[KING] ABSORPTION PROBLEMS IN RADIOACTIVITY 101 
TABLE I. 
x = F(z) x —T f(z) x Er if ae) 
€ € € 
0 1-0000 | 1-0000 1 9048 220 1-3 -2725 -0964 
-0001 -9999 -9990 2 8187 -5742 1-4 - 2466 -0839 
-O01 -9990 -9927 3 7408 -4691 1-5 -2231 -0731 
-O1 -9900 -9497 +f 6703 -3894 1-6 -2019 -0638 
-02 -9802 -9131 5 6065 -3266 1-7 -1827 -0558 
-03 -9704 -8817 6 5488 -2762 1:8 -1653 - 0488 
-04 -9608 -8535 a 4966 - 2349 1-9 - 1496 -0428 
-05 -9512 -8278 8 4493 - 2009 2-0 -1353 -0375 
-06 -9418 -8040 -9 4066 -1724 3-0 -0498 -0106 
+07 -9324 -7819 1-0 3679 -1485 4-0 -0183 -0032 
-O8 -9231 -7610 oil 3329 -1283 5-0 -0067 -0010 
-09 -9139 -7412 1-2 3012 LIRE 6-0 -0025 -0003 
— TT == 
Table giving the values of e andf(x) —e + x E1i(—x). 
When x is small, we have 
: Le FE 
Hi(— 2) = Y + log z — x + — SE NET 
2.2! 3-3! 
when 7 is Euler’s constant, + = -5772. 
Thus the expansion for f(x) when x is small is 
x 
Pret TR Vet St Nene: (8) 
dd 
When z is large the asymptotic expansion for f(x) is easily found from 
(9) by successive partial integrations to be 
al Tea eet | 
oy == ay a FO wh A (9) 
ae 
a | 4p Gr 
3. Returning to (5), we see that the intensity at a distance z from 
the slab is given by 
ea 
FR K 
I i (dz) — FR + Kh) } MARNE (10) 
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, considered by Eve; 
1 Eve “On the Ionization of the Atmosphere due to Radioactive Matter, ”” Phil. 
Mag., XXI, Jan. 1911, pp. 26-46. 
