  A model independent expression for the electromagnetic corrections to a
phenomenological hadronic pion-nucleon scattering length, extracted from pionic
hydrogen, is obtained. In a non-relativistic approach and using an extended
charge distribution, these corrections are derived up to terms of order
(alpha)**2 log(alpha) in the limit of a short-range hadronic interaction. We
infer a charged pion-proton scattering length of 0.0870(5) in units of inverse
pion mass, which gives for the charged pion-proton-neutron coupling, through
the GMO relation, a value of 14.04(17).
