Spectra of four lines (CI5380.3 A, MnI 5394.7 A, FeI 5930.2 A and SiI 5948.5 A) have been obtained in the quiet photosphere, at regular intervals along the polar axis and the equator. The spatially averaged spectra have been analyzed, studying the center-to-limb variation (CLV) and possible changes with the heliographic latitude of the residual intensity (RI), equivalent width (EW), full width at half line minimum (FWHM), and bisector of the line profiles. The aim of this spectroscopic study is to complete the photometric work carried out and recently published by the authors (Rodriguez Hildago et al. 1992, hereafter Paper I). It allows us to test some conclusions of Paper I and to extend our analysis to higher photospheric layers. Firstly the general behavior of the CLV is shown and discussed. From the comparison betwen the CLV along the North-South and East-West diameters, it is observed that the Cl line, formed very deep in the photosphere, broadens and shows raised minima with latitude, not showing variations in its EW, except at very high latitudes. The other three lines, which inform about the physical conditions in the middle photosphere, become deeper and stronger, and the FeI one seems broader, with latitude. The observational results are discussed in terms of physical scenarios based on changes in the velocity fields present in the photosphere (mainly of the granulation), possible spatial anisotropies in the distribution of network bright points (which would be related to differences in the mean temperature gradient) and the latitudinal variation of the granulation contrast found in Paper I.