  In this note, we analyze the classical magneto-static approach to the theory
of type I superconductors, and a Debye source representation that can be used
numerically to solve the resultant equations. We also prove that one of the
fields, $\boldsymbol{J}^-$, found within the superconductor via the London
equations, is the physical current in that the outgoing part of the magnetic
field is given as the Biot-Savart integral of $\boldsymbol{J}^{-}$. Finally, we
compute the static currents for moderate values of London penetration depth,
$\lambda_L,$ for a sphere, a stellarator-like geometry and a two-holed torus.
