9 ^ 
94- Mr. Whewell on calculating 
rhomboids which lie without this plane to be removed, have 
a proper representation of a secondary crystalline form con- 
stituted by the aggregation of primary ones. 
Before we proceed to the calculations founded on this 
mode of viewing the subject, we may observe, that by in- 
creasing or diminishing the three indices p, q, r in any ratio, 
the plane represented by them is not altered. Thus (p; q; r) 
i^np\ nq% nr) i|, &c. are the same plane. Hence 
[p; q; q') IS the same as ; i ; i j [p\ p ; o) as (i ; i ; o) ; 
and the primary faces are (1,0,0). 
8. Prop. To find the dihedral angle contained between two 
planes {p;q',r) r'), the dihedral angle at the ter- 
minal edges of the primary rhomboid being a. 
If there be three co-ordinates any how situated so that the 
dih,edral angle at the axis x between the planes xy and xz is 
oc ; the dihedral angle at the axis y, jS ; and at the axis y : 
and if d be the cosine of the angle which a line perpendicular 
to the plane yz makes with x ; e the cosine of the angle which 
a line perpendicular to xz makes with y ; f the cosine of the 
angle which a line perpendicular to xy makes with % : and if 
0 be the angle of two planes whose equations are Ax By 
-^Cz = m, A'x + B'y C% = m'; we shall have (see 
Transactions of the Cambridge Philosophical Society, Vol. II. 
P. I. p. 200) 
AA' , BE' , ce 
~V e* “T“ /» 
