211] E. B. Mathews 13 



The presentation of a single " average " analysis possesses 

 all the charm of simplicity and ease of comprehension but 

 fails to convey a proper conception of the complex variability 

 underlying it. The student, with retentive memory, may hold 

 the values assigned to the type but may gain thereby little 

 knowledge of the real content of the term. If the rock se- 

 lected is in itself sharply defined., or if the examples collected 

 are sufficiently numerous the " average " analysis may be 

 satisfactory. If, on the other hand, the individual rocks in- 

 cluded under a given name are aggregates of minerals of vary- 

 ing composition in various proportions such as might occur in 

 a complex of numerous related and unrelated continuous gra- 

 dations without any semblance of "clustering," then the 

 " average " analysis gives nothing more than the arithmetical 

 mean of the quantities which have been included. As Cross x 

 remarked in his criticism of the classification proposed by 

 Loewinson-Lessing, " the grist of this mill depends entirely 

 upon what is put into the hopper." 



While even a momentary consideration shows that what has 

 been said regarding individual concepts applies even more 

 strongly to group concepts, the writer has considered it worth 

 while to test quantitatively the variabilities actually involved 

 in " average " analyses. The test is limited to anorthosites 

 and non-feldspathic pyroxenites and peridotites and the 

 methods employed are both graphic and arithmetic. 



EXAMPLES 



Anorthosite is composed of approximately a single mineral 

 or at least of representatives of a single isomorphous series. 

 The natural presumptions are that their analyses would repre- 

 sent a continuous series and their -average an intermediate 

 member. A graph of the analyses found in the literature 

 shows no such evenly distributed series, at least so far as lime 

 and soda are concerned, but three distinct types; one with 



1 J. Geol., vol. X, 1902, p. 481. 



