Thin Films of Elements exposed to Rdntgen l\ays. 133 



of the /3-rays from gold (produced by the incidence of silver 

 X-rays) was calculated from the expression 



and the mini mum speed v 2 from 



The ratio of i\ to r 2 agreed well with the experimental 

 result obtained from the logarithmic absorption coefficients 

 ■of the two sets of rays and by assuming Whiddington's 

 fourth-power law Xv 4l = constant, where \ is the logarithmic 

 absorption coefficient. 



I do not think it safe to assume an exponential or any 

 theoretically derived law * in connexion with these experi- 

 ments. The problem of tiie range of the sub-groups has 

 therefore been attacked in a totally different manner. 

 Unfortunately, it lias to presume the existence of the sub- 

 group, but the result obtained points strongly to the accuracy 

 ■of this assumption and also to the general agreement with 

 the photo-electric hypothesis of the sub-groups. 



Figs. 8 and 9 (PI. III.). — A close examination of figs. 5 

 and 6 (PI. III.) shows that the curves cannot be members 

 of the same family, but that the irregularities might be due 

 to the superposition on curves belonging to the same family 

 of other curves varying among themselves. Figs. 8 and 9 

 represent the results of an attempt to analyse geometrically 

 the curves of figs. 5 and 6 (PI. III.). 



Suppose these curves, tigs. 5 and 6 (PL III.), to be 

 represented by N JP =N /(ct'), where N is tne ionization due 

 to the total absorption of the /3-ray energy in the air of the 

 chamber, N^ the total ionization in air at 0° C. and 76 cm. 

 pressure between the illuminated screen and the imaginary 

 plane x cm. from the screen. The variation of the density 

 of ionization with distance from the screen is given by 

 N /'( t e), and the variation of a logarithmic absorption 

 coefficient of the /3-particles with the distance from the 



screen by ^}og e ^ f'(x). 



If the curves of figs. 5 and 6 (PI. III.) could be repre- 

 sented by Nr=Nij(l — e~ yv ), this operation would yield 

 — \ constant. The value of A, so obtained gives a measure 



* The theoretically derived laws deal only with radiators without a 

 boundary ; in practice a boundary is necessary. The condition of 

 absorption in the gas near the boundary of the screen will be different 

 from that obtaining in the central region. Unless a guard-ring method 

 were employed, an empirical formula would be required for each chamber 

 of different dimensions. 



