A new polarimeter and an extension of the polarimetric technique of Do
nati et al. (1990) to higher polarisation values are presented. With t
his system, which allows low-noise polarimetric observations in the bl
ue and near-UV part of the solar spectrum, we have recorded more than
200 Q/I profiles of Ca I 4227 Angstrom with an accuracy of 2-3 x 10(-4
). We find that while the Q/I line shape outside the line core is very
stable from one part of the solar surface to the next, the line core
exhibits large variations relative to the rest of the profile. These v
ariations are best interpreted in terms of partial depolarisation prod
uced by the Hanle effect in the presence of weak fields. We obtain a q
uantitative and model-independent estimate of the depolarisation, from
which we deduce field strengths of 5-15 G at the level of line-core f
ormation, i.e. in the low to mid chromosphere. We also find evidence t
hat the field strength is distributed around these average values with
a FWHM that is approximately the same as the average value.