Magnetometer data acquired as the Galileo Orbiter apoapsis rotated from dawn to dusk across the magnetotail of the Jovian magnetosphere between late 1995 and the end of May 2000 are used to characterize the magnetic field and the distribution of magnetic pressure in the inner part of the Jovian magnetotail. The distances probed extend to ~150 RJ or roughly 3 times the distance to the nose of the magnetopause, analogous to distances within 30 RE in the magnetotail of Earth. The magnetic pressure in the center of the plasma sheet is typically almost an order of magnitude smaller than the lobe pressure, which therefore is roughly equal to the peak thermal plasma pressure in the plasma sheet. The lobe magnetic pressure decrease with radial distance can be described roughly as a power law with an exponent of -2.74, and the lobe field magnitude decreases with distance to the -1.37. In comparing radial variations of the lobe magnetic fields of Jupiter and Earth we argue that rescaled lengths based on nominal magnetopause standoff distances and rescaled field magnitudes based on planetary dipole field strengths are required. Comparison of rescaled fits suggest that the power law dependence on radial distance should not be extrapolated beyond 150 RJ and that beyond this distance the trend may become asymptotically constant. Systematic asymmetries of the field structure and magnetic pressure across the midnight meridian in the region beyond 25 RJ downtail are notable, with the flux tubes being less stretched (with larger equatorial Bz) near dusk than near dawn. The lobe pressure attains its minimum value in the dusk sector where the plasma sheet magnetic pressure maximizes. We argue that only a small fraction of the magnetic flux remaining in the lobes in the magnetotail beyond 100 RJ closes across the plasma sheet, but the structure of open and closed flux tubes may be nonuniform across the tail. We discuss briefly mechanisms that may lead to the observed asymmetry.