1881.] 



as a Means of Calculating Logarithms, fyc. 



403 



twenty-two to be correct, as was actually the case, except for tab. 

 logs of 1'4, 1"0 4 5, and 1"0 8 9, for which, only twenty-one places were 

 correct. To use this radix he gave three rules, all original, called 

 the " direct," the "reverse," and the "reflected" rules. It is the last 

 one which is most valuable, and which he mainly exemplifies. This 

 rule consists in preparing the number by reducing it to a decimal 

 fraction having as its whole number, and then multiplying it in 

 succession by numbers of the form l'0 m r till the result is unity, then 

 the sum of the complements of the logarithms of these numbers 

 (given in the radix) will be the logarithm of the reduced number. 

 This was at the time an entirely original conception, and the 

 method of working it out, which was totally different from Briggs's, 

 gave the simplest means for finding tabular logarithms to twenty 

 places. I give these details because Raper and Horsley, as well as 

 Hutton (who reports their opinions, in the *jvrst edition only, 1785, of 

 his mathematical tables, p. 72, foot note), who had evidently very 

 insufficiently studied Flower's work, considered his process to be 

 merely " a large exemplification " of Briggs's. Although Flower's 

 method of finding the number from the logarithm agrees with Briggs, 

 and although he speaks of Vlacq, I believe that he never saw either 

 Briggs's or Ylacq's works containing the radix, which were expensive 

 aud difficult to procure. He seems to have known of them chiefly 

 from # Sherwin's tables. Robert Flower was an obscure writing- 

 master at Bishop's Stortford, where he was buried, aged 63 years and 

 unmarried, on the 23rd of February, 1774, just three years after his 

 book, " printed for the author," was published. It consequently 

 rapidly disappeared. It is not mentioned in Mr. Glaisher's catalogue 

 (Rep. Br. As., 1873), it is not in De Morgan's catalogue ; I found no 

 copy at the British Museum, at Oxford, or Cambridge, or at the 

 Royal Society. But there were two copies in Mr. Graves's collection 

 at University College, London, one of which, at my suggestion, has 

 been presented to the British Museum. 



1802. Leonelli, Z. " Supplement Logarithmique," Bordeaux, An. 

 XI (1802-3). Leonelli re-discovered Briggs's method, and having 

 fortunately obtained a copy of Flower's book from M. Eveque, who 

 bought it in London, reproduced his radix for tabular logarithms to 

 1'0 10 1 and up to twenty places only, added another radix for natural 

 logarithms to the same extent, and gave Flower's rule, with his name. 

 This work was translated into German by *Leonhardi in 1806, with 

 numerous changes. Only one copy of the original work was known 

 to exist, presented by the author to the city library of Bordeaux, from 

 which it was freprinted, with a preface, in 1876, by M. Hoiiel, who 

 had already given from it an account of Flower's rule, with a radix, 

 name, and date, in his f" Tables de Logarithmes a Cinq Decimales," 

 Table V, where he styles it " la methode la plus simple de toufces celles 



