A comparison of He3 and He4 vapor pressures, (P 3, P 4), has been made in an apparatus designed to reduce the number and magnitude of corrections associated with the refluxing film in the He4 pressure sensing tube and the attached bulb. The critical pressure of He3 has been redetermined to be at 873.0 ±1.5 mm Hg at 0° C and standard gravity; the corresponding temperature as measured by a He4 thermometer is 3.3240±0.0018° K on the 1958 He4 scale. These (P 3, P 4) comparisons and the 1958 He4 scale are the basis of the 1962 He3 scale of temperatures derived and evaluated in the papers following this one. Empirical interpolation equations containing only P 3 and P 4 are described by means of which existing P 4 measurements may be converted to an equivalent P 3. A comparison has been made between this interpolation and a conversion in which the 1958 He4 and 1962 He3 scales are used as parameters. Deviations between the two procedures are within the estimated errors of the (P 3, P 4) measurements. In subsidiary experiments on techniques for He4 thermometry a typical vapor pressure bulb arrangement was tested. It is shown that the refluxing film introduces a heat flux, Q̇, and a resulting Kapitza temperature drop, ΔT k , between the He ii and its container, which may amount to many millidegrees. The feasibility of calculating ΔT K for a particular He4 vapor pressure bulb was studied. The necessity of measuring ΔT k /Q f at least once in situ is pointed out. In addition, it is necessary to redetermine the film flow rate periodically at the same time that He4 vapor pressure measurements are being made.