648 RICE ART. L 



together equal to two right angles (not necessarily confined to 

 rectilinear triangles) can the situation for equilibrium be repre- 

 sented as in Gibbs' Figure 15. The case represented by Figure 16 

 is said by Gibbs to be one in which the tensions of the new sur- 

 faces "are too small to be represented by the distances of an in- 

 ternal point from the vertices of the triangle representing the 

 tensions of the original surfaces," as is the case in Figure 15. 

 The cases represented in Figures 8 and 9 of this text are said to 

 be of the type in which the tensions of the new surfaces are 

 too large to be represented as in Gibbs' Figure 15. 



52. The Stability of a New Homogeneous Mass Formed at a Line 



of Discontinuity. A Summary of the Steps 



in the Argument 



Having laid down these general ideas and definitions Gibbs 

 proceeds to the argument concerning the stability of a mass 

 formed in this way. It is long and detailed, covering more 

 than four pages, and it may be well for the reader first 

 to glance through a summary of the steps, with certain details 

 left out which can be filled in later. (In following such details 

 at first, one is apt to lose the thread of the argument.) 



The first step is on page 292 and concerns equilibrium, stable 

 or not. It is shown that if Ws and Wv are the two quantities 

 defined in [626] and [627] then if the system is in equilibrium 



Ws = 2Wy. 



(Notice that a similar type of numerical relation holds for cog- 

 nate quantities in cases of equilibrium treated previously. See 

 equations [563], [564], [569] of pages 260, 261.) It is also shown 

 that for equilibrium the quantity Ws — Wv must be at a maxi- 

 mum or minimum value as compared with any configuration 

 (equilibrium or not) of the surfaces adjacent to the equilibrium 

 configuration, i.e., so long as tensions and pressures are main- 

 tained unchanged at the values corresponding to the tempera- 

 ture and potentials throughout the system. 



In the second step it is shown that, since for stable equilibrium 

 Ws — Wv must be at a minimum value as compared with 

 adjacent configurations, there is instability if Wv is a positive 



