68 Scientific Intelligence. 



and for each set of concentrations, one temperature and one pres- 

 sure. If however one of the variables be arbitrarily fixed the 

 system is again completely defined. If the number of phases be 

 n, the system is called a divariant system, there being in it two 

 variables which can be arbitrarily fixed before the system is com- 

 pletely defined. In studying the possible variations in equilibrium 

 caused by changing the different variables and the number of 

 phases, the author makes use of the Theorem of Le Chatelier, 

 which says: "Any change in the factors of equilibrium from 

 outside is followed by a reverse change within the system." He 

 then passes to the discussion of nonvariant, monovariant and 

 divariant systems, starting with a single component and increas- 

 ing to four. Taking, as the most familiar example of a 

 nonvariant system made up of one component, the equilibrium 

 between solid, liquid and vapor, as observed for example 

 in the system composed of ice, water and water vapor, the 

 author points out that according to the Phase Rule a system 

 of this type can be in equilibrium at only one temperature and 

 one pressure, this temperature for water being +0*0066° and the 

 pressure 4'6 mm of mercury ; these being the inversion temperature 

 and pressure. Applying the theorem of Le Chatelier to the 

 changes in the relative masses of a nonvariant system, we see that 

 if the system is kept at the inversion temperature and the exter- 

 nal pressure is continuously increased, a system will result occupy- 

 ing a lesser volume, the vapor condensing until the vapor phase 

 has disappeared and the monovariant system solid and liquid, is 

 left. So changes may be effected by varying the temperature, 

 the pressure being kept constant, the addition or subtraction of 

 heat taking place while the system is kept at constant pressure or 

 at constant volume. The three monovariant resulting systems 

 may exist over a series of temperatures and a series of pressures 

 bounded only by the appearance of new phases. Representing 

 these results in the case of water graphically, the author passes to 

 consider sulphur and phosphorus similarly. In the fourth chap- 

 ter, he takes up the question of two components, first as anhy- 

 drous salt and water, as hydrated salts and as volatile solutes, 

 and then as two liquid phases, as consolute liquids and as solid 

 solutions. Systems of three components are next treated under 

 the heads of two salts and water, pressure curves, solid solutions, 

 isotherms, fractional evaporation, two volatile components, com- 

 ponents and constituents and two liquid phases. A single chapter 

 on the general theory of systems of four components completes the 

 book. It appears to us that the task which Dr. Bancroft has set 

 before himself has beeu admirably done, whether we consider the 

 plan of his work or the manner of its execution. His volume is an 

 admirable presentation of a somewhat abstruse subject which will 

 be most useful to both the chemist and the physicist. g. f. b. 



6. Vorlesungen iiber Bildung unci Spaltung vo?i Doppelsalzen / 

 von J. H. Van't Hoff, Professor zu der Universitat Berlin. Deutsch 

 bearbeitet von Dr. Theodor Paul. 8vo, pp. iv, 95. Mit 54 



