MODIFICATIONS OF CRYSTALS. 



41 



stated that the basal edges were never truncated, but, when 

 modified, were replaced by planes unequally inclined to the 

 basal and lateral faces of the primary. These secondary 

 planes do not however occur at random, at any possible in- 

 clination ; but there is a direct relation, in all instances, to 

 the comparative height and breadth of the fundamental form 

 of the mineral. The same is true of planes on the angles, 

 and in secondaries to all the fundamental forms. 



Take a cube and cut off evenly one of the edges : this 

 removes parts of two other edges, at each end of the plane 

 It is found that in cubic crystals these parts are either equa 

 to one another, or one is double of the other, or treble ; or 

 in some other simple ratio. The same is true in the other 

 fundamental forms, except that, as stated, the relative height 

 and breadth of the prism come into account, and influence 

 the result. 



For example : in figure 70, 70 



(a section of a cube,) P M and p , J f .._» 

 P N are equal edges, divided /P^^ 

 into equal parts ; now a plane a ^/ 

 on an edge of a cube, as a b, 

 removes, as is seen, equal parts 

 of P M and P N ; another, as 

 a c, removes twice as many parts of one 

 edge as of the other ; and so other planes hiiV'ii like simple 

 ratios. In figure 71, a section of a prism, the lines P M and 

 P N (height and breadth of the prism) are unequal : let them 

 be divided into a like number of parts ; then a plane on an 

 edge, as a b, will cut off as many parts of P M as of P N ; 

 others, as a c, b d, twice as many parts of one as the other : 

 and so on. a b truncates the edge in figure 70 ; but not so 

 in figure 71. It is evident to the mathematical scholar that 

 the inclination of a plane a b to P N or P M, is sufficient to 

 determine the relative dimensions of P a and P b, or the rela- 

 tive height and breadth of the fundamental form. 



These principles give a mathematical basis to the 

 science. 



Thus we perceive that the attraction which guides each 

 particle to its place in crystallization, produces forms of 

 mathematical exactness. It covers the crystal with scores 

 of facets of finished brilliancy and perfection ; and these 



What other law is there, respecting the occurrence of secondary 

 aUnes? Explain by the figures. 



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