3 12 Entetijive Logarithmic and Trigonometncal Tables. 



Citizen Prony divided his afliftants into three feftlons. 



The firfl: was compofed of five, or fix mathematicians of very great merit, who were 

 employed on the analytical part of the work, and in general on the application of the 

 method of difFerences to the formation of tables, the calculation of various fundamental 

 numbers, &c. Citizen Legendre, who for fome tinie belonged to this feftion, gave very 

 elegant formulae for determining the fuccefllve difFerences of the fines apriori. 



The fecond fedtlon confided of calculators to whom the analyfis was familiar. They 

 <lire£lly calculated the differences of the feveral orders npceilary to form by fuccefllve addi- 

 tions, according to the method of interpolation, the values of the trigonometric lines de- 

 parting from a given firfl; value through the whole interval, wherein the differences of the 

 mofl elevated order might, without fenfible error, be confidered as conftant. 



The filling ofthefe intervals was reduced to fimple addition performed by the thir4 

 ^c£iion, the papers of which were afterwards tranfmitted for examination by the fecond. 



The calculators of each feflion formed two divifions, each of which performed the 

 whole work without communication with the other. The comparifon of the refults thus 

 obtained afforded the verification. 



By thefe means two manufcript copies of the whole of the table was formed, compofed 

 of feventeen volumes large folio, and containing, 



1. An introdufllon, confifliing of an expofition of the analytical formulae, the ufe of the 

 trigonometrical tablp, and a greaf number of particular and auxiliary tables. 



2. The natural fines for each for iO,OOOth part of the quadrant, calculated to twenty- 

 five places of decimals, with feven or eight columns of differences, to be publifticd with 

 twenty-two decimals, and five columns of differences. 



3. The logarithms of the fines for each ioo,cooth of the quadrant, calculated to four- 

 teen decimals with five columns of differences. 



4. The logarithms of the ratios of the fines to the arcs for the firft five thoufand 

 •100,000th part of the quadrant, calculated to fourteen decimals, with three columns of 

 differences. 



5. The logarithms of the tangents correfponding with the logarithm of the fines. 



6. The logarithms of the ratios of the tangents to the arcs calculated like thofe of the 

 fourth article- 



7. Logarithms of numbers from i to 100,000, calculated to nineteen places of decimals. 



8. The logarithms of 100,000 to 200,000, calculated to twenty-four decimals, in order 

 to be publiftied to twelve decimals, and three columns of differences. 



This explanation fliews how far fuperior this work is to the Opus Palatimim de TnaiiguUs, 

 began by Rheticus, the difciple of Copernicus, and compleated in 1596 by Otho, the difci- 

 ple of Rheticus, or to the Thcfaurus Mathematicus, publjftied by Pitifcus in 1613, and the 

 laft tables of Vlacq. This was the judgment of the Commiffaries, which the Clafs of the 

 Phyfical and Mathematical Societies of the National Inftitute nominated to give an account. 



of 



