320 Afeafure ef the Meridian in France, (^c, 



taken th2 necefTary excurfions to examine the place, and fettle the ftations ; »nd he even laid 

 down on paptir the triangles neceffary to be meafured ; (a that the whole of this part is 

 Sketched out, anJ by the adivity and care he has beftowed upon it, it will be eafy to add 

 that arc to what has already been meafured, and by that means to prolong the meridian two 

 degrees. Let us hope that more favourable circumftances may hereafter permit that to be 

 carrier! into efre6l which hitherto has been impracticable*. 



The obfervers made ufe, for the meafurement of every kind of ang'es, of the entire circle 

 of Bor.la, which is juftiy called the repeating circle, from the valuable advantage winch it 

 affords of repeating tiie angle to be oblerved any number of times, and confequently diminifh- 

 ing the errors in tiie fame proportion. This circle, which was co.iftrudlcd by the celebrated 

 Lenoir, under the infpeilion of Borda himfelf, was fully tried by the obfervations made in 

 the year 1787 by Cafiini, Mechain, and Legendre, in the operations for the junction of the 

 obfervatories of Paris and Greenwich. 



More than one feries of obfervations was made at each ftation, and the obfervers formed 

 each feries out of fuch a number of obfervations as they thought neceffary to produce a con- 

 ftant and fufficicntly accurate refult. They noted in their regifter the numbers indicated by 

 each obfervation, as well as the particular circumftances whicri took place, fuch as the flate 

 of the atmofphere, the dirediion of the light, and, in a word, every thing which could ferve to 

 determine the intrinfic value of an obfervation. 1 he members of the commifHon nominated 

 for the arrangemcDt of thefe obfervations were, therefore, capable of judging of this value, not 

 only from the fads fo recorded, but alfo from the information they received from the ob- 

 fervers themfelves. 



From fuch an attention to the agreement or variations between the different feries of 

 obfervations, the commiflioners were enabled to determine the value of each angle abftrad- 

 edly, without paying any attention to the others, nor to the fum of the three angles of each 

 triangle. They have thought it their duty to take the angles, fuch as they were, without 

 making the leaft corrc£lion, or proceeding in any other manner than by taking the means 

 of the obfervations, according to the authority which the regifter appeared to give to each. 

 Thefe careful difcuflions for the moft part related to the determination of tenth parts of fe- 

 conds, and very feldom to whole feconds. The commillioners in this manner formed tables 

 of all the triangles, which have ferved for the determination of the medium. They have 

 prefented this to the general commiflion, together with a detail of the method they have em- 

 ployed, and the reafons of their determinations. The commiffion has received thefe tables, 

 and paffed their refolutions, by "which they are depofited in the Inftitute as authentic, as in- 

 cluding all the principles applicable to the computation of the triangles and the pans of the 

 meridianj and, in fait, the calculations were afterwards made from them. 



* On account of the length of this report, I (hall confine myfelf to fuch extra£ls as relate to the immediate 

 opcratioES and refutes, omitting his general remarks. Cit. Dclambrc has pubh'lhed an account of his re- 

 fearchcs, under the title of Miibodti analytiques four la Determination d'un Arc du Meredien, in quarto. This 

 woik it preceded by a memoir of Legendre oa the fame fubje6t.*-N. 



The 



