§ 11. We are now in a position to understand how Napier completed his Tables.

We take, to begin with, his First Table. The logarithm of the first term is zero.From § 10, Theorem I., the logarithm of the second term lies between r-s and (r-s)r/s; that is, between 1.000 000 0 and 1.000 000 I.If this is taken as the A.M. of these two numbers, we have for the logarithm of the second term in that Table the value 1.000 000 05. The remaining terms in that Table form with these two a G.P., so that the logarithms have a common difference 1.000 000 05, and the logarithm of the last term can be taken as 100.000 005.