53 
NAPIER COMMEMORATIVE LECTURE. 
C, = 10000000:00000 
5000-00000 
c, = 9995000-00000 
4997-50000 
¢ = 9990002-50000 | 
4995-00125 
c, = 9985007-49875 
4992-50374 
c, = 9980014-99501 
and so on up to 
C=  9900473°57808. 
This Third Table of Napier’s, in which these c’s form the © 
first column, contains 69 columns. The terms at the top 
of these columns are the terms of the G.P., beginning with 
co and 9,900,000, a number differing slightly from cz. If 
we denote these terms by 
do, di, dg up to deg, 
ae 2808! 
This common ratio we denote by 74. 
Thus we have 
Cos = ll, = ah 
a, — 29, Gi; = 10" 
ad — One 45 1 
1, va 1 1023 
deg= dyr,® 
These form the terms in the first row of the Third Table. 
The columns each contain 21 terms in G.P., the common 
; : ft 
ratio being now 1 — 9000° 
This Third Table, except for the c’s and d’s, reads as 
follows :— 
First column. Second column. | Third column. Siatyninth column 
dy d, a, des 
€, 10000000-0000 | 9900000-0000; 9801000-0000 5048858:8900 
¢, 9995000-0000 | 9895050:0000| 9796099-5000 5046334:4605 
99900025000 
9985007 -4987 
up to 
€ 9900473-5780 
9890102:4750 
98851574237 
9801468°8423 
9791201°4503 
9786305°8495 
9703454:1539 
5043811-°2932 
5041289°3879 
4998609-4034 
