of Crystalline Combinations. 399 
V.2. Let pRm, qRr be the forms. In order that the acute 
terminal edges of pRm may truncate the edges of gRr, we must 
have 
1 OB 2 OB 
7 OF Geen oy ee eee 
Square Pyramidal System. 
Crass II. Comb. 2. In order that the faces of pQr, replacing 
the summit of gqQn, may be rhombs, we must have ¢Qx coincident 
with an eight-sided pyramid, derived from pQr (see B). Now, 
if this deduction’ from pQr be according to m, the form will be 
3 —1 
the same as one derived from pQ, thus, —_ pQ at. Hence, 
' : ies l xs 
this form and qgQz will coincide if om =n, and _ a = q: 
2 
whence 
mm —_ 
(n—1) qQr, Qn. 
II. 6. In order that the faces of the four-sided pyramid pQ 
may truncate the scalene terminal edges of the pyramid qQn, they 
must make the same angle with the axis which those edges do. 
But the tangent of the angle which the faces of the pyramid pQ 
make with the axis is manifestly 
7 =n, and p=q(n—1), and the combination is 
b b nbv2 2np 
SSS SS ae F —S>—_-_—__——— = — 23 
/2.pa Se J/2.pa n+i.qa’ Era 
And the combination is pQ, 2uF Qn. 
II. 7. In order that the faces of the four-sided pyramid pQr 
may truncate the principal terminal edges of the figure gQn, they 
must make the same angle with the axis which those edges make. 
But the angle which the faces of the first pyramid make, has for 
its tangent aa and the angle which the edges of gQn make has 
: b ity Pebec 
for its tangent Bails ena And the combination is gnQr, qQn. 
