THE MINERALOGRAPHY OF THE FELDSPARS 259 
to that developed by Rosiwal. The outlines of the different 
phases in a given field of the thin section were traced upon paper 
with the aid of a camera lucida. The areas of these grains were 
measured by a polar planimeter. The sum of the areas occupied 
by the grains of the different minerals was assumed to be propor- 
tional to their volumes. By multiplying the volumes by the specific 
gravities of the minerals the proportion by weight was secured and 
then calculated to too per cent. Usually four different micro- 
_ scopic fields in each slide were analyzed and their results averaged. 
Care was taken to use an optical system (objectives and oculars) 
which would give the largest practical field. The composition of 
each phase was determined by the extinction angles of crushed 
fragments. The first portion of each table shows the percentage of 
each of the phases present and their composition. ‘The composi- 
tion of each phase is given in percentages of each of the three feld- 
spar components, totaling roo per cent. In the second portion of 
the tables the percentage of each component is calculated upon a 
basis of 100 per cent for the entire specimen. The sum of the 
different components thus obtained gives the composition of the 
entire specimen after the manner of a recast chemical analysis. 
Consequently a chemical analysis, recast, would have to be rear- 
ranged by distributing the components into the various phases 
present in order to appreciate the true nature of the specimen. 
This indicates that the perthitic feldspars are much more com- 
plicated than is generally thought. The accuracy of the proper 
distribution of the components into the phases is directly depend- 
ent upon the accuracy of the thermo-equilibrium diagram and 
the degree of undercooling of the feldspar system under considera- 
tion. Until the diagrams of these minerals can be put upon a 
quantitative basis our examinations will be approximate only. 
