Magnetic field vector measurements are always ambiguous, that is, two or more field vectors are solutions of the observed polarisation. The aim of the present paper is to solve the ambiguity by comparing the ambiguous field vectors obtained in the same prominence observed on two consecutive days. The effect of the solar rotation is to modify the scattering angle of the prominence radiation, which modifies the symmetry of the ambiguous solutions. This method, which is a kind of tomography, was successfully applied in the past to the average magnetic field vector of 20 prominences observed at the Pic du Midi. The aim of the present paper is to apply this method to a prominence observed with spatial resolution at the THEMIS telescope (European site at Izana, Tenerife Island). The magnetic field vector is measured by interpretation of the Hanle effect observed in the He I D3 5875.6 A line, within the horizontal field vector hypothesis for simplicity. The ambiguity is first solved by comparing the two pairs of solutions obtained for a big pixel determined by averaging the observed Stokes parameters in a large region at the prominence centre. Each pixel is then disambiguated by selecting the closest solution in a propagation from the prominence centre to the prominence boundary. The results previously obtained on averaged prominences are all recovered. The polarity is found to be inverse with a small angle of about -21{deg} between the magnetic field vector and the long axis of the filament. The magnetic field strength of about 6 G is found to slightly increase with height, as previously observed. The new result is the observed decrease with height, of the absolute value of the angle between the magnetic field vector and the long axis of the filament. This result is in excellent agreement with prominence magnetohydrodynamical models.
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