18 



ransfe lost by passing normally through the absorbing sheet 

 be D. 



Let the stopping power of the radio-active material per 

 radio-active atom be s. This means that if an a particle 

 passes parallel to the axis along a cylinder containing only as 

 much matter as goes with one radio-active atom of the radio- 

 active material, the loss of range is on the average s times 

 the loss when an average air molecule is substituted for the 

 radio-active matter. The length of the cylinder is, of course, 

 immaterial. 



The a particles emerging into the air will penetrate to 

 distances depending on the quantity of matter traversed be- 

 fore emerging. Consider, in the first place, all those whose 

 ranges in air after emergence lie between r and r + dr. 

 These move at various inclinations to the normal to the sur- 

 face of the layer ; the number depends on the inclination, and 

 may be reckoned as follows : — 



Consider only those whose inclinations to the normal lie 

 between and $ + S0. All these come from a layer of a certain 

 thickness at a certain depth below the surface. The depth 

 does not concern us, but the thickness does, for we need to 

 know the number of radio-active atoms in the layer. 



Let n be the number of radio-active atoms in a c.c. of the 

 material. Let n„ be the number of molecules in a c.c. of air. 

 The molecules are not uniform, of course, but are averaged for 

 our purpose. 



Then an a particle loses the same range in traversing a 



Wo 



distance Sr in air as in traversing a distance - . 8r in the radio- 

 es 



active material. 

 Hence, if PF' is the 

 layer in question, 

 the radio-active atom, 

 OS the course of 

 the a particle, 



then 0Q=^ and 



ns 



ON = -^- ■ cos 0- 



This last expression 



is also the volume of the layer from which the a particles come, since 



we are considering unit area of the material ; and therefore the 



number of radio-active atoms in it is ° '— 



