86 BELL SYSTEM TECHNICAL JOURNAL 



logarithm of the disintegration-constant of the emitting substance. 

 This is the way in which this, the " Geiger-Nuttall " relation, is usually- 

 expressed : 



\og\ = A + B log R. (12) 



The constant B is given (by Hevesy and Paneth) as 53.9 for all three 

 series of radioactive substances, which signifies that the disintegration- 

 constant varies as the fifty-fourth power of the range of the ejected 

 particles! I do not know of any other relation between physical 

 variables in which so high a power occurs; radioactivity, like astron- 

 omy, is the home of colossal numbers. The constant A varies from 

 one series to another; it is given as —37.7 for the radium series. 



The Geiger-Nuttall relation, like most simple formulae, is a mere 

 approximation. For the radium series its degree of accuracy is illus- 

 trated by Fig. 4; the curve drawn through the various points is not 

 quite a straight line. In the actinium series there is a jolt; the point 

 for actinium X lies quite away from the place it should occupy on the 

 straight line drawn to fit closest to the points for the other members, 

 and in fact the half-period of AcX is shorter than that of RdAc, though 

 its alpha-particles are slower. A straight line can be drawn to pass 

 near the points for the remaining members of this series, and another 

 to pass near the points for the descendants of thorium, about as success- 

 fully as the line in Fig. 4 fits the points for the radium family. Extend- 

 ing the line drawn for the thorium family to the value of the range for 

 the fastest of all alpha-particles,^^ those of thorium C, one obtains by ex- 

 trapolation for the half-period of this substance the fantastically small 

 value 10~^^ second. There is no discernible prospect of verifying this 

 by direct measurement, and in quoting it one should remember the 

 risks of extrapolation. 



An alpha-particle is a helium nucleus; when it acquires two 

 electrons, the combination is a helium atom. Helium therefore is a 

 daughter-substance of every radioactive substance which transmutes 

 itself by emitting alpha-rays. 



Passing over from alpha-rays to beta-rays, we take at once a great 

 step backward from the clear to the obscure. 



The great trouble arises from the fact that beta-rays are electrons, 

 and electrons exist both in the atom-nuclei and in the electron-systems 

 which surround them, or at least they come out of both localities. 

 Whereas the emergence of an alpha-particle from a substance is a clear 

 sign of the transmutation of one atom of that substance, the emer- 

 gence of a beta-particle need not mean anything of the sort; it may 



2^ Reservation being made for the particles mentioned in footnote 22, 



