PETROGRAPHY. 17 
TRANSITIONAL TYPES. 
In the list of types given above, as well as in the descriptions which follow, there 
will be noticed a considerable number of types which fall almost on the borders 
between two or more magmatic divisions, or are "transitional." Their occurrence 
is of importance as illustrating a feature of the quantitative classification which, as 
has been said elsewhere,* is not peculiar to it, but is inherent in the character of 
igneous rocks, so that no "natural" division lines exist, and those which are selected 
must be arbitrary, in the nature of the case. As has been said, such transitional 
types are just as important as those which fall at the centers of the various divi- 
sions a fact clearly brought out in the present region, where transitional types are 
very numerous, and to which belong some of the most abundant and characteristic 
rocks. 
To emphasize this fact of the equality in importance of "central" and "tran- 
sitional" types, the last have in nearly every case been described separately, even 
though this involved an increase in the number of types. 
In this connection the question naturally arises: How close to the border of a 
given division must a magma fall to be considered transitional ? The answer to 
this is debatable, and one which has been under consideration by the proposers of 
the quantitative system for some time. While no definite conclusion has been 
reached as yet, it would seem that the decision must rest largely upon the petrog- 
rapher himself in any given case. The need for arbitrary boundaries is not felt 
here as in the establishment of the definite magmatic divisions, and, furthermore, 
it is evident that, were the attempt made to establish rigid borders within or outside 
of which rocks should be said to be or not to be transitional, the difficulty would 
only be shifted, not eliminated entirely. Thus it might easily happen that the 
carrying out of the molecular ratios to four instead of three decimal places, or the 
determination and introduction into the calculation of such minor constituents as 
zirconia, baryta, or strontia, could change the type from a transitional to a non- 
transitional one, or vice versa. 
The treatment adopted here is rather a tentative than a final one, and in places 
may not be wholly consistent. As a general rule, a type or a magma has been con- 
sidered transitional when the ratio in question differs from that of the border line by 
0.05 or 0.10. Thus where the border ratio is 7:1, the magma is regarded as 
transitional if the ratio falls between 6.90 and 7.10. If the ratio of the border is 
5:3 = 1.666 + , the magma is regarded as transitional if it falls between 1.60 and 
1.70, a difference here of only about 0.05, as the border ratio is less than in the 
other case. But these are only in the nature of general and tentative suggestions, 
and this seems to be one of the features of the quantitative classification which it 
were best to leave somewhat indefinite, just as are the limits of identity or simi- 
larity in mode and texture which may define a type, and which are briefly dis- 
cussed on another page. 
* Cross, Iddings, Pirsson, and Washington, op. cit., pp. 121, 166, 231; Iddings, Prof. Paper U. S. Geol. Surv. 
No. 18, 1903, p. 69; Pirsson, Bull. U. S. Geol. Surv. No. 237, 1905, p. 120. 
