126 ISOMORPHISM. [SECT. xrv. 



tallisation. There are other crystals which, though bounded 

 by the same number of sides, and having the same form, are 

 yet susceptible of variation; for instance, the eight-sided 

 figure with a square base, called an octahedron (N. 165), 

 which is sometimes flat and low, and sometimes acute and 

 high. It was formerly believed that identity of form in all 

 crystals not belonging to the Tessular system indicated 

 identity of chemical composition. Professor Mitscherlich, 

 however, has shown that substances differing to a certain 

 degree in chemical composition have the property of assum- 

 ing the same crystalline form. For example, the neutral 

 phosphate of soda and the arseniate of soda crystallise in 

 the very same form, contain the same quantities of acid, 

 alkali, and water of crystallisation; yet they differ so far, 

 that one contains arsenic and the other an equivalent quan- 

 tity of phosphorus. Substances having such properties are 

 said to be isomorphous, that is, equal in form. Of these 

 there are many groups, each group having the same form, 

 and similarity though not identity of chemical composition. 

 For instance, one of the isomorphous groups is that consisting 

 of certain chemical substances called the protoxides of iron, 

 copper, zinc, nickel, and manganese, all of which are identical 

 in form and contain the same quantity of oxygen, but differ 

 in the respective metals they contain, which are, however, 

 nearly in the same proportion in each. All these circum- 

 stances tend to prove that substances having the same crys- 

 talline form must consist of ultimate atoms, having the same 

 figure and arranged in the very same order; so that the 

 form of crystals is dependent on their atomic constitution. 



All crystallised bodies have joints called cleavages, at 

 which they split more easily than in other directions ; on this 

 property the whole art of cutting diamonds depends. Each 

 substance splits in a manner and in forms peculiar to itself. 

 For example, all the hundreds of forms of carbonate of lime 

 split into six-sided figures, called rhombohedrons (N. 166)> 

 whose alternate angles measure 105-55 and 75-05, however 



