SURFACES OF DISCONTINUITY 



615 



stated in Gibbs' text is somewhat confusing. We have limited 

 the matter to the second differential coefficients, as that is suffi- 

 cient to make the meaning of the sentence more apparent to 

 the reader. (As the order of Hg, ma, m», • • • is immaterial, the 

 conditions are, that the constituents in the principal diagonal 

 of the determinant 



av 



dfikdug 



av 



av 



av 



dfXgdnh dugdm 



av av 



av 



dfjLhdm 



av 



dfjLidug dfiidnh dfifi 



and all the minors of the third, fifth, seventh, etc. order, formed 

 by erasing the necessary number of rows and corresponding 

 columns, shall be negative, while the minors of the second, fourth, 

 etc. order formed by similar erasures shall be positive in value.) 



4^. Determination of a Condition Which Is Sufficient though Not 



Necessary for Stability when the Dividing Surface Is 



Not Plane and Is Free to Move 



The investigation so far has been limited by the proviso that 

 the surface is plane and does not move. The removal of this 

 limitation renders the problem more difficult, although it is 

 easy to derive a condition which in this case will insure stability, 

 without actually being necessary for it. Gibbs' treatment of this 

 occurs at the very end of this subsection, on pages 251, 252, but 

 it is so relatively simple compared to the other material of the 

 subsection that the reader may find it helpful to have his 

 attention directed to it at once. To make the presentation as 

 direct as possible, consider a system with two homogeneous 

 masses separated by one surface of discontinuity, the whole 

 enclosed in a rigid envelop. We can suppose that two fine tubes 

 inserted through the envelop put each mass in communication 



