20 



NEW YORK STATE MUSEUM 



Tetragonal system 



Crystals in the tetragonal system can be referred to three 

 axes, all at right angles to one another, two of which are equal 

 and interchangeable (denoted in fig. 66 by a) and the third (c) 

 is at right angles to the plane of the other two and is of a 

 different length (greater or less) from the a axes. 



The relative lengths of the a and the c axes vary in each tet- 

 ragonal species, though there are several instances where this 

 ratio differs to such a small degree in several species as to war- 

 rant placing them together in what is known as an isomorphous 

 group. 1 



Normal group 



The general symmetry of this group is shown in fig. 66. The 

 vertical axis c is an axis of tetragonal symmetry and the hori- 



Fig. 66 Fig. 67 



zontal axes a a are axes of binary symmetry. There are more- 

 over two axes of binary symmetry which bisect the angles be- 

 tween the axes a a. Any form in the group is symmetric to 

 the planes shown in fig. 67. Compare model 6. 



Pyramids. A form composed of planes which intersect the 

 horizontal axes a a at equal distances and which also intersect 

 the vertical axis c is known as a pyramid of the first order and 

 is composed of eight isosceles triangular faces. When the in- 

 tercept on c as compared with that on a gives the axial ratio 

 for any species the form is said to be the unit pyramid for that 

 species. Fig. 68 shows the unit pyramid of zircon, the value 

 of c for zircon being .64. Fig. 69 shows the unit pyramid of 

 octahedrite where e=1.777. 



1 See p. 45. 



