  We consider, within BCS weak coupling theory, the instability of a
$d_{x^2-y^2}$-wave superconductor to a state of mixed symmetry $d+iq$,
$q=d_{xy},s$. In zero magnetic field we show that there is a large and
physically reasonable range of interaction strengths for which a pure
$d_{x^2-y^2}$ state is stable down to T=0. In this case a magnetic field,
assumed to couple to quasiparticles via their Doppler shifts in the vortex
superflow field, is shown to induce a phase transition at $T=T_c^*\sim
\sqrt{H}$. Below $T_c^*$, the density of states remains gapless but its field
dependence is substantially supressed. The theory explains many features of
recent striking thermal conductivity measurements on BSCCO by Krishana et al.
