138 



'SCIENCE. 



[N. S. ■ Vol: VII. No.- 161. 



"and fragmental volcanics, with occasional sedi- 

 ments interbedded. The Clarksburg formation 

 is described by Dr. Bayley, who also, in Chapter 

 v., discusses the various intrusive rocks that 

 preceded the Clarksburg and those that follow 

 it. In Chapter VI. , H. L. Smyth describes in 

 detail the interesting trough that runs off from 

 the main Marquette syncline to the Republic 

 mine. While the general relations are much 

 like the large area, there are present of the 

 Lower Marquette series only the Aj ibik quartz- 

 ite and the Negaunee iron-bearing formations, 

 and of the Upper Marquette only the Goodrich 

 quartzite and the Michigamme mica-schist. 

 Minor peculiarities in local geology are also 

 met. In Chapter VII., C. R. Van Hise gives a 

 broad, general, structural discussion of the 

 whole area. The monograph is illustrated by 

 many plates and figures. The former include 

 beautiful, colored reproductions of the rocks of 

 the Negaunee formation that are associated 

 with the iron-ores. An atlas of maps also ac- 

 companies the letterpress. Besides a general 

 map there are thirty-five sheets of quarter town- 

 ships, four inches to the mile. 



The entire work is a monument to its authors 

 and of incomparable interest alike to students 

 of metamorphism, of economic geology and of 

 structural geology. The mining operators of 

 the region should find it a suggestive guide in 

 new developments and exploratory work. The 

 book is written in a clear and pleasing style 

 which deserves commendation no less than does 

 the scientific matter. J. F. Kemp. 



TTie Phase Rule. By Wilder D. Bancroft. 



Ithaca, N. Y., The Journal of Physical 



Chemistry. Large 8vo. Pp. viii+255. Paper. 



With numerous diagrams. Price, $3.00. 



This intefesting volume presents the subject 

 of qualitative equilibrium of heterogeneous 

 substances, on the basis of Gibbs' ' phase rule' 

 and Le Chatelier's theorem. Mathematical 

 theory, electro-chemistry and quantitative 

 equilibrium are not discussed, but diverse 

 phenomena in great variety, including the 

 temperature, pressure and concentration of 

 components are coordinated as examples of a 

 few general principles. The general scope of 

 the work can best be illustrated by a few 



subjects, selected from the many experimental 

 data brought under review. 



Water in an open vessel is not usually in a 

 state of equilibrium, since evaporation takes 

 place at the surface, and the liquid gradually 

 diminishes in quantity. When the vapor is 

 confined, in a limited space, its mass increases 

 at any given temperature, until it exerts a 

 certain definite pressure upon the surface of 

 the water, and equilibrium results. With any 

 change of temperature, some new pressure will 

 be found before equilibrium is established ; and 

 if rectangular coordinates are used to represent 

 the varying temperatures and pressures, some 

 curved line will contain all the points which 

 express conditions of equilibrium. Here is a 

 system consisting of a single component in two 

 phases, and the conditions of equilibrium are 

 expressed graphically by a line. A definite 

 change of either temperature or pressure or the 

 density of water or vapor requires some definite 

 change in another condition also. In this sense 

 the conditions of equilibrium have but one degree 

 of freedom, and the system is monovariant. 

 Now, let the water be cooled until it begins to 

 freeze. This implies a fixed temperature 

 (0° C.) and a fixed vapor pressure of about 4.6 

 millimeters of mercury. If the system includes 

 all three phases it is said to he nonvariant, and 

 the conditions are represented by a single point 

 in the diagram. At lower temperature the 

 liquid will all freeze ; at higher temperature 

 the ice will melt. With increased pressure at 

 zero all the vapor will be condensed ; with 

 diminished pressure all the liquid will gradu- 

 ally vaporize ; in either case the system is 

 reduced to two phases. A second curve of 

 pressure can be drawn for ice in contact with 

 vapor, and a third for ice in contact with liquid 

 water, either system of two phases being mono- 

 variant. 



When a salt, as potassium chloride, is added 

 to the system in excess, there are two compo- 

 nents, with the possibility of four phases ; with 

 the further addition of potassium nitrate, there 

 are three components and may be five phases. 

 In each case, if all components are present in 

 the solid state, together with the saturated 

 solution of all and the superincumbent vapor, 

 the conditions of temperature, pressure and 



