. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. SURFACES OF DISCONTINUITY 673 The gist of the long footnote on page 320 is that since two pieces of ice, for example, do not freeze together spontaneously but only under pressure, the free energy of the discontinuous region formed between the two pieces on freezing, denoted by (T// is not less than, and is most probably greater than, the sum of the free energies of the two surfaces in existence before the regelation, denoted by 2(tjw. The argument concerning crystalline sol
. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. SURFACES OF DISCONTINUITY 673 The gist of the long footnote on page 320 is that since two pieces of ice, for example, do not freeze together spontaneously but only under pressure, the free energy of the discontinuous region formed between the two pieces on freezing, denoted by (T// is not less than, and is most probably greater than, the sum of the free energies of the two surfaces in existence before the regelation, denoted by 2(tjw. The argument concerning crystalline solids follows the same course. To enable the reader to grasp the reason for the second part of the expression on page 320, Figure 11 is supplied. It represents a section of the crystal at the edge V which is sup- posed to extend at right angles to the plane of the paper; BE is part of the section of the surface s by the paper, AB a. part of. Fig. 11 the section of s'; CF is a part of the section of the surface s after growth of the crystal, so that the angle EBC is w', and CD is equal to bN. The face s' has, as far as the phenomena around the edge at D are concerned, increased by an area I'BC, V ⢠CD cosec co' or V ⢠cosec co' 8N; the face s has decreased by an area I' â BD or V cot w' 8N. Of course if co' is greater than a right angle, at any edge, the term involving cot co' in the correspond- ing portion of the summed expression will be essentially nega- tive and the term will be virtually an addition term, as is clear from the fact that at such an edge s increases in area. The argument on page 322 concerning stability follows precisely the same course as those employed earlier in the case of fluids, on which we have already commented fully. It should offer no difficulty. Nor is there anything in the three following. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance
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