FORMS OF CLEAVAGE AND CRYSTALS. 73 



may be conceived to be derived from their cleavage solids, 

 agreeably to the symmetrical transitions explained in . 50. 



1. Thus the form of cleavage in Galena is a Cube, which corres- 

 ponds with the most common form of crystal belonging to this min- 

 eral: that in Idocrase a right square Prism, and that in Muriacite a 

 right rectangular Prism; in both of which cases, there exists the 

 same correspondence as in the first.* Additional instances among 



* It may appear to the student, who has made trial of cleaving crys- 

 tals, somewhat arbitrary to dis(inguish the three kinds of quadrangular 

 prism referred to above, in all of which the angles are 90; since it is ob- 

 vious from the nature of cleavages that any crystal capable of affording 

 one, may also give rise to the other two ; from which it would naturally 

 seem, that these three forms of cleavage should rather be treated of as 

 one. But if we pay attention to the nature of the cleavages in the three 

 cases, we shall perceive there is good cause for the distinction intro- 

 duced. 



For example, if (as is the case) in a crystal of Galena, a parallele- 

 piped with square faces, the three cleavages are equally distinct, it is ev- 

 ident that any one of the three faces of the prism (with its opposite) 

 sustains the same relation to the others, as the cleavage which corres- 

 ponds to it, does to the other cleavages, that is, they are all similar, and 

 may be regarded as being situated at an equal distance from a central 

 point, as is the fact with the faces of the Cube. This solid is therefore, 

 very properly denominated a Cube. 



If two kinds of cleavage are equally distinct; and the third more or 

 less so than the first, or scarcely perceptible at all, as is the fact in the 

 crystals of Idocrase, the four faces w r hich result from the similar cleava- 

 ges are similar, and similarly situated as respects an imaginary line join- 

 ing the centres of the two other faces ; this line must therefore be con- 

 sidered as the prismatic axis, and then, in order to represent the similar- 

 ity of position among the lateral faces to this axis, we must consider the 

 bases (i. e. the other faces) as square ; which makes the solid in ques- 

 tion, the right square Prism. 



If the three cleavages, parallel to the faces of the right quadrangular 

 prism, are unequal as respects their distinctness, as in Muriacite, then 

 each of the three sets of faces of the prism considered along with the cor- 

 responding cleavages, rsay be regarded as distinct from one another, a 



7 



