. 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. 
 
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THE HEXAGONAL SYSTEM. 
 
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THE HEXAGONAL SYSTEM. 
 
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 NOTES ON CRYSTALLOGRAPHY. 
 
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THE HEXAGONAL SYSTEM. 
 
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 NOTES ON CRYSTALLOGRAPHY. 
 
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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 : <x>, 
 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 <! ^Z } 
 
 DIRECTIONS FOR STUDYING ISOMETRIC CRYSTALS 
 
 1. Prove that the crystal is Isometric by finding 
 that it has three equal directions at right angles to 
 one another. These directions coincide with the crys- 
 tallographic axes and with the axes of tetragonal or 
 binary symmetry. 
 
 2. Note the dominant and modifying forms in the 
 order of their importance. 
 
 3. Determine the parameters (i. e., the symbol) of 
 each set of similar planes, and from the parameters 
 name the forms in accordance with the rules, distin- 
 guishing the holohedral, hemihedral, and tetartohe- 
 dral forms. 
 
 4. Locate the planes, axes, and centers of sym- 
 metry. 
 
CHAPTER VIII 
 
 MINERAL AGGREGATES, PARALLEL GROWTHS, AND 
 TWINS 
 
 A. Minerals are either Crystalline -or Amorphous, 
 from the Greek a, " without," and Morphe, " form." 
 When Crystalline they show an internal crystalline 
 structure, and may or may not possess a more or less 
 perfect crystal form. 
 
 When Amorphous they have neither a regular ex- 
 ternal form nor any internal crystalline structure. 
 The only apparent exception is when percolating 
 waters or other agents remove the original material 
 partially or entirely and replace it by other materials, 
 which assume the form of the mineral it has replaced. 
 For example, a crystal of pyrite is often replaced by 
 the amorphous limonite, which keeps the outlines of 
 the original pyrite crystal ; something like a wolf in 
 sheep's clothing. Minerals when they masquerade in 
 the form belonging to other minerals are said to be 
 Pseudomorphs, from the Greek Pseudes, " false," and 
 Morphe, "form." 
 
 (148) 
 
MINERAL AGGREGATES. 149 
 
 B. COMPOUND MINERALS OR CRYSTALS 
 
 It is usual to find minerals grown together or 
 united either regularly or according to some law, or 
 else irregularly or without regard to any apparent 
 law. 
 
 I. A Mineral Aggregate is formed by the irregular 
 union of many minerals. The minerals composing 
 the Aggregate are generally imperfect crystals, and 
 hence the Mineral Aggregate can often be justly styled 
 a Crystalline Aggregate. See Fig. 446. 
 
 II. When the minerals joined together are so ar- 
 ranged that similar parts are parallel they are called 
 Parallel Growths or Parallel Groups. See Figs. 23- 
 27, 447-457. There may be two divisions of these 
 growths : 1. When all the parts of a crystal are par- 
 allel to all the similar parts of the conjoined crystals. 
 2. When one part of a crystal is parallel to the sim- 
 ilar parts of its attached crystals. 
 
 III. When the two parts of a crystal are joined so 
 that by revolving one part 180 degrees it will form 
 with the other part a simple crystal, the crystal is 
 said to be a Twin. That is to say one part occupies a 
 reverse position relative to the other part, so that by 
 turning one of the parts half way around a simple 
 crystal will result. See Figs. 463-579. 
 
 In ordinary language the term twin refers to two 
 only but in Crystallography it relates to two or more 
 
150 NOTES ON CRYSTALLOGRAPHY. 
 
 forms joined together by crystallographic planes. 
 When the twinned form is composed of three individ- 
 ual crystals united, the individuals can be spoken of 
 as twins or as trillings. See Figs. 517, 565, 567. If 
 there are four or five individuals, then the twins can 
 be designated as fourlings or fivelings ; if there are 
 eight individuals, then the twins can be called eight- 
 lings; and so on. 
 
 C. Mineral Aggregates, Parallel Growths, and Twinned 
 Crystals form Reentrant Angles. See Figs. 458, 461, 
 464, 466-468, 470, 476, 477, 479, 481-486, 488, 493- 
 495, 498-561, 563-565, 567, 571-573. 
 
 It often happens that owing to the minuteness of 
 he Reentrant Angle, or from other causes, this feature 
 is only brought out by the minute structure of the 
 crystals or by means of polarized light. 
 
 While Reentrant Angles are usually considered to 
 indicate Aggregates, Parallel Growths or Twins, yet there 
 are some exceptions ; therefore every case of these 
 angles needs to be examined for itself, to see whether 
 it falls under the common rule or not. See Figs. 
 471-474. 
 
 D. Certain of the Parallel Growths and Twins are 
 often made up partly or entirely of numerous thin 
 plates that are arranged parallel to one .another. 
 When the plates are extremely thin, the reentrant 
 angles often show as very fine parallel lines or striations 
 
MINERAL AGGREGATES. 151 
 
 which look as if they had been scratcKed by a diamond 
 point or a needle, something like a diffraction grating. 
 See Figs. 452-457, 459-460, 462. In most cases they 
 can be seen only when the mineral is held at a special 
 angle or examined under a lens. 
 
 When the striations are considered to be due to the 
 alternate formation of two different crystal faces the 
 structure is called an Oscillatory Combination. It is 
 usual to speak of the forms produced by this combina- 
 tion as simple or single crystals. This Oscillation is 
 illustrated in the pyrite crystals, which show an 
 Oscillatory Combination of the cube and pentagonal 
 dodecahedron. See Figs. 455, 456. 
 
 When these striations are considered to be caused 
 by parallel growths or by repeated twinning the struc- 
 ture is designated as Polysynthetic Growths or Poly- 
 synthetic Twinning, as the case may be, from the Greek 
 Polysynthetos meaning " compounded of many things." 
 See Figs. 459-462. 
 
 E. TWIN CRYSTALS 
 
 There are two different classes of twins, which, for 
 convenience, are frequently distinguished as follows : 
 I. Contact Twins. 
 II. Penetration Twins. 
 
 These classes are so closely allied that their distinc- 
 tion one from the other is often difficult if not impos- 
 
152 NOTES ON CRYSTALLOGRAPHY. 
 
 sible. Fortunately their distinction is not an import- 
 ant matter except in well-marked cases. 
 I. Contact Twinning 
 
 The great majority of twinned crystals are united 
 by some crystallographic plane known as the Compo- 
 sition Plane. Such compound crystals are called 
 Contact Twins. The Composition Plane is often, but 
 not always, coincident with a plane known as the 
 Twinning Plane. This latter plane is the plane that 
 will separate the twinning crystal into two parts, so 
 that if one part is revolved 180 and again joined to 
 the other part," the union of the two parts will make a 
 complete and symmetrical crystal form. 
 
 The axis about which one part of the crystal is to 
 revolve 180 is known as the Twinning Axis. It is 
 perpendicular to the twinning plane. For example, in 
 Figs. 463, 465, 469, 471, 473 and 478, the plane a, b, 
 c, d, e, f, is not only a composition plane, but also a 
 twinning plane ; for not only are the two parts united 
 by it, but also if one part of Fig. 464 is revolved 180 
 on the other, the resulting form is the simple and 
 complete octahedron shown in Fig. 463. The same 
 thing can be observed in various other forms. See 
 Figs. 466-519. 
 
 As previously stated, twin forms are often desig- 
 nated as trillings, fourlings, fivelings, etc., according to 
 the number of individual forms. This repeated twin- 
 ning takes place in two ways : 
 
MINERAL AGGREGATES. 153 
 
 1. The twinning plane may remain parallel to 
 itself, in which case we have the earlier described 
 Polysynthetic Twinning. See page 151 and Figs. 
 458-461. 
 
 2. The twinning planes may change their direc- 
 tions, giving rise to groups that tend to assume more 
 or less circular forms. These forms are often called 
 Cyclic Twins, from the Greek Kyklos, "a ring, a cir- 
 cle, a round and circular body, a wheel, a sphere or a 
 globe." See figs. 509-514, 516-519. 
 
 II. Penetration Twinning 
 
 If we imagine that one crystal can penetrate an- 
 other and leave, mutually projecting from each, their 
 solid angles, we shall have a form known as a Pene- 
 tration Twin. In Figs. 522-530, illustrating this 
 structure, it will be noticed that the projecting solid 
 angles of one cube look as if they had been cemented 
 upon the sides of another cube. By the exercise of a 
 little imagination we can readily suppose that the 
 lines connecting the edges of the various solid angles 
 are produced so as to complete the cube. Figs. 520, 
 521, 531-556 show similar Penetration Twins of vari- 
 ous other forms. 
 
 MIMICRY 
 
 The term Mimicry is employed to designate the 
 condition whereby a crystal belonging to one system- 
 
154 NOTES ON CRYSTALLOGRAPHY. 
 
 may simulate the appearance of a crystal belonging 
 to another. 
 
 Good examples of the progressive steps taken by 
 one form simulating that of another, can be seen in 
 Figs. 557-580. In Figs. 557-559 it is shown that by 
 increasing the number of twin crystals of one system 
 a form roughly resembling one belonging to another 
 system is produced. In this case twinned ortho- 
 rhombic crystals produce a seemingly hexagonal form. 
 
 This is observed in Aragonite as shown by Figs. 
 563, 551, 561, 564 and 580, which Inark in the order 
 named the progressive steps from a simple ortho- 
 rhombic twin to a nearly complete hexagonal crystal. 
 This is strikingly shown in Figs. 565 and 566 for 
 Cerussite ; and in Figs. 575-579 for Witherite. Figs. 
 568 and 569 show the completed Mimicry of a hexa- 
 gonal crystal by the orthorhombic Bromelite. Figs. 
 560 and 562 show simulating forms of Marcasite, and 
 Fig. 567 one for Chrysoberyl. 
 
 Figs. 570-574 show successive stages in the twinning 
 of the monoclinic Phillipsite until it resembles an 
 isometric dodecahedron. 
 
 By Mimicry, it can be seen from the above examples, 
 that the simulation, as a rule, is only approximate, and 
 often quite largely imaginary. In all cases either de- 
 fects in the perfection of the form mimicked or its 
 'structure as observed in polarized light will distinguish 
 the real form from the imitation. 
 
CHAPTER IX 
 
 CLEAVAGE 
 
 THE Cleavage of Minerals is their property of split- 
 ting indefinitely parallel to certain crystal planes. In 
 actual cleavage it is practically impossible to obtain 
 cleavage plates so thin that they could not be split into 
 still thinner leaves, provided we had the necessary me- 
 chanical means to accomplish this. 
 
 It is to be noted that cleavage in minerals does not 
 run at random, but is parallel to certain crystal faces. 
 In designating the Cleavage it is customary to use the 
 name- of the form to whose faces the cleavage is parallel. 
 Thus, if the mineral splits parallel to the faces of an 
 octahedron, the cleavage is said to be Octahedral. 
 Again if the cleavage runs parallel to the plane of a 
 cube, a dodecahedron, a pinacoid, a prism, a pyramid, 
 or a rhombohedron, then the Cleavage is said to be 
 Cubical, Dodecahedral, Pinacoidal, Prismatic, Pyra.- 
 midal, or Rhombohedral, respectively. In the case of 
 pinacoidal cleavage it is customary to designate the 
 pinacoid to which the cleavage is parallel, as brachy- 
 or clino-, or macro-, or ortho-pinacoidal or basal, ac- 
 
 (155) 
 
156 NOTES ON CRYSTALLOGRAPHY. 
 
 cording to the pinacoid in question, whether it is a 
 brachy-, or clino- or a macro-, or an ortho-, or a basal 
 pinacoid. 
 
 The faces to which the cleavage is parallel belong to 
 some of the simple principal or dominant forms. 
 From this in order to indicate the cleavage, it is cus- 
 tomary to use the crystallographic shorthand by stating 
 that it is parallel to 0, or 111, when it is octahedral ; 
 or in every case it is usual to employ the symbols of the 
 crystal planes that are parallel to the cleavage planes. 
 
 The principal cleavages in each system are given 
 below. 
 
 TRICLINIC CLEAVAGE 
 
 In the Triclinic system the cleavage is chiefly Pina- 
 coidal, and less commonly Prismatic. The usual 
 symbols are as follows : 
 
 1. Basal Cleavage, P, or c, 001. 
 
 2. Brachypinacoidal Cleavage, oo P oo, i-1 or b, 010. 
 
 3. Macropinacoidal Cleavage, oo P oo, i-l or a, 100. 
 
 ( oo P', I' or m, 110. 
 
 4. Hemiprismatic Cleavage | ^ p> ^ ^ -^ 
 
 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 <j 521 } 123,135 
 
 Fig. 354. Isometric. Simple Form. Tetrakis Hexahedron 
 (/jfeO) with half its planes lined to show the method of 
 derivation of the Pentagonal Dodecahedron TT { hko } , 123, 136 
 
238 DESCRIPTIONS OF THE PLATES. 
 
 PAGE 
 
 Fig. 355. Isometric. Simple Form. Pentagonal Dodeca- 
 hedron TT-{ hkO }> 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 </ 00 
 
XIX 
 
 Fig.452 
 
 100 Fig 454 
 
 Fig-455 
 
 Fig 4-53 
 
 Growths 
 
 oo/oc IOO 
 
 -*<**,} sstS& 
 
 Fig 46o 
 
 roo 
 7T{AM 
 
 F*> 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 
 

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