506 REPORT—1904. 
-gnd merely sought for those arrangements of congruent molecules in which the 
arrangement of parts is the same about every molecule; he thus arrived at 
sixty-five regular ‘point systems.’ By the discovery of these, most, though not 
quite all, of the symmetrical relationships of the properties of crystals became 
explicable. Sohncke further developed his theory of crystal structure by intro- 
ducing the assumption that two or more regular point systems, consisting of 
different kinds of molecules, may be interlaced or supposed to interpenetrate in 
such a way that equilibrium results. This, however, is only possible when the 
different point systems possess the same ‘coincidence movements’ (Deckschie- 
bungen)—that is to say, when they are built up from space lattices of identical 
dimensions. This form of the theory is also deducible from the theory of regular 
point systems if the different individual atoms constituting the molecule are con- 
sidered in place of the centres of gravity of the molecules; each set of analogous 
atoms then form a regular point system, and, by the interlacing of the several 
systems, a compound system is obtained consisting of as many component systems 
as there are kinds of atoms in the chemical molecule. This, the most general 
theory of crystal structure, may be summarised by the following definition. 
A erystal—considered as indefinitely extended—consists of » interpenetrating 
recular- point systems, each of which is formed from similar atoms ; each of these 
point systems is built up from a number of interpenetrating space lattices, each 
of the latter being formed from similar atoms occupying parallel positions. All 
the space lattices of the combined system are geometrically identical or are charac- 
terised by the same elementary parallelepipedon. 
In this form the theory is capable of elucidating all the observed regularities 
of crystal structure, and it is unnecessary to assume the operation of any ‘molecular 
forces’ in addition to the forces which act upon the atoms themselves. No diffi- 
culties now arise in ascribing to the atoms the power of assuming a definite 
orientation, since, according to J. J. Thomson, the atoms are not mere points, 
but highly complex structures. 
If acrystal is built up of but one kind of atom it consists of a crystalline element, 
and is produced from but one kind of regular-point system the properties of which 
depend upon the forces exercised upon each cther by the similar atoms involved, 
In the case of a chemical compound, however, there must be just as many 
regular-point systems in the combined system as there are kinds of atoms in the 
chemical molecule, and the arrangement of the combined system must correspond 
with the equilibrium of the forces with which similar and dissimilar atoms act 
upon each other. 
On solution, melting, or evaporation of the crystal the combined system 
separates into its component and freely moving molecules, and the relative posi- 
tions in space of the point systems or space lattices, composed from the several 
kinds of atoms, must therefore be such as to correspond with the arrangement of 
the atoms in the chemical molecule. The difference between the crystalline and 
the amorphous state thus consists in that in the latter the chemical molecules 
have a mutually independent existence, whilst in the crystal the idea attached to 
the term molecule is different, the molecule being regarded only as a group or 
assemblage of atoms belonging to several interpenetrating point systems. Such 
an assemblage can under certain conditions be quite an arbitrary one; thus, the 
structure of crystalline sodium chloride—making the simplest conceivable 
assumption—consists of a cubic space lattice of sodium atoms and a similar 
space lattice of chlorine atoms, the latter atoms occupying the mean points 
in the lattice of sodium atoms. It is obviously a matter of quite arbitrary 
choice with which of the neighbouring sodium atoms a particular chlorine 
atom will remain combined as a molecule of sodium chloride when the mole- 
cules of the latter separate during the passage into the amorphous state by 
melting, solution, &e. The same considerations naturally hold when, instead of 
two simple space lattices, two regular-point systems consisting of chlorine and 
sodium atoms are imagined to coalesce. In this case any multiple of the complex 
NaCl may be regarded as the ‘ molecule,’ and thus has arisen the failure of all 
attempts hitherto made to determine the molecular magnitudes of crystalline bodies, 
