Niiu Syjlem of Weights and Meafures of Fi-ance. I9J 



any fenfible Influence on the ufual indruments of meafure, but to prefent to Europe, in 

 all the parts of tliis great operation, a degree of precifion honourable to the Sciences and 

 to the Republic. 



It -vj'as not thought necefTary to wait the termination of their work previous to afcertain- 

 ing the diftance from the pole to the equator in the ancient meafures. It is fufficiently 

 known, by the obfervations of learned men, that the length of a degree of the meridian, 

 taken at an equal diftance from the pole aiul the equator, is 57027 toifes. 



It is likewife known, that from this mean degree the degrees become longer each by about 

 twelve toifes in approaching the pole, and fliorter in the fame proportion by advancing to- 

 wards the equator, on account of the oblate figure of the terreftrial globe towards the poles. 

 This degree, interfe£led by the forty-fifth parallel, is therefore the mean term of an arithme- 

 tical progrelTion, which multiplied by 90 will give the diftance from the pole to the equator. 



57027 multiplied by 90 produces 5132430 toifes, or 30794580 feet. 



This is the fundamental unity expreffed in ancient meaftires from the iron toife of the 

 Academy, fuppofed to be at the temperature of 13 degrees of Reaumur's thermometer. 



If the new obfervation fliould give this diftance a minute quantity larger or fmaller, it 

 will not be neceflary on that account to change the number of toifes which reprefent it. It. 

 will be fufficient to vary in the proper direSion the aflumed temperature of the iron toife *. 



The unity being thus determined, the fecond ftep was to divide and fubdivide it in 

 fuch a manner as to obtain linear meafures appropriated to the different ufes. An eflen- 

 tial condition was to choofe a proper number to be employed, and to employ it conftantly 

 and exclufively, in order to reduce the arbitrary elements of the fyftem as much as poihble. 

 Some learned men were defirous that the number 12 might be adopted, becaufe divifible 

 immediately into the half, the quarter, r.nd the fixth ; others, on the contrary, being im- 

 preflcd with the inconvenience of thefe fraftions of variable denominators, would have 

 preferred fome prime number, fuch as 7 or 11, which would have rendered the ufe of all 

 fuch fradions imprafticable. But very effe£l:ual confiderations proved decifive in favour 

 of the number 10. For, i. This number is in fome refped pointed out by nature, finCe 

 we find the decimal numeration among nations which do not appear to have had any 

 communication. 



2 Nothing can be better adapted to facilitate calculations, than to fubjeiSl the Jivifion of 

 meafures to the ordinary laws of arithmetic ; whence the converfion of one meafure into 

 another of a fuperior or inferior order is effected by a fingle ftroke of the pen, and frac- 

 tions may be worked with the fame eafe as whole numbers. This laft advantage could 

 not be united to thofe which were fuppofed to cxift in the numbers 7, 11 and 12, with- 

 out entirely changing the fyftem of oral and written numeration ; an entelrprife which 

 perhaps is out of the power of any government to accomplifh. 



The diftance from the pole to the equator being taken as the fundamental unity, and 

 the number 10 for the only divifor, conftitute the fimple and produdlive principles on 



' Men of fcioite agree that the meafure of the arc of the merkliaii may he depended on to the five thou- 

 findih part (or barely to four places of figures. N.). If therefore it (hould happcrt that the error amounts to 

 the uimoit pollible quantity, it would be entirely remedied by fuppofing the toife to be lengthened or (hortencd 

 one fivc-ihoufandth part by the cffcft of temperature. Every dcgrc* of variation, accordirg to the fcale of 

 tltaumur, prodOces on the length of an iron bar a variation of onc-7500oth p.irt. C. 



C c 2 which 



