634 RICE ART. L 



alent to oac + (Tbc If, however, the temperature and poten- 

 tials are such that pc > Pa, then presumably a lentiform mass 

 might be in equilibrium both as regards pressures and also 

 surface tensions, since the resultant of the force equivalent to 

 <tac and ffBc being less than their numerical sum could pos- 

 sibly be equal and opposite to the force equivalent to ctab- 

 However, the argument on pages 259, 260 of the original shows 

 that the existence of such a lentiform mass would yield a 

 system of greater energy than the one from which it starts. 

 Hence in general there would be no tendency to form it. The 

 mathematical steps of the argument will offer no trouble pro- 

 vided the reader notes one or two points. Let us designate by X' 

 the center of the surface EH'F, and by X" that of the surface 

 EH"F. The cosine of the angles between EI and the tangent 

 to EH'F at E is (r' — x')/r'. The area of the spherical cap, 

 represented by EH'F in Gibbs' Figure 10 and denoted by Sac, is 

 known to be 2x(l - cos e')r"^, where d' is the angle EX'H'; 

 so that, since cos 6' = (r' — x')/r', the area is 2Trr'x'. The 

 volume of the spherical sector standing on Sac with its centre 

 at X' is ^Sac-t' = ^irr'^x'. The volume of the cone standing 

 on the base Sab (i.e., the circle with EF as diameter) is 

 f Sab-X'I = ^rR^ir' — x'). Hence the volume of the spheri- 

 cal segment between Sab and Sac, being equal to the difference 

 of the sector and cone, is as given in [566]. 



So far we have maintained the condition pA{t, n) = psit, n). 

 If, however, this condition be abandoned, and if the functions 

 are such that in general pA{t, fj.) > psit, m), all the preceding Hne of 

 reasoning can easily be adapted to the wider condition. This is 

 done on pages 262-264. As before, the condition (Xab > (Tac + (Tbc 

 is set aside. If <tab = o-ac + (Tbc, a thin film of C would just be 

 in equilibrium between the surfaces of A and B, which would 

 have a curvature given by Ci + C2 = (Pa — Pb)I(Tab provided 

 that 



, . (TBcit, fl) PA(t, m) + (TAcit, (J.) PB{t, H) 



Vc^t, n) = — , [571] 



as proved on page 262. If pc(t, n) were less than this critical 

 value the film would not form. If the values of i, /xi, m2, • • • 



