238 THE AMERICAN NATURALIST. [Vor. XXXV. 
processes of differentiation in rock magmas. Rocks resulting from 
admixture must therefore be excluded from the main scheme and 
be relegated to an appendix. Any discussion which tends to the 
recognition of this principle and to the establishment of some crite- 
rion of distinction will forward the object by disembarrassing the 
problem of a disturbing element." 
The most recent and most complete discussion of the chemical 
elements of rocks is by Osann,' who proposes a formula for each rock 
which shall represent approximately its chemical composition and at 
the same time be capable of easy plotting. He also proposes a 
method of plotting by which the composition of a rock is indicated 
by the position of a dot in a triangular diagram. The dot in its 
relation to the bounding lines of the triangle exhibits at once the 
relative proportion of the important constituents in the rock mass. 
A single dot thus represents an entire rock. By plotting a large 
number of rocks on the same diagram their chemicalrelationships are 
easily and conveniently studied. The plotting at once exhibits a 
grouping of closely related rocks and differentiates those whose mineral 
composition may be similar but whose chemical composition is 
different. The personal element has no place in the system of 
plotting. The types are determined solely by the grouping of the 
dots which express by their position the composition of individ- 
ual specimens. In the constructure of his rock formulas Osann 
transforms the percentage analyses into molecular proportions and 
recalculates to the sum of 100. The mean of two analyses of the 
norite ? of Montrose Point on the Hudson River thus treated becomes 
SiOz Al203 FeO MnO MgO CaO NasO K0 
59.50 10.35 7.38 36 8.14 8.65 4.23 1.39 
The percentage of SiO, (including ZrO, and TiO,) in the recalcu- 
lated analyses is represented by S with the corresponding exponent. 
By A is represented the alkalies in the molecular group (NaK)s 
AlO, In the above instance 4 = 5.62. The lime is considered 
as in the group CaALO, and is represented by C. But CaO may 
be present in another molecular group, whereas the Al,O, occurs only 
in groups Aand C. Hence C= 10.35 (molecular percentage of Al,Q; 
in analyses) minus 5.62 (the proportion of Al,Q, in group 4) = 4.73- 
The remaining oxides are regarded as being present in the group 
(Fe, Mn, Mg, Sr, Ba, Ca)O, and this is represented by Æ, which 
1 Tscher. Min. u. Petrog. Mitth., Bd. xix, p. 351- 
2 Amer. Jour. Sci, vol. xxxiii (1887), p. 193. 
