A systematic survey of asteroids down to photographic magnitude 16.5 is described. The ecliptic belt was photographed nearly twice around in 1950-1952, to a width of 40°. The 10-inch f/7 Ross-Fecker telescope on loan from the Cook Observatory was used, and 1094 pairs of plates were taken, each 8×10 inches in size and covering 6°5×8°1. In addition, 149 plates were taken on Selected Areas for magnitude calibration, as were special sequences for the determination of field corrections, etc. The plate pairs were blinked independently of previous knowledge and only afterward were re-examined for known objects missed. The asteroids found were measured for position, daily motion, and magnitude; and the subsequent identification work with the Ephemeris asteroids and objects having provisional designations was done with great care. The statistics of the Survey are summarized in Table 1. Previously announced objects, not found in the Survey and either below the plate limit or, in some cases, probably spurious, are listed in Table 2. Asteroids missed because they were outside the 40° belt are given in Table 3. Ephemeris asteroids not found, presumably because they were too faint, are listed in Table 4; in addition, 182 objects were not observed because they were definitely too faint. Six new objects are probably Trojans. For 2 of them and for 2 other new asteroids, circular orbits are given in Table 5. For 33 additional new objects our data suffice to compute circular orbits; they are listed in Table 6A. The measures resulting from the Survey are contained in Table A. The positions have a probable error of about ±3″. The Survey magnitudes of Table A are combined with other magnitude data in Table 7. This table is on the International Photographic System and represents the final compilation of this paper; both the mean photographic opposition magnitude, $p_0$, and the absolute magnitude, g, are given. The resulting magnitude system was calibrated photoelectrically afterward, and the scale was found to be precise over the entire range, 7-16 mag. Table 7 is recommended for future use, with one reservation: for some three hundred fainter asteroids, present data are still inadequate; for these objects new measures will be published as Paper VIII. It was found that magnitudes derived during a single opposition are not representative, no matter how accurate, because of fluctuations due to the aspect of the asteroid amounting to about ±0.11 mag. (p.e.). This comparatively large effect indicates that a good fraction of the asteroids have large obliquities. The importance of good magnitudes in future identification work is stressed. Numerous controls and revisions were made which are described in Section IX. The results of the Survey are not limited to an inventory for the years 1950-1952 of asteroid positions, identifications, and magnitudes on the photometric system. Since the blinking was carried out independently of previous knowledge, the completeness of the Survey could be determined in two independent ways: from overlapping Survey regions and from comparison with the Ephemeris asteroids. The degree of completeness of different Survey fields is found in Table 11; the asteroid numbers corrected for incompleteness are given in Table 12; and a quadratic interpolation formula representing these numbers as a function of apparent photographic magnitude is given in equation (5). The representation of the data by equation (5) is shown in Table 13. The counted numbers in the 1957 Ephemeris, arranged by mean opposition magnitude, $p_0$, are found in Table 14. The figures are essentially complete for $p_0$ < 14.5. The representation by two interpolation formulae, equations (6) and (7), is also given in Table 14. These formulae are estimated to give approximate minimum and maximum numbers of asteroids for 14 < $p_0$ < 18, and lead to estimates of the completeness factors of the Ephemeris asteroids for this interval (Tables 16 and 17 and Fig. 4). These factors, in turn, are used in Tables 15 and 19 to derive the distributions in absolute magnitude, g, for six distance groups of asteroids 1.85-2.00-2.60-3.00-3.50-4.30 astronomical units and the Trojans. The results for the three main zones, between 2.0 and 3.5 a.u., are plotted in Figure 5. Remarkable population differences are found, and the frequency-curves appear to consist of two parts, separated by a flat portion near g = 11, which corresponds to asteroid sizes near d = 30 km. One could surmise that this flat portion separates two modes of asteroid formation (condensation by accretion and collisional breakup), but it is considered premature to conclude this. Because of the population differences between the zones (Fig. 5), the center of gravity of the asteroid zone shifts toward the larger a-values for increasing g (smaller sizes). The ring 3.0 < a < 3.5 contributes 23 per cent of the 2.0 < a < 3.5 ring for 4.0 < g < 8.0; 39 per cent for 8.0 < g < 10.0; 70 per cent for 10.0 < g < 11.0; 89 per cent for 11.0 < g < 12.0; and 95 per cent for 12.0 < g < 13.0; the geometric-mean diameters of these five subgroups are about 300, 80, 40, 25, and 15 km. This result has important implications for the collisional production of meteorites. The results for the fringe zones are as follows. The 3.5 < a < 4.3 group, of which 27 members are known, allows a fair analysis, which shows this group to have the same composition with g or diameter as the main asteroid zone (range 8.5 < g < 12), with an abundance of 3 per cent of the main zone. The 1.85 < a < 2.00 group, with 11 known members, is inadequate for statistical treatment. Around g = 14 the abundance appears to be about 0.5 - 1 per cent of either the 2.0 < a < 2.6 or the 2.6 < a < 3.0 zone, but at g = 15 the fraction seems smaller. The Trojans (a ≈5.2) are represented by 13 members, but their degree of completeness is uncertain because of special searches that have been made for them. Because of the rapid increase of faint asteroids, it is not possible at this time to estimate the total mass of the asteroid ring.