106 



TERMINOLOGY. 



. 106. 



That these limits are prisms of the kind above mentioned, 

 follows from . 95. But, as has been shewn in . 102. re- 

 garding the rectangular four-sided prisms, the eight-sided 

 prisms must, for the same reasons, be considered in 

 either position, the parallel as well as the diagonal one ; 

 and, therefore, two limits of infinitely long axes must be 

 assumed for the series of scalene eight-sided pyramids, one 

 in a parallel, the other in a diagonal position to the funda- 

 mental form. The positions of these prisms are determined, 

 like the positions of scalene eight-sided pyramids. 



If n becomes = co, (P 4- n) m is transformed into (P + co) , 

 (P n) m into (P co) m ; the latter, not being different 

 from P oa, is denoted by that sign. In (P 4- co) m the 

 position, which cannot follow from n = co, must be indicat- 

 ed by the designation, and this is effected as in four-sided 

 prisms, by giving to the parallel prism the sign (P + co) m , 

 to the diagonal prism the sign [(P + co) m ]. The designa- 

 tion of the whole series between its limits, is therefore : 



The above-mentioned algebraic expressions give for 

 n = + <, the cosines of the angles in the transverse sec- 

 tions of the unequiangular eight-sided prisms. Thus, 



CO, 



-_ 



m 2 + 1 



COS.* -- 



m 2 4- 1 



The following result is obtained, for the above-mention- 

 ed determined values of m (. 103.). 



