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Proceedings of the Boyal Society 
7. On the Khombohedral System in Crystallography. By 
Alfred K. Catton, B.A., Scholar of St John’s College, Cam- 
bridge, and Fellow of the Cambridge Philosophical So- 
ciety. Communicated by Professor Tait. 
1. The science of Crystallography has for its object the classifi- 
cation of crystalline forms. 
The principles which must guide us in attempting to arrive at a 
natural classification of crystals are the same as those which have 
been so successfully applied to the formation of a natural classifi- 
cation of plants by Eay and Jussieu, and of animals by Cuvier. 
By the application of these principles it has been found that 
crystals are formed on six different types or plans of structure, and 
in consequence crystals have been arranged in six primary classes, 
termed crystallographic systems. They are named the cubic, pyra- 
midal, rhombohedral, prismatic, oblique, and anorthic systems. 
It is the object of this paper to show that the type on which 
crystals of the rhombohedral system are constructed is the same as 
that of the prismatic system. 
The establishment of this proposition necessitates the abolition 
of the rhombohedral system, and all crystals hitherto included in 
it must in future be referred to the prismatic system. 
2. In order to establish this proposition it is necessary to show, 
(1.) That three axes of symmetry can be found at right angles 
to each other, such that for them the crystallographic para- 
meters become unequal. 
(2.) That the laws of symmetry of crystals of the rhombo- 
hedral system are the same as those of the prismatic sys- 
tem. 
Now it is easily seen that the three straight lines perpendicular 
to the planes 101, 121, and 111 are at right angles to each other. 
For the forms 101 and 211 differ only in position, the one being 
the same as the other turned through an angle of 30*^ about the 
optic axis. 
Also the faces of the form 111 are perpendicular to the faces of 
