450 Mr Crowther, On the Transmission of ^-rays. 



substances emitting /S-rays over a very wide range of absorptions. 

 N. R Campbell * found that for aluminium the exponential law- 

 was certainly true to within 0"5 °/^ even when the rays had been 

 reduced to one hundredth part of their initial intensity. 



W. Wilsonf, on the other hand, using a magnetic deflection 

 method, found that the absorption of the " homogeneous " rays 

 obtained by the magnetic deflection method certainly did not 

 follow an exponential law, but a law which was practically linear. 

 It is difficult to conceive any mechanism which would produce 

 a linear law of absorption. Wilson, who worked principally with 

 aluminium, notes that tin showed some departures from the linear 

 law, but does not state either the nature or amount of these 

 departures. It seems probable, therefore, that the linear law found 

 for aluminium is only approximate and represents the balance of 

 a variety of causes and conditions. 



For example the gradual change of velocity of the /S-rays in 

 their passage through the aluminium would tend to transform an 

 exponential law of absorption into a law which might approximate 

 to a straight line. For consider a beam of homogeneous /8-rays of 

 velocity v, and with a coefficient of absorption A,. If the exponen- 

 tial law is accurately obeyed, and if the rays retain their original 

 velocity, the curve connecting the logarithm of the intensity with 

 the thickness of material traversed will be a straight line. As 

 a matter of fact, however, after passing through a thickness d of 

 material, the velocity of the rays has diminished to v', and the 

 coefficient of absorption has increased to some value \'. Since X, 

 varies rapidly with v (probably as the inverse fourth power of v) 

 the change in A, will be quite perceptible even if the change in 

 velocity is only small. Thus a change of velocity of only 2 °/^ 

 such as was found to occur in 0*47 mm. aluminium might produce 

 a change in \ of as much as 16 7o- Thus instead of the curve 

 for log / being a straight line it would be some curve falling 

 below this line, and its slope, which gives the value of X, becomes 

 steeper and steeper as the thickness of material is increased. 

 In fact we should have a curve similar in appearance to that 

 given by Wilson for the absorption of homogeneous /3-rays by 

 aluminium |. 



Prof. Sir J. J. Thomson § has very recently published a theory 

 of the transmission of the /S-rays through matter, according to which 

 the absorption of homogeneous rays should vary as (1 — e~*'^), where 

 X is the thickness of material traversed, and ^ is a constant. This 

 would give an absorption curve decreasing at first very slowly, 



* N. E. Campbell, Phil. Mag. Vol. xvii. 1909, p. 180. 



t W. Wilson, Proc. Boy. Soc. A, Vol. lxxxii. 1909, p. 612. 



X Wilson, loc. cit. p. 616. Fig. 4. 



§ Proc. Camb. Phil. Soc. Vol. xv. Part v. 1910. 



