440 EVENING DISCOURSES 
the bulky elements Ca, Na, K. The tetrahedral framework is the hardest 
part of the mineral, its skeleton, and it has the chief influence in deciding the 
form of the structure. 
The relative abundarice of the most common minerals is shown in Fig. 3. 
The minerals are quartz, felspar, mica, pyroxenes and amphiboles. The 
basic ferro-magnesium silicates such as olivine may also be included. ‘These 
great natural divisions of minerals have strikingly different physical charac- 
teristics, and are built up as follows : 
(a) Olivine (Mg, Fe)SiO,. The SiO, tetrahedra are not linked directly 
to each other, only by intermediate octahedral groups round Mg or Fe. 
(Fig. 4a.) 
(b) Pyroxenes and Amphiboles. MgCa(SiO;)2, Mg;Ca2(Si,O1;)(OH)>. 
The tetrahedral groups are linked into endless chains by stringing them 
together corner to corner. These chains are held together sideways by 
magnesium and iron octahedra. (Fig. 4b.) 
(c) Micas. K(Al,, Mg,)(AlSi;0,.)(OH):. The tetrahedral groups, 
Felspar 60% 
Mica Other Minerals 
_ Amphibole 
Felspar Quartz Mica Pyroxene Olivine 
Density 2°75-2°55 2°65 2°86 3°3-3'1 3°4 
(Cp. Blende 4, Pyrites 5:1, Copper Pyrites 4:2) 
Fic. 3.—Relative abundance and densities of common minerals. 
containing both Si and Al, are linked into endless sheets. These sheets lie 
on each other like the leaves of a book, and are bound together in various 
ways. (Fig. 4c.) 
(d) Felspars. KAISi,0,, NaAISi,0,, CaAl,Si,0,. The tetrahedra form 
a framework in three dimensions, each tetrahedron being linked by every 
corner to another. ‘The framework has the composition (Al, Si)O,. The 
bulky ions K, Na, Ca are in open spaces within it. (Fig. 4d.) 
(e) Quartz. SiO,. This is a structure composed entirely of tetrahedra 
containing Si, linked everywhere corner to corner. 
Typical structures are shown in a diagrammatic way in Fig. 4. 
The type of structure corresponds to the composition of the mineral, 
in particular to the ratio of the first group of elements (those inside 
tetrahedra) to the available oxygen. For instance, if there are four oxygens 
or more to every silicon we have separate SiO, groups. If there are only 
two oxygens to every silicon, the tetrahedra must share every corner in 
order that each Si may have four oxygens around it, and the structure of 
quartz is the result. The intermediate types of linking represent inter- 
mediate ratios : 
(a) SiO, Separate SiO, groups Olivine 
(6) SiO; Single chains Pyroxenes 
Si,04, Double chains Amphiboles 
(c) (Si,Al),O; Sheets Mica 
(d) (Si, ANO, Networks Felspar 
(e) SiO, Networks Quartz 
