  We derive the physical properties at the base of the jet from DG Tau both
along and across the flow and as a function of velocity. We analysed seven
optical spectra of the DG Tau jet, taken with the Hubble Space Telescope
Imaging Spectrograph. The spectra were obtained by placing a long-slit parallel
to the jet axis and stepping it across the jet width. The resulting
position-velocity diagrams in optical forbidden emission lines allowed access
to plasma conditions via calculation of emission line ratios.
  We find at the base of the jet high electron density, $n_e \sim $ 10$^5$, and
very low ionisation, $x_e \sim 0.02-0.05$, which combine to give a total
density up to $n_H \sim $ 3 10$^6$. This analysis confirms previous reports of
variations in plasma parameters along the jet, (i.e. decrease in density by
several orders of magnitude, increase of $x_e$ from 0.05 to a plateau at 0.7
downstream at 2$''$ from the star). Furthermore, a spatial coincidence is
revealed between sharp gradients in the total density and supersonic velocity
jumps. This strongly suggests that the emission is caused by shock excitation.
The position-velocity diagrams indicate the presence of both fast accelerating
gas and slower, less collimated material. We derive the mass outflow rate,
$\dot{M}_j$, in the blue-shifted lobe in different velocity channels, that
contribute to a total of $\dot{M}_j \sim$ 8 $\pm$ 4 10$^{-9}$ M$_\odot$
yr$^{-1}$. We estimate that a symmetric bipolar jet would transport at the low
and intermediate velocities probed by rotation measurements, an angular
momentum flux of $\dot{L}_j \sim$ 2.9 $\pm$ 1.5 10$^{-6}$ M$_\odot$ yr$^{-1}$
AU km s$^{-1}$.
  The derived properties of the DG Tau jet are demonstrated to be consistent
with magneto-centrifugal theory. However, non-stationary modelling is required
in order to explain all of the features revealed at high resolution.
