A new formulation of the Wal¿n test [Wal¿n, 1944> to locate rotational discontinuities (RD) or Alfv¿n wave trains is constructed that is more appropriate for use within and across the current-carrying layers of these structures. This generalized test is to be distinguished from the traditional rigorous jump condition that is only appropriate for connecting asymptotic, current free states on either side of the discontinuity or wave train. The generalized test is most simply formulated as a vector difference equation relating changes in the electron flow velocity vector and changes of the magnetic field vector, ΔUe(x)=&agr;eΔB(x) with a prescribed scalar constant of proportionality. For an electron proton plasma this paper shows that &agr;e is precisely the same constant of the jump condition that has long been in use. Small corrections to &agr;e are computed for minor helium populations. This new formulation is used with Polar plasma, E, and B measurements to search for rotational discontinuities at the magnetopause. Of the 44 cases where electrons gave acceptable theoretical correlations and coefficients &agr;e predicted by the theory, nearly 95% of the simultaneous ion fits gave corresponding values of &agr;i that were smaller in magnitude than implied by simple ideal MHD jump conditions. Possible explanations for this discrepancy are discussed. In addition, these data have been used to provide the first empirical evidence of the importance of the electron pressure gradient in these RD current layers and represent the first direct determination of the sizes EnHT≃0.3--5 mV/m of the deHoffmann-Teller electric field in RD current layers at the magnetopause. ¿ 1999 American Geophysical Union