662 HENRY S. WASHINGTON 



calculate the volumes of the several spherical shells, which must 

 also be assumed to represent the true ellipsoidal ones. The 

 results are given below, including the relative volumes and 

 weights (obtained by correction of the former for specific 

 gravity), and the average composition deduced from this latter. 



This result is notably less basic than the former calculated 

 from the curves, and approaches somewhat closely to the com- 

 positions of the foyaite and the arkite, though in a general way 

 intermediate between the two. This is so, since these two form 

 (on this basis) 90 per cent, of the whole. It must be remem- 

 bered, however, that this method is not based on curves, but on 

 a succession of steps, and that the influence of the greater 

 width of the more acid phases is intensified by their greater 

 distance from the center. At the same time both methods 

 indicate a magma rich in Al^Og, CaO and alkalis, low in SiOg 

 and MgO, and with moderate iron. 



Inasmuch as there must be a (probably rather large) cor- 

 rection made for the greater mass of foyaite, on the analogy of 

 the Shonkin Sag laccolith, all these figures can, for the present, 

 be regarded as only suggestive and illustrative of the method 

 of investigation proposed, than representing exactl}" the actual 

 state of affairs. 



It is of course hazardous to theorize on such limited data as 

 are yet available, but the methods indicated in Pirsson's paper 

 and the present one would seem to be of not uncommon appli- 

 cability, and well worth further trial in the investigation of other 

 favorable localities. Indeed, as Pirsson has remarked,^ "it 

 would seem as if this should be the point of departure in the 

 study of other series." The methods indicated certainly put 

 the study of rock differentiation upon a purely mathematical 

 basis, which in the hands of a competently mathematical petro- 

 grapher, should surely lead to an exact quantitative knowledge 

 of the laws which control this, and very probably, with the aid 

 of physical chemistry, to a knowledge of the rationale of the 

 process. 



^ Pirsson, op. cit., p. 576. 



