PENETRATI.N G RADIATIOX FROM THE EARTH 



99 



v' = i27r Q»o M,; 1 / P- 1 2i) — / /^i^i +/^ z,) \ 



(3) 



agreeing with the value obtained in the previous paper, where a 

 numerical table o^ the function f{x) is given, enabling (2) and (3) to be 

 evaluated. It is shown that n and n' are practically identical if z^ 

 exceeds 11 cm. so that the entire contribution to the penetrating 

 radiation is limited to that coming from a few centimetres depth of 

 radium bearing rock or soil at the earth's surface. 



TABLE I. 



The number of ions produced in a small cavity at a depth Z2 below 

 the surface is easily obtained by writing down the contribution at the 

 surface of a slab of thickness z.^ lying above the cavity and that due 

 to the semi-infinite solid below it : we thus have 



„, = ?^Q!!£|l_f(,.., I +?^^" = ^^^i2-f (/<,.=)!. . . (4) 

 We note that when the cavity is at a considerable depth 



f (fji^z^) becomes negligible and (:n.,)œ = 



4-7r Qr?c 



, agreeing with 



the value calculated directly to correspond to this condition.* Also 

 if we take 23=0, corresponding to the intensity at the earth's surface, 

 we have since f (o) =1, for the corresponding ionization the value 

 (n^)^ = 27T Q n^lfi^^. In this connection Rutherford points out 



*Kin<ï, Plul. M<i(J-, 23 Feb., 1912, p. 24.'. The writer takes the occasion to 

 correct the description of Fig. II which should read: Curve I, h=-llcm.: Curve II, 

 h=Ucin.: Curve III, /i,=ll cm.; Curve IV,/i=oo . Rutherford, Radio-activity, 

 1913, p. 637. 



