182 



Tn- the next place consider the effect B. The propoiti.")n 

 of ionisation to energy spent varies from molecule to molecule, 

 and is dependent on the velocity of the a particle. The re- 

 sults described in this paper show that, as already said, 

 cli^k ffv) de. The nature of the function f(v) is of great 

 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 ionisation produced to be proportional to 

 the energ-y spent, and both to v'\ and also assumed all ohe 

 energy to be spent on ionisation, 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 ionisation, but that much still remained when ionisa- 

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

 this modification of the hypothesis it seemed probable that 

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

 work shows that the hypothesis is still fundamentally wrong, 

 because the ionisation 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, (1 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 ionisa- 

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

 is proportional to \^f.r-}-d) — \^d- where c? = l"33. The two 

 values of d may be taken to be the same. Hence di jdr is pro- 

 portional to Xj \/(r-^f1 ), i.e., to \/v; which means that 

 ffr) = llv, or that the ionisation produced at different points 

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

 tlie a particle in crossing the atom. 



The formula which I have used here for the ionisation 

 was calculated on the hypothesis that the a particle lost its 

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

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

 Ra film. Bronson's results (Phil. Mag.. June, 1906) 

 seem to show that the loss of ionising power is not quite so 

 sudden as I supposed it to be. But I find that this does nob 

 affect the calculation of the form of ffv). 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 ionisation curve represents the effects of one particle. 

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

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

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

 v'l'75 = l*36: which is very nearly 4/3. Tlius the ionisation 

 on this hypothesis also is inversely pra))ortioual to \^(r + d), 



