The properties of events having the topology and kinematic features of double Pomeron exchange are described. The data were taken at the CERN $p\overline{p}$ collider at $\sqrt{s}=0.63$ TeV in the UA1 detector. A calorimeter trigger was used to isolate events in which a central cluster of particles was separated from forward particles by large rapidity gaps. The invariant mass $M$ of the central cluster (possibly a colliding Pomeron-Pomeron system) covers the range 10-70 GeV/${\mathit{c}}^{2}$. The $M$ dependence of charged particle multiplicity distributions in these double Pomeron events is strikingly different from their $\sqrt{s}$ dependence in $\mathrm{pp}$ and $p\overline{p}$ interactions.