We apply the conformal gravity theory to a sample of 111 spiral galaxies whose rotation curve data points extend well beyond the optical disk. With no free parameters other than galactic mass to light ratios, the theory is able to account for the systematics that is observed in this entire set of rotation curves without the need for any dark matter at all. In previous applications of the theory a central role was played by a universal linear potential term $V(r)=\gamma_0 c^2r/2$ that is generated through the effect of cosmology on individual galaxies, with the coefficient $\gamma_0=3.06\times 10^{-30} {\rm cm}^{-1}$ being of cosmological magnitude. Because the current sample is so big and encompasses some specific galaxies whose data points go out to quite substantial distances from galactic centers, we are able to identify an additional globally induced universal term in the data, a quadratic $V(r)=-\kappa c^2r^2/2$ term that is induced by inhomogeneities in the cosmic background. With $\kappa$ being found to be of magnitude $\kappa=9.54\times 10^{-54} {\rm cm}^{-2}$, through study of the motions of particles contained within galaxies we are thus able to both detect the presence of a global de Sitter-like component and provide a specific value for its strength. Our study suggests that invoking dark matter may be nothing more than an attempt to describe global physics effects such as these in purely local galactic terms.