Improved V I Log(gf) Values and Abundance Determinations in the Photospheres of the Sun and Metal-Poor Star HD 84937

New emission branching fraction measurements for 836 lines of the first spectrum of vanadium (V I) are determined from hollow cathode lamp spectra recorded with the National Solar Observatory 1 m Fourier transform spectrometer (FTS) and a high-resolution echelle spectrometer. The branching fractions are combined with recently published radiative lifetimes from laser-induced fluorescence measurements to determine accurate absolute atomic transition probabilities for the 836 lines. The FTS data are also used to extract new hyperfine structure A coefficients for 26 levels of neutral vanadium. These new laboratory data are applied to determine the V abundance in the Sun and metal-poor star HD 84937, yielding log epsilon(V) = 3.956 +/- 0.004 (sigma = 0.037) based on 93 V I lines and log epsilon(V) = 1.89 +/- 0.03 (sigma = 0.07) based on nine Vi lines, respectively, using the Holweger-Muller 1D model. These new V I abundance values for the Sun and HD 84937 agree well with our earlier determinations based upon V II.