We present the results of a ship survey conducted from Italy to Antarctica and back during the 1996--1997 solar minimum measuring the latitude variation in the neutron component of cosmic radiation at sea level. High-energy atmospheric neutrons were detected by a 3NM-64 and thermalized atmospheric neutrons were detected by two bare BF3 counters. Discussions of the internal consistency of the data and the stability of the detectors, investigations of meteorological effects, and data corrections are presented in two companion papers. In this paper we compute updated vertical cutoff rigidities corrected for the penumbra effect, and we estimate apparent cutoff rigidities, which take into account the contribution of nonvertically incident particles to the counting rate. When comparing cosmic ray intensities observed in the same place, a small forward-backward effect is found and explained as the effect of an asymmetric shielding structure around the monitor. Latitude dependencies (i.e., neutron intensities versus cutoff rigidity) and associated coupling functions are computed for both monitors and compared. The NM latitude dependence obtained for the 1996--1997 solar minimum is found to be almost identical to that obtained by other authors in the previous solar minimum. The absence of the so-called crossover effect when comparing coupling functions of subsequent solar minima is discussed also on the basis of cosmic ray intensity changes observed by neutron monitor stations. ¿ 2000 American Geophysical Union