The bulk magnetic susceptibility (BMS) shift of a nuclear resonance frequency caused by a paramagnetic compound is of importance in vivo NMR, both magnetic resonance spectroscopy and magnetic resonance imaging. However, since it is a rather complicated phenomenon, it has been the source of many misinterpretations in the literature. We have reworked and organized the theory of the BMS shift. This includes accounting for the important effects of local susceptibility. We have conducted experiments on phantom samples in order to illustrate the principles involved. Our phantoms consist of capillaries and coaxial cylinders. They simulate the situations of blood vessels oriented parallel and perpendicular to the magnetic field and the interstitial spaces surrounding them. In most of our experiments, the paramagnetic compound was one of several different hyperfine shift reagents for cation resonances. These were chosen to cover a range of potencies, in both magnitude and sign, of the shifts they produce. However, we also used a reagent which was incapable of inducing a hyperfine shift and thus could cause only a BMS shift. Although we report only 23Na spectra in this paper, the latter samples simulate the cases where one observes the water 1H resonance in experiments employing hyperfine shift reagents for cations. There have been a number of such investigations recently reported in the literature. The principles considered in this paper allow us to offer new interpretations for the results of several experiments published in the last few years.