52 H. S. CARSLAW. 
The numbers in Napier’s Second Table are the 51 terms — 
of the G.P., beginning with bo, bi, and with the common 
1 
| a= 10 
b 
YT, = 1 =z 8 
bso = bor.” 
This Second Table, except for the b’s, reads as follows :— 
Second Table. 
ratio re. 
Thus 6, 
Ay 
bors 
2 
bors 
b, = 10000000-000000 
100:000000 - 
6b, = 9999900-000000 
~ 99-999000, 
b, = 9999800:001000 
99:998000 
6, = 9999700-003000 
99-997000 
6b, = 9999600-006000 
and so on up to 
b., = 9995001-°2248041 
Next another G.P. is formed. This consists of 21 terms.. 
The first term is the same as ao or bo. We shall denote it. 
by co. The second is 9,995,000, very nearly the same as. 
_ eCige pe 
bso. We shall denote it by ci. The ratio ee 1 2000 
to be denoted by 73. ; 
This G.P. will be as follows :— 
05 1 Op — 8 
GC, = Cs @, == UG? 
a ue va 
; 2000 
Co = Cor” 
It is easily calculated. It forms the first column of 
Napier’s Third Table, and reads as follows :— 
1 Napier has 9995001°222927, and this mistake affects certain numbers. 
in his Radical Table. 
