266 HENRY S. WASHINGTON 
are found. To the left of the orthoclase-albite line OA there is an 
excess of silica over that needed for the feldspars, so that the norms 
must contain quartz. 
Connecting O and L is the line LO, which is the locus of purely 
potassic norms (the ordinal center-points of subrang 1), consisting of 
varying amounts of orthoclase and leucite, from pure orthoclase at O 
to pure leucite at L. Below this line soda is present, forming either 
albite or nephelite, or both, while above it no norms can exist, for the 
reason to be mentioned presently. 
Although irrelevant to the immediate discussion, the line OQ may 
be mentioned. This is continuous with LO, and is the locus of 
norms composed only of orthoclase and quartz in varying propor- 
tions, orthoclase occurring at O and quartz at Q. Above and to the 
left of this orthoclase-quartz line, as well as its continuation OL men- 
tioned above, no norms can exist, since, for any given point in this 
region, the sum of the silica, alumina, and potash will be greater than 
too per cent if alumina and potash remain equal, or, if the necessary 
alumina is excluded, the potassium metasilicate molecule will be 
present, and this we have excluded from consideration. ‘To the right 
of and below this line the norms will contain increasing and varying 
amounts of albite and nephelite, and decreasing amounts of quartz, 
until the orthoclase-albite line OA is reached, when quartz vanishes 
and to the right of which nephelite enters into the norm. 
Within the area LOAN, therefore, are to be found all norms 
composed only of orthoclase, albite, leucite, and nephelite. The 
purely potassic ones will lie along the leucite-orthoclase line LO, and 
those richest in leucite toward the top of the area around the point L, 
while the purely sodic ones will be found along the albite-nephelite 
line AN, the albitic ones being around the point A. As albite and 
leucite cannot coexist in the norm, ex hypothese, it is clear that in one 
part of the area LOAN leucite must be present without albite, while 
in another part albite will be present without leucite, in each case in 
combination with varying amounts of orthoclase and nephelite. 
The line separating these two is the line ON, which is the locus of 
norms composed only of orthoclase and nephelite in varying amounts, 
from pure orthoclase at O to pure nephelite at N. To the left of 
this the norms contain orthoclase, albite, and nephelite, but no 
