398 
ON A PROPERTY OF THE STEREOGRAPHIC PROJECTION. 
[475 
circle AB of the oblique direction: to define this position, we may use either the arc 
NM which in the direct projection determines the co-latitude of the centre M of the 
oblique projection (say NM = A, that is, NV = A), or by the arc NM which in the 
oblique projection determines the distance of N from the centre, or co-latitude of the 
K 
L 
centre (say NM = A', that is, BW = A'). The obliquity in the oblique projection is thus 
90 — A', viz., this is the inclination of the plane of projection to that of the horizon- 
meridian in the direct projection. We have also c = NX, c' = WY. The relation 
between the angles A, A', is easily found to be 
tan | A = tan 2 ^ A', 
viz., taking the radius in the direct projection to be =1, we have 
OM = tan 1(90° -A), 
MA = Vl — tan 2 ^ (90° — A), 
MN = 1 — tan | (90° — A) ; 
wherefore 
Vl — tan 2 1 (90° — A). tan \ A' = 1 — tan | (90° — A), 
and thence 
the required relation.