DECIMAL GROUPING OF THE PLAGIOCLASES 159 



seems the more logical as well as the more accordant with usage. 

 It leaves equal spaces between the several types; for, if the most 

 typical andesine is average andesine, the most typical albite is 

 pure albite. 



It is therefore proposed that the divisions be placed, as in 

 Diagram 11, where the ratios of anorthite to albite are T V, T 3 -<y, t \, 

 and T V- 



The questions of priority and of average practice have thus far 

 been left in the background. If priority determined preference, 

 Tschermak's plan (No. 4) should be preferred; and the belief 

 seems general that his plan is most in use. But, rather oddly, 

 the scheme that currently passes for Tschermak's is a modification 

 thereof by Rosenbusch (No. 5). The scheme proposed in the 

 present note resembles Tschermak's more closely than does any 

 other. Still more closely does it resemble the scheme (No. 10) 

 deduced by averaging the ranges of species in Diagrams 4 to 9. 

 The slightest alteration that will regularize this "average" plan 

 and close its gaps produces the decimal grouping. 



A decimal grouping goes naturally with centesimal symbols, 

 of which the most-used form is Ab n An IOO - n (e.g., Ab 4 oAn 6 o, or 

 Ab 2 5An 7 5); these, moreover, present certain practical advantages. 

 They give, more quickly than those like Ab 2 An 3 and Ab t An 3 a 

 definite idea of relative composition — -which is merely saying that 

 decimals are more easily subtracted than common fractions. The 

 decimal co-ordinates, too, upon which extinction-angle curves are 

 plotted, indicate the composition corresponding to a given angle 

 in percentages, which it is a needless trouble to reduce to a frac- 

 tion of a small denominator. Since in such curves the anorthite 

 increases toward the right, it is by the percentage of anorthite, 

 rather than by that of albite, that the composition is naturally 

 measured. Therefore, a symbol such as An 60%, or An. 60, which 

 indicates this percentage alone, conveys the essential informa- 

 tion more economically than the symbol Ab 40 An6 ; the former's 

 greater convenience, however, is possibly outweighed by the greater 

 currency of the latter. 



