  Starting with a finite $k$-mesh version of a well-known equation by Blount,
we show how various definitions proposed for the polarization of long chains
are related. Expressions used for infinite periodic chains in the 'modern
theory of polarization' are thereby obtained along with a new single particle
formulation. Separate intracellular and intercellular contributions to the
polarization are identified and, in application to infinite chains, the
traditional sawtooth definition is found to be missing the latter. For a finite
open chain the dipole moment depends upon how the chain is terminated, but the
intracellular and intercellular polarization do not. All of these results are
illustrated through calculations with a simple H\"uckel-like model.
