54£ Mr. G. H. Henderson on the Range and Ionization 



Adoptiug the same method as was used by Flamm, it may 

 be seen that the number of a particles whose ranges are 

 increased by an amount varying between f and £ + d% is 



, N 2 _p/^if 



2 Vt * 



Hence on the above assumptions the total ionization at « 

 will be 



i,» M p(»«»y-«i * * .-■*'* .... (4, 



Jx-6-592 IN 2 V^TT a 



a readily integrable expression. 



The parameter a, which governs the magnitude of the 

 variations in range, has been calculated by Flamm and Bohr. 

 It is not independent of the range and its treatment as a 

 constant in equation (4) is not strictly justified, since all of 

 the N particles getting beyond x have not the same range. 

 However, the variation of a over the group of ranges here 

 considered is small, so it is taken as constant as a first 

 approximation. The value of a for RaC in air is '072, 

 calculated by Flamm's formula, using the most recent values 

 of the radioactive constants involved. This value takes into 

 account the probability effect of electronic encounters only 

 («! in the nomenclature of Flamm's paper), the effect of 

 nuclear encounters having been shown to be negligible by 

 Bohr. The calculation of « by Bohr's somewhat more com- 

 plicated formula gives an almost identical value for a. 



The values of I have been calculated for various values of 

 x by means of equation (4), and the results are shown in the 

 form of crosses in fig. 3 (PI. XVII.). For values of x less 

 than about 6*55 cm. the equation (4) reduces to the straight 

 line (1). 



The values of « calculated for ThCi and ThC 2 are '051 and 

 *087 respectively. The values of I calculated by means of 

 the equations corresponding to (4) are shown in the form of 

 crosses in figs. 5 and 6. 



An inspection of the curves in all three cases will show 

 that the agreement between calculated and observed values 

 is very satisfactory, when the experimental errors and the 

 approximate nature of the calculation are considered. Inter- 

 preting this agreement, it seems evident that variations in the 

 ranges of the individual « particles are the cause of the 

 gradual flattening out of the ionization curve at the extreme 

 end of the range, for which an explanation had not previously 

 been offered. These variations in range are due to probability 



