CLA SSIFICA HON OF IGNEO US RO CKS S77 



characters it is plain that any system of classification must be 

 arbitrary. 



As has been pointed out, the efforts to express the quantita- 

 tive variation in rocks by means of several variables have shown 

 that such a method is undesirably complicated. And we have 

 sought to find a way for making groups of different taxonomic 

 value by subdivision in a dichotomous manner based on the 

 comparison of successive pairs of factors, since the simplest 

 mode of construction is best. 



The mineral constituents of igneous rocks may exist in all 

 proportions from o to ioo per cent, whether considered as part 

 of the whole rock, or as part of the group of standard minerals 

 to which they may belong. For example one rock may consist 

 entirely of feldspar, while another has none. And there are 

 intermediate rocks containing all possible percentages of feld- 

 spar between these extremes. There are equally wide ranges 

 for some of the chemical constituents, considered either with 

 reference to rocks or to mineral groups. Thus the feldspars of 

 one rock may be wholly alkalic, those of another wholly calcic, 

 and between these extremes there are all possible gradations. 

 Among alkalic feldspars are those purely potassic, others wholly 

 sodic, besides all possible intermediate mixtures of these. 



On account of the absence of natural division lines in such 

 series of two variable factors, it is necessary to establish arbitrary 

 divisions. We have accomplished this by considering certain 

 simple proportions as center- points, about which variations may 

 be allowed within limits, which limits become the boundaries 

 between petrographical units. 



The simplest proportions are : first, those two in which one fac- 

 tor constitutes the whole, and the other factor is absent; second, 

 that in which both factors are present in equal amounts. 



Other center-points should be selected with equal respect to 

 these, and may be placed either midway between the three just 

 mentioned, or at shorter intervals. It has appeared to us best to 

 select those midway between the first three, namely, at points 

 representing the proportions three to one, and one to three, 

 making in all five divisions. 



