554 THE POPULAR SCIENCE MONTHLY 



ently variable components, is capable of n -\- 2 — r degrees of free- 

 dom or variations in phase, of which not more than n -\- 2 can coexist 

 at the same pressure and temperature. Such systems, in Trevor's 

 nomenclature, are spoken of as invariant, monovariant, divariant, etc., 

 according to the number of possible variations of state. Thus water 

 (HgO) has three independent phases, ice, liquid and steam, and is 

 invariant, the three phases being in equilibrium at only one pressure 

 and temperature, called the triple point, where the steam-line, ice-line 

 and hoar-frost line meet. But when calcium carbonate (CaCOs), 

 calcium oxide (CaO) and carbon dioxide (COo) are in equilibrium, 

 we have three coexistent phases formed of two components (CaO, CO2) 

 and the system is monovariant. By this rule the chemist is able to 

 predict the number of modifications of which a chemical substance is 

 capable from observation of its physical properties alone, or the number 

 of substances in a mixture from notation of the number of phases pos- 

 sible, or the strength of a saturated solution from its temperature and 

 pressure. Many different proofs of the phase rule have been given by 

 mathematicians and physicists from varied and independent points of 

 view,^^ and there is every indication that it is a complete and accurate 

 statement of a general chemical law. Its practical significance re- 

 mained for a long time undiscovered until the Dutch chemist Van der 

 Waals took it up, and when, in 1884-6, his colleague, Bakhuis Rooze- 

 boom, found himself unable to explain certain puzzling phenomena 

 connected with the equilibrium of gaseous hydrates and of double am- 

 monium salts, van der Waals was able to direct his attention to Gibbs's 

 theorem and showed him, by working out a special case, how thermo- 

 dynamic methods might be applied to practical chemistry.^^ From 

 that time on Roozeboom became the devoted champion of the phase 

 rule, which he compares to the ground plan of a gigantic building in 

 which all the collected phenomena of chemical equilibrium can be 

 stored in a convenient and comprehensive manner. " This structure," 

 he adds with pride, " has since been completed, almost exclusively by 

 the work of the laboratories of Leyden and Amsterdam."^" In fact, 

 the investigations of Roozeboom and van't Hoff upon double salts, solid 

 solutions and metals are among the most brilliant results of modern 

 chemistry. It is in connection with the graphic study of chemico- 

 physical changes by the phase rule that Gibbs's diagrams and surfaces 



^ Nernst, " Lehrb. d. theoret. Chemie," 2. Aufl., 564. Wind, Ztschr. f. phys. 

 Chem., 1899, XXXI., 390. Kuenen, Proc. Roy. Soc. Edinb., 1899-1901, XXIIL, 

 317; J. Phys. Chem., 1899, III., 69. Le Chatellier, Rev. g4n. d. sc, 1899, 759, 

 Saurel, J. Phys. Chem., 1901, V., 31, 401. Trevor, ibid., 1902, VI., 185. Weg- 

 scheider, Ztschr. f. phys. Chem., 1903, XLIII., 93, 113. Raveau, Compt. rend. 

 Acad. d. sc, 1904, CXXXVIII., 621. Mueller, ibid., 1908, CXLVI., 866. 



"^ Roozeboom, "Die heterogenen Gleichgewichte," 1901, I., 7. 



'"'Ztschr. f. Elektrochem., 1907, 94. 



