Moving Electrified Particles passing through Matter. 13 



limit for the action of the electrons on the velocity of the 

 particles — and consequently the value of the absorption of 

 the rays — which we get in this way will depend purely on 

 the frequency of the electrons- and the velocity of the par- 

 ticles, and may for the same velocity of the particles be very 

 different for the different electrons inside the same atom, 

 according to their different frequencies. The limit in question 

 will, at least for some of the electrons in elements of high 

 atomic weight, in which elements the existence of vibrations 

 with very high frequencies is observed, be much smaller 

 than for the electrons in the elements of low atomic weight. 

 This circumstance seems, as it will be shown, to account for 

 the comparatively much smaller absorption of such elements 

 for the same weight of matter per cm. 2 



It will be perceived that the theory of the decrease of 

 velocity of moving electrified particles on passing through 

 matter in this form bears a great analogy to the ordinary 

 electromagnetic theory of dispersion ; the different times of 

 vibration for the different wave-lengths considered in the 

 theory of dispersion is here replaced by the different times 

 of collision of particles of different velocities and at different 

 distances from the electrons. In fact it will be shown, that 

 the information about the number and the frequency of the 

 electrons in the atoms, which we get from the theory of 

 dispersion, will enable us to calculate values for the absorption 

 of a-rays for the lightest elements which are in very close 

 agreement with the observed values. Since, however, the 

 decrease in the effect of the electrons corresponding to an 

 increase in their frequency is much more rapid for the 

 dispersion than for the loss of velocity of moving particles, 

 it seems possible by considering the latter to get more infor- 

 mation about the higher frequencies in the atoms, and from 

 this some more information about the internal structure of 

 the atoms. 



In considering the collisions between the electrons and the 

 particles we shall at first neglect the forces from the side of 

 the atoms. Let E and M be the charge and the mass of a 

 particle, and e and m be corresponding quantities for an 

 electron. Let us further assume that the electron is at rest, 

 and that the particle has a velocity V before the collision, 

 and let the distance apart of the electron from the path of 

 the particle before the collision be p ; then the calculation. 



