JO SI AH WILLARD GIBBS 555 



have proved of greatest value. The triangular diagram which he orig- 

 inally proposed for this purpose^^ has been so improved by Eoozeboom'^ 

 that the study of the chemical changes of a heterogeneous system and 

 the prediction of its possible degrees of freedom become for the skilled 

 vs'orker a simple and easy matter. 



Scientific Applications of the Phase Rule. — The doctrine of phases 

 giTes 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 contra- 

 distinction to the older gravimetric chemistry which dealt with some 

 one continuous state of an isolated substance, it inaugurates the chem- 

 istry 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 quali- 

 tative in its application it gives the chemist a new fundamentuyn, 

 divisionis by components and phases, necessitating a revision of sub- 

 stances, of which many formerly recognized as compounds are now no 

 longer listed as such, while many new compounds have been intro- 

 duced.'^^ 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, Eoozeboom 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, neerl, 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. 8oc. 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. 



