  We have carried out a detailed abundance analysis for 21 elements in a sample
of 25 stars with a wide range in luminosity from luminous giants to stars near
the main sequence turnoff in the globular cluster M13 and in a sample of 13
stars distributed from the tip to the base of the RGB in the GC M3. Most
elements, including Fe, show no trend with Teff, and low scatter around the
mean between the top of the RGB and near the main sequence turnoff. We have
detected an anti-correlation between O and Na abundances, observed previously
among the most luminous RGB stars in both of these clusters, in both M3 and in
M13 over the full range of luminosity of our samples, i.e. in the case of M13
to near the main sequence turnoff. M13 shows a larger range in both O and Na
abundance than does M3 at all luminosities, in particular having a few stars at
its RGB tip with unusually strongly depleted O. Although CN burning must be
occurring in both M3 and in M13, and ON burning is required for M13, we combine
our new O abundances with published C and N abundances to confirm with quite
high precision that the sum of C+N+O is constant near the tip of the giant
branch, and we extend this down to the bump in the luminosity function. Star
I-5 in M13 has large excesses of Y and of Ba, with no strong enhancement of Eu,
suggesting an s-process event contributed. The mean abundance ratios for M3 and
for M13 are identical to within the errors. The abundance ratios for 13
Galactic GCs with recent detailed abundance analyses are compared to those of
published large surveys of metal-poor halo field stars. For most elements, the
agreement is very good, suggesting a common chemical history for the halo field
and cluster stars.
