  We consider a one-dimensional Josephson junction array, in the regime where
the junction charging energy is much greater than the charging energy of the
superconducting islands. In this regime we critically reexamine the continuum
limit description and establish the relationship between parameters of the
array and the ones of the resulting sine-Gordon model. The later model is
formulated in terms of quasi-charge. We argue that despite arguments to the
contrary in the literature, such quasi-charge sine-Gordon description remains
valid in the vicinity of the phase transition between the insulating and the
superconducting phases. We also discuss the effects of random background
charges, which are always present in experimental realizations of such arrays.
