Table 2: Magnetic fields derived from the H$\gamma $ and H$\beta $ lines for our sample of white dwarfs. $B({\sigma })$ provides the magnetic field in units of the$\sigma $ level. Detections exceeding the $3\sigma $ levels are given in bold. $\sigma (V)$ is the standard deviation of the observed (V/I)-spectrum obtained inthe region 4500-4700  Å. Lower limits on the detectability of the magnetic field from the line polarisation peaks, calculated at the $1\sigma $ level of the noise, are given in the last two columns. Multiple observations that were averaged prior to analysis are labeled AVERAGE.
Target Date $\sigma (V)$ B(G) $B({\rm G})$ $B({\sigma })$ B(G) at $1\sigma $
    (10 $^{-3}I_{\rm c}$) H$\gamma $ H$\beta $ H $\gamma, \beta$ H $\gamma, \beta$    H$\gamma $    H$\beta $
WD 0135-052 29/11/02 1.2 $1112\pm625$ $492\pm373$ $654\pm320$ 2.04 1277 861
WD 0227+050 28/12/02 1.0 $493\pm1177$ $-776\pm707$ $-439\pm606$ 0.72 2486 -1928
  29/01/03 1.0 $-710\pm971$ $1854\pm709$ $962\pm572$ 1.68 -2969 1989
  AVERAGE 0.7 $-105\pm789$ $590\pm469$ $408\pm403$ 1.01 -1924 1194
WD 0310-688 24/02/03 0.8 $-504\pm741$ $114\pm548$ $-104\pm440$ 0.24 -2106 1404
WD 0346-011 28/12/02 1.8 $-9299\pm8510$ $-6815\pm5295$ $-7508\pm4495$ 1.67 -36860 -16600
  03/02/03 2.6 $3222\pm9374$ $7542\pm6717$ $6076\pm5459$ 1.11 28440 24820
  AVERAGE 1.1 $-5967\pm7087$ $-1496\pm4226$ $-2668\pm3629$ 0.74 -23060 -10680
WD 0446-789 30/11/02 1.3 $417\pm1403$ $4251\pm910$ $3115\pm763$ 4.08 3731 2340
  28/01/03 1.4 $7771\pm1476$ $5370\pm1196$ $6321\pm929$ 6.80 4118 2815
  AVERAGE 0.9 $3612\pm1005$ $4743\pm832$ $4283\pm 640$ 6.69 2495 1594
WD 0612+177 30/11/02 1.3 $2416\pm1456$ $-1148\pm1203$ $297\pm927$ 0.32 4060 -2620
  01/02/03 1.4 $86\pm1154$ $236\pm1171$ $156\pm821$ 0.19 3742 2915
  AVERAGE 0.9 $1132\pm920$ $-457\pm789$ $216\pm598$ 0.36 2672 -1939
WD 0631+107 01/03/03 2.2 $-1310\pm1785$ $-170\pm1815$ $-749\pm1272$ 0.59 -7300 -5890
  03/03/03 2.1 $-790\pm1870$ $310\pm1775$ $-211\pm1287$ 0.16 -6630 4340
  AVERAGE 1.2 $-990\pm1440$ $260\pm1090$ $-195\pm869$ 0.22 -4010 2630
WD 0839-327 29/11/02 0.7 $-313\pm325$ $402\pm261$ $121\pm203$ 0.60 -1008 761
WD 0859-039 03/02/03 1.5 $2083\pm1164$ $11\pm987$ $877\pm752$ 1.17 4400 2727
  25/02/03 1.2 $2183\pm1372$ $-401\pm911$ $389\pm758$ 0.51 3234 -2222
  AVERAGE 0.8 $1186\pm928$ $382\pm607$ $622\pm507$ 1.23 2319 1511
WD 1042-690 28/01/03 1.3 $-719\pm2333$ $-2850\pm2301$ $-1799\pm1638$ 1.10 -3624 -3247
  03/02/03 1.0 $1627\pm1464$ $-865\pm1163$ $99\pm910$ 0.11 2963 -3560
  24/02/03 0.9 $-2374\pm1060$ $103\pm864$ $-885\pm669$ 1.32 -2764 1804
  AVERAGE 0.6 $141\pm745$ $-406\pm620$ $-182\pm476$ 0.38 1833 -1508
WD 1105-048 01/01/03 1.1 $-1153\pm632$ $55\pm807$ $-693\pm497$ 1.39 -2863 1599
  29/01/03 1.1 $-4686\pm1032$ $-3305\pm979$ - $3959\pm710$ 5.58 -2756 -2164
  AVERAGE 0.8 $-2760\pm598$ $-1337\pm675$ - $2134\pm447$ 4.77 -2156 -1538
WD 2359-434 04/11/02 1.0 $-3003\pm1433$ $-5719\pm1289$ - $4504\pm958$ 4.70 -2914 -2975
  29/11/02 1.0 $-1905\pm702$ $-4224\pm796$ - $2919\pm526$ 5.55 -4880 -3907
  AVERAGE 1.0 $-2066\pm546$ $-4738\pm667$ - $3138\pm422$ 7.44 -1785 -1532


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