ORDINARY MEETING, June 3, 1867. 
Captain E. G-. Fishbourne, R.N., C.B., in the Chair. 
The Minutes of the last Meeting were read and confirmed, after which the 
following paper was read by the author : — 
ON THE GEOMETRICAL ISOMORPHISM OF CRYSTALS 
AND THE DERIVATION OF AML OTHER FORMS 
FROM THOSE OF THE CUBICAL SYSTEM. By 
Rev. Walter Mitchell, M.A. 
1. When elementary substances, or their chemical com- 
binations, pass from a state of vapour; or from a fluid 
condition into that of a solid ; or if they are deposited by 
evaporation from a fluid holding them in solution, there is a 
tendency of their particles to arrange themselves according 
to certain laws of symmetry. 
2. Thus solids more or less symmetrical, and with few 
exceptions bounded by smooth, plane, or flat surfaces, are 
produced. Such solids are called crystals, and their plane 
surfaces are termed faces. 
3. Some crystals are remarkable for perfect symmetry of 
form. Among these may be found solids formed with 
mathematical accuracy, whose geometrical properties had 
fascinated the ancient geometers ages before they were 
known to exist in the productions of nature. Others are 
exceedingly complex, being formed by the combination of 
faces parallel to those belonging to several simpler forms ; 
the relative positions of these simpler forms to each other 
being regulated by certain mathematical laws. 
4. The more complex forms being reduced to the com- 
bination of the simplest from which they can be derived, it is 
found that all the simpler forms can be grouped together in 
six distinct classes or systems. 
5. The crystals of any one substance may generally be 
reduced to forms belonging to one system; but there stems 
to be no limit to the number of combinations of different 
species of these forms which may take place in any indi- 
vidual crystal. 
6. To the rule that all the crystals of a particular substance 
should have their faces parallel to those of the forms of one 
system, there are numerous exceptions. 
