  We attempt to rehabilitate a sum rule (proposed long ago by Bernab\'eu and
Tarrach) which relates the electric polarizability of a particle to the total
photoabsorption of quasi-real longitudinally polarized photons by that
particle. We discuss its perturbative verification in QED, which is largely
responsible for the scepticism about its validity. The failure of the QED test
can be understood via the Sugawara-Kanazawa theorem and is due to the
non-vanishing contour contribution in the pertinent dispersion relation. We
show another example where this contribution is absent and the perturbative
test works exactly. On the empirical side, we show that the sum rule gives a
reasonable estimate of the $\pi N$-channel contribution to the proton electric
polarizability. If this sum rule is valid indeed, there should be a sum rule
for the so-called ``subtraction function'' entering the data-driven
calculations of the polarizability effects in the Lamb shift. We have written
down a possible sum rule for the subtraction function and verified it in a
perturbative calculation.
