64 SCIENCE PROGRESS 



in combination with anorthite as a mixed felspar. Classes IV. 

 and V. are divided into Orders on the basis of certain ratios 

 between the femic minerals, an arrangement criticised later in 

 this paper. 



The Orders in Classes I., II., and III. are subdivided into five 

 arithmetically bounded compartments, called rangs, based on 

 the molecular proportions of potash and soda as against lime in 

 the salic minerals ; that is, on the ratio between alkali-felspars 

 plus lenads to anorthite. The rangs therefore quantitatively 

 express the relations between alkali-felspars plus felspathoids to 

 anorthite felspar in igneous rocks, less accurately the relation 

 between alkali-felspars and felspathoids to plagioclase felspar. 

 They give a quantitative expression to the conception of 

 "alkalic" and "calcic" types amongst igneous rocks. The 

 rangs are further subdivided, on the same five-fold basis, into 

 compartments called subrangs, according to the ratio between 

 the salic potash and soda. The subrangs therefore express the 

 quantitative relations between orthoclase and leucite on the one 

 hand, to albite and nepheline on the other — that is, between the 

 potassic and sodic constituents of magmas. Subdivision of the 

 subrangs is made into grads which depend on ratios subsisting 

 between the subordinate femic minerals. The grads have been 

 very seldom used. 



In Classes IV. and V. the orders, sections of orders, rangs, 

 and subrangs are based on certain ratios subsisting between the 

 predominant femic constituents, which it is not necessary to 

 particularise here. Further subdivision into grads is based 

 upon the proportions obtaining among the subordinate salic 

 minerals. 



Other refinements of classification are also to be found in the 

 system, as, for example, the formation of sub-classes in Classes 

 I., II. and III. for the reception of rocks rich in corundum, 

 zircon, etc. 



Many criticisms of this classification have been made. The 

 commonest, perhaps, is that it is " arbitrary," " unnatural," " a 

 priori," and constructed without regard to the possible discovery 

 of a " natural " mode of classification. This is the gist of 

 Harker's unsparing criticism. 1 In answer C.I.P.W. 2 admit that 



1 Natural History of Igneous Rocks, 1909, pp. 362-6. 



2 A convenient contraction for the names of the authors of the Quantitative 

 Classification — Cross, Iddings, Pirsson, and Washington. 



