High-resolution global images of Earth's auroras in the visible emissions of atomic oxygen at 557.7 nm with a camera on board the Polar spacecraft were used to determine the magnetic latitude of the auroral arc which brightens at the onset of a substorm. Six events were analyzed: an intensification and an onset on December 17, 1997, three substorms on January 6, 1998, and a substorm on March 1, 1999. The Tsyganenko [1989> model for the global magnetic field was used to map the field lines threading the center of the auroral arc to equatorial distances. During the period of relative magnetic quiescence on December 17 the equatorial distances were ~9 RE. During the magnetically disturbed periods of January 6 and March 1 the magnetic field lines for the auroral onset brightenings were mapped to equatorial distances in the range of 5--7 RE, and thus in the region of the extraterrestrial ring current. The equatorial position of the field lines was independently verified for the substorm on March 1 by observing the atmospheric footprint of proton precipitation from the ring current. This footprint was seen in the emissions of atomic hydrogen at 656.3 nm. The onset arc was located near the earthward edge of the ring current at magnetic shell parameter L=4 RE and within 1 RE of the equatorial position computed with the global magnetic field model. The equatorial distance of the elusive substorm onset is important in establishing plasma parameters for quantitative evaluation of candidate mechanisms for the explosive instability that initiates substorsm. ¿ 2000 American Geophysical Union