ELISHA MITCHELL SCIENTIFIC SOCIETY. 67 



imagining of lines that do not exist, the so-called crystallographic 

 axes. Without a clear conception of this fundamental principle 

 it is well-nigh impossible to impress upon the mind of the stu- 

 dent the idea of a crystal. 



The following scheme, after mature deliberation and consul- 

 tation with Dr. Chas. Phillips, Professor Emeritus of Mathe- 

 matics in the University, was adopted, and found to be of con- 

 siderable help in directing attention to these lines. It is given 

 here in the hope that other teachers, not only of Mineralogy but 

 of Mathematics as well, may find it of value. 



In every crystal there are three imaginary lines termed crys- 

 tallographic axes. These three axes are either 



(1). All of one length, or 



(2). Two of one length, and the third of another, or 



(3). All three of different lengths. 



Under (1). we may have 



a. Each perpendicular to the plane of the other two. 



b. One perpendicular to the plane of the other two, which 



(two) are oblique to each other. 



c. One oblique to the plane of the other two, which (two) 



are perpeudicular to each other. 

 The same is true under (2). and under (3). 

 Adopting the following notation 



la lb 1c Id 



2a 2b 2c 2d 



3a 3b 3c 3d we have 

 la= Isometric system 

 lb has no crystal system 



1,1 u u u a 



2a=Tetragonal system. 



2b=Hexagonal system, but as the 60° axis may lie on either 



side of its principal this system has four axes instead 



of three. 

 2c has no crystal system 

 2d " " " " 



