PETROLOGY. 173 
or of monzonose and vesuvose. Similar criticisms could be made of the rare and 
very rare magmas, though the positions of the last two are almost certain, but all 
of these are so exceptional that they have little bearing on the immediate problem. 
THE AVERAGE MAGMA. 
As we have seen that the relative amounts of the different subrangs vary greatly, 
from those which are very abundant to those which are only met with excep- 
tionally, it is clear that the composition of the whole, or of the original magma, 
can not be arrived at by simply taking the average of all the analyses. This would 
lead to correct results if the number of analyses of each type were proportional to 
its relative abundance or less accurately to the number of occurrences. But as 
this is not true we must, in our final calculation, weight the analyses of the rocks 
belonging to each type or subrang according to the relative abundance as best 
we may. This is a somewhat difficult proceeding, and in the nature of the case 
and the absence of exact quantitative data, must be somewhat arbitrary and depend 
largely on the judgment of the calculator. The matter has been the subject of 
considerable thought and numerous calculations, the latter indicating that the 
range of possible variation in different directions was much smaller than had been 
thought probable, and it was also found that the influence of small amounts of 
the rarer magmas was almost, if not quite, negligible. 
As a final basis of calculation it was decided to employ only the more abundant 
magmas, the relative amounts of which could be approximately estimated with a 
fair degree of satisfaction. The introduction of the rarer ones into the calculation 
must be regarded as a small correction, to be applied in the future, when the main 
data are more accurately known. To a certain extent also these rarer magmas are 
of such characters that they compensate for each other more or less, so that their 
introduction or neglect does not seem to affect the final result seriously. 
The magmas selected for use were ciminose (II. 5. 2. 2), braccianose (II. 7. 
2. 2), vicose (II. 6. 2. 2), vulsinose (II. 5. 2. 2), albanose (III. 8. 2. 2), phlegrose 
(I. 5. i. 3), and monzonose (II. 5. 2. 3). The average of the analyses of the rocks 
of the various types which fall in each of these* was calculated, and each average 
was weighted as follows: Ciminose, braccianose, and vicose = weight 5; vulsinose = 
weight 4; albanose, phlegrose, and monzonose = weight 2. 
It would have been well to include vesuvose, with a weight of 2, but no chemical 
analysis of this was available, and it is probable that its neglect is compensated for by 
the possible greater abundance of phlegrose over albanose. Also, it might have 
been somewhat more accurate to include pulaskose, auruncose, and harzose with 
a weighting of i each, but it was thought that this was giving these rather rare 
magmas undue importance, and it was found that a less relative weighting had but 
little effect on the final result. 
In any accurate estimate corrections for the specific gravities of the different 
types should also be made. But the data in regard to the relative abundance 
are so rough in themselves that this was deemed to be an unnecessary refinement. 
* Except that of the viterbal vulsinose from below San Rocco, at the Vico Volcano (cf. p. 39). 
