480 RICE ART. K 



(In this iii(t, p, Wr) is a contraction for ni{t, p, mi, mo, ms, . . .) 

 indicating the functional dependence of m on t, p, mi, m2, 

 mz, . . .;m is of course the mass of the soHd.) The treatment by 

 Gibbs on pages 198-201 is based on certam geometrical postu- 

 lates. In the state of reference he chooses lines parallel to the 

 edges of his unit cube as axes of reference. In the state of 

 strain he takes OZ to be perpendicular to the faces in contact 

 with the fluid, i.e., to be one of the principal axes of stress. The 

 other two axes OX, OY are of course in the plane containing 

 the other two principal axes of stress, and one of them, OX, is 

 chosen so as to be parallel to one of the edges of the oblique 

 parallelopiped. Thus all points which have the same s'-co- 

 ordinates in the state of reference have the same s-coordinates 

 in the state of strain; in consequence ^ is a function of z' alone 

 being independent of x' and y', and so a^i and 032 are zero. (See 

 [398].) Moreover all points which have the same y' and z' co- 

 ordinates in the state of reference, i.e., lie on a line parallel to 

 OX', have the same y and z coordinates in the state of strain. 

 Thus yisa, function of y' and z' and is independent of x', and so 

 021 is also zero, (again see [398]). From this point on he pursues 

 the analysis as above with the absence of certain terms which 

 vanish on account of the conditions 



«21 = «31 = ^32 = 0. 



Thus the determinant of the ar, coefficients becomes 



which is just aiia22as3 as in [402]. The reader will find no 

 difficulty now in following the steps in the remaining three 

 pages, having had these postulates explained and having 

 followed the argument already in a more general manner. 



Finally, before leaving this sub-section we shall refer to the 

 remark at the top of page 199. The increase in the energy of 



