mathemati 

 cally. 



23S SCIENTIFIC NEWS. 



sided prisms with wedge shaped summits ; but it is d!so iriet 

 with in six-sided prisms variously modified. Alum crystallises 

 in octahedrons, but it likewise assumes the shape of a cube. It 

 is found nevertheless, that a certain number Of figures are 

 peculiar to each particular crystallisable material ; and the cry- 

 stals of that substance assume some one of those forms, or their 

 modifications, and no other. 

 Theelemen- This however is not all. When we penetrate into the 



r^ry parts are interior structure of these solids, we become convinced, that 

 uisposed in _ _ ' ' 



symmetry ac- their mechanical elements are symmetrically placed according 

 cording to ^Q certain laws, which have their measure and their value. 

 Their aggregation is absolutely geometrical, and appears as if it 

 had been effected by instruments guided by skill and intelli- 

 gence, 

 (leducible To exhibit these laws of crystalline architecture, is the pro- 



vince of crystallography. This science has in our time been so 

 successfully cultivated, that it gives a dignified aspect to the 

 philosophy of minerals, as grounded upon the results of the most 

 elaborate and skilful analysis. By these we are enabled to 

 calculate with the fewest possible data, simple in the extreme, 

 and mathematically certain, the vast variety of forms of 

 crystals, with a lil^e degree of accuracy as astronomers attain in 

 calculating the motion of the heavens. 

 Great advan- Sut as the knowledge of crystallography in its improved 

 tages ofmode'.s g^gte abounds in mathematical and algebraic calculations, and 

 for expla ning , r , i- i ■ i , i 



this doctrine, cannot therefore be studied with success by such as are unac- 

 quainted with the mathematics ; it has been proposed to illus- 

 trate its elements by the help of geometrical models, which, 

 in other departments of knowledge, are so singularly useful 

 in rendering mathematical demonstrations obvious to the sen- 

 ses. Undoubtedly the human mind is capable of receiving 

 information from the mathematics with much greater facility 

 for demonstrations afforded by tangible solids, than by mere 

 reasoning from designs drawn upon a plane surface. It requires 

 an eye familiarised with the rules of linear perspective to com- 

 prehend the diversified and often complicated forms of angular 

 polyhedrons represented by projections by straight lines only, 

 which must naturally cross each other in many directions in 

 the representation of crystalline bodies. 

 Advancement Tlie general advancement of science and arts must be greatly 



dependant 



