86 Eev. W, Mitchell on a New Method of rendering [March 18, 



WEEKLY EVENING MEETING, 

 Friday, March 18, 1859, 

 Charles Wheatstone, Esq. F.R.S. Vice-President, in the Chair. 



Rev. Walter Mitchell, M.A. 



On a Neio Method of rendering visible to the Eye some of the more 

 abstruse problems of Crystallography, hitherto considered only as 

 Mathematical Abstractions. 



The unpopularity of crystallography "may be attributed to the dif- 

 ficulties so many people, especially those who have not had a good 

 mathematical training, meet with in attempting to master the concep- 

 tion of forms involving some of the principles of solid geometry. To 

 a certain extent this may be removed by a well-arranged system of 

 solid models: thus the first three propositions of the 15th book of 

 Euclid, " the inscription of a regular tetrahedron in a cube, of a 

 regular octahedron in the tetrahedron, and of the octahedron in the 

 cube," may be demonstrated to the eye by a dissected cube, illustrating 

 the natural cleavage of fluor spar. Indeed the cleavage of a cube of 

 fluor spar is a natural demonstration of the three principal propositions 

 of the last book of Euclid's Elements of Geometry. 



There are many propositions of crystallography which require 

 some mechanical means beyond that of the use of solid models to make 

 them appeal to the eye for clearer perception. The most perfectly 

 symmetrical solid forms of the crystallographer belong to the cubical 

 or tessular system. There are seven different kinds or orders of forms 

 belonging to this system, perfectly symmetrical ; four of which admit 

 of an infinite variety of species. These forms are associated in nature 

 as well as in their mathematical relations to each other. They are 

 found in crystals of the same substance, either in their simple forms or 

 else associated in combination with each other, in the different faces of 

 a compound crystal ; thus the cube, the octahedron, and the rhombic 

 dodecahedron, are found as simple crystals of the diamond, or faces 

 parallel to all three or two of them, may be discovered on a more 

 complex natural crystal. 



The three forms we have just enumerated, the cube, the regular 

 octahedron, and the rhombic dodecahedron, may be considered as the 

 permanent or limiting forms of the cubical system ; they admit of no 

 varieties ; their angles, whether those of the inclination, of adjacent 

 faces, or of the planes constituting their faces, are invariable ; they are 



