xxii CONTENTS 



44. Illustration of Gibbs' Method by a Special 



Problem 619 



45. An Approach to this Problem from a Consideration 



of the Purely Mechanical Stability of the Surface. 622 

 XV. The Formation of a Different Phase within a Homo- 

 geneous Fluid or between Two Homogeneous Fluids . . . 625 



46. A Study of the Conditions in a Surface of Dis- 



continuity Somewhat Qualifies an Earlier Con- 

 clusion of Gibbs Concerning the Stable Coexist- 

 ence of Different Phases 625 



47. The Possibility of the Growth of a Homogeneous 



Mass of One Phase from a Heterogeneous 

 Globule Formed in the Midst of a Homogeneous 

 Mass of Another Phase 627 



48. The Possibility of the Formation of a Homogeneous 



Mass between Two Homogeneous Masses 631 



XVI. The Formation of New Phases at Lines and Points of 



Discontinuity 640 



49. The Possible Growth of a Fifth Surface at a Line 



of Discontinuity Common to Four Surfaces of 

 Discontinuity Separating Four Homogeneous 

 Masses 640 



50. The Possible Growth of a New Surface at a Point 



of Meeting of a Number of Lines of Discon- 

 tinuity 642 



51. Some General Ideas and Definitions Concerning 



the Possibility of a New Homogeneous Mass 

 Being Formed at a Line of Discontinuity or at a 

 Point of Concurrence of Such Lines 644 



52. The Stability of a New Homogeneous Mass Formed 



at a Line of Discontinuity. A Summary of the 

 Steps in the Argument 648 



53. The Details of the Argument Omitted from the 



Summary in (52) 650 



54. Consideration of the Case When the New Homo- 



geneous Mass is Bounded by Spherical Lunes . . . 655 



55. The Stability of a New Homogeneous Mass 



Formed at the Point of Concurrence of Four 



Lines of Discontinuity 657 



XVII. Liquid Films 659 



56. Some Elementary Properties of Liquid Films. 



The Elasticity of a Film 659 



57. The Equilibrium of a Film 662 



58. Foams. The Draining of a Film. The "Gibbs 



Ring" 667 



59. The Black Stage of a Soap Film 668 



