The positron and extent of the region in which electrons with energies less than 40-keV are durably trapped in the nightside magnetosphere is found for both normal and disturbed geomagnetic conditions by using data from the P78-2 (SCATHA) satellite. The region of the magnetosphere from 5.3 to 7.9 RE was studied. In this region neither solar-magnetic nor geocentric-solar magnetospheric coordinates order the data satisfactorily. A new coordinate systems called composite coordinates is introduced. It takes account of the fact that this region of the magnetosphere is strongly influenced by both the earth's ddipole field and the direction of the solar wind. In composite coordinates when Kp≤4+, 40-keV electron fluxes were almost continuously present in a region centered on the equatorial palne and 1.2 RE in half width. At larger composite coordinate latitudes there is another region more than 1 RE thick within which 40-keV electron fluxes routinely appear and disappear on time scales of one hour as the trapping boundary actively moves over the satellite. We have no evidence that SCATHA over entered the tail lobes where no particles are trapped. When Kp≥6- the region in which 40-keV electron fluxes were always present moved earthward and/or thinned but remained ordered in composite coordinates. We suggest that the new coordinate system will be useful for ordering other data sets taken in this region of the magnetosphere.