SURFACES OF DISCONTINUITY 671 



of a tension depending on a stretching of the surface arising 

 from a deformation of the soHd itself, but this is entirely- 

 different from the surface energy. In the case of a fluid the 

 quantity o-, whatever name we give it, is not the measure of the 

 work of a force stretching the fluid surface by unit amount but 

 of the increased energy acquired by molecules which have come 

 from the interior of the fluid to form a new unit of surface, the 

 surface itself being otherwise in the same physical condition as 

 before. It may be, as Gibbs remarks, that in certain cases the 

 actual numerical values for the two quantities in the case of a 

 solid approximate to each other, and so, for example, equation 

 [661] can receive an interpretation, as explained in the last 

 paragraph of page 317, which makes its content identical with 

 that of equation [387]. However, the writer has some reserva- 

 tions to make on this matter which will be given presently. 



A reminder to the reader may not be out of place when he 

 begins to read this subsection. The words isotropic and 

 anisotropic can be applied to states of stress in solids, as well as 

 to the solids themselves. This matter has been already dealt 

 with in the commentary on "The Thermodynamics of Strained 

 Elastic Solids" (Article K) which may well be referred to in 

 this connection. 



On pages 316-320 the equation equivalent to [387], viz. [661], 

 is deduced for isotropic solids. On pages 320-325 crystalline 

 solids are considered. The proof of [661] will offer no difficulty, 

 as the reader will now be familiar with the type of argument 

 employed. One special point alone calls for comment. If a 

 closed curved surface is displaced by an amount ^A'" along its 

 normals so as to take up a new position "parallel" to its original 

 form, each element of its surface, Ds changes in area by an 

 amount (ci + C2)8NDs where Ci and C2 are the principal curva- 

 tures of the element. This fact, the proof of which will be 

 found in the section on curvature in Article B of this volume, 

 is used in the expression for the increment of energy with which 

 the argument starts and in the subsequent expressions for incre- 

 ment of entropy, etc. Just after equation [661] there occurs a 

 statement concerning the expression p" -{- (ci + C2)a. This is 

 dependent on the same considerations as were used in our dis- 



