  In the pure U(1) lattice gauge theory with the Villain action we find that
the monopole mass in the Coulomb phase and the monopole condensate in the
confinement phase scale according to simple power laws. This holds outside the
coupling region in which on finite toroidal lattices the metastability
phenomena occur. A natural explanation of the observed accuracy of the scaling
behaviour would be the second order of the phase transition between both phases
in the general space of couplings not far away from the Villain action.
