670 RICE 



AKT. L 



Space permits us to mention only one more point, first clearly 

 established by Perrin, viz., that soap films can be "stratified," 

 the layers of a stratified film being formed by the superposition 

 of identical elementary leaflets in suitable numbers. The 

 thickness of each layer is an integral multiple of an elementary 

 thickness which is of the order of 5 to 6 millimicrons. Actually 

 it is known also that under certain circumstances more than 

 one thickness of black film can be formed ; but the thicker blacks 

 do not last long and quickly give place to the thinnest. With 

 this extreme tenuity of the ultimate black film, it becomes 

 porous and the air inside a bubble which has reached the black 

 stage is gradually forced out by the excess of internal pressure, 

 thus leading to the collapse of the bubble. The reader will find 

 a wealth of interesting material in Lawrence's book, with abun- 

 dant references to original papers on the subject. 



XVIII. Surfaces of Solids 



[Gihhs, I, pp. 314-831] 



60. The Surface Energy and Surface Tension of the Surface 



of a Solid 



In the first portion of this subsection Gibbs returns to the 

 treatment of a problem which he has previously considered in 

 pages 193 et seq. of the section on the conditions of equilibrium 

 for solids in contact with fluids, viz., the expression of the con- 

 dition which relates to the dissolving of a solid or its growth 

 without discontinuity. The problem is now studied with 

 regard to the effect of the existence of surface energy on the 

 course of events, a point not raised in the earlier discussion. 

 He defines his terms for surfaces between a solid and a fluid in a 

 manner similar to that employed for fluid interfaces, and it is 

 to be observed that his symbol a is now definitely associated 

 with surface energy and not surface tension. We have already 

 referred to common misconceptions in this connection in the 

 case of fluids, where, however, the concept of a surface tension 

 may prove serviceable at times as a fiction whose use can be 

 justified by mathematical convenience. But here the various 

 states of strain in a solid can perhaps justify us in the conception 



