  We continue numerical studies of the spectrum of the pure U(1) lattice gauge
theory in the confinement phase, initiated in our previous work. Using the
extended Wilson action $ S = -\sum_P [\beta \cos(\Theta_P) + \gamma
\cos(2\Theta_P)] $ we address the question of universality of the phase
transition line in the ($\beta,\gamma$) plane between the confinement and the
Coulomb phases. Our present results at $\gamma= -0.5$ for the gauge-ball
spectrum are fully consistent with the previous results obtained at $\gamma=
-0.2$. Again, two different correlation length exponents, $\nu_{ng} = 0.35(3)$
and $\nu_{g} = 0.49(7)$, are obtained in different channels. We also confirm
the stability of the values of these exponents with respect to the variation of
the distance from the critical point at which they are determined. These
results further demonstrate universal critical behaviour of the model at least
up to correlation lengths of 4 lattice spacings when the phase transition is
approached in some interval at $\gamma\leq -0.2$.
