406 



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



Vienna. This is an extended positive numerical radix of the form r 

 and l + '0 m r, where r varies from 001 to 999, and mfrom 1 to 2. The 

 rule is one of continual division by the three, six, and nine first places 

 respectively, similar to the first example in this paper, and, after nine 

 figures are obtained, by a table of proportional parts. 



1865. Gray, Peter. " Tables for the formation of Logarithms and 

 Anti-Logarithms to twelve places, with explanatory introduction." 

 This is an abridged anticipation of Mr. Gray's great tables to twenty- 

 four places, calculated in 1856, and not published till 1876. It consists 

 of an extended positive numerical radix for tabular logarithms, consist- 

 ing of the tab. logs and complements of tab. logs of 1 to 9, and of the 

 tab. logs of It, 1 + '0- dm r, from r=001 to r=999 and m=l to m=3. 

 The process is the same as in the paper- of 1848, but with periods of 

 three digits. 



1867. *Thoman, Fedor. " Tables de Logarithmes a 27 Decimales 

 pour les Calculs de precision," Paris. These consist essentially of a 

 positive and negative numerical radix, the first used for finding anti- 

 logarithms by a process resembling Flower's and Hearn's, and the 

 second to find logarithms by a process resembling Weddle's. His 

 principal novelty consists in his table for preparation. After the 

 result is reduced to the form l'0 m r, where r consists of m digits, 

 Thoman completes by adding M x '0 m r, for which he gives a special 

 table. The positive radix extends to 1"0 13 1, and the negative tc 

 1 — '0 13 1, both calculated to twenty-seven places by an undescribed 

 process. He makes no references to former writers ; but one of his 

 examples makes it probable that he knew Gray, 1865. 



1871. Fineto, S. " Tables de Logarithmes vulgaires a 10 Decimales, 

 construites d'apres un nouveau mode, approuvees par l'Academie 

 Imperiale des Sciences de S. Petersbourg," St. Petersburgh. An 

 auxiliary table gives opposite the first four figures (or next least first 

 four figures) of a number, a multiplier of at most three digits (with 

 the complement of its logarithm, which will reduce the number to 

 one between 1000 and 1010, and for all such reduced numbers tables 

 are given, by which their logarithms can be readily found to ten 

 places. The process of finding both logarithms and an ti- logarithms 

 by these tables (extending only to 56 pages octavo), is much simpler 

 than by Vega's Thesaurius. But no new process of calculating 

 logarithms originally is involved. 



1873. fWace, Rev. Henry. " On the Calculation of Logarithm" in 

 the "Messenger of Mathematics," New Series, No. 29, 1873. The 

 tables consist of a positive and negative numerical radix to l + '0 10 l, 

 and to twenty places of decimals for both tabular and natural loga- 

 rithms. The tabular were taken partly from Shortrede, and read with 

 Callet, and partly from H. M. Parkhurst's astronomical calculations. 

 The natural logarithms were calculated independently, with a few 



