The center-to-limb variations of the linear polarization observed by S
tenflo et al. (1980) outside active regions, in the resonance lines of
CaI at 4227 angstrom and of SrII at 4078 angstrom, are analyzed. Both
lines are formed in the low chromosphere by multiple scattering. Thei
r linear polarization is a consequence of the coherent scattering of t
he anisotropic radiation field by the atoms. It is very sensitive to p
artial frequency redistribution, depolarizing collisions, turbulent ve
locity fields and to the Hanle effect due to weak magnetic fields. The
rates of depolarizing collisions may be determined by fitting the pol
arization profiles observed in the line wings, which are not affected
by the Hanle effect. The quadratic mean of the turbulent velocity fiel
d is adjusted in order to recover the observed line core intensity. It
is then possible to estimate the resonance polarization in the line c
ores. These estimates are in good agreement with the observations perf
ormed close to the solar limb (at heliocentric angles larger than abou
t 70-degrees). Closer to disk center the observed polarization rates a
re significantly larger than what is expected in the absence of a magn
etic field. We investigate the Hanle effect of an almost horizontal ma
gnetic field of random azimuthal orientation lying in the chromosphere
, which may constitute the base of a magnetic canopy. If the base of t
he canopy lies slightly below the depth where the line core is formed,
i.e. between 700km and 1000km above tau5000 = 1, then the line core p
olarization close to disk center is actually enhanced as compared to i
ts non-magnetic value. This surprising effect is a consequence of mult
iple scattering of line photons in the chromosphere. The enhancement i
s however somewhat smaller than what is required to fit the observatio
ns. In contrast, the polarization is reduced when the canopy base lies
in the region where the line core is formed, i.e. between 1000km and
1300km above tau5000 = 1; it becomes insensitive to any horizontal mag
netic field lying higher in the chromosphere.