﻿Problems in Radioactivity. 

 has been tabulated by Grlaisher* who writes 

 e r 

 u 



245 



1 



du = Ei { — x). 

 We thus have, denoting the integral by/(#), 



/•/ \ i 5 • . 7 , r^ e_W ^ W 7-T./ N 



/(#)-= 1 ^-^ sec ^sin^tfc/) = ^^ — 2— =e~ u + xEi{ — a), 

 We note that 



I e -xsecp sin <pd(p — X 1 r-y - 



= x I „ cos 9 a; sec d> 1 



.1 " 2 J* 



(6) 



see 



^ "tew 

 ~~ 9" 



= f{x)—, cos (j>f(x sec $). . . . (7) 



From (fi) the function f(x) is easily tabulated by the use 

 of tables of the exponential functions and of the exponential 

 integral. A short table of values of the function f(x) is 

 given below. The results are shown graphically on Plate VII. 

 fig. 1, with a curve of the function e~ x added lor comparison. 



Table I. 

 Table giving the values of er x and f(x) = e~ x -\- xEi(-x). 



1 



X. 



-X 



e . 



1-0000 



X. 



— X 



e 



/(*)■ 



X - 



— X 



e 



/<*). 







1-0000 



1 



•9048 



•7225 



1-3 



•2725 



•0964 



•0001 



•9999 



•9990 



; -2 



•8187 



•5742 



1-4 



•2466 



•0839 



•001 



•9990 



•9927 



•3 



•7408 



•4691 



1-5 



•2231 



•0731 



•01 



•9900 



•9497 



•4 



•6703 



•3894 



1 1-6 



•2019 



•0638 



•02 



•9802 



•9131 



•5 



•6065 



•3266 



1-7 



•1827 



•0558 



•03 



•9701 



•8817 



•6 



•5488 



•2762 



1-S 



•1653 



•0488 



•04 



•9608 



•8535 



"7 



•4966 



•2349 



1-9 



•1496 



•0428 



•05 



•9512 



•8278 



•8 



•4493 



•2009 



20 



•1353 



•0375 



•06 



•9418 



•8040 



•9 



•4066 



•1724 



30 



•0498 



•0106 



•07 



•9324 



•7819 



10 



•3679 



•1485 



4-0 



•0183 



•0032 



•08 



•9231 



•7610 



1-1 



•3329 



•1283 



50 



•0067 



•0010 ' 



•09 



•9139 



•7412 



1-2 



•3012 



•1111 



60 



•0025 



•0003 



* GlaUier, Phil. Trans. 1870, p. 36 7 . An abridged table of the 

 Exponential-Integral, Ei{ — x), is given in Dale's ' Five-figure Tables of 

 Mathematical Functions/ Arnold's, London, 1908. Extensive tables of 

 the integrals 



\ — - — -, \ — ■ =Ei( — .r), \ ue~"du and \ ur e~ u du. 



to 9 significant figures nt intervals of ■ 

 at intervals of *01 between x — 1 and 

 W. Lash Miller and T. R. Roseberg in the ' Transactions of the Roj-al 



Society of Canada/ 2nd series, vol. ix. 1903. sect. iii. pp 73- 107. 



001 between .r=0 and .r=\. and 

 ,r = 2, have been published b\- 



