The validity of the modified Bloch equations (MBE) for liquids in extremely weak dc magnetic fields and large values of electron spin saturation, using linear rf fields, has been checked for anthracene-negative-ion solutions (ANI). Strictly numerical solutions of the MBE were obtained by use of a computer to show the electron spin saturation as functions of rf field strength and frequency. These functions were strongly nonmonotonic and exceed unity in some cases. Dynamic nuclear polarizations were measured by a low-field transient method in which proton free-precession was observed in a weak field. Conventional epr measurements at 3000 and 18 G, cw dynamic nuclear polarization measurements at 18 G, and the low-field transient dynamic nuclear polarization measurements were all compatible with T1=T2=T=50 nsec for the ANI at 29°C. The ratio k of nuclear polarization enhancement to the electron spin saturation was found to be very nearly constant, in agreement with the Solomon two-spin relaxation theory. By use of MBE with T=50 nsec and setting k=-162, the results of the dynamic nuclear polarization measurements were fit to very nearly within known experimental errors despite the wide range of low-field resonant and nonresonant conditions and the strongly nonmonotonic curves. No dynamic polarization of the ANI could be obtained with the rf field parallel to the dc field, in agreement with the MBE. However, a crude-oil-derived free radical with T1>T2~10 nsec yielded about one-third as large a dynamic nuclear polarization with the rf field parallel to the dc field as perpendicular. It was noticed for a deteriorated ANI sample that the time constant for the establishment of a dynamic nuclear polarization exceeded the proton relaxation time and also varied markedly with the strength of the rf field.