of Edinburgh, Session 1863-64. 
235 
of its several faces when referred to the new axes can be determined, 
and also the ratios of the new parameters. 
The simple forms of the rhombohedral system are then taken in 
succession, and the indices of their faces when referred to the new 
axes are found. It is then seen that the new indices follow in all 
cases the laws of symmetry of the prismatic system. 
This is done at length in the paper. The general process is 
exemplified here by its application to one or two simple forms 
only. 
7. The simple form 101, consists of the following faces. 
By the formulae (1.), it is found that the new indices are, respectively, 
Now, it will be observed that in the first group, the indices 
always occur in the order 1, 1, 0 ; and that the symbols of the faces 
consist of every possible arrangement of the symbols ±1, ±1, 0, in 
which unity occupies the first and second places, and zero the last. 
The faces of the first group, therefore, follow the law of sym- 
metry of the prismatic system, and belong to the form 110. 
Similarly, the faces 
belong to the form 100. 
Hence, the form 101 of the rhombohedral system, is a combina- 
tion of the forms 110 and 100 of the prismatic system. 
In a similar manner it can be shown, that the form 211, is a 
combination of the forms 310 and 010. 
101 Oil 110 
roi on lIO 
100 no no 
100 ITo llo 
These indices are divisible into two groups. 
( no no 
I ilo no 
100 
100 
