237 
of Edinburgh^ Session 1863 - 64 . 
Hence the face llik becomes 2a o h. 
Similarly, the face hlil becomes 2a o h. 
Hence the group of faces (B) becomes, 
2a oh, 2a 0 li 
2a 0 h, 2a o h 
Now it will be observed that, in the group (A'), the indices always 
occur in the order aah ; and that the symbols of the faces consist 
of every possible arrangement of the indices rba, rl=a, zi=h, in which 
a occupies the first and second places and h the last. The faces of 
the group (A') are therefore subject to the law of symmetry of the 
prismatic system, and belong to the form 
aah. 
Similarly the faces of the group (B') belong to the form 
2a 0 h. 
Hence the form hhl of the rhombohedral system, where 2h — h-\-l 
is a combination of the forms aah and 2a o hoi the prismatic system, 
, h — h 
where a = — ^ . 
If 2h — l-\-h, it can be shown in a similar manner that hhl is a 
k — l 
combination of the forms and 2/5 o k, where ^ , 
A 
And if 2Z = A + Z;, a combination of the forms yyl and 2y o I, where 
l-h 
Ex . — Transfer the forms 131 and 175 to the prismatic system. 
a. The form 131. 
2 
Here h=l,k— -1, .\a = -^ = l, 
A 
131, is a combination of 111 and 201. 
/5. The form 175. 
Here A = 1,X:= -5, .•.a = ?4- = 3, 
175 is a combination of 331 and 601. 
9. The results of the examination of the other simple forms of 
the rhombohedral system will be given without demonstration. 
