The literature values of the limiting ionic conductivities of H(+), OH(-), K(+), Cl(-), Ag(+), and Na(+) in water between 0 and 156 degrees C are analyzed as for the two possible mechanisms of conduction, i.e., controlled by an activation process or by the rotation of the water molecules. Plots of the data versus T(1/2) give straight lines for H(+) and OH(-), which supports the rotation control mechanism for these ions. The other ions give curved plots and therefore are investigated in terms of the activation control mechanism. A remarkable phenomenon is discovered, namely, that except for H(+), the graphs for the other ions on extrapolation to lower temperatures have a common intersection point, T(0)(1/2), with the abscissa corresponding to T(0) = 243.4 K, i.e., -30 degrees C. This seems to indicate the presence of a virtual phase transition at about -30 degrees C, foreboding itself at higher temperatures. Below this temperature the supercooled water does not allow ions to migrate. Also, diffusion of solutes is found to cease, and dissociation constants drop to zero. The values of many physical properties of water appear also to approach zero at -30 degrees C, viz. the self-diffusion coefficient, reciprocal dielectric relaxation time, and solubilities of sparingly soluble salts. From data on the fluidity (reciprocal viscosity) and self-ionization constant it follows that the transition temperature of supercooled D(2)O is 9 degrees higher than of H(2)O. From the nearly quadratic shape of the several temperature dependencies it is inferred that the phase transition in question possibly is of some higher order. Implications for the transport number of protons to be expected in supercooled water are finally discussed.