124 On Crystallography. 



the moment to the consideration of the effect of the de- 

 crement which takes place parallel to the ridge BC, 

 ascending above the parallelogram A BCD. 



If we suppose that the form of the integrant molecule 

 which is similar to the generator parallelopipedon is deter- 

 mined, and that the law of decrement is known, it will be 

 easy to find the angle formed with ABCD by the face pro- 

 duced in virtue of This decrement. 



Let a g (fig. 2) be one of the molecules, of which the 

 faces analogous to those of the parallelopipedon, fig. 1, are 

 marked with the same letters. From the point c I draw 

 cs and cr perpendicular on h c. Now, by the hypothesis, 

 the relation between these two lines is given, as well as the 

 angle res which measures the incidence of abed upon 

 b c g h. 



Now let op (fig. 1) be the distance between the ridge 

 BC and the first lamina of superposition, which distance 

 is regarded as being measured on the plane ABCD. It is 

 clear that op is equal to c r (fig. 2) multiplied by the num- 

 ber 7? of rows subtracted. Therefore op = n xcr. From 

 the point p (fig. 1) raise pu lying upon that of the lateral 

 faces of the first lamina, which is turned from the same 

 side, and equal to the height of this face. We shall have 

 puz=cs (fig. 2) and opu = scr. Complete the triangle 

 upo (fig. I). It is visible that the line ou will coincide 

 with the face of the secondary crystal, which rises on the 

 ridge BC, and that the angle pou will measure the inci- 

 dence of this face on the parallelogram ABCD. Thus, 

 since in the triangle up we know the two sides op, p u, 

 and the comprehended angle opu, it will be easy to get 

 the angle pou which gives the incidence wanted. 



] 1. The triangle p ou is caFled mensurator triangle ; and 

 1 shall subsequently give this name to all the triangles 

 which perform the same function. 



12. Let us now consider the effect of the decrement 

 wtirch takes place parallel to the same ridge BC, by de- 

 scending on the face BCGH. Let ik be the mensurator 

 triangle, in which i is the distance between the ridge 

 BC and the first lamina of superposition, ill coincides 

 with that of the lateral faces of this lamina, which looks to- 

 wards the ridge BC, and besides it is equal to the height 

 of the face in question; finally, oh is laid on the face 

 which results from the decrement. 



Let w' be the number of rows subtracted. We shall 

 have oi (fig. 1,) = n' xcs (fig. 2). Also ill (fig. 1) = cr 



(fig- 



