A Packard-Varian type experiment was done, in which the free precession of proton magnetic moment about a very weak magnetic field was observed, by first lining up the protons in an aqueous sample with a separate magnetic field and then allowing them to execute the free precession. In out experiment the studies on the non-adiabatic process of withdrawing the polarizing field, the absolute value of the signal strength and the reduction of sample size to minimize the effect of inhomogeneity of the magnetic field were emphasized. The effect of rotating the sample coil upon the measured signal frequency was also noted, and it is pointed out that this is the most direct way to determine the sign of the nuclear magnetic moment.The phenomenon of proton free precession in weak magnetic field has important practical applications in earth's magnetic field measurement at high altitudes, in geological prospecting, and in petroleum recovery from oilfield rocks. The present studies may be helpful in solving the problems likely to occur in these applications.In order to check the performance of the entire experimental set-up for field works, and especially to investigate the influence of magnetic substances in surroundings on the signal frequency, a series of experiments was carried out on a lake. Affirmative results were obtained. The relative accuracy of the measurement of the precessional signal frequency, which in turn determines the magnetic field strength, is 1×10-5.