have proved of greatest value. The triangular diagram which he originally proposed for this purpose has been so improved by Roozeboom that the study of the chemical changes of a heterogeneous system and the prediction of its possible degrees of freedom become for the skilled worker a simple and easy matter.
Scientific Applications of the Phase Rule.—The doctrine of phases gives the chemist a new way of looking at things, serving at once as a basis of classification and a guide in qualitative research, and in contradistinction to the older gravimetric chemistry which dealt with some one continuous state of an isolated substance, it inaugurates the chemistry of substances in contiguity. Here the phase rule bears the same relation to physical chemistry that the periodic law of Lothar Meyer and Mendelejeff does to inorganic chemistry. Although only qualitative in its application it gives the chemist a new fundamentum divisionis by components and phases, necessitating a revision of substances, of which many formerly recognized as compounds are now no longer listed as such, while many new compounds have been introduced. In analytical chemistry the phase rule has found its widest application in classifying our knowledge of the dissociation of solid substances such as alloys, solid solutions, cryohydrates, tartrates, basic double and racemic salts, or in the solution of such special problems as the changing solubilities of metallic hydrates or the distributions of a dissolved substance between two solvents which do not mix. For example, Roozeboom discovered by the phase rule that four different hydrates can be formed with ferric chloride, of which only two were known before his investigation, while van der Heide's studies of the double sulphate of potassium and magnesium (Schonite) revealed the possibility of at least fifteen heterogeneous modifications of phase. No less than thirty different ferric sulphates are now on record, and Bancroft has said that a general system of qualitative research is not possible until we have studied the properties of such multi-component systems. Tammann's researches on the equilibria subsisting between solids and their melted states indicate that nearly all such substances have more than one solid modification of phase, while van't Hoff
- Gibbs, Tr. Connect. Acad., III., 176.
- Roozeboom, Ztschr. f. phys. Chem., 1894, XV., 143; Arch, néerl, 1895-6, XXIX., 71. Bancroft, J. Phys. Chem., 1896-7, I., 403. In 1891, Sir G. Stokes suggested the graphic representation of physical states of ternary alloys by means of an equilateral triangle which he derived independently from Maxwell's color diagram. (Proc. Roy. Soc. Lond., 1891, XLIX., 174.)
- See Professor Bancroft's Journal of Physical Chemistry (passim), from which most of the results in this section are taken.
- Roozeboom, Ztschr. f. phys. Chem., 1892, X., 477.
- Van der Heide, ibid., 1893, XII., 416.
- Cameron, J. Phys. Chem., 1907, XI., 641.
- Tammann, "Kristallisieren und Schmelzen," Leipzig, 1903.