Using the Cottingham formula, we give an estimate of the electromagnet
ic mass splitting of pseudoscalar heavy mesons in the beauty and charm
sector. We include in the dispersion relation the Born term, the 1(-)
resonance and the positive parity 1(+) resonance. We also evaluate th
e contribution to the mass difference from the isospin breaking quark
mass differences. Our results: m(B)+-m(B)o= -0.83 +/- 0.34 MeV and m(D
)+-m(D)0 = + 4.33 +/- 0.37 MeV, are in agreement with the experimental
measurements: m(B)+-m(B)o= -0.35 +/- 0.29 MeV and m(D)+-m(D)o = + 4.7
8 +/- 0.10 MeV. We also compute the mass differences in the infinite h
eavy quark mass limit, which show small deviations from the finite mas
s results for the B case and 30% effects in the charm case. (C) 1998 E
lsevier Science B.V.