350 Prof. W, H. Bragg on the Ionization of 



interest. In two previous papers I have made attempts to 

 find it. In the first (Phil. Mag. Sept. 1905) I showed that 

 if we assumed the ionization produced to be proportional to 

 the energy spent, and both to v'% and also assumed all the 

 energy to be spent on ionization, then the form of the curve 

 was most readily explained by taking n= — ^. Later Ruther- 

 ford showed that the energy of the a particle was not all 

 spent on ionization, but that much still remained when ioniza- 

 tion ceased. Using his figures, J then pointed out that with 

 this modification of the hvpothesis it seemed probable that 

 n=-2 (Phil. Mag. Nov."^ 1905). But Rutherford's recent 

 work shows that the hvpothesis is still fundamentally wrong', 

 because the ionization is not proportional to the energy spent. 

 His results settle the whole question. 



If v = the velocity of the particle, r the range yet to be 

 run, d a constant, which Rutherford estimates at 1*25 cm., 

 then his conclusion is that v is proportional to ^/(r + d). 

 Now I have shown (Phil. Mag. Nov. 1905) that the ioniza- 

 tion produced by the particle during the last r cm. of its path 

 is proportional to \/(r-)- d)— ^/d where d=l'33. The two 

 values of d may be taken to be the same. Hence difdr is 

 proportional to l/\/(r-M), i. e., to 1/v ; which means that 

 f(v) = l/v, or that the ionization produced at different points 

 of the path in any gas is proportional to the time spent by 

 the a particle in crossing the atom. 



The formula which I have used here for the ionization 

 was calculated on the hypothesis that the a particle lost its 

 ionizing power abruptly, and that the slope of the top of the 

 ionization curve was due to the effects of the thickness of the 

 Ra film. Branson's results (Phil. Mag. June 1906) seem 

 to show that the loss of ionizing power is not quite so 

 sudden as I supposed it to be. Bat I find that this does not 

 affect the calculation of the form off(v). For we may take 

 an extreme view and suppose the whole of the top slope to be 

 due to a gradual decay of the a particle's powers, and none 

 to the thickness of the radium layer. In that case the form 

 of the ionization curve represents the effects of one particle. 

 Now, the ionization at 6' 5 cm. (in air) for RaC is nearly 4/3 

 of the ionization at 5 cm. At the former distance r + d = '5 

 + 1-25 = 75, and at the latter 2 + 1-25 = 3-25. But y3*25/ 

 v /l-75 = 1*36 ; which is very nearly 4/3. Thus the ionization 

 on this hypothesis also is inversely proportional to \/(r-j-d), 

 and the true explanation of the top slope must lie between 

 the two extremes. 



It seems clear, then, that the ionization in the molecule 

 is proportional to the energy spent in it (i.e., to the stopping- 

 power, or the amount of the effect A), to the velocity of the 



