We have performed spin-echo experiments on β-phase He3 and have measured the exchange interaction J between He3 atoms in a consistent way, both by the "exchange narrowing" of the line (exchange lengthening of T2) and by the strong reduction of T1 at low magnetic fields (γH0J). J is found to increase very rapidly with increasing molar volume, ranging from less than 20 kc/sec at a lattice constant of 3.4 to 90 kc/sec at 3.5 , and to about 300 kc/sec at 3.6 . These exchange interactions are much too small to account for the "departure from the Curie law" found by Adams, Meyer, and Fairbank. It is shown that the susceptibility is, in fact, "Curie law" (in their temperature range) and we believe that they were reporting-as a susceptibility anomaly-the effect of a long exchange bath-lattice relaxation time (observed for the first time in the present experiment). This exchange-lattice relaxation time varies as T-n(7<n<11) and is 100 sec at 1 °K for β-phase He3 of 3.5 lattice constant. The results for the exchange-lattice relaxation time are compared with a modification of a theory by Griffiths. A major mystery remains-the exchange-bath heat capacity as measured by the spin-echo method exceeds the calculated value by >103. The exchange interaction is discussed and compared with the prediction of Saunders and others. © 1964 The American Physical Society.