In this paper we identify an apparently previously unappreciated regul
arity in the systematics of galactic rotation curves; namely, we find
that at the last detected points in galaxies of widely varying luminos
ity, the centripetal acceleration is found to have the completely univ
ersal form (upsilon(2)/c(2)R)(last) = gamma(0)/2 + gammaN*/2 + beta*N
/R-2, where gamma(0) and gamma* are new universal constants, beta* is
the Schwarzschild radius of the Sun, and N is the total amount of vi
sible matter in each galaxy. This regularity points to a possible role
for the linear potentials associated with conformal gravity, with the
galaxy-independent gamma(0) term being found not to be generated from
within individual galaxies at all but rather to be of cosmological or
igin, being due to the global Hubble flow of a necessarily spatially o
pen universe of 3-space scalar curvature k = -(gamma(0)/2)(2) = -2.3 x
10(-60) cm(-2).