SEDIMENTARY FORMATIONS. 31 
mass of the original rock (average of analyses A and B) are shown by 
appropriate areas on the sectors already determined from the analysis 
of the altered rock. The construction for any constituent is effected 
by using the ratio of the percentages of this constituent in the orig- 
inal and in the altered rock, as follows: Lay off the determined ratio 
on the radial percentage scale of the base figure, and through the 
point thus formed draw a circle concentric with the base circle. The 
portion of the sector of the chosen constituent lying within the circle 
thus drawn represents the amount of this constituent in a 100-unit 
mass of the original rock. In order to make this relation clear, let 
us consider magnesia as an example. Since the altered rock (analysis 
H) contains 6.3 per cent of magnesia, take an arc of the base circle 
equal to 6.3 of the unit divisions. The area of the sector subtended 
by this arc is 6.3 per cent of the area of the base circle, so that the 
sector represents the number of unit masses of magnesia present in 
a 100-unit mass of the altered rock, or, what is the same thing, it 
represents the percentage of magnesia in the rock. Now, the original 
rock (analyses A and B) contains 3.7 per cent magnesia and the altered 
rock (analysis H) 6.3 per cent. The ratio of these numbers, 0.59, 
expresses the fact that the magnesia in a 100-unit mass of the original 
rock is only 59 per cent of that in an equal mass of the altered rock. 
Now, 59 per cent of the base circle and also 59 per cent of any sector 
lies within the circle drawn through point 59 on the radial scale, so 
that the area common to the magnesia sector and the 59 per cent 
circle (which may be called the magnesia circle) is 59 per cent of 6.3, 
or 3.7, which is the percentage of magnesia which it is desired to 
represent. 
The proportional masses or percentages of the various constituents 
in both rocks being represented in the manner indicated, the com- 
pleted diagram furnishes all the factors necessary for making any 
desired comparisons when it is assumed that the amount of any 
chosen constituent has remained unchanged. 
An example will serve to indicate the principle on which the com- 
parisons are made. The rock of analysis H has been derived by 
alteration from the rock of analyses A and B. Both analyses are 
represented on PL IX, B. Assume silica to have remained constant, 
what has been the gain or loss of magnesia during alteration? Apart 
from the diagram the change in magnesia may be calculated from 
the data given in the analyses in the following manner: A 100-unit 
mass of the original rock contains 7.5 units of silica, while a 100-unil 
mass of the altered rock contains 50 units of the same constituent 
Therefore 15 units of the altered rock contain the same amount of 
silica as a 100-unit mass of the original rock. Now, 15 units of the 
altered rock contain 0.15x6.3=0.95 unit of magnesia. Evidently 
there has been a loss, since in 100 units of the original rock there are 
