12 Dr. N. Bohr : Theory of Decrease of Velocity of 



latter by the collision, will therefore be very nearly inde- 

 pendent of the simultaneous effect of other electrons on the 

 particle. 



Darwin, in his theory of absorption of a-rays, proceeds in 

 another way and avoids the difficulty by assuming that the 

 forces on the electrons from the side of the atoms can be 

 neglected during the very short and violent collisions between 

 an electron and an a-particle, which occur when the particle 

 traverses the same atom to which the electron belongs ; and 

 further, that the velocity of the a-particle will be unaltered 

 if the particle during its path does not enter the atom. 

 Using these assumptions and comparing the theory with the 

 experiments, Darwin finds values for the diameter of the 

 atoms which decrease for increasing atomic weight, and 

 which for the lightest elements are several times greater 

 than the generally adopted values for this quantity, and for 

 the heaviest elements several times smaller. It seems, how- 

 ever, to me not to be justifiable to take the surface of the 

 atoms as the limit of the effect of the electrons in the atoms 

 on the particles. Outside an atom the forces on the particle 

 from the electrons and the central positive charge will 

 certainly very nearly neutralize each other ; but the decrease 

 of velocity of the particles depends only on the motion of the 

 electrons during the collision, and not on the total force 

 exerted on the particle by the whole atom, the latter force 

 producing only the scattering of the rays. 



We can, however, get a natural limit for the effect of the 

 electrons on the velocity of the moving particles by taking 

 into account the forces by which the electrons are kept in 

 their positions in the atoms. Under the influence of these 

 forces the electrons will have a sort of vibratory motion if 

 they are disturbed by an impulse from outside. We see 

 immediately that the forces in question will materially alter 

 the motion of the electrons during the collision, and con- 

 sequently the loss of energy of the particle, if the time of 

 vibration of the electrons is of the same order of magnitude 

 as the time of collision, i. e., the time which the particle 

 takes to travel through a distance of the same order of 

 magnitude as the shortest distance apart of the electron from 

 the path of the particle *. We see, further, that the effect 

 of the electrons on the velocity of the particle will decrease 

 very rapidly with the distance of the electrons from the 

 particle, if this distance is so great that the time of collision 

 is great compared with the time of vibration. The effective 



* Compare J. J. Thomson, loc. cit. Phil. Map;, xxiii. p. 454 (1912). 



