The profile of the helium resonance line at &lgr; 584 ¿ from the full solar disk has been investigated through analysis of data obtained by sounding rockets flown in 1977 and in 1980. The instrument, a helium-filled spectrometer, made use of a curve-of-growth technique. In the analysis, the solar He I line profile was represented by a Gaussian distribution. Between 6.5 and 13% of the Gaussian core area was found to be missing to self-reversal. Data from our 1980 experiment gave a line width of 101¿10 m¿ (full width at half maximum). The 1977 line width, obtained with less experimental reliability, was 128¿20 m¿ (full width at half maximum). Results obtained in a similar experiment in 1974, corrected for background radiation and for solar line self-reversal, gave a revised 1974 line width of 103 m¿ (full width at half maximum). While the measured line width did vary, a comparison of the 1974, 1977, and 1980 data showed no consistent relationship between the measured widths and solar activity. An observation of the solar He I 537-¿ emissions during the 1980 sounding rocket flight provided a measurement of that line width, giving a value of 148¿27 m¿ (full width at half maximum).