LECTURE XVI. ] HISTORY OF CHEMISTRY. 335 



If there are n + 2 phases and only n components, equilibrium 

 is only possible at singular points ; that is to say, at some 

 definite temperature (multiple point, transition or transforma- 

 tion temperature). If there are just as many phases as there 

 are components, the equilibrium is incomplete ; that is, to each 

 temperature there corresponds a series of pressures. 



This phase rule has received numerous practical applica- 

 tions, the work of Roozeboom 4 deserving especial mention. 

 Roozeboom studied the connection of the states of aggregation, 

 the equilibrium between water and sulphurous anhydride, the 

 hydrates of ferric chloride, etc. The phase rule can also be 

 applied to dissociation phenomena, to the reciprocal trans- 

 formation of allotropic modifications of elements, and so forth. 5 



More important perhaps than the phase rule (the significance 

 of which is exaggerated by many, seeing that it merely furnishes 

 a scheme for the representation of heterogeneous equilibrium) 

 are van der Waals's theories of corresponding conditions, 5 * and 

 van 't Hoff's theory of solution. 6 



Van der Waals makes a distinct advance by substituting 

 for the gas equation, 



PV=RT, 



deduced from the laws of Boyle-Mariotte and of Henry-Gay- 

 Lussac, the expression, 



in which a and b are constants which depend upon the co- 

 hesion of the gases and the not altogether negligible volume of 

 the molecules. (According to van der Waals b is to be con- 

 sidered as representing four times the volume of the molecules.) 

 This equation not only represents the behaviour of gases 



4 Z. physik. Chem. 2, 449, 513 ; 4, 31 ; 5, 198 ; 10, 477 ; Rec. Trav. 

 Chim. 4 et seq. 5 Compare the summaries by Meyerhoffer, Leipzig 1893, 

 and by Bancroft, Ithaca, New York, 1897. 5a Die Continuitat des gas- 

 formigen und fliissigen Zustandes, Leipzig 1881. 6 Lois de 1'equilibre 

 chimique dans 1'etat dilone ou dissous. Stockholm iS86. Abstracted, Z. 

 physik. Chem. I, 481, 



