154 TERMINOLOGY. . 143, 



comparing them with each other, as obtained from the ob- 

 servation of the angles of incidence at the edges of these 

 simple forms themselves, or at the edges of combination : 

 this process, however, being deficient in geometrical preci- 

 sion, cannot lead to any generality, and is therefore not an 

 appropriate foundation for a scientific method of Crystallo- 

 graphy. Besides, it would suppose a great number of mea- 

 surements, which, in establishing general laws, we must 

 avoid as much as possible, because the crystals themselves 

 are very seldom found in such perfection, and under such 

 circumstances, as to allow of any observations of this kind, 

 upon the correctness of which we might rely. 



The method of Crystallography intended for the use of 

 the Natural History of the Mineral Kingdom, and em- 

 ployed in the present work, is founded solely upon the si- 

 tuation of those edges, in which the faces of several simple 

 forms intersect each other ; that is to say, of the edges of 

 combination ; and this method is therefore independent of 

 all measurement. The situation of those edges is a conse- 

 quence of the relations among the simple forms, and it is 

 changed as soon as any change takes place in these. It 

 will be possible, therefore, to determine the simple forms 

 contained in the combination, provided the situation of 

 the edges affords sufficient data. Only if these be wanting, 

 it will be necessary to resort to immediate measurement. 



The number of data required for this purpose, de- 

 pends entirely upon the quality of the form itself. Thus 

 a rhombohedron depends upon a single datum ; for in or- 

 der to determine it exactly, nothing is required but to 

 know the relative length of its axis, or what place it occu- 

 pies in one of the series developed above. At the same 

 time, it appears whether it be a member of the principal 

 series or of a subordinate one. For a scalene six-sided 

 pyramid, two data are required, in order to determine, first, 

 the rhombohedron from which it is derived, and then with 

 what number the axis of this rhombohedron must be mul- 

 tiplied in the derivation. In general, since the situation 

 of any plane is perfectly determined by three points given 



