CONTENTS. INTRODUCTION. PAGE Art. 1...4. Minerals. Kinds or species . ..... 1 5. Descriptive characters 3 6. Form in general 3 7- Angles between normals to the faces 3 8, 9. Geometry of crystals 4 10. Axes. Parameters. Indices of faces .... 5 11. ..15. Geometrical illustrations ...... 5 10. Geometrical elements of a crystal ..... 8 17. Sphere of projection 6 18. Zone. Zone-cirele. Axis of a zone 7 It). Symbol of a zone containing two given faces ... 7 20. Symbol of a face common to two zones .... 7 21. Condition that a face may be in a zone .... 7 22...25. Relations between the indices and mutual inclinations of four faces in a zone 7 20. To chnngo the axes 8 27. To chango the parameters 8 28, 29. Arrangement of crystals in Systems .... 8 30. Forms. Ilolohedral and hemihedral forms. Combinations 9 31. Number of arbitrary elements in each of the different Systems. Geometrical description of a crystal . . 9 32...03. Cubic System 10 04...110. Pyramidal System 19 111... 103. Rhombohedral System ...... 28 104...190. Prismatic System ....... 39 197...215. Oblique System 44 210...219. Anorthic System ...... .47 220...223. Twin crystals 49 224...231. Goniometers and the method of using them . . 50