. 91. OF THE CONNEXION OF FORMS. 77 



certain determined member of the series, of which P is the 

 fundamental form, there is nothing required but to substi- 

 tute for n that number which denotes the peculiar place of 

 the member in the series. These general formulae are very 

 useful in all crystallographic calculations. 



. 91. LIMITS OF THE SERIES OF SCALENE FOUR- 

 SIDED PYRAMIDS. 



The limits of the series, . 90., are on one side an 

 oblique-angular four- sided prism, whose transverse 

 section is equal and similar to the base of the fun- 

 damental form, and its axis infinite ; on the other 

 side a plane, perpendicular to that axis. 



The series (. 90.) may be continued on both sides, as 

 long as the members obtained, or as long as their axes, are 

 finite quantities ; and there can be no reason why we should 

 consider oe of these pyramids as the last, because the de- 

 rivation always will produce new members of the series. 

 But when the axis becomes infinite, no more new members 

 are produced ; and in this case the series breaks off, or ar- 

 rives at its limits (. 86.). These limits are therefore sca- 

 lene four-sided pyramids of known bases and infinite axes. 



But suppose now the axis to decrease, the terminal edges 

 will approach to the parallelism with the diagonals of the 

 base, the inclination of the faces in these lines, or the ter- 

 minal edges, to 180, and the magnitude of the lateral edges 

 to 0. The final term of these approximations is obtained, 

 when the axis becomes infinitely small ; in this case the 

 pyramid is transformed into a plane figure, similar to the 

 base. 



The prism of an infinite axis is infinitely distant from P in 

 the series of pyramids; or, in other words, there is an infinite 

 number of members of the series between the fundamental 

 form and that prism. The number n in that form, is there- 

 fore = co . In the same manner, n is = eo for the prism 



