The Rankine-Hugoniot equations for MHD shocks are generalized by the addition of a term to the energy conservation equation representing a nonzero heat flow in the plasma in the neighborhood of the shock. This generalization is found to be compatible with the assumption of infinite electrical conductivity, E+(V¿B)/c=0. The effects of plasma waves in this treatment are of the order of the reciprocal Alfv¿nic Mach number squared and hence are neglected. The effect of alpha particles in the solar wind is discussed. Seven crossings of the earth's bow shock by Explorer 35 in lunar orbit are analyzed. Sufficient data are available so that the determination of a dimensionless parameter &psgr; characterizing the heat flow difference across the bow shock is possible. The values of &psgr; indicate energy flux densities due to heat flow which are a nonnegligible fraction of the total energy flux. Two possible interpretations of &psgr; are discussed.