38 Dr. A. S. Eve on the Ionization of the 



the ionization at P will be 



.0 



•J «. o 



27Txda:dYQK _y v 



\r 



(r+yy 



where y is small compared with r, 



h cot 6 . h cosee 2 6 dd 

 27rQK ^ ^r- 



Xh cosec 9 „ — XT cosec 



= 2,rQK \ 



A 2 cosec 2 d 

 V2 C ot0d0 



dX 



Xh cosec 



V cosec 6 



2ttQK f W 

 2ttQK 



V 



c 



cos 



s0 



-XA/ sin 



<?<? 



■"/*&. 



(17) 



In order to evaluate this troublesome integral I have 

 drawn the curve y = e~ Kh ' z , and determined the area from 

 £ = to z=l, for various values of h, and substituted the 

 values of X, V, Q, and K given in this paper. When h is 

 zero we have 27rQK/A/, agreeing with our former work. 



Thus the numbers of ions produced per cm. 3 per sec. at 

 various altitudes by the penetrating radiation due to radium 

 C in the earth is given in the following table : — 





Penetrating Eadiation. 



Height in matres. 



Batio. 



Ions per em. 3 

 per sec. 







TOO 



•80 



1 



■9S 



•78 



10 



•83 



•67 



100 



•36 



•29 



1000 



•COl 



•008 



(18) 



The values in the ri^ht column should perhaps be doubled 

 if we add the effect of thorium to that of radium. 



In this calculation I have not made any correction for the 

 decrease of density of the air with increase of altitude. This 

 would tend to augment the lower figures, because the ravs 

 would be less readily absorbed ; but, on the other hand, the 

 number of ion? produced would be diminished with a decrease 

 of pressure. 



