Confinement and monopole condensation: some properties of the disorder parameter

We demonstrate that the disorder parameter $<\mu>$ to detect dual superconductivity in the confining phase of QCD is the v.e.v. of a magnetically charged, Dirac like, gauge invariant operator $\mu$. We also show that the abelian projection on the lattice is determined up to terms O(a^2) (a = lattice spacing).