NAPIER COMMEMORATIVE LECTURE. 51 
for his purpose. They are contained in his First Table, 
which, except for the letters a, reads as follows :— 
first Table. 
a = 10000000-0000000 
1:0000000 
ah, = 9999999-0000000 
9999999 
Ay 9999998-0000001 
9999998 
as 9999997 -0000003 
O90 
a, = 9999996-0000006 
to be continued up to 
Gog = 9999900:0004950. 
I 
Now the last term of this G.P. is 
aig — Got” 
100 
do 
terms can be formed, with ao and adjoo for its first two 
terms, and p2 for its common ratio. 
If we write p2 = = r;'°, a new G.P. containing 51 
Let us denote its terms by :— 
Po PB; Boy »+ Bro 
Then £) = % Pe 0: 
1 = Pop, = Gry = Mp : l 
Bo = Pops’ = ar” = Apo r=l— 107 
Bele’ 
Bso= Pope? = Ur = Azoo9 Para 
Napier does not calculate the terms of this series. To 
do so would have been a more formidable task than the 
calculation of the set of numbers he proceeded to obtain. 
Instead of 2: = 9,999,900°0004950 he takes the number 
9999900, which differs from it by only a small fraction. 
We shall denote this number by 01 . 
5 Ri 
We shall write bo = ao and rz = ie 1 10°” 
