94 TERMINOLOGY. . 98. 



ral expressions of these quantities for P 4- n, one 



of the diagonals after the other is supposed infinite. In the 

 horizontal prisms belonging to P, the values of the cosines 

 are as follows : 



a 2 _b 2 



for Pr, cos. y = 



for Pr, 



As to the limits of the horizontal prisms, it is evident, 

 that in the same proportion in which the axis of the pyra- 

 mid Si-. P + n increases, the angle of the horizontal 



prism at the axis must diminish ; and that it must entirely 

 disappear, when the axis becomes infinite. The supple- 

 ment of this evanescent angle is = 180, and the hori- 

 zontal prism therefore is transformed in two unlimited pa- 

 rallel planes, perpendicular to those diagonals to which they 

 belong. If on the other side the axis decreases, the same 

 angle becomes greater and greater, and at last = 180, if 

 the axis is infinitely small. The supplement of this angle 

 is = ; the faces of the horizontal prism contiguous to the 

 opposite ends of the axis, coincide with the plane of the 

 basis ; and they appear as faces perpendicular to the axis. 



This is the result of m + 1 Pr + co and m+1 Pr + co, 



and of m .! Pr - co and m -I Pr - oo. 

 2 2 



The series of horizontal prisms between their limits, are 

 expressed by 



P _ co ... ELL! Pr + n ... P r + n, 



P co ... m _i Pr + n ... Pr + eo. 



The face perpendicular to the axis has received its sign 

 as the limit of the principal series ; and in the limits for 

 n = + co, it is unnecessary to attend to the co-efficients of 

 the different series. 



