  Recent theories of the NMR in the CuO superconductors are based on a
spin-singlet $d_{x^2-y^2}$ order parameter. Since this state has nodal lines on
the Fermi surface, nonlinear effects associated with low-energy quasiparticles
become important, particularly at low temperatures. We show that the
field-dependence of the supercurrent, below the nucleation field for vortices,
can be used to locate the positions of the nodal lines of an unconventional gap
in momentum space, and hence test the proposed $d_{x^2-y^2}$ state.
