78 EOYAL SOCIETY OF CANADA 



{Table I), and from a; = 1.00 ^o x = 2.00 af. intervals o/ .01 {Table 

 II). Obtained by subtraction 



and cheeked by addition. 



t» ^ 



Values of /-î^. dx — - — log^ x from x = to x = 0. 100 at in- 



J X^ X 



X 



tervals of .001 {Table I). These numbers supplement the values of 



00 00 



/^ dx in the same way that /_f^ dx + log^ x supplements those of 

 x'^ "J X 



X X 



00 



y ^ dx. They were obtained by subtraction, 

 X 



X 



00 00 



f£l dx — J_ — loge X = e,-^—' ^ _ { f^dx -\- loge x ) 

 •^ .x^ X X ^*^ X ^ 



X X 



00 



and checked by addition. As in the case of I A^ dx -\- loge x the num- 



•^ X 



X 



hers tabulated are negative in sign. For example: for x = 0.001 



QO 



/-If dx — J_ — loge X = 

 'i. x'^ X 



0.423 283 252 



hence fH Jj; = — 0.423 283 252 + 1000 — 6.907 755 279 



•^ x'^ 



= 992.668 961 469 

 Values of fxe-^ dx from x = to x = 1.000 at intervals of .001 



X 



{Table I), and from x = 1.00 to x = 2.00 ai intervals of .01 {Table II). 

 Prepared from Newman's values of e-^ by multiplication, according to 

 the formula 



00 



fxe-^dx = {1 + x) e-^ 



X 



anu checked by taking first and second differences from x = to x = 1, 

 and first, second, and third differences from x' = 1 to a; = 2, on the type- 

 written sheets. 



00 



Values of j xh-^ dx from x=0 to x = 1.000 at intervals of .001 



X 



{Table 1), and from x = 1.00 to x = 2.00 at intervals of .01 {Table II) 

 From Newman's Table of e-^ by multiplication, 



J'xh-^ dx = I 1 + (I + a;)2 1 



