402 



Mr. A. J. Ellis. On the Potential Radix [Feb. 3, 



1628. *Vlacq, A. In his second edition of Briggs, 1G28, and not 

 in those printed later, gives Briggs's § Radix to ten places only, but 

 repeats the two internal errors mentioned above, correcting both of 

 them, however, in his chiliads. There is no notice of this radix in 

 * Vega's edition of Vlacq, under the name of " Thesaurus Logarith- 

 morum," 1794. 



1714. *Long, J. "Philosophical Transactions," vol. 29, 1717, 

 No. 339, pp. 52 — 54. A radix of logarithms of the form 'r, '0 m r from 

 r=l to r=9, and m=l to m—7, and their corresponding natural 

 numbers, intermediates being found by continual divisions. He finds 

 the numbers by " one extraction of the fifth or sursolid root for each 

 class," and for a method of performing that extraction refers to 

 Halley's paper on finding the roots of equations, in *" Phil. Trans," 

 vol. 18, for 1694, pp. 136—148. 



1742. f Gardiner, W. Tables of Logarithms. He gives a table of 

 logarithms to twenty places of decimals for the numbers 1 to 1143, 

 101000 to 101139, and 00000 to 00139 (the two last with the first, 

 second, and third differences), and a rule whence, by the help of these 

 tables, the logarithm to any number is found to twenty places of 

 decimals. No explanations. 



1771. § Flower, Robert. " The Radix, a new way of making 

 Logarithms." Flower introduces the word Radix, here preserved in 

 memoriam. He apparently used it because he considered all numbers 

 between 1 and 10 to be roots of 10. He applies the term to several 

 tables. First, " the cube radix of 10," a series of cube roots, 

 10, 3 \/10, 3 v /3 \/10, &c, each expressed as decimals to ten places, 

 ending at 1'0 9 2 — r, and then each term is again expressed as a 

 series of cubes of r. He shows how to find the tabular logarithms of 

 any number from this table, and actually finds tab. log 2 to ten places 

 of decimals in two different ways. He next calculates " the square 

 Radix of 10," a series of square roots, 10, a/10, */ </10, &c, with 

 indices of the powers of the last, l*0 9 2=r. By this he proved the 

 work with the cube radix. But finding the labour much lessened 

 by the smaller intervals between these square roots, and still more 

 so when the two radixes were combined, he was led (p. 9) to the 

 " classical radix," which is so called because of the " classes " into 

 which the numbers l'0 m r were divided by the different values of 

 m, corresponding to my positive numerical radix, the number of 

 the class being m+1. This he calculated, apparently from the two 

 first radixes separately, or " both ways," as he says, to ten decimal 

 places, to 1'0 9 1. He subsequently enlarged his "square radix," 

 under the name of the square-square radix, and added another, 

 called the cube-square radix, of the form 10, 3 a/10, a/ s a/10, 

 ^v^a/IO, &c, and from these he calculated his classical radix up to 

 PO-qI and twenty- three places of decimals, of which he believed 



