We present results from the analysis of Fe i 630 nm measurements of the quiet Sun taken with the spectropolarimeter of the Hinode satellite .
Two data sets with noise levels of 1.2 \times 10 ^ { -3 } and 3 \times 10 ^ { -4 } are employed .
We determine the distribution of field strengths and inclinations by inverting the two observations with a Milne-Eddington model atmosphere .
The inversions show a predominance of weak , highly inclined fields .
By means of several tests we conclude that these properties can not be attributed to photon noise effects .
To obtain the most accurate results , we focus on the 27.4 % of the pixels in the second data set that have linear polarization amplitudes larger than 4.5 times the noise level .
The vector magnetic field derived for these pixels is very precise because both circular and linear polarization signals are used simultaneously .
The inferred field strength , inclination , and filling factor distributions agree with previous results , supporting the idea that internetwork fields are weak and very inclined , at least in about one quarter of the area occupied by the internetwork .
These properties differ from those of network fields .
The average magnetic flux density and the mean field strength derived from the 27.4 % of the field of view with clear linear polarization signals are 16.3 Mx cm ^ { -2 } and 220 G , respectively .
The ratio between the average horizontal and vertical components of the field is approximately 3.1 .
The internetwork fields do not follow an isotropic distribution of orientations .