592 Dr. N. Bohr on the Decrease of 



aluminium sheet considered above we have approximately 

 A r T/Q r =16r. 



From these considerations it will appear that the proba- 

 bility distribution of the loss of energy suffered by a ft par- 

 ticle of given initial velocity in penetrating through a thin 

 sheet of matter will show a sharp maximum at a value very 

 close to A T T, if t=1, and fall rapidly off on both sides. 

 The value for the decrease of energy measured in the ex- 

 periments is evidently this maximum, and not the mean value 

 for AT given by the formula (5), such as was supposed in 

 my former paper. The considerable difference between the 

 two values is due to a very small number of very violent 

 collisions left out in deducing the formula (16) but included 

 in (5). Putting t = 1 and introducing for p v and p r , we get 

 from (16) 



A T 27r. 2 E 2 NA^ " ,_/ FV 2 NnAn n 7 , 



AlT== --^v 2 — | l0 4— w~)- • ( 17 > 



In section 5 we shall consider the question of the loss of 

 energy suffered by a beam of rays when penetrating 

 through a sheet of matter of greater thickness. 



§ 3. Effect of the velocity of ft particles being comparable 

 with the velocity of light. 



The calculations in the former sections are based on the 

 formula (1) for the energy transferred to an electron by a 

 collision with an a. or ft particle. In the deduction of this 

 formula it is assumed that the velocity V is small compared 

 with the velocity of light c. This condition is not fulfilled 

 in case of high speed ft particles. If V is of the same order 

 of magnitude as c, the calculation of the amount of energy 

 transferred by a collision involves complicated considerations 

 for the general case. The problem, however, with which we 

 are concerned is very much simplified by the circumstance 

 considered in the former section, that the value for the loss 

 of energy of /3 particles, measured in the experiments, will 

 depend only on collisions in which the energy transferred 

 is very small compared with the total energy of the ft par- 

 ticle, i. e. collisions in which a is small compared with p. 

 Considering such collisions and calculating the force exerted 

 on the electron by the ft particle, we can neglect the- 

 displacement of the electron during the collision as well 

 as its reaction on the ft particle. We need, therefore, only 

 consider the way in which this force is influenced by the 

 velocity of the ft particle itself. 



