It was pointed out some time ago by Abragam and Pryce that there was an anomalous part of the hyperfine field (approximately −200 000 G per unit electron spin) that was essentially constant in the 3dions. This anomalous field arises from admixture of configurations with unpairedselectrons. Alternatively, it has been viewed as a spin polarization of the inner coreselectrons by the outer 3delectrons. Increased precision of measurement, aided by ENDOR in some cases, reveals some striking constancies with regard to this core polarization hyperfine field (cphf). First, it is found that the cphf within an isoelectronic sequence in the same type of ligand coordination is constant to within a few percent. It may change as much as 40% depending upon environment but in the same type of environment (same ligand number and ligand ion) it is constant, i.e., the cphf isindependent of the charge on the nucleus. The second interesting fact is that the cphf isindependent of ligand distance, i.e., it is the same within a few percent in MgO, CaO, and SrO. Aside from these two invariant features, there seems to be a monotonic increase across the 3dseries in the cphf field in accord with the prediction of Freeman and Watson. These systematics will be illustrated in detail and some very tentative explanations for this behavior offered.