Context : Magnetic fields have been detected in several hundred white dwarfs , with strengths ranging from a few kG to several hundred MG. Only a few of the known fields have a mean magnetic field modulus below about 1 MG .

Aims : We are searching for new examples of magnetic white dwarfs with very weak fields , and trying to model the few known examples .
Our search is intended to be sensitive enough to detect fields at the few kG level .

Methods : We have been surveying bright white dwarfs for very weak fields using spectropolarimeters at the Canada-France-Hawaii telescope , the William Herschel telescope , the European Southern Observatory , and the Russian Special Astrophysical Observatory .
We discuss in some detail tests of the WHT spectropolarimeter ISIS using the known magnetic strong-field Ap star HD 215441 ( Babcock ’ s star ) and the long-period Ap star HD 201601 ( \gamma Equ ) .

Results : We report the discovery of a field with a mean field modulus of about 57 kG in the white dwarf LTT 16093 = WD 2047+372 .
The field is clearly detected through the Zeeman splitting of H \alpha seen in two separate circularly polarised spectra from two different spectropolarimeters .
Zeeman circular polarisation is also detected , but only barely above the 3 \sigma level .

Conclusions : The discovery of this field is significant because it is the third weakest field ever unambiguously discovered in a white dwarf , while still being large enough that we should be able to model the field structure in some detail with future observations .