In conclusion, I would express my thanks to Sir William Ramsay, whose guidance and counsel have been constantly {x} at my disposal; and to my colleagues, Dr. T. Slater Price and Dr. A. McKenzie, for their friendly criticism and advice. To Messrs. J. N. Friend, M.Sc., and W. E. S. Turner, B.Sc., I am also indebted for their assistance in reading the proof-sheets. A. F. _November, 1903._ {xi} CONTENTS PAGE CHAPTER I INTRODUCTION 1 General, I. Homogeneous and heterogeneous equilibrium, 5. Real and apparent equilibrium, 5. CHAPTER II THE PHASE RULE 7 Phases, 8. Components, 10. Degree of freedom. Variability of a system, 14. The Phase Rule, 16. Classification of systems according to the Phase Rule, 17. Deduction of the Phase Rule, 18. CHAPTER III TYPICAL SYSTEMS OF ONE COMPONENT 21 A. _Water._ Equilibrium between liquid and vapour. Vaporization curve, 21. Upper limit of vaporization curve, 23. Sublimation curve of ice, 24. Equilibrium between ice and water. Curve of fusion, 25. Equilibrium between ice, water, and vapour. The triple point, 27. Bivariant systems of water, 29. Supercooled water. Metastable state, 30. Other systems of the substance water, 32. B. _Sulphur_, 33. Polymorphism, 33. Sulphur, 34. Triple point--Rhombic and monoclinic sulphur and vapour. Transition point, 34. Condensed systems, 36. Suspended transformation, 37. Transition curve--Rhombic and monoclinic sulphur, 37. Triple point--Monoclinic sulphur, liquid, and vapour. Melting point of monoclinic sulphur, 38. Triple point--Rhombic and monoclinic sulphur and liquid, 38. Triple point--Rhombic sulphur, liquid, and vapour. Metastable triple point, 38. Fusion curve of rhombic sulphur, 39. Bivariant systems, 39. C. _Tin_, 41. Transition point, 41. {xii} Enantiotropy and monotropy, 44. D. _Phosphorus_, 46. Enantiotropy combined with monotropy, 51. E. _Liquid Crystals_, 51. Phenomena observed, 51. Nature of liquid crystals, 52. Equilibrium relations in the case of liquid crystals, 53. CHAPTER IV GENERAL SUMMARY 55 Triple point, 55. Theorems of van't Hoff and of Le Chatelier, 57. Changes at the triple point, 58. Triple point solid--solid--vapour, 62. Sublimation and vaporization curves, 63. Fusion curve--Transition curve, 66. Suspended transformation. Metastable equilibria, 69. Velocity of transformation, 70. Law of successive reactions, 73. CHAPTER V SYSTEMS OF TWO COMPONENTS--PHENOMENA OF DISSOCIATION 76