An experimental study of the relative critical-magnetic-field curves of three isotopically enriched and one natural sample of osmium has been carried out between 0.08 and 0.675°K. Temperatures below 1°K were produced by the magnetic cooling method and superconductivity was detected by means of a dc mutual-inductance method. Data were obtained by first cooling, in the same experiment, three osmium samples to a temperature of approximately 0.08°K and then observing, independently, their differential magnetic susceptibilities, as the samples slowly warmed up in the presence of an externally applied magnetic field. In this manner, one obtains differences in the transition temperatures (∆Tc) as a function of the critical magnetic field Hc. These data show that the critical-magnetic-field curves of the four samples are indeed distinct. Deviations of the critical-magnetic-field curves from the parabolic law are consistent with the Bardeen, Cooper, Schrieffer (BCS) theory of superconductivity. For the natural sample the quantity HcH0-[1-(TT0)2] attains a maximum value of -0.037 at a value for (TT0)2 of 0.52. Here Hc is the measured critical magnetic field, H0(=80.4 G) is the critical magnetic field at absolute zero, and T0(=0.671°K) is the transition temperature in zero magnetic field. The other samples exhibited deviations from the appropriate parabolas which range from 0.037 to 0.041. The values of γ, the electronic specific heat coefficient for the four samples, are found to lie in the range of (4.77+/-0.07)×10-4 cal/mole-deg2. Magnetically induced superconducting to normal-state transitions indicated that all of these samples displayed good "Meissner" properties. In view of this and the fact that the sample with the heavier mean mass M̄ possesses the lower critical-magneticfield curve, we conclude that an isotope effect does exist in Os. The data suggest that the effect be represented by the relationship T0~M̄-0.21.