On Crystallography. 1 27 



Let AG (fig. 4) always be the generator parsllelopipedon. 

 Suppose that the decrement which takes place in breadth 

 upon the angle BCD has such a measurement, that the 

 lower edge of the first lamina of superposition passes by 

 m r, in which case such of the lines Cm, Cr will contain 

 as many ridges of molecule equal to c d, or cb (fig. 2), as 

 there will be rows subtracted by the decrement. Having 

 taken upon CG (fig. 4) a part Cc equal to eg (fig. 2), 

 make a plane pass by the points m,c,r. / say that this 

 plane is parallel to the face which results from the decrement. 

 In order to prove it, having drawn indefinitely the lines 

 m s and ru parallel to CG, I prolong them each upwards, 

 so as lo have him, or Rr equal to Cc. Now these pro- 

 longations M m and R r represent two of the ridges situated 

 on the lateral face of the first lamina. Therefore the face 

 produced by the decrement passes by the points M, R. But 

 besides it passes by the point C, which is the term of de- 

 parture of the decrement; therefore the plane MCR coin- 

 cides with it. Now the small lines Cc, M?n, Rr, being 

 three longitudinal ridges of molecule, situated parallel to 

 each other between the two planes mcr, MCR, it is visible 

 that these two planes are themselves parallel, i.e. that mcr 

 is parallel to the face which arises from the decrement. 



The same reasoning applies to the hypothesis in which 

 the decrement should take place in height. In this case it 

 would be necessary, in order to make the, plane mcr be 

 parallel to the face produced, that we should have cm — cd 

 (fig. 2) ; cr=:cb', and that the line Cc (fig. 4) should 

 contain as many times eg (fig. 2) as there would be ranges 

 subtracted in the direction of the height. 



18. Let us suppose that the plane MCR is prolonged 

 above the faces CDFG, BCGH, and consider the pro- 

 longations as two faces which would be the effect of two 

 decrements, the one upon the angle DCG, the other upon 

 BCG. These decrements being equal, we shall confine 

 ourselves to that which acts upon the angle DCG. Since 

 the plan cmr is parallel to the face which results from 

 this decrement, it is clear that cm coincides with ttie 

 lower edge of the first lamina of superposition applied 

 upon CDFG, and that Cr contains as many ridges of 

 molecule as there are ranges subtracted in height. 



1Q. If the decrement relative to the angle BCD takes 

 place by one row, it is evident that the two other decre- 

 ments relative the one to the angle DCG, the other to the 

 angle BCG, will also take place by one row : since then the 

 three lines Cm, Cr, Cc, are equal each to one ridge of 



molecules, 



