  We use the Cottingham method to calculate the pion and kaon electromagnetic
mass differences with as few model dependent inputs as possible. The
constraints of chiral symmetry at low energy, QCD at high energy and
experimental data in between are used in the dispersion relation. We find
excellent agreement with experiment for the pion mass difference. The kaon mass
difference exhibits a strong violation of the lowest order prediction of
Dashen's theorem, in qualitative agreement with several other recent
calculations.
