129 
tlie angles of crystals. 
be in their natural position when they are drawn so as to 
touch the ellipsoid ; and we may consider as the centre of 
the face, the point of contact. The latitude and longitude 
and A,) of this point, are given by the formulae which follow. 
In the rhomboid, the axis of the rhomboid being the axis 
of the crystal 
, cos. X varies with z j> — q — r 
^ pq^ pr qr) 
sin. 
p •¥ q + 
In the prism, the axis being the axis of the prism 
tan. X varies with — 
p 
sin. ^ 
V (p^ + 9 * + r*) 
And hence the situation of the planes is known. Also if any 
of the planes, instead of touching the ellipsoid, be nearer to 
or farther from the centre of the crystal, the order of the 
planes will not be altered. 
Having thus determined what planes are adjacent, we find 
the angles which they make, by the formulae given Art. 8. 
In the rhomboid (p; q ; r)(p; q; r^ being the planes, 6 their 
angle, and the dihedral angle of the primary form, 
.Qg pp'-i- q q'+ rr'— {p'q 4. q'p p'r + r';? -f q'r r'q) COS. « 
V iP^+q^-\-r^—z pq-^pr-^ qr cos. a) q'^-\- r''^—zp' q'-\-p' y'r'cos. «) 
This is true also for the tetrahedron, and for the right rec- 
tangular prism, making cos. a = o. In the other cases we 
have a formula involving the three dihedral angles of the pri- 
mary form. 
We can also find the angles contained between any two 
edges by first finding the equations to the edges, and then 
employing a formula given, p. 125. 
MDCCCXXV. S 
