A b r ie f review o f the experimental and th eoretical properties o f low pressure liquid He3 as related to the present work is given. This is followed by a d iscussion o f the magnetic cooling method as applied to cooling He3 using both nuclear and electron ic paramagnetics. A number o f possib le metals fo r nuclear cooling are suggested, while cerium magnesium nitrate (dflN) is taken to be the best electronic paramagnetic known fo r the present purposes. The spin-bath thermal resistance is discussed in both cases. In the case o f CMV recent work on the spin-bath r e s i s tance, due to a phonon bottleneck, shows it to be remarkably low. This is borne out in the present experiments. I t is concluded that for temperatures in the m illidegree range CMN is the best p o s s ib il it y. A careful discussion is given o f the techniques developed fo r obtaining and maintaining temperature below 0.010°K fo r many hours in an apparatus o f moderate s iz e using superconducting magnets. D etails are given o f the method o f using epoxy resins for producing apparatus fo r using He3 with application to the measurement o f heat capacity and magnetic prop erties. The method o f executing the experiments is presented together with a thermodynamic analysis o f the effectiv en ess o f the fin a l cooling process. New measurements o f the heat capacity o f a mixture o f low pressure He3 and CM are presented down to a magnetic temperature o f 0.00b°K. No anomalous results are obtained. The experimental technique is analyzed and c r itic iz e d. The resu lts are compared with ea rlier data. The limiting value o f C/nRT s t i l l cannot be p r e c is e ly assessed but seems to be in the range 3 .0 to 3.2°K~. Detailed comparison is made o f the present work with that o f Peshkov, whose resu lts are in terpreted in terms o f an experimental e f f e c t. The thermal boundary resistance from epoxy walls to He3 compares favorably with previous work. Measurements by the spin-echo method o f the s e lf-d iffu s io n c o effic ien t D, and the s u s c e p tib ility. X, o f the He> are presented do™ to a t e v e n W e o f O. m SN o anomalous behavior is observed. D obeys the law D * Work supported by the U.S. Atomic Energy Commission under Contract AT(11-1)-1198.