The thermodynamically reversible phase transition of a metal into a superconducting state has a critical field curve, which can be represented by: The difference in the specific heat of the two phases is given by These equations predict a first order phase transition in a magnetic field and a second order transition in zero field. A singularity in the specific heat at Tc, similar to the singularity for liquid heldum at the -point due to the onset of long range order, would mean that A system of measuring the magnetization of a superconductor in an applied field has been constructed and utilized to determine the critical field curve near The system consists of a closed superconducting loop enclosing the sample, a nulling solenoid and a magnetometer probe; situated in a region of low nagnetic fields. Magnetization curves have been obtained for a sample of 99.999% pure indium over a temperature range of 3.365°K to 3.398°K. The reversibility of the curves was found to depend on the rate at which the magnetic field was applied. The critical temperature was found to be 3.409°K. The slope (dHc/dT) for measurements made was -150 oe./°K. The agreement between values found from this experiment and previous work was reasonable. There was no indication of a singularity in the temperature range investigated. [see PDF for formulas]