We have obtained radial velocities of the components of the short-period su
bsystem of the B-type triple star 64 Orionis, covering a full cycle of the
long-period orbit since the date of our earlier paper by Fekel & Scarfe. We
use all of our radial velocities, together with available speckle interfer
ometry, to derive a three-dimensional orbit for the long-period system. The
system has orbital periods of 14.57213 days and 12.98 yr. We also determin
e spectroscopically a magnitude difference at 4500 Angstrom of 1.0 +/- 0.1
between the components of the close pair. Although radial velocities of the
third component continue to elude us, we are able to derive masses and lum
inosities for all three components by requiring that they lie within the po
pulated band of the observed mass-luminosity relationship. With this constr
aint, the orbital parallax is 0." 00374 +/- 0." 00017. Our results are cons
istent with the spectral types and colors derived previously and with the b
magnitude difference determined by earlier lunar occultation observations,
within the uncertainties of those parameters.