12S On Crystallography. 



molecules, the three decrements must necessarily hare the 

 same measurement. 



20. But if the decrement relative to the angle BCD is 

 produced by more than one row, then the two others will 

 necessarily be intermediate, and it will be sufficient to have 

 the law of the first decrement for determining the two 

 others. Let us suppose, for example, that the decrement in 

 the angle BCD is made by three ranges in breadth. In 

 this case Cm and Cr will each of them he equal to three 

 ridges of molecules, and C c will be equal to one ridge. 

 Therefore the decrement on the angle DCG is produced in 

 such a manner that there are three ridges of molecules sub- 

 tracted in the direction of CD, upon one alone in the direction 

 of CG; and besides this decrement is made by. three rows 

 in height, since Cr answers to three ridges of molecules, 

 it is the same with the decrement which takes place on the 

 angle BCG. 



21. In all cases of this description, the theory only con- 

 siders the effect of the decrement which takes place accord- 

 ing to the ordinary laws, because there results from it a 

 much more simple solution; and the two other decrements, 

 of which abstraction has been made, are considered as in- 

 tervening in a subsidiary manner to second the effect of 

 the first, and prolong towards the parts adjacent the face to 

 ■which it has given birth. 



-22. The greatest number of faces which the secondary 

 crystal can have, in the hypothesis of a decrement on all 

 the angles, is twenty-four, since there are eight solid angles 

 each composed of three plane angles, which are the terms 

 of departure of as many decrements. The minimum of 

 the number of faces in the same hypothesis is eight; and 

 although strictly speaking there are always twenty-four de- 

 crements, we only consider eight, which gives us the fa- 

 cility of employing ordinary laws only, for determining the 

 form of the secondary crystal. 



23. The simplest case is that in which the generator pa- 

 raliclopipedon being a cube, all the decrements are done by 

 one row. The secondary solid isthen a regular octahedron. 



But it may happen that the three decrements which take 

 place around one and the same solid angle are all inter- 

 mediary. In this case it is sufficient that one of them be 

 determined, in order to render it easy to conclude from 

 thence the two others, by the help of a construction similar 

 to that which we have previously employed. 



24. Let us suppose that fig. 5 represents the. generator 

 parallelopipedon, marked with the letters relative to the 



method 



