aaa 5 NEW SERIES for the 
Exampie IV. The reciprocal of Naprer’s logarithm of 
10, (which is the modulus of the common fyftem), calculated by 
the fecond feries for logarithms. (See Art. 63.). 
x ==10, and hence X= 5.05 X*’ = 1.010 373154 20... 
X' = 1.739 252 713 092 7 X” = 1.002 589 934 6... 
X’ = 1.170 310 367 614 6 x" = 7.000647 27x cis 
X" = 1.041 707 820 748. Be. GO, VOT BOR cam, 
x 
7 = .123 456 790123 5 
vz = 083 333 333 333 3 
Sum of pofitive terms, .206 790 123 456 8 
aXe = 16 867 116 4758 
ee = .001 226 137 7606 
7% 
I X“oS % to’ 6 8 
re se 709 5180 
ead ay = .000 005 038 8826 
4° 
t X* —T — \000 00 31 
a“ Xv+1 Tr 3 5 745 2 
T xXx*'—Tt_ 6 
px = .000 000 019 746 9 
1 X¥""=1 = .000 000 oor 
Bee ae 7.34 4 
R > .0000000000822,9 2 
R <.0000000000823,1 5 i 
Sum of negative terms, 0018 178 426 445 8° 
Difference of the a I__ — 388611697 0110 
, and negative terms, log* ro 
y tF 
log 10 
R = .000 000 000 082 3 
= -434 294 481 903. 
EXAMPLE 
