8CT. XIV. ISOMORPHISM. 107 



variation, as the die or cube (N. 163), which may be 

 small or large, but is invariably a solid bounded by six 

 square surfaces or planes. Such also is the tetrahedron 

 (N. 164) or four-sided solid contained by four equal- 

 sided triangles. Several other solids belong to this class, 

 which is called the Tessular system of crystalization. 

 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 some- 

 times acute and high. It was formerly believed that 

 identity of form in all crystals not belonging to the 

 Tessular system indicated identity of chemical compo- 

 sition. Professor Mitscherlich however has shown, 

 that substances differing to a certain degree in chemical 

 composition have the property of assuming the same 

 crystaline form. For example, the neutral phosphate 

 of soda and the arseniate of soda crystalize in the very 

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

 and water of crystalization ; 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 chemi- 

 cal 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 circumstances tend 

 to prove that substances having the same crystaline 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 crystalized bodies have joints called cleavages, at 

 which they split more easily than in other directions ; 

 on this property the whole art of cutting diamonds de- 

 pends. Each substance splits in a manner and informs 

 peculiar to itself. For example, all the hundreds of 



