296 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1909. 
Titanium is, as we have seen, far from being the rare element 
which it was formerly considered, and it is probably never wholly 
absent from any rock. It is distinctly much more abundant in basic 
than in acid rocks, and its affinities in the magma seem to be de- 
cidedly rather with iron than with magnesium, and still less with 
lime. While it is not commonly associated with alkalic rocks, yet 
when these are low in silica it shows a tendency to be present in con- 
siderable amount when the rock is sodic, as indicated by recent rock 
analyses; and this tendency to association of titanium with sodium 
appears mineralogically, as in the soda-amphiboles, some of which 
are highly titaniferous, and in certain rare minerals, as astrophyllite 
and rosenbuschite. Highly potassic and highly caleic rocks seldom 
show large amounts of titanium, though most of the mineral titanates 
contain calcium as the base. 
Zirconium, so closely allied to titanium chemically, also shows 
certain analogies in its magmatic relations. While unlike titanium 
in being rare in the basic rocks, those high in iron, magnesia, and 
lime, and referred by Vogt to the acid rocks, presumably because 
of the common occurrence of zircons in granites, it is now commonly 
recognized by petrographers that zirconium is by far most abundant 
in the rocks which are high in soda. Indeed, zirconium may be 
considered to be a characteristic minor chemical constituent of the 
sodic rocks, whether the silica be so high that quartz is present, or 
whether it be so low that nephelite is abundant, as in the nephelite- 
syenites and phonolites. Practically all modern, complete analyses 
bear out this view, which is confirmed by the common association of 
sodium and zirconium mineralogically, as in eudialyte, catapleiite, 
wohlerite, and the zirconium pyroxenes. 
Phosphorus, as a constituent of apatite, is universally diffused in 
small amounts through igneous rocks, and is most abundant in the 
basic ones, though its relations to the constituents other than silica 
are not clear. Study of large collections of analyses indicates that it 
is usually, but not always, associated with high lime, rather than 
with high iron or magnesia, and in some distinctly sodic provinces 
the more basic rocks with high soda and abundant nephelite show 
high figures for phosphorus pentoxide. Some of the phosphates are 
met with in granitic and syenitic pegmatites. 
Vanadium has been shown by the researches of Hillebrand to be 
quite widely distributed, but always in very small amount and al- 
most wholly confined to the basic rocks. As it exists as the sesqui- 
oxide, V,O,, replacing alumina and ferric oxide in ferromagnesian 
minerals, it is especially abundant in rocks composed largely of 
pyroxene, hornblende, or biotite, while it is present only in traces 
or not at all in rocks very rich in olivine, where the iron is present 
mostly as ferrous oxide, as in the peridotites, It is associated with 
