1907-8.] 
Classification of Igneous Rocks. 
87 
From these data we obtain the following totals : — 
Rock I. 
Rock II. 
a) 
AL.O, + (Fe 2 0 3 + FeO) + MgO + CaO 
18-3 
53-3 
(2) 
(Fe 2 0 3 + FeO) + MgO + CaO + Na 2 0 
15-1 
435 
(3) 
MgO + CaO + Na 2 0 + K 2 0 
9-2 
33-5 
(4) 
CaO 4* Na 2 0 + lv 2 0 -t* A1 2 0 3 
18-2 
31-6 
(5) 
Na 2 0 + K 2 0 + A1,0 3 + (Fe 2 0 3 + FeO) 
23-7 
28-0 
(6) 
K 2 0 + A1 2 O s + (Fe 2 O s + FeO) + MgO 
17-9 
39-7 
On looking np the table of constants, page 150, we obtain the following 
formulas : — 
Rock I . — a b a a a a 
Rock II . — b b b b b a 
We find thus that Rock I. belongs to group 17, and Rock II. to 
group 63. 
Table II. (page 91), which contains the same numbers to be found in 
Table I. (page 90), is intended to illustrate more clearly the dichotomous 
evolution of the 64 groups, and will require no further explanation. 
The following diagram, pages 154 to 156, is intended to illustrate the 
relation between the various groups. It is constructed as follows : — 
Vertical lines are drawn at distances equal according to the scale (page 154) 
to the percentage of the respective bases which are present in the average 
of 1000 rocks (see page 152). A line is drawn from a point on the left edge 
of the first band at an inclination of 45° downwards, and from the point 
(d) in which this line cuts the next vertical a distance is measured upwards 
equal to the percentage of A1 2 0 3 present in the group. Proceeding thence 
to the intersection (/) of the inclined line and the third vertical, we 
measure upwards a distance equal to Al 2 0 3 + Fe 2 0 3 , then from the inter- 
section ( g ) a distance equal to Al 2 0 3 + Fe 2 0 3 + Fe0. We thus continue 
until all the bases are added, and by connecting the upper ends of all the 
vertical distances we obtain the quasi-curves of the diagram. We notice 
that a rock with a composition equal to the grand average, if there were 
such a one, would be represented by a straight horizontal line. In con- 
templating the 64 curves we are struck by the marked effect of the 
continued dichotomous division. We have successions of 8 or of 4 groups 
which are similar to each other. There is also a pronounced similarity 
between successive odd and successive even groups, and successive pairs of 
groups are therefore also more or less similar. The first 32 groups are 
symmetrically opposed to the second 32 groups on respective sides of: the 
straight line which represents the average composition. 
