630 RICE 



ART. L 



then W{tQ, fxo) is infinite for these values. It is to be noted that 

 near the top of page 255 Gibbs says that W can only become 

 infinite when p' = p", which is true enough in view of [555] or 

 [556]; for since at such values of the potentials equilibrium 

 between the two phases could only occur at a plane surface, r 

 must be infinite, and so W might be infinite, but not necessarily 

 infinite on account of [556], since by that equation r could be 

 infinite when p' = p" even if W were finite. But in any case W 

 could not be infinite under other conditions. However, on 

 page 256, Gibbs says quite definitely that when p' = p" the 

 value of W is infinite, thus invoking implicitly some other reason 

 than the purely mathematical, but not perfectly cogent, 

 argument just cited. Apparently it is the physical fact that an 

 infinitely extended sphere of the first phase will have an excess 

 of energy of infinite amount over the same sphere of the second 

 phase, since v'{iY' — c/') tends to infinity with v' if €y' — ty" 

 remains positive and finite, which must be assumed to be true 

 or otherwise the discussion would be pointless. Returning 

 therefore to the state indicated by the values to, yuio, M20, • . . 

 let the temperature and potentials change gradually from these 

 so as to make p'{t, n) increasingly greater than p"(t, n) ; W{t, n) 

 will gradually decrease. It may ultimately reach the value 

 zero, but if it does so then r and a will also vanish for the values 

 of t, Hi, H2, ... which make W vanish, the difference p' — p" 

 still being finite. For any values of temperature and potentials 

 in the range up to this stage the conditions of stability remain 

 as stated ; the second phase is stable, there would be no tendency 

 for a "fault" to form in it. At this stage the matter is in doubt. 

 The argument in the last few lines of page 256 is very subtle 

 indeed. The quantity r may be zero, but this does not imply 

 that a heterogeneous globule might not exist in equilibrium 

 since r is not the radius of the globule. If, however, the 

 globule dimension vanishes when r is zero, Gibbs says that the 

 second phase would be unstable at the corresponding value of 

 temperature and potentials. To see this we must remember 

 that if, at any values of temperature and potentials, we created 

 by any physical means the internal mass corresponding to the 

 finite r for these values of t, ni, H2, . . . , then the slightest dis- 



