44 ALBERT JOHANNSEN 



Kf-Plag base line. This determines the vertical series of pigeon- 

 holes, and its intersection with the horizontal series gives the proper 

 position for the family. (If plotted graphically, the family is 

 directly determined by the position of the intersection of three lines, 

 as shown in Example i, below.) Only when the point falls very 

 close to a division line is it necessary to compute the position 

 accurately. The separation points for Kf-Plag are at 0-5-35-65- 

 95-100. 



In Class 4, Orders 1,2, and 3, recalculate the olivine, pyroxene, 

 and biotite plus amphibole to 100 (Fig. 5) and find the proper 

 position graphically, or find the position analytically by taking 

 the ratio of the mineral of one corner to each of the others; thus 

 amphibole to olivine, amphibole to pyroxene, and olivine to 

 pyroxene. The division points are 0-5-50-95-100. 



In Class 4, Order 4, the writer groups all the ores in a single 

 family, but classifies the various hematite, ilmenite, magnetite, 

 etc., ores as subfamilies. If desired, they may be further separated. 

 If accessory dark minerals, not used in the computation, are abun- 

 dant, they determine subfamilies and may be mentioned in the 

 rock name. 



4. Subfamilies. In all classes subfamilies are based on 0-5-50- 

 95-100 division points, after the manner shown in Figure i, 



A FEW POINTS TO BE OBSERVED 



Any percentage value falling exactly on a line should be moved 

 toward the opposite apex of the triangle except as indicated below. 

 Thus a syenite with 5 per cent quartz is classified with granite, 

 a rock with 95 per cent mafites belongs to Class 4, and one with 

 95 per cent quarfeloids to Class 2; AbsjAng belongs to Order 2, and"" 

 AbgAnps to Order 4. If the divisions fall on the 50-50 line of quartz 

 they are moved upward, or on the 50-50 line of folds downward, 

 toward the apices; that is, they are placed in Families i to 5 or 

 26 to 30. Rocks falling on the 50-50 light-dark line are classed 

 with the dark, while along the plagioclase line AbsoAngo is classed 

 with basic plagioclase. Rocks falling on the line separating the 

 two triangles, namely, on the feldspar base line, usually should 

 be classed on the quartz side, that is, on the normal side, but if 



