. 102. OF THE CONNEXION OF FORMS. 101 



. 102. LIMITS OF THE SERIES. 



The limits of the series . 101. are, on one side 

 a plane perpendicular to the axis, on the other two 

 rectangular four- sided prisms, one of which is in 

 a parallel, the other in a diagonal position with 

 the fundamental form. 



The origin of these prisms is sufficiently evident from 

 . 91. If the diagonals of the base of the pyramid be sup- 

 posed equal, a rectangular four-sided prism is obtained, 

 instead of an oblique-angular one. It appears likewise, from 

 the calculations in . 101., that an isosceles four-sided pyra- 

 mid of an infinite axis is transformed into a rectangular 

 four-sided prism. 



The series of scalene four-sided pyramids is limited on one 

 side by a plane perpendicular to the axis, on the other by 

 a single prism, because there exists no difference in the 

 position of its members. But there is a difference of that 

 kind, in the series of isosceles four-sided pyramids, in which 

 the position of two subsequent members changes from 

 the parallel to the diagonal, and from the diagonal again to 

 the parallel position ; and since the last member, or the 

 limit of the series, may be considered in the one, as wel| 

 as in the other of these positions, it becomes necessary to 

 assume two rectangular four-sided prisms of infinite axes, 

 as limits of this series, one for the parallel, the other for 

 the diagonal position of two prisms limiting the series. 

 This supposition is exactly conformable to experience. 



The limits on the opposite side are squares equal to the 

 horizontal projection, because the isosceles four-sided py- 

 ramid, if its axis becomes infinitely small, is transformed 

 into a square plane figure. Here the difference of the 

 position can no longer be considered, because this pyramid 

 being nothing but a plane figure, cannot appear by itself in 

 nature, and receives its boundaries from the intersection 

 with the planes of other pyramids and prisms. 



The designation of the limits is, agreeably to what has 



