OWA ACADEMY OF SCIENCES 
9 
To Weiss and Mohs chiefly is due the credit of making the Axes of 
Symmetry the bases for the arrangement of crystalline forms into sys- 
tems, which arrangem.ent has been confirmed hy the other properties of 
minerals that received attention at about the same time. Sir David 
Brewster, in his optical researches, discovered that double refraction per- 
tained solely to crystals of the rhomhohedral system. Later he found 
that all crystals of the pyramidal and rhomhohedral systems which from 
their geometrical character have a single axis of symmetry are optically 
uniaxial, while the prismatic system which has three unequal axes of 
symmetry is optically biaxial and has three rectangular axes of unequal 
elasticity. While Brewster’s discoveries and conclusions were reached 
independently of Weiss and Mohs, they cover very much the same ground, 
tho’ reached by a very different path, and support the conclusions of the 
last named investigators in a remarkable manner. Later investigations 
along both lines have resulted in establishing a very high degree of cor- 
respondence between mathematical and optical symmetry and have given 
to crystallography an assured place of first class importance in miner- 
alogy. 
Hauy had assumed that the same chemical elements, combined in the 
same proportion, would always have the same crystalline form, and, 
consequently, the same form and angles implied the same ciiemfical con- 
stitution. But there were continually arising very perplexing exceptions 
to this view. Fuchs was led to account for this on the principle that one 
element might take the place of another in some instances without alter- 
ing the crystalline form. To such elements he applied the term vicar- 
ious. He is said afterward to have withdrawn from his position in this 
matter. But Mitscherlich, by many careful analyses, clearly established 
the fact that several substances such as “the carbonates of lime, of mag- 
nesia, of protoxide of iron and of protoxide of manganese agree in m-any 
respects of form, while the homologous angles vary thru one or two 
degrees only”. These and similar substances were said to be isomor- 
phous, if the agreement was complete, or exact; while the term plesiomor- 
phic was given to such as varied slightly. This discovery resulted in 
stimulating great activity among chemists and crystallographers in the 
expectation of discovering definite laws pertaining to the relation between 
chemical composition and crystalline form. One result of such effort 
was the recognition of cases that seem to be exceptional and outside of 
the usual laws governing mineral form and composition, such as dimor- 
phism and trimorphism, an illustration of the former of w'-hich we have 
in calcite and aragonite. 
It vzill be seen from the discussion of the development of crys.allo- 
graphy that the establishment of any satisfactory system has depended, 
upon the agreement of fixity of form and angle with kind. While Hauy 
and his followers were unfolding the principles of crystallography and 
placing them upon a sure basis, Abraham Werner was laboring to find 
in the fixity of the other properties of minerals as certain a basis for a 
different system of classification and determination. Possessed of exact 
and methodical mental powers and great acuteness of the senses, he was. 
■eminently adapted to the founding of such a system. In this work he^ 
