. 98. OF THE CONNEXION OF FORMS. 93 



. 98. SERIES OF HORIZONTAL PRISMS, AND THEIR 

 LIMITS. INCLINATION OF THE AXIS. 



Every series of scalene four-sided pyramids has 

 two concomitant series of horizontal prisms. The 

 limits of these series are planes, which are perpen- 

 dicular to those diagonals to which they belong, 

 if + n becomes infinite, and perpendicular to the 

 axis of the fundamental form, if n becomes in- 

 finite. 



The designation of an indeterminate member in each of 



these series is m __! p r + n an( j m + 1 p r _j_ n> wn i c h, if 



2 2 



tn = 1, signifies a member of the principal series. From 

 every other value of m, provided m + 1 be not a power of 

 the number 2, a member of a subordinate series is obtain- 

 ed. If m + 1 be a power of the number 2 greater than 1, 

 yet the co-efficient nevertheless will remain = 1, as in 

 every other member of the principal series ; but the n in 

 its crystallographic sign is augmented for the exponent of 

 that power, just as has been mentioned above, in respect 

 to members of subordinate series. 



There is no particular designation required for such hori- 

 zontal prisms as belong to pyramids of dissimilar bases, 

 . 92. and . 95., because their principal sections coincide 

 with those of the pyramids, already expressed by the above 

 mentioned signs. This may be proved, for some of them, 

 by considering in general the ratio between the axis and the 

 two diagonals of pyramids, derived according to an undeter- 

 mined m ; and for others, by taking the determined value 

 of m, as obtained from observation. 



A horizontal prism is determined by the cosine of that 

 terminal edge, which is contiguous or parallel to the infinite 

 diagonal, or by that angle of the principal section of the 

 pyramid, which lies in the terminal point of the axis. 



The values of these cosines are obtained, if in the gene- 



