42 ME. H. J. BEOOKE ON THE GEOMETEICAE ISOMOEPHISM OF CRYSTALS. 
The assumed new primary form of Quartz has been obseiwed by M. Descloizeaux as 
an inverse and as a direct face, and gives 56° 44' as the angle between the new 10 0 
and 111. 
The new primary form of Calcite corresponds to the old direct form 811, deduced 
from the old inverse form 4 5 5, and gives 10 0, 1 1 1 = 55° 57'. 
Table T also contains many additional symbols with their coiTesponding angles, to 
show the relations between greatly disagreeing symbols and nearly agreeing angles. 
Thus the angle of 1 1 1 with the face denoted by 82 23 23, differs but 19' from the 
nearly corresponding angle of 1 1 1 vrith the face denoted by 7 2 2. The difference 
between the angle 111, 122 43 43, and 1 1 1, 17 6 6 is only 2', rendering the distinction 
of these faces by ordinary measurement impracticable. 
This Table is open to other remarks of the same nature, but after the previous expla- 
nations it appears unnecessary to pursue the subject further. 
These new elementary angles, as well as those in the pyramidal system, will doubtless 
undergo alterations as more numerous and better crystals present themselves for exami- 
nation 
