244 WARREN J. MEAD 
Fig. 1 represent percentages of silica, and the two amounts of silica 
are plotted on the two vertical lines marked A and B, and the points 
connected by a straight line. ‘This line represents by its ordinates the 
amount of silica in any possible combination of the two rocks, from 
100 per cent. of one at one end to Ioo per cent. of the other at the 
opposite end. ‘To find what point on the line represents a combina- 
tion containing 4o per cent. of silica, a horizontal line is drawn at a 
distance of 4o units from the base. Now, if the point O, at the inter- 
section of the two lines, 
be projected vertically 
downward to the base, 
the percentages of the 
two rocks in the com- 
bination may be read at 
once; the figures above 
the base line representing 
percentages of A and 
those below the line per- 
centages of B. It is seen 
that the combination is 
made up of 25 parts of B 
and 75 partsof A. Ina 
similar manner it 
is possible to deal 
with each element 
in the rocks. 
To apply the same 
general principle to the 
Fic. 2 case of the combination 
of three rocks: Suppose, for example, it is desired to ascertain what 
combination of three rocks, Y, Y, and Z, having respectively ro, 60, 
and 4o per cent. silica, will contain 25 per cent. of silica. It is apparent 
at once that this problem cannot be considered in two dimensions, 
as was done in the case of a combination of two rocks; but the same 
general method may be employed by considering the problem in 
three dimensions. In Fig. 3 the three uprights are erected perpen- 
dicular to the base at the corners of an equilateral triangle. The 
