The profiles of Stokes I and V of FeI 5247A, CrI 5247A, FeI 5250.2A and Fe I 5250.6A have been measured in the quiet photosphere with ZIMPOL, a new polarimeter, with very low noise level. The spatial resolution element of about 1Mm was essentially determined by seeing. In about 15% of the observed area, the signal-to-noise ratio was sufficiently large to determine the strength of the magnetic field and to derive various properties of the Stokes V profiles (asymmetries, zero-crossing shift and thermal line ratio). Our results show that, at least in this fraction of area, the magnetic field in the quiet Sun is dominated by strong flux concentrations which must be rather small. The data on the Stokes V properties provide observational constraints for theoretical models of flux concentrations.