  The globular cluster M15 is unique in its display of star-to-star variations
in the neutron-capture elements. Comprehensive abundance surveys have been
previously conducted for handfuls of M15 red giant branch (RGB) and red
horizontal branch (RHB) stars. No attempt has been made to perform a single,
self-consistent analysis of these stars, which exhibit a wide range in
atmospheric parameters. In the current effort, a new comparative abundance
derivation is presented for three RGB and six RHB members of the cluster. The
analysis employs an updated version of the line transfer code MOOG, which now
appropriately treats coherent, isotropic scattering. The apparent discrepancy
in the previously reported values for the metallicity of M15 RGB and RHB stars
is addressed and a resolute disparity of $\Delta(RHB-RGB) \approx 0.1$ dex in
the iron abundance was found. The anti-correlative behavior of the light
neutron capture elements (Sr, Y, Zr) is clearly demonstrated with both Ba and
Eu, standard markers of the {\it s}- and {\it r}-process, respectively. No
conclusive detection of Pb was made in the RGB targets. Consequently for the
M15 cluster, this suggests that the main component of the {\it s}-process has
made a negligible contribution to those elements normally dominated by this
process in solar system material. Additionally for the M15 sample, a large Eu
abundance spread is confirmed, which is comparable to that of the halo field at
the same metallicity. These abundance results are considered in the discussion
of the chemical inhomogeneity and nucleosynthetic history of M15.
