290 APPENDIX CALCULATION OF THE 



Let us suppose the edge i A*, of the primary form, 

 to be to the edge i d, in the ratio of m to n, m and n 

 being any numbers whatsoever. 



It follows from what has been before stated, that 

 the ratios of the corresponding edges of the molecules 

 which compose this form, will also be as m to n; and 

 consequently that the primary edges are composed of 

 equal numbers of edges of molecules, and may there- 

 fore be regarded as multiples of m and n, by some 

 indefinite whole number. 



Let us further suppose that the decrement had 

 begun to act at the edge a b, and had proceeded along 

 the plane a b c. 



In the first plate of molecules superimposed on 

 that plane, the row 1 would have been omitted. In 

 the second plate, the additional row 2. In the third 

 plate, the additional row 3, and so on. 



Now the evident result of these abstractions from 

 the several superimposed plates, would have been 

 the production of a new plane, a b g f, replacing the 

 edge h , of the enlarged crystal ; and the triangular 

 prism, whose base is the triangle b if, represents the 

 defect of the primary form occasioned by this decre- 

 ment. 



But it is obvious from the figure, that the ratio of 

 the lines i f to i b of the defect, is as 3 m to 3 n, or 

 as m to n. Hence when a decrement by 1 row of 

 molecules takes place on the edge of any parallele- 

 piped, the ratio of the edges of the defect, correspond- 

 ing to if, i b, is similar to the ratio of those edges of 

 the primary form, of which these are respectively 

 supposed to be portions. And as the edge b f, of the 

 new plane, coincides with a diagonal of the molecules, 

 it is evidently parallel to a diagonal of the plane d i k e. 



