438 EVENING DISCOURSES 
just as the fun of postage stamp collecting of our boyhood has been spoilt 
for our children by the vast numbers of issues in which countries now 
indulge. 
The minerals are limited in number because they are the last survivors 
of the wear and tear of ages. ‘They represent matter in the ultimate state 
of equilibrium. ‘They have sunk into so deep a pit of low potential energy 
that no chemical change can tempt them to desert it. 
This state of lowest potential energy is one of order and not of disorder. 
A crystal is more stable than a jumble of atoms. The perfect geometrical 
arrangement of a crystal represents matter in its most dead and inert form, 
from which nothing further in the way of change can be expected, just as 
the various utopian schemes of society which have been put forward from 
time to time represent the most dull state in which it is possible to conceive 
living. 
The world we are to study, then, is to be ruled by the laws of geometry. 
We will speak of tetrahedra, octahedra, angles, faces and edges. ‘To appre- 
ciate this world, we must be like the Greek geometers who were ravished by 
Other eee 
PTY 
4 
Ca K Na Mg 
Oxygen 50 % Silicon 26% Aluminium 8% Tron 4% 
Calcium 3 % Potassium 2°75 % Sodium 275% Magnesium 2 % 
Total 98 % 
Fic. 1.—Relative abundance of common elements. 
the beauty of the symmetrical solid figures. In no other science do these 
geometrical figures play so important a part, they are peculiar to crystal- 
lography. Though all crystals are based on geometrical patterns, the 
simplest regular geometrical forms are of outstanding importance in 
mineralogy just because minerals are so extremely inert. ‘The condition 
for low potential energy imposes upon their configurations certain geo- 
metrical requirements, which are broken by the ephemeral compounds we 
prepare in the laboratory. 
(3) Eight elements compose 98 per cent. of the earth’s solid crust. In 
our broad survey, we will neglect all the other elements, most of which only 
occur in odd cracks here or there where we laboriously search for them. 
The common elements are oxygen, silicon, aluminium, iron, calcium, 
potassium, sodium, and magnesium. Their proportions are shown in 
Fig. 1. 
The bulk of the crust is oxygen. Not only is it the commonest element, 
but also it takes up the most room. The rocks are made of oxygen atoms 
cemented together by silicon, aluminium, and a few other elements. Accord- 
ing to the way in which they build up structures with oxygen, these elements 
are divided into three classes, to which we will have frequent occasion to 
refer. 
(a) Elements forming the centre of a tetrahedral group. Four oxygen 
atoms are grouped together at the corners of a tetrahedron, and the element 
