234 Proceedings of the Royal Society 
The new parameters are given by the following formulfe. 
a'x = sin J CO 
l)x = - 7 ^ sin I CO 
V 3 
I 1 + 2 cos CO I ^ 
( 3 j 
Where a? is a constant. 
5. Let a be the “ angular element” of a crystal of the rhombo- 
hedral system, i.e. the angle between normals from the origin to 
the faces 100 and 111 . 
Then it is shown in the paper, that the expressions for the new 
parameters become, — 
f ^ 'i 1 
2 
J ^ 1 
[ 4 + tan ) 
Vx~ - 
1 
{4 + tan 
, 
tan a 
{4 + tan^«p 
Hence, a, 6 ', c', are respectively proportional to \/3, 1, tan a; 
• ct h c ') C2 ^ 
V3~ 1 ~ tan a ) 
Hence, given the angular element and the indices of a face, the 
ratios of the new parameters are determined by the formulae ( 2 .), 
and the new indices by the formulae ( 1 .) 
Ex . — Find the new indices of the faces Oil, 131. 
a. The face Oil. 
0 + 1 ,, 2-0 + 1 0 + 1-1 
0 
the new symbol is 110 . 
/3. The face 131. 
6-1 + 1 1 + 3-1 
3 
= 1 . 
= 1 =1 
.*. the new symbol is 111 . » 
6 . Also, given the symbol of a simple form belonging to the 
rhombohedral system, and also the angular element, the indices 
