166 Prof. E. Rutherford on Radioactivity 



Case II.— We will now consider the case of a radio-active 

 cylinder, where the current is measured between two con- 

 centric cylinders. Let fig. 2 b represent a cross-section of 

 the cylinders. Let a = radius of radio-active cylinder D, 5 = 

 radius of concentric cylinder E. Suppose length of cylinder D 

 to be large compared with the distance between the cylinders. 

 If A is the coefficient of absorption of the radiation, the 

 intensity I at a distance r (outside D) from the centre is 

 easily seen to be 



I a 



I 



- e 

 r 



-\(r-a) 



l O 



where I = intensity of radiation at the surface, since without 

 any absorption ihe value of I would fall off inversely as the 

 distance. The total energy of the radiation near the surface of 

 the external cylinder is given per unit length by 



Io^V A( *- a) , 2irb, 



the energy per unit length close to the surface of the active 

 cylinder by I . lira. 



The total energy absorbed in the gas is thus equal to 



I .27ra{l-£-* 6 ~">}. 



If n = the number of ions produced per second due to the 

 length / of the active rod, 



W. n = I . Viral \ 1 — e-W-O j. 



= I . S{l-e-W- a >\, 



where S is surface-area of active cylinder ; 



W i 



Or SI = gM g -A(*-a) p Where i= ™, 



= i w* ^ i where A = — = constant. 



In both of the cases considered, half the radiation has been 

 absorbed in the substance which is made radio-active, and the 

 other half passes through the gas, since the radiation is given 

 out from the surface in all directions. In the case of complete 

 absorption of the radiation in the passage through the gas, 

 the maximum current i is given by 



SI = Ai. 

 An investigation is now in progress to determine the value 

 of A, that is, W/e. If A. is determined, the intensity of the 

 radiation can at once be expressed in absolute measure. 



