  The phase variation of the superconducting gap over the (normal) Fermi
surface of the high-temperature superconductors remains a significant
unresolved question. Is the phase of the gap constant, does it change sign, or
is it perhaps complex? A detailed answer to this question would provide
important constraints on various pairing mechanisms. Here we propose a new
method for measuring the relative gap PHASE on the Fermi surface which is
direct, is angle-resolved, and probes the bulk. The required experiments
involve measuring phonon linewidths in the normal and superconducting state,
with resolution available in current facilities. We primarily address the
La_1.85Sr_.15CuO_4 material, but also propose a more detailed study of a
specific phonon in Bi_2Sr_2CaCu_2O_8.
