398 ALFRED HARKER 



from such averages a diagram expressing the variation of the 

 several bases. Further, we might note the limits of variation of 

 each base within each group averaged, and express these limits 

 also on the diagram. Each base would therefore be represented, 

 not by a simple curve, but by a curved band of varying width. 

 A still further refinement would be to indicate, say by different 

 depths of color within the bands, the frequency of different 

 degrees of departure from the average. On such a diagram it 

 would be possible to test with some precision the principle here 

 advanced, that mixtures, even of two normal igneous rocks and 

 still more of an igneous and a sedimentary rock, must often be 

 abnormal in chemical composition. 



So much labor is, however, not necessary for our present 

 purpose. We have hitherto considered only the bulk analyses of 

 the rocks; but we know that a close relation exists between the 

 chemical composition and the mineralogical ; a relation which is 

 a matter of very nice adjustment. Expressing it in a crude 

 empirical way, we may say that the chemical variation evinced 

 in normal igneous rocks is not of an arbitrary kind, but is such 

 that the rock-magmas have been able to crystallize as mineral- 

 aggregates consisting of species selected from a comparatively 

 small category, and selected subject to certain laws of pangene- 

 sis which control the permissible associations of those mineral 

 species. In a natural assemblage of rock types, whether a 

 " Gesteinsserie," a " Faciessuite," or any other kind of grouping, 

 the limitations are of course narrower still. To inquire into the 

 significance or rationale of such rules would be to enter upon a 

 theoretical discussion of the processes of differentiation, a subject 

 outside our scope : they are introduced here as affording in 

 great measure a test for mixed igneous rocks. For it follows 

 that any variation of an arbitrary kind [i. e., not on the lines of 

 magmatic differentiation) imposed on the chemical composition 

 of an igneous rock-magma may produce much more considerable 

 modification in the mineral composition of the resulting rock. It 

 is well known that, when a magma has absorbed material from 

 sedimentarv rocks, this often results in the formation of such 



