100 THE ROYAL SOCIETY OF CANADA 
tabulated by Glaisher,’ who writes— —2£ 
u 
e du = Ei(-x) 
— © U 
We thus have, denoting the integral by f(x) 
T —X SeCp le ea TT 
f(x) = De sing de =x e du=e+x Ei(-x)...(6) 
Ww 
0 v 
We note that 
@ —xX sece xsecp —U 
e sing dg = x e du 
ru 
0 £ 
o -U DO —Y 
= À e du = cose x sece e du 
uw uv 
it xLsece 
= CE), = (GORD GAL SCOP) AN acces LE hes ice 
From (6) the function f(x) is easily tabulated by the use of tables 
of the exponential function 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 I with a curve of the function e” added 
for comparison. 
! Glaisher, Phil. Trans., 1870, p. 367. An abridged table of the Exponential- 
Integral, Hi( — x), is given in Dales’ “ Five-Figure Tables of Mathematical Functions,” 
Arnold’s, London, 1908. Extensive tables of the integrals 
% x —u + —u c —u 
— 4 e du ue du and we du 
edu  Ei(—x) = : 
: U 
x vu? a Te x 
to 9 significant figures at intervals of -001 between wo and z=1 and at in- 
tervals of -01 between x — 1 and x — 2 have been published by W. Lash Miller 
and T. R. Rosebrugh in the Transactions of the Royal Society of Canada, 2nd series, 
Vol. IX, 1903: Sec. III, pp. 73-107. 
