Doppler shifts of a solar line of Fe I at λ5123.7, averaged over a large central zone of the Sun (0.66 of the size of solar disk D⊙), relative to the mean position of this line for the outer rim (0.66−1.0D⊙), were measured during 1974–76 (61 days, 348 hr of observations), with the aid of a modified solar magnetograph (Section 2). The power spectra of the difference (central zone) – (rim) (after subtracting parabolic daily drifts) show the strongest concentration of power in the range of periods P = 120–180 min, in contrast with similar measurements for telluric lines where power is concentrated near 70 min. High-resolution analysis of fluctuations in this range for 6001 values of periods P (increment ΔP = 0.01 min) has shown the highest significance of five oscillations with P = 134.498, 148.359, 160.004, 171.099, 175.061 min. The 160-min oscillation is most significant; it lasts four years and shows a coherence in phase. These values are in close correspondence with predicted ones for g9, g10, g11, g12 modes of quadrupole l = 2 oscillation of a standard model of the Sun with Z = 0.04 (except 175.061 min which can eventually be the beat period of p1 and p2 modes of l = 2). Preliminary data point to possible variations, with the 160-min period, of the mean magnetic field and luminosity of the Sun. Detailed discussion of possible errors is given in Section 4.