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This paper describes results of magnetic field measurements of white dwarfs carried out on the 6-m telescope for the last years. A magnetic field of about Be ~ 28 kG has been discovered in the degenerate star WD 1953-011. A rotational period of WD 0009+501, 1.83 hours, has been discovered, the average magnetic field of the star is <Be> = -42.3 +/- 5.4 kG and its semi-amplitude of the rotational variability is 32.0 +/- 6.8 kG. The variable magnetic field of the bright normal (non-magnetic) degenerate star 40 Eridani B was confirmed in January 1999 by Zeeman time-resolved spectroscopy. Both the Halpha and the Hbeta lines give about the same results, we have selected two best periods in the magnetic field variability, 2h25m and 5h17m. The semi-amplitude of the rotational variations B_ max ~ 4000-5000 G and the average field is about zero +/- 500 G. If the magnetic field of 40 Eridani B is a central dipole, then the rotational axis inclination to the line of sight is i ~ 90 DEG, and the magnetic axis inclination to the rotational axis is about the same, beta ~ 90 DEG. For the first time an ultra-high signal-to-noise spectrum of the white dwarf has been obtained (S/N > 1000). We have found in this hydrogen-rich DA white dwarf 40 Eridani B (16500 K) that helium abundance is low (N(He)/N(H) < 10^{-7}), but the spectrum is rich in ultra-weak absorption lines of metals in low ionization states. It was proposed that these lines were produced in both circumstellar and interstellar gas.