The J-H-T critical surface has been measured at temperatures near 4.2 K for diffusion-processed Nb
3Sn and for Nb+60 wt % Ti superconducting alloys. The apparatus used for these measurements consists of a split Nb
3Sn superconducting solenoid capable of fields up to 65 kOe, a 4-probe potentiometric sample holder capable of carrying currents up to 1000 A, and an enclosed cryostat which allowed one to vary the temperature of the coil and the sample from 3.4 to 4.8 K by varying the pressure over the liquid helium. Data are presented for the critical current density J
cand for the temperature dependence of critical current density (

) observed at 4.2 K. From these data, the values for the two stability parameters of interest, the fractional temperature dependence of critical current density [

] and the stability parameter
![J_{c}^{2} [-(1/J_{c})(\\partial J_{c}/\\partial T)]](/images/tex/8498.gif)
, were calculated and are presented along with an estimate of the wire diameter required for adiabatic stabilization.