. 153. OF COMBINATIONS. 199 



with such forms as are known, will always suffice for its 

 perfect determination. 



viii. Pr + n. Pr + n'. 



1. Let n' be = n. The combination Pr -f- n. Pr + n will 

 be the intermediate form belonging to P + n (. 97-) 



2. If the two forms do not belong to one and the same 

 series, due attention must be given to the co-efficients of 

 the different series. If n or n' become infinite, the edges 

 of combination are parallel to the terminal edges of that 

 scalene four-sided pyramid, to which the finite prism be- 

 longs, whatever may be its co-efficient. 



3. If both n and n' are = + co, the combination P oo. 

 Pr + co. Pr 4- oo is transformed into a right rectangular 

 prism, whose transverse section is an oblong. This prism 

 must not be confounded with the right rectangular four- 

 sided prism of the pyramidal system, whose transverse sec- 

 tion is a square, and whose crystallographic sign may be 

 either P co. P + po or P . co, [P + oo]. 



. 153. HEMI-PRISMATIC COMBINATIONS. 



A combination possesses a Hemi-prismatic Cha- 

 racter, if one or several of the forms contained in 

 it, and bearing to each other the general relations 

 of those in the prismatic system, appear only with 

 half the number of their faces, or in which these 

 faces shew differences in their angles referring to an 

 axis which is inclined in a plane perpendicular upon 

 the base, and passing through one of its diagonals. 



The hemi-prismatic combinations depend upon the fun- 

 damental form, . 98. Fig. 41., whose axis is inclined in a 

 plane perpendicular to the base, and passing through one of 

 its diagonals. 



The hemi-prismatic forms are designated like the pris- 

 matic ones, with that difference only, that the signs of 



