Time-resolved eclipse spectroscopy of the nova-like variable UX UMa obtained with the HST/FOS on 1994 August and November is analyzed with eclipse mapping techniques to produce spatially resolved spectra of its accretion disc and gas stream as a function of distance from disc centre. The inner accretion disc is characterized by a blue continuum filled with absorption bands and lines which cross over to emission with increasing disc radius, similar to that reported by Rutten et al (1994) at optical wavelengths. The comparison of spatially resolved spectra at different azimuths reveals a significant asymmetry in the disc emission at UV wavelengths, with the disc side closest to the secondary star showing pronounced absorption by an `iron curtain and a Balmer jump in absorption. These results suggest the existence of an absorbing ring of cold gas whose density and/or vertical scale increase with disc radius. The spectrum of the infalling gas stream is noticeably different from the disc spectrum at the same radius suggesting that gas overflows through the impact point at disc rim and continues along the stream trajectory, producing distinct emission down to 0.1 RL1. The radial temperature profiles of the continuum maps are well described by a steady-state disc model in the inner and intermediate disc regions. There is evidence of an increase in the mass accretion rate from August to November (from Mdot= 10^{-8.3 +/- 0.1} to 10^{-8.1 +/- 0.1} Msun/yr), in accordance with the observed increase in brightness. Since the UX UMa disc seems to be in a high mass accretion, high-viscosity regime in both epochs, this result suggests that the mass transfer rate of UX UMa varies substantially (~ 50 per cent) on time scales of a few months.
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