104 Mr, Whewell on calculating 
in the direction AB, b in the direction AC, c in the direction 
Az. Then putting i-, -1 for A, B, C in the formula, Art. 
8, we shall have the angles made by secondary planes. 
Conversely, knowing the angles made by secondary planes 
we may determine A, B, C, as before, and when we have 
found in crystals the same substance, various values of 
A, B, C, we have 
q B 6 r C c _ 
p Aa ’ p A a ' 
and a, b, c are to be assumed so that q : p and r : p may be 
numerical ratios as simple as possible. 
2. The oblique rhombic Prism, fig. 8. 
19. In this case the angles s:AB, 2; AC, and the sides AB, 
AC are equal ; and consequently the two faces 2; AB, 2; AC 
are symmetrical ; and whatever secondary plane is formed 
with reference to one, we must have a co-existent plane cor- 
responding to the other. Hence, if we have a plane (p;q; r) 
we must have a plane {q\p\ r) and we may express both 
these by the symbol {p, q\r) the (,) indicating that the co-or- 
dinates X and y may be exhanged, % remaining the same. 
And this is true whether p, q, r be positive or negative. 
Here having found p, q, and r we have ha,ka,lc, because 
a and b are equal, and their values are to be determined as 
before. 
3. The oblique rectangular Prism, fig. 9. 
20. Here the solid angles A and C are similar in all re- 
spects, A being contained by two right angles BAC, CAz 
and the angle BA;?;, and C by the angles DCA, AC 0, oCD 
equal to them. Hence whatever plane be formed on A, we 
must have a coexistent plane on C, agreeing with it, except 
