174 The American Naturalist. [February, 
Lüneburg, Hanover, contains the new planes œ O$, œ O13, œo OY. 
Beginning with the Le Bel and Van t’ Hoff theory with regard to the 
connection between the structure of the molecule (z. e., the arrange- 
ment of the atoms within the molecule) and the activity of circularly 
polarizing substances, and applying the principles of this theory to 
the Sohacke-Wulff® theory of crystal structure, Becke® is forced to 
conclude that this theory of crystallization is not satisfactory, since it 
does not accourit sufficiently well for the close relation that exists 
between the crystallization of a body and its chemical nature. Becke 
thinks that the symmetry of crystals is intimately dependent upon the 
symmetry of arrangement of the atoms within the molecules. If this 
be true, all circularly polarizing bodies should possess an unsymmetri- 
cal molecule, which should reveal itself through the unsymmetrical 
character of its crystallization. Becke publishes a list of all the 
circularly polarizing substances known, and discusses in detai 
the crystallization of grape sugar, since this has been regarded 
as a triclinic substance, without evidence of hemimorphism or 
hemihedrism—the only two modes of crystallization that can yield 
enantiomorphous, 7. e., unsymmetrical figures. As a result of 
measurements of crystals of pure sugar, Becke concludes that it is 
monoclinic with @: 6: c=1.735: 1: 1.908. f=97° 59’, and hemi- 
morphic in the direction of the ¢ axis (really hemihedral, as indi- 
cated by Williams, ref. above). It is therefore enantiomorphous. 
The symmetry of its form corresponds with that of other circularly 
polarizing bodies, and corresponds also with the unsymmetrical struc- 
ture of its chemical molecule, shown by recent synthetical methods. 
Two of these unsymmetrical molecules may be so arranged as to yield 
a crystal with one plane of symmetry (holohedrally developed mono- 
clinic form), and four to produce forms with three planes of symmetry 
(orthorhombic forms). The symmetry of crystal forms thus de- 
pends primarily upon the distribution of the atoms within the molecule, 
Von Goldschmidt,” carrying out this idea more fully, attempts to sim- 
plify the discussion of the chemical relations of the silicates by making 
certain assumptions with regard to the conditions necessary to the 
mixture of molecules in groups of isomorphous silicates. He regards 
the particles as the primary constituent of the molecule, just as the 
atoms are the constituent parts of the molecule. Chemistry he defines as 
relating to molecules and their composing atoms; crystallography as 
relating to crystals and their composing particles. Isomorphism is the 

15 AMERICAN NATURALIST, 1889, p. 221. 
16 Min. u. Petrog. Mitth., 1889, p. 464. 
