656 RICE 



ART. L 



plane in d, and let de, df, dg be the line sections of the plane by 

 the three surfaces. If a, h, c are three points on de, df, dg, we 

 can conceive an arc of a circle drawn through diadi and similarly 

 arcs also drawn through dihd2, dicd^. Further, we can conceive 

 a portion of a sphere (a "spherical lune") drawn so as to connect 

 the arc ^16^2 with dicdi, etc. The mass D, if formed, is supposed 

 to be inside the space bounded externally by three such lunes, 

 and the lune joining dihd^ with dicd^ is the surface D~A, and so 

 on. We now name various portions of surface as follows. 

 The lune dibd^cdi is named Sad, and so on. The portion of the 

 surface B-C which is marked off between the arc diadi and the 

 line diddi is named Sbc- It is in fact the portion of the surface 

 B-C which is, as it were, destroyed by the formation of the 

 phase D. Similar definitions are given to Sca and Sab- Simi- 

 larly Vd stands for the volume occupied by the phase D and 

 Va, vb, Vc for the volumes of the three portions of it originally 

 occupied by the phases A, B, C before the phase D was formed. 

 The discussion of the stability follows the same course as before. 

 Representing the expression 



Cad' Sad + . . . — (^bcSbc — • • • 



by Ws, and the expression 



Pd Vd — PaVa — PbVb — Pc Vc 



by Wr, we have to investigate when Ws — Wv is a minimum or 

 maximum in the assumed state of equilibrium. (Its variation 

 is zero when we neglect higher powers than the first of the 

 variations of the variables.) We can find the ratio of Ws to Wr 

 in an equilibrium state by the same method as before. The only 

 difference in the result is that although, in the changes of size 

 which keep the figure similar to itself, cxad, (Tbc, etc. all vary as the 

 linear dimensions of the figure (since, for instance, ^cjadItad is 

 to be maintained constant and equal to pt> — Pa), the surfaces 

 Sab, etc. vary now as the squares of the linear dimensions. 

 From this it follows that 



d{(TAD Sad) = 3cr^o dsAo 



