Magnetic field measurements made over a 21-hour interval during the Mariner 10 encounter with Venus were used to study the downstream region of the solar wind--Venus interaction over a distance of ?100Rg (Venus radii). Mariner 10 encountered Venus on February 5, 1974, with closest approach at 1702 UT. For most of the day before closest approach the spacecraft was located in sheathlike region which was apparently bounded by the planet's bow shock on the outer side and either a planetary 'wake boundary' or a transient boundarylike feature on the inner side. The spacecraft made multiple encounters with the wakelike boundary during the 21-hour interval with an increasing frequency as it approached the planet. Each pass into the wake boundary from the sheath region was consistently characterized by a slight decrease in magnetic field magnitude, a marked increase in the frequency and amplitude of field fluctuations, and a systematic clockwise rotation of the field direction when viewed from above the plane of Venus' orbit. These boundary crossings were not accompanied strictly by hydromagnetic directional discontinuities, however, but occasionally (~1/3 of the crossings) such a discontinuity was sufficiently close to the crossing zone to be considered part of the boundary transition. There were a significantly larger number of discontinuities in the overall 21-hour period than were observed on average during other comparable periods both before and after encounter. A simple large-scale draped field model in the sense of a magnetic 'comet tail' was found not to hold for the downstream region. The sporadic observation of the wake during the near-encounter period may have been controlled by changes in the direction of the interplanetary field.