736 EVENING DISCOURSES. 
EVENING DISCOURSES. 
THURSDAY, AUGUST 26. 
The Seven Styles of Crystal Architecture. 
By Dr. A. E. H. Turton, F.R.S. 
The proverbial importance of the number seven is once more illustrated in 
regard to the systems of symmetry exhibited by solid matter in its most perfectly 
organised form, the crystalline. For there are seven such systems or styles of 
architecture of crystals, just as there are seven distinct notes in the musical 
octave, and seven chemical elements in the octave or period of Newlands and 
Mendeléeff, the eighth or octaval note or element being but a repetition on a 
higher scale of the first. 
A crystal appeals to us in two distinct ways, first compelling our admiration 
for its beautifully regular exterior shape, and next impressing us with the fact of 
its internal homogeneity, expressed in the cases of transparent crystals by its 
perfect limpidity, and the obvious similarity throughout its internal structure. 
As it is with human nature at its best, the external appearance is but the expres- 
sion of the internal character. 
The purpose of this discourse is not so much to dilate upon the seven geometri- 
cal systems of crystals, as to show how they are occasioned by differences in the 
internal structure, and to demonstrate this internal structure in an ocular manner, 
unfolding at the same time some interesting phases of recent investigation. 
In order to remind ourselves of the seven crystal systems, a series of seven 
lantern slides will be exhibited, prepared from photographs of real small crystals, 
taken by the lecturer with the aid of the microscope and camera while in the act 
of formation on a microscope slide. To the Greeks, whose wonderfully perfect 
knowledge of geometry we are ever admiring, the cube was the emblem of 
perfection, for like the Holy City, lying ‘ foursquare,’ described in the inimitable 
language of the book of Revelation, ‘The length and the breadth and the height 
of it are equal.’ Moreover, even when we have added that all the angles are 
right angles, these are not the only perfections of the cube, for they carry with 
them, when the internal structure is developed to its highest possibility, no less 
than twenty-two elements (thirteen axes and nine planes) of symmetry. 
At the other extreme is the seventh, the triclinic, system, in which the sym- 
metry is at its minimum, neither planes nor axes of symmetry being developed, 
but merely parallelism of faces, sometimes described as symmetry about a centre, 
and in which there are no right angles and there is no equality among adjacent 
edges. Between these two extremes of maximum and minimum symmetry we 
have the five systems known as the hexagonal, tetragonal, trigonal, rhombic, 
and monoclinic, possessing respectively, 14, 10, 8, 6, and 2 elements of symmetry, 
Photographs of real crystals belonging to all these seven respective systems 
will now be thrown on the screen. All crystals do not possess the full 
symmetry of their system, each system being subdivisible into classes possessing 
a definite number of the possible elements. Altogether there are thirty-two 
such classes, and their definite recognition we owe to the genius of von Lang 
and Story Maskelyne. 
The characteristic property possessed in common by all crystals is that 
the exterior form consists of and is defined by truly plane faces, inclined, in 
accordance with one of the thirty-two classes of symmetry, at specific angles 
which are characteristic of the substance. This has only been proved to be an 
absolute fact within the last few years, although asserted by Haiiy so long ago as 
the year 1783 ; for the numerous cases of so-called ‘ isomorphous’ salts, the first 
