At this stage of our knowledge it is of great importance to test whether the law of force breaks down for the distance of closest approach of an _α_ particle to a nucleus. This can be done by comparing the observed with the calculated number of _α_ particles scattered through angles of nearly 180°. It seems almost certain that the inverse square law must break down when swift _α_ particles are used. This can be seen from the following argument. If an _α_ particle, of the same speed as that ejected during the transformation of uranium, is fired directly at the uranium nucleus, _it must penetrate into the nuclear structure_. If a still swifter _α_ particle is used, _e. g._ that from radium C, which has about twice the energy of the uranium _α_ particle, it is clear that it must penetrate still more deeply into the nuclear structure. This is based on the assumption that the field due to a nucleus is approximately symmetrical in all directions. If this is not true, it may happen that only a fraction of the head-on collisions may be effective in penetrating the nucleus. It is hoped soon to attack this difficult problem experimentally. We have so far dealt with collisions of an _α_ particle with a heavy atom. We know, however, from the results of Rutherford, Chadwick and Bieler that in a collision of an _α_ particle with the lightest atom, hydrogen, the law of the inverse square breaks down entirely when swift particles are used. Not only are the numbers of H nuclei set in swift motion much greater than is to be expected in the simple-point nucleus theory, but the change of number with the velocity of the _α_ particle varies in the opposite way from the simple theory. Such wide departures between theory and experiment are only explicable if we assume either that the nuclei have sensible dimensions or that the inverse square law of repulsion entirely breaks down in such close collisions. If we suppose the complexity in structure and in laws of force is to be ascribed to the _α_ particle rather than to the hydrogen nucleus, Chadwick and Bieler, as the result of a careful series of experiments, concluded that the _α_ particle behaved as if it were a perfectly elastic body, spheroidal in shape with its minor axis 4 x 10^-13 cm. in the direction of motion and major axis 8 x 10^-13 cm. Outside this spheroidal region the forces fell off according to the ordinary inverse square law, but inside this region the forces increased so rapidly that a particle was reflected from it as from a perfectly elastic body. No doubt such a conception is somewhat artificial, but it does serve to bring out the essential points involved in the collision, viz., that when the nuclei approach within a certain critical distance of each other, forces come into play which vary more rapidly than the inverse square. It is difficult to ascribe this break-down of the law of force merely to the finite size or complexity of the nuclear structure or to