THE CLASSIFICATION OF THE IGNEOUS ROCKS 13 
In connection with his class in petrology, the writer has for 
some time made use of diagrams which set forth the average 
composition of rock types. There are two ways in which such 
diagrams may be constructed. On the one hand, the diagram 
may be prepared after the same manner as composite photo- 
graphs. The Brogger diagrams of a considerable number of 
representative rocks faintly outlined are superimposed upon the 
same radius vectors, so as to indicate the range in ratios of each 
constituent and in the darkest part of the figure the character- 
istics of the type. A composite diagram, better adapted for 
general use, because so much less intricate and so much easier to 
prepare, is obtained by first averaging the molecular ratios of 
each constituent for the group of analyses, and using the results 
to prepare a single diagram, which then becomes the diagram of 
a type instead of that of an individual. 
The writer has so far modified the Brégger diagram as to 
draw the radius vectors so as to make equal angles with one 
another. The closed polygon obtained by connecting the inter- 
cepts on the different radius vectors has a form which changes 
in a marked degree to correspond with the changes in the length 
of any radius vector. Since the soda, potash, and alumina are 
all measured below the horizontal, acid rocks show diagrams 
stretched out along the horizontal and developed also below the 
horizontal; while the protoxide bases being all entered above 
the horizontal basic rocks are short and ‘‘fat above.” Soda- 
rich or potash-rich rocks give respectively left-handed and right- 
handed diagrams, etc. All these facts the eye soon accustoms 
itself to take in at a glance and subconsciously, as it does 
in the case of handwriting. It is hardly necessary for the eye to 
estimate the lengths of the intercepts (a feat it is but poorly 
qualified to accomplish) for the ratios of the quantities of the 
constituents to one another is shown by the angles of slope of the 
polygonal sides —something which the eyes easily measures. 
The larger the number of correct and properly selected analyses 
which are utilized in obtaining the ‘‘ composite” 
the greater is its value. 
of any type, 
