292 



APPENDIX- 



CALCULATION OF THE 



We may perceive from the figures 323 and 324, 

 that if we had conceived the new plane to be pro- 

 duced by the superposition of a single plate of mole- 

 cules, the edges of the defect would still be in the 

 same ratio to each other as if the new plane were 

 produced by a series of decreasing plates. We may 

 therefore express the character of this plane by the 

 ratio of the edges of the defect of the first plate of 

 molecules, consisting of one or more molecules in 

 thickness, according to the nature of the decrement. 



Fig. 325. 



Let us derive another illustration of this propo-r 

 sition from a decrement on the angle of a parallel o- 

 piped ; and, to render the example more general, let 

 us suppose an intermediary decrement acting on that 

 angle to have produced a plane a b c, fig. 325, by the 

 abstraction of a compound molecule, consisting of 

 three molecules in height, two in the direction of i h, 

 and four in the direction of i k. If we suppose the 

 lines i #, and i d, to be to each other in the ratio of 

 m to n, and the line i h, to be as o, the corresponding 

 edges of the compound molecules would consequently 

 be in the same ratio, and the edges, i c, i b, i a, of the 

 defect, would be as 4 m 9 3 n, and 2 o, and would, 

 when divided by m, n 9 and o, express the law of de- 

 crement by which the new plane is produced. 



