The technique of adiabatic fast passage has been used to measure the relative magnetic susceptibility, X , of He3 and mixtures of He3-He4 with an experimental r.m.s. deviation of ±1%. Two types of measurements were made: (1) Measurement of X versus temperature (from 1.96°X to 0.93°K) of pure He3 liquid, and He3-He4 mixtures containing 35%, 14%, and 5% He3. (2) Measurement of relative X versus density of pure He3 gas at 2.99°K, with density varying from 1.1 x 10-3 to 4.5 x 10-3 moles/cc. Preliminary measurements of X versus density, p , of He3 atoms, for 2 x 10-3 <p< 26 x 10-3 moles/cc. at 1.96°K were made by using liquid He3-He4 mixtures ranging from 5% to 100% He3. The method of relating these individual measurements is explained. The above results are compared to theory and other previous work. Experimental difficulties affecting precision measurements are discussed.