388 NUMERICAL VALUES OF THE SINE-INTEGRAL, COSINE-INTEGRAL, ETC. 
The Sine-integral Curve, y=Six, for positive abscissae. 
The Cosine-integral Curve, y=Cix. 
Note added July 30, 1870. 
Professor Oppermann, of Copenhagen, who was present at the reading of this paper, 
shortly afterwards presented to the Royal Society two pamphlets, “ Tabulae logarithmi 
integralis, auctore L. Stenberg, Malmogise, Pars I. 1861, Pars II. 1867,” containing 
values of lil(P from x= — 15 to #=3-5 at intervals of ’01 to 18 places of decimals; 
the arguments differ therefore from those in this paper by the modulus of the common 
logarithms as a factor. From a reference in the second of these tracts the author 
found that Tables of Si#, Ci x, Ei x, and Ei( — x) from 0 to 1 at intervals of ’01 and 
from 1 to 7-5 at intervals of 0T, had been computed by Bretschneider, and published 
in the 6 th volume of Schlomilch’s ‘ Zeitschrift fiir Mathematik und Physik.’ The 
referees recommended the comparison of the parts common to these Tables and those 
given in this paper; this has been made, and the following errors have been found in 
Bretschneider’s values : — 
\\e a for a= 0-34 should be — 0T3036 32936 instead of — 0T3030 32936 
\ie~ a for £1=1*9 should be — 0-05620 43781: instead of — 0-05620 43780: 
a 
li e a 
li e~ a 
Si a 
si a 
4-9 
37-33237 06037: 
-0-00121 14833. 
18-66679 10435: 
1-56963 89381 
should be 
4-9 137-33245 06037 : | —0*00129 14833 . 1 18*66687 10435 :| 1*56955 89381 
the error previouly alluded to in Ei( — 5) is corrected in this paper. 
Bretschneider has indicated by dots certain limits between which the eleventh figure 
must lie, and the agreement between these and the eleventh figure in the Tables V. to 
VIII. was so close, that it seemed worth while to retain this figure, on the understanding 
that it may be in error to the extent of a unit. 
