278 SCIENCE PROGRESS 



limited number of rocks that have yet been analysed, and that as 

 the number of analyses of igneous rocks, selected without bias 

 in one direction or another, is indefinitely increased, the points 

 representing them will tend to distribute themselves in such a 

 manner as to approximate to perfect uniformity. 



As a matter of fact, analyses are not selected impartially from 

 all occurrences of igneous rocks. It is not the most widely 

 developed rocks that are the most frequently analysed. They 

 belong, as a general rule, to well-known types that are easily 

 recognised in hand specimens or thin sections. Analysis is, 

 in their case, often considered unnecessary, and when it is 

 resorted to, the number of analyses is not in proportion to 

 the extent to which the rocks occur. It is of the exceptional 

 rock which presents difficulties in determination, that the 

 worker most frequently obtains an analysis to verify his deter- 

 minations and to illustrate his description. Such a rock is often 

 of very local occurrence and so inconstant in character, that it 

 may well be considered worthy of more than one analysis. It is 

 therefore inevitable that a tabulation of analyses gives an alto- 

 gether false idea of the frequency of occurrence of different types, 

 and such a diagram as is above described exhibits a much greater 

 uniformity of distribution than actually exists. 



If we could adequately represent the quantitative occurrence 

 of rocks of different chemical types by points in a diagram, we 

 should find, there can be little doubt, that the whole resembled 

 a complex star cluster, which throws out arms in this direction 

 or that, and contains within its boundaries condensations of 

 various shapes separated by regions more sparsely occupied. 

 Unfortunately the value of the method of representing rocks 

 by means of points in a diagram is seriously diminished by the 

 fact that whether the simple oxides or the larger molecules be 

 taken as units, the number of variants far exceeds the dimensions 

 which are available. It is only by a kind of projection that the 

 different components, which would require a space of at least 

 six or seven dimensions for even approximately complete ex- 

 pression, can find their places in the two dimensions of a 

 diagram. The variants must be reduced to two by a process 

 of combination or exclusion, or both. 1 The result is, so to 



1 One more variant may be introduced into plane diagrams by the use of 

 the triangular diagrams of Ozann and others, but these are somewhat more 

 difficult to construct and to read. 



