_Decimal or Briggian Antilogarithms._--In the ordinary tables of logarithms the natural numbers are all integers, while the logarithms tabulated are incommensurable. In an antilogarithmic table, the logarithms are exact quantities such as .00001, .00002, &c., and the numbers are incommensurable. The earliest and largest table of this kind that has been constructed is Dodson's _Antilogarithmic canon_ (1742), which gives the numbers to 11 places, corresponding to the logarithms from .00001 to .99999 at intervals of .00001. 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). Both are similar to Dodson's tables, from which they were derived, but they only give numbers to 7 places. _Hyperbolic or Napierian logarithms_ (i.e. to base e).--The most elaborate table of hyperbolic logarithms that exists is due to Wolfram, a Dutch lieutenant of artillery. His table gives the logarithms of all numbers up to 2200, and of primes (and also of a great many composite numbers) from 2200 to 10,009, to 48 decimal places. The table appeared in Schulze's _Neue und erweiterte Sammlung logarithmischer Tafeln_ (1778), and was reprinted in Vega's _Thesaurus_ (1794), already referred to. Six logarithms omitted in Schulze's work, and which Wolfram had been prevented from computing by a serious illness, were published subsequently, and the table as given by Vega is complete. The largest hyperbolic table as regards range was published by Zacharias Dase at Vienna in 1850 under the title _Tafel der natürlichen Logarithmen der Zahlen_. _Hyperbolic antilogarithms_ are simple exponentials, i.e. the hyperbolic antilogarithm of x is e^x. Such tables can scarcely be said to come under the head of logarithmic tables. See TABLES, MATHEMATICAL: _Exponential Functions_.