  New experimental absolute atomic transition probabilities are reported for
203 lines of V II. Branching fractions are measured from spectra recorded using
a Fourier transform spectrometer and an echelle spectrometer. The branching
fractions are normalized with radiative lifetime measurements to determine the
new transition probabilities. Generally good agreement is found between this
work and previously reported V II transition probabilities. Use of two
spectrometers, independent radiometric calibration methods, and independent
data analysis routines enables a reduction in systematic uncertainties, in
particular those due to optical depth errors. In addition, new hyperfine
structure constants are measured for selected levels by least squares fitting
line profiles in the FTS spectra. The new V II data are applied to high
resolution visible and UV spectra of the Sun and metal-poor star HD 84937 to
determine new, more accurate V abundances. Lines covering a range of wavelength
and excitation potential are used to search for non-LTE effects. Very good
agreement is found between our new solar photospheric V abundance, log
{\epsilon}(V) = 3.95 from 15 V II lines, and the solar-system meteoritic value.
In HD 84937, we derive [V/H] = -2.08 from 68 lines, leading to a value of
[V/Fe] = 0.24.
