554 W.CROSS, J. P. IDDINGS, L. V. PERSSON, H. S. WASHINGTON 
I.q]. 5.2-3-=Class I, Subclass II, Order 5, Rang 2, Subrang 3. 
IV.]]. 2.3-2.2.=Class IV, Subclass II, Order 2, Section 3, Rang 2, Sub- 
rang 2. 
IV. 4.,.1.4.=Class IV, Order 4, Suborder 2, Rang 1, Subrang 4. 
It is to be observed, however, that the number for subrang is 
placed on the line with rang. This arrangement makes it possible 
to express the intermediate magmatic divisions by means of marks 
above the line in the manner explained in the next paragraph. 
Intermediate divisions——In a continuous series of varieties of 
rock magmas those near one another on opposite sides of any 
division line are more alike than varieties at the extremities of any 
one division. And so it happens that some rocks differing but little 
in composition may be given different names, because they belong 
on two sides of a division line, while other rocks not so much alike 
are called by the same name and belong to the extremes of the same 
magmatic division. This condition is inherent in any rigid system 
of divisions of continuous series. It has not been felt to the same 
extent in the qualitative system because each petrographer adjusts 
the elastic definitions of that system to suit his own requirements, 
and to the confusion of everyone else. 
In order to distinguish the extremes of the magmatic divisions 
already established in the first publication of the Quantitative 
System, and meet the needs of closer classification, or correlation, it 
is desirable to establish zntermediate divisions throughout the system 
by placing the boundaries of these divisions half-way between the 
extremities of the divisions and the centers of the divisions from 
which the intermediate divisions are to be taken, in conformity with 
the methods pursued in establishing the first division in the Quantita- 
tive System. The boundary between adjacent divisions becomes in 
this way a new centerpoint for each pair of intermediate divisions. 
In the notation of intermediate divisions the halves of each pair 
of divisions falling within the adjacent large divisions are desig- 
nated as parts of the large divisions, and are not given new and 
independent designations. ‘Thus the intermediate divisions in any 
fivefold series are as follows: 
