  In a previous paper Crater and Van Alstine applied the Two Body Dirac
equations of constraint dynamics to the meson quark-antiquark bound states
using a relativistic extention of the Adler-Piran potential and compared their
spectral results to those from other approaches, ones which also considered
meson spectroscopy as a whole and not in parts. In this paper we explore in
more detail the differences and similarities in an important subset of those
approaches, the quasipotential approach. In the earlier paper, the
transformation properties of the quark-antiquark potentials were limited to a
scalar and an electromagnetic-like four vector, with the former accounting for
the confining aspects of the overall potential, and the latter the short range
portion. A part of that work consisted of developing a way in which the static
Adler-Piran potential was apportioned between those two different types of
potentials in addition to covariantization. Here we make a change in this
apportionment that leads to a substantial improvement in the resultant
spectroscopy by including a time-like confining vector potential over and above
the scalar confining one and the electromagnetic-like vector potential. Our fit
includes 19 more mesons than the earlier results and we modify the scalar
portion of the potential in such a way that allows this formalism to account
for the isoscalar mesons {\eta} and {\eta}' not included in the previous work.
Continuing the comparisons made in the previous paper with other approaches to
meson spectroscopy we examine in this paper the quasipotential approach of
Ebert, Faustov, and Galkin for a comparison with our formalism and spectral
results.
