We have computed the convection potential drop across the polar cap from data obtained on high-inclination low-altitude satellites (AE--C, AE--D, S3--3) and correlated these potential measurements with various combinations of parameters measured simultaneously in the upstream solar wind. These combinations of solar wind parameters consist of predictions based on magnetic merging theory and suggestions based on earlier empirical work. We find that the bulk of the potential drop, and its variation with interplanetary magnetic field (IMF) parameters, are successfully predicted by merging theory (to the accuracy with which they can presently be measured), but that a significant 'background' potential drop (~35 kV) does not depend on IMF parameters and may thus be attributed to an unknown process other than merging. Our results indicate that small values of the IMF are amplified by a factor of 5--10 at the dayside magnetopause as a combined effect of bow shock compression and the Zwan--Wolf depletion layer effect; correlations between IMF parameters and the polar cap potential drop are dramatically improved when this amplification is taken into account. The potential drop is better correlated with IMF parameters than with geomagnetic activity indices, presumably because the latter are affected by nonlinear reponses of the magnetosphere to the polar cap input.