Measurements were made of the critical magnetic field for the transition from the superconducting to the normal state in polycrystalline rods of the substitutional solid solution In-Hg, containing 0-7 atomic percent Hg. The treatment given these alloys was designed to assure homogeneity in composition in which case the transitions to the normal state were found to be similar to those for pure elemental superconductors. It was, moreover, possible to distinguish between properties that are characteristic of the ideal alloy system and properties which arise from structure within the specimen. Tc, the transition temperature at zero field, was measured as a function of composition and was found initially to decrease (up to a concentration of 1.75 atomic percent Hg) after which it began to increase with added Hg concentration. The width of the transition to the normal state, as measured by the variation of specimen resistance in a longitudinal magnetic field, was found to show a regular dependence upon composition, and also reached a minimum value at 1.75 atomic percent Hg. The superconducting properties of pure indium were measured and used as a standard. For indium it was found that: Tc=3.407+/-0.002°K H0=293+/-2% oersted and (dHcdT)|Tc=-155.5+/-3% oersted/°K.