. 137. GENERAL IDEAS OF FORMS. 147 



is determined for a particular case; or, which is the same 

 thing, it will produce a Series of Crystallisation. 



From these considerations it follows that the tessular sys- 

 tem, being the only one in which the simple forms possess 

 invariable dimensions, will comprehend only one Series of 

 Crystallisation ; while all the other systems, which possess 

 variable dimensions, may comprehend an unlimited num- 

 ber of such series, that is to say, as many as there may be 

 differences in the dimensions of their fundamental forms. 



Since these series represent the systems of crystallisa- 

 tion themselves, though determined for particular dimen- 

 sions ; it is plain that they must not be confounded with 

 the series of homogeneous simple forms (. 85.) considered 

 above, as, for instance, with the series of rhombohedrons, 

 or of the different pyramids. It is also evident that, if 

 different members of the same series, for instance R, 

 R 4- 3, II 1, &c., be considered as fundamental forms, 

 they will not yield different series of crystallisation, because 

 upon this supposition, the results obtained by derivation 

 will be identical. 



. 137. THE SYSTEM OF CRYSTALLISATION DETER- 

 MINED FROM A SINGLE FORM. 



From the observation of any single form, except 

 the right rectangular prism, the System of Crystal- 

 lisation to which this form belongs may be inferred. 

 This extends to the Series of Crystallisation, if the 

 dimensions of the form be given or known. 



The facility of ascertaining the System of Crystallisation 1 , 

 by observing one single form, is obvious, and is founded 

 upon the difference among those simple forms, which consti- 

 tute the different systems. Thus the rhombohedral system 

 is composed of rhombohedrons, of six-sided pyramids, and of 

 six-sided and twelve-sided prisms ; the pyramidal system, of 

 isosceles four-sided pyramids, and of scalene eight-sided py- 



