The only other mathematician besides Napier who grasped the idea on which the use of logarithm depends and applied it to the construction of a table is Justus Byrgius (Jobst Bürgi), whose work _Arithmetische und geometrische Progress-Tabulen_ ... was published at Prague in 1620, six years after the publication of the _Descriptio_ of Napier. 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, 1,0001 0000 20, l,0002 0001 . . . . 990, l,0099 4967 . . . . In the arithmetical column the numbers increase by 10, in the geometrical column each number is derived from its predecessor by multiplication by 1.0001. Thus the number 10x in the arithmetical column corresponds to 10^8 (1.0001)^x in the geometrical column; the intermediate numbers being obtained by interpolation. If we divide the numbers in the geometrical column by 10^8 the correspondence is between 10x and (1.0001)^x, and the table then becomes one of antilogarithms, the base being (1.0001)^{1/10}, viz. for example (l.0001)^{1/10·990} = 1.00994967. The table extends to 230270 in the arithmetical column, and it is shown that 230270.022 corresponds to 9.9999 9999 or 109 in the geometrical column; this last result showing that (1.0001)^{23027.022} = 10. The first contemporary mention of Byrgius's table occurs on page 11 of the "Praecepta" prefixed to Kepler's _Tabulae Radolphinae_ (1627); his words are: "apices logistici J. Byrgio multis annis ante editionem Neperianam viam praeiverent ad hos ipsissimos logarithmos. Etsi homo cunctator et secretorum suorum custos foetum in partu destituit, non ad usus publicos educavit." Another reference to Byrgius occurs in a work by Benjamin Bramer, the brother-in-law and pupil of Byrgius, who, writing in 1630, says that the latter constructed his table twenty years ago or more.[4] As regards priority of publication, Napier has the advantage by six years, and even fully accepting Bramer's statement, there are grounds for believing that Napier's work dates from a still earlier period. The power of 10, which occurs as a factor in the tables of both Napier and Byrgius, was rendered necessary by the fact that the decimal point was not yet in use. Omitting this factor in the case of both tables, the connexion between N a number and L its "logarithm" is N = (e^-1)^L (Napier), L =(1.0001)^[(1/10)N] (Byrgius), viz. Napier gives logarithms to base e^{-1}, Byrgius gives antilogarithms to base (1.0001)^{1/10}.