268 HENRY S. WASHINGTON 
mathematically from the change in the norm. Starting from the 
top, where the magmas are perpotassic, increase in soda necessitates 
an increase in the amount of nephelite, this being the only sodic 
mineral present, and orthoclase being the only feldspar possible 
within the leucitic area. This brings about a decided decrease in the 
silica percentage, as that of nephelite is much less (42.25) than those 
of orthoclase (64.75) and leucite (55.05). On the other hand, left 
of the orthoclase-nephelite line ON, where the potash enters only into 
orthoclase and the relative amount of nephelite remains constant 
along the ordinal line, increase in soda necessitates an increase in the 
amount of albite. This causes a rise in the silica percentage, since 
that of albite (68.70) is higher than that of orthoclase (64.75). 
The other set of lines, dtfte'Q, d?f?e?Q, etc. are the loci of different 
ratios of potash to soda, corresponding to the border-points and 
center-points of subrangs. Since along these subrang lines the rela- 
tion of potash to soda remains constant and the variation is in the 
amount of silica, an increase in silica causes an absolute decrease in 
the amount of potash, expressed by a slope of the line to the left. 
They are therefore straight and continuous, vanishing at the left in 
the point Q, which is the locus of pure quartz. 
A study of the sizes and forms of the various areas included 
between the dotted lines corresponding to the limits of the various 
magmatic divisions of persalane (except the rangs, those here repre- 
sented being all peralkalic) is of interest as showing the differences 
between these and their possible normative characters in different 
directions. But this is apart from our subject, and would lead us 
too far astray. 
We have been dealing so far only with persalic and peralkalic 
magmas, in which only quartz, orthoclase, albite, leucite, and nephe- 
lite can form. But it is well known that such rocks are extremely 
rare, plagioclase feldspars and femic minerals entering into the norms 
of nearly all igneous rocks to a greater or less extent. To render our 
theoretical data adequately comparable with actual rocks, therefore, 
we must consider magmas which contain salic lime, and an equal 
amount of alumina, furnishing anorthite, and those which contain 
femic molecules, in both cases with varying amounts of silica and 
alkalies. It is clear that it would be a very complicated undertaking 
