56 Hi; i' OKI— 1873. 



Several lists of errata in this work have been given — viz. by Vlacq 

 in his ' Arithinctica,' by Shekwin in his tables, by Vuga (folio, 1794), by 

 Ly.FOET (' Annalcs de rObscrvatoire dc Paris'). The introduction occujncs 

 88 pages, and is in Latin. 



In some copies there is an additional chiliad added, so that the range of 

 the second portion of the table is from 90,000 to 101,000 ; and there is a 

 table of square roots of numbers up to 200, to 10 places, occupying the last 

 two pages : these copies are very rare. There is one in the Library of 

 Trinity College, Cambridge, with the following note in it by Dr. Brinkley : — 



" This is a very scarce copy, having an addition very rarely to be met 

 with. Vide Ilutton's preface to his ' Logarithms,' p. 33, Avho could never 

 find a copy with the addition." Mr. Merrifield has also one of the.se 

 copies. 



On this v.'ork sec the introductory remarks to this Article. 



Tables du Cadastre. On the proposition of Carnot, Prieur, and Brunct, 

 the French Government decided in 1784 that new tables of sines, tangents, 

 &c., and their logarithms, should be calculated in relation to the centesimal 

 division of the quadrant. Prony was charged with the direction of the work, 

 and was expressly required " non sculement a composer des Tables qui ne lais- 

 sasscnt ricn a dcsirer quant a I'exactitudc, maisa en faire le monument de calcul 

 le plus vaste et le plus imposant qui eiit jamais etc execute ou meme congu," — - 

 an order faithfully carried out. Prony divided the calculators &c. into three 

 sections : the first consisted of five or six mathematicians (including Lcgendre), 

 who were engaged in the purely analytical work, or the calculation of the 

 fundamental numbers ; the second section consisted of seven or eight calcu- 

 lators possessing some mathematical knowledge ; and the third comprised 

 the ordinary computers, 70 or 80 in number. The woi'k, which was done 

 wholly in duplicate, and independently by the two divisions of computers, 

 occupied two years. 



As a consequence of the double calculation, there arc two manuscripts in 

 existence, one of which has been long deposited in the Archives of the Obser- 

 A'atory ; the other, though supposed to be in the Archives of the Bureau des 

 Longitudes, was in reality in the possession of Prony's heirs, by whom it was 

 presented to the Library of the Institute in 1858. 



Each of the two manuscripts consists essentially of 17 large folio volumes, 

 the contents being as follows : — 



Logarithms of numbers to 200,000 8 vols. 



Natural sines 1 vol. 



Logarithms of the ratios of arcs to sines from O^-OOOOO to 1 , . , 

 0''-05000, and log sines throughout the quadrant . . J ' 



Logarithms of the ratios of arcs to tangents from 0«-00000 1 



to O''0-5000, and log tangents throughout the 14 „ 

 quadrant J 



It would take too much space to state the intervals &c. in detail. Speaking 

 generally, the trigonometrical functions are given for every hundred-thousandth 

 of the quadrant (10" centesimal or 3"-24 sexagesimal). The tables were all 

 calculated to 14 places, with the intention of publishing only 12 ; but M. Le- 

 fort, who has recently examined them, states that the twelfth figure may be in 

 error by as much as 0-8 of a unit in this place, though a little additional care 

 would have rendered it more accurate. The Institute copy has also a table of the 

 first 500 multiples of certain sines and cosines ; and the Observatory copies 

 have an introduction containing, among several other subsidiary tables, the first 



