  I consider the quantity delta(m_1m_2m_3) = M_{q_1q_2q_3} - [M_{q_1q_2bar} +
M_{q_2q_3bar} + M_{q_1q_3bar}]/2, where the M's represent the ground state
spin-averaged hadron masses with the indicated quark content and the m's the
corresponding constituent quark masses. I assume a logarithmic interquark
potential, the validity of a nonrelativistic approach, and various standard
potential model inputs. Simple scaling arguments then imply that the quantity
R(x)=delta(mmm_3)/delta(m_0m_0m_0) depends only on the ratio x=m/m_3, and is
independent of m_0 as well as any parameters appearing in the potential. A
simple and accurate analytic determination of delta(mmm_3), and hence R(x), is
given using the 1/D expansion where D is the number of spatial dimensions. When
applicable, this estimate of R(x) compares very well to experiment -- even for
hadrons containing light quarks. A prediction of the above result which is
likely to be tested in the near future is M_{Sigma_b^*}/2 + [M_{Lambda_b} +
M_{Sigma_b}]/4 = 5774 +/- 4 MeV/c^2.
