SEDIMENTARY FORMATIONS. 29 
marked "Si0 2 " (which maybe called the " silica circle"). This circle 
is drawn with such a radius that its area is 15 per cent of the base 
circle, and it follows that the portion of the silica sector included is 15 
per cent of the whole silica sector. 
In the same way the alumina (analysis H) makes up nearly 15 per 
cent of the altered rock and (average of analyses A and B) about 1.5 
per cent of the fresh rock; that is, the alumina in the fresh rock is 10 
per cent of that in the altered rock. In the diagram, therefore, the 
alumina in the altered rock is represented by a sector occupying 15 
per cent of the area of the base circle, and to show the relations of that 
in the fresh rock a circle is drawn so as to include 10 per cent of the 
total area and consequently 10 per cent of the area of the alumina 
sector. In a similar manner the relations of the various other con- 
stituents in the altered and fresh rock are shown. 
The important feature of the diagram is the fact that starting from 
the silica circle, or the circle representing any other constituent 
assumed to have remained constant, the actual gains or losses of 
other constituents may be obtained from the diagram by a simple 
subtraction. 
If silica be assumed constant, the amount of magnesia, for instance, 
necessary to make up the percentage of magnesia in the altered rock 
is measured by the area of the magnesia sector included in the silica 
circle. But on the magnesia sector the magnesia in the original rock 
is represented by the area of the magnesia sector within the magnesia 
circle. There are indicated, therefore, both the amount of magnesia 
required, on the assumption that the silica is constant, and the amount 
of magnesia actually present in the original rock, which in this case 
is more than is necessary to meet the required proportion in the 
altered rock. Magnesia has therefore been lost by an amount meas- 
ured by the area of the annulus between the silica and the magnesia 
circles as they cross the magnesia sector. If soda be assumed con- 
stant, all constituents other than soda have been lost in amounts 
measured by the difference between the area of their sectors inside 
their circles and that inside of the soda circle, which may be taken 
from radial scale. From the numbers thus obtained the percent age 
change is readily calculated. If, at the other extreme, calcium car- 
bonate has remained constant, there has been gain of all other con- 
stituents, their circles all being smaller than the carbonate circle. 
Complete or nearly complete removal of a constituent is represented 
by an arrow. 
In general it will be noted that the constituents whose circles lie 
outside of the circle of the constituent assumed as constant have suf- 
fered loss, while those whose circles lie inside have gained. The 
amount of gain or loss is proportional to the difference between the 
areas controlled by the superimposed polar coordinates of the several 
