Velocity of Electrified Particles passing through Matter. 11 



of the distance apart *. By help of some further simple 

 assumptions about the distribution of the electrons in the 

 atoms and the effect of the forces acting upon them, Darwin 

 obtained results for the scattering as well as for the ab- 

 sorption of the rays, which agree approximately with the 

 experiments. 



The above theories make use, however, of some special 

 assumptions which seem to me to be open to objections of a 

 principal character, and I have in this paper made an attempt 

 to treat the problem in a somewhat different manner. The 

 theory in question assumes that the loss of velocity of a 

 moving electrified particle in passing through matter is due 

 to a transfer of kinetic energy to the electrons of the atoms 

 with which it collides. If we assume that the effect of the 

 forces which keep the electrons in their position — or their 

 orbits — inside the atoms can be neglected durino- the verv 

 short collisions between the electrons and the particles, we 

 can very simply calculate the orbits of the electrons during 

 the collisions, and consequently the energy transferred to 

 them and the loss of volocity of the particle. If, however, 

 we integrate the total loss of energy due to all the electrons in 

 the matter, we get in this way an infinitely great value for 

 the absorption. Sir J. J. Thomson, in his above mentioned 

 theory of the decrease of velocity of cathode-ray s, avoids 

 this difficulty by introducing, as an effective limit for the 

 action of the electrons on the velocity of the particles, a 

 distance comparable in size with the distance apart of the 

 single electrons in the atoms. This limit is chosen from the 

 consideration that for distances greater than this, the effect 

 of the different electrons on the moving particles will mutually 

 disturb each other. The simultaneous influence of the different 

 electrons on the particles will, as it will be seen, highly affect 

 the deflexions of the particles for the distances in question, 

 and the limit mentioned will therefore hold for the calculation 

 of the scattering of the rays. The limit will, however, not 

 hold for the calculation of the decrease of velocity of the 

 particles ; for, on account of the great velocity, the motion of 

 the particles will be very slightly affected by collisions in which 

 the distance of the electrons from the path of the particle is of 

 the order of magnitude assumed for the distance apart of the 

 electrons in the atoms. The forces exerted by a particle on 

 an electron, and consequently the energy transferred to the 



* Corresponding assumptions are also used by Sir J.J. Thomson in a 

 recent paper on the ionization of moving electrified particles, Phil. Mag. 

 xxiii. p. 449 (1912). 



