. 105. 106. OF THE CONNEXION OF FORMS. 105 



The magnitude of the plane angles of the base, and there- 

 fore of all sections perpendicular to the principal axis of the 

 scalene eight-sided pyramid, depend consequently solely 

 upon m, and these bases are equal, whenever m is the same. 



. 105. SERIES OF SCALENE EIGHT-SIDED PYRA- 

 MIDS. 



Every member of the series . 101., gives for 

 every determined m likewise a determined scalene 

 eight-sided pyramid. The forms of this kind, de- 

 rived from consecutive members of the series, ac- 

 cording to one and the same m, produce a parti- 

 cular series among themselves, the axes of which 



n 



increase and decrease, as the powers of V 2, or as 2 J . 



These series arise like those in . 95. The axes of their 

 members are products of m, the number of derivation, 

 with the axes of the members of the series of isosceles four- 

 sided pyramids, = 2 2 . m. a ; and since m. a is a factor 

 common to them all, they will be among each other in 



the ratio of 9*. 



n 



If in the algebraic expressions . 56., 2 5 .a be substituted 

 for a, the result will be expressions of the same kind for 

 the cosines of the edges of (P+ n) m . 



. 106. LIMITS OF THE SERIES OF SCALENE EIGHT- 

 SIDED PYRAMIDS. 



The limits of the series of scalene eight-sided py- 

 ramids are, on one side a plane perpendicular to the 

 axis, on the other unequiangular eight-sided prisms, 

 whose transverse sections are equal and similar to 

 those of the members of the series, and their axes 

 infinite. The latter must be considered in two dif- 

 ferent positions. 



