. 95. OF THE CONNEXION OF Foil MS. 85 



yet it is very well calculated to shew the agreement be- 

 tween the forms derivable from the scalene, and those de- 

 rivable from the isosceles four-sided pyramid. This me- 

 thod also tends to preserve the sameness of the value of m 

 in both, at least in respect to those numbers of derivation, 

 which are most commonly met with in nature. 



This method of derivation consists in applying the process 

 . 92., not to the pyramid P itself, but to the interme- 

 diate form which belongs to that pyramid. It is exactly 

 the same as that by which the scalene four-sided pyramids 

 of dissimilar bases are obtained from the fundamental py- 

 ramids themselves, and therefore requires no particular 

 description. 



The first result is a compound form, as obtained above, 

 which, by a further resolution, yields a pair of scalene 

 four-sided pyramids, one of which refers to the long, the 

 other to the short diagonal of the fundamental form ? al- 

 though in the derivation, none of these diagonals remain 

 unchanged. The correspondence of these pyramids to the 

 diagonals of the fundamental form, is determined as in . 92. 

 Their crystallographic designation, in as far as they are 

 obtained by the application of the last mentioned process, 

 is (Pr + n) m and (Pr + n) m . 



The ratio of the diagonals of the bases is entirely de- 

 pendent upon m. For, considering one and the same m, 

 aH the bases of (Pr + n) ra on one side, and all the bases of 

 (Pr + n) m on the other, are equal and similar to each other, 

 as may easily be deduced from . 93. The two lines MS, 

 MS", Fig. 39., are in the same ratio as the diagonals c and b. 

 From the consideration of the figure it appears, that 



TVTCJ 2 m 



Mo = . c. 



m+ 1 



MS"- 2m .b. 

 m + 1 



The co-efficients of the three perpendicular lines in this 

 derivation are different from those obtained in . 94. If the 

 axis, the longer, and the shorter diagonal of P + n be in the 

 ratio of 



