Summary: We consider a system of \(N\) particles which are confined to the surface of a sphere and which interact via a potential that depends logarithmically on their separation. The groundstate properties of this system are investigated for \(N=2\) to \(65\). Unilike the case of Coulomb interactions, this system has ground-state configurations with zero dipole moment for all \(N\). The thermal properties of a selected set of systems in the range \(N=2\) to \(500\) are determined by Monte Carlo simulation . The results are compared with analytical calculations in the small- and large-\(N\) limits.