Although the method is usually known by the names of Weddle and Hearn, it is really, in its essential features, due to Briggs, who gave in the _Arithmetica logarithmica_ of 1624 a table of the logarithms of 1 + .1^(r)n up to r = 9 to 15 places of decimals. It was first formally proposed as an independent method, with great improvements, by Robert Flower in _The Radix_, _a new way of making Logarithms_, which was published in 1771; and Leonelli, in his _Supplement logarithmique_ (1802-1803), already noticed, referred to Flower and reproduced some of his tables. A complete bibliography of this method has been given by A. J. Ellis in a paper "on the potential radix as a means of calculating logarithms," printed in the _Proceedings of the Royal Society_, vol. xxxi., 1881, pp. 401-407, and vol. xxxii., 1881, pp. 377-379. Reference should also be made to Hoppe's _Tafeln zur dreissigstelligen logarithmischen Rechnung_ (Leipzig, 1876), which give in a somewhat modified form a table of the hyperbolic logarithm of 1 + .1^(r)n. The preceding methods are only appropriate for the calculation of isolated logarithms. If a complete table had to be reconstructed, or calculated to more places, it would undoubtedly be most convenient to employ the method of differences. A full account of this method as applied to the calculation of the _Tables du Cadastre_ is given by Lefort in vol. iv. of the _Annales de l'Observatoire de Paris_. (J. W. L. G.) FOOTNOTES: [1] Dr Thomas Smith thus describes the ardour with which Briggs studied the _Descriptio_: "Hunc in deliciis habuit, in sinu, in manibus, in pectore gestavit, oculisque avidissimis, et mente attentissima, iterum iterumque perlegit,..." _Vitae quorundam eruditissimorum et illustrium virorum_ (London, 1707). [2] William Lilly's account of the meeting of Napier and Briggs at Merchiston is quoted in the article NAPIER. [3] It was certainly published after Napier's death, as Briggs mentions his "librum posthumum." This _liber posthumus_ was the _Constructio_ referred to later in this article. [4] Frisch's _Kepleri opera omnia_, ii. 834. Frisch thinks Bramer possibly relied on Kepler's statement quoted in the text ("Quibus forte confisus Kepleri verbis Benj. Bramer...."). See also vol. vii. p. 298. The claims of Byrgius are discussed in Kästner's _Geschichte der Mathematik_, ii. 375, and iii. 14; Montucla's _Histoire des mathématiques_, ii. 10; Delambre's _Histoire de l'astronomie moderne_, i. 560; de Morgan's article on "Tables" in the _English Cyclopaedia_; Mark Napier's _Memoirs of John Napier of Merchiston_ (1834), p. 392, and Cantor's _Geschichte der Mathematik_, ii. (1892), 662. See also Gieswald, _Justus Byrg als Mathematiker und dessen Einleitung in seine Logarithmen_ (Danzig, 1856). [5] See Mark Napier's _Memoirs of John Napier of Merchiston_ (1834), p. 362.