OF COPPER-PYJIITES. 
-7 
belong P and P+l. Lastly, the octagonal faces are evi-^ 
dently perpendicular to the axis of the combination, or to 
the common axis of the three pyramids, and give therefore 
a four-sided pyramid of an infinitely short axis, the limit 
of the series of isosceles four- sided pyramids, P — 00. 
The combination contains the faces of 
00 . P— 1 . P . P-fl. 
The angle at the basis of P, and the relations of all the 
other pyramids to it being known, it will not be difficult to 
find the dimensions of all these forms. By immediate mea- 
surement the angle at the basis of P has been found 
= 108° 40'. From this follows by the formula, 
1 
cos. s 
1 4- cos. z 
the axis 2a of F =z V7.7648. The axes of the members 
of the series being in the ratio of 1 : * ^5 Sec., that of 
P— 1 will be = V3.8824, that of P+l = V15.5296. 
If 2a signifies the axis of any isosceles four-sided pyra- 
mid, a: the angle at one of its terminal, z the angle at one 
of its lateral edges, we have the formulae, 
] . l—a^ 
cos iC = 
and cos z 
The following table contains the angles of the three py- 
ramids, calculated according to these formulae, of P 
being supposed equal to V'T.TO^Sc 
PYRAMIDS. 
X 
z 
P— 1 
120° m 
89° 9' 
P * 
109° 5S' 
108° 40' 
P-fl 
101° 49' 
126° 11' 
® As it is given in M. Mohs' characteristic. 
