igZ N/10 Syjliin of Weights and Meafurcs cf FrMiict. 



tlcvelopments, will find them in the works publifhed by the temporary Commifflon of 

 Weights and Meafurcs, and by the Agency inflitutc-d to conduct this great and ufcful ope- 

 ration to its end. Wc have thought it nccedary to annex to this memoir, i. A table of the 

 new fyftem. 2. Tables of the rel.ition between the old (French) meafures and the new ; by 

 which it is cafy to reduce the one to the other. The object of thcfe tables is to reduce all 

 the calculations relative to this transformation to fimplc addition. They will likewife 

 fcrve to determine the price of tlie new meafurcs from that of the old. In order to render 

 them lefs volutninous, the fimple unities are given from one to nine only. From the value 

 of the unities it is, cafy to infer the value of decimal multiples or fra(Slions,,by fliiftlng the 

 decimal point. 



']"o thcfe tables we have added the logarithms of the ratios between the old and the new 

 mcafures. 



By this means every one who is engaged either in the art of mining, or the fclenccs re- 

 lating to the fame, will find collefted in one view all that is wanting to facilitate the ftudy 

 and the pradlice of the new fyflem. 



',• The tabic numbered 2 in the original, occupies confiderable fpace, and, though of great utility to the in- 

 habitant of France, is compardtively of fmall importance to any other nation. It is merely a table for facilitating 

 reductions of the old and new meafurcs of France into each other, and does not convey any additional informa- 

 tion to that in the memoir. For thefe reafcns I have not copied it. 



In the way of curfory ohfenation on theobjeftsof this honourable and ufcful undertaking, it maybe remarked, 

 that arguments deduced fromconfiderationsof the immediate numerical application of an original nicafure.are of 

 little confequcncc as to the choice of the means of obtaining it. The chief, and indeed the I'olc, motive of pre- 

 ference mull confift in the greater degree of accuracy, or more perfeft agreement of the refults wrought out by 

 diScrent obfcrvcrs. In experiments to determine the length of a pendulum vibrating through any known por- 

 tion of the time employed by the eaith in its rotation, we have to enquire, i. Whether that rotation be theo- 

 retically uniform ? and if not, what are the quantities and periods of ii regularity, perceptible in fuch an eipcri- 

 nicnt ? i. What are the beft methods and limits of error in meafuring the length of a pendulum between its 

 centres of ofcillation and fufpenfion ? 3. Whether die errors from temperature can be rendered infenfiblc in this 

 meafure of time and length ; and if not, what are their limits ? And above all, 4. What arc the elTedts of the 

 efcapcmcnt part, or fimpltft maintaining power in a clock ; and wh.it arc the beft means of diminifhing or re- 

 moving ihcm altogether. 



Iti the method of deriving an original ftandard from the meafuremcnt of lines and angles upon the earth, the 

 objeOs of enquiry arc certainly not lefs numerous than in the pendulum ; but the lupL-riority of one method beyond 

 the other would require a complete ticatife for its difcuHion. Among the lateft modern furveys, thofe of Genernl 

 Roy, in tlie Philofophic ^I Tranfaftions, made with inftruments of wonderful accuracy, will afford the greateft 

 inftruCtion to fuch as may wilh to enter this path of invcftigation. In the laft paper of the continuation of this 

 furvcy, by Lieutenant Colonel Williams, Captain Mudge, and Mr. Dalby, inferttd in the Tranfaftiems for 

 1795, '' fundamental bafc was meafured on Houndow Heath, equal to 17404.2 Englilh feet, and connecled, by 

 obfcrvaiion of the angles of feventccn triangles, \vith a bafe of verification meafured on Salilbury i'lain. As the 

 triangles prefcnted fcvcral ranges of conneftion, thefe were computel from the fundamental bafe, and gave the 

 numbers 36^74.8 and 36573. S Jox the extreme refults, exprcjnng the bafc of vcrificiiion in feet. The mean of 

 thcfe, namely, 56574 3, proved to be about one inch (lion of the a£tual admeafuremcni of the bafe of veiificatlon- 

 It fttms probable that there may have been Tome fortunate compenf.ition of errors in this wonderful co-incidtnce \ 

 but the refult appears to prove, that the method of terreltrial admeafurement will give an original meafure to 

 be depended on for more ilian four pUccs of figures, and lefs than five. 



When furfaces and folids are to be derived from linear meafurcs, if there be any error in the original linej 

 the error in the furfacc or area will be twice as great, and that in the folid three limes as great, as in the line 

 very nearly, as may be eafily deduced from the common proccfs of involution. That is to fay, in mod caftt it 

 wilt affcft the fame figure of the rcfult. N. 



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