CrystaUogensis. — Hcn^oldt. 305 
Thermic classification. 
One system equally expanding in all directions. (Isometric.) 
Two systems equally expanding in two directions. (Tetra- 
gonal and Hexagonal.) 
Three systems unequally expanding in three directions. 
(Orthorh., Monocl. and Tricl.) 
It has also been established that the conducting powers of 
crystals in reference to heat, sound and electricity are, in like 
manner, governed by their axial relations, so that we might 
produce additional classifications in which the numbers 1, 2, 
and 3 are exhibited in precisely the same way. 
To sum up : The crj^stals of one system have three axes of 
equal length, are singly refractive and expand, on heating, 
equally in all directions. The crystals of two systems have 
two axes of equal length, are optically uniaxial and expand 
equall»5^ in two directions, viz., those of their equal axes. The 
crystals of three systems have all their axes unequal, are op- 
tically biaxial and expand unequally in three directions. 
What are the conclusions which these facts enable us to 
draw with regard to the internal structure of crystals, the 
groupings, arrangement or shape of their ultimate particles? 
Crystals, like all other aggregates, are composed of minute 
particles, and the difference between crystallized and amor- 
phous matter may be likened to that between a well-drilled 
regiment and an unorganized mob. In crystals the compo- 
nent particles are symmetrically grouped or arranged, while in 
amorphous bodies they are piled up in a confused mass. More 
than 70 years ago the subtle Brewster^ exi^ressed his con- 
viction that the optical properties of crystals "must depend on 
the form of their integrant molecules and the variation in their 
density" and it is astonishing how completely his views have 
been supported and confirmed l)y more recent speculations and 
research, or rather, what little progress has been made in this 
direction by our modern parlor scientists, who apparently at- 
tach more value to the discovery of a new mineral than to the 
solution of the great problems of crystallogenesis. 
We will, for the sake of convenience, retain the commonly 
accepted term of molecules for the small particles, of which 
crystals are composed, and in considering the external forms 
of the latter, their optical, thermotic and other properties, we 
'Philos. Transactions 1818, p. 204. 
