This table distinctly involves the principle of logarithms and may be described as a modified table of antilogarithms. It consists of two series of numbers, the one being an arithmetical and the other a geometrical progression: thus 0, 1,0000 0000 10, I,0001 0000 20, 1,0002 000 I 9 90, 1,0099 4967 In the arithmetical column the numbers increase by io, in the geometrical column each number is derived from its predecessor by multiplication by i 0001.
If we divide the numbers in the geometrical column by lo g the correspondence is between lox and (I 000l) x, and the table then becomes one of antilogarithms, the base being (1.0001) 1 / 10, viz.
Napier gives logarithms to base e ', Byrgius gives antilogarithms to base (I.coo')='a.
Decimal or Briggian Antilogarithms. - In the ordinary tables of logarithms the natural numbers are all integers, while the logarithms tabulated are incommensurable.
Antilogarithmic tables are few in number, the only other extensive tables of the same kind that have been published occurring in Shortrede's Logarithmic tables already referred to, and in Filipowski's Table of antilogarithms (1849).