  We investigate the scaling behaviour of gauge-ball masses and static
potential in the pure U(1) lattice gauge theory on toroidal lattices. An
extended gauge field action $-\sum_P(\beta \cos\Theta_P + \gamma
\cos2\Theta_P)$ is used with $\gamma= -0.2$ and -0.5. Gauge-ball correlation
functions with all possible lattice quantum numbers are calculated. Most
gauge-ball masses scale with the non-Gaussian exponent $\nu_{ng}\approx 0.36$.
The $A_1^{++}$ gauge-ball mass scales with the Gaussian value $\nu_{g} \approx
0.5$ in the investigated range of correlation lengths. The static potential is
examined with Sommer's method. The long range part scales consistently with
$\nu_{ng}$ but the short range part tends to yield smaller values of $\nu$. The
$\beta$-function, having a UV stable zero, is obtained from the running
coupling. These results hold for both $\gamma$ values, supporting universality.
Consequences for the continuum limit of the theory are discussed.
