Molecular dipole moments, charges, and difference electron densities have been calculated from Hartree-Fock calculations for each individual molecule along geometry-optimized water chains with n=1,...,12,infinity. The complementarity of the three properties is discussed. Although yielding rather different aspects of the polarization they all show that the polarization converges much faster for the molecules at the ends of the chains compared to the middle. Moreover, the middle molecules in the long chains acquire an induced dipole moment about twice as large as those at the ends. An electron charge transfer along the chains leaves only the central water molecules neutral, and creates an additional contribution to the net system dipole, a phenomenon which should arise also in small real finite clusters and chains.