 
Summary: IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME30, NO. 2, FEBRUARY 1983
which saved about 40 percent of computing time (van Ooste
rom [5]).
In a discussion of this problem, Dr. F. A. Muller of the De
partment of Physics of the University of Amsterdam pointed
out that the numerical stability involved in (5) might be
poorer than in (4). He also suggested that a more drastic
reduction might be possible by considering the triple scalar
product R1 
(R2 X R3). While examining the various expres
sions for Q2 alternative to (3) as described in (old) textbooks
on spherical geometry, it became apparent how this advice
could be put to use.
In Casey [4, result (359)], it is shown that
fI\ 1 + cos (a) + cos (b) + cos (c)
c 2  4 cos (a) cos (tb) cos (ic) (6)
with a, b, and c the arcs among A, B, and C as indicated in
Fig. 1. This can be noted as
1 + cos (Xi)
cos2 =4 Hcos ('xi)'
