the ol Particles of Radium. 327 



Hence the rate of expenditure of energy on ionization 



_k 

 if 1 



1 



s n+2 



If the strip of air (supposed thin) in which the ionization 

 is measured is at such a height above the radium layer that 

 the a rays from the top of the layer pass it by a distance a, 

 and those from the bottom by a distance x — ol, then the 

 ionization produced in this strip by the a particles from all 

 parts of the layer 



oc x n+2 dx 



Jx-d 



= aL^+ 2 - (x-dy^X 



where A is a constant. If the rays from the top of the layer 

 pass the strip by %, and those from the bottom do not reach 

 it, then the ionization 



2 



= A* n+2 . 



In the curves as found experimentally the effect is further 

 complicated by the fact that the ionization-ch amber has an 

 appreciable depth of 2 mm., and that the cones of rays have 

 an appreciable vertical angle. We need not, however, take 

 these factors into account in the formula. We can give n 

 different values, plot the corresponding curves as found from 

 the formula, and round off the corners in accordance with the 

 effect which the two disturbing factors must have. 



When this is done, it is found that n = J gives a curve 

 which is very near to the actual form. Choosing the value 

 5 mm. for d, which seems proper from an inspection of the 

 curve and from trial, the ionization is equal to Aa^ from 

 x = to •*• = 5 mm,, and thereafter to A{a;^ — (x— -5)*}. The 

 curve obtained from this formula is plotted in fig. 1, P ; and 

 the corners are rounded off by the dotted line. The value of 

 A is chosen so as to make the curve more easily comparable 

 with the experimental curve E (portion d a be). 



Curves Q and R are derived from the formula when n is 

 put equal to 1 and to 1/3 respectively. It will be seen that 

 they do not approach the experimental form so well, and err 

 in opposite directions. 



