582 Dr. N. Bohr on the Decrease of 



from those used in the following*. Another question which 

 will be considered more fully in the present paper is the 

 effect of the velocity of ft rays being comparable with the 

 velocity of light. These calculations are contained in the first 

 three sections. In the two next sections the theory is com- 

 pared with the measurements. It will be shown that the 

 approximate agreement obtained in the former paper is im- 

 proved by the closer theoretical discussion, as well as by 

 using the recent more accurate measurements. Section 6 

 contains some considerations on the ionization produced by 

 a and ft rays. A theory for this phenomenon has been given 

 by Sir J. J. Thomson t. 



§ 1. The average value of the rate of decrease of velocity. 



For the sake of clearness it is desirable to give a brief 

 summary of the calculations in the former paper. Re- 

 ferences to the previous literature on the subject will be 

 found in that paper. 



Following Sir Ernest Rutherford, we shall assume that the 

 atom consists of a central nucleus carrying a positive charge 

 and surrounded by a cluster of electrons kept together by 

 the attractive forces from the nucleus. The nucleus is the 

 seat of practically the entire mass of the atom and has 

 dimensions exceedingly small compared with the dimensions 

 of the surrounding cluster of electrons. If an a or ft par- 

 ticle passes through a sheet of matter it will penetrate 

 through the atoms, and in colliding with the electrons and 

 the nuclei it will suffer deflexions from its original path and 

 lose part o£ its original kinetic energy. The deflexions will 

 give rise to the scattering of the rays, and the second effect 

 will produce the decrease in their velocity. The relative 

 parts played by the nuclei and the electrons in these two 

 phenomena are very different. On account of the intense 

 field around the nuclei the main part of the scattering will 

 be due to collisions of the a or ft particles with them ; but 

 on account of the great mass of the nuclei the total kinetic 

 energy lost in such collisions will be negligibly small com- 

 pared with that lost in collisions with the electrons. In cal- 

 culating the decrease of velocity we shall therefore consider 

 only the effect of the latter collisions. 



* Note added in proof. I have only now had an opportunity of seeing" 

 a recent interesting- paper by L. Flamm {Sitzungsber. d. K. Akad. d. Wiss. 

 Wien, Mat.-nat. Kl. cxxiii. II a, 1914), who has discussed the problem of 

 the probability variation in the ranges of a particles in air on assumptions 

 corresponding with those used in the present paper, and has obtained 

 some of the results deduced in section 2 (see the note on page 599). 



t Phil. Mag. xxiii. p. 449 (1912). 



