We examine the change deltaG in the two-probe electrical conductance G of a mesoscopic sample due to the switching on of superconductivity and prove that when conductance of the normal mesoscopic host is sufficiently high, the onset of superconductivity always produces a decrease in G. If the superconducting order parameter is of magnitude DELTA, we focus attention on the susceptibility chiDELTA = lim(DELTA-->0) partial derivative G(DELTA)/partial derivative (DELTA2). For weakly disordered, (i.e. ballistic) normal hosts, the average value of this quantity is negative. For diffusive hosts, the mean of chiDELTA increases linearly with [N - G(0)], where N is the number of open channels in the external, current carrying probes, while the fluctuations about the mean are found to be independent of G(0). With increasing normal disorder, chiDELTA undergoes a transition to a region of large fluctuations, before approaching a strongly localized regime, where typical values of chiDELTA are of order [ln2G(0)]-1.