1911-12.] 
The Geometry of Twin Crystals. 
457 
§ 30. Less Regular Combinations. 
There are other compound crystals which do not contain contact or 
abstract twin planes or cross planes. Such crystals will rarely contain 
a co-spatial or cross-spatial plane, for these, as we have seen, are usually 
accompanied by a twin plane. There may he a single common line and 
a common plane at right angles to it {Min. Mag., vol. xv., 1910, p. 395), or 
a co-spatial line with or without a co-spatial plane, or only a line or lines 
in which the molecular distances in the two components are approximately 
equal. The consideration of such combinations does not fall within the 
scope of the present paper. 
{Issued separately December 2 , 1912 .) 
