L.AWS OF DECREMENT. 293 



From these examples it appears that the edges of 

 the defect of the primary form are multiples of the cor- 

 responding edges of the molecules / and the ratios of 

 the edges of the defect are consequently multiples of the 

 ratios of the corresponding edges of the primary form. 



For let the ratio of i k : id, which is that of m : /z, 



be represented by the fraction - 



n 

 and the ratio of i b : i c being that of 4 m : 3 n, be 



represented by the fraction t??. 



a n 



It is evident that the ratio is a multiple of 



o n 



by t 

 n 7 3 



Hence the problem of ascertaining the law of decre- 

 ment producing any secondary plane, is reduced to that 

 of ascertaining the ratios of the edges of the^ defect of 

 the primary form occasioned by such decrement, and 

 dividing these ratios by the ratios of the correspond- 

 ing edges of the primary form. 



We may also discover the law of decrement in 

 some particular case?, by dividing the ratios of the 

 edges of the defect, by the ratio of an edge to some 

 other line upon the crystal. 



Whatever ratio we may use for this purpose, will 

 be termed the unit of comparison. 



This unit of comparison is, generally, the ratio of 

 certain edges or other lines, either on the surface, or 

 passing through the interior of crystals, of which, pro- 

 portional parts would be intercepted by any new plane, 

 resulting from a decrement by one row of molecules. 



According to the theory already explained, the 

 molecules of all parallelepipeds are similar parallejo- 

 pipeds, and their edges are consequently propor- 

 tional to the corresponding edges of the primary form. 



