The proton spin-lattice relaxation time, T1, for hydrogen gas has been measured, using pulse techniques, as a function of gas density, ρ, temperature, and orthohydrogen concentration. The maximum density investigated was of order 900 amagats and the temperature range extended from 20 to 400°K. The radial dependence of the anisotropic part of the intermolecular potential due to the interaction of two hydrogen molecules has been deduced from a comparison of the temperature dependence of T1ρ in the dilute gas above 80°K with some calculations based on the theory of Oppenheim and Bloom. It is, approximately, an inverse thirteenth power of the intermolecular separation for the ortho-para interaction and an inverse sixth power for the ortho-ortho interaction. The results above 80°K are found to be sensitive to quantum-mechanical diffraction effects, in the manner suggested by Lipsicas and Bloom, and the temperature independence of T1ρ for dilute normal hydrogen gas above 80°K is shown to result from the different radial dependence of the ortho-ortho and ortho-para interactions. The results for T1 in the very dense gas appear to be consistent with the idea of a liquid-like assembly of molecules with predominantly short-range inter-molecular interactions. Calculations are not available at the present time for comparison with any of the results below about 80°K, which are expected to be strongly influenced by quantum-mechanical effects. Some qualitative discussion is given of the dilute and dense gas results in this temperature range. At very low orthohydrogen concentrations, an unusual density dependence of T1 is observed in the temperature range 34-42°K. It appears that this effect is connected with the critical temperature phenomena, but it is not understood at present.