78 



ALBERT JOHANNSEN 



average runs across the Ab S0 An S0 line. Of course if the nucleus 

 as well as the rim falls entirely between the 0-5, 5-50, 50-95, or 

 95-100 lines, there is no need for computation unless it be to 

 determine the exact position of the rock in the triangle. 



Families. — The quarfeloid face of the double tetrahedron 

 (Fig. 9), or any face parallel to it, will appear as shown in Fig. 16. 

 To locate the lines separating the various families it was necessary 

 to determine the logical divisions in two directions; namely, between 



Plae 

 Kf 





 100 



10 

 90 



20 

 80 



30 

 70 



40 



60 



50 

 40 



60 

 40 



70 

 SO 



80 

 80 



TOO 







Percentage plagtoclase 



Fig. 14. — Ratios of Kf to plagioclase in Families 1 to 15, Orders 1 to 3, and totals. 

 Vertical scale of totals is one-half of other curves. The numbers indicate the orders. 



the potash feldspar and the plagioclase and between rocks with or 

 without quartz or feldspathoids. 



In Fig. 14 the curves for the proportions of potash-feldspar to 

 plagioclase are shown for Orders 1, 2, and 3 and for the sum of all 

 f eldspathoid-f ree rocks ; the writer having no mode-analyses showing 

 potash-feldspar with anorthite in Order 4. The curves show 

 rather excessive increases on the 50-50 line, due to the fact that 

 many writers speak of labradorite as AbxAn^ the deduction of 

 rocks where this was done would slightly reduce the lines. In all 

 the curves the dividing lines may be made at 0-5-35-65-95-100, 

 corresponding to the subdivisions in vogue of alkali-granite, 

 granite, quartz-rrionzonite, granodiorite, quartz-diorite, etc. 



