70 TERMINOLOGY. . 86. 



Series may also be produced, although the derived form 

 be not of the same kind as the given form ; yet this does 

 not take place so immediately as under the circumstances 

 noticed. 



These series form a peculiar feature, and are of the 

 greatest importance in the Method of Crystallography de- 

 veloped in this work. 



A constant ratio exists between every two subsequent 

 members of those series. The general expression of this 

 ratio is the Law of the Series. 



Upon the series themselves is founded the method of 

 Crystallographic Designation (. 90.), 



. 86. LIMITS. 



The limits of the series of those forms which pos- 

 sess one axis, are Prisms of infinite axes. 



There is no reason why a series produced by derivation 

 (. 85.), should stop at a member, as long as another ulte- 

 rior one can still be derived from it. This is always pos- 

 sible, as long as those dimensions, which are altered by 

 the derivation, remain finite. All members in which this 

 is the case, are termed finite members. If a member re- 

 ceives infinite dimensions, the derivation can no longer be 

 continued. The limits of derivation, and consequently 

 the limits of the series arising from it, are therefore at- 

 tained, if the dimensions of these forms become infinite. 



The dimensions of forms which most conveniently may 

 be supposed to grow infinite, or infinitely small, are the 

 axes ; if these be infinite, the form becomes a prism ; on 

 the contrary, if they be infinitely small, it becomes a plane. 

 Prisms of infinite axes, and planes of infinite extent, are, 

 therefore, limits of all the series of those forms which 

 contain one axis. 



Forms of infinite dimensions can never appear by them- 

 selves. Those which occur in nature, and consist of termi- 

 nal and lateral faces, are only segments, or parts of those 

 prisms of infinite axes. The lateral faces of the prism 

 represent the limit of the series on one side ; the termi- 



