  At altitudes of about 1.05 solar radii or more, the corona above quiet solar
regions becomes essentially isothermal. This obviates many of the difficulties
associated with the inverse problem of determining emission measure
distributions, and allows for fairly straightforward relative element abundance
measurements. We present new values for the He abundance. The first is based on
a reanalysis of the He/O ratio studied previously using data acquired by SUMER.
A more thorough evaluation of the atomic physics for He II, including a
detailed treatment of radiative recombination, increases the predicted emission
in the He II Balmer series compared to earlier analyses. We use a recently
revised value of the O abundance to derive an He/H abundance ratio of 0.038,
(mass fraction, Y=0.13), with an error of ~17% coming mainly from the O
abundance uncertainty. We demonstrate that this result may be affected by
gravitational settling of O relative to He. We also derive an abundance for He
by direct comparison to emission lines of the H I Lyman series, with the result
He/H =0.052 +/- 0.005 (Y=0.17), a value similar to He abundances determined in
the slow speed solar wind.
