﻿24:6 Mr. L. V. King on Absorption 



When x is small we have 



Ei (- lV )=y + log*— *+ 22"j - 3^37 + &c - 



where 7 is Euler's constant, 7=*5772. 



Tims the expansion for/(#) when <r is small is 



/(.*) = 1 + * log . i- (1 -7) .*-£ (8) 



When * is large the asymptotic expansion for /(#) is 

 easily found from (6) by successive partial integrations to be 



A.)-g{i-^ + J,'- ......}. • ■ (») 



Returning to (5) we see that the intensity at a distance z 

 from the slab is given by 



i=~{n^)-fi^+^)~\. . . do) 



§ 3. This result has an immediate application to the theory 

 of the decrease with height above the earth's surface of the 

 intensity of the penetrating radiation in the earth's atmosphere, 

 a problem considered by Eve'', who has worked out the case 

 for a homogeneous distribution of radioactive matter (radium) 

 throughout an infinite depth. With a slight change in notation 

 the result is there obtained in the form 



»=^»fV?&, .... (ii) 



where K Ji 



ft=number of ions produced per second per c.c., 

 Q = 2*7 x 1*4 x 10 -12 gramme per c.c. = the mean radium 



content for sedimentary rocks (Strutt). 

 k = '034:X2*7 cm. _1 = mean coefficient of absorption of 



7 rays by rocks (McClelland). 

 n —'6'74: x 10* = number of ions produced per c.c. per sec. 

 in air at normal temperature and pressure at a 

 distance of 1 cm. from 1 curie of radium supposed 

 concentrated at a point (absorption of 7 rays by air 

 and by the substance of the radium salt neglected) 

 (Eve)t 

 X,=*000044 cm. ^coefficient of absorption of 7 rays by 

 air at normal pressure and temperature J. 



* Eve, "On the Ionization of the Atmosphere due to Radioactive 

 Matter," Phil. Maz. xxL Jan. 1911, pp. 26-46. 



t Eve, Phil. Mag. Oct. 1911, p. 561. 



X Hess, " Ueber die Absorption der y-Strahlen in der Atmosphare," 

 Pkys. Zeit.xii. Nov. 1911. p. 998. A mean value of \=447xl0- 4 is 

 obtaii.ed, in substantial agreement with the value employed by Eve. 



