404 Mr. A. J. Ellis. On the Potential Badix [Feb. 3. 



qui out ete proposees pour le meme objet." From this work an 

 account of Flower's method was introduced into an appendix to Don 

 Vicente Vazquez Queipo's " Tablas de los Logarithmos Vulgares," 

 from the f French edition of which I first heard of Flower's rule- 

 Queipo added a twenty-first place from Thoman. Schron gives 

 Flower's radix to sixteen places, tabular and natural, with the rule, in 

 his " Interpolations-Tafel," 1861, p. 76, probably from Leonhardi, 

 but does not mention Flower's name, and the same omission occurs in 

 fHouel's translation of the same. 



1806. *§ Manning, Thomas. " New Method of Computing Loga- 

 rithms," " Phil. Trans.," 1806, p. 327. Manning was evidently un- 

 acquainted with Briggs, Flower, and Leonelli. His table is essentially 

 a potential negative radix for natural logarithms, and as such was 

 partly an anticipation of my conception, explained below. But he did 

 not form the powers of 1 — '0 m l, he merely tabulated — r log (1 — '0 m l) 



10 m 



from r—1 to r=9'and m = l to m=8, conceived only as r log — • . 



' ^ ° 



He therefore performed the division by the values of the powers of 

 1 — *0»1, by means of a continual multiplication by '0 m l and subtrac- 

 tion, which makes his process simple, but very lengthy. It is, how- 

 ever, entirely original. He did not apply his method to the discovery 

 of the number from the logarithm. 



1845. *§Weddle. "Computation of Logarithms and Anti-Loga- 

 rithms," in " The Mathematician," November, 1845, pp. 17-25. He 

 says his method was discovered in 1838, and gives it as a modification 

 of Manning's. But it consists, in fact, of a complete negative numerical 

 radix for both tabular and natural logarithms for sixteen decimal places 

 down to —log (1 — "0 6 1), calculated by the usual series for —log (1—x), 

 and applied, not only to finding the logarithms to numbers, but to 

 finding numbers from logarithms. It is, therefore, really an original 

 method, completely worked out, and the most important since Flower's. 

 Extended tables were given by Shortrede, 1849. 



1846. §Gray, Peter. " A Practical Method of Forming Logarithms 

 and Anti-Logarithms," 8th December, 1846, reprinted from the 

 " Mechanics' Magazine " for October and November, 1846, contains a 

 re-arrangement of Weddle's plan, with improved tables. 



1847. *§I7eam, Professor. " Practical Method of Forming Loga- 

 rithms and Anti-Logarithms, independently of extensive Tables," in 

 "The Mathematician " for March, 1847, pp. 249—252. This was an 

 independent discovery of Weddle's method for finding logarithms by 

 the negative nnmerical radix, but for finding numbers from logarithms 

 he used the positive numerical radix. He gives tables to ten places 

 of decimals, down to —tab. log (1 — '0 9 1), but does not mention how 

 they were calculated. Extended tables were given by Shortrede, 

 1849. 



