TRANSACTIONS OF SECTION B, 507 
In order to ascertain the crystal structure of a substance with any degree of 
probability the most complete possible knowledge is required concerning it, such 
as of its optical properties, its cohesion relationships, the orientation of its 
different solubility directions (etch figures), and more especially the knowledge of 
its crystalline form under the most widely differing conditions of formation. If 
the product of only one crystallisation is examined, the possibility is incurred that 
the crystals so produced exhibit casual forms developed under quite special conditions 
of growth; and only by investigating many different crystallisations separated 
from different solvents under different conditions of temperature, &c., does it 
become possible to recognise those faces the development of which is most 
favoured during growth or, what is the same thing, to learn which planes are parallel 
to the greatest density of structure. Ifthese planes are taken as the elementary faces, 
it is always found, not only that they are identical with the cleavage plane, with 
the most stable plane of twinning, &c., but also that the other forms present on the 
crystal assume the simplest indices. The greater the number of forms observed 
upon the crystals, so much the greater is the probability of being able to choose 
the correct elements for the crystal, because the faces most likely to be favoured 
during the growth of the crystal are those the indices of which are composed of 
the simplest numbers. Jlaving found the correct elements of the crystal, it is a 
simple matter of calculation to ascertain the ratio of the three parameters and the 
angles of the elementary parallelepipedon upon which the structure of the crystal is 
built up, and which is therefore a prime characteristic of the structure. 
Since the equilibrium in a crystal structure is dependent on the conditions of 
movement of the component atoms, the stability of the equilibrium must alter with 
the temperature; and since each form of structure may possess several stable 
equilibrium positions of different degrees of stability, it follows that a particular 
crystal structure will assume the most stable of the possible kinds of equilibrium 
only within a certain range of temperature, constant pressure being assumed. 
Outside these limits other kinds of arrangement will be in more stable equilibrium, 
and on exceeding the limits a discontinuous change of all the physical properties 
of the body will occur—that is to say, a change into another modification of 
different crystal structure will ensue. Polymorphism, the property of existing in 
different crystalline phases, must be distinguished from polysymmetry, or the 
power possessed by pseudosymmetrical crystals of forming apparently simple 
crystals of higher symmetry by repeated twinning. Amongst the latter the 
change into the form of true higher symmetry can indeed take place at a specific 
temperature, but the change is not accompanied by a discontinuous change in the 
density and the specific heat. Amongst the truly polymorphous bodies, however, 
even when the crystalline forms of the several modifications exhibit a certain 
similarity, so great a dissimilarity still exists between them in physical and 
erystallographical respects that the various modifications must be referred to quite 
ditterent elementary parallelepipeda. A difference in the crystal structure is thus 
introduced, and this may arise from the regular point systems, which compose 
the combined system, consisting each of one or of several space lattices. 
On comparing the polymorphous relationships of two different but chemically 
similar substances it 1s found that the temperature (or pressure) limits of the 
stability of the several modifications are not the same—thus, considering analogous 
chloro-, bromo-, and iodo-compounds, it is often observed that the temperatures of 
change for the chloro- and bromo-compounds are lower than for the iodo-com- 
pound, just as is often the case with the melting-points of such analogous sub- 
stances. As a result totally different polymorphous modifications of the various 
members of analogous series exist at one and the same temperature. 
The foregoing leads to the definite conclusion that the relationships between 
the crystal structures of two chemically related substances can only be recognised 
if their corresponding modifications are available for comparison; every chemico- 
erystallographical comparison of two or more substances must therefore be based 
upon a study of the polymorphism relationships. If the existence of correspond- 
ing modifications is established by such a study, the further complete investiga- 
tion of these forms leads to the determination of the most probable values of the 
