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tokens: represents an effect of the detailed distribution of the magnetic field over the visible hemisphere of the MWD as viewed during our second observation. It is very interesting to consider our data for WD 1703−267 in the light of our earlier effort (see Sect. 3 ) to calibrate the order-of-magnitude relationship of Eq. ( 1 ). For this star, we have accurate values of both ⟨| B |⟩ and ⟨ B z ⟩, and judging from the simple V ∕ I profiles through the Balmer lines, a relatively simple magnetic field structure. With ⟨ B z ⟩≈ 2.75 MG in our second observation, we predict from our calibration of the coefficient of Eq. ( 3 ) that there should be continuum circular polarisation of V ∕ I ≈ 0.2%. Rebinning our data over 16 pixels to improve the S/N, we find that a weak continuum circular polarisation is indeed present at the level of V ∕ I ≈ 0.25% (see Fig. 4 ). Furthermore, the relationship between the sign of the continuum polarisation and that of V ∕ I in the blue σ components of the Balmer lines is the same as in G99-47. This result reinforces confidence in the use of broad-band circular polarisation as a tool for measuring ⟨ B z ⟩, and in the general accuracy of our calibration. 5.3 DA star WD 0810−353 = UPM J0812−3529 This star was identified as a WD within the 20 pc volume by the USNO parallax programme ( Finch et al. 2018 ), and is included in the list of WDs within the 20 pc volume established by Hollands et al. (2018) on the basis of the Data Release 2 dataset ( Gaia Collaboration 2018 ). For the reasons discussed in connection with WD 1703−267, we provide an (unofficial) Villanova WD number for the star, which we use throughout. Physical parameters based on Gaia astrometry and photometry ( Hollands et al. 2018 ; Gentile Fusillo et al. 2019 ) are provided in Table 1 . The spectral class is unknown, asno previous spectra of the star appear to have been taken. As the effective temperature is high enough that we would expect H β to be observable if the atmosphere of this object is H-rich, while possible metal lines around 4000 Å would be of great interest, we obtained circular spectropolarimetry of this star with the 600B and 1200B grisms. WD 0810−353 is bright enough that we were able to obtain quite high S/N (450–500 per Å). Fig. 4 WD 1703−267 (observations of September 30, 2019): circular polarisation (red solid line) and null profile (blue solid line, offset by − 3%), superposed to the V ∕ I error bars (light blue). Spectra are rebinned at about 11 Å. The three Stokes V ∕ I spectra are in quite good agreement in that they all show a region of weak positive polarisation around 4720 Å, and two regions of stronger negative polarisation around 4830 and 4960 Å. The I spectra obtained with grism 1200B show a series of weak depressions (with an amplitude of the order of 1%) that are hard to disentangle from instrumental features, even after applying flat-fielding correction. After an approximate normalisation to the continuum (clearly difficult to