17 



result is a function of the relation of the stopping power of 

 the screen to the range of the particle ; so that if experiir ent 

 is made tlie one can be found in terms of the other. The 

 stopping power of the screen may be made the subject of a 

 direct measurement, and so the range of the a particle can 

 be determined. I find it better, however, to compare the 

 range of tlie uranium or thorium with that of radium, work- 

 ing the experiment by a substitution method ; for the range 

 of radium is known with some accuracy, and the method itself 

 is accurate enough when employed in comparing ranges, but 

 a little uncertain m its application to direct determinations, 

 as will be exjolained later. 



Experiments of this kind have already been made by 

 several observers, notably by Professor Rutherford and Miss 

 Brooks (^Thil. Mag.," July, 1900). But at the time when 

 they were made it was believed that the a rays were ab- 

 sorbed according to an exponential law : it was not known 

 that each a particle possessed a definite range or penetrating 

 power. Consequently the results were not in all cases ex- 

 pressed in such a way as to render them available for the cal- 

 culation of the range. I have, therefore, found it convenient 

 to repeat them. 



In the following theoretical treatment of the question 

 the following cases are considered : — 



(a) When the layer of radio-active material is so thick 

 that the a rays from the bottom of it are unable 

 to reach the air above. Such a thickness is of the 

 order "002 cm. 



fh) When the layer is extremely thin. 



(c) When the layer is thicker than in (h), but not so 



thick as in (a). 



(d) When the radio-active material is in the form of 



small spheres scattered over the floor of the iouisa- 

 tion chamber. 



The first and second are really special cases of the third. 

 Uranium and thorium are conveniently treated under (a), in- 

 duced activities under (h), and radium under (c). 



CASE (a). 



lonisation jjroduced in air above a thick layer of radio- 

 active material, on which sheets of absorbing material 

 are laid. 

 Let the surface of the radio-active material be of unit 



area. Let the full range of the a particle be R, and the 



