89 
the angles of crystals. 
primary form of a crystalline body, P QR will be a secondary 
surface deduced from a certain arrangement of these primary 
elements. 
Let the three upper edges of the rhomboid, A x, Ay, A z, 
be considered as three axes of co-ordinates ; and let the cor- 
responding co-ordinates be x,y,z. We can then express 
the plane P Q R by means of these co-ordinates. If, for in- 
stance, we consider an edge of the small rhomboid as unity, 
and if AP, AQ, AR contain respectively 9, 6, and 3 of these 
edges, the equation to the plane P, Q, R, will be 
^ + i+T = i-* 
X 
9 I 0 • 3 
and if the numbers of small rhomboids in AP, AQ, AR be 
respectively h, k, I, the equation to the plane will be 
^ I 
T + 
k 
I 2 
+ T~ 1- 
If h, k, I be multiplied by any common quantity m, so that 
the equation becomes 
I 3/ 
mA * 
mk 
+ ^ = ^>°>'T + f + f 
it is clear that the plane P Q R will continue parallel to its 
former position, and may be considered as deduced from the 
same law as before. Hence it appears, that in the equa- 
tion -1 ^ = w, the quantity m does not serve to de- 
termine the position or law of formation of the plane, and 
may be any whatever. If we make m = o, the plane P O R, 
still continuing parallel to its former position, will pass 
through the point A ; and as we have to consider only the 
angles made by planes and their intersections, we may in 
such calculations suppose all our planes to pass through this 
point A. 
MDCCCCXXV. 
N 
