48 abstracts: geology 



sary for the derivation of the theorems bearing on the chemical side of 

 equilibrium. The applications of these theorems to actual cases will 

 be discussed in later papers. R. B. S. 



PHYSICAL CHEMISTRY. — Pressure-temperature curves in mono- 

 variant systems. George W. Morey and Erskine D. William- 

 son. Joum. Amer. Chem. Soc. 40: 59-84. January, 191 8. 



Willard Gibbs, in his paper "On the equilibrium of heterogeneous 

 substances," derives expression giving the relation between the varia- 

 tions in pressure and temperature in monovariant systems. The authors 

 derive from this equation two fundamental theorems concerning the 

 relations of the P—T curves in such a system, for the case where a linear 

 relation exists between the compositions of r or fewer phases in a sys- 

 tem of r components. These considerations make possible (with no 

 other knowledge than the composition of the phases at an invariant 

 point) the fixing of the order of succession of the (n + 2) P~ T 

 curves which proceed from an invariant point in a system of n com- 

 ponents and (when the state of aggregation of the phases is known in 

 addition) the fixing of their actual position within fairly narrow limits. 

 This is illustrated by considering the P — T curves which proceed from 

 the five quintuple points in the ternary system H20-K2Si03-Si02. 

 Gibbs' general equation is not in a form which is convenient to apply. 

 A general method is given for casting it into a convenient form for 

 practical use and a concrete interpretation of the coefficients involved 

 is given. The application of this equation to the actual slope of the 

 P — T curves, and especially to the change in slope with change in 

 composition of phases of variable composition, is discussed in detail, 

 taking as examples typical P — T curves from the ternary system 

 HzO-KsSiOa-SiOa. R. B. Sosman. 



GEOLOGY. — Some manganese deposits in Madison County, Montana. 

 J. T. Pardee. U. S. Geol. Survey Bull. 690-F. Pp. 131-143. 

 1918. 



The deposits are along the west side of Madison Valley near Cherry 

 and Wigwam creeks and in the foothills east of Jefferson Valley, near 

 Renova, localities that are, respectively, 70 and 30 miles southeast 

 of Butte, Mont. Though the deposits are small, they yield ore that is 

 almost free of silica and is therefore very desirable for making ferro- 

 alloys. They are also of interest because the manganese in them is 



