﻿Absorption and Scattering of the a Rays. 909 



I proceed by assuming for cr the three values 10 ~ 8 , 10 ~ 8 ' 5 , 

 10 ~ 9 cm. The last is very small, the reason why it is in- 

 cluded will appear hi the discussion of the motion of the 

 a. particles through hydrogen. With these three values the 

 parameters of the velocity curves are 3*82, 2*82, and 1*82, 

 all values which would give a curve resembling fairly closely 

 the experimental curve. There is now only one unknown in 

 (7) and by solving we can find the value of n. In the three 

 cases I find for volume distribution ?i 1 = 7*4, 11*1, 19*2, and 

 for surface n 2 = 8'7, 13*2, 22*7. Thus, although a is very 

 uncertain, it appears that n is somewhere near the atomic 

 weight. The slow variation of n 1 and n 2 with <j is due to the 

 fact that for these parameters E 2 and E 2 are approximately 



so that a only appears in (7) by its logarithm. These values 

 of n are in good agreement with those determined by other 

 methods ; in particular, Rutherford * found the number of 

 electrons as half the atomic weight from experiments on large 

 scattering of the a rays. Some of the other determinations 

 of n are on hypotheses contrary to the present, so that for 

 these confirmation is meaningless. 



§ 4. Applications to other Substances. 

 We must next examine the absorption under other con- 

 ditions. Any mechanical hypothesis would give the correct 

 law for variations of pressure and for compound substances. 

 We need therefore only consider elements. In doing so it is 

 not convenient to consider the whole range in each substance, 

 as the end of the range can only be observed in a gas and 

 also because it fails to convey part of the information which 

 can be obtained. We take, as do experimenters, air as a 

 standard, and compare the absorbing powers of thin layers of 

 various elements with those of air. If we denote by accents 

 the various quantities pertaining to the substance to be 

 examined, the a. particle in this substance will lose a velocity 

 Av in a length Ax' where 



Av = W7ra /2 A,r'.2k^(\og(l + ic')-f(w / )\ 



where as always w' = cr'V//VA The same velocity is lost in a 

 distance Ax of air, where 



Ar = N^A,. . 2^{log(l + 1 ,)-/( W )|- 

 * Rutherford, he. cit. 



