmetry, and six axes of binary symmetry, but they have neither plane nor center of symmetry. See pages 138, 139; Fig. 606. 4. The Tetartohedral Forms have four axes of tri- gonal symmetry, and three axes of binary symmetry, but they have neither plane nor center of symmetry. See pages 140, 141 ; Fig. 607. CHAPTER XI THE THIRTY-TWO CLASSES OF CRYSTALS As a result of the labors of Frankenheim, Hessel, Bravais, Gadolin, and others it is possible within the six crystallographic systems to arrange thirty-two classes of crystals which shall be distinguished by a difference in their symmetry. This method is em- ployed largely in the more recent works relating to Crystallography and Mineralogy, particularly in Eu- rope. Perhaps no one has done more in recent times to popularize this method of studying Crystallography than has Groth, whose work will be chiefly followed below. Edward S. Dana has made extensive use of these classes in his valuable Text-Book of Mineralogy (1898), as have also Penfield, Kraus, and Moses and Parsons in their works. The chief class or group names used in this book and by Groth are denoted by heavy- faced type. A. TRI CLINIC SYSTEM (1). I. Asymmetric Class, Unsymmetrical Class, Asymmetric Group, Hemihedral Class, Hemipina- coidal Class, Pedial Class. (167) 168 NOTES ON CRYSTALLOGRAPHY. This crystal form is found only amongst artificial crystals, and was therefore not given in the preceding text. The form consists of one face only, and it has no plane, axis or center of symmetry. (Fig. 608.) Each form that consists of a single face is called a Pedion (Greek Pedion, a " plain, flat or field "). The forms of the Asymmetric Class are given below. In all these classes seven forms are placed. 1. First Pedion : a. Positive, 100. b. Negative, 100. 2. Second Pedion : a. Positive, 010. b. Negative, 010. 3. Third Pedion : a. Positive, 001. b. Negative, 001. 4. Primary Pedion, Qkl. 5. Secondary Pedion, hOL 6. Tertiary Pedion, MO. 7. Quaternary Pedion, hkl (2.) II. Pinacoidal Class, Holohedral Class, Centro- symmetric Class, Normal Group. See pages 19, 20 and 162 ; Fig. 581. The forms of this class are as follows : 1. First Pinacoid, 100. 2. Second Pinacoid, 010. THE THIRTY-TWO CLASSES OF CRYSTALS. 169 3. Third Pinacoid, 001. 4. Primary Pinacoid, OH. 5. Secondary Pinacoid, hOL 6. Tertiary Pinacoid, hkO. 7. Quaternary Pinacoid, hkl. B. MONOCLINIC SYSTEM (3). I. Sphenoidal Glass, Hemimorphic Glass. The forms of this class have one axis of binary sym- metry, but they have neither plane nor center of sym- metry. Fig. 609. As crystals of this class occur only in artificial pro- ducts like lithium sulphate, sugar, tartaric acid, etc., they have not been mentioned on the preceding pages. The forms of this class are as follows : 1. First Pinacoid, 100. 2. Second Pedion : a. Right-handed, 010. b. Left-handed, 010. 3. Third Pinacoid, 001. 4. Primary Sphenoid, Okl. 5. Secondary Pinacoid, hQL 6. Tertiary Sphenoid, hkQ. 7. Quaternary Sphenoid, hkl. (4). II. Domatic Class, Clinohedral Group, Hemi- hedral Class. See pages 48, 162 ; Fig. 583. 170 NOTES ON CRYSTALLOGRAPHY. The forms are as follows : 1. First Pedion : a. Positive [Front], 100. b. Negative [Back], 100. 2. Second Pinacoid, 010. 3. Third Pedion : a. Positive [Over] , 100. b. Negative [Under], TOO. 4. Primary Dome, Okl. 5. Secondary Pedion, hQL 6. Tertiary Dome, hkO. 7. Quaternary Dome, hkl. (5). III. Prismatic Class, Holohedral Class, Normal Group. See pages 45, 162 ; Fig. 582. Forms : 1. First Pinacoid, 100. 2. Second Pinacoid, 010. 3. Third Pinacoid, 001. 4. Primary Prism, Qkl 5. Secondary Pinacoid, hQl. 6. Tertiary Prism, MO. 7. Quaternary Prism, hkl. C. ORTHORHOMBIC SYSTEM (6). I. Bisphenoidal Class, Hemihedral Class, Sphe- noidal Group, Tetrahedral Hemihedral Class. See pages 51, 52, 162, 163 ; Fig. 585. THE THIRTY-TWO CLASSES OF CRYSTALS. 171 Forms : 1. First Pinacoid, 100. 2. Second Pinacoid, 010. 3. Third Pinacoid, 001. 4. Primary Prism, Okl. 5. Secondary Prism, hOL 6. Tertiary Prism, MO. 7. Sphenoid, hkl. (7). II. Pyramidal Class, Hemimorphic Class. See pages 56, 163 ; Fig. 586. Forms : 1. First Pinacoid, 100. 2. Second Pinacoid, 010. 3. Third Pedion : a. Over, 001. b. Under, OOL 4. Primary Dome, OK. 5. Secondary Dome, hOL 6. Tertiary Prism, hkQ. 7. Quaternary Pyramid, hkl. (8). III. Bipyramidal Class, Holohedral Class, Nor- mal Group. See pages 51, 52, 162 ; Fig. 584. Forms : ->;-. 1. First Pinacoid, 100. 2. Second Pinacoid, 010. 3. Third Pinacoid, 001. 4. Primary Prism, Qkl. 172 NOTES ON CRYSTALLOGRAPHY. 5. Secondary Prism, hOL 6. Tertiary Prism, MO. 7. Pyramid, likl. D. TETRAGONAL SYSTEM (9). I. Bisphenoidal Class, Sphenoidal Tetartohe- dral Class, Tetartohedral Group, Tetartohedral Class, Tetrahedral Tetartohedral Class. The forms of this class have one axis of binary sym- metry, but they have neither plane nor center of sym- metry. See Fig. 610. As there is no known example of this class, the forms have not been mentioned in the earlier pages of this book. Forms : 1. Basal Pinacoid, 001. 2. Primary Prism, 110. 3. Secondary Prism, 100. 4. Tertiary Prism, hkQ. 5. Primary Sphenoid, hhl. 6. Secondary Sphenoid, hOl. 7. Tertiary Sphenoid, hkl. (10). II. Pyramidal Class, Hemimorphic Hemihe- dral Class, Hemimorphic Tetartohedral Class, Pyra- midal Hemimorphic Class, Hemimorphic Group of the Pyramidal Hemihedral Class, Class of Tetragonal Pyramid of the Third Order, Tetartomorphic Class. THE THIRTY-TWO CLASSES OF CRYSTALS. 173 These forms have one axis of tetragonal symmetry, but they have neither plane nor center of symmetry. See Fig. 611. Inasmuch as Wulfenite is the only mineral assigned to this class, and there is reason to doubt whether it really belongs in this group, the Pyramidal Class was not touched upon in the earlier pages of this book. Forms : 1. Basal Pinacoid : a. Over [Positive], OOJ. b. Under [Negative] , 001. 2. Primary Prism, 110. 3. Secondary Prism, 100. 4. Tertiary Prism, hkO. 5. Primary Pyramid, hhl. 6. Secondary Pyramid, hQL 7. Tertiary Pyramid, hkl. (11). III. Scalenohedral Class, Sphenoidal Hemi- hedral Class, Tetrahedral Hemihedral Class, Sphe- noidal Group. According to the majority of crystallographers this class, in the preceding text, is said to have two planes of symmetry and three .axes of binary symmetry, but to have no center of symmetry. Groth, and after him Moses and Parsons, give the symmetry of this class as follows : Two planes of symmetry, one axis of tetragonal symmetry, and two axes of binary symmetry, but no center of symmetry. 174 NOTES ON CRYSTALLOGRAPHY. The axis of tetragonal symmetry is coincident with the vertical axis of each form. See pages 66, 67, 163 ; Fig. 588. Forms : 1. Basal Pinacoid, 001. 2. Primary Prism, 110. 3. Secondary Prism, 100. 4. Ditetragonal Prism, MO. 5. Primary Sphenoid, hhl. 6. Secondary Pyramid, hOL 7. Scalenohedron, hkl (12). IV. Trapezohedral Class, Trapezohedral Group, Trapezohedral Hemihedral Class. See pages 69, 163 ; Fig. 590. Forms : 1. Basal Pinacoid, 001. 2. Primary Prism, 110. 3. Secondary Prism, 100. 4. Ditetragonal Prism, MO. 5. Primary Pyramid, hhl. 6. Secondary Pyramid, hQl. 7. Trapezohedron, hkl. (13). V. Bipyramidal Class, Pyramidal Group, Pyr- amidal Hemihedral Class. See pages 68, 69, 163; Fig. 589. Forms : 1. Basal Pinacoid, 001. THE THIRTY-TWO CLASSES OF CRYSTALS. 175 2. Primary Tetragonal Prism, 110. 3. Secondary Tetragonal Prism, 100. 4. Tertiary Tetragonal Prism, hkO. 5. Primary Tetragonal Pyramid, hhl. 6. Secondary Tetragonal Pyramid, hOL 7. Tertiary Tetragonal Pyramid, hkl. (14). VI. Ditetragonal Pyramidal Class, Hemi- morphic Holohedral Class, Hemimorphic Group, Pyramidal Hemihedral Class, Class of the Ditetra- gonal Pyramid, Hemimorphic Hemihedral Class. The forms of this class possess four planes of sym- metry and one tetragonal axis of symmetry, but no center of symmetry. As no mineral is known to occur in the Ditetragonal Pyramidal Class, this group was omitted from the earlier part of this work. See Fig. 612. Forms : 1. Basal Pinacoid : a. Over [Positive], 001. b. Under [Negative], 001. 2. Primary Tetragonal Prism, 110. 3. Secondary Tetragonal Prism, 100. 4. Ditetragonal Prism, hkQ. 5. Primary Tetragonal Pyramid, hhl. 6. Secondary Tetragonal Pyramid, hOl. 7. Ditetragonal Pyramid, hkl. (15). VII. Ditetragonal Bipyramidal Class, Holo- hedral Class, Normal Group, Class of the Ditetra- gonal Bipyrarnid. See pages 64, 163 ; Fig. 587. 176 NOTES ON CRYSTALLOGRAPHY. Forms : 1. Basal Pinacoid, 001. 2. Primary Tetragonal Prism, 110. 3. Secondary Tetragonal Prism, 100. 4. Ditetragonal Prism, hkQ. 5. Primary Tetragonal Pyramid, hhl. 6. Secondary Tetragonal Pyramid, hOL 7. Ditetragonal Pyramid, hkl. E. HEXAGONAL SYSTEM A. Trigonal or Rhombohedral Division (16). I. Trigonal Pyramidal Class, Ogdohedral Class, Ogdomorphous Class, Hemimorphic Tetarto- hedral Class, Hemimorphic Trigonal Tetartohedral Class, Sodium Periodate Type, Class of the Hemi- morphic Trigonal Pyramid of the Third Order. See pages 103, 104, 165 ; Fig. 602. Forms : 1. Basal Pinacoid : a. Over [Positive], 0001. b. Under [Negative], OOOL 2. Primary Trigonal Prism : a. Positive, 1010. b. Negative, 1010. 3. Secondary Trigonal Prism: ; a. Right-handed, 1120. b. Left-handed, 2110. THE THIRTY-TWO CLASSES OF CRYSTALS. 177 4. Tertiary Trigonal Prism, MlO. 5. Primary Trigonal Pyramid, hQhl. 6. Secondary Trigonal Pyramid, h.h.2h.l. 7. Tertiary Trigonal Pyramid, hkll. (17). II. Rhombohedral Class, Rhombohedral Te- tartohedral Class, Trigonal Tetartohedral Class, Class of the Rhombohedron of the Third Order, Tri-rhom- bohedral Group, Trigonal Rhombohedral Class. See pages 98, 164 ; Fig. 596. Forms : 1. Basal Pinacoid, 0001. 2. Primary Hexagonal Prism, 1010. 3. Secondary Hexagonal Prism, 1120. 4. Tertiary Hexagonal Prism, hklQ. 5. Primary Rhombohedron, hQhl 6. Secondary Rhombohedron, h.h.2h.l. 7. Tertiary Rhombohedron, hkil. (18). III. Trigonal Trapezohedral Class, Trapezo- hedral Tetartohedral Class, Class of the Trigonal Tra- pezohedron, Trapezohedral Group. See pages 98-100, 164 ; Fig. 597. Forms : 1. Basal Pinacoid, 0001. 2. Primary Hexagonal Prism, 1010. 3. Secondary Trigonal Prism, 1120. 4. Ditrigonal Prism, hklQ. 5. Primary Rhombohedron, 12 178 NOTES ON CRYSTALLOGRAPHY. 6. Secondary Trigonal Pyramid, h.h.Zh.L 7. Trigonal Trapezohedron, hkil. (19). IV. Trigonal Bipyramidal Class, Trigonotype Tetartohedral Class, Sphenoidal Tetartohedral Class, Trigonal Tetartohedral Class, Trigonal Group, Class of the Trigonal Bipyramid of the Third Order, Class of the Trigonal Pyramid of the Third Order. There is no example of this class known. See pages 101, 164 ; Fig. 598. Forms : 1. Basal Pinacoid, 0001. 2. Primary Trigonal Prism, 1010. 3. Secondary Trigonal Prism, 1120. 4. Tertiary Trigonal Prism, hklQ. 5. Primary Trigonal Pyramid, hOhl 6. Secondary Trigonal Pyramid, h.h.2h.l. 7. Tertiary Trigonal Pyramid, hkll. (20). V. Ditrigonal Pyramidal Class, Hemimorphic Hemihedral Class, Ditrigonal Pyramidal Tetartohedral Class, Rhornbohedral Hemihedral Class, Hemimorphic Trigonal Hemihedral Class, Class of the Ditrigonal Pyramid, Hemimorphic Class, Rhornbohedral Hemi- morphic Class, Hemimorphic Rhornbohedral Hemi- hedral Class, Second Hemimorphic Tetartohedral Class, Tourmaline Type. See pages 103, 165 ; Fig. 601. THE THIRTY-TWO CLASSES OF CRYSTALS. 179 Forms : 1. Basal Pinacoid : a. Over, 0001. b. Under, OOOf. 2. Primary Trigonal Prism : a. Positive, lOlO. b. Negative, 1010. 3. Secondary Hexagonal Prism, 1120. 4. Ditrigonal Prism, hkiQ. 5. Primary Trigonal Pyramid, htihl. 6. Secondary Hexagonal Pyramid, h.h.2h.L 7. Ditrigonal Pyramid, hkll. (21). VI. Ditrigonal Scalenohedral Class, Rhombo- hedral Hemihedral Class, Scalenohedral Rhombo- hedral Class, Class of the Ditrigonal Scalenohedron, Scalenohedral Class, Normal Rhombohedral Group, Rhombohedral Group. See pages 90, 91, 164 ; Fig. 592. Forms : 1. Basal Pinacoid, 0001. 2. Primary Hexagonal Prism, 1010. 3. Secondary Hexagonal Prism, 1120. 4. Dihexagonal Prism, hk~Q. 5. Primary Rhombohedron, hfthl. 6. Secondary Hexagonal Pyramid, h.h.2h.l. 7. Hexagonal Scalenohedron, hlcll. (22) VII. Ditrigonal Bipyramidal Class, Trigono- 180 NOTES ON CRYSTALLOGRAPHY. type Hemihedral Class, Sphenoidal-Hemihedral Class, Trigonnl Hemihedral Class, Class of the Ditrigonal Bipyramid, Class of the Ditrigonal Pyramid, Trigonal Group. No examples are known of this class. See pages 96, 164 ; Fig. 595. Forms : 1. Basal Pinacoid, 0001. 2. Primary Trigonal Prism, 1010. 3. Secondary Hexagonal Prism, 1120. 4. Ditrigonal Prism, hklO. 5. Primary Trigonal Pyramid, hQhl. 6. Secondary Hexagonal Pyramid, h.h.2h.l. 7. Ditrigonal Pyramid, hkll. B. Hexagonal Division (23). VIII. Hexagonal Pyramidal Class, Hemimor- phic Hemihedral Class, First Hemimorphic Tetarto- hedral Class, Tetartomorphic Class, Hemimorphic Pyramidal Hemihedral Class, Pyramidal Hemimor- phic Class, Hexagonal Pyramidal Tetartohedral Class, Class of the Third Order Hexagonal Pyramid, Nephe- lite Type. See pages 103, 165 ; Fig. 600. Forms : 1. Basal Pinacoid : a. Over [Positive], 0001. b. Under [Negative], 0001. 2. Primary Hexagonal Prism, 1010. THE THIRTY-TWO CLASSES OF CRYSTALS. 181 3. Secondary Hexagonal Prism, 1120. 4. Tertiary Hexagonal Prism, hk7Q. *5. Primary Hexagonal Pyramid, hOhl. 6. Secondary Hexagonal Pyramid, h.h.2h.L 7. Tertiary Hexagonal Pyramid, hkil. (24). IX. Hexagonal Trapezohedral Class, Trape- zohedral Hemihedral Class, Trapezohedral Class, Trapezohedral Group, Class of the Hexagonal Trape- /ohedron. Only some artificial chemical compounds occur in the forms of this class. See pages 94, 164 ; Fig. 594. Forms : 1. Basal Pinacoid, 0001. 2. Primary Hexagonal Prism, 1010. 3. Secondary Hexagonal Prism, 1120. 4. Dihexagonal Prism, hklQ. 5. Primary Hexagonal Pyramid, hQhl. 6. Secondary Hexagonal Pyramid, h.h.2h.l. 7. Hexagonal Trapezohedron, hlcil. (25). X. Hexagonal Bipyramidal Class, Pyramidal Hemihedral Class, Bipyramidal Class, Pyramidal Group, Tripyramidal Group, Class of the Third Order Hexagonal Bipyramid, Class of the Third Order Hex- agonal Pyramid. See pages 93, 164 ; Fig. 593. Forms : 1. Basal Pinacoid, 0001. 2 Primary Hexagonal Prism, 1010. 182 NOTES ON CRYSTALLOGRAPHY. 3. Secondary Hexagonal Prism, 1120. 4. Tertiary Hexagonal Prism, hklQ. 5. Primary Hexagonal Pyramid, hOhl. 6. Secondary Hexagonal Pyramid, h.h.2h.l. 7. Tertiary Hexagonal Pyramid, hkll. (26.) XL Dihexagonal Pyramidal Class, Hexagonal Hemimorphic Class, Hemimorphic Holohedral Class, Hemimorphic Hemihedral Class, Hemimorphic Group, Class of the Dihexagonal Pyramid, Class of Hemimor- phic Dihexagonal Pyramid, lodyrite Type- See pages 102, 165 ; Fig. 599. Forms : 1. Basal Pinacoid : a. Over [Positive] , 0001. b. Under [Negative] , OOOl. 2. Primary Hexagonal Prism, 1010. 3. Secondary Hexagonal Prism, 1120. 4. Dihexagonal Prism, hkiO. 5. Primary Hexagonal Pyramid, hQhl 6. Secondary Hexagonal Pyramid, h.h.2h.l. 7. Dihexagonal Pyramid, hkil. (27). XII. Dihexagonal Bipyramidal Class, Holo- hedral Hexagonal Class, Holohedral Class, Holohedral Group, Normal Group, Class of Dihexagonal Pyramid, Class of the Dihexagonal Bipyramid. See pages 84, 85, 163 ; Fig. 591. THE THIRTY-TWO CLASSES OF CRYSTALS. 183 Forms : 1. Basal Pinacoid, 0001. 2. Primary Hexagonal Prism, 1010. 3. Secondary Hexagonal Prism, 1120. 4. Dihexagonal Prism, hkW. 5. Primary Hexagonal Pyramid, hOhl. 6. Secondary Hexagonal Pyramid, h.h.2h.l. 7. Dihexagonal Pyramid, hkil. F. ISOMETRIC SYSTEM (28). I. Tetrahedral Pentagonal Dodecahedral Class, Tetartohedral Class, Tetartohedral Grup, Class of the Tetartoid. See pages 140, 166 ; Fig. 607. Forms : 1. Hexahedron or Cube, 100. 2. Dodecahedron, 110. 3. Tetrahedron : a. Positive, 111. b. Negative, 111. 4. Pentagonal Dodecahedron : a. Right-handed, hkO. b. Left-handed, khO. 5. Trigonal Triakis Tetrahedron : a. Positive, Jill. b. Negative, hit. 6. Tetragonal Triakis Tetrahedron : a. Positive, hhl. b. Negative, hhl. 184 NOTES ON CRYSTALLOGRAPHY. 7. Tetrahedral Pentagonal Dodecahedron : a Positive Right-handed, hkl. b Positive Left-handed, Ikh. c. Negative Right-handed, Ikh. d Negative Left-handed, hkl. (29). II. Pentagonal Icositetrahedral Class, Plagi- hedral Hemihedral Class, Plagihedral Group, Gyroidal Hemihedral Class, Gyroidal Group, Class of the Gyroid. See pages 138, 166 ; Fig. 606. Forms : 1. Hexahedron or Cube, 100. 2. Dodecahedron, 110. 3. Octahedron, 111. 4. Tetrakis Hexahedron, hkO. 5. Tetragonal Triakis Octahedron, hll 6. Trigonal Triakis Octahedron, hhl. 7. Pentagonal Icositetrahedron : a. Right-handed, hkl. b. Left-handed, Ikh. (30). III. Dyakis Dodecahedral Class, Parallel Hemihedral Class, Pentagonal Hemihedral Class, Pyritohedral Group, Pyritohedral Hemihedral Group, Class of the Diploid. See pages 135, 166 ; Fig. 605. Forms : 1. Hexahedron or Cube, 100. 2. Dodecahedron, 110. 3. Octahedron, 111. THE THIRTY-TWO CLASSES OF CRYSTALS. 185 4. Pentagonal Dodecahedron : a. Right-handed, hkQ. b. Left-handed, khQ. 5. Tetragonal Triakis Octahedron, hll. 6. Trigonal Triakis Octahedron, hhl. 7. Dyakis Dodecahedron : a. Right-handed, hkl. b. Left-handed, kill. (31). IV. Hexakis Tetrahedral Class, Inclined Hemihedral Class, Inclined-Faced Hemihedral Class, Tetrahedral Group, Tetrahedral Hemihedral Class, Class of the Hextetrahedron, Hextetrahedral Class, Oblique Hemihedral Class. See pages 131, 165 ; Fig. 604. Forms : 1. Hexahedron or Cube, 100. 2. Dodecahedron, 110. 3. Tetrahedron : a. Positive, 111. b. Negative, 111. 4. Tetrakis Hexahedron, hkO. 5. Tetragonal Triakis Tetrahedron : a. Positive, hhl. b. Negative, hhl. 6. Trigonal Triakis Tetrahedron : a. Positive, hll. b. Negative, hll. 186 NOTES ON CRYSTALLOGRAPHY. 7. Hexakis Tetrahedron : a. Positive, hkl. b. Negative, hkl. (32). V. Hexakis Octahedral Class, Holohedral Class, Normal Group, Class of the Hexoctahedron, Hexoctahedral Class. See pages 125, 165 ; Fig. 603. Forms : 1. Hexahedron or Cube, 100. 2. Dodecahedron, 110. 3. Octahedron, 111. 4. Tetrakis Hexahedron, hkQ. 5. Tetragonal Triakis Octahedron, Jill. 6. Trigonal Triakis Octahedron, hhl. 7. Hexakis Octahedron, hkl. CHAPTER XII CRYSTALLOGRAPHIC NOMENCLATURE THE names in Crystallography are undoubtedly a serious stumbling-block to most students, yet in point of fact crystals are named in a way that is very similar to that in which men are named the world over. Again, the crystallographic names are no more diffi- cult to pronounce than are the names of persons of one nationality to those of different nations and speech. Foreigners make havoc with our proper names, and we have difficulty in learning how to pronounce the names of the emigrants who come to our shores from Russia, Poland, and Bohemia. The object of applying a name to an individual, variety or species is to distinguish it absolutely from all others. When men live in comparatively small communities and each individual leads a somewhat stationary life, one name has been generally found sufficient ; every one is known amongst his fellows as Smith, Brown or Jones, or, it may be, as William, Robert, John or James. When men live in larger communities, or intermingle freely as a result of polit- (187) 188 NOTES ON CRYSTALLOGRAPHY. ical commotions or the increased facilities for travel, a necessity arises for binomial, or trinomial, or even longer names. When several individuals of the same name were associated together, some other term than that of the family name was necessary to distinguish each one from his fellows. Accordingly, for the sake of dis- tinction, to a man's given name was added a nick- name referring frequently to some personal pecu- liarity, as, e. g., Red Angus, Black Douglas or Fred- erick Barbarossa. Later, a secondary name, without any peculiar personal significance, was attached to a man's family name, as, e. g., William Shakespeare, John Milton or Ben Johnson. Later it became neces- sary or desirable to add one or several middle names, as, e. g., Henry Wadsworth Longfellow, Josiah Dmght Whitney and Louis Jean Rudolphe Agassiz ; and thus the modern method of personal nomenclature has been developed. In the nomenclature of Crystallography the student can observe a marked resemblance to the system fol- lowed in the naming of persons. He can notice the single name in the Octahedron ; the nickname in the Cube and Gyroid, the family names in the Pinacoids, Pyramids, and Prisms ; the double names in the Dyakis Dodecahedron and the Hexakis Octahedron ; the trinomial names in the Trigonal Triakis Octa- hedron, Primary Hexagonal Pyramid, and others. CRYSTALLOGRAPHIC NOMENCLATURE. 189 The resemblance to personal nomenclature can be well seen in the case of the various tribes and families of Prisms, Pyramids, and Pinacoids, and in the Isometric System. The change of one family name to another, as is common amongst men, is observed in the Domes which are in truth Prisms. Again, the various Tri- gonal Prisms are descended from the various Hex- agonal Prisms, and the Sphenoids from the Pyramids, as are also the Trapezohedrons, Rhombohedrons, and Scalenohedrons. In the Isometric Tribe can be found the families of the Tetrakis Hexahedrons and Octa- hedrons, with their various descendants. It is thought that the tabulation given below, which associates the related forms and enumerates many of their names, will furnish the observant student with a new method of retaining in his memory the true rela- tionship of the various forms. W. THE FAMILIES OF THE PRISM TRIBE A. THE FAMILY OF TRICLINIC PRISMS I. Triclinic Hemi Vertical Prism,* alias Triclinic Hemi Vertical Dome, Hemi Prism, Vertical Prism, Triclinohedral Prism, Klinorhombohedral Prism, etc. * In these lists the names used chiefly in this book are printed in heavy-faced type. 190 NOTES ON CRYSTALLOGRAPHY. II. Triclinic Hemi Brachy Prism, alias Triclinic Hemi Brachy Dome, Hemi Brachy Dome, Brachy Dome, Horizontal Prism, Second Horizontal Prism, Hemi Dome, etc. III. Triclinic Hemi Macro Prism, alias Triclinic Hemi Macro Dome, Hemi Macro Dome, Macro Dome, Horizontal Prism, First Horizontal Prism, Hemi Dome, etc. B. THE FAMILY OF MONOCLINIC PRISMS I. Monoclinic Vertical Prism, alias Monoclinic Ver- tical Dome, Vertical Prism, Oblique Rhombic Prism, Rhombic Prism, etc. II. Monoclinic Clino Prism, alias Monoclinic Glino Dome, Clino Dome, Clino Diagonal Prism, Horizontal Prism, Horizontal Prism of a Rhombohedral Section. III. Monoclinic Hemi Ortho Prism, alias Mono- clinic Hemi Ortho Dome, Hemi Ortho Dome. C. THE FAMILY OF ORTHORHOMBIC PRISMS I. Orthorhombic Vertical Prism, alias Orthorhombic Vertical Dome, Vertical Prism, Rhombic Prism, Ver- tical Rhombic Prism, Oblique Angled Quadralateral Prism, Vertical Quadralateral Prism, etc. II. Orthorhombic Brachy Prism, alias Orthorhom- bic Brachy Dome, Brachy Dome, Brachy Diagonal Dome, Brachy Diagonal Prism, Horizontal Prism, Second Horizontal Prism, etc. CRYSTALLOGRAPHIC NOMENCLATURE. 191 III. Orthorhombic Macro Prism, alias Orthorhom- bic Macro Dome, Macro Dome, Macro Diagonal Dome, Macro Diagonal Prism, Horizontal Prism, First Hori- zontal Prism, etc. D. THE FAMILY OF TETRAGONAL PRISMS I. Primary Prism, alias Direct Prism, Unit Prism, Prism of the First Order, Quadratic Prism, Tetragonal Prism of the First Order, Primary Tetragonal Prism, Direct Tetragonal Prism, etc. II. Secondary Prism, alias Inverse Prism, Diamet- ral Prism, Prism of the Second Order, Secondary Tetragonal Prism, Inverse Tetragonal Prism, Quad- ratic Prism, Tetragonal Prism of the Second Order, etc. III. Di Tetragonal Prism, alias Di Octahedral Prism, Octagonal Prism, etc. 1. Hemi Di Tetragonal Prism, alias Tertiary Prism, Prism of the Third Order, Tetragonal Prism of the Third Order. E. THE FAMILY OF HEXAGONAL PRISMS I. Primary Hexagonal Prism, alias Hexagonal Prism of the First Order, Unit Prism, Regular Hexa- gonal Prism, Hexagonal Prism of the Principal Series, First Hexagonal Prism, etc. 192 NOTES ON CRYSTALLOGRAPHY. 1. Henri Primary Hexagonal Prism, alias Pri- mary Trigonal Prism, Trigonal Prism, etc. a. Positive Primary Trigonal Prism. b. Negative Primary Trigonal Prism. II. Secondary Hexagonal Prism, alias Hexagonal Prism of the Second Order, Diagonal Prism, Regular Hexagonal Prism, Second Hexagonal Prism, Hexa- gonal Prism of the Second Series. 1. Henri Secondary Hexagonal Prism, alias Sec- ondary Trigonal Prism, Prism of the Second Order. a. Positive or Right-Handed Trigonal Prism. b. Negative or Left-Handed Trigonal Prism. III. Di Hexagonal Prism, alias Do Decagonal Prism, Twelve-sided Prism, etc. 1. Henri Di Hexagonal Prism, alias Tertiary Hexagonal Prism, Hexagonal Prism of the Third Order. a. Positive or Right-Handed Hexagonal Prism. b. Negative or Left-Handed Hexagonal Prism. 2. Hemi Di Hexagonal Prism, alias Primary Di Trigonal Prism, Di Trigonal Prism of the First Order. a. Positive Di Trigonal Prism. b. Negative Di Trigonal Prism. 3. Hemi Di Hexagonal Prism, alias Secondary CRYSTALLOGRAPHIC NOMENCLATURE. 193 Di Trigonal Prism, Di Trigonal Prisin of the Second Order. a. Right-Handed Di Trigonal Prism. b. Left-Handed Di Trigonal Prism. 4. Tetarto Di Hexagonal Prism, alias Tertiary Trigonal Prism, Trigonal Prism of the Third Order. a. Positive Eight-Handed Tertiary Trigonal Prism. b. Positive Left- Handed Tertiary Trigonal Prism. c. Negative Right-Handed Tertiary Trigonal Prism. d. Negative Left- Handed Tertiary Trigonal Prism. X. THE FAMILIES OF THE PYRAMID TRIBE A. THE FAMILY OF TRICLINIC PYRAMIDS I. Triclinic Tetarto Pyramid, alias Triclinic Pyra- mid, Clinorhombic Octahedron, etc. Nicknames, An- orthotype, Anorthoid. B. THE FAMILY OF MONOCLINIC PYRAMIDS I. Monoclinic Hemi Pyramid, alias Monoclinic Pyr- amid, etc. Nicknames, Augitoid, Hemiorthotype. 13 194 NOTES ON CRYSTALLOGRAPHY. 0. THE FAMILY OF ORTHORHOMBIC PYRAMIDS I. Orthorhombic Pyramids, alias Rhombic Pyramid, Rhombic Pyramidohedron, Rhombic Octahedron, Or- thorhombic Octahedron, etc. Nickname, Orthotype. 1. Orthorhombic Hemi Pyramid, alias Ortho- rhombic Sphenoid, Sphenoid, Rhombic Sphe- noid, Rhombic Sphenoidohedron, Rhombic Tetrahedron, Irregular Tetrahedron, etc. Nick- name, Tartartoid : a. Positive or Right-handed Orthorhombic Sphenoid. b. Negative or Left-handed Orthorhombic Sphe- noid. D. THE FAMILY OF TETRAGONAL PYRAMIDS I. Primary Tetragonal Pyramid, alias Primary Pyr- amid, Direct Tetragonal Pyramid, Direct Pyramid, Unit Pyramid, Tetragonal Pyramid of the First Order, Pyramid of the Unit Order, Pyramid of the First Order, Direct Octahedron, Quadratic Octahedron, Quadratic Octahedron of the First Order, Pyramid Octahedron of the First Order, Tetragonal Pyramido- hedron of the First Direction, Quadratic Octahedron of the First Series. 1. Hemi Tetragonal Pyramid, alias Tetragonal Sphenoid, Sphenoid, Quadratic Tetrahedron, Irregular Tetrahedron : CRYSTALLOGRAPHIC NOMENCLATURE. 195 a. Positive Sphenoid. b. Negative Sphenoid. II. Secondary Tetragonal Pyramid, alias Secondary Pyramid, Inverse Tetragonal Pyramid, Inverse Pyr- amid, Diametral Pyramid, Trigonal Pyramid of the Second Order, Pyramid of the Second Order, Inverse Octahedron, Quadratic Octahedron, Quadratic Octa- hedron of the Second Order, Quadratic Octahedron of the Second Series, Tetragonal Pyramidohedron of the Second Direction, Pyramid of the Diametral Order, Quadratic Pyramid, etc. III. Di Tetragonal Pyramid, alias Di Tetragonal Octahedron, Di Octahedron, Di Tetragonal Pyramid of the First Direction. Nickname, Zirconoid. 1. Hemi Di Tetragonal Pyramid, alias Tertiary Tetragonal Pyramid, Tertiary Pyramid, Tetra- gonal Pyramid of the Third Order, Pyramid of the Third Order, Hemi Di Octahedron : a. Positive Tertiary Pyramid. b. Negative Tertiary Pyramid. 2. Hemi Di Tetragonal Pyramid, alias Tetra- gonal Scalenohedron, Di Tetragonal Scaleno- hedron. Nickname, Disphene, Diplo Tetra- hedron : a. Positive Tetragonal Scalenohedron. b. Negative Tetragonal Scalenohedron. 196 NOTES ON CRYSTALLOGRAPHY. 3. Hemi Di Tetragonal Pyramid, alias Tetra- gonal Trapezohedron, Quadratic Trapezo- hedron, Trapezoidal Octahedron, etc.: a. Positive or Eight-handed Tetragonal Trapezo- hedron. b. Negative or Left-handed Tetragonal Trapezo- hedron. E. THE FAMILY OF HEXAGONAL PYRAMIDS I. Primary Hexagonal Pyramid, alias Hexagonal Pyramid of the First Order, Di Hexahedron of the Principal Series, Hexagonal Dodecahedron of the First Order, Right Angled Dodecahedron, Hexagonal Pyramid of the First Division, Hexagonal Pyramido- hedron of -the First Normal Direction, Quartzoid of the First Order, etc. Nickname, Quartzoid. 1. Hemi Primary Hexagonal Pyramid, alias Rhombohedron, Primary Rhombohedron, Rhombohedron of the First Order, Eight- Angled Hexahedron, Rhombohedron of the Principal Series, Hemi Dodecahedron of the First Order, Rhombohedron of the Vertical Primary Zone. 2. Hemi Primary Hexagonal Pyramid, alias Pri- mary Trigonal Pyramid, Trigonal Pyramid of the First Order. II. Secondary Hexagonal Pyramid, alias Hexagonal CRYSTALLOGRAPHIC NOMENCLATURE. 197 Pyramid of the Second Order, Di Hexahedron of the Second Order, Di Hexahedron of the Principal Series, Hexagonal Dodecahedron of the Second Order, Eight- Angled Dodecahedron, Hexagonal Pyramid of the Second Division, Hexagonal Pyramidohedron of the Second Normal Direction, Quartzoid of the Second Order, etc. Nickname, Quartzoid. 1. Hemi Secondary Hexagonal Pyramid, alias Secondary Rhombohedron, Rhombohedron of the Second Order, etc. a. Positive Secondary Rhombohedron or Posi- tive Rhombohedron of the Second Order. b. Negative Secondary Rhombohedron or Nega- tive Rhombohedron of the Second Order. 2. Hemi Secondary Hexagonal Pyramid, alias Secondary Trigonal Pyramid, Trigonal Pyra- mid of the Second Order. a. Positive or Right-Handed Trigonal Pyramid. b. Negative or Left-Handed Trigonal Pyramid. III. Dihexagonal Pyramid, alias Di Dodecahedron. Nickname, Berylloid. 1. Hemi Di Hexagonal Pyramid, alias Hexa- gonal Scalenohedron, Scalenohedron, Di Hex- agonal Scalenohedron, Hemi Dodecahedron, Bi Pyramid. Nickname, Calcite Pyramid. a. Positive Scalenohedron. b. Negative Scalenohedron. 198 NOTES ON CRYSTALLOGRAPHY. 2. Hemi Di Hexagonal Pyramid, alias Tertiary Hexagonal Pyramid, Hexagonal Pyramid of the Third Order, Di Hexagonal Hemi Di Do- decahedron, Hemihedral Di Hexahedron. a. Positive or Right-Handed Tertiary Hexagonal Pyramid. b. Negative or Left-Handed Tertiary Hexagonal Pyramid. 3. Hemi Di Hexagonal Pyramid, a lias Hexagonal Trapezohedron, Di Hexagonal Trapezohedron, Trapezoid Di Hexahedron. Nickname, Di- plagihedron. a. Right-Handed Hexagonal Trapezohedron. b. Left- Handed Hexagonal Trapezohedron. 4. Tetarto Di Hexagonal Pyramid, alias Hemi Hexagonal Scalenohedron, Tertiary Rhombo- hedron, Rhombohedron of the Third Order. a. Positive Right-Handed Tertiary Rhombohe- dron. b. Negative Right-Handed Tertiary Rhombohe- dron. c. Positive Left-Handed Tertiary Rhombohe- dron. d. Negative Left-Handed Tertiary Rhombohe- dron. 5. Tetarto Di Hexagonal Pyramid, alias Di Tri- gonal Pyramid. CRYSTALLOGRAPHIC NOMENCLATURE. 199 a. Positive Di Trigonal Pyramid. b. Negative Di Trigonal Pyramid. 6. Tetarto Di Hexagonal Pyramid, alias Hemi Hexagonal Scalenohedron, Trigonal Trapezo- hedron, Di Trigonal Trapezobedron, Trigon Trapezohedron. Nickname, Plagihedron : a. Positive Eight-handed Trigonal Trapezo- hedron. b. Negative Right-handed Trigonal Trapezo- hedron. c. Positive Left-handed Trigonal Trapezohedron. d. Negative Left-handed Trigonal Trapezo- hedron. 7. Tetarto Di Hexagonal Pyramid, alias Tertiary Trigonal Pyramid, Trigonal Pyramid of the Third Order : a. Positive Eight-handed Tertiary Trigonal Pyramid. b. Negative Right-handed Tertiary Trigonal Pyramid. c. Positive Left- handed Tertiary Trigonal Pyr- amid. d. Negative Left-handed Tertiary Trigonal Pyr- amid. Y. THE FAMILIES OF THE PINACOID TRIBE I. Basal Pinacoid, alias Vertical Pinacoid, Basal Plane, Base, End Plane, etc. 200 NOTES ON CRYSTALLOGRAPHY. II. Brachy Pinacoid, alias Brachy Diagonal Pin- acoid. III. Macro Pinacoid, alias Macro Diagonal Pinacoid. IV. Clino Pinacoid. V. Ortho Pinacoid. Z. THE FAMILIES OF THE ISOMETRIC TRIBE I. Hexahedron. Nickname, Cube. II. Dodecahedron, alias Rhombic Dodecahedron, Regular Rhombic Dodecahedron, etc. Nicknames, Garnet Crystallization, Garnetohedron, Garnetoid, Garnet Dodecahedron. III. Tetrakis Hexahedron, alias Tetra Hexahedron, Hexahedral Trigonal Icosi Tetrahedron, Pyramidal Cube, etc. Nickname, Fluoroid. 1. Hemi Tetrakis Hexahedron, alias Pentagonal Dodecahedron, Hexahedral Pentagonal Dode- cahedron, Dornatic Dodecahedron, etc. Nick- names, Pyrite Dodecahedron, Pyritohedron, Pyritoid. IV. Octahedron, alias Regular Octahedron, Regular Four-sided Double Pyramid, etc. 1. Hemi Octahedron, alias Tetrahedron, Regular Tetrahedron, etc. V. Trigonal Triakis Octahedron, alias Triakis Octa- hedron, Tris Octahedron, Pyramid Octahedron, Octa- hedral Trigonal Icosi Tetrahedron, Octahedral Pyr- amidal Icosi Tetrahedron. Nickname, Galenoid. CRYSTALLOGRAPHIC NOMENCLATURE. 201 1. Hemi Trigonal Triakis Octahedron, alias Tetragonal Triakis Tetrahedron, Tetragonal Tris Tetrahedron, Tris Tetrahedron, Deltoid Dodecahedron, Tetragonal Dodecahedron, Trapezoidal Dodecahedron, Deltohedron, Trap- ezoid Tetrahedron, etc. VI. Tetragonal Triakis Octahedron, alias Trapezo- hedron, Icosi Tetrahedron, Trapezoidal Icosi Tetra- hedron, Deltoid Icosi Tetrahedron, etc. Nicknames, Leucite Crystallization, Leucitohedron, Leucitoid. 1. Hemi Tetragonal Triakis Octahedron, alias Trigonal Triakis Tetrahedron, Triakis Tetra- hedron, Pyramidal Tetrahedron, Trigonal Dodecahedron, Pyramidal Dodecahedron, Hemi Icosi Tetrahedron, etc. Nickname, Cuproid. VII. Hexakis Octahedron, alias Hex Octahedron, Octakis Hexahedron, Trigonal Polyhedron, Pyramidal Garnetohedron, etc. Nickname, Adamantoid. 1. Hemi Hexakis Octahedron, alias Hexakis Tet- rahedron, Trigonal Icosi Tetrahedron, Tetra- hedral Trigonal Icosi Tetrahedron, etc* Nick- name, Boracitoid. 2. Hemi Hexakis Octahedron, alias Dyakis Do- decahedron, Hemi Octakis Hexahedron, Tet- ragonal Icosi Tetrahedron, Trapezoid Icosi Tetrahedron, Trapezoid Di Dodecahedron, etc. 202 NOTES ON CRYSTALLOGRAPHY. Nicknames, Diploid, Diplo-Pyritohedron, Diplo- Pyritoid, Diplohedron, etc. 3. Hemi Hexakis Octahedron, alias Pentagonal Icosi Tetrahedron. Nickname, Gyroid. 4. Tetarto Hexakis Octahedron, alias Tetrahedral Pentagonal Dodecahedron. Nickname, Tetar- toid. DESCRIPTIONS OF THE PLATES PLATE I PAGE Fig. 1. Triclinic Axes with Semi-Axial Notation, 7, 9, 10, 29, 33 Fig. 2. Monoclinic Axes with Semi-Axial Notation, 7, 40-42, 47 Fig. 3. Orthorhombic Axes with Semi- Axial Notation, 7,50,51,57 Fig. 4. Tetragonal Axes with Semi-Axial Notation . . . . 7, 60 Fig. 5. Isometric Axes with Semi-Axial Notation . . 7, 122, 126 Fig. 6. Hexagonal Axes with Semi- Axial Notation, 8, 73, 75, 109 Fig. 7. Orthorhombic Pyramid (111), with the Axes drawn in. Sulphur 7, 25, 51 Fig. 8. Monoclinic Crystal showing Plane of Symmetry (A B C D) and Axis of Binary Symmetry. Forms : Clino- Pinacoid (010); Prism (110), and Clino-Dome (Oil). Natron 8,11,12,17,18,26,41,44,46,47 Fig. 9. Monoclinic Crystal showing Plane of Symmetry (A B C D) and Axis of Binary Symmetry. Forms : Clino- Pinacoid (010); Prism (110), and a Clino-Dome (Oil). Gypsum ......... 3, 11, 12, 15, 17, 18, 26, 41, 44, 46, 47 Fig. 10. Monoclinic Crystal showing Plane of Symmetry (A B C D H) and Axis of Binary Symmetry (A C). Forms: Clino-Pinacoid (010); Prism (110); Clino-Dome (Oil), and a Hemi-Pyramid (111). Gypsum, 3, 11, 12, 15, 17, 18, 26, 41, 44, 46, 47 Fig. 11. Monoclinic Crystal showing Plane of Symmetry (A B C D) and Axis of Binary Symmetry. Forms: Clino-Pinacoid (6 or 010); Ortho-Pinacoid (r or 100); Prism (M or 110), and Clino Dome (s or Oil). Augite, 17, 18, 26,41, 44,46 (203) 204 DESCRIPTIONS OF THE PLATES. PAGE PLATE II Fig. 12. Isometric. Octahedron (111). Magnetite, 3, 14, 23, 123, 128 Fig. 18. Isometric. Octahedron (111), distorted by being shortened in the direction of the Cubic Axes. Alum . . 3 Fig. 14. Isometric. Octahedron (111), distorted the same as Fig. 13. Alum 3 Fig. 15. Isometric. Octahedron (111 ), with its Solid Angles truncated by a Cube (100) Linnseite ... 3, 14, 23, 26, 123, 141 Fig. 16. Isometric. Octahedron (111), distorted the same as Fig. 13 and modified by a Cube (100). Chrome Alum, 3, 26 Fig. 17. Isometric. Octahedron (111), with its solid angles truncated by a Cube (100) and its edges truncated by a Dodecahedron (110). Galenite ... 3, 14, 23, 26, 27, 123, 141 Fig. 18. Isometric. Octahedron (111) modified by a dis- torted Cube (100) and a distorted Dodecahedron (110). Chrome Alum 8, 14, 26 Fig. 19. Isometric. Octahedron (0 or 111), distorted, and modified by a Cube ( oo oo or 100) and a Dodecahedron (co or 110). Chrome Alum ,,3 Fig. 20. Isometric. Octahedron (111). A curved and dis- torted form of the Diamond in which the curved Faces approximate those of an Octahedron, or it can be consid- ered a twin form ,. -.$ Fig. 21. Hexagonal. Distorted. Primary Prism (lOlO) ; modified by a Primary Pyramid (1011), or by two Rhom- bohedrons : <{ loll } and * { OlTl } . Quartz "f. Fig. 22. Orthorhombic. Distorted. Pyramid (111); modi- fied by a second Pyramid (112); a Prism (110), and a Brachy-Pinacoid (010). Niter * Fig. 23. Isometric. Parallel Growths. Octahedrons (111). Alum 3, 149 Fig. 24. Isometric. Parallel Growths. Octahedrons (111). Alum 3, 149 DESCRIPTIONS OF THE PLATES. 205 Fig. 25. Tetragonal. Parallel Growths, united by Pinacoids (001) 3, 149 Fig. 26. Hexagonal. Parallel Growths. Primary Pyramid ( 1 Oil ), and a Primary Prism (1 010). Quartz . . . .3,28,149 Fig. 27. Hexagonal. Parallel Growths. A Primary Pyra- mid (lOll) and a Primary Prism (lOlO). Quartz . . . . 3, 149 Fig. 28. Triclinic. Composed of 4 Tetarto-Pyramids (111, ill, 111, 111) 13,19-21,25,26,33,34,44 Fig. 29. Triclinic. A Compound Crystal showing a Tetarto- Pyramid (ill); a Hemi-Prism (llo); and a Macro-Pina- coid(lOO). Axinite 12,13,19-21,25,26,33,34,44 Fig. 30. Triclinic. A Compound Crystal showing three Tetarto-Pyramids (111, 221, 311); one Hemi-Prism (HO); a Hemi Macro-Dome (021); and a Macro-Pinacoid (100). Axinite 12,13,19-21,25,26,33,34,44 Fig. 31. Triclinic. A Compound Crystal showing a Tetarto- Pyramid (111); two Hemi-Prisms (110, flO); a-Hemi- Macro Dome (101); a Basal Pinacoid (OOl), and a Brachy- Pinacoid (010). Albite . . . .12,13,19-21,25,26,33,34,44 Fig. 32. Triclinic. A Compound Crystal showing four Tetarto-Pyramids (111, ill, 111, 111); two Hemi-Prisms (110, HO); a Brachy-Pinacoid (010), and a Macro-Pina- coid (100). Chalcanthite .... 12, 13, 19-21, 25, 26, 33, 34, 44 Fig. 33. Triclinic. A Compound Crystal, composed of two Hemi-Prisms (110 and HO); two Basal Pinacoids (001 and 001); a Brachy-Pinacoid (010), and a Macro-Pinacoid (100) 11,12,19-21,26,33,34,44 Fig. 34. Triclinic. A Compound Crystal showing two Tet- arto-Pyramids (111, 2Pi or 121): six Hemi-Prisms (110, 110, 101, 102, 'P t oo or 011,2'P, oo or 021); a Basal Pina- coid (001); a Brachy-Pinacoid (010); and a Macro-Pina- coid (100). Chalcanthite . . . .12, 13, 19-21, 25, 26, 33, 34, 44 206 DESCRIPTIONS OF THE PLATES. PAGE PLATE III Fig. 35. Triclinic. Compound Crystal showing a Tetarto- Pyramid (111); two Hemi-Prisms (110, llo); a Brachy- Pinacoid (010), and a Macro-Pinacoid (100). Chalchan- thite 12,13,19-21,25,26,33,34,44 Fig. 36. Hexagonal. Compound Form composed of a Pri- mary Pyramid (1011), and a Primary Prism (10TO). Quartz -18,26,74,76,81,83,104 Fig. 37. Hexagonal. Compound Form composed of a Pri- mary Prism (lOK)), a Primary Pyramid (1011); a Second- ary Pyramid (1121), and Basal Pinacoids (0001, OOOl). Apatite 18,26,74,76,80-83,104 Fig. 38. Hexagonal. Compound Form composed of a Pri- mary Prism (1010); a Primary Pyramid (1011), and Basal Pinacoids (0001, 0001). Apatite ... 18, 26, 74, 76, 80-83, 104 Fig. 39. Hexagonal. Compound Form composed of a Pri- mary Pyramid (1011), and Basal Pinacoids (0001, OOoT). Apatite 18, 26, 74, 76, 80-83, 104 Fig. 40. Hexagonal. Compound Form composed of a Pri- mary Prism (1010), modified by a Secondary Pyramid (1122) and a Dihexagonal Pyramid (hkil), 18, 26, 74, 76, 81-83, 104 Fig. 41. Tetragonal. Compound Form composed of a Pri- mary Prism (110) terminated by a Primary Pyramid (111). Zircon ...... 18, 26, 70, 73, 74 Fig. 42. Tetragonal. Compound Form composed of a Pri- mary Pyramid (111) and a Secondary Prism (100). Zircon, 18, 26, 70, 73, 74 Fig. 43. Tetragonal. Compound Crystal. Composed of a Primary Prism (110); a Primary Pyramid (111), and a Secondary Pyramid (201). Zircon 18, 26, 70, 73, 74 Fig. 44. Tetragonal. Compound Form. Composed of a Primary Pyramid (111); a Ditetragonal Pyramid (hkl or 311) and a Secondary Prism (100). Zircon . . 18, 26, 70, 73, 74 DESCRIPTIONS OF THE PLATES. 207 PAGE JMJJT. 45. Hexagonal. A Positive Primary Rhombohedron K <{ 2021 } modified by a Negative Primary lihombohedron A- {0111}-. Calcite . 18,26,74,76,87,88,104 Fig. 46. Hexagonal. A Positive Primary Rhombohedron { loll } modified by Secondary Hexagonal Prism (1120). Calcite 18,27,74,76,81,104 Fig. 47. Hexagonal. A Primary Rhombohedron *<{ lOfl }> , modified by a Scalenohedron K \ 3251 } . Calcite, 18,26, 74,76,81,104 Fig. 48. Hexagonal. A Scalenohedron { 2131 }> , modified by a Rhombohedron { loll }. Calcite . . 18, 26, 74, 76, 104 Fig. 49. Hexagonal. A Primary Prism (lofo;, modified by a Negative Rhombohedron <{ 0112 }> . Calcite, 18, 26, 74, 76, 81, 104 Fig. 50. Hexagonal. A Primary Rhombohedron { 1011 }> and a Secondary Prism (1120). Calcite . 18, 26, 74, 76, 81, 104 Fig. 51. Qrthorhombic. Compound Form showing the planes of a Vertical Prism (110); a Brachy-Dome (Oil); Macro-Dome (101), and a Macro-Pinacoid (100). Barite. 26 Fig. 52. Isometric. Positive Pentagonal Dodecahedron (210). Pyrite 24, 25, 51, 123, 135, 137 Fig. 53. Isometric. Negative Pentagonal Dodecahedron (120). Pyrite 24,25,51,123,135,137 Fig. 54. Hexagonal. Positive Right-handed Trigonal Trapezohedron, r^ hkll } 125,76,100,104 Fig. 55. Hexagonal. Positive Left-handed Trigonal Trape- zohedron, KT\ ikTd f . .,. ,...... 25, 74, 76, 100, 104 PLATE IV Fig. 56. Isometric. Octahedron (111) with its edges beveled bya Trigonal Triakis Octahedron (221). Galenite, 27, 123, 141 Fig. 57. Isometric. Dodecahedron (110) with its edges beveled by a Hexakis Octahedron (321). Garnet . 27, 123, 141 208 DESCRIPTIONS OF THE PLATES. PAGE Fig. 58. Isometric. Cube (100) with its edges beveled by a Tetrakis Hexahedron (310). Fluorite 27, 128, 141 Fig. 59. Monoclinic. Compound Form showing a Prism (110); a Hemi-Pyramid (111); a Basal Pinacoid (001); a Clino-Pinacoid (010), and an Ortho-Pinacoid (100). Py- roxene 41-44, 46, 47 Fig. 60. Monoclinic. A Prism (110) with the Axes drawn in, and terminated by Basal Pinacoids (001) . . . 41-44, 46, 47 Fig. 61. Monoclinic. Composed of Basal Pinacoids (001); Clino-Pinacoids (010), and Ortho-Pinacoids (100), 41-44, 46, 47 Fig. 62. Monoclinic. Compound Form showing planes of a Prism (110); a Positive Hemi-Ortho-Dome (101); a Basal Pinacoid (001), and a Clino-Pinacoid (010). Melan- terite 41-47 Fig. 63. Monoclinic. Showing the planes of a Prism (110); a Clino-Dome (Oil), and a Basal Pinacoid (001). Melan- terite ..... 41, 47 Fig. 64. Monoclinic. Axes drawn in. Compound Form composed of a Positive and a Negative Hemi-Pyramid (111,111) .. 26,41-47 Fig. 65. Monoclinic. Compound Form showing the planes of two Prisms (110, 120); a Clino-Dome (Oil); a Basal Pinacoid (001); and a Clino-Pinacoid (010) 41-47 Fig. 66. Monoclinic. Compound Form composed of two Prisms (110, 130); a Hemi-Orthodome (Toi) and Basal Pinacoids (001) . .41-47 Fig. 67. Monoclinic. Compound Form showing Prisms (110, 120); a Clino-Dome (Oil); a Hemi-Ortho-Dome (201); a Positive Hemi-Pyramid (111), Clino-Pinacoid (010), and a Basal Pinacoid (001) 41-47 Fig. 68. Monoclinic. Compound Form showing two Prisms (110, 120); Positive and Negative Hemi-Pyramids (111, 111); a Clino-Dome (Oil); a Clino-Pinacoid (010); an Ortho-Pinacoid (100), and a Basal Pinacoid (001) . . . 41-47 DESCRIPTIONS OF THE PLATES. 209 PAGE Fig. 69. MoDOclinic. Compound Form showing planes of a Prism (110), a Negative Henri-Pyramid (111); three Hemi- Ortho-Domes (201, 201 and ^401); a Basal Pinacoid (001),andaClino-Pinacoid (010) .... ... .... .41-47 Fig. 70. Monoclinic. Compound Form showing planes of two Prisms (110, 210); a Positive-Henri Pyramid (111); a Hemi-Ortho-Dome (101); a Clino-Pinacoid (010); and a Basal Pinacoid (001) -.. * . . . . 41-47 Fig. 71. Monoclinic. Compound Form showing planes of a Prism (110); a Hemi-Pyramid (111); a Clino-Pina- coid (010), and an Ortho-Pinacoid (100). Augite . . 41, 43-47 Fig. 72. Monoclinic. Compound Form showing the planes of a Prism (110); Positive and Negative Henri-Pyramids 111, 111, and "221), and Clino-, Ortho-, and Basal-Pina- coids(010, 100, 001). Augite 41,43-47 Fig. 73. Monoclinic. Compound Crystal showing planes of two Prisms (110,^01); a Positive Pyramid (Til); a Basal Pinacoid (001), and an Ortho-Pinacoid (100) . . 41, 42, 44-47 Fig. 74. Monoclinic. Crystal showing planes of a Prism (110); a Basal Pinacoid (001), and a Clino-Pinacoid (010). Sugar 41-47 Fig. 75. Monoclinic. Compound Crystal showing the planes of a Prism (110); a Hemi-Ortho Dome (Oil); a Clino-Dome (101); an Ortho-Pinacoid (100), and a Basal Pinacoid (001). Sugar . . 41-47 Fig. 76. Monoclinic. Compound Form showing planes of a Prism (110); a Positive Hemi-Pyramid (111), and a Basal Pinacoid (001) 41-47 Fig. 77. Monoclinic. Compound Form showing planes of a Prism (110); a Negative Hemi-Pyramid (111); a Clino- Pinacoid (010), and a Basal Pinacoid (001) 41-47 Fig. 78. Monoclinic. Compound Form showing the planes of two Henri-Pyramids (HI, 111); a Prism (T21): a Hemi- 210 DESCRIPTIONS OF THE PLATES. PAGE Ortho-Dome (101); a Basal Pinacoid (001); a Clino-Pina- coid (OlO), and an Ortho-Pinacoid (100). Melanterite, 41,43,44,46,47 Fig. 79. Monoclinic. Compound Form showing planes of a Prism (110); a Negative Hemi-Pyramid (111); two Clino-Domes (101, 103); a Basal Pinacoid (001), and a Clino-Pinacoid (010). Melanterite 41,43-47 Fig. 80. Monoclinic. Compound Crystal showing planes of a Prism (110). and two Hemi-Pyramids, (111, 111). Gypsum 41,43-47 Fig. 81. Monoclinic. Compound Crystal showing planes of a Prism (110); of a Positive and a Negative Hemi- Pyramid (111, 111), and a Clino-Pinacoid (010). Gypsum, 41,43-47 Fig. 82. Monoclinic. Compound Form showing planes of a Prism (110); two Hemi-Pyramids (111, "221); a Basal Pinacoid (001), and an Ortho-Pinacoid (100). Borax, 41, 43-47 Fig. 83. Monoclinic. Compound Form showing planes of two Positive Hemi-Pyramids (111, x or 221); a Basal Pinacoid (001); a Clino-Pinacoid (010), and an Ortho- Pinacoid (100). Borax 41, 43-47 Fig. 84. Monoclinic. Compound Form showing planes of a Prism (110); a Clino-Dome (Oil); an Ortho-Dome (101); a Basal Pinacoid (001), and an Ortho-Pinacoid (100). Melanterite 41, 43-47 Fig. 85. Monoclinic. Compound Form showing planes of a Prism (110); a Negative Hemi-Pyramid (111), three Hemi-Ortho-Domes (Toi, 10l, 103); a Basal Pinacoid (001), and a Clino-Pinacoid (010). Melanterite . . .41, 43-47 DESCRIPTIONS OF THE PLATES. 211 PAGE PLATE V Fig. 86. Monoclinic. Compound Form showing planes of a Prism (110); two Hemi-Pyramids (111, T21); a Clino- Dome (Oil); two Hemi-Ortho-Domes (Poo or 101, and P oo or 101); a Basal Pinacoid (001), and a Clino-Pina- coid (010). Melanterite - 41,43-47 Fig. 87. Orfchorhombic. Hemimorphic. Principal Form a Prism (210) with a Brachy-Pinacoid (010). The over forms are two Macro-Domes (201, 101), two Brachy- Domes (V or 032, X or 012), and a Basal Pinacoid (001); the under form is a Pyramid (llT). Calamine, 45, 50, 51, 56, 57 Fig. 88. Orthorhombic. Compound Form, easily mistaken for a Hemimorphic crystal, consisting of a Prism (110) and a Brachy-Pinacoid (010) and terminated at both ends by -p the planes of a sphenoid/c<{ 111 } or Fig. 89. Orthorhombic. Compound Form showing planes of a Brachy-Dome (021); a Macro-Dome (101), and a Basal Pinacoid (001). Niter 50, 51, 57 Fig. 90. Orthorhombic. Compound Form showing the planes of two Brachy-Domes (011,021); a Macro-Dome (101), and a Basal Pinacoid (001). Niter 50,51,57 Fig. 91. Orthorhombic. Compound Crystal showing the planes of two Brachy-Domes (Oil, 021); a Macro-Dome (101); a Pyramid (111), and a Basal Pinacoid (001). Niter ..>..... ;....... . * . .50,51,57 Fig. 92. Orthorhombic. Compound Form showing planes of a Brachy-Dome (021); a Macro-Dome (101); a Basal Pinacoid (001) and a Pyramid (111). Niter . . . . 50, 51, 57 Fig. 93. Orthorhombic. Compound Form showing the Plane of a Brachy-Dome (Oil); a Macro-Dome (101); a Basal Pinacoid (001), and a Prism (110). Barite . . 50, 51, 57 Fig. 94. Orthorhombic. Compound Form showing the 212 DESCRIPTIONS OF THE PLATES. PAGE planes of a Prism (110); a Macro-Dome (101); a Brachy- Dome (Oil), a Basal Pinacoid (001) and a Pyramid (111). Barite 50,51,57 Fig. 95. Orthorhombic. Compound Form showing planes of a Macro-Dome (101) and a Brachy-Dome (Oil). Bar- ite 51, 57 Fig. 96. Orthorhombic. Compound Form showing planes of a Brachy-Dome (Oil); two Macro-Domes (101, 301), and a Pyramid (111) 51, 57 Fig. 97. Orthorhombic. Compound Form showing planes of two Prisms (110, 120), two Brachy-Domes (Oil, 021); a Basal Pinacoid (001); a Macro-Pinacoid (100); a Brachy- Pinacoid (010); and a Pyramid (111) 50,51,57 Fig. 98. Orthorhombic. Compound Form showing the planes of a Brachy-Dome (Oil), and a Macro-Dome (101). Stibnite 51, 57 Fig. 99. Orthorhombic. Compound Form showing the planes of a Brachy-Dome (Oil) and a Macro-Dome (101). Calamine 51, 57 Fig. 100. Orthorhombic. Compound Form showing the planes of a Brachy Dome (Oil); a Macro-Dome (101), and a Prism (120). Barite 51,57 Fig. 101. Orthorhombic. Compound Form showing the planes of a Macro-Dome (101); a Brachy-Dome (Oil); a Prism (120); and a Brachy Pinacoid (010). Barite . 50, 51, 57 Fig. 102. Orthorhombic. Compound Form showing the planes of a Brachy-Dome (Oil); a Macro-Dome (101); and a Basal Pinacoid (001). Barite . , 50,51,57 Fig. 103. Orthorhombic. Compound Form showing planes of a Brachy-Pinacoid (Oil); a Macro-Pinacoid (101), and a Basal-Pinacoid (001). Barite 50, 51, 57 Fig. 104. Orthorhombic. Compound Form showing the planes of a Prism (110); a Macro-Dome (101), and a Basal Pinacoid (001). Barite 50,51,57 DESCRIPTIONS OF THE PLATES. 213 PAGE Fig. 105. Orthorhombic. Simple Form showing planes of a Pyramid (111). Sulphur 51,57 Fig. 106. Orthorhombic. Compound Form showing planes of two Pyramids (111, 113). Sulphur 51,57 Fig. 107. Orthorhombic. Simple Crystal showing the planes of a Pyramid (111) 61,57 Fig. 108. Orthorhombic. Compound Crystal showing planes of a Pyramid (111) modified by a Brachy-Pin- acoid(OlO) 50,51,67 Fig. 109. % Orthorhombic. Compound Form showing a Pyramid (111) modified by a Macro-Pinacoid (100) . 50, 51, 57 Fig. 110. Orthorhombic. Compound Form showing planes of a Pyramid (111) modified by those of a Brachy-Dome (Oil) . . . . . . . . ......-. 51,57 Fig. 111. Orthorhombic. Compound Form showing planes of a Pyramid (111) and a Brachy-Dome (Oil) 51, 57 Fig. 112. Orthorhombic. Compound Form showing the planes of a Pyramid (111) and a Prism (110) 51, 57 PLA.TE VI Fig. 113. Orthorhombic. Compound Form showing plane of a Pyramid (111) and a Brachy-Dome (Oil) 51,57 Fig. 114. Orthorhombic. Compound Form showing planes of two Pyramids (111, hkl) ......... 51,57 Fig. 115. Orthorhombic. Compound Form showing planes of a Pyramid (111) and a Macro-Dome (101) . . . . . .51,57 Fig. 116. Orthorhombic. Compound Form showing planes of two Pyramids (111, hkl) .. . ....>.. ...... 51, 57 Fig. 117. Orthorhombic. Compound Form showing the planes of a Pyramid (111) and a Prism (210) 61, 57 Fig. 118. Orthorhombic. Compound Form showing planes of a Pyramid (111); a Prism (210), a Brachy-Dome (Oil), and a Brachy-Pinacoid (010) 50,51,57 214 DESCRIPTIONS OF THE PLATES. PAGE Fig. 119. Orthorhombic. Compound Form showing plane of a Pyramid (111), and a Brachy-Dome (021). Niter . . 51, 57 Fig. 120. Orthorhombic. Compound Form showing planes of a Pyramid (111); a Prism (110); a Brachy-Dome (021), and a Brachy-Pinacoid (010). Niter .50,51,57 Fig. 121. Orthorhombic. Compound Form showing planes of two Pyramids (111, 113); a Brachy-Dome (Oil), and a Basal-Pinacoid (001). Sulphur 50, 51, 57 Fig. 122. Orthorhombic. Compound Form showing planes of a Pyramid (111), and a Basal Pinacoid (001) . . , . 50, 51, 57 Fig. 123. Orthorhombic. Crystal showing Prismatic (110) and Pyramidal (111) planes. Goslarite 51,57 Fig. 124. Orthorhombic. Crystal showing Prismatic (210) and Pyramidal (111) planes . 51,57 Fig. 125. Orthorhombic. Crystal showing planes of a Prism (110);. a Pyramid (111), and a Brachy-Pinacoid (010). Stibnite 50,51,57 Fig. 126. Orthorhombic. Crystal showing planes of a Prism (210); a Pyramid (111), and a Brachy-Pinacoid (010) 50,51,57 Fig. 127. Orthorhombic. Compound Form showing planes of a Prism (110); a Pyramid (111); a Brachy-Dome (Oil), and a Brachy-Pinacoid (010). Goslarite 50,51,57 Fig. 128. Orthorhombic. Compound Form showing planes of two Prisms (110, 210) and a Pyramid (111). Topaz, 50, 51, 57 Fig. 129. Orthorhombic. Crystal showing the planes of two Prisms (110, 210); a Pyramid (111); a Brachy-Dome (021), and a Basal Pinacoid (001). Topaz 50, 51, 57 Fig. 130. Orthorhombic. Compound Form showing the planes of a Pyramid (111); a Macro-Pinacoid (100), and a Brachy-Pinacoid (010) 51 , 57 Fig. 131. Orthorhombic. Crystal showing planes of a Pyra- mid (111); a Brachy-Pinacoid (010); a Macro-Pinacoid (100), and a Brachy-Dome (Oil) 50,51,57 DESCRIPTIONS OF THE PLATES. 215 PAGE Fig. 132. Orthorhombic. Compound Form showing planes of a Pyramid (111); two Prisms (110, 210); a Brachy- Dome (Oil); a Brachy-Pinacoid (010), and a Macro-Pina- coid(lOO) . . . .50,51,57 Fig. 133. Orthorhombic. Compound Form showing planes of a Pyramid (111); a Prism (210), and a Basal Pinacoid (001) ....;.. ... . .'., '.-... . ... . >.. r , .50,51,57 Fig. 134. Orthorhombic. Compound Crystal showing planes of two Pyramids (111,113); a Prism (110), and a Brachy-Pinacoid (010). . . > . . ... . ...... .50,51,57 Fig. 135. Orthorhombic. Compound Form showing planes of a Pyramid (111); a Prism (110); a Brachy-Pome (012); a Macro-Dome (102), and a Basal Pinacoid (001) . . 50, 51, 57 Fig. 136. Isometric. Simple Form. Positive Dyakis Do- decahedron (321) 51,135,137,138 Fig. 137. Isometric. Simple Form. Negative Dyakis Dodecahedron (231) 51,135,137,138 Fig. 138. Hexagonal. Simple Form. Negative Rhombo- hedron { OlTl }> ............ 52, 74, 76, 85, 86, 104 Fig. 139. Hexagonal. Simple Form. Positive Bhombohe- dron <( lOll } 52,74,78,85,86, 104 Fig. 140. Hexagonal. Simple Form. Positive Scalenohe- dron K] hkll } or 2131 52, 74, 78, 88-90, 94, 104 Fig. 141. Hexagonal. Simple Form. Negative Scaleno- hedron *<( ikJil } or 1231 . . . .... . 52, 74, 78, 89, 90, 94, 104 Fig. 142. Orthorhombic. Simple Form. Negative Sphe- noid K] hhl \ . . . . . . ... v . . ... . .!..... 55 Fig. 143. Orthorhombic. Simple Form. Negative Sphe- noid K.\ hhl \ . . . . . . ''* .... V. 55 Fig. 144. Orthorhombic. Simple Form. Positive Sphe- noid K\hhl\ - 55 216 DESCRIPTIONS OF THE PLATES. PAGE PLATE VII Fig. 145. Orthorhombic. A Positive or Right-handed Sphenoid { hkl \ with an inscribed Pyramid (hkl) show- ing the method of deriving the former from the later 55, 56 Fig. 146. Orthorhombic. A Negative or Left-handed Sphenoid K.\ Mel } with an inscribed Pyramid (hkl) show- ing the method of deriving the former from the later . 55, 56 Fig. 147. Orthorhombic. Simple Form. A Positive or Right-handed Sphenoid K.\ tikl\ 55 Fig. 148. Orthorhombic. Simple Form. A Negative or Left-handed Sphenoid \ hkl } 55 Fig. 149. Orthorhombic. Compound Form showing a Prism (110), terminated by the Planes of a Positive or Right-handed Sphenoid K] 111 } . Epsomite . . . . .55,61 Fig. 150. Orthorhombic. Compound Form showing planes of a Prism (110) and a Brachy-Pinacoid (010), with the ends of the Crystal terminated by the planes of a Positive Sphenoid { 111 } and a Negative Sphenoid K {!!!}. Goslarite 55, 61 Fig. 151. Tetragonal. A Primary Prism (110) terminated by Basal Pinacoids (001) 60,61,70 Fig. 152. Tetragonal. Compound Form showing planes of a Primary Prism (110); a Secondary Prism (100); and a Basal Pinacoid (001) 60, 61, 70 Fig. 153. Tetragonal. Compound Form showing planes of a Primary Prism (110); a Secondary Prism (100); a Sphenoid *-j 111 } , and a Basal Pinacoid (001) . . .60, 61, 70 Fig. 154. Tetragonal. A Cross-section showing the rela- tions of the Primary Prism (110) and the Primary Pyra- mid (111) to the Lateral Axes 61,70,73 Fig. 155. Tetragonal. A Primary Prism (110) terminated by a Primary Pyramid (111) .. 61, 70, 73,74 Fig. 156. Tetragonal. Cross-section showing the relation DESCRIPTIONS OF THE PLATES. 217 PAGE of a Secondary Pyramid (101) and a Secondary Prism (100) to a Primary Pyramid (111) and a Primary Prism (110), and of all to the Lateral Axes 61, 62, 70, 73 Fig. 157. Tetragonal. A Primary Pyramid (111), termin- ating a Secondary Prism (100). Apophyllite . . 61, 70, 73, 74 Fig. 158. Tetragonal. A Primary Octahedron (111) trun- cating the solid angles of a Secondary Prism (100), which is terminated by a Basal Pinacoid (001). Apophyllite, 61,70,73,74 Fig. 159. Tetragonal. A Primary Prism (110) modified by a Secondary Prism (100) and terminated by a Primary Pyramid (111). Zircon 61,70,73,74 Fig. 160. Tetragonal. A Cross-section of a Ditetragonal Pyramid (hkl) and Ditetragonal Prism (frfcO) showing their relations to a Primary Prism (110) and to the Lateral Axes .. 61,62,70,73 Fig. 161. Tetragonal. A Ditetragonal Prism (fcfcO) termi- nated by Basal Pinacoids (001) 61,70,73,74 Fig. 162. Tetragonal. A Primary Pyramid (111) with the Axes drawn in . . , ".'. . 60,61,70,73,74 Fig. 163. Tetragonal. A Secondary Pyramid (101) with the Axes drawn in 62, 70, 73, 74 Fig. 164. Tetragonal. A Primary Pyramid (hhl) with the Axes drawn in .'"..' 61,70,73,74 Fig. 165. Tetragonal. A Secondary Pyramid (hOl) with the Axes drawn in ...... .\ .... . . 62, 70, 73, 74 Fig. 166. Tetragonal. A Primary Pyramid (111) modified by another Primary Pyramid (Mil) 61, 70, 73, 74 Fig. 167. Tetragonal. A Primary Pyramid (111) with its terminal solid angles truncated by Basal Pinacoids (001), 61,70,73,74 Fig. 168. Tetragonal. A Primary Pyramid (111) with its lateral edges beveled by the planes of another Primary Pyramid (hhl) 61, 70, 73, 74 218 DESCRIPTIONS OF THE PLATES. PAGE Fig. 169. Tetragonal. A Primary Pyramid (111) with its lateral edges truncated by the planes of a Primary Prism (110) 61,70,73,74 PLATE VIII Fig. 170. Tetragonal. A Primary Pyramid (111) with its terminal solid angles truncated by Basal Pinacoids (001). 61,70,73,74 Fig. 171. Tetragonal. Compound Form showing the planes of two Primary Pyramids (111, 112) and a Basal Plane (001). Mellite 61,70,73,74 Fig. 172. Tetragonal. A Primary Pyramid (111) with its lateral solid angles truncated by a Secondary Prism (100) 61,70,73,74 Fig. 173. Tetragonal. A Primary Pyramid (111) with its lateral solid angles truncated by a Secondary Prism (100), 61, 70, 73, 74 Fig. 174. Tetragonal. A Primary Pyramid (111) with its lateral solid angles truncated by a Secondary Prism (100). The last three figures show the change in the appearance of compound Crystals made by the enlargement of the modifying planes 61,70,73,74 Fig. 175. Tetragonal. A Primary Pyramid (111) with its lateral solid angles replaced by the planes of a Secondary Pyramid (/iOZ) 61,62,70,73,74 Fig. 176. Tetragonal. Compound Form showing planes of two primary Pyramids (111, 113), and a Secondary Pyra- mid (201). Octahedrite 61,62,70,73,74 Fig. 177. Tetragonal. A Primary Pyramid (111) modified by a Secondary Pyramid (101) 61,62,70,73,74 Fig. 178. Tetragonal. A Primary Pyramid (111) with its terminal solid angles modified by a Secondary Pyramid (TiOJ) 61,62,70,73,74 DESCRIPTIONS OF THE PLATES. 219 PAGE Fig. 179. Tetragonal. A Primary Pyramid (111) termin- ating a Primary Prism, and both modified by the planes of a Secondary Pyramid (hOl) 61, 62, 70, 73, 74 Fig. 180. Tetragonal. Compound Form showing the planes of a Primary Pyramid (111) modified by the planes of a Primary Pyramid (112), a Secondary Pyramid (101), and a Basal Pinacoid (001) ~ ... 61, 62, 70, 73, 74 Fig. 181. Tetragonal. Compound Form showing the planes of three Primary Pyramids (111, 112, 113); a Secondary Pyramid (101); and a Basal Pinacoid (001) . . 61, 62, 70, 73, 74 Fig. 182. Tetragonal. Compound Form showing the planes of three Primary Pyramids (111, 112, 113); a Secondary Pyramid (101); a Secondary Prism (100); and a Basal Pinacoid (001) 61, 62, 70, 73, 74 Fig. 183. Tetragonal. Compound Form showing the planes of two Primary Pyramids (111,112); a Secondary Pyra- mid (101); a Secondary Prism (100); and a Basal Pina- coid (001) 61,70,73,74 Fig. 184. Tetragonal. Simple Form. A Ditetragonal Pyra- mid (fikl). The shaded planes show the planes sup- pressed, while the other planes are extended to form a Tetragonal Trapezohedron. See page 69 ... 62, 69, 70, 73, 74 Fig. 185. Tetragonal. A Primary Pyramid (111) with its lateral solid angles replaced by the planes of a Ditetra- gonal Pyramid (Ml) . . , . . . . 61, 62, 70, 73, 74 Fig. 186. Tetragonal. A Primary Pyramid (111) with its terminal solid angles replaced by the planes of a Ditetra- gonal Pyramid (hkl) .. . 61,62,70,73,74 Fig. 187. Tetragonal. A Primary Pyramid (111) with the terminal edges beveled by the planes of a Ditetragonal Pyramid (313) 61, 62, 70, 73, 74 Fig. 188. Tetragonal. Compound Form showing the planes of a Secondary Prism (100); a Primary Pyramid (111); and a Ditetragonal Pyramid (313). Zircon . 61, 62, 70, 73, 74 220 DESCRIPTIONS OF THE PLATES. PAGE Fig. 189. Tetragonal. A Primary Pyramid (111) with its lateral solid angles replaced by the planes of a Ditetra- gonal Prism (hkO) 61, 70, 73, 74 Fig. 190. Tetragonal. Compound Form showing planes of a Primary Pyramid (111); a Primary Prism (110); and a Ditetragonal Prism (320). Cassiterite 61,70,73,74 Fig. 191. Tetragonal. Compound Form showing the planes of a Primary Pyramid (111); a Ditetragonal Pyra- mid (321); and a Primary Prism (110). Cassiterite, 61, 62, 70, 73, 74 Fig. 192. Tetragonal. Simple Form. A Positive Sphenoid <{ hhl j> 66, 67, 69, 70, 73 Fig. 193. Tetragonal. Simple Form. A Negative Sphen- oid M Mill 66, 67, 69, 70, 73 Fig. 194. , Tetragonal. Showing the inscribed Primary Pyramid (Mil) from which the Positive Sphenoid { hhl\ is derived and showing their mutual relations, 66, 67, 69, 70, 73 Fig. 195. Tetragonal. Compound Form showing the planes of a Positive Sphenoid * \ hhl } ; a Negative Sphen- oid K. \hkl\\ and two Secondary Pyramids (101, 201). Chalcopyrite 66, 67, 70, 73 Fig. 196. Tetragonal. Simple Form. A Positive Tetra- gonal Scalenohedron * \ hkl I 66,67,69,70,73,89 Fig. 197. Tetragonal. Simple Form. A Negative Tetra- gonal Scalenohedron /c ] hkl [ 66. 67, 69, 70, 73, 89 Fig. 198. Tetragonal. A Cross section showing the relation of the planes of the Tertiary Pyramid * \hkl \ to the Lateral Axes and to the planes of the Primary Pyramid (111) or Prism (110) 40,68,70,73 DESCRIPTIONS OF THE PLATES. 221 PAGE PLATE IX Fig. 199. Tetragonal. Compound Form showing the planes of a Primary Pyramid (111); a Secondary Pyramid (201); and a Tertiary Pyramid (421). Scheelite . . . . 40, 68, 70, 73 Fig. 200. Tetragonal. Simple Form. A Kight-handed or Positive Trapezohedron r\hkl\ 69, 70, 73 Fig. 201. Tetragonal. Simple Form. A Left-handed or Negative Trapezohedron r \hkl\- 69,70,73 Fig. 202. Hexagonal. Section showing the relation of the Primary Prism (10TO) and Primary Pyramid (loll) to each other and to the lateral axes 74, 76, 81-83, 104 Fig. 203. Hexagonal. Simple Form. A Primary Pyramid (lOll) 74, 76, 81-83, 104 Fig. 204. Hexagonal. Simple Form. A Secondary Pyra- mid (1122) 74, 76, 81-83, 104 Fig. 205. Hexagonal. A Primary Prism (IQlO) terminated by Basal Pinacoids (0001) 74,76,80-83,104 Fig. 206. Hexagonal. A Secondary Prism (1120) termi- nated by Basal Pinacoids (0001) 74, 76, 80-83, 104 Fig. 207. Hexagonal. A Dihexagonal Prism (/tHO) or (2130) terminated by Basal Pinacoids (0001) . 74, 76, 80, 81, 104 Fig. 208. Hexagonal. Simple Form. A Dihexagonal Pyramid (hkil) 74, 76, 82, 104 Fig. 209. Hexagonal. A Diagram to demonstrate the rela- tion of the parameters of Secondary Prisms and Pyramids to those of the corresponding Primary forms. See pages 83, 84 ....... /'. , .->_ . i ...... 74, 76, 82-84, 104 Fig. 210. Hexagonal. Simple Form. A Positive or Bight- handed Trapezohedron T \ hkll ^ 74, 76, 94, 95, 104 Fig. 211. Hexagonal. Simple Form. A Negative or Left- handed Trapezohedron T <[ ikld \' 74, 76, 94, 95, 104 Fig. 212. Hexagonal. A Cross Section showing the position of the planes of a Secondary Prism (1120) or Pyramid 222 DESCRIPTIONS OF THE PLATES. PAGE (lf22) relative to a Primary Prism (loTO) or Pyramid (lOll) and to the Lateral Axes 74, 76, 81-83, 104 Fig 213. Hexagonal. A Cross Section showing the rela- tive position of the planes of a Tertiary Prism IT ( /iHO } or Pyramid * \ hkil \ to the planes of a Primary Prism (10TO) or Pyramid (lOTl) and to the Lateral Axes, 74,76,81,91-93,104 Fig. 214. Hexagonal. Hemimorphic Form. lodyrite Type showing the planes of an over Hemi-Pyramid (1011); a Prism (10TO), and a Basal Pinacoid (0001) . 74, 76, 81, 102, 104 Fig. 215. Hexagonal. Hemimorphic Form. lodyrite Type showing the planes of a Secondary Prism (1120); the over planes of a Primary Pyramid (4041 ) and Basal Pinacoid (0001), and the under planes of a Primary Pyramid (4045) and a Dihexagonal Pyramid (9-9-18- 20). lodyrite, 74, 76, 80, 81, 102, 104 Fig. 216. Hexagonal. Hemimorphic Form. lodyrite Type showing the planes of a Secondary Prism (1120); the over planes of a Primary Pyramid (4041) and a Basal Pinacoid (0001), and the under planes of a Primary Pyramid (4045). lodyrite 74, 76,80,81,102,104 Fig. 217. Hexagonal. Hemimorphic Form. Nephelite Type showing the planes of a Primary Prism (10TO); the over planes of a Primary Pyramid (1011), and the under planes of another Primary Prism (20~21) . . 74, 76, 81, 103, 104 Fig. 218. Hexagonal. A Primary Pyramid (loll) with the alternate planes shaded. If the shaded planes are sup- pressed and the others are extended until they meet a Rhombohedron K-{ loll } will be produced. See page 85, 74, 76,81,83,85,104 Fig. 219. Hexagonal. A Cross-section of a Dihexagonal Prism (ftfctO) and Pyramid (hkil) to the Primary Prism (lOlO) and Pyramid (loll) respectively, and to the Lateral Axes 74,76,81,82,91,99,104 DESCRIPTIONS OF THE PLATES. 223 PAGE Fig. 220. Hexagonal. A Secondary Prism (1120) termin- ated by Basal Pinacoids (0001). The alternate planes are shaded. If the shaded planes are suppressed and the non- shaded ones extended a Secondary Trigonal Prism will result KT^ 1120 } . See Figure 221 and page 99, 74, 76,80, 81,99, 104 PLATE X Fig. 221. Hexagonal. A Secondary Trigonal Prism KT\ 1120 } terminated by Basal Pinacoids (0001), 74, 76, 80, 99, 104 Fig. 222. Hexagonal. A simple form. A Negative Blwm- bohedron ( 0221 j> 74, 76, 87, 104 Fig. 223. Hexagonal. A simple form. A Negative Rhom- bohedron $A* or -{ 0112 } 74,76,85,87,104 Fig. 224. Hexagonal. Compound Form, showing the planes of two Positive Primary Rhoinbohedrons /c-j 1011 } , K-J1012}-, and a Negative Primary Rhombohedron H OlTl } . . . 74, 76, 87, 104 Fig. 225. Hexagonal. Compound Form showing the planes of a Positive Primary Rhombohedron { 1011 } and two Negative Primary Rhombohedrons { 0221 };{ 0112 } 74, 76, 87, 88, 104 Fig. 226. Hexagonal. Compound Form showing the planes of a Positive Primary Rhombohedron { 1011 } and a Negative Primary Rhombohedron { OlTl j- . . 74,76, 87, 104 Fig. 227. Hexagonal. A Positive Rhombohedron K-{ 4041 } terminated by a Positive Rhombohedron { 1011 }-. Cal- cite * . .-. ,\. .... .... - . .74,76,87,104 Fig. 228. Hexagonal. A Negative Rhombohedron K-{ 0221 } with its vertical edges truncated by a Positive Rhombo- hedron K-jloTl}-. Calcite 74,76,87,88,104 224 DESCRIPTIONS OF THE PLATES. PAGE Tig. 229. Hexagonal. Holohedral. A Simple Form. A Dihexagonal Pyramid (hkil) with its alternative pairs of planes shaded to show the planes extended to form the Scalenohedron K-{ hkil } the non-shaded planes are sup- pressed. See page 88 74, 76, 82, 88, 104 Fig. 230. Hexagonal. Showing a Cross-section of a Scaleno- hedron { hkil }- 74, 76, 89, 99, 104 Fig. 231. Hexagonal. Figure showing the relation of the Bhombohedron K-{ 1011 J> of the Middle Edges to a Scaleno- hedron K <{ 2131 } 74, 76, 89, 90, 104 Fig. 232. Hexagonal. A Dihexagonal Pyramid (hkil) with an inscribed Scalenohedron K-{ hkil } . 74, 76, 88, 89, 104 Fig. 233. Hexagonal. Showing the relation of a Primary Pyramid (1011) to a Primary Rhombohedron -{ loll }, 74, 76, 104 Fig. 234. Hexagonal. A Simple Form. The Dihexagonal Pyramid (hkil) with the alternate planes above and the planes below, joining them base to base, shaded. If the sets of the shaded or of the non-shaded planes are ex- tended a Tertiary Pyramid n\ hkil } can be formed. See page 92 74, 76, 82, 92, 104 Fig. 235. Orthorhombic. Simple Form. Pyramid (111) with its alternate planes shaded. If either set of alter- nate planes is extended and the other set suppressed a Sphenoid -{ 111 [- will be formed 55,56 Fig. 236. Tetragonal. Simple Form. A Primary Pyramid (111) with its alternate faces shaded. If either set of shaded or non-shaded faces are suppressed and the other set extended, a Sphenoid will be formed K-{ ill } . . . 65, 66 Fig. 237. Tetragonal. A Simple Form. A Ditetragonal Pyramid (hkl) with its alternate pairs of planes shaded. If the four alternate pairs of shaded planes or of the non- shaded planes are suppressed and the other alternate pairs DESCRIPTIONS OF THE PLATES. 225 PAGE of planes extended, a Tetragonal Scalenohedron { kkl } will be formed 66 Fig. 238. Tetragonal. Compound Form. A Ditetragonal Prism (hkQ) terminated by Basal Pinacoids (0001). Each alternate plane of the Prism is shaded. If the shaded planes are suppressed and the others extended, the result- ing form is a Tertiary Prism * \ hkQ } 67 Fig. 239. Tetragonal. Simple Form. A Ditetragonal Pyramid (hkl). If the alternate or shaded planes above and the alternate or shaded planes immediately below (or base to base) are considered suppressed and the other planes are considered extended, the resultant form is a Tertiary Pyramid ir\hkl\ 67,68 Fig. 240. Tetragonal. Compound Form showing planes of three Primary Pyramids (111,221,441); of two Second- ary Pyramids (101,201); of four Ditetragonal Pyramids (121, 421, 132, 411); of a Primary Prism (110); of a Secondary Prism (100); of a Ditetragonal Prism (210), and a Basal Pinacoid (001). Vesuvianite . * 69, 74 Fig. 241. Hexagonal. A Simple Form. A Dihexagonal Pyramid (hktl). The alternate upper and lower planes are shaded. If these shaded planes are suppressed and the others are extended, a Trapezohedron r\ hkil } will be formed. See pages 93, 94 74, 76, 82, 93, 104 Fig. 242. Hexagonal. A Dihexagonal Prism (hklO) ter- minated by Basal Pinacoids (0001). The alternate planes of the Prism are shaded. If the shaded or non-shaded planes are suppressed and the other alternate set of planes are extended, the result produced will be a Ter- tiary Prism TT 1 hkiQ } . See pages 91 , 92 . . 74, 76, 80, 81 , 91 , 104 Fig. 243. Hexagonal. Simple Form. A Secondary Pyra- mid (h'h'Zh'l) with the axes drawn in. The alternate upper and lower faces of this Pyramid are shaded. If the 226 DESCRIPTIONS OF THE PLATES. PAGE shaded or non-shaded planes are suppressed and the others extended a Secondary Rhombohedron, -{ h' h' 2h' I } will be the resulting form. See pages 96, 97. 74, 76, 82, 83, 96, 104 Fig. 244. Hexagonal. Simple Form. A Scalenohedron K] Jikil \ with its axes drawn in. The alternate lower ' and upper planes of the Scalenohedron are shaded. If either the shaded or non-shaded planes are suppressed and the other planes extended a Tertiary Rhombohedron TT/C-J hkil }> will be produced. See pages 97, 98, 74, 76, 82, 96, 104 Fig. 245. Hexagonal. A Scalenohedron { fikll } similar to Fig. 244, but the other planes are shaded. See pages 97, 98 74, 76, 89, 97, 104 PLATE XI Fig. 246, Hexagonal. Compound Form showing planes of a Dihexagonal Prism (/iJBO) and of a Basal Pinacoid (0001). The alternate pairs of planes are shaded. If these or the non- shaded pairs of planes are suppressed and the other pairs of planes extended, the form produced will be the Ditrigonal Prism KT ] hklQ } . See page 99, 74, 76,80, 81,99, 104 Fig. 247. Hexagonal. Simple Form. A Negative or Left- handed Ditrigonal Prism KT^ ikhO }> terminated by Basal Pinacoids (0001) . . 74,76,80,99,104 Fig. 248. Hexagonal. Simple Form. A Positive or Right- handed Ditetragonal Prism KT^ hkiQ }- terminated by Basal Pinacoids (OC01) 74, 76, 80, 99, 104 Fig. 249. Hexagonal. Simple Form. A Secondary Pyra- mid (h' h' 2/i I). The alternate planes above and the planes below, whose bases are coincident, are shaded. If these shaded planes are suppressed and the other planes are extended, the result forms a Secondary Trigonal Pyramid r ^ h'h'Vh'l \ . See pages 99, 100 . 74, 76, 82, 83, 100, 104 DESCRIPTIONS OF THE PLATES. 227 PAGE Fig. 250. Hexagonal. Simple Form. A Positive or Eight- handed Secondary Trigonal Pyramid KT \ h~ li- 2k- 1 }> . See pages 99, 100 74, 76, 100, 104 Fig. 251. Hexagonal. Simple Form. A Negative or Left- handed Secondary Trigonal Pyramid KT { 2h' /F/FZ } . See pages 99, 100 74, 76, 100, 104 Fig. 252. Hexagonal. Simple Form. Negative Scalenohe- dron K -{ ikhl } with the alternate upper and lower planes joined base to base, shaded. If the shaded planes are suppressed and the non-shaded ones extended, or vice versa a Negative Bight or Left-handed Trigonal Trapezohedron is produced KT -{ Mhl } . See page 100 . 74, 76, 89, 90, 94, 100, 104 Fig. 253. Hexagonal. Simple Form. A Positive Scaleno- hedron { 2131 }- with the alternate upper and lower planes, joined base to base, shaded. If the shaded planes are suppressed and the non-shaded ones extended, or vice versa a Positive Right- or Left-handed Trigonal Trapezo- hedron K.T \ 2131 } is formed. See page 100, 74, 76, 89, 90, 94, 100, 104 Fig. 254. Hexagonal. A Compound Form showing the planes of a Primary Prism (loTo) terminated by the planes of a Primary Pyramid (lOfl). Quartz . . . 74, 76, 81, 83, 104 Fig. 255. Hexagonal. Compound Form showing planes of a Primary Prism (1010), of a Primary Pyramid (1011), and of a Dihexagonal Pyramid (h- lv 2&- I) . 74, 76, 81, 83, 104 Fig. 256. Hexagonal. Compound Form, showing the planes of a Primary Pyramid (1011) with its solid lateral angles truncated by the planes of a Secondary Prism (1120) 74,76,81,83,104 Fig. 257. Hexagonal. Compound Form showing the planes of a Primary Pyramid ( lOTl ) with its lateral solid angles replaced by the planes of a Dihexagonal Prism (ABO), 74,86,81,83,104 228 DESCRIPTIONS OF THE PLATES. PAGE Fig. 258. Hexagonal. Compound Form showing the planes of a Primary Pyramid (loll) with its lateral solid angles replaced by the planes of a Secondary Pyramid (1122), 74, 76, 81, 83, 104 Fig. 259. Hexagonal. Compound Form showing the planes of a Primary Pyramid (loll) with its lateral solid angles replaced by the planes of a Dihexagonal Pyramid (hM), 74,76, 81-83,104 Fig. 260. Hexagonal. Compound Form showing the planes of a Primary Pyramid (loTl) with its lateral edges beveled by a second Primary Pyramid (htihl) . . . .74, 76, 81, 83, 104 Fig. 261. Hexagonal. Compound Form showing the planes of a Primary Pyramid (loTl) with its vertical edges trun- cated by the planes of a Secondary Pyramid (1122), 74, 76, 81-83, 104 Fig. 262. Hexagonal. Compound Form showing a Primary Pyramid (loTl) with its vertical edges beveled by the planes of a Dihexagonal Pyramid (2133) 74, 76, 81-83, 104 Fig. 263. Hexagonal. Compound Form composed of a Primary Pyramid (1011) with its vertical solid angles truncated by Basal Planes (0001) . . . .74,76,80,81,83,104 Fig. 264. Hexagonal. A Primary Pyramid (loTl) with its vertical solid angles replaced by a second Primary Pyra- mid (hOhl) 74,76,81,83,104 Fig. 265. Hexagonal. A Primary Pyramid (loll) with its vertical solid angles replaced by a Secondary Pyramid (1122) 74, 76, 81, 83, 104 Fig. 266. Hexagonal. A Primary Pyramid (loll) with its -vertical solid angles replaced by the planes of a Dihexa- gonal Pyramid (2133) 74, 76, 81-83, 104 Fig. 267. Hexagonal. A Secondary Pyramid (1122) with its vertical solid angles replaced by the planes of a Primary Bhombohedron K -{ hOhl }- 74, 76, 82, 83, 104 DESCRIPTIONS OF THE PLATES. 229 PAGE Fig. 268. Hexagonal. Compound Form composed of a Posi- tive Rhombohedron K \ lofl }> joined to a Negative Rhom- ' bohedron ^ oiTl \ . United they form a Primary Pyra- mid (lOll) . . . . \ . i . .74,76,83,104 Fig. 269. Hexagonal. A Primary Rhombohedron *{ 1011 } with its vertical solid angles truncated by a Basal Pina- coid (0001) .74,76,80,104 PLATE XII Fig. 270. Hexagonal. A Positive Rhombohedron K-{ 2021 }- with its vertical solid angles replaced by the planes of another Positive Rhombohedron { 0332 J- ... 74, 76, 87, 104 Fig. 271. Hexagonal. A Positive Rhombohedron { 2021 }- with its vertical solid angles replaced by the planes of a Negative Rhombohedron *-{ Qhhl } 74, 76, 87, 104 Fig. 272. Hexagonal. A Positive Rhombohedrpn -{ idll } with its vertical solid angles replaced by Basal Planes (0001) 74, 76, 87, 104 Fig. 273. Hexagonal. A Positive Rhombohedron { 10U } with its lateral solid angles replaced by the planes of a Scalenohedron *{ hkil \ . . . . . . 74, 76, 104 Fig. 274. Hexagonal. A Positive Rhombohedron -{ lOll }- with its lateral solid angles replaced by the planes of a Negative Rhombohedron -{ Qhhl } ....... .74,76,104 Fig. 275. Hexagonal. A Positive Rhombohedron { loll }- with its solid lateral angles replaced by the planes of a Negative Rhombohedron K -( 0221 } and its terminal solid angles truncated by Basal Pinacoids (0001) . 74, 76, 80, 87, 104 Fig. 276. Hexagonal. A Positive Rhombohedron { hQhl } modified by the planes of a Secondary Pyramid *\h'h-2h'l\ 74,76,82,87,104 Fig. 277. Hexagonal. A Positive Rhombohedron *\ 1011 } modified by the planes of a Secondary Pyramid K\ 2243 } , 230 DESCRIPTIONS OF THE PLATES. PAGE and those of a Positive Rhombohedron -{ 10U } . Hema- tite 74,76,87,104 Fig. 278. Hexagonal. A Secondary Prism (1120) termin- ated by the planes of a Secondary Rhombohedron K -\ 0221 } . Dioptase 74,76^81,104 Fig. 279. Hexagonal. A Positive Rhombohedron { 1011 } with its lateral edges truncated by a Secondary Hexa- gonal Prism (1120) 74,76,81,104 Fig. 280. Hexagonal. A Positive Rhombohedron { 1011 }- with its lateral solid angles replaced by the planes of a Negative Rhombohedron { Olll } , and its lateral edges by the planes of a Secondary Prism (1120) . 74, 76, 8K, 87, 104 Fig. 281. Hexagonal. A Positive Rhombohedron { 20~21 J- with its terminal solid angles replaced by the planes of a Scalenohedron /<*! hk\l\ 74,76,104 Fig. 282. Hexagonal. A Positive Rhombohedron .\ 16- 0- 16- 1 \ with its terminal solid angles replaced by the planes of a Negative Rhombohedron K.\ 0112 \. Calcite 74, 76, 104 Fig. 283. Hexagonal. A Primary Prism (10TO) termin- ated by the planes of a Negative Rhombohedron *\ 0112 \. Calcite 74,76,81,104 Fig. 284. Hexagonal. Hemimorphic Form showing planes of a Primary Trigonal Prism KT\ 1010 \ and a Secondary Prism (1120). It is terminated at the over end by a Posi- tive Primary Rhombohedron K-{ 1011 }-,and a Negative Primary Rhombohedron { OH2 } which truncates the edges of the Positive Rhombohedron. The under end is formed by a Positive Primary Rhombohedron { 1011 } , and a Negative Rhombohedron -j 0221 j- . Tourmaline, 74, 76, 104 Fig . 285. Hexagonal. A Positive Rhombohedron K { 2021 } with its vertical or terminal edges beveled by the planes of a Scalenohedron K \h~kil\- 74,76,104 DESCRIPTIONS OF THE PLATES. 231 PAGE Fig. 286. Hexagonal. .A Compound Form showing the planes of a Positive Rhombohedron -j 1011 } and of a Negative Rhombohedron K\ 0112 } . Calcite . . 74, 76, 87, 104 Fig. 287. Hexagonal. A Scalenohedron { 2131 \ with its lateral angles replaced by the planes of a Primary Pyra- mid (4041) 74, 76, 89, 104 Fig. 288. Hexagonal. A Scalenohedron n\ 2131 } with its lateral solid angles replaced by the planes of a Dihexa- gonal Pyramid (hkil) . . . . 74,76,89,104 Fig. 289. Hexagonal. A Scalenohedron \ 2131 \ with its terminal solid angles truncated by Basal Pinacoids (0001) 74,76,81,89,104 Fig. 290. Hexagonal. A Scalenohedron K \ 2131 \ with its terminal solid angles replaced by another Scalenohedron K-J2134}- 74,76,89,104 Fig. 291. Hexagonal. A Scalenohedron K\ 2131 \ with its terminal solid angles replaced by a Positive Rhombohe- dron K\ 20"21 \ 74, 76, 89, 104 Fig. 292. Hexagonal. A Scalenohedron K \ 2131 \- with its terminal solid angles replaced by another Scalenohedron *\ 4153 }- 74, 76,89, 104 Fig. 293. Hexagonal. A Scalenohedron -{ 2131 } with its alternate terminal edges truncated by the planes of a Ehombohedron { 15- 5- 20- 4 } 74, 76, 89, 104 Fig. 294. Hexagonal. A Scalenohedron { 2131 } with its alternate terminal edges truncated by a Negative Rhom- bohedron ^0221 } 74,76,89,104 Fig. 295. Hexagonal. A Scalenohedron <{ 2131 }> with its lateral zigzag edges beveled by the planes of another Scalenohedron K \ 11- 1- 12- 10 } 74, 76, 89, 104 Fig. 296. Hexagonal. A Scalenohedron { 2131 } with its alternate vertical edges beveled by the planes of a second Scalenohedron <{ 6lT4 }- 74, 76, 89, 104 232 DESCRIPTIONS OF THE PLATES. PAGB Fig. 297. Hexagonal. A Scalenohedron { 2131 } with its alternate vertical edges beveled by the planes of a second Scalenohedron <{ 8- 4- 12- 5 j- 74, 76, 89, 104 PLATE XIII Fig. 298. Hexagonal. A Scalenohedron * { 2131 } with its lateral edges truncated by a Secondary Prism (1120). Calcite 74,76,81,89,104 Fig. 299. Hexagonal. A Scalenohedron { 2131 } with its lateral edges truncated by a Secondary Prism (1120). This form shows a greater development of the prismatic planes than does Fig. 298. Calcite . . 74, 76, 81^89, 104 Fig. 300. Hexagonal. A Positive Scalenohedron *\ 2131 } with its lateral solid angles replaced by another Positive Scalenohedron -{ 4041 }-. Calcite 74, 76, 89, 104 Fig. 301. Hexagonal. A Positive Scalenohedron *-{ 2131 } with its terminal solid angles replaced by a Positive Rhombohedron -{ loll }-. Calcite 74,76^,89,104 Fig. 302. Hexagonal. A Positive Scalenohedron { 2131 } with its lateral solid angles replaced by a Primary Prism ( 1010) and with its terminal solid angles replaced by the planes of a Positive Scalenohedron -j 2134 } . Calcite, 74, 76, 81, 89, 104 Fig. 303. Hexagonal. A Positive Scalenohedron <{ 2131 } with its alternate vertical edges truncated by the planes of a Negative Rhombohedron *{ 0221 } , its lateral solid angles replaced by the planes of a Primary Prism (1010) and its terminal solid angles replaced by the planes of a Positive Rhombohedron K-{ 1011 } . Calcite, 74, 76, 81, 89, 104 Fig. 804. Hexagonal. Compound Form showing the planes of two Positive Scalenohedrons K -{ 2131 } and K { 3251 } ; of two Positive Rhombohedrons K ^ 1010 1- and ^ 4041 } , and a Primary Prism (lOlO). Calcite . . .74,76,81,89,104 DESCRIPTIONS OF THE PLATES. 233 PAGE Fig. 305. Hexagonal. Compound Form showing the planes of a Negative Scalenohedron /c-{ 1341}*; of a Positive Scalenohedron + #3 or K-{ 2131 } , with its ends terminated by the planes of a Positive Rhombohedron *{ lOfl }- ; and of a Negative Rhombohedron <{ 0221 [-. Calcite, 74, 76, 89, 104 Fig. 306. Hexagonal. A Secondary Pyramid (1122) with its lateral solid angles replaced by the planes of a Positive Rhombohedron -{ 0332 } 74,76,82,104 Fig. 307. Hexagonal. A Primary Prism (loTo) terminated by the planes of a Positive Rhombohedron K-{ loll } and a Negative Rhombohedron *-j OlTl }- ... 74, 76, 81-83, 87, 104 Fig. 308. Hexagonal. A Primary Prism (loTo) terminated by a Positive Rhombohedron K-{ loll } and a Negative Rhombohedron K -{ OlTl }- , and its lateral solid angles re- placed by the planes of a Secondary Pyramid (1121). Quartz ... .74,76,81,83,100,104 Fig.' 309. Hexagonal. A Compound Form showing the planes of a Primary Prism (1010); of a Positive and a Negative Rhombohedron -J loTl }-,*-{ OlFl } ; and of two Trigonal Trapezohedrons KT-{ 5161 }- and -{ 1121 }-. Quartz 74,76,81,83,87,100,104 Fig. 310. Hexagonal. Compound Form showing the planes of a Primary Prism (1010); of two Positive Rhom- bohedrons -{ loll }- and -{ 3031 }- ; of a Negative Rhom- bohedron K \ 0111 }-, and two Trigonal Trapezohedrons KT\ 5l"61 \ , and KT\ 1121 } . Quartz, 74, 76, 81, 83, 87, 100, 104 Fig. 311. Hexagonal. Compound Form showing the planes of Primary Prism (1010); of a Positive Rhombo- hedron K-{ 1011 }; of a Negative Rhombohedron -{ 0111 }; and of two Trigonal Trapezohedrons KT-{ 1121 }- and Kr-15161}-. Quartz 74,76,81,83,87,100,104 Fig. 312. Hexagonal. Compound Form showing the planes of a Primary Prism (1010); of two Positive Rhombo- 234 DESCRIPTIONS OF THE PLATES. PAGE hedrons { lofl }-,:-{ 5051 } ; of a Negative Ilhombohedron K-jOlTl}-; two Trigonal Trapezohedrons KT-{ 1121 }-, *r-{516U. Quartz . . .74,76,81,83,87,100,104 Fig. 313. Hexagonal. A Compound Form showing the planes of a Primary Prism ( oo p or 1010); of two Rhom- bohedrons R or K\ loll }-, 4 E or *{ 4041 }- and two Scalenohedrons E z or { 2131 }- and J? 5 or { 3251 }-. Caleite 74, 76, 81, 83, 104 Fig. 314. Hexagonal. Compound Form showing planes of a Primary Prism (1010); of a Positive Rhombohedron E or { 1011 }; of three Negative Rhombohedrons -\ E or K-{ OlT2 }- , -4/5 J? or { 0445 }- , -2 J? or -{ 0221 }- , and of two Scalenohedrons / 3 or -{ 2131 }-, i J? 3 or /c^{ 2134 }-. Caleite 74, 76,81,83,87,104 Fig. 315. Hexagonal. A Primary Pyramid (loll) with its vertical or terminal solid angles truncated by Basal Pina- coids (0001). Apatite 74,76,80,81,83,104 Fig. 316. Hexagonal. Compound Form showing planes of a Primary Prism (1010); of a Primary Pyramid (loll); and of a Basal Pinacoid (0001). Apatite. 74,76,80,81,83,104 Fig. 317. Hexagonal. Compound Form showing planes of a Primary Prism (lOlb); of a Secondary Pyramid (2 P 2 or 1121); and of a Basal Pinacoid (0001). Apatite. 74, 76, 80-83, 104 Fig. 318. Hexagonal. Compound Form showing planes of a Primary Prism (10lO); of a Secondary Prism (1120); of a Primary Pyramid (loll); and one of a Basal Pinacoid (0001). Apatite 74,76,80,81,83,104 Fig. 319. Hexagonal. Compound Form showing planes of a Primary Prism (lolo); of a Secondary Prism (1120); of two Primary Pyramids (loTl), (2021); two Secondary Pyramids (P 2 or 1122, 1121); and a plane of a Basal Pina- coid (0001). Apatite .74,76,80-83,104 DESCRIPTIONS OF THE PLATES. 235 PAGE PLATE XIV Fig. 320. Hexagonal. Compound Form showing the planes of a Secondary Prism (1120); of a Positive Rhombohe- dron (loTl); of a Secondary Pyramid (2243), and of a Basal Pinacoid (0001). Corundum, ... 74, 76, 80, 81, 83, 104 Fig. 321. Hexagonal. Compound Form showing the plane of a Primary Prism (1010); of the two Primary Pyramids (P or lOll, 2P or 2021); of a Secondary Pyramid (2P2 or 1121); of a Dihexagonal Pyramid (3P3/2 or 2131), and one of a Basal Pinacoid (0001). Beryl ... 74, 76, 80, 83, 104 Fig. 322. Hexagonal. Compound Form showing the planes of a Primary Prism (1010); a Secondary Prism (1120); a Tertiary Prism (2130); two Primary Pyramids (loll, 2021); two Secondary Pyramids (1122, 1121); a Tertiary Pyramid (2131), and a Basal Pinacoid (0001 ), 74, 76, 80-83, 104 Fig. 323. Hexagonal. Compound form showing the planes of a Primary Prism (1010); a Secondary Prism (1120); three Primary Pyramids (loTl, 10l2, 2021); three Second- ary Pyramids (1121, 1122, 2241), and a Basal Pinacoid (0001) 74, 76, 80, 103, 104 Fig. 324. Hexagonal. Hemimorphic. Tourmaline Type. A Compound Form showing the planes of a Secondary Prism (1120); a Primary Trigonal Prism (lolO); a Pri- mary Rhombohedron { 1011 } , and a Secondary Rhom- bohedron ,{ OU2 } 74,76,80,103,104 Fig. 325. Hexagonal. Simple Form. A Ditrigonal Pyra- mid { hkil \ ... . ,. . .... .., f > 95, 104 Fig. 326. Hexagonal. Simple Form. A Dihexagonal Pyra- mid (hkll) 95, 104 Fig. 327. Hexagonal. Compound Form. A Hemimorphic Form of the Periodate Type showing the planes of a Positive Primary Trigonal Pyramid KT^ loTl } ; a Nega- tive Primary Trigonal Pyramid KT ^ 0221 } ; a. Negative Secondary Trigonal Pyramid KT ] OlT2 } , and a Tertiary Trigonal Pyramid Kr^54i9 j- 104 236 DESCRIPTIONS OF THE PLATES. PAGE Tig. 328. Isometric. Simple Form. Hexahedron or Cube (100) 123, 126 Fig. 329. Isometric. Simple Form. Dodecahedron (110), 123, 127 Fig. 330. Isometric. Simple Form. Tetrakis Hexahedron (210) 123, 127 Fig. 331. Isometric. Simple Form. Trigonal Triakis Octa- hedron (221) 123, 129 Fig. 332. Isometric. Simple Form. Tetragonal Triakis Octahedron (211)'.- 123,129 Fig. 333. Isometric. Simple Form. Tetragonal Triakis Octahedron (311) . 123, 129 Fig. 334. Isometric. Simple Form. Hexakis Octahedron (312) 123, 130 Fig. 335. Isometric. Simple Form. Hexakis Octahedron (421) 123, 130 Fig. 336. Isometric. Simple Form. Cube (100) showing the Cubic or Crystallographic Axes (a) and the Octahe- dral Axes (6) drawn in 123, 126, 131 Fig. 337. Isometric. Simple Form. Cube (100) showing the Dodecahedral Axes (c) drawn in 123, 131 Fig. 338. Isometric. Simple Form. Octahedron (111) with the alternate planes lined to show the derivation of the Tetrahedron <{ 111 } . . 123,128,131,132 Fig. 339. Isometric. Simple Form. Tetrahedron *{ 111 }> showing the inscribed Octahedron (111) from which it was derived . . 123, 128, 131, 132 PLATE XV Fig. 340. Isometric. Simple Form. Positive Tetrahedron { HI } 123, 131, 132 Fig. 341. Isometric. Simple Form. Negative Tetrahe- dron /c<{ ill } 123, 131, 132 Fig. 342. Isometric. Simple Form. Trigonal Triakis Oc- DESCRIPTIONS OF THE PLATES. 237 PAGE tahedron (332) with its alternate sets of three planes lined to show the method of derivation of the Tetragonal Triakis Tetrahedron <{ hhl\ . 123,131,133 Fig. 343. Isometric, Simple Form. Tetragonal Triakis Tetrahedron K \ hhl \ with the Trigonal Triakis Octahe- dron (hhl], from which it is derived, inscribed . . 123, 131, 133 Fig. 344. Isometric. Simple Form. Positive Tetragonal Triakis Tetrahedron *\ 332 \ 123,131,133 Fig. 345. Isometric. Simple Form. Negative Tetragonal Triakis Tetrahedron *\ 332 \ . 123,131,133 Fig. 340. Isometric. Simple Form. Tetragonal Triakis Octahedron (211) with its alternate sets of three planes lined to show the method of derivation of the Trigonal Triakis Tetrahedron { hll \ 123,131,134 Fig. 347. Isometric. Simple Form. Trigonal Triakis Tetra- hedron n{hll\ with the Tetragonal Triakis Octahedron (hll), from which it is derived, inscribed 123, 131, 134 Fig. 348. Isometric. Simple Form. Positive Trigonal Triakis Tetrahedron * \2\l\ 123,131,134 Fig. 349. Isometric. Simple Form. Negative Trigonal Triakis Tetrahedron K\ 211 } 123,131,134 Fig. 350. Isometric. Simple Form. Hexakis Octahedron (hkl) with its alternate sets of six planes lined to show the derivation of the Hexakis Tetrahedron K\ hkl }> .123, 131, 134 Fig. 351. Isometric. Simple Form. Hexakis Tetrahedron K\ hkl } with the Hexakis Octahedron (tiki), from which it is derived, inscribed .-.;.. 123,131,134 Fig. 352. Isometric. Simple Form. Positive Hexakis Tetrahedron *\ 521 \ ! 123,131,134 Fig. 353. Isometric. Simple Form. Negative Hexakis Tetrahedron K with an inscribed Tetrakis Hexahedron (MO), from which it is derived 123,136 Fig. 356. Isometric. Simple Form. Positive Pentagonal Dodecahedron * -j hkQ j> 123, 135-137 Fig. 357. Isometric. Simple Form. Negative Pentagonal Dodecahedron K\ khQ } 123, 135-137 Fig. 358. Isometric. Simple Form. Positive Pentagonal Dodecahedron * 1 /ifcO } 123,135,136 Fig. 359. Isometric. Simple -Form. Positive Pentagonal Dodecahedron Tr-j/ifcO }> 123,135,136 Fig. 360. Isometric. Simple Form. Hexakis Octahedron (hkl). One half of its planes are lined to show the method of derivation of the Dyakis Dodecahedron HfofeZ}- 123,137 Fig. 361. Isometric. Simple Form. Dyakis Dodecahedron TT ] likl \ with an inscribed Hexakis Octahedron (hkl), from which it is derived 123,137 Fig. 362. Isometric. Simple Form. Positive Dyakis Dode- cahedron K\ 321 } 123, 137 Fig. 363. Isometric. Simple Form. Negative Dyakis Do- decahedron TT \ 23i\. 123, 137 Fig. 364. Isometric. Simple Form. Positive Dyakis Do- decahedron TT ^ 421 } 123, 137 Fig. 365. Isometric. Simple Form. Hexakis Octahedron (hlcl) with its alternate planes lined to indicate the method by which the Pentagonal Icositetrahedron y \ hkl \ is de- rived from it . 123, 138 PLATE XVI Fig. 366. Isometric. Simple Form. Positive Pentagonal Icositetrahedron y \ hkl \ 123,138 Fig. 367. Isometric. Simple Form. Negative Pentagonal Icositetrahedron y \ Ikh }- 123,138 DESCRIPTIONS OP THE PLATES. 239 PAGE Fig. 368. Isometric. Simple Form. Hexakis Octahedron (hkl) with each alternate plane in each alternate octant lined to show the method by which the Tetrahedral Pent- agonal Dodecahedron KT-J hkl }- is derived from it. See page 140 123 Fig. 369. Isometric. Simple Form. Positive Tetrahedral Pentagonal Dodecahedron KT-{ hkl } 123,141 Fig. 370. Isometric. Simple Form. Negative Tetrahedral Pentagonal Dodecahedron KT-{ Ikh } 123,141 Fig. 371. Isometric. Compound Form. An Octahedron (111) truncating the solid angles of an inscribed Cube (100) 123, 141 Fig. 372. Isometric. Compound Form. A Cube (100) with its solid angles truncated by the planes of an Octahedron (111) 123, 141 Fig. 373. Isometric. Compound Form. A Cube (100) trun- cating the solid angles of the inscribed Octahedron (111), 123, 141 Fig. 374. Isometric. - Compound Form. An Octahedron (111) with its solid angles truncated by the Cube planes (100) 123,141 Fig. 375. Isometric. A Cube (100) with its solid angles truncated by the planes of an Octahedron (111). In this case where the planes of both forms are equally developed the form is commonly called a Cubo-Octahedron . . 123, 141 Fig. 376. Isometric. Compound Form. A Dodecahedron (110) with its terminal solid angles truncated by the planes of a Cube (100) 123,141 Fig. 377. Isometric. Compound Form. A Cube (100) with its edges truncated by the planes of a Dodecahedron (110) 123, 141 Fig. 378. Isometric. Compound Form. An Octahedron (111) with its edges truncated by the planes of a Dodeca- hedron (110) 123, 141 240 DESCRIPTIONS OF THE PLATES. PAGE Fig. 379. Isometric. Compound Form. A Dodecahedron (110) with itstriedral solid angles truncated by the planes of an Octahedron (111) 123,141 Fig. 380. Isometric. Compound Form. A Cube (100) with its solid angles truncated by the planes of an Octahedron (111) and its edges truncated by the planes of a Dodecahe- dron (110) 123, 141 Fig. 381. Isometric. Compound Form. A Cube (100) with its edges beveled by the planes of a Tetrakis Hexahedron (hko) 123, 141 Fig. 382. Isometric. Compound Form. An Octahedron (111) with its solid angles replaced by the planes of a Tetrakis Hexahedron (hko) 123, 141 Fig. 383. Isometric. Compound Form. A Dodecahedron (110) with its terminal solid angles replaced by the planes of a Tetrakis Hexahedron (hko) 123, 141 Fig. 384. Isometric. Compound Form. A Cube (100) with its solid angles replaced by the planes of a Trigonal Triakis Octahedron (hhl) 123, 141 Fig. 385. Isometric. Compound Form. A Dodecahedron (110) with its solid triedral angles modified by the planes of a Trigonal Triakis Octahedron (hhl) 123, 141 PLATE XVII Fig. 386. -Isometric. Compound Form. An Octahedron (111) with its solid angtes replaced by the planes of a Tetragonal Triakis Octahedron (hll) 123, 141 Fig. 387. Isometric. -Compound Form. A Cube with its solid angles modified by the planes of a Tetragonal Triakis Octahedron (211) 123, 126, 141 Fig. 388. Isometric. Compound Form. A Dodecahedron (110) with its edges truncated by the planes of a Tetra- gonal Triakis Octahedron (211) 123,141 DESCRIPTIONS OF THE PLATES. 241 PAGE Fig. 389. Isometric. Compound Form. A Dodecahedron (110) with its terminal solid angles replaced by the planes of a Tetragonal Triakis Octahedron (/iZZ) 123, 141 Fig. 390. Isometric. Compound Form. A Dodecahedron (110) with its triedral solid angles replaced by the planes of a Tetragonal Triakis Octahedron (Ml) 123, 141 Fig. 391. Isometric. Compound Form. A Dodecahedron (110) with its terminal solid angles replaced by the planes of a Hexakis Octahedron (hkl) 123, 141 Fig. 392. Isometric. Compound Form. A Dodecahedron (110) with its triedral angles replaced by the planes of a Hexakis Octahedron (hkl) 123, 141 Fig. 393. Isometric. Compound Form. An Octahedron (111) with its solid angles replaced by the planes of a Hexakis Octahedron (321) 123, 141 Fig. 394. Isometric. Compound Form. A Cube (100) with its solid angles replaced by the planes of a Hexakis Octa- hedron (421) 123, 141 Fig. 395. Isometric. Compound Form. An Octahedron (111) with its solid angles truncated by the planes of a Cube (100), and modified by the planes of a Tetragonal Triakis Octahedron (211) 123, 141 Fig. 396. Isometric. Compound Form. A Dodecahedron (110) with its triedral solid angles truncated by the planes of an Octahedron (111), and its terminal solid angles replaced by the planes of a Tetragonal Triakis Octahedron (311) 123, 141 Fig. 397. Isometric. Compound Form. A Dodecahedron (110) with its triedral angles truncated by the planes of an Octahedron (111), and its edges beveled by the planes of a Tetragonal Triakis Octahedron (211) 123,141 Fig. 398. Isometric. Compound Form. An Octahedron (111) with its edges truncated by the planes of a Dodeca- hedron (110), and its solid angles replaced by the planes 242 DESCRIPTIONS OF THE PLATES. PAGE of a Cube (100), and by the planes of a Tetragonal Triakis Octahedron (211) 123.141 Tig. 399. Isometric. Compound Form. A Tetragonal Triakis Octahedron (211) modified by the planes of a Cube (100); the planes of a Dodecahedron (110), and the planes of an Octahedron (111) . 123,141 Fig. 400. Isometric. Compound Form. An Octahedron (111) modified by the planes of a Dodecahedron (110); of a Tetragonal Triakis Octahedron (hll)-, a Tetrakis Hexa- hedron (M-0), and a Hexakis Octahedron (hkl) .... 123, 141 IFig. 401. Isometric. Compound Form. A Positive Tetra- hedron K-{ 111 }- modified by, a Negative Tetrahedron KflTl 1- 123,141 JFig. 402. Isometric. Compound Form. A Positive Tetra- hedron K-{ 111 [- modified by the planes of a Negative Tetrahedron -{ 111 }- . . . . 123, 141 JTig. 403. Isometric. Compound Form. A Positive Tetra- hedron K-{ ill } with its edges truncated by the planes of a Cube (100) 123, 141 Pig. 404. Isometric. Compound Form. A Positive Tetra- hedron /c-j 111 }- modified by the planes of a Dodecahedron K-l ifo^ 123,141 Fig. 405. Isometric. Compound Form. A Positive Tetra- hedron K-{ ill }- with its edges beveled by the planes of a Cube (100) and its solid angles replaced by the planes of a Dodecahedron -{ 110 }- 123,141 Fig. 406. Isometric. Compound Form. A Positive Tetra- hedron K-{ ill }. with its edges truncated by the planes of a Cube (100), and its solid angles replaced by the planes of a Negative Tetrahedron { ifl } and the planes of a Dodecahedron -{ 110 } 123,141 Fig. 407. Isometric. ' Compound Form. A Positive Tetra- hedron /c-j ill } with its edges beveled by the planes of a Trigonal Triakis Tetrahedron K -j 211 }- 123,141 DESCRIPTIONS OF THE PLATES. 243 PAGE Tig. 408. Isometric. Compound Form. A Positive Tetra- hedron *-{ 111 } with its edges beveled by the planes of a Trigonal Triakis Tetrahedron -{211}-, and its solid angles replaced by the planes of a Dodecahedron *{ 110 }- . 123, 141 Tig. 409. Isometric. Compound Form. A Positive Tetra- hedron K-{ ill }- with its edges beveled by the planes of a Trigonal Triakis Tetrahedron -{ 211 } and its solid angles replaced by the planes of a Dodecahedron *\ 110 } , and the planes of a Negative Trigonal Tetrahedron *\ 211 \ , 123, 141 Fig. 410. Isometric. Compound Form. A Dodecahedron (110) with its terminal angles truncated by the planes of a Cube (100) and its alternate Triedral angles truncated by the planes of a Tetrahedron *{ 111 } 123,141 Fig. 411. Compound Form. A Tetrahedron K\ 111 \ modi- fied by the planes of a Trigonal Triakis Tetrahedron *\Ul\ . 123,141 Fig. 412. Isometric. Compound Form. A Cube with its alternate solid angles truncated by the planes of a Tetra- hedron K\\\\\ 123, 141 Fig. 413. Isometric. Compound Form. A Cube (100) with its edges truncated by the planes of a Dodecahedron (110) and its angles alternately replaced by the planes of a Positive Tetrahedron K\ ill }- , and of a Negative Tetra- hedron *\U\\ 123, 141 Fig. 414. Isometric. Compound Form. A Cube (100) with its edges truncated by the planes of a Dodecahedron (110) and its solid angles alternately replaced by the planes of a Positive Tetrahedron K\ ill }- and a Hexakis Tetra- hedron K { 531 }- , and by a Negative Tetrahedron K { ill } , 123, 141 Fig. 415. Isometric. Compound Form. A Dodecahedron (110) with its alternate edges modified by the planes of a Negative Trigonal Triakis Tetrahedron -{ Jill } . . . 123, 141 244 DESCRIPTIONS OF THE PLATES. PLATE XVIII Fig. 416. Isometric. Compound Form. A Dodecahedron (110) with its terminal solid angles modified by the planes of a Hexakis Tetrahedron K -\hkl\- ..... 123, 141 Fig. 417. Isometric. Compound Form. A Dodecahedron (110) modified by the planes of a Trigonal Triakis Tetra- hedron { 211 }- ................... 123, 141 Fig. 418. Isometric. Compound Form. A Dodecahedron (110) modified by the planes of a Hexakis Tetrahedron K^hJcl}- ....................... 123, 141 Fig. 419. Isometric. Compound Form. A Dodecahedron (110) modified by the planes of a Trigonal Triakis Tetra- hedron K\hll\ . . ................. 123, 141 Fig. 420. Isometric. Compound Form. A Dodecahedron (110) modified by the planes of a Trigonal Triakis Tetra- hedron K 1 hll \ ................... 123,143 Fig. 421. Isometric. Compound Form. A Dodecahedron (110) modified by the Tetragonal Triakis Octahedron * \hhl\- ....................... 123, 141 Fig. 422. Isometric. Compound Form. A Dodecahedron (110) with its terminal solid angles truncated by the planes of a Cube (100) and its alternate Trigonal Angles truncated by the planes of a Tetrahedron n\ 111 }- . . 123, 141 Fig. 423. Isometric. Compound Form. A Positive Tri- gonal Triakis Tetrahedron \ hll \ modified by the planes of a Cube (100); of a Negative Trigonal Triakis Tetra- hedron K\ Jill } ; of a Tetrahedron /c-| 111 } ; of a Dodeca- hedron (110); of a Tetrakis Hexahedron (/ifcO); and of a Negative Hexakis Tetrahedron K ^ h~kl } ....... 123,141 Fig. 424. Isometric. Compound Form. A Pentagonal Dodecahedron JT-{ 120 } modified by the planes of a Cube (100) ........................ ]23, 141 Fig. 425. Isometric. Compound Form. A Cube (100) with DESCRIPTIONS OF THE PLATES. 245 PAGE its edges truncated by the planes of a Pentagonal Dodeca- hedron TT { 120 } , and its solid angles truncated by the planes of an Octahedron (111) 123,141 Pig. 426. Isometric. Compound Form. A Cube (100) modified by the planes of an Octahedron (111), and of a Pentagonal Dodecahedron TT ^ 120 j- 123,141 Fig. 427. Isometric. Compound Form. An Octahedron (111) with its solid angles modified by the planes of a Pentagonal Dodecahedron *-{ 120 }- 123 y 141 Fig. 428. Isometric. Compound Form. A Pentagonal Dodecahedron K\ 120 \ modified by the planes of an Octahedron (111) 123, 141 Fig. 429. Isometric. Compound Form. A Pentagonal Dodecahedron TT{ 120 } . modified by the planes of an Octahedron (111) 123, 141 Fig. 430. Isometric. Compound Form. A Pentagonal Dodecahedron * \ 120 J- modified by the planes of a Penta- gonal Dodecahedron * \ 320 \ 123, 141 Fig. 431. Isometric. Compound Form. A Cube (100) with its solid angles modified .by the planes of a Dyakis Dode- cahedron TT \ likl \ 123,141 Fig. 432. Isometric. Compound Form. Pentagonal Dode- cahedron TT \ 120 \ . modified by .the planes of a Dyakis Dodecahedron K\ 142 \ 123,141 Fig. 433. Isometric. Compound Form. A Pentagonal Dodecahedron K\ 120 \ modified by the planes of a Tetra- gonal Triakis Octahedron (211) 123,141 Fig. 434. Isometric. Compound Form. A Pentagonal Dodecahedron w \ 120 \ modified by the planes of a Dyakis Dodecahedron *\ 123 \ 123,141 Fig. 435. Isometric. Compound Form. A Pentagonal Dodecahedron w \ 120 } modified by the planes of a Dyakis Dodecahedron TT \ 123 \ 123,141 Fig. 436. Isometric. Compound Form. A Pentagonal 246 DESCRIPTIONS OF THE PLATES. PAGE Dodecahedron K\ 120 \ modified by the planes of another Pentagonal Dodecahedron *\ 130 }- 123,141 Fig. 437. Isometric. Compound Form. A Positive Penta- gonal Dodecahedron K\ 120 } modified by the planes of a Negative Pentagonal Dodecahedron K \ khQ } . . . .123,141 Fig. 438. Isometric. Compound Form. A Dyakis Dode- cahedron 7r<( 132 }> modified by the planes of a Cube (100). 123, 141 Fig. 439. Isometric. Compound Form. A Dyakis Dode- cahedron TT -{ 421 } modified by the planes of a Pentagonal Dodecahedron TT<| 210 }- 123,141 Fig. 440. Isometric. Compound Form. An Octahedron (111), with its solid angles modified by the planes of a Dyakis Dodecahedron *\ 123 \ 123,141 Fig. 441. Isometric. Compound Form. A Negative Penta- gonal Dodecahedron K \ 102 \ modified by the planes of a Negative Dodecahedron * \ 123 \ 123,141 Fig. 442. Isometric. Compound Form. A Pentagonal Dodecahedron K \ 120 \ modified by the planes of a Dyakis Dodecahedron * \ 142 \ 123,141 Fig. 443. Isometric. Compound Form. A Pentagonal Dodecahedron K \ hkQ [ modified by the planes of a Dyakis Dodecahedron TT { hkl }- 123,141 Fig. 444. Isometric. Compound Form. An Octahedron (111) with its solid angles modified by the planes of a Cube (100); a Tetragonal Triakis Octahedron (121); and by a Pentagonal Dodecahedron TT| 120 } , and its edges truncated by the planes of a Dodecahedron (110) . . . 123, 141 Fig. 445. Isometric. Compound Form. A Cube (100) modified by the planes of a Tetragonal Triakis Octa- hedron (211); a Dyakis Dodecahedron TT-| 132 }> ; a second Dyakis Dodecahedron * \U2\-, a Pentagonal Dodeca- hedron TTHJ 210 \ ; and an Octahedron (111) 123, 141 DESCRIPTIONS OF THE PLATES. 247 PAGE PLATE XIX Fig. 446. A Mineral Aggregate composed of irregular grains joined together and forming one compound mass. 149 Figs. 447, 448, 449, 450, and 451. These figures (110, 111) illustrate different types of Parallel Growths 149 Fig. 452. Isometric. A Cubical Form (100) produced by the joining together along the diagonals of the cubic faces of parts of four Cubes (100) 149,151 Fig. 453. Isometric. A Cubical Form (100) composed of parts of four cubical forms united along the diagonals of the cube faces. Each of the four parts is made up of a series of parallel growths forming an Oscillatory Com- bination 149, 151 Figs. 454, 455, 456, 457. Isometric. Cubes (100) and Penta- gonal Dodecahedrons K\ hkQ } showing various Oscilla- tory Combinations 149, 151 Fig. 458. Orthorhombic. Compound Form (110, 100, Okl) showing a simple twinned form, Aragonite 150, 153 Figs. 459, 460, 461. Orthorhombic. Compound Forms (110) showing Polysynthetic Twinning . . . -150,151,153 Fig. 462. Triclinic. Cleavage Plate showing Polysynthetic Twinning 151 Fig. 463. Isometric. Simple Form. Octahedron (111) showing a Twinning Plane (vibcdef) 149, 152 Fig. 464. Isometric. A Contact Twin Form. (Octahedral, 111) produced by turning part of the crystal (Fig. 463) half way around upon the Twinning Plane (afcccZe/), 149, 150, 152 Fig. 465. Isometric. Simple Form. Octahedron (111) showing Twinning Plane (alcdef) 149,152 Fig. 466. Isometric. A Contact Twin Form (Octahedral, 111) produced by revolving one part of Fig. 465 half way around upon the Twinning Plane (abcdef) .... 149, 150, 152 Figs. 467, 468. Isometric. Octahedral (111) Contact Twin Forms 149, 150, 152 248 DESCRIPTIONS OF THE PLATES. PAGE Fig. 469. Isometric. Simple Form. A Cube (100) show- ing a Twinning Plane (abcdef) 149, 152 Fig. 470. Isometric. A Contact Twinned Cube (100) formed by turning one part of Fig. 469 one half way around upon the Twinning Plane (abcdef) .... 149, 150, 152 Fig. 471. Isometric. Simple Form. A Dodecahedron (110) showing a Twinning Plane (abcdef) 149, 150, 152 Fig. 472. Isometric. A Contact Twinned Dodecahedron (110) produced by turning one part of Fig. 471 one-half way around on the Twinning Plane (abcdef) . . 149, 150, 151 PLATE XX Fig. 473. Isometric. A Dodecahedron (110) showing a Twinning Plane (alcdef) 149, 150, 152 Fig. 474. Isometric. A Contact Twinned Dodecahedron (100) produced by turning one part of Fig. 473 around for 180 on the Twinning Plane (abcdef) 149,150,152 Fig. 475. Isometric. Simple Form. A Tetrakis Hexa- hedron (fcfcO) showing a Contact Twinning Plane (dbcdefgliijK). 149, 152 Fig. 476. Isometric. A Contact Twinned Tetrakis Hexa- hedron (/i/cO) produced by turning one part of Fig. 475 on the Contact Twinning Plane (abcdefyhijk) for a distance, of 180 149, 150, 152 Fig. 477. Isometric. A Contact Twinned Cube (100), 149, 150, 152 Fig. 478. Isometric. Simple Form. A Cube (100) showing a Contact Twinning Plane (abcdef) ........ 149, 152 Fig. 479. Isometric. A Contact Twinned Cube (100) pro- duced by revolving one part of Fig. 478 on the Contact Twinning Plane (abcdefy through an angle of 180, 149, 150, 152 Fig. 480. Monoclinic. A Compound Form (111, 110, 010) showing a Contact Twinning Plane (abcdcf). Gypsum. 149, 152 DESCRIPTIONS OF THE PLATES. 249 PAGE Fig. 481. Monoclinic. A Contact Twin Form produced by revolving one-half of Fig. 480 through an angle of 180 upon the Twinning Plane (abcdef). This gives the com- mon spear- or arrow-head form of Gypsum. . . . 149, 150, 152 Fig. 482. Hexagonal. A spear- or arrow-head form of a Scalenohedron produced by revolving one-half of the crystal through an angle of 180 about a Contact Plane (dbcdefgh). Calcite 149, 150, 152 Fig. 483. Monoclinic. A spear- or arrow-head form pro- duced by the rotation of one-half of the crystal about the Contact Twinning Plane (abcdef). Gypsum. . . 149, 150, 152 Fig. 484. Triclinic. A Contact Twinned Form produced by the turning of one part 180 upon the Twinning Plane (abcdef). Albite 149, 150, 152 Fig. 485. Monoclinic. A Contact Twinned Crystal formed by the rotation of one part upon the Twinning Plane (abcdef) through an angle of 180. Augite . . . 149, 150, 152 Fig. 486. Monoclinic. A Contact Twinned Crystal formed by rotating one part on the Twinning Plane (abcdef) through an angle of 180. Orthoclase 149, 150, 152 Fig. 487. Monoclinic. A Compound Form (001, 110, 120, 111) with a Contact Twinning Plane (abed) drawn in. 149, 152 Fig. 488. Monoclinic. A Contact Twinned Crystal formed by turning one part of Fig. 487 through an angle of 180 upon the Twinning Plane (abed). . . . ..;. . . .149,150,152 Fig. 489. Triclinic. A Compound Crystal Form (001,010, 110, 101, 111) showing a Twinning Plane (abcdef) drawn in. Albite ^. , . 149,152 Fig. 490. Triclinic. A Contact Twinned Crystal produced by turning part of Fig. 489 through an angle of 180 upon the Contact Twinning Plane. Albite .....;.. 149, 152 Fig. 491 . Monoclinic. Crystal showing a dividing line (a&) and a Contact Twinning Plane (cdefgh). Orthoclase. 149, 152 Fig. 492. Monoclinic. The crystal is the same as Fig. 491, 250 DESCRIPTIONS OF THE PLATES. PAGE but it has been turned around 180. The dividing line (afc) and the Contact Twinning Plane (cdefgh) have been drawn in. Orthoclase 149, 152 Fig. 493. Monoclinic. A Contact Twinned Crystal produced by uniting the front half of Fig. 491 with the back half of Fig. 492 along the Contact Plane (cdefgh). Orthoclase, 149, 150, 152 Fig. 494. Monoclinic. A Contact Twinned Crystal produced by uniting the front half of Fig. 492 with the back half of Fig. 491. Orthoclase 149, 150, 152 Fig. 495. Orthorhombic. A Contact Twinned Crystal pro- duced by revolving through an angle of 180 of one part of Fig. 501 upon the Contact Plane (abcdef). Aragonite, 149, 150, 152 Fig. 496. Monoclinic. A Contact Twinned Crystal. Ortho- clase 149, 152 Fig. 497. Monoclinic. Crystal with the Contact Twinning Plane (abcdef) drawn in 149, 152 Fig. 498. Monoclinic. A Contact Twinned Form pro- duced by turning part of Fig. 497, 180 about the Contact Plane (abcdef) 149, 150, 152 Fig. 499. Hexagonal. Contact Twin formed by the growing together of two Ehombohedrons, E and E'. Calcite, 149, 150, 152 Fig. 500. Hexagonal. Contact Trilling formed by the union of three Bhombohedrons, E, R', and R". Calcite. 149, 150, 152 PLATE XXI Fig. 501. Orthorhombic. The Crystal has the Contact Twinning Plane (abcdef) drawn in. Aragonite . 149, 150, 152 Fig. 502. Orthorhombic. A Contact Twin produced by the revolution of one-half of the form for 180 upon the Contact Plane (abcdef). Aragonite 149, 150, 152 DESCRIPTIONS OF THE PLATES. 251 PAGE Tig. 503. Hexagonal. A Contact Twin Form produced by revolving the upper half of a Scalenohedron \ hkll } terminated by the planes of a Hexagonal Pyramid (hkll) through an angle of 180 upon the lower half of the Scalenohedron -{ hkil \ which is also terminated by the planes of a Hexagonal Pyramid (hkil). Calcite . 149, 150, 152 Fig. 504. Hexagonal. A Contact Twin Form produced by revolving one-half of a Scalenohedron * { hkll } upon the other half of the form. The Contact Plane is parallel to a Basal Pinacoid (0001). Calcite 149, 150, 152 Fig. 505. Hexagonal. A Contact Twin Form showing the Contact Plane (abed). This form can also be artificially produced by taking a cleavage rhombohedron of Calcite. Then press one of the terminal edges with a dull knife blade. As the knife gradually enters the Calcite it is slightly pressed towards the rhombohedral apex, when a series of thin laminae glide along each other parallel to the Contact Plane (abed), giving rise to a form like the one here represented. This is Secondary Twinning, and the planes parallel to the Contact Twinning Plane (abed) are known as Gliding Planes or *' Gleitflachen." Calcite, 149, 150, 152 Fig. 506. Hexagonal. Contact Twinned Khombohedrons (B and B 1 ) joined by the Contact Plane (abcde). Calcite, 149, 150, 152 Fig. 507. Hexagonal. Contact Twinned Rhombohedrons (B and B') joined by the Contact Twinning Plane (abcde). Calcite . . . .149,150,152 Fig. 508. Tetragonal. Compound Form, showing the planes of a Primary Prism (110), with its lateral edges truncated by the planes of a Secondary Prism (100) and terminated by the planes of a Primary Pyramid (111) and a Secondary Pyramid (101). A Contact Twinning Plane (ab) is drawn in. Cassiterite 149, 150, 152 252 DESCRIPTIONS OF THE PLATES. PAGE Fig. 509. Tetragonal. Compound Contact Twin Form. The same figure as 508, showing the twinning produced by revolving one part 180 around the plane (a&). Cas- siterite 149, 150, 152, 153 Fig. 510. Tetragonal. Compound Contact Twin Form similar to Fig. 510. Cassiterite 149, 150, 152, 153 Fig. 511. Hexagonal. Compound Contact Twin Form showing the planes of a Hexagonal Prism (1010) termi- nated by the Basal Planes (0001, OOOl), and twinned along the plane (a&). Calcite 149, 150, 152, 153 Fig. 512. Hexagonal. Compound Contact Twin Form showing the planes of a Hexagonal Prism (1010), termi- nated by Basal Planes (0001, 0001), and twinned along the plane (a&). Calcite 149, 150, 152, 153 Fig. 513. Hexagonal. A Compound Contact Twin Form similar to Fig. 512, but twinned along the plane (abcdef). Calcite 149, 150, 152, 153 Fig. 514. Tetragonal. Compound Contact Twin Form showing the planes of a Primary Prism (110), a Secondary Prism (100), and a Primary Pyramid (111). Cassiterite, 149, 150, 152, 153 Fig. 515. Tetragonal. A Compound Contact Twin Form showing the planes of a Primary Prism (110), a Secondary Prism (100), and a Primary Pyramid (111). Cassiterite, 149, 150, 152 Fig. 516. Tetragonal. A Compound Contact Twin show- ing the planes of a Ditetragonal Prism (310) and a Pri- mary Pyramid (111). Kutile 149,150,152,153 Fig. 517. Tetragonal. A. Compound Contact Twin. A Geniculated Form showing the planes of a Ditetragonal Prism terminated by the planes of a Primary Pyramid (111). The form is twinned along the planes ab and cd. Rutile 149, 150, 152, 153 Fig. 518. Orthorhombic. A Compound Contact Twin DESCRIPTIONS OF THE PLATES. 253 PAGE Crystal, twinned about the plane (abed) and showing the planes of a Prism (210), a Brachy-Dome (OM), and a Pyramid (111) 149, 150, 152, 153 Fig. 519. Tetragonal. A Compound Contact Twin, twin- ning along the plane (a&) and showing the planes of a Primary Pyramid (111), two Secondary Pyramids (101, 201) and two Basal Planes (001, GOT). Chalcopyrite, 149, 150, 152, 153 Fig. 520. Isometric. Penetration Twin formed by the intergrowth of Octahedrons (111). Haiiynite, 149, 150, 153 Fig. 521. Isometric. Penetration Twin formed by the intergrowth of Tetrahedrons { 111 }> . Sphalerite, 149, 150, 153 Fig. 522. Isometric. A Penetration Twin formed by the intergrowth of two Hexahedrons or Cubes (100). Ga- lenite 149,150,153 Fig. 523. Hexagonal. A Penetration Twin formed by the interpenetration of two Khombohedrons (loTl). Chab- azite 149,150,153 Fig. 524. Isometric. A Penetration Twin formed by the intergrowth of two Cubes (100). Galenite . . . 149, 150, 153 PLATE XXII Fig. 525. Isometric. A Penetration Twin Form produced by the interpenetration of two Cubes (100). Galenite, 149, 150, 153 Fig. 526. Isometric. A Penetration Twin produced by the intergrowth of two Cubes (100). Galenite . . . 149, 150, 153 Fig. 527. Isometric. Penetration Twin. Similar to Fig. 526. Fluorite 149, 150, 153 Fig. 528. Isometric. Penetration Twin. Similar to Fig. 525. Galenite 149, 150, 153 254 DESCRIPTIONS OF THE PLATES. PAGE Fig. 529. Isometric. Penetration Twin. Similar to Fig. 526. Galenite 149, 150, 153 Fig. 530. Isometric. Penetration Twin. Similar to Fig. 529 149, 150, 153 Fig. 531. Isometric. A Penetration Twin formed by the intergrowth of two Pentagonal Dodecahedrons K\ 210 } andTr^ 120 }-. Pyrite . 149, 150, 153 Fig. 532. Isometric. Penetration Twin. Similar to Fig. 531. Pyrite 149, 150, 153 Fig. 533. Isometric. Penetration Twin. Similar to Fig. 537. Pyrite 149, 150, 153 Fig. 534. Isometric. A Penetration Twin produced by the intergrowth of a Cube (100) and the two Pentagonal Dodecahedrons TT ^ 210 } and K\ 120 \- 149, 150, 153 Fig. 535. Isometric. A Penetration Twin formed by the interpenetration of Dodecahedrons (110). Sodalite, 149, 150, 153 Fig. 536. Isometric. A Penetration Twin produced by the intergrowth of an Octahedron (111) with a Dyakis Dode- cahedron TT { Tiki \ 149,150,153 Fig. 537. Isometric. A Penetration Twin formed by the intergrowth of a Tetrahedron K\ 111 }-, a Dodecahedron (110) and a Trigonal Triakis Tetrahedron /c-j211}>. Tetrahedrite . . . 149, 150, 153 Fig. 538. Isometric. A distorted Penetration Twin formed by the intergrowth of an Octahedron (111) and a Cube (100). Galenite 149, 150, 153 Fig. 539. Isometric. A Penetration Twin produced by the interpenetration of two Tetrahedrons K\ 111 \ , K\ ill \ . Diamond 149, 150, 153 Fig. 540. Isometric. A Penetration Twin produced by the interpenetration of two Tetrahedrons -{ ill }-, { 111 }-. Tetrahedrite 149, 150, 153 Fig. 541. Hexagonal. A Penetration Twin formed by the DESCRIPTIONS OF THE PLATES. 255 PAGE intergrowth of a Primary and a Secondary Hexagonal Prism (1010, 1120) and a Positive and a Negative Rhombo- hedron^ loll }-,.{ 0111 }-. Quartz 149,150,153 Fig. 542. Hexagonal. A Penetration Twin produced by the intergrowth of two crystals showing the planes of a Primary Prism (lOTl) and two Rhombohedrons { loll }-, { Olll }>. Quartz . ., . 149, 150, 153 Fig. 543. Hexagonal. A Penetration Twin made by the intergrowth of two forms showing the planes of a Pri- mary Hexagonal Prism (10TO), a Bhombohedron K -j loll }- , and a Dihexagonal Pyramid (5161). Quartz . . . 149, 150, 153 Fig. 544. Hexagonal. A Penetration Twin showing the planes of a Secondary Pyramid (2-2-I-3), of Rhombo- hedrons -{ loll } , and of Basal Pinacoids (0001). Hem- atite . 149, 150, 153 Fig. 546. Hexagonal. A Penetration Twin composed of intergrowths of Secondary Hexagonal Prisms (1120) , and three Rhombohedrons -{ loll } , { 0221 f , \ Oll2 } . Chabazite 149, 150, 153 Fig. 546. Monoclinic. A Penetration Twin. The Twin- ning Plane is parallel to the Clino-Pinacoid (010). The form shows the planes of Basal-Pinacoids (001), Clino- Pinacoids (010), Hemi-Orthodomes (201) and Prisms (110). Orthoclase. A Carlsbad Twin 149, 150, 153 Fig. 547. Monoclinic. A Penetration Twin similar to Fig. 546. A Carlsbad Twin. Orthoclase . . , . . . 149, 150, 153 Fig. 548. Monoclinic. A Penetration Twin similar to Fig. 547. A Carlsbad Twin. Orthoclase 149, 150, 153 PLATE XXIII Fig. 549. Monoclinic. A Penetration Twin produced by the intergrowth of Prisms (110) and Clino-Pinacoids (010). Resembles closely a Tetragonal Form. Phillip- site . 149, 150, 153 256 DESCRIPTIONS OF THE PLATES. PAGE Fig. 550. Monoclinic. A Penetration Twin similar to Fig. 549. Harmotome .... 149, 150, 158 Fig. 551. Orthorhombic. A Penetration Twin showing the planes of Prisms (110) and Brachy-Domes (Oil). Aragonite 149, 150, 153 Fig. 552. Orthorhombic. A Penetration Twin produced by the interpenetration of two crystals showing the planes of Prisms (110), Brachy-Pinacoids (010) and Basal- Pinacoids (001). Staurolite 149, 150, 153 Fig. 563. Orthorhombic. A Penetration Twin showing the planes of Pyramids (111), Prismatic Planes (110),Brachy- Dome Planes (021, 012) and Brachy-Pinacoids (010). Cerussite 149, 150, 153 Fig. 554. Orthorhombic. A Penetration Twin formed by the interpenetration of two crystals showing the planes of Brachy-Pinacoids (010), Basal-Pinacoids (001),. Brachy- Domes (Oil), and Prisms (110). Staurolite . . . 149, 150, 153 Fig. 555. Orthorhombic. A Penetration Twin produced by the interpenetration of three crystals. This form is known as a Trilling. It exhibits the planes of Basal- Pinacoids (001), Brachy-Pinacoids (010), Prisms (110) and Macro-Domes (101). Staurolite 149, 150, 153 Fig. 556. Orthorhombic. Similar to Fig. 555. Staurolite, 149, 150, 153 Figs. 557, 558, 559. Orthorhombic. Figures illustrating the building up of penetration twins in such a manner as to produce a pseudo-hexagonal form as outlined in Fig. 559 or a case of Mimicry 149, 150, 154 Fig. 560. Orthorhombic. A Twin form or an imperfect Fiveling roughly simulating a hexagonal form. Marca- site 149, 150, 154 Fig. 561. Orthorhombic. Mimicry. Section of the top of a twinned form similar to Fig. 564, showing a resemblance to a hexagonal form, but the twinning is indicated by the re-entering angles. Aragonite 149, 150, 154 DESCRIPTIONS OF THE PLATES. 257 PAGE Fig. 562. Orthorhombic. A Twin Form of a Fiveling type, roughly simulating a hexagonal form. Marcasite, 149, 154 Fig. 563. Orthorhombic. A Contact Twin showing the planes of Prisms (110), Macro-Pinacoids (100), and formed by revolving one part of the crystal for 180 about the plane (abcdef). This form shows the com- mencement of Mimicry that leads to the production of a pseudo-hexagonal form as seen in Figs. 551, 564, 559, 561 and 580. Aragonite 149, 150, 154 Fig. 564. Orthorhombic. A Combination Twin forming a pseudo-hexagonal form produced by repeated twinning. Mimicry. Aragonite 149, 150, 154 Fig. 565. Orthorhombic. A Penetration Twin showing the planes of Prisms (110) and Pyramids (111), making a form roughly simulating the hexagonal forms. Mimicry com- pleted in Fig. 566. Cerussite 149, 150, 154 Fig. 566. Orthorhombic. A Penetration Twin produced by the complete twinning of Fig. 565, so as to fill out the re-entering angles. Complete Mimicry of the Hexagonal Pyramid. Cerussite 149, 154 Fig. 567. Orthorhombic. A Penetration Twin or Trilling, simulating a Hexagonal Crystal. Mimicry. Chryso- beryl 149, 150, 154 Fig. 568. Orthorhombic. Mimicry. Repeated twinning producing a pseudo-Hexagonal Pyramid. Bromelite, 149, 164 Fig. 569. Orthorhombic. Mimicry. A cross section of Fig. 568. The lines with looped ends show the position of the optic axes in the different individuals composing the pseudo-hexagonal form. Bromelite 149, 154 Figs. 570, 571, 572, 573, 574. Monoelinic. Mimicry. These figures illustrate successive stages in twinning, simulating Orthorhombic, Tetragonal, and Isometric Forms. Fig. 258 DESCRIPTIONS OF THE PLATES. PAGE 574 is so twinned that if it were not for the obtuseness of the facial angles it would simulate the Hexakis Octa- hedron, but as it occurs it closely mimics the Dodeca- hedron. Phillipsite 149. 150, 154 Figs. 575, 576, 577, 578, 579. Orthorhombic. Mimicry. Sim- ulating hexagonal forms. Fig. 579 is a cross section of one of them in which the optic axes are shown by lines with looped ends. Witherite 149, 154 Fig. 580. Orthorhombic. Mimicry. A cross section of a twin like Fig. 564, taken approximately midway between the two ends. The striations show the different indi- viduals of which it is composed, while the slightly re- entering angles indicate the twinning. Aragonite . . 154 PLATE XXIV Fig. 581. Triclinic. Holohedral. This shows by its central ring that it has a Center of Symmetry. The dotted straight lines with feathered ends show that the Crystal- lographic Axes are not Axes of Symmetry. The dotted circle indicates that there is no Plane of Symmetry. The figure indicates that the Triclinic System has neither Plane nor Axis of Symmetry but that it has a Center of Symmetry 161, 162, 168 The Triclinic Hemihedral or Asymmetric is shown in Fig. 608 167, 168 Fig. 582. Monoclinic. Holohedral. This figure shows that the Holohedral Monoclinic crystals have a Center of Sym- metry, an Axis of Binary Symmetry and a Plane of Sym- metry 161, 162, 170 Fig. 583. Monoclinic. Hemihedral or Clinohedral. One Plane of Symmetry only 161,162,169 The Monoclinic Hemimorphic is shown in Fig. 609, page 169. DESCRIPTIONS OF THE PLATES. 259 PAGE Fig. 584. Orthorhombic. Holohedral. The figure shows a Center of Symmetry, three Axes of Binary Symmetry and three Planes of Symmetry >'''. .161,162,170 Fig. 585. Orthorhombic. Hemihedral. The figure has three Axes of Binary Symmetry only ...... 161-163, 170 Fig. 586. Orthorhombic. Hemimorphic. The figure shows one Axis of Binary Symmetry and two Planes of Sym- metry . , . . ...*,. . . 161-163, 170 Fig. 587. Tetragonal. Holohedral. This figure shows a Center of Symmetry, four Axes of Binary Symmetry, one Axis of Tetragonal Symmetry, and five Planes of Sym- metry 161-163, 175 Fig. 588. Tetragonal. Sphenoidal. This figure has three Axes of Binary Symmetry and two Planes of Symmetry, 161-163, 174 Fig. 589. Tetragonal. Pyramidal. This figure has a Center of Symmetry, an Axis of Tetragonal Symmetry, and a Plane of Symmetry 161-163, 174 Fig. 590. Tetragonal. Trapezohedral. This figure has four Axes of Binary Symmetry and one Axis of Tetragonal Symmetry only 161-163, 174 The Tetragonal Bisphenoidal or Tetartohedral is shown in Fig. 610, page 172; the Tetragonal Pyramidal or Hemi- morphic is illustrated in Fig. 611, pages 172, 173, and the Ditetragonal Pyramidal or Hemimorphic is exhibited in Fig. 612, page 175. Fig. 591. Hexagonal. Holohedral. This figure shows a Center of Symmetry, six Axes of Binary Symmetry, one Axis of Hexagonal Symmetry and seven Planes of Sym- metry ... .... 161-163, 182 Fig. 592. Hexagonal. Hemihedral. Khombohedral. This figure shows a Center of Symmetry, three Axes of Binary Symmetry, one Axis of Trigonal Symmetry, and three Planes of Symmetry .161,162,164,179 260 DESCRIPTIONS OF THE PLATES. PAGE Fig. 593. Hexagonal. Pyramidal. Hemihedral. The fig- ure exhibits a Center of Symmetry, one Axis of Hex- agonal Symmetry, and one Plane of Symmetry, 161, 162, 164, 181 Fig. 594. Hexagonal. Hemihedral. Trapezohedral. This figure shows six Axes of Binary Symmetry and one Axis of Hexagonal Symmetry 161,162,164,181 Fig. 595. Hexagonal. Hemihedral. Trigonal. This fig- ure shows a Center of Symmetry, three Axes of Binary Symmetry, one Axis of Trigonal Symmetry, and four Planes of Symmetry 161,162,164,180 PLATE XXY Fig. 596. Hexagonal. Tetartohedral. Rhombohedral. This figure exhibits a Center of Symmetry and one Axis of Tri- gonal Symmetry only . 161,162,164,177 Fig. 597. Hexagonal. Tetartohedral. Trapezohedral. This figure shows three Axes of Binary Symmetry and an Axis of Trigonal Symmetry 161, 162, 164, 177 Fig. 598. Hexagonal. Tetartohedtal. Trigonal. This fig- ure shows an Axis of Trigonal Symmetry and a Plane of Symmetry 161, 162, 165, 178 Fig. 599. Hexagonal. Hemimorphic. lodyrite Type. This Type has an Axis of Hexagonal Symmetry and six Planes of Symmetry 161, 162, 165, 182 Fig. 600. Hexagonal. Hemimorphic. Neph elite Type. This Type possesses an Axis of Hexagonal Symmetry only, 161, 162, 165, 178 Fig. 601. Hexagonal Hemimorphic. Tourmaline Type. This Type has an Axis of Trigonal Symmetry and three Planes of Symmetry 161, 162, 165, 178 Fig. 602. Hexagonal. Hemimorphic. Sodium Periodate Type. This Type possesses an Axis of Trigonal Sym- metry only 161,162,165,176 DESCRIPTIONS OF THE PLATES. 261 PAGE Fig. 603. Isometric. Holohedral. This figure shows a Cen- ter of Symmetry, six Axes of Binary Symmetry, four Axes of Trigonal Symmetry, three Axes of Tetragonal Sym- metry, and nine Planes of Symmetry . . . .161, 162, 165, 186 Fig. 604. Isometric. Hemihedral. Oblique. This figure indicates three Axes of Binary Symmetry, four Axes of Trigonal Symmetry, and four Planes of Symmetry, 161, 162, 165, 185 Fig. 605. Isometric. Hemihedral. Parallel. This figure shows a Center of Symmetry, three Axes*of Binary Sym- metry, four Axes of Trigonal Symmetry, and three Planes of Symmetry 161, 162, 166, 184 Fig. 606. Isometric. Hemihedral. Gyroidal. These forms possess six Axes of Binary Symmetry, four Axes of Tri- gonal Symmetry, and three Axes of Tetragonal Sym- metry 161,162,166,184 Fig. 607. Isometric. Tetartohedral. This figure has three Axes of Binary Symmetry, and four Axes of Trigonal Symmetry only 161,162,166,183 Fig. 608. Triclinic. Asymmetric. This figure, as its name implies, is destitute of symmetry 161, 162, 168 Fig. 609. Monoclinic. Sphenoidal or Hemimorphic. This figure has one Axis of Binary Symmetry only . .161, 162, 169 Fig. 610. Tetragonal. Bisphenoidal or Tetartohedral. This figure has one Axis of Binary Symmetry only . .161, 162, 173 Fig. 611. Tetragonal. Pyramidal. Hemimorphic. This figure possesses one Axis of Tetragonal Symmetry only, 161, 162, 173 Fig. 612. Ditetragonal. Pyramidal. Hemimorphic. This figure has one Axis of Tetragonal Symmetry and four Planes of Symmetry -. ; .. . .. : . .. . .161,162,175 EKEATA. Page 7. 7 lines from the top. For "A B C D E F H" read "A B C It." Page 11. 2 lines from the bottom. For "001" read "001." Page 12. 13 lines from the top. For "110 < 111" read "Oil < Oil." Page 21. 8 lines from the top. For ' ' equal ' ' read ' ' unequal. ' ' Page 26. 7 lines from the top. For "35" read "64." Page 32. 2 lines from the bottom. For "P" read "P." Page 33. 5 lines from the top. For '"P read "'P." Page 35. 6 lines from the bottom. For "n&" read " nb." Page 35. 2 lines from the bottom. For " & " read " 6. " Page 41. 12 lines from the bottom. Strike out "shortest" and for ' ' them ' > read < ' their centers. ; ' Page 43. 11 lines from the top. For "65, 70" read "67, 68." 10 lines from the bottom for "82-86" read "82, 84-86." Page 45. 12 lines from the bottom. For "65 72" read "65-72." Page 47. 2 lines from the top. For the second b read &. Page 54. 9 lines from the top. For "Ortho" read "Macro," 10 lines from the top. For " ortho-" read "macro-." 11 lines from the bottom. For "clino-" read "brachy-" and for " Clino-" read " Brachy-." 10 lines from the bottom. For ' ' ortho- ' ' read ' ' macro-. ; ' 9 lines from the bottom for "Ortho-" read Brachy-." Page 57. 13 lines from the top. For " 87 135 " read ' ' 87-135. ' ; Page 60. .2 lines from the bottom. For ' ' 147-149 ' ' read ' ' 151- 153." Page 61. 6 lines from the top. For " 147, 150 and " read "151- .' (262) Page 83. 7 lines from the bottom for "(d) 77 read " (s) 77 and for " (b and g) 77 read " (b and d). 77 Page 125. 14 lines from the top. For "Petagonal 77 read "Pentagonal. 7 ' Page 132. 4 and 7 lines from the bottom. Place "upper 77 before "edge. 77 Page 133. 10 lines from the bottom. Place "upper 77 before " edge. 77 7 lines from the bottom for " 845 77 read " 345. 77 3 lines from the bottom. Tor " octohedral 7 7 read "octahedral. 77 Page 134. 7 lines from the top. Place "upper 77 before "edge. 77 Page 140. 10 lines from the bottom. For "alteration 77 read ' * alternation. 7 7 Page 144. 14 lines from the top. For " four 77 read " five. 77 6 lines from the bottom add: " if the planes are pentagonal; but if they are triangular they belong to the Kexakis Tetrahedron. Page 147. 9 lines from the top. For "llch" read "Ikh." Page 151. 3 lines from the top. For " 459-460 77 read "459, 460. 77 Page 157. 11 lines from the top. For "101 77 read "101. 77 Page 169. Last line. For "48 77 read "45. 77 (263) Pte Fig. I -b - z Monoclinic Plane of Symmetry Axis of Binary Symmetry Triclinic Axes Fig. 4 -t-x +Y - fetratbnal Ares -0 -X - Isometric Axes Fig. 2 -b r*Y Fig. 3 t- -y Monoclinic Axes noclinic ne of Symmetry s of Binary Symmetry Fig. 6 t c a a Hexagonal Axes -a -t Fig. II -y Orthorhombic Axes Fig.9 Monoclinic Plane of 'Symmetry Axis of Binary Symmetry Monoclinic Plane of Symmetry Fig. 12 Fig. 1 3 Isometric Distorted Oclahdrons Fig. 18 no 110 III Fig. 1 9 Isometric Distorted Octahedrons Fig. 20 Isometric Curved Octahedron Fig. 2 4 Isometric Parallel Growths Fig. 25 Fig. 26 Tetragonal Parallel Growths Hexagonal Parallel Growths Fig. 3 1 Fig. 32 Hexagonal Parallel Growths II Fig. 21 Hexagonal Distorted Form Fig. 28 Fig. id 001 Fig. I 7 Orthorhombic Distorted Crystal Isometric Octahedron Modified Fig. 23 Insometric Parallel Growths Fig. 3o Fig. 3 5 PM1 \ Nix / oo-Poo 100 no Fig.36 Fig.37 101 1010 OCtP 000 Hexagonal Triclinic Center of Symmetry Hexagonal Tetragonal System Hexagonal Axf Axes of Tetragonal Symmetry FigJ* Fig. 5 ^ 021 101 IOO 00 P no 201 Hexagonal Axes of Trigonal SkmmaieL Orthorhombic three Planes of Symmetry Isometric Pentagonal Dodecahedrons .1 ' ' 'v ' / 'n Fig. 40 Hexagonal Fig. 41 110 Hexaaonal Hexagonal Symmetry Fig. 46 Tetragonal Axis of Tetragonal Symmetry Fig. 4 8 Hexagonal f Trigonal Symmetry Hexagonal Trigonal Trapezohedrons Three Planes of Symmetry Fig. 58 Pla f ^" OOT ^^^ f^ f T0 o 3o/ b d a |0 ec, 0~> oio /oo * I I i& Isometric Isometric Fig Jb 2 J^Fig 7/o / ' / ' ^AP- '-^/^ c?/c? / /y0 :u....L..L.^_ Fig. 88 O2T Orthorhombic Fig. io 3 teV Fig. 89 TQI POO OP ^-001. -- s IOI Fig. 90 TOI Poo ^ oP v -QPJ__ IOI .0 F Orthorhombic i>. 95 Orthorhombic Fig.Tl-3 Orthorhom Fig. II 9 Fig. 1 20 Orthorhombic Fig. 135 . . , Isometric DyaKis pAsr^ Dodecahedrons nrthnrhnmbic Suhenoids Fig'i4d Fig.i47 Fig Fig.l5i Orthorhom Fig. 153 no no -L^ \ \ i -IP 1 L -F-! -p no iod no 1 i i I- i Primary Prism Fig.i57 Primary and Secondary Prisms K^ fifc^ p -p * 9 o IOO no M & J J Tetragonal Prisms and Pyramids Cross Section of a Secondary Prism Tetragonal Pyramids Fig- HP Fig. 172 Pli Tetragonal Pyramid and Basal Planes Pyramid and Prism Fig. 1 80 Sonenoid Fig.177 Fig. 199 Fig. 200 Tetragonal Scheelite Cross Section lodyriU Type Fig. 203 r , 8 u u c T )\ oop ;-> 10 c v OIT . i - 1 Primary Hexagonal Pyramid Secondary Hexagonal Pyramid Fig.2IO Fig. 205 Primary Hexagonal Prism Fig.2II 1122 Pyramidal Relations Fig.2i8 Fig- 2 20 Fig.2i7 ephelite Type 10 Cross Section Dihexagonal Pyrami4 KT(|I20) Oo P 2 4 Secondary Trigonal -Prism Fig. 2 27 Fig. * 28 Fig. Rhombohedrons Fig.235 Fig.239 F 'Z~ 23 Ft? 237 A Dihexa 9 nal * ^ 7 A Pyramid Pyramids Pyramids Tetrannnal Hexagonal Pyramids ig.263 Hexagonal Pyramids \/Fig267 Fig. 2 69 Ftg.277^^ ^W^ ASAWt pi ?8 ~. Rhombohedrons Fig.279 Scalenohedrons X/7 Hexagonal y Scalenohedrons Fig- 298 Fig. 300 Fig. 30 1 7ZP Hexagonal Compound Form ^z'oii JP\ rS^\ 202 O . ooP ooP ^2* Hexagonal Fig.3Q2 Fig-304 Fig. 3 '20 Fig. 32 1 Fig. 322 00 |P, 1126 oo P roTo Fig 326 Diitexagonal Pyramid Fig. 330 Hexagonal Compound Forms Fig. 327 Periodate Type . Fig.334 Hexakis Octahdrons IOO Fig. 325 Hexahedron or Cube Dodecahedron Fig-332 Fig.333 Tetrahdron Fig.34i Fig. 34 2 JD r ; Tetrahedrons Flg.346 Fig. 3 47 Trigonal Tria Octahedror Fig. 3 48 Pentagonal s Dodecahedron l\1 h k I \ Dyakis ^iv.363 Pentagonal Fi S- 364^T^~J^ Fig.365 Dodecahedrons Hexakis Octahedron Fig. 366 Dlak Fig. 367 Fig.3 68 mOn Pentagonal y Fig. 372 Icositetrahedrons Fig. 37 3 QQ000 IOO Cube modified by an Octahedron Octahedron modi a Cube Fig-376 F'g-377 no IOO .A > X_ Dodecahedron modified by a Cube Cube and Dodecahedron Fig.382 Fig. 38o ooOoo IOO Fig.38l !ioo Modified Cubes F'g. 369 Fig.370 Ff ^ ^ *fr o Oo0ao III Tetrahedral Pentagonal Dodecahedron IOO Fig- 374 Fi * 375 Cube modified by an Octahedron nedron modified >y a Cube Fig, 378 Cubo-Octahedron Fig. 379 Octahedron and Dodecahedron Fig. 383 pig. 384 Dodecahedron and Octahedron Fig. 385 Modified lodecahedron Modified Cube Modified Dodecahedron Fig.4i6 Fig. 446 oo oo jQO Parallel Growths oo I O O Om 7l{hko} Fig.463 Twinning Fig 462 Polysynthetic Twinning d Octahedron Fig.467 Fig.468 Fig. 469 00 467 Polysynthetic Twinning Polysynthetic Twinning Fig 4 64 Polysynthetic Twinning * ^ Fig. 465 Fig- 46 6 Contact Twin Octahedron Contact Twin Fig. 470 Fig. 471 Fig. 472 Fig.473, Fig. 41 '8 Fig.483 Fig.484 Fig.485 Pic. \x<* 1 /:\ /: \ *^ f \ / b ,p 00 A. P 1 ?y no ^ -4 ..... I'OJJ p \ / X>\ ' c ^^ Fig.501 Fig.507 teXXI Plate Fig.525 are I*/// Plate Conventional Signs for Axes /' of Symmetry /^ V / ^ | Bjnar > .---'\L ^ Trigonal "0t''~'~ 5 U-'-""' 3 *r ^ Tetragona \ Hexagonal x x x / \ x N. O Center of ~~', Symmetry Fig r" ^r^ 5^/ F/^.552 Triclinic Monoclinic \ \ \ \ V / Orthorhombic Hemimorphic Fig. 58 7 Tetragonal Holohedral Fig. 5 9 Tetragonal Trapezohedral Fig.5?i Hexagonal Holohedral Hexagonal Hemihedral Rhombohedral iXIV "*-... Fig.588 Tetragonal Sphenoidal Fig-5%9 Tetragonal Pyramidal Fig.593 Hexagonal Hemihedral Pyramidal Fig.594 Hexagonal Hemihedral Traoezohedral Fig.595 Hexagonal Hemihedral Trigonal Fig. 596 Fig.597 JL V Hexagonal Tetartohedral Rhombohedral Hexagonal Tetartohedral Trapezohedral Hexagonal Tetartohedral Trigonal Fig. 602 Fig. 60 3 Hexagonal Hemimorphic Socfium Periodate Type Isometric Holohedral Fig ^6 08 Fig -60 7 V Fig.609 x IX V Fig. 599 Fig- 600 Fig. ()O l \ ' ^ Hexagonal Hemimorphic lodyrite Type Hexagonal Hemimorphic Nephelite type Fig- ^605 Hexagonal Hemimorphic Tourmaline Type Fig. 606 Tetragonal Pyramidal Hemimorphic \ Tetragonal Bisphenoidal or INDEX. Acute Bhombohedron, 87 Adamantoid, 124, 130, 137, 144, 186, 188, 201, 207, 236-239, 241, 242 Agassiz, Louis Jean Budolphe, 188 Aggregate, Mineral, 149, 150, 247 Albite, 12, 13, 19-21, 25, 26, 33, 34, 44, 149, 150, 152, 205, 249 Alum, 3, 149 Amorphous Minerals, 148 Angles, Axial, 7, 8, 9, 40, 50, 73 Angles of the Hexagonal Scale- nohedron, 89 Angles, Ehombohedral, 86 Angles, Variation of Crystal angles, 3 Animal Kingdom, 1 Anorthoid, 193 Anorthotype, 193 Apatite, 18, 26, 74, 76, 80-83, 104, 206, 234 Apophyllite, 61, 70, 73, 74 Aragonite, 149, 150, 153, 154, 247, 250, 256-258 Asymmetric Class, 167, 261 Asymmetric Class, Symmetry of, 168, 261 Asymmetric Group, 167, 261 Augite, 17, 18, 26, 41, 43-47, 149, 150, 152, 203, 209, 249 Augitoid, 193 Axenite, 12, 13, 19-21, 25, 26, 33, 34, 44, 205 Axes, Crystal, 6-10 Axes, Crystallographic, how rep- resented, 161 Axes, Cubic, 131, 139 Axes, Dodecahedral, 131, 139 Axes, Hexagonal, 8, 73, 75, 109, 203 Axes, Octahedral, 131, 135, 139 Axes of Symmetry, 18, 19, 23- 25, 41 Axes of Symmetry, how repre- sented, 161, 162 Axes of the Isometric System, 7, 122, 126, 203 Axis of Trigonal Symmetry, how represented, 162 Axes, Orthorhombic, 7, 50, 57, 203 Axes, Monoclinic, 7, 40-42, 47, 203 Axes, relation to Planes, 43, 51, 62 Axes, relation to Hexagonal Planes, 75 Axes, Tetragonal, 7, 60, 203 Axes, Triclinic, 7, 9, 10, 29, 33, 203 Axial Angles, 7, 8, 9, 40, 50, 73 Axial Models, 13 Axis of Binary Symmetry, 18, 19, 23-25, 41, 44, 51-56, 64, (265) 266 INDEX. 67, 69, 84, 90, 91, 94, 96, 100, 123, 131, 135, 138, 139, 141, 162-166, 258-261 Axis of Binary Symmetry, how represented, 162 Axis or Hexagonal Symmetry, 18, 19, 41, 74, 76, 85, 93, 94, 103, 121, 163-165, 259, 260 Axis of Tetragonal Symmetry, 18, 19, ^3, 41, 64, 68, 69, 123, 130, 131, 139, 163, 165, 166, 259, 261 A.XIS of Trigonal Symmetry, 19, . 23-25, 41, 52, 74, 76, 85, 91, 96, 98, 100, 102, 103, 104, 121, 130, 135, 138, 139, 141, 164-166, 259-261 Axis, Twinning, 152 Axis, Vertical, 10, 41 Barite, 26, 50, 51, 57, 207, 212 Basal Cleavage, 155-158 Basal Pinacoid, 11, 21, 42, 44, 60, 63, 80, 104, 172-183, 199 Basal Pinacoid, Hexagonal, 176- 183 Basal Plane, 11, 21, 42, 44, 60, 63, 80, 104, 172-183, 199 Base, 199 Bauerman, H., x, 34 Beryl, 74, 76, 80, 83, 104 Berylloid, 197 Bevelment, 27, 28 Binary Symmetry Axis, how represented, 162 Binomial Names, 188 Biology, 1 Bi Pyramid, 197 Bipyramidal Class, 181, 182 Bipyramidal Class, Orthorhom- bic, 171, 172, 259 Bipyramidal Class, Tetragonal, 174, 175, 261 Bisphenoidal Class, Tetragonal, 172 Black Douglas, 188 Black Hexagon, 162 Black Quadrilateral, 162 Black Spindle-shaped Figure, 162 Black Triangle, 162 Bohemia, 187 Botany, 1 Boracitoid, 201 Borax, 41, 43-47, 210 Brachy-Axis, 10 Brachy-Diagonal, 10 Brachy Diagonal Dome, 190 Brachy Diagonal Pinacoid, 200 Brachy Diagonal Prism, 190 Brachy-Dome, 12, 22, 54, 190 Brachy-Pinacoid, 3, 12, 21, 54, 200 Brachy-Pinacoidal Cleavage, 155-157 Brachy-Semi-Axis, 50 Bravais, C., 29, 167 Bromelite, 149, 154, 257 Brush and Penfield's Manual, x Calamine, 51, 57, 212 Calcite, 18, 27, 74, 76, 81, 83, 87-89, 104, 149, 150, 152, 207, 223, 231, 234, 249-252 Calcite Pyramid, 197 Cassiterite, 61, 62, 70, 73, 74, 149, 150, 152, 153, 220, 251, 252 Center of Symmetry, 19, 23-25, 55, 56, 59, 64, 67, 68, 72, 85, 91, 93, 98, 100, 121, 131, 135, 139, 141, 147, 162-166, 258- 261 INDEX. 267 Center of Symmetry, how rep- ' resented, 162 Centrosymmetric Class, 168, 205, 206, 258 Cerussite, 149, 150, 153, 154, | 256, 257 Chabazite, 149, 150, 153, 253, ! 255 Chalcanthite, 12, 13, 19-21, 26, ; 33, 34, 44, 205 Chalcopyrite, 149, 150, 192, 153, j 253 Characteristics of Hexagonal Crystals, 76 Characteristics of Isometric Crystals, 123 Characteristics of Monoclinie Crystals, 44 Characteristics of Orthorhombic Crystals, 53, 54 Characteristics of Tetragonal Crystals, 62 Characteristics of Triclinic Crystals, 19-21 Chrome Alum, 3, 14, 26, 204 Chrysoberyl, 149, 150, 154, Class of the Dihexagonal Bi- pyramid, 182, 183 Class of Dihexagonal Pyramid, 182, 183 Class of the Diploid, 184, 185 Class of the Ditetragonal Bi- pyramid, 175, 176 Class of the Ditetragonal Pyra- mid, 175 Class of the Ditrigonal Bipyra- mid, 180 Class of the Ditrigonal Pyra- mid, 178-180 Class of the D^crigonal Scale- nohedron, 179 Class of the Gyroid, 184 Class of the Hemimorphic Di- hexagonal Pyramid, 182 Class of the Hemimorphic Tri- gonal Pyramid of the Third Order, 176, 177 Class of the Hexagonal Trape- zohedron, 181 Class of the Hextetrahedron, 185, 186 Class of the Rhombohedron of the Third Order, 177 Class of the Tetartoid, 183, 184 Class of the Tetragonal Pyra- mid of the Third Order, 172, 173 ulass of the Third Order Hexa- gonal Bipyramid, 181, 182 Class of the Third Order Hexa- gonal Pyramid, 180-182 Class of the Trigonal Bipyra- mid of the Third Order, 178 Class of the Trigonal Pyramid of the Third Order, 178 Class of the Trigonal Trapezo- hedron, 177, 178 Cleavage, Cubical, 155, 159 Cleavage Dodecahedral, 155, 159 Cleavage, Hexagonal, 158 Cleavage, Isometric, 159 Cleavage, Mineral, 155-160 Cleavage, Monoclinie, 157 Cleavage, Octahedral, 155, 159 Cleavage, Orthorhombie, 157 Cleavage, Pinacoidal, 155-158 Cleavage Plate, 155 Cleavage, Prismatic, 155-158 Cleavage, Pyramidal, 155-158 Cleavage, Rhombohedral, 155, 158 268 INDEX. Cleavage Shorthand, 156-159 Cleavage, Slaty or Rock, 160 Cleavage, Tetragonal, 157, 158 Cleavage, Triclinic, 156 Clino-Axis, 42 Clino-Diagonal, 42 Clino-Diagonal Prism, 190 Clino-Dome, 43, 44, 190, 203 Clinohedral Group, 46, 169, 170, 258 Clinohedrite, 46 Clinorhombic Octahedron, 193 Clino-Pinacoid, 8, 11, 12, 17, 18, 26, 41, 43, 44, 46, 47, 200, 203 Clino-Pinacoidal Cleavage, 155- 157 Colby University, vi Composition Plane, 152, 247- 253, 257 Compound Crystals, 25, 26 Compound Forms, Hexagonal System, 104 Compound Isometric Forms, 141, 142 Compound Minerals or Crys- tals, 149-154 Compound Monoclinic Forms, 46 Compound Orthorhombic Forms, 57 Compound Tetragonal Forms, 69 1 Contact Twins, 151-153, 247- 253, 257 Cooke, J. P., xiii Corundum, 74, 76, 80, 81, 83, 104, 235 Crystal, 2, 3 Crystal, Compound, 25, 26 Crystal Models, viii, 56 Crystal, Number of Forms on, 39 Crystal, Simple, 25 Crystalline Aggregate, 149, 247 Crystalline Minerals, 148 Crystallographic Axes, how rep- resented, 161 Crystallographic Drawings, Beading of, 28-34, 46, 47 Crystallographic Nicknames, 188-202 Crystallograpmc Nomenclature, 187-202 CrystaAlographic Shorthand, 28- 34, 46, 47, 57, 70, 75, 109-113 Crystallographic Symmetry, 161- 166 Crystallography, 2 Crystallography, Books relating to that subject, x-xiii Crystallography, location of a point, 3-6 Crystallography, Mathematical, 5 Crystallography, Methods of Study, v-x, xiv-xvi Cube, 123, 126, 141, 142, 183- 186, 188, 200, 204, 208, 236- 248, 253, 254 Cubical Cleavage, 155, 159 Cubic Axes, 131, 139 Cuproid, 201 Cyclic Twin, 153, 252, 253 Dana, E. S., 34, 46, 74, 167 Dana, E. S., Text Book of Min- eralogy, x, 167 Dana, J. D., xiii, 28, 32, 33, 34, 46, 70, 74, 112 Dana, Notation, 29, 32, 46, 47, 70, 112 Dana's Division of the Hexa- gonal System, 74 Deltohedron, 200 INDEX. 269 Deltoid Dodecahedron, 124, 132, 133, 142, 143, 183, 185, 200 Deltoid Icosi Tetrahedron, 201 Des Cloizeaux, A., 29 Diagonal Prism, 192 Diametral Prism, 191 Diametral Pyramid, 195 Diamond, 3, 149, loO, 153, 204 Dido decahedron, 125, 137, 138, 144, 185, 197, 201 Dihexagonal Bipyramidal Class, 182, 183 Dihexagonal Henri Di Dode- cahedron, 198 Dihexagonal Prism, 81-85, 99, 101, 105, 179, 181-183, 192 Dihexagonal Pyramid, 82, 93, 95, 101, 107, 182, 183, 197, 206 Dihexagonal Pyramidal Class, 182 Dihexagonal Scalenohedron, 197 Dihexagonal Trapezohedron, 198 Dihexahedron of the Principal Series, 196, 197 Dihexahedron of the Second Order, 197 Dioctahedral Prism, 191 Dioctahedron, 62, 195 Diplagihedron, 198 Diplohedron, 202 Diploid, 125, 137, 138, 144, 185, 202 Diploid, Symmetry of, 51, 52, 138 Diplo-Pyritohedron, 202 Diplo-Pyritoid, 202 Diplo-Tetrahedron, 195 Directions for Studying Hexa- gonal Crystals, 121 Directions for Studying Iso- metric Crystals, 147 Directions for Studying Mono- clinic Crystals, 49 Directions for Studying Ortho- rhombic Crystals, 59 Directions for Studying Tetra- gonal Crystals, 72 Directions for Studying Tre- clinic Crystals, 38, 39 Direct Octahedron, 194 Direct Prism, 191 Direct* Pyramid, 194 Direct Tetragonal Prism, 61, 63, 175, 176, 191 Direct Tetragonal Pyramid, 61, 63, 175, 176, 194 Disphene, 195 Distinction between Mineral Cleavage and Eock or Slaty Cleavage, 160 Distinction between Parting Structure and Cleavage Struc- ture, 159, 160 Distinction between the Positive and Negative Dyakis Dode- cahedrons, 137 Distinction between the Positive and Negative Hexakis Tetra- hedrons, 135 Distinction between Holohedral and Hemihedral iorms, 46 Distinction between Orthorhom- bic and Tetragonal Sphenoids, 65, 66 Distinction between the Positive and Negative Pentagonal Do- decahedrons, 136, 137 Distinction between the Positive and Negative Tetragonal Triakis Tetrahedrons, 133 Distinction between the Positive and Negative Tetrahedrons, 132 270 INDEX. Distinction between the Positive and Negative Tetrahedral Pentagonal Dodecahedrons, 140, 141 Distinction between the Positive and Negative Trigonal Triakis Tetrahedrons, 134 Distinction between Primary and Secondary Tetragonal Prisms, 64 Distinction between Primary and Secondary Tetragonal Pyramids, 65 Distinction between the Bight- handed and Left-handed Pen- tagonal Icositetrahedrons, 138, 139 Distinction between Tetragonal Sphenoids and Scalenohe- drons, 66 Distinction "between the Tetra- gonal and Hexagonal Sys- tems, 73, 74 Distinguishing Characteristics of Hexagonal Crystals, 76 Distinguishing Characteristics of the Isometric Crystals, 123 Distinguishing Characteristics of Monoclinic Crystals, 44 Distinguishing Characteristics of Orthorhombic Crystals, 53, 54 Distinguishing Characteristics' of Tetragonal Crystals, 62 Distinguishing Characteristic^ of Triclinic Crystals, 19-21 JDitetragonal-Bipyramidal Class, 175, 176 Ditetragonal Octahedron, 195 Ditetragonal Prism, 61, 63, 98, 99, 174, 191 Ditetragonal Pyramid, 62, 63, 121, 175, 176, 195 Ditetragonal Pyramid of the First Direction, 195 Ditetragonal Pyramidal Class, 175 Ditetragonal Pyramidal Class, Symmetry of, 175 Ditetragonal Scalenohedron, 195 Ditrigonal Bipyramidal Class, 179, 180 Ditrigonal Prism, 98, 99, 105, 177, 179, 180, 192 Ditrigonal Prism of the First Order, 192 Ditrigonal Prism of the Second Order, 193 Ditrigonal Pyramid, 95, 96, 107, 179, 180, 198 Ditrigonal Pyramidal Class, 178, 179 Ditrigonal Pyramid, Symmetry of, 96 Ditrigonal Pyramidal Tetarto- hedral Class, 178 Ditrigonal Scalenohedral Class, 179 Ditrigonal Trapezohedron, 199 Dodecagonal Prism, 192 Dodecahedral Axes, 131, 139 Dodecahedral Class, 183, 184 Dodecahedral Cleavage, 155, 159 Dodecahedron, 123, 126, 127, 141-144, 183-186, 200, 204, 207, 236, 239-244, 248, 254 Dodecahedron, Dyakis, 51, 125, 135, 137, 138, 144, 185, 188, 201, 202, 215, 238, 245, 246, 254, 261 Dodecahedron, Pentagonal, 24, 25, 51, 52, 125, 135-138, 142, INDEX. 271 143, 183, 185, 200, 207, 237, 238, 244-246, 254 Dodecahedron, Rhombic, 123, 126, 127, 141-143, 183-186, 200, 204, 207, 236, 239-244, 248, 254 Dodecahedron, Tetrahedral Pen- tagonal, Symmetry of, 123, 141, 166, 261 Dodecahedron, Tetrahedral Pen- tagonal, 123, 125, 140-142, 144, 166, 183, 184, 202, 238, 239, 261 Domatic Dodecahedron, 200 Domatic Class, 169, 170 Dome, 12, 13, 21, 42-45, 50, 54 Dome, Primary, 170 Dome, Quaternary, 170 Dome, Tertiary, 170 Dome, Vertical, 43, 44 Dominant Form, 26 Drawings, Crystallographic, 28- 34 Dyakis Dodecahedron, 51, 125, 135, 137, 138, 144, 185, 188, 201, 202, 215, 238, 245, 246, 254, 261 Dyakis Dodecahedral Class, 184, 185 Dyakis-Dodecahedron, Symme- try of, 51, 52, 138, 261 Edges, Ehombohedral, 86, 106 Edges, Zigzag, of the Rhombo- hedron and Scalenohedron, 86, 89, 90 Eight Angled Dodecahedron, 197 Eight Angled Hexahedron, 196 End Plane, 199 Epsomite, 55, 61, 216 Family Names, Change in, 188, 189 Family of Hexagonal Prisms, 191-193 Family of Hexagonal Pyramids, 196-199 Family of Monoclinic Prisms, 190 Family of Monoclinic Pyramids, 193 Family of Orthorhombic Prisms, 190, 191 Family of Orthorhombic Pyra- mids, 194 Family of Tetragonal Prisms, 191 Family of Tetragonal Pyramids, 194-196 Family of Triclinic Prisms, 189, 190 Family of Triclinic Pyramids, 193 Families of the Isometric Tribe, 200-202 Families ol the Pinacoid Tribe, 199, 200 Families of the Prism Tribe, 189-193 Families of the Pyramid Tribe, 193-199 First Hexagonal Prism, 191 First Hemimorphic Tetarto- hedral Class, 180, 181 First Horizontal Prism, 190, 191 First Order of Hexagonal Prism, 80-85, 91, 101, 104, 177, 179-183, 191 First Order of Hexagonal Pyra- mid, 81-85, 93, 102, 106, 181- 183, 188, 196 272 INDEX. First Order Bhombohedron, 88, 97, 106, 177, 179, 196 First Order, Tetragonal Prism, 61, 63, 175, 176, 191 First Order, Tetragonal Pyra- mid, 61, 63, 175, 176, 194 Fivelings, 152, 256, 257 Fluoroid, 200 Fluorite, 27, 123, 141, 149, 150, 153, 208 Foote Mineral Company, viii Form, 22-25 Forms of the Hexagonal Sys- tem, 76-80 Fourlings, 152 Frankenheim, M. L., 167 Frederick Barbarossa, 188 Fundamental Bhombohedron, 87 Gadolin, A., 161, 167 Galenoid, 200 Galenite, 3, 14, 23, 26, 27, 123, 141, 149, 150, 153, 204, 207, 253, 254 Garnet, 27, 123, 141, 207 Garnet Crystallization, 200 Garnet Dodecahedron, 200 Garnetohedron, 200 Garnetoid, 200 Geniculated Twin, 153, 252 Goslarite, 51, 57, 214, 216' Groth, P., 29, 34, 167, 173 Groth, Divisions of the Hexa- gonal System, 74 Groth 'a Notation, 29 Group, Hexagonal, Trapezo- hedron, 93-95, 164 Groups, Parallel, 3, 149, 150, 204, 205, 247 Group, Pyramidal Hexagonal, 91-93, 121, 164 Group, Pyramidal Tetragonal, 67-69, 163, 174, 175 Group, Ehombohedral, 85-91, 121, 164 Group, Sphenoidal Tetragonal, 65-67, 163, 173, 174 Group, Tetartohedral Ehombo- hedron, 96-98, 164 Group, Trapezohedral Hexa- gonal, 94, 164 Group, Trapezohedral Tetarto- hedral, 98-100, 164 Group, Trapezohedral Tetra- gonal, 69, 163 Group, Trigonal Hexagonal, 95, 96, 164 Group, Trigonal Tetartohedral, 101, 102, 164, 165 Growths, Parallel, 3, 149, 150, 204, 205, 247 Growths, Polysynthetic, 151, 153, 247 Gypsum, 3, 11, 12, 15, 17, 18, 26, 41, 43-47, 149, 150, 152, 203, 210, 248, 249 Gyroid, 123, 125, 139, 142, 144, 166, 184, 188, 202, 238, 261 Gyroidal Group, 184 Gyroidal Hemihedral Forms, 123, 125, 138, 139, 142, 144, 166, 184, 202, 238, 261 Gyroidal Hemihedral Forms, Symmetry of, 139, 166, 261 Gyroid Hemihedral Class, 184 Gyroids in Combination with other forms, 142 Harmotome, 149, 150, 153, 256 Harvard University, v Hauy-L6vy-Des Cloizeaux No- tation, 29 INDEX. 273 Haiiynite, 149, 150, 153, 253 Hematite, 149, 150, 153, 255 Henri Brachy Dome, 190 Hemi Di Hexagonal Prism, 192 Henri Di Hexagonal Pyramid, 197, 198 Hemi Di Octahedron, 195 Hemi-Ditetragonal Prism, 67, 191 Hemi-Ditetragonal Pyramid, 67, 68, 195, 196 Hemi Dodecahedron, 197 Hemi Dodecahedron of the First Order, 196 Henri-Dome, 25, 45, 55, 190 Hemihedral and Bolohedral Forms, Distinction between, 46 Hemihedral Class, Monoelinie, 45, 162, 169, 170, 208-211, 258 Hemihedral Di Hexahedron, 198 Hemihedral Forms, 24, 25, 45, 46, 55-57, 65-69, 85-96, 131- 139 Hemihedral Forms Denned, 25 Hemihedral Forms, Symmetry of, 24 Hemihedral Gyroidal Forms, 123, 125, 138, 139, 142, 144, 166, 184, 202, 238, 261 Hemihedral Hexagonal Forms, 77, 85-96, 121, 164, 176-182, 207, 215, 223, 229-235 Hemihedral Isometric Forms, 123-125, 131-139, 141-144, 165, 166, 200, 201, 207, 215, 236-238, 242-246, 253, 254, 261 Hemihedral Monoelinie Forms, 45, 46, 161, 162, 169, 170, 258 Hemihedral Notation, 36-38 Hemihedral Oblique Forms, 124, 131-135, 141-144, 165, 185, 186, 236, 237, 242-244, 253, 254 Hemihedral Orthorhombic Form, 55, 56, 162, 163, 170, 171, 259 Hemihedral Parallel Forms, 125, 135-138, 141-144, 166, 200-202, 207, 215, 237, 238, 244-246, 254 Hemihedral Plagihedral Forms, 123, 125, 138, 139, 142, 144, 166, 184, 202, 238, 261 Hemihedral Pyramidal Group, Symmetry of, 93, 164, 260 Hemihedral Rhombohedral Group, Symmetry of 52, 90, 91, 164, 259 Hemihedral Tetragonal Forms, 65-69, 163, 220, 221, 259 Hemihedral Trapezohedral Group, Symmetry of, 94, 164, 260 Hemihedral Trigonal Group, Symmetry of, 96, 164, 260 Hemi Hexagonal Scalenohedron, 198, 199 Hemi Hexakis Octahedron, 201 Hemi Icosi Tetrahedron, 201 Hemi Macro Dome, 190 Hemimorphic Class, 178, 179 Hemimorphie Class, Monoelinie, 169 Hemimorphic Forms, 45, 46, 56, 57, 102-104 Hemimorphic Group, 182 Hemimorphic Group of the Pyramidal Hemihedral Class, Tetragonal, 172, 173, 261 Hemimorphic Group, Tetra- gonal, 175 274 INDEX. Hemimorphic Hemihedral Class, 178-182 Hemimorphie Hemihedral Class, Tetragonal, 175 Hemimorphic Hemihedral Class, Tetragonal, 172, 173, 261 Hemimorphic Hexagonal Forms, 80, 102-104, 108, 109, 165 Hemimorphic Hexagonal Form, Symmetry of, 103, 104, 165, 260 Hemimorphic Holohedral Class, 182 Hemimorphic Holohedral Class, Tetragonal, 175 Hemimorphic Orthorhombic Forms, 56, 57, 163, 171, 259 Hemimorphic Orthorhombic Forms, Symmetry of, 56, 163, 259 Hemimorphic Pyramidal Hemi- hedral Class, 180, 181 Hemimorphic Rhombohedral Hemihedral Class, 178, 179 Hemimorphic Tetartohedral Class, 176, 177 Hemimorphie Tetartohedral Class, Tetragonal, 172, 173, 261 Hemimorphic Trigonal Hemi- hedral Class, 178, 179 Hemimorphie Trigonal Tetarto- hedral Class, 176, 177 Hemimorphism, 45, 46, 56 Hemi Octahedron, 45, 200 Hemi Octakis Hexahedron, 201 Hemi-Ortho-Dome, 45, 190 Hemiorthotype, 193 Hemipinacoidal Class, 167, 261 Hemi Primary Hexagonal Prism, 192 Hemi Primary Hexagonal Py- ramid, 196 Hemi-Prism, 25, 55, 189 Hemi-Pyramid, 3, 11, 12, 15,17, 18, 26, 41, 44-46, 47, 55, 203 Hemi Secondary Hexagonal Prism, 192 Hemi Secondary Hexagonal Pyramid, 197 Hemi Tetragonal Triakis Octa- hedron, 201 Hemi Tetragonal Pyramid, 194 Hemi Tetrakis Hexahedron, 200 Hemi Trigonal Triakis Octa- hedron, 201 Hessel, J. F. C., 167 Hexagonal and Orthorhombic Crystals, Distinction between, 52 Hexagonal and Tetragonal Sys- tems, Distinctions between, 73, 74 Hexagonal Axes, 8, 73, 75, 109, 203 Hexagonal Basal Pinacoid, 176- 183 Hexagonal Bipyramidal Class, 181, 182 Hexagonal Cleavage, 158 Hexagonal Compound Forms, 104 Hexagonal Crystals, Directions for Studying, 121 Hexagonal Crystals, distinguish-, ing Characteristics of, 76 Hexagonal Crystals, Beading Drawings of, 109-113 Hexagonal Division, 74, 121 Hexagonal Dodecahedron of the First Order, 196 INDEX. 275 Hexagonal Dodecahedron of the Second Order, 197 Hexagonal Hemihedral, Sym- metry of, 90, 91, 93, 94, 96, 164, 259, 260 Hexagonal Hemimorphic Class, 182 Hexagonal Hemimorphic Forms, 102-104, 108, 109 Hexagonal Hemimorphic Forms, Symmetry of, 103-104, 165, 260 Hexagonal Holohedral Symme- try, 74, 84, 85, 163, 259 Hexagonal Lateral Axes, 73 Hexagonal Nomenclature, 75 Hexagonal Parallel Growths, 3, 28, 149, 205 Hexagonal Pinacoid, 76, 176, 183 Hexagonal Planes, Rules for naming them, 104-109 Hexagonal Primary Prism, 61, 63, 80-85, 91, 101, 104, 177, 179-183, 191 Hexagonal Primary Pyramid, 81-85, 93, 102, 106, 181-183, 188, 196 Hexagonal Prism, 189, 204 Hexagonal Prism of the First Order, 80-85, 91, 101, 104, 177, 179-183, 191 Hexagonal Prism of the Prin- cipal Series, 191 Hexagonal Prism of the Second Order, 81-85, 91, 93, 99, 101, 105, 177, 179-183, 192 Hexagonal Prism of the Second Series, 192 Hexagonal Prism of the Third Order, 91, 92, 105, 181, 18:2, 192 Hexagonal Pyramidal Class, 18, 181 Hexagonal Pyramidal Group, 91-93, 121, 164 Hexagonal Pyramidal Tetarto- hedral Class, 180, 181 Hexagonal Pyramid of the First Division, 196 Hexagonal Pyramid of the First Order, 81-85, 93, 102, 106, 181-183, 188, 196, 204 Hexagonal Pyramid of the Second Division, 197 Hexagonal Pyramid of the Second Order, 82-85, 96, 106, 179-183, 196, 197 Hexagonal Pyramid of the Third Order, 91-93, 181, 182, 198 Hexagonal Pyramidohedron of the First Normal Direction, 196 Hexagonal Pyramidohedron of the Second Normal Direction, 197 Hexagonal Scalenohedron, 88- 91, 94, 97, 100, 107, 179, 197, 207, 215, 223-227, 231, 234 Hexagonal Scalenohedron, La- teral Edges, 89, 107 Hexagonal Secondary Prism, 81- 85, 91, 93, 99, 101, 105, 177, 179-183, 192 Hexagonal Secondary Pyramid, 82-85, 96, 106, 179-183, 196, 197 Hexagonal Semi-Axes, Nota- tion for, 75 Hexagonal Shorthand or Nota- tion, 114-120 Hexagonal System, 8, 52, 73-121, 203-207, 215, 221-235, 249- 255, 254, 255, 259, 260 Hexagonal System, Divisions of, 74 276 INDEX. Hexagonal System, Symmetry, of, 25, 74, 76, 84, 85, 90, 91, 93, 94, 96, 100, 102, 163-165, 259, 260 Hexagonal Tertiary Prism, 91, 92, 105, 181, 182, 192 Hexagonal Tetartohedral Forms, 96-102 Hexagonal Tetartohedral Form, Symmetry of, 100, 102, 164, 165, 260 Hexagonal Trapezohedral Class, 181 Hexagonal Trapezohedral Group, 93-95, 164 Hexagonal Trapezohedron, 93- 95, 107, 121, 181, 198 Hexagonal Trigonal Group, 95, 96, 164 Hexahedral Pentagonal Dode- cahedron, 200 Hexahedral Trigonal Icosi Te- trahedron, 200 Hexahedron, Tetrakis, 123, 127, 128, 135, 136, 141-143, 184- 186, 189, 200, 208, 236-238, 240, 244, 248 Hexahedron, 123, 126, 141, 142, 183-186, 188, 200, 208, 236- 248, 253, 254 Hexoctahedron, 124, 130, 137, 144, 186, 188, 201, 207, 236- 239, 241, 242 Hexakis Octahedron, 124, 130, 137, 144, 186, 188, 201, 207, 236-239, 241, 242 Hexakis Tetrahedral Class, 185, 186 Hexakis Tetrahedron, 124, 134, 135, 144, 186, 201, 237, 244, 261 Hextetrahedral Class, 185, 186 Hextetrahedron, 124, 134, 135, 140, 144, 186, 201, 237, 244, 261 Holohedral and Hemihedral Forms, Distinction between, 46 Holohedral Class, 182, 183 Holohedral Forms, Symmetry, of, 23, 24 Holohedral Hexagonal Class, 182, 183 Holohedral Isometric Forms, 123-131, 141-144, 165, 186, 200, 201, 236, 239-242, 247, 248, 253, 254, 261 Holohedral Isometric Forms Symmetry of, 123, 130, 131, 165, 261 Holohedral Isometric Forms in Combination, 141 Holohedral Class, Monoclinic, 45, 162, 170, 208-211, 258 Holohedral Class, Ortborhom- bie, 171, 172, 259 Holohedral Class, Tetragonal, 175, 176 Holohedral Class, Triclinic, 23, 162, 168, 169, 205, 206, 258 Holohedral Forms, 23, 24, 45, 46, 54-57, 63-65, 80-8^, 125- 131 Holohedral Group, 182, 183 Holohedral Hexagonal Form, 76, 80-85, 121, 163, 204, 206, 221-224, 226-228, 233-235 Holohedral Hexagonal Symme- try, 84, 85, 163, 259 Holohedral Monoclinic Forms, 45, 162, 170, 208-211, 258 Holohedral Orthorhombio Forms, 54, 55, 162, 171, 172, 259 INDEX. 277 Holohedral Tetragonal Forms, 63-65, 163, 216-220, 259 Horizontal Prism, 190-191 Horizontal Prism of a Rhom- bohedral Section, 190 Icositetrahedron, 124, 129, 141- 144, 201, 236, 237, 240-242, 244-246 Icositetrahedrons, Pentagonal, 123, 125, 138, 139, 142, 144, 166, 184, 202, 238, 261 Inclined Axis, 42 Inclined-Faced Hemihedral Class, 185, 186 Inclined Hemihedral Class, 185, 186 Individual Names, 187, 188 Indices, 32-34, 75 Inorganic World, 1 Inscribed Rhombohedron, 90 Inverse Octahedron, 195 Inverse Prism, 191 Inverse Pyramid, 195 Inverse Tetragonal Prism, 61, 63, 175, 176, 191 Inverse Tetragonal Pyramid,195 lodyrite, /4, 76, 80, 81, 102, 104, 222 lodyrite Type, 74, 76, 81, 102- 104, 108, 121, 165, 222 lodyrite Type, Symmetry of, 103, 165, 260 Irregular Tetrahedron, 194 Isometric and Orthorhombic Crystals, Distinction between, 51, 52 Isometric Axes, 7, 122, 126, 203 Isometric Cleavage, 159 Isometric Compound Forms, 141, 142 Isometric Crystals, Directions for Studying, 147 Isometric Crystals, Distinguish- ing Characteristics of, 123 Isometric Gyroidal Hemihedral Forms, Symmetry of, 139, 166, 261 Isometric, Hemihedral Forms, 123-12o, 131-139, 141-144, 165, 166, 200, 201, 207, 215, 236-238, 242-246, 253, 254, 261 Isometric Hemihedral Forms, Symmetry of, 51, 52, 123, 135, 138, 139, 165, 261 Isometric Holohedral Forms, 123-131, 141-144, 165, 186, 200, 201, 236, 239-242, 247, 248, 253, 254, 261 Isometric Holohedral Forms, Symmetry of, 23, 24, 123, 130, 131, 165 Isometric Hemihedral Oblique Forms, Symmetry of, 123, 135, 165, 261 Isometric Parallel Hemihedral Forms, 51, 52, 123, 138, 166, 261 Isometric Shorthand or Nota- tion, 146, 147 Isometric System, 7, 122-147, 165, 166, 183-186, 189, 200- 204, 207, 208, 215, 236-248, 253, 254, 261 Isometric System, Symmetry of, 23, 24, 51, 52, 123, 130, 131, 135, 138, 139, 141, 147, 165 166, 261 Isometric Tetartohedral Forms, 123, 125, 140-142, 144, 166, 183, 184, 202, 238, 239, 261 278 INDEX. Isometric Tetartohedral Forms, Symmetry of, 123, 141, 166, 261 Isometric Tribe, 189, 200-202 Isometric Twins, 247, 248, 253, 254 Jointing, Bock, 160 Johnson, Ben, 188 Klinorhombohedral Prism, 189 Krantz, F., viii Kraus, E. H., 167 Kuntze, Otto, viii Lateral Angles, Bhombohedral, 86, 87 Lateral Axes, 10, 42, 60, 73 Lateral Axes Hexagonal, 73 Lateral Axes, Monoclinic, 42 Lateral Axes, Tetragonal, 60 Lateral Axes, Triclinic, 10 Lateral Edges, Hexagonal Scale- nohedron, 89, 107 Lateral Edges, Bhombohedral, 86, 106 Left-handed Ditrigonal Prism, 98, 99, 193 Left-handed Hexagonal Pyra- mid of the Third Order, 91- 93, 198 Left-handed Hexagonal Trape- zohedron, 93-95, 198 Leit-handed Negative Bhomb- ohedron, 96-98, 198 Left-handed Negative Tri- gonal Pyramid, 98-100 Left-handed Pentagonal Icosi- tetrahedron, 125, 138, 139, 184 Left-handed Positive Secondary Bhombohedron, 96, 97 Left-handed Positive Tertiary Bhombohedron, 96-98, 198 Left-handed Positive Trigonal Pyramid, 98-100 Left-handed Secondary Tri- gonal Prism, 98, 99, 176, 192 Left-handed Sphenoid, 56 Left-handed Tetrahedral Penta- gonal Dodecahedron, 125, 140, 141, 184 Left-handed Tertiary hexagonal Prism, 91-93, 192 Left-handed Tertiary Hexagonal Pyramid, 91-93, 198 Left-handed Tertiary Trigonal Prism, 101, 102, 193 Left-handed Tertiary Trigonal Pyramid, 101, 102, 199 Left-handed Tetragonal Trape- zohedron, 69, 196 Leucite Crystallization, 201 Leucitohedron, 124, 129, 141- 144, 201, 236, 237, 240-242, 244-246 Leucitoid, 129, 141-144, 201 Levy, A., 29 Liebisch, T., 34, 74 Limonite, 148 Lines, broken, 161 Lines, full, 161 Linnseite, 3, 19, 23, 26, 123, 141, 204 Literature of Crystallography, x-xiii Lithium Sulphate, 169 Longfellow, Henry Wadsworth, 188 Macro-Axis, 10 Macro-Diagonal, 10 Macro-Diagonal Pinacoid, 200 INDEX. 279 Macro-Diagonal Prism, 191 Macro-Dome, 12, 22, 54, 190, 191 Macro-Pinacoidal Cleavage, 155-157 Macro-Pinacoid, 12, 21, 54, 200, 205 Macro-Semi-Axis, 50 Magnetite, 3, 14, 23, 123, 128, 204 Mallard, E., 34 Marcasite, 149, 150, 154, 256, 257 Melanterite, 41-47, 208, 210 Mellite, 61, 70, 73, 74, 218 Method 01 Representing Sym- metry, 161, 162 Michigan College of Mines, vi Miller, W. H., xiii, 32, 33, 34, 37, 47, 70, 7* Miller, Axes of Hexagonal Sys- tem, 74 Miller-Bravais Notation, 29, 75, 103, 111 Miller Notation, 32-34, 47, 70 Milton, John, 188 Mimicry, 153, 154, 256-258 Mineral, 2, 3 Mineral Aggregate, 149, 160, 247 Mineral Chemistry, 2 Mineral Kingdom, 1 Mineralogy, 1, 2 Mineralogy, Instruction in, viii, xv Models, Crystal, vii, 56 Monoclinic Axes, 7, 40-42, 47, 203 Monoclinic Cleavage, 157 Monoclinic Clino-Dome, 43, 44, 190, 203 Monoclinic Clinohedral Forms, 46, 161, 162, 169, 170, 258 Monoclinic Clino Pinacoids, 43 Monoclinie Clino Prism, 190 Monoclinic Compound Forms, 46 Monoclinic Crystals, Directions for Studying, 49 Monoclinic Crystals, Distin- guishing Characteristics of, 44 Monoclinic Crystals, Beading Drawings of, 46, 47 Monoclinic Crystals, Symmetry of, 40, 41, 44, 49, 162, 169, 258, 261 Monoclinic Domes, 43, 44, 170, 190 Monoelinic Forms, 48 Monoclinic Hemihedral Forms, 45, 46, 161, 162, 169, 170, 2oS Monoclinic Hemihedral Forms, Symmetry of, 40, 41, 162, 258 Monoclinic Hemimorphic Forms, 45, 46, 163, 169 Monoclinic Hemimorphic Forms, Symmetry of, 169, 261 Monoclinic Hemimorphism, 45, 46 Monoclinic Hemi Ortho Dome, 190 Monoclinic Hemi Pyramid, 193, 203 Monoclinic Holohedral Forms, 45, 162, 170, 208-211, 258 Monoclinic Holohedral Forms, Symmetry of, 40, 41, 162, 258 Monoclinic Nomenclature, 41-43 Monoclinic Notation, 46-48 Monoclinic Ortho-Domes, 43, 44, 190 Monoclinic Ortho Pinacoids, 43, 44 280 INDEX. Monoclinic Pinacoids, 42-44, 169, 170 Monoclinic Planes, relation to the Axes, 43 Monoclinic Planes, Rules for naming, 44, 45 Monoclinic Prisms, 43, 44, 170, 190, 203 Monoclinic Pyramid, 43, 45, 193, 203 Monoclinie Shorthand or Nota- tion, 48 Monoclinic Symmetry, 40, 41, 44, 49, 162, 169, 258, 261 Monoclinic System, 7, 40-49, 162, 169, 170, 203, 208-211, 248, 250, 255,258, 261 Monoclinic Vertical Dome, 190 Monoclinic Vertical Prism, 190 Moses, A. J., x, 74, 167, 173 Moses and Parsons. Elements of Mineralogy, x, 167, 173 Moses, Division of the Hexa- gonal System, 74 Names of Individuals, 187, 188 Natron, 8, 11, 12, 17, 18, 26, 41, 44, 46, 47, 203 Naumann, C. F., xiii, 29, 32, 33, 47 Naumann Notation, 29, 32, 33, 47, 70, 111, 112 Negative Ditrigonal Prism, 98, 99, 192 Negative Ditrigonal Pyramid, 95, 96, 199 Negative Dyakis Dodecahedron, 51, 125, 135, 137, 138, 215 Negative Forms, 36 Negative Hexagonal Pyramid of the Third Order, 91-93, 198 Negative Hexagonal Scaleno- hedron, 89, 197 Negative Hexagonal Semi-Axes, 109, 110 Negative Hexagonal Trapezo- hedron, 93, 94 Negative Hexakis Tetrahedron, 124, 135, 186 Negative Left-Handed Tertiary Trigonal Prism, 193 Negative Left-handed Tertiary Trigonal Pyramid, 199 Negative Left-Hanaed Tertiary Ehombonedron, 198 Negative Left-handed Trigonal Trapezohedron, 199 Negative or Left-Handed Ter- tiary Hexagonal Pyramid, 198 Negative or Left-Handed Hexa- gonal Prism, 192 Negative or Left-Handed Or- thorhombic Sphenoid, 194 Negative or Left-handed Tetra- gonal Trapezohedron, 196 Negative or Left-Handed Tri- gonal Prism, 192 Negative or Left-Handed Tri- gonal Pyramid, 197 Negative Pentagonal Dodeca- hedron, 125, 136, 137, 185, 20T Negative Primary Trigonal Prism, 101, 176, 192 Negative Primary Trigonal Pyramid, 101, 102 Negative Ehombohedron, 85-88, 198 Negative Ehombohedron of th Second Order, 197 Negative Eight-Handed Ter- tiary Ehombohedron, 198 INDEX. 281 Negative Eight-Handed Ter- tiary Trigonal Prism, 193 Negative Eight -handed Tertiary Trigonal Pyramid, 199 Negative Right-handed Trigonal Trapezohedron, 199 Negative Scalenohedron, 197 Negative Secondary Rhombo- hedron, 96, 97, 197 Negative Secondary Trigonal Prism, 98, 99, 176, 192 Negative Secondary Trigonal Pyramid, 98-100, 197 Negative Sphenoid, 56, 195 Negative Tertiary Trigonal Prism, 101, 102, 193 Negative Tertiary Trigonal Pyramid, 101, 102, 199 Negative Tertiary Hexagonal Prism, 91, 93, 192 Negative Tertiary Hexagonal Pyramid, 91-93, 198 Negative Tertiary Pyramid, 195 Negative Tertiary Rhombohe- dron, 96-98, 198 Negative Tetragonal Scaleno- hedron, 195 Negative Tetragonal Triakis Tetrahedron, 124, 132, 133, 183, 185 Negative Tetragonal Trapezo- hedron, 69, 196 Negative Tetrahedral Penta- gonal Dodecahedron, 125, 140, 141, 184 Negative Tetrahedron, 124, 132, 183, 185 Negative Trigonal Triakis Te- trahedron, 124, 134, 183, 185 Negative Trigonal Trapezohe- dron, 98, 100, 199 Nephelite Type, 74, 76, 81, 103, 104, 109, 121, 165, 180, 181, 222 Nephelite Type, Symmetry of, 106, 165, 260 Nicknames in Crystallography, 1*8-202 Niter, 3, 51, 57, 204, 214 j Nomenclature, Crystallographic 187-202 Nomenclature, Hexagonal, 75 Nomenclature, Isometric, 122, 123 Nomenclature, Monoclinic, 41-43 Nomenclature, Orthorhombio 50, 51 Nomenclature, Tetragonal 60-62 Nomenclature, Triclinic, 10-13 Normal Class, Monoclinic, 170, 208-211, 258 Normal Group, 168, 182, 183, 205, 206, 258 Normal Group, Orthorhombic, 171, 172, 259 Normal Group, Tetragonal, 175, 176 Normal Rhombohedral Group, 179 Oblique Angled Quadralateral Prism, 190 Oblique Axis, 42 Oblique Hemihedral Class, 185, 186 Oblique Hemihedral Forms, 124, 131-135, 141-144, 165, 185, 186, 236, 237, 242-244, 253, 254 Oblique Hemihedral Forms, Symmetry of, 123, 135, 165, 261 282 INDEX. Oblique Hemihedral Forms in combination, 141 Oblique Ehombic Prism, 190 Obtuse Khombohedron, 87 Octagonal Prism, 191 Octahedral Axes, 131, 135, 139 Octahedral Cleavage, 155, 159 Octahedrite, 61, 62, 70, 73, 74, 218 Octahedron, 3, 12, 13, 14, 22, 23, 42-45, 51, 54, 123, 128, 132, 141, 143, 184, 186, 188, 189, 200, 204, 207, 236, 239- 242, 245-247, 253, 254 Octahedron, Distorted, 3, 26, 204, 254 Octahedron, Hexakis, 124, 130, 137, 144, 186, 188, 201, 207, 236-239, 241, 242 Octahedral Pyramidal Icosi Tetrahedron, 200 Octahedron, Tetragonal Triakis 124, 129, 141-144, 201, 236, 237, 240-242, 244-246 Octahedral Trigonal Icosi Te- trahedron, 200 Octahedron, Trigonal Triakis, 124, 128, 129, 133, 134, 141- 143, 188, 200, 207, 236-237, 240 Octakis Hexahedron, 201 Octants, 7 Optical Mineralogy, 2 Organic World, 1 Ortho-Axis, 42 Orthoclase, 149, 150, 152, 153, 249, 250, 255 Ortho-Diagonal, 42 Ortho-Dome, 43, 44 Ortho-Pinacoidal Cleavage, 155- 157 Ortho-Pinacoid, 3, 11, 12, 15, 17, 18, 26, 41, 43, 44, 46, 47, 50, 51, 54, 203 Orthorhombie Axes, 7, 50, 57, 203 Orthorhombic and Hexagonal Crystals, Distinction between, 52 Orthorhombic and Isometric Crystals, Distinction between, 51, 52 Orthorhombic Brachy-Dome, 50, . 51, 54, 190 Orthorhombic Brachy-Pinacoids, 50, 54 Orthorhombic Brachy Prism, 190 Orthorhombic Cleavage, 157 Orthorhombic Crystals, Direc- tions for Studying, 59 Orthorhombic Crystals, Distin- guishing Characteristics of, 53, 54 Orthorhombic Crystals, Beading Drawings of, 57, 58 Orthorhombic Forms, 58 Ogdohedral Class, 176, 177 Ogdomorphous Class, 176, 177 Orthorhombic Hemihedral Forms, 55, 56, 162, 163, 170, 171, 259 Orthorhombic Hemimorphic Forms, 51, 52, 56, 57, 163, 171, 259 Orthorhombic Hemihedral Forms, Symmetry of, 55, 162, 163, 259 Orthorhombic Hemimorphic Forms, Symmetry of, 56, 163, 259 Orthorhombic Hemi Pyramid, 194 INDEX. 283 OrtliorhombiCjHolohedral Forms, 54, 55, 162, 171, 172, 259 OrthorhombiCjHolohedralForms, Symmetry of, 23, 51, 52, 55, 162, 259 Orthorhombic Macro-Domes, 50, 51, 54, lyl Orthorhombic Macro-Pinacoids, 50, 54 Orthorhombic Macro-Prism, 191 Orthorhombic Nomenclature, 50, 51 Orthorhombic Notation, 58 Orthorhombic Octahedron, 194 Orthorhombic Pinacoid, 50, 54, 171, 203 Orthorhombic Planes, Rules for naming, 54 Orthorhombic Prism, 50, 51, 54, 171 Orthorhombic Pyramid, 7, 25, 51, 54, 171, 172, 194 Orthorhombic Shorthand or No- tation, 58 Orthorhombic Sphenoid, 55, 56, 66, 171, 194, 215, 216 Orthorhombic Symmetry, 23, 51, 52, 55, 56, 59, 162, 163, 259 Orthorhombic System, 7, 50-59, 162, 163, 170-172, 203, 204, 211-216, 247, 250, 252, 256- 259 Orthorhombic Vertical Dome, 190 Orthorhombic Vertical Prism, 190 Orthotype, 194 Oscillatory Combination, 151, 247 Parallel Groups, 3, 149, 150, 204, 205, 247 Parallel Growths, 149, 150, 247 Parallel Hemihedral Class, 184, 185 Parallel Hemihedral Forms, 125, 135-138, 141-144, 166, 200-202, 207, 215, 237, 238, 244-246, 254 Parallel Hemihedral Forms in combination, 141 Parallel Hemihedral Forms Symmetry of, 51, 52, 123, 138, 166, 261 Parallel Eock Jointing, 360 Parameters, 31-33, 75 Parameters of the Secondary Hexagonal Prism and Pyra- mid, 83, 84 Parsons, C. L., x, 167, 173 Parting Planes, 159, 160 Parting Plane Shorthand, 159 Partings, 159, 160 Patton, H. B., vi Penetration Twins, 151-153, 253-257 Penfield, S. L., x, 167 Pentagonal Dodecahedron, 24, 25, 51, 52, 125, 135-138, 142, 143, 183, 185, 200, 207, 237, 238, 244-246, 254 Pentagonal Dodecahedron, Sym- metry of, 51, 52, 138, 166, 261 Pentagonal Hemihedral Class, 184, 185 Pentagonal Icositetrahedral Class, 184 Pentagonal Icositetrahedron,123, 125, 138, 139, 142, 144, 166, 184, 202, 238, 261 Pentagonal Icositetrahedrons in combination with other forms. 142 284 INDEX. Pentagonal Icositetrahedrons Symmetry of, 139, 166, 261 Pentagonal Tetrahedral Dode- cahedron, 123, 125, 140-142, 144, 166, 183, 184, 202, 238, 239, 261 Pedial Class, 167, 261 Pedion, 168-171 Pedion, First, 168, 170 Pedion, Primary, 168 Pedion, Second, 168, 169 Pedion, Secondary, 168, 170 Pedion, Third, 168, 170, 171 Pedion, Tertiary, 168 Pedion, Quaternary, 168 Phillipsite, 149, 150, 153, 154, 255, 258 Pinacoid, 11, 12, 13, 42, 44, 50, 54, 60, 63, 80, 104, 168-183, 188, 199, 200, 203, 205 Pinacoidal Class, 168, 169, 205, 206, 258 Pinacoidal Cleavage, 155-158 Pinacoid, Basal, 11, 21, 42, 44, 60, 63, 80, 104, 172-183, 199 Pinacoid, First, 168-171 Pinacoid, Hexagonal 76, 176-183 Pinacoid, Macro, 12, 21, 54, 200, 205 Pinacoid, Primary, 169 Pinacoid, Quaternary, 169 Pinacoid, Second, 168, 170, 171 Pinacoid, Secondary, 169, 170 Pinacoid, Tertiary, 169 Pinacoid, Third, 169-171 Pinacoid, Vertical, 11, 21, 42, 44, 199 Plagihedral Group, 184 Plagihedral Hemihedral Class, 184 Plagihedral Hemihedral Forms, 123, 125, 138, 139, 142, 144, 166, 184, 202, 238, 261 Plagiohedron, 199 Plane of Symmetry, 15-18, 23- 25, 39, 40, 41, 44, 46, 49, 51- 56, 59, 64, 67-69, 72, 74, 84, 90, 93, 94, 96, 98, 100, 102, 103, 121, 130, 131, 135, 138, 139, 141, 147, 161-166, 168, 169, 172, 173, 175, 203, 258- 261 Planes of Symmetry, how rep- resented, 161 Planes, relation to Axes, 43, 51, 62, 75 Planes, relation to Hexagonal Axes, 75 Planes, Eules for naming them in the Hexagonal System, 104-109 Planes, Variation of Crystal Planes, 3 Poland, 187 Polarized Light, 150 Polynomial Names, 188 Polysynthetic Twinning, 151, 153, 247 Popular Science Monthly, viii Position Ditrigonal Prism, 98, 99, 192 Positive Ditrigonal Pyramid, 95, 96, 199 Positive Dyakis Dodecahedron, 51, 125, 135, 137, 138, 215 Positive Forms, 36 Positive Hexagonal Scaleno- hedron, 89, 197 Positive Hexagonal Semi-axes, 109, 110 Positive Hexagonal Trapezo- hedron, 9rf, 94 INDEX. 285 Positive Hexakis Tetrahedron, 124, 135, 186 Positive Left-Handed Tertiary Bhombohedron, 198 Positive Left-Handed Tertiary Trigonal Prism, 193 Positive Left-handed Tertiary Trigonal Pyramid, 199 Positive Left-handed Trigonal Trapezohedron, 25, 76, 100, 104, 199, 207 Positive or Eight-Handed Hex- agonal Prism, 192 Positive or Eight-Handed Or- thorhombic Sphenoid, 194 Positive or Eight-Handed Ter- tiary Hexagonal Pyramid, 198 Positive or Eight-handed Tetra- gonal Trapezohedron, 196 Positive or Eight-Handed Tri- gonal Prism, 192 Positive or Eight-Handed Tri- gonal Pyramid, 197 Positive Pentagonal Dodeca- hedron, 125, 136, 137, 185,^ 207 Positive Primary Trigonal Priam, 101, 176, 192 Positive Primary Trigonal Pyramid, 101, 102 Positive Ehombohedron, 85, 87, 88, 198 Positive Bhombohedron of the Second Order, 197 Positive Eight-Handed Tertiary Trigonal Prism, 193 Positive Eight-handed Tertiary Trigonal Pyramid, 199 Positive Eight -handed Trigonal Trapezohedron, 25, 76, 100, 104, 199, 207 Positive Eight-handed Tertiary Ehombohedron, i98 Positive Scalenohedron, 197 Positive Secondary Ehombo- hedron, 96, 97, 197 Positive Secondary Trigonal Prism, 98, 99, 176, 192 Positive Secondary Trigonal Pyramid, 98-100, 197 Positive Sphenoid, 56, 195 Positive Tertiary Hexagonal Pyramid, 91-93, 198 Positive Tertiary Hexagonal Prism, 91-93, 192 Positive Tertiary Pyramid, 195 Positive Tertiary Ehombohe- dron, 96-98, 198 Positive Tertiary Trigonal Prism, 101, 102, 193 Positive Tertiary Trigonal Pyramid, 101, 102, 199 Positive Tetrahedral Penta- gonal Dodecahedron, 125, 140, 141, 184 Positive Tetrahedron, 124, 132, 183, 185 Positive Tetragonal Scalenohe- dron, 195 Positive Tetragonal Trapezohe- dron, 69, 196 Positive Tetragonal Triakis Te- trahedron, 124, 132, 133, 183, 185 Positive Trigonal Trapezohe- dron, 25, 76, 98, 100, 104, 199, 207 Positive Trigonal Triakis Tetra- hedron, 124, 134, 183, 185 Primary and Secondary Tetra- gonal Prisms, Distinction be- tween, 64 286 INDEX. Primary and Secondary Hexa- gonal Prisms, Eelations to each other, 82, 83 Primary and Secondary Tetra- gonal Pyramids, Distinction between, 65 Primary Di Trigonal Prism, 192 Primary Hexagonal Prism, 80- 85, 91, 101, 104, 177, 179- 183, 191 Primary Hexagonal Pyramid, 81-85, 93, 102, 106, 181-183, 188, 196 Primary Pyramid, 194, 204 Primary Khombohedron, 18, 26, 27, 74, 76, 81, 87, 88, 104, 204, 207 Primary Tetragonal Prism, 61, 63, 175, 176, 191 Primary Tetragonal Pyramid, 61, 63, 175, 176, 194 Primary Tetragonal Pyramids, Number of, 65 Primary Trigonal Prism, 101, 105, 176, 178-180, 192 Primary Trigonal Pyramid, 101, 102, 106, 177-180, 196 Principal Khombohedron, 87 Prism, 12, 13, 21, 22, 43, 44, 50, 54, 61, 63, 64, 67, 68, 76-83, 91-93, 98, 99, 101-106, 108, 109, 170-183, 188-193, 203 Prismatic Class, 170 Prismatic Cleavage, 155-158 Prism, Dihexagonal, 81-85, 99, 101, 105, 179, 181-183, 192 Prism, Ditetragonal, 61, 63, 98, 99, 174, 191 Prism, Ditrigonal, 98, 99, 105, 177, 179, 180, 192 Prism, Hemi Ditetragonal, 67, 191 Prism, Hexagonal of the First Order, 80-85, 90, 101, 104, 177, 179-183, 191 Prism, Hexagonal of the Second Order 81-85, 91, 93, 99, 101, 105, 177, 179-183, 192 Prism, Hexagonal of the Third Order, 91, 92, 105, 181, 182, 192 Prism, Monoclinic, 43, 44, 170, 190, 203 Prism of the First Order, 191 Prism of the Second Order, 191 Prism of the Third Order, Te- tragonal, 67, 68, 175, 191 Prism, Parameters of the Secon- dary Hexagonal, 83, 84 Prism, Primary, 170-174, 191 Prism, Primary Hexagonal, 80- 85, 91, 101, 104, 177, 179- 183, 191, 204 Prism, Primary, Monoclinic, 170, 190 Prism, Primary, Orthorhombic, 171 Prism, Primary, Tetragonal, 61, 63, 175, 176, 191 Prism, Primary Trigonal, 101, 105, 176, 178-180, 192 Prism, Quaternary, 170 Prism, Secondary Hexagonal, 81-85, 91, 93, 99, 101, 105, 177, 179-183, 192 Prism, Secondary, Orthorhom- bic, 171 Prism, Secondary Trigonal, 98, 99, 105, 176-178, 192 Prism, Tertiary, 170-173, 191 Prism, Tertiary Hexagonal, 91, 92, 105, 181, 182, 192 Prism, Tertiary, Orthorhombic, 171, 1/2 INDEX. 287 Prism, Tertiary Tetragonal, 67, 68, 175, 191 Prism, Tertiary Trigonal, 101, 102, 106, 177, 178, 193 Prism Tribe, 189-193 Pseudo-hemimorphic Form, 46 Pseudomorphs, 148 Pyramid, 12, 13, 22, 42, 43, 45, 51, 54, 61-63, 65, 67, 68, 76- 79, 81-83, 85, 88, 91-93, 95, 96, 98-103, 106-109, 121, 172-183, 188, 189, 193-199, 204 Pyramid, Dihexagonal, 82, 93, 101, 107, 182, 183, 197 Pyramid, Ditetragonal, 62, 63, 121, 175, 176, 195, 206 Pyramid, Ditrigonal, 95, 96, 107, 179, 180, 198 Pyramid, Hemi-Ditetragonal 67, 68, 195, 196 Pyramid, Hexagonal of the First Order, 81-85, 93, 102, 106, 181-183, 188, 196 Pyramid, Hexagonal of the Second Order, 82-85, 96, 106, 179-183, 196, 197 Pyramid, Hexagonal of the Third Order, 91-93, 181, 182, 198 Pyramid, Hexagonal, Tertiary, 91-93, 181, 182, 198 Pyramid Octahedron, 124, 128, 129, 141-143, 200 Pyramid of the Diametral Or- der, 19o Pyramid of the First Order, 194 Pyramid of the First Order, Tetragonal, 61, 63, 175, 176, 194 Pyramid of the Second Order, 195 Pyramid of the Third Order, 195 Pyramid of the Third Order, Tetragonal, 67, 68, 175, 195 Pyramid of the Unit Order, 194 Pyramid, Orthorhombic, 7, 25, 51, 54, 71, 72,, 194 Pyramid, Parameters of the Secondary Hexagonal, 83, 84 Pyramid, Primary, 173, 174 Pyramid, Primary Hexagonal, 81-85, 93, 102, 106, 181-183, 188, 196 Pyramid, Primary Tetragonal, 61, 63, 175, 176, 194 Pyramid, Primary Trigonal, 101, 102, 106, 1/7-180, 196 Pyramid, Quaternary, 171 Pyramid, Secondary, 173, 174 Pyramid, Secondary Hexagonal, 82-85, 96, 106, 179-183, 196, 197 Pyramid, Secondary Tetragonal, 61, 63, 175, 176, 19o Pyramid, Secondary Trigonal, 98-100, 107, 177, 178, 197 Pyramid, Tertiary, 173 Pyramid, Tertiary Tetragonal, 67, 68, 175, 195 Pyramid, Tertiary Trigonal, 101, 102, 108, 177, 178, 199 Pyramid Tetrahedron, 124, 133, 134, 142, 144, 183, 185, 201 Pyramid Tribe, 19^-200 Pyramidal Class, Orthorhombic, 171, 259 Pyramidal Class, Tetragonal, 172, 173 Pyramidal Cleavage, 155-158 Pyramidal Cube, 200 Pyramidal Dodecahedron, 201 Pyramidal Garnetohedron, 201 Pyramidal Group, 181, 182 288 INDEX. Pyramidal Group, Tetragonal, 174, 175 Pyramidal Hemihedral Class, Tetragonal, 174, 175, 181, 182, 259 Pyramidal Hemimorphie Class, Tetragonal, 172, 173, 180, 181, 261 Pyramidal Hexagonal Group, 91-93, 121, 164, 260 Pyramidal Hexagonal, Symme- try of, 93, 164, 260 Pyramidal Tetragonal Group, 67-69, 174, 175 Pyramidal Tetragonal Group Symmetry of, 68, 69, 163 Pyramidal Tetrahedron, 201 Pyrite, 24, 25, 51, 123, 125, 135- 137, 148-150, 153, 207 Pyrite Dodecahedron, 200 Pyritohedral Group, 184, 185 Pyritohedral Hemihedral Group, 184, 185 Pyritohedron, 24, 25, 51, 52, 125, 135-138, 142, 143, 183, 185, 200, 207, 237, 238, 244- 246, 254 Pyritohedron, Symmetry of, 51, 52 Pyritoid, 200 Pyroxene, 41-44, 46, 47 Quadratic Octahedron, 194, 195 Quadratic Octahedron of the First Order, 194 Quadratic Octahedron of the First Series, 194 Quadratic Octahedron of the Second Series, 195 Quadratic rrism, 191 Quadratic Pyramid, 195 Quadratic Tetrahedron, 194 Quartz, 3, 18, 26, 74, 76, 81, 83, 87, 100, 104, 149, 150, 153, 204-206, 233, 234, 255 Quartzoid, 196, 197 Quartzoid of the First Order, 196 Quartzoid of the Second Order, 197 Reading Drawings of Hexagonal Crystals, 109-113 Beading Drawings of Isometric Crystals, 145-157 Reading Drawings of Ortho- rhombic Crystals, 57, 58 Reading Drawings of Tetra- gonal Crystals, 69, 70 Reading Drawings of Triclinic Crystals, 30-34 Reading Drawings of Mono- clinic Crystals, 46, 47 Red Angus, 188 Re-entrant Angles, 150, 256-258 Regular Four-sided Double Pyramid, 200 Regular Hexagonal Prism, 191, 192 Regular Octahedron, 200 Regular Rhombic Dodecahedron 200 Regular Tetrahedron, 200 Relation of Primary and Secon- dary Hexagonal Prism or Pyramid to each other, 82, 83 Replacement, 26, 27 Rhombic Dodecahedron, 123, 126, 127, 141-143, 183-186, 200, 204, 207, 236, 239-244, 248, 254 Rhombic Octahedron, 194 INDEX. 289 Rhombic Prism, 190 Rhombic Pyramid, 194 Rhombic Pyramidohedron, 194 Rhombic Sphenoid, 194 Rhombic ISphenoidohedron, 194 Rhombic Tetrahedron, 194 Rhombohedral Class, 177 Rhombohedral Cleavage, 155, 158 Rhombohedral Division, 74, 121 176-180 Rhombohedral Group, 85-91, 121, 164, 179 Rhombohedral Group, Symme- try of, 90, 91 Rhombohedral Hemihedral Class, 178, 179 Rhombohedral Hemimorphic Class, 176, 179 Rhombohedral Lateral Angles, 86, 87 Rhombohedral Lateral Edges, 86, 106 Rhombohedral Solid Angles, 86 Rhombohedral System, 74, 121, 176-180 Rhombohedral Terminal Edges, 86 Rhombohedral Tetartohedral Class, 177 Rhombohedral Tetartohedral Group, 96-98, 164 Rhombohedral Tetartohedral Group, Symmetry of, 98, 164, 260 Rhombohedral Zigzag Edges, 86, 90 Rhombohedron, 18, 26, 27, 74, 76, 81, 85-88, 104, 106-108, 177, 179, 189, 196, 204, 207, 215, 226,. 229-231, 233 Rhombohedron, Acute, 87 Rhombohedron, Obtuse, 87 Rhombohedron of the First Order, 88, 97, 106, 177, 179, 196 Rhombohedron of the Middle Edges, 90 Rhombohedron of the Principal Series, 196 Rhombohedron of the Second Order, 96-98, 107, 177, 197 Rhombohedron of the Third Order, 96-98, 108, 177, 198 Rhombohedron, Position of Axes in, 88 Rhombohedron, Principal or Fundamental, 87, 88 Rhombohedron, Relation of a Positive to a Negative, 87, 88 Rhombohedron, relation to the Scalenohedron, 90 Rhombohedron, Secondary, 96- 98, 107, 177, 197 Rhombohedron, Subordinate, 87 Rhombohedron, Symmetry of, 52, 90, 91, 164, 259 Rhombohedron, Symmetry of the Secondary and Tertiary, 98 Rhombohedron, Tertiary, 96-98, 108, 177, 198 Rhombohedron of the Vertical Primary Zone, 196 Right -Angled Dodecahedron, 196 Right-handed Ditrigonal Prism, 98, 99, 193 Right-handed Forms, 32 Right-handed Positive Secon- dary Rhombohedron, 96, 97 Right-handed Positive Tertiary Rhombohedron, 96-98, 198 290 INDEX. Eight-handed Positive Trigonal Pyramid, 98-100 Right-handed Negative Rhombo- hedron, 96-98, 198 Right-handed Negative Tri- gonal Pyramid, 98-100 Right-handed Secondary Tri- gonal Prism, 98, 99, 176, 192 Right-handed Tetragonal Trape- zohedron, 69, 196 Bight-handed Tertiary Hexa- gonal Prism, 91-93, 192 Right-handed Tertiary Hexa- gonal Pyramid, 91-93, 198 Right-handed Tertiary Trigonal Prism, 101, 102, 193 Right-handed Tertiary Trigonal Pyramid, 101, 102, 199 Right-handed Tetrahedral Pen- tagonal Dodecahedron, 125, 140, 141, 184 Right-handed Hexagonal Trape- zohedron, 93-95, 198 Right-handed Pentagonal Icosi- tetrahedron, 125, 138, 139, 184 Right-handed Sphenoid, 56 Right-handed Trigonal Trape- zohedron, 25, 76, 98, 100, 104, 199, 207 Rock Cleavage, loO Rules for naming Hexagonal Planes, 104-109 Rules for naming Monoclinic Planes, 44, 45 Rules for naming Orthorhombic Planes, 54 Rules for naming Isometric Planes, 142, 144 Rules for naming Tetragonal Planes, 62, 66 Rules for naming Triclinic Planes, 21, 22 Russia, 187 Rutile, 149, 150, 152, 153, 252 Saw teeth of the Hexagonal Scalenohedron, 89, 90, 94 Scalene Triangles, 94 Scalenohedral Class, 179 Scalenohedral Class, Tetragonal, 173, 174 iScalenohedral Rhombohedral Class, 179 Scalenohedron, 189, 197, 215 Scalenohedron, Hexagonal, 88- 91, 94, 97, 100, 107, 179, 197 Scalenohedron, Hexagonal Sym- metry of, 52 90, 91 Scalenohedron Negative Hexa- gonal, 89, 197 Scalenohedron, Positive Hexa- gonal, 89, 197 Scalenohedron, relation to the Rhombohedron, 90 Scalenohedron Saw teeth, 89, 90 Scalenohedron, Tetragonal, 65, 66, 89, 174, 195 Scheelite, 40, 68, 70, 73, 221 Schrauf, A., 74 Schrauf, Axes of the Hexa- gonal System, 74 Seaman, A. E., xv Second Hemimorphic Tetarto- hedral Class, 178, 179 Second Hexagonal Prism, 192 Second Horizontal Prism, 190 Second Order, Hexagonal Prism, 81-85, 91, 93, 99, 101, 105, 177, 179-183, 192 Second Order Hexagonal Pyra- mid, 82-85, 96, 106, 179-183, 196, 197 Second Order, . Tetragonal Prism of, 61, 63, 175, 176, 191 INDEX. 291 Second Order, Tetragonal Pyra- mid of, 61, 63, 175, 176, 195 Second Order, Trigonal Prism, 98, 99, 105, 176-1/8, 192 Secondary and Primary Tetra- gonal Prisms, Distinction be- tween, 64 Secondary and Primary Tetra- gonal Pyramids, Distinction between, 65 Secondary Di Trigonal Prism, 192, 193 Secondary Forms, 26 Secondary Hexagonal Prism, 81- 85, 91, 93, 99, 101, 105, 177, 179-183, 192 Secondary Hexagonal Prism and Pyramid, Parameters of, 83, 84 Secondary Hexagonal Pyramid, 82-85, 99, 102, 106, 179-183, 196, 197 Secondary Prism, 191 Secondary Pyramid, 195 Secondary Rhombohedron, 96- 98, 107, 177, 197 Secondary Bhombohedron, Sym- metry of, 98 Secondary Tetragonal Prism, 61, 63, 175, 176, 191 Secondary Tetragonal Pyramid, 61, 63, 175, 176, 195 Secondary Tetragonal Pyramids, Number of, 65 Secondary Trigonal Prism, 98, 99, 105, 176-178, 192 Secondary Trigonal Pyramid, 98-100, 107, 177, 178, 197 Shakespeare, William, 188 Shorthand, Crystallographic, 28- 34, 46, 47, 57, 70, 75, 109- 113, 146, 147, 156 Similar Axes, Planes, Edges, and Angles, 13, 14 Simple Crystals, 25 Slaty Cleavage, 160 Sodalite, 149, 150, 153, 254 Sodium-Periodate Type, 103, 104, 109, 165, 176, 177, 235 Sodium-Periodate Type, Sym- metry of, 104, 165, 260 Solid Angles, Rhombohedral, 86 Sphalerite, 149, 150, 153 Sphenoid, 55, 56, 65, 66, 69, 169, 171, 172, 174, 189, 194, 195, 215, 216 Sphenoid, Orthorhombic, 55, 56, 66, 171, 194 Sphenoid, Primary, 169, 172, 174 Sphenoid, Quaternary, 169 Sphenoid, Tertiary, 169, 172 Sphenoid, Tetragonal, 65, 66, 69, 172, 174, 194, 195 Sphenoidal Class, Monoclinic, 169 Sphenoidal Hemihedral Class, 180 Sphenoidal Hemihedral Class, tetragonal, 173, 174 Sphenoidal Tetartohedral Class, Tetragonal, 172 Sphenoidal Group, Tetragonal, 65-67, 163, 173, 174 Sphenoidal Tetragonal Group, 65-67, 163, 173, 174 Sphenoidal Tetartohedral Class, 178 Staurolite, 149, 150, 153, 256 Stibnite, 50, 51, 57, 212, 214 Straight Axis, 42 Striations on Crystals and Cleavage Plates, 150, 151, 247 Subordinate Form, 26 Subordinate Rhombohedron, 87 292 INDEX. Sugar, 41-47, 169, 209 Sulphur, 7, 25, 50, 51, 57, 203, 213, 214 Symmetry, 14-19, 23-25, 37, 39, 40, 41, 44-46, 49, 51-56, 59, 64, 67-69, 72, 74, 76, 84, 85, 90, 91, 93, 94, 96, 98, 100, 102-104, 130, 131, 135, 138, 139, 141, 147, 161-166, 168, 169, 172, 173, 175, 203, 258- 261 Symmetry, Axes of, 18, 19, 23- 25, 44, 51-57, 59, 64, 67-69, 72, 74, 76, 84, 85, 90, 91, 93, 94, 96, 98, 100, 102-104, 121, 123, 130, 131, 135, 138, 139, 141, 147, 162-166, 258-261 Symmetry, Center of, 19, 23-25, 55, 56, 59, 64, 67, 68, 72, 85, 91, 93, 98, 100, 121, 131, 135, .139, 141, 147, 162-166, 258- 261 Symmetry, Center of, how rep- resented, 162 Symmetry, Hexagonal Holohe- dral, 84, 85, 163, 259 Symmetry, how represented, 161, 162 Symmetry, Number of Planes of, 15, 40 Symmetry of the Asymmetric Class, 168, 261 Symmetry of the Ditetragonal Pyramidal Class, 175 Symmetry of the Gyroidal Hemihedral Forms, 139, 166, 261 Symmetry of Hemihedral Iso- metric Forms, 123, 135, 138, 165, 166, 261 Symmetry of the lodyrite Type, 103, 165, 260 Symmetry of Isometric Crys- tals, 23, 24, 51, 52, 123, 130, 131, 135, 138, 139, 141, 147, 165, 166, 261 Symmetry of Isometric Holo- hedral Forms, 123, 130, 131, 165, 261 Symmetry of the Isometric Sys- tem, 23, 24, 123, 130, 131, 135, 138, 139, 141, 147, 165, 166, 261 Symmetry of the Monoelinic System, 40, 41, 44, 49, '162, 169 Symmetry of the Nephelite Type, 103, 165, 260 Symmetry of Oblique Hemihe- dral Forms, 123, 135, 165, 261 Symmetry of the Orthorhombic Hemimorphic Forms, 56, 163, 259 Symmetry of the Orthorhombic System, 23, 51, 52, 55, 56, 59, 162, 163, 259 Symmetry of Parallel Hemihe- dral Forms, 51, 52, 123, 138, 166, 261 Symmetry of the Periodate Type, 104, 165, 260 Symmetry of the Bhombohe- dron Group, 52, 90, 91, 164 Symmetry of the Ehombohedral Tetartohedral Group, 98, 164, 260 Symmetry of the Tetragonal Pyramidal Group, 68, 69, 163 Symmetry of the Tetragonal Sphenoidal Group, 66, 67, 163, 173 Symmetry of the Tetrahedral Pentagonal Dodecahedron, 123, 141, 166, 261 INDEX. 293 Symmetry of the Tourmaline Type, 103, 165, 260 Symmetry of the Triclinic Sys- tem, 23-25, 162, 168, 258, 261 Symmetry of the Trigonal Hexagonal Group, 96, 164, 260 Symmetry of the Trigonal Te- tartohedral Group, 102, 164, 165, 260 Symmetry of the Trigonal Trapezohedron, 25, 100 Symmetry, Plane of, 15-18, 23- 25, 39, 40, 41, 44, 46, 49, 51- 56, 59, 64, 67-69, 72, 74, 84, 90, 93, 94, 96, 98, 100, 102, 103, 121, 130, 131, 135, 138, 139, 141, 147, 161-166, 168, 169, 172, 1/3, 175, 203, 258- 261 Symmetry Pyramidal Hexag- onal Group, 93, 164, 260 Table I. Triclinic Forms and Notations, 35 Table II. Monoelinic Forms and Notations, 48 Table III. Orthorhombic Forms and Notations, 58 Table IV. Tetragonal Forms and Notations, 71 Table V. Hexagonal Forms and Notations, 114-120 Table VI. Isometric Forms and Notations, 146, 147 Tartaric Acid, 169 Terminal Edges, Ehombohedral, 86 Tertiary Hexagonal Prism, 91, 92, 105, 181, 182, 192 Tertiary Hexagonal Pyramid, 91-93, 107, 181, 182, 198 Tertiary Prism, 191 Tertiary Pyramid, 195 Tertiary Ehombohedron, 96-98, 108, 177, 198 Tertiary Ehombohedron Symme- try of, 98 Tertiary Tetragonal Prism, 67, 68, 175, 191 Tertiary Tetragonal Pyramid 67, 68, 175, 195 Tertiary Trigonal Prism, 101, 102, 106, 177, 178, 193 Tertiary Trigonal Pyramid, 101, 102, 108, 177, 178, 199 Tetarto Di Hexagonal Prism, 193 Tetarto Di Hexagonal Pyramid, 198 Tetartohedral Class, 183, 184 Tetartohedral Class, Tetragonal, 172 Tetartohedral Forms, 25, 96-102, 140, 141 Tetartohedral Forms, (Symmetry of, 25 Tetartohedral Group, 183, 184 Tetartohedral Group, Tetra- gonal, 172 Tetartohedral Hexagonal Forms, 25, 77-79, 96-102, 121 Tetartohedral Isometric Forms, 123, 125, 140-142, 144, 166, 183, 184, 202, 238, 239, 261 Tetartohedral Notation, 36-38 Tetartohedral Ehombohedrali Group, 96-98, 164 Tetartohedral Khombohedral Group, Symmetry of, 96, 164, 2t>0 Tetartohedral Trapezohedral Group, Symmetry of, 25, 100, 164, 260 294 INDEX. Tetartohedral Trigonal Group Symmetry of, 102, 164, 165, 260 Tetarto Hexakis Octahedron, 202 Tetartoid, 125, 140-142, 144, 184, 194, 202 Tetartomorphic Class, 180, 181 Tetartomorphic Class, Tetara- gonal, 172, 173 Tetragonal Axes, 7, 60, 203 Tetragonal and Hexagonal Sys- tems, Distinctions between, 73, 74 Tetragonal Cleavage, 157, 158 Tetragonal Compound Forms, 69 Tetragonal Crystals, Directions for Studying, 72 Tetragonal Crystals, Distin- guishing Characteristics, 62 Tetragonal Crystals, Beading Drawings of, 69, 70 Tetragonal Dodecahedron, 201 Tetragonal Forms, 71 Tetragonal Hemihedral Forms, 65-69, 163, 220, 221, 259 Tetragonal Hemihedral Forms Symmetry of, 66-69, 163, 173, 174, 259, 261 Tetragonal Hemihedral Hemi- morphic Forms, Symmetry of, 172, 173, 261 Tetragonal Hemihedral Pyra- midal Group, Symmetry of, 68, 69, 163, 259 Tetragonal Hemihedral Sphe- noidal Group, Symmetry of, 66, 67, 163, 173, 174, 259 Tetragonal Hemihedral Trape- zohedral Group, Symmetry of, 69, 163, 259 Tetragonal Holohedral Forms, 63-65, 163, 216-220, 259 Tetragonal Holohedral Forms, Symmetry of 64, 74, 163, 172, 259, 261 Tetragonal Holohedral Hemi- morphic Forms, Symmetry of, 175, 261 Tetragonal Icosi Tetrahedron, 201 Tetragonal Notation, 71 Tetragonal Parallel Growths, 3, 149, 205 Tetragonal Planes, Rules for naming, 62, 63 Tetragonal Primary and Secon- dary Prisms, Distinction be- tween, 64 Tetragonal Primary and Secon- dary Pyramids, Distinction between, 65 Tetragonal Prism of the First Order, 61, 63, 175, 176, 191 Tetragonal Prism of the Second Order, 61, 63, 175, 176, 191 Tetragonal Prism of the Third Order, 67, 68, 175, 191 Tetragonal Pyramidal Group, 67-69, 174, 175 Tetragonal Pyramidal Group, Symmetry of, 68, 69 Tetragonal Pyramid of the First Order, 61, 63, 175, 176, 194 Tetragonal Pyramid of the Second Order, 61, 63, 175, 176, 195 Tetragonal Pyramidohedron of the First Direction, 194 Tetragonal Pyramidohedron of the Second Direction, 195 INDEX. 295 Tetragonal Pyramid of the Third Order, 67, 68, 175, 195 Tetragonal Scalenohedron, 65, 66, 89, 174, 195 Tetragonal Sphenoid, 65, 66, 69, 172, 174, 194, 195 Tetragonal Shorthand or Nota- tion, 71 Tetragonal Sphenoidal Group Symmetry of, 66, 67, 163, 173 Tetragonal System, 7, 60-72, 149, 163, 172-176, 203, 205, 206, 216-221, 224, 225, 251, 253, 259, 261 Tetragonal System, Symmetry of, 64, 67, 69, 74, 163, 172- 175, 259, 261 Tetragonal Tertiary Prism, 67, 68, 175, 191 Tetragonal Tertiary Pyramid, 67, 68, 175, 195 Tetragonal Tetartohedral Forms, Symmetry of, 172, 261 Tetragonal Trapezohedral Group, 69, 163, 174 Tetragonal Trapezohedron, Sym- metry of, 69, 163 Tetragonal Triakis Octahedron, 124, 129, 141-144, 201, 236, 237, 240-242, 244-246 Tetragonal Triakis Tetrahedron, 124, 132, 133, 142, 143, 183, 185, 200, 237, 244 Tetragonal Tristetrahedron, 124, 132, 133, 142, 143, 183, 185, 200, 237, 244 Tetrahedral Group, 185, 186 Tetrahedral Hemihedral Class, 185, 186 Tetrahedral Hemihedral Class, Tetragonal, 173, 174 Tetrahedron, Hexakis, 124, 134, 135, 140, 144, 186, 201, 237, 244, 261 Tetrahedral Isometric Forms, Symmetry of, 123, 141, 166, 261 Tetrahedral Pentagonal Dode- cahedral Class, 183, 184 Tetrahedral Pentagonal Dode- cahedron, 123, 125, 140-142, 144, 166, 183, 184, 202, 238, 239, 261. Tetrahedral Pentagonal Dode- cahedrons in combination with other forms, 142 Tetrahedral Pentagonal Dode- cahedron, Symmetry of, 123, 141, 166, 261 Tetrahedral Trigonal Icosi Te- trahedron, 201 Tetrahedral Tetartohedral Class, 172 Tetrahedrite, 149, 150, 153, 254 Tetrahedron, 124, 132, 142, 143, 183, 185, 200, 236, 237, 242 Tetrahedron, Tetragonal, Tria- kis, 124, 132, 133, 142, 143, 183, 185, 200, 237, 244 Tetrahedron, Trigonal Triakis, 124, 133, 134, 142, 144, 183, 185, 201 Tetrahexahedron, 123, 127, 128, 135, 136, 141-143, 184-186, 200, 208, 236-238, 240, 244, 248 Tetrakis Hexahedron, 123, 127, 128, 135, 136, 141-143, 184- 186, 189, 200, 208, 236-238, 240, 244, 248 The Pennsylvania State Col- lege, vii 296 INDEX. Third Order, Hexagonal Prism, 91, 92, 105, 181, 182, 192 Third Order, Tetragonal Prism, 67, 68, 175, 191 Third Order, Tetragonal Pyra- mid, 67, 68, 1/5, 195 Topaz, 50, 51 Tourmaline Type, 74, 76, 108, 104, 109, 165, 178, 179, 230, 235 Tourmaline Type, Symmetry of, 103, 165, 260 Trapeziums, 94, 137 Trapezohedral Class, 181 Trapezohedral Group, 177, 178, 181 Trapezohedral Hemihedral Class, 181 Trapezohedral Hexagonal Group, 93-95, 164 Trapezohedral Hexagonal Group, Symmetry of, 94, 164, 260 Trapezohedral Tetartohedral Group, 98-100, 164, 177, 178 Trapezohedral Tetartohedral Class, 177, 178 Trapezohedral Tetartohedral Group, Symmetry of, 25, 100, 164, 260 Trapezohedral Tetragonal Group, 69, 163 Trapezohedron, 124, 129, 141- 144, 189, 201, 207, 236, 237, 240-242, 244-246 Trapezohedron, Hexagonal, 93- 95, 107, 121, 181, 198, 221 Trapezohedron, Hexagonal, Sym- metry of, 94 Trapezohedron, Left-handed Hexagonal, 93-95, 198 Trapezohedron, Negative Hexa- gonal, 93, 94 Trapezohedron, Positive Hexa- gonal, 93, 94 Trapezohedron, Bight-handed Hexagonal, 93-95, 198 Trapezohedron, Tetragonal, 69, 174, 196 Trapezohedron, Tetragonal, Sym- metry of, 69 Trapezohedron Trigonal, 25, 74, 76, 98, 100, 104, 108, 178, 207 Trapezoidal Dodecahedron, 201 Trapezoidal Icosi Tetrahedron, 201 Trapezoid Di Dodehedron, 201 Trapezoid Di Hexahedron, 198 Trapezoid Icosi Tetrahedron, 201 Trapezoid Tetrahedron, 200 Triakis Octahedron, 124, 128, 129, 133, 134, 141-143, 200, 207, 236, 237, 240 Triakis Tetrahedron, 124, 133, 134, 142, 144, 183, 185, 201, 237, 242-244, 261 Tribe, Isometric, 189, 200-202 Tribe, Prism, 189-193 Tribe, Pyramid, 193-200 Triclinic Axes, 7, 9, 10, 29, 33, 203 Triclinic Cleavage, 156 Triclinic Crystals, Directions, for Studying, 38, 39 Triclinic Crystals, Distinguish- ing Characteristics of, 19-21 Triclinie Crystals, Obliquity of Angles of, 20, 21 Triclinic Crystals, Beading Drawings < x, 30-34 INDEX. 297 Triclinic Domes, 21, 22 Trj clinic Forms, 35 Triclinic Henri Brachy Dome, 190 Triclinic Hemi Brachy Prism, 190 Triclinic Hemihedral Class, 167, 261 Triclinic Hemihedral Forms, I 24, 25, 167, 168, 257, 258 Triclinic Hemihedral Forms, Symmetry of, 168, 261 Triclinic Hemi Macro Dome, 190 Triclinic Hemi Macro Prism, 190 Triclinic Hemi Vertical Dome, 189 Triclinic Hemi Vertical Prism, 189 Triclinic Holohedral Forms, 23, 162, 168, 169, 205, 206, 258 Triclinie Holohedral Forms, Symmetry of, 23-25, 162, 258 Triclinie Notation, 35 Triclinic Pedion, 168 Triclinic Pinacoids, 12, 13, 19- 21, 25, 26, 33, 34, 44, 200, 205 Triclinic Planes, Eules for naming, 21, 22 Triclinic Prism, 21, 22 Triclinic Pyramid, 12, 13, 19-21, 25, 26, 33-35, 44, 193, 205 Triclinic Shorthand or Nota- tion, 35 Triclinic System, 7, 9-39, 44, 162, 167-169, 203, 205, 206. 247, 249, 258, 261 Triclinic System, Symmetry of, 23-25, 162, 168, 258, 261 Triclinic Tetartohedral Forms. 25 Triclinic Tetarto Pyramid, 13, 19-21, 25, 26, 33, 34, 44, 193, 205 Triclinohedral Prism, 189 Trigonal Bipyramidal Class, 178 Trigonal Division, 74, 121, 176 180 Trigonal Dodecahedron, 201 Trigon-Dodecahedron, 124, 133, 134, 142, 144, 183, 185, 201 Trigonal Group, 178 Trigonai Hexagonal Group, 95, 96, 164 Trigonal Hexagonal Group, Symmetry of, 96, 164, 260 Trigonal Hemihedrai Class, 180 Trigonal Icosi Tetrahedron, 201 Trigonal Polyhedron, 201 Trigonal Prism, 189, 192 Trigonal Prism of the First Order, 101, 105, 176, 178- 180, 192 Trigonal Prism, Primary, 101, 105, 176, 178-180, 192 Trigonal Prism of the Second Order, 98, 99, 105, 176-178, 192 Trigonal Prism of the Third Order, 101, 102, 106, 177, 178, 193 Trigonal Prism, Secondary, 98, 99, 105, 176-178, 192 Trigonal Prism, Tertiary, 101, 102, 106, 177, 178, 193 Trigonal Pyramidal Class, 176, 177 Trigonal Pyramid of the First Order, 101, 102, 106, 177-180, 1UU 298 INDEX. Trigonal Pyramid, Frimary, 101, lOiS, 106, 177-180, 196 Trigonal Pyramid of the Second Order, 98-100, 107, IV 7, 1/8, 195, 197 Trigonal Pyramid of the Third Order, 101, 102, 108, 177, 178, 199 Trigonal Pyramid, Secondary, 98-100, 107, 177, 178, 197 Trigonal Pyramid, Tertiary, 101, 102, 108, 177, 178, 199 Trigonal Khombohedral Class, 177 Trigonal Symmetry, Axis, how represented, 162 Trigonal System, 74 Trigonal Trapezohedron, 25, 74, 76, 98, 100, 104, 108, 178, 207 Trigonal Tetartohedral Class, 177, 178 Trigonal Tetartohedral Group, 101, 102, 164, 165 Trigonal Tetartohedral Group, Symmetry of, 102, 164, 165, 260 Trigonal Trapezohedral Class, 177, 178 Trigon Trapezohedron, 199 Trigonal Triakis Octahedron, . 12*, 128, 129, 133, 134, 141- 143, 188, 200, 207, 236-237, 240 Trigonal Triakis Tetrahedron, 124, 133, 134, 142, 144, 183, 185, 201, 237, 242-244, 261 Trigonal Tristetrahedron, 124, 133, 134, 142, 144, 183, 185, 201 Trigonotype Hemihedral Class^ 179, 180 Trillings, 152, 256 Trinomial Names, 188 Tripyramidal Group, 181, 182 Tri-rhombohedral Group, 177 Trisoctahedron, 124, 128, 129, 333, 134, 141-143, 200 Tristetrahedron, 124, 132, 133, 142, 143, 183, 185, 201, 237, 242-244, 261 Truncation, 27 Twelve-sided Prism, 192 Twin, 149-154, 247-258 Twin, Contact, 151-153, 247- 253, 257 Twin, Cyclic, 153, 252, 253 Twin, Penetration, 151-153, 253-256, 257, 258 Twinned Crystals, 150-154, 247- 258 Twinning Axis, 152 Twinning Plane, 152, 247-253, 257 Twinning, Polysynthetic, 151, 153, 247 Type, lodyrite, 74, 76, 81, 102- 104, 108, 121, 165, 222 Type, Nephelite, 74, 76, 81, 103, 104, 109, 121, 16o, 180, 181, 222 Type, Sodium Periodate, 103, 104, 109, 165 Type, Tourmaline, 74, 76, 103, 104, 109, 165, 178, 179, 230 Unit Prism, 191 Unit Pyramid, 194 Unsymmetrical Class, 167, 261 Vegetable Kingdom, 1 Vertical Axis, Monoclinic, 41 Vertical Dome, 43, 44 INDEX. 299 Vertical Pinacoid, 11, 21, 42, 44, 199 Vertical Prism, 189, 190 Vertical Quadrilateral Prism, 190 Vertical Ehombic Prism, 190 Vertical Semi-Axis, Orthorhom- bic, 50 Vertical Axis, Tetragonal, 60 Vertical Axis, Triclinie, 10 Vesuvianite, 69, 74, 225 Ward's Natural Science Estab- lishment, viii Weiss, C. S., 28, 29, 32, 33, 47, 70, 84 Weiss Natation, 29-34, 47, 70, 75, 84, 111, 132, 136 Whewell-Grassmann-Miller Sys- tem, 29 Whitney, J. D., iii, 188 Witherite, 149, 154, 258 Wulfenite, 173 Zigzag Edges of the Ehombo- hedron, 86, 90 Zigzag Edges of the Scalenohe- dron, 89, 90 Zircon, 18, 26, 61, 62, 70, 73. 74, 206, 217, 219 Zirconoid, 62, 195 Zoology, 1 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. books are subject to immediate recall. 1AY2 LD 21A-50m-ll,'62 LD 21- (D3279slO)476B General Library University of California Berkeley **u-