the Corpuscular Hypothesis of the 7 and X Rays. 409 



tiling. If we take different substances and take I to be always 

 the same, the " /3 ray density " in each substance is repre- 

 sented relatively by kd. 



Suppose a cavity to be made in the substance. This makes 

 no difference whatever in the value of kd anywhere in the 

 metal, even on the borders of the cavity. This follows from 

 the fact that every /? particle has to cross a weight d of the 

 substance : crossing the cavity does not count in its total 

 path. The only inaccuracy in this statement arises from the 

 fact that the value of I may not be the same in all parts of 

 the substance that border on the cavity. It will be found to 

 have little importance so far as our present purpose is con- 

 cerned, and we will not take it into account. Then we can 

 say that just as many /3 rays cross each unit volume of the 

 cavity as would cross it if it were filled with substance of 

 the kind considered, or of any other substance having the 

 same kd. The shape of the cavity is immaterial. We may 

 in fact take it to be the inside space of an ionization vessel, 

 provided only that the walls are thick enough to prevent the 

 passage of /3 rays either way. 



It is curious but not uninstructive to consider that if we 

 had a substance with no k, but with the power of reflecting 

 every (3 ray that fell upon it, and made a closed vessel of the 

 substance, and shot y rays across it, we should then get the 

 following results. If a vacuum existed in the vessel, kd 

 would be zero : if a single atom of any ordinary substance 

 were placed in the vessel, kd would in time mount to its full 

 value for that substance, and would not increase if the one 

 atom were added to by putting in any number of like kind. 

 If atoms of other kinds were inserted, there would be a 

 compromise, the density of /3 rays becoming 2A;/X(l/<i). 



To go back to the cavity in the substance traversed by 

 7 rays, the introduction of air into it makes little difference 

 in the value of kd in different parts of it unless the kd of the 

 substance differs considerably from the kd of air, and there 

 is so much air that an appreciable fraction of /3-ray energy 

 is used up when a stream of such rays tries to cross the 

 cavity. Hence the cavity must not be so big, nor the pressure 

 of air inside it so great, that this source of inaccuracy becomes 

 serious. If there were any doubt about it in a given case, it 

 could be tested by varying the pressure of the air ; if the 

 relation between pressure and ionization required a curved 

 line to represent it, it would be necessary to use the initial 

 portion of the curve for which the pressure is small. This 

 precaution is usually unnecessary, and we may take the. 

 ionization in the air of the cavity as proportional to kd. If, 



