400 Mr. WuHewe.t on Crystalline Combinations. 
Il. 8. In order that the faces of the eight-sided pyramid ¢Qx, 
meeting at the scalene edge, may replace the terminal edge of 
the pyramid pQr, the angles which these edges make with the 
axis must be equal; and equating their tangents, we have (see F) 
bY2 mBbV2, _ n+l 
pa ~ n+l .qa’ dip cahiae 
II. 9. In order that the faces of the eight-sided pyramid, 
meeting at the principal edge, may replace the terminal edge of 
the pyramid pQ, the angles which these two edges make with the 
axis must be equal; and, equating their tangents, we have 
eS Seg et, PIR IL 
III. 4. In order that in the eight-sided pyramid pQm, the 
principal terminal edges may be replaced by the faces, in pairs, 
of the pyramid gQn, meeting at its principal terminal edges, we 
must havé the angles which the principal terminal edges make 
with the axis, equal in the two pyramids. Hence, equating the 
iiigents,) aedeent tin Syn 
angents, oma qna’” ale 
Oblong Pyramidal System. 
Crass II. Comb. 3,4. When the terminal edges of the py- 
ramid pP are replaced by the faces, in pairs, of gPnz, we must 
have the proportion of the axes a and & the same in the two 
forms; .. by £, p = qn. 
III. 3. When we have the prism qP’r, cutting pP and pPr 
so as to make the figure APB’Q, (Fig. 3.) it is required that 
this figure should be a rhomb. For this purpose it is requisite 
that the diagonals of the figure 4B’ and PQ should bisect each 
other in V; .. AB’ =2 AN, and=2B’N, and BM’ =2BN'. Hence 
AM 2s Ss Now the prism which passes through the line 
MB! | 2 0N UR § é 
B'G is pP’r. Hence, the prism which passes through 4B’ is Lp P’r. 
