344 NEW SERIES for the 
Exampie VI. To thew that the feries inveftigated in this 
Paper are applicable in every cafe, whether the number whofe 
logarithm is required be large or fmall, let it be required to 
calculate the common logarithm of the large prime number 
1243 to feven decimal places, by the fecond feries, (Art. 63.). 
me: X” = 1.42356148 
MX = 621.50040225 XY = 1.10080913 
X'= 17.64228446 XY = 1.0248925. 
X’= = 33.05 305457 a =| T:G0G8047 
nae = -000 805 Sor 
vz = +083 333 333. 
Sum of pofitive terms, -084 139134 
X'’—1 
= Xp = 1055 794 813 
xe 
X41 Ee : = .007 914 766 
Mt 
aa = .000 682 688 
sa pee = .000 046 861 
# ar = .000 003 OO 
oa : = .000 000 189 
R > .000000012,6 R = ston e00083 
R. < .000000012,7 
Sum of negative terms, -004 442 331 
Ce. See 68 
Nap. log* x on9 ati 
I at 
Maes ee 
i A ed 
Common log of 1243 = ae = 3.094 471 I. « 
No. IX. 
