444 EVENING DISCOURSES 
consequence, magnesium and iron, which are characteristically in octahedral 
groups of oxygen atoms, are excluded from the felspar structures. We 
never find these metals in felspar. 
In the second place, the felspars are divided into two great families. 
The more symmetrical orthoclase, KAISi,;Og, is typical of the one family, 
and the less symmetrical albite and anorthite, NaAlSis;0, and CaAl,Si.O,, 
of the other. ‘The difference is simply a question of the size of the large 
cation. Potassium is so large that when inserted into the framework it 
holds it distended into the symmetrical form, whereas the smaller Na or 
Ca allow it to sag over into a lop-sided unsymmetrical shape. This explana- 
tion is due to Taylor, who first analysed the felspars. 
(6) Finally, I wish to refer to another broad feature of minerals, their 
densities. 
The densities again depend to a large extent upon considerations of 
geometry. If we pack isolated tetrahedra together with octahedra, as in 
olivine, space can be utilised in a most economic way. It is geometrically 
possible to arrange the structure so that a maximum number of oxygen 
atoms, with their concomitant cations, are included in a given volume. 
On the other hand, building up a structure by attaching tetrahedra corner 
to corner is most wasteful as regards volume. It produces an expanded 
structure containing large open spaces. 
In consequence we find that olivine is the heaviest, and felspar and 
quartz are the lightest, of the common minerals, others being intermediate. 
The greater the extent of the tetrahedral linking, the lighter the structure, 
as the following list shows : 
Density. 
Olivine . : ; 4 j x13 a 
Pyroxene, amphibole : : > Qa serL 
Mica. : ‘ : . amp2r85 
Quartz . ; ‘ : 3 Lt xis 
Felspar . . é ; : »  2°75-2°55 
The fact is, of course, that the earth’s crust is mostly composed of these 
minerals, with felspar and quartz predominant, just because they are the 
lightest and so float to the top. The light felspars float on the heavier 
ferro-magnesian silicates, and these in turn probably on metallic sulphides 
and metals which are much denser. Geometry is again triumphant. The 
fortunate existence of a raft of rock on which life is possible is seen to be 
a result of the geometrical properties of tetrahedra and octahedra. 
