324 Meajure of the Meridian in France, (^c% 



of Dunkirk taken as a bafe, and the azimuths adlually obfervcd at thcfe three ftations. Thefs 

 two fadls eventually conlirm and fupport each other ; and when combined, they indicate, ei- 

 ther an irregularity in the terreftrial meridian, or an elliptic form in the equator and its pa- 

 rallels, or an irregularity in the internal ftrudture of the earth, or an effe6i of the attrac^tioa 

 of mountains, or a powerful aftion of ail thefe caufes, or a certain number of them united. 

 It isa tafli worthy of the mod celebrated mathematicians to fix their attention upon thefe fads, 

 and endeavour to develope their elements, in order to obtain a more perfect theory of the earth 

 than we have hitherto pjfl'efled. 



The commiffioners, whofe objedt it was to determine the Knglh of the fourth part of the 

 meridian, and thence the unity of meafure, direfted their whole attention towards that 

 objedt. They employed the whole arc comprized between Dunkirk and Montjouy in 

 their calculations, which were Uri&ly made, according to the elJi tical hypothcfis. To 

 make this calculation, it was rcquifite to know the difference between the equatorial and 

 polar diameters. This was obtained by comparing the newly-meafured arc with the largeft 

 and beft fituated of the arcs already meafured ; namely, that in Pei u. The computations 

 carefully made, and by different formula;, gave one three hundred and thirty-fourth part for 

 the flattening of the earth, which is the fame as refults from the combination of a great num- 

 ber of experiments at different places on the earth, on the length of the fimple pendulum, as 

 well as conformable to the theory of th: nutation of the earth's axis, and preceffion of the 

 equino£lial points. It is, moreover, obferved, that as the middle of the entire arc, termi- 

 nated by Dunkirk and Montjouy, pafTes near the forty-fifth, or mean degree, of latitude, a 

 flight error would have the lefs influence on the final determination. 



By various methods of computation, employing the arc between Dunkirk and Montjouy, 

 of two hundred and feventy- five thoi.fand feven hundred and ninety-two modules, and thirty- 

 fix hundredth parts ; and the quantity, three hundred and thirty-four for the oblate figure; it 

 was found that the fourth part of the terreftrial meridian is two million five hundred and 

 fixty-five thoufand three hundred and feventy modules; and conf^quently, that its ten mil- 

 lioneth p irt, or the metrey or unity of meafure, is 256537 millioneth parts of the module. 



To reduce this length to the ancient meafures, it is obferved that if the module and the 

 toife of Peru were fuppofed to be each at the temperature of the latter when employed by 

 the academicians, which anfwers to ihe thirteenth degree of the thermometer of Mer- 

 cury, divided into 80 patts, or fixteen and a quarter ot the centigrade thermometer, the 

 netre would be equal to 443,291 lines of that toife; but by reducing the module to the 

 temperature (as it oi'ght to be) to which it was reduced in the cxj reffion of the l:ngth of 

 the bafes which was ufed to calculate the triangles, and the length of the portion of the ter- 

 reftrial meridian, the true and dejinhive metre is four hundred and forty -three lines, and two 

 hundred and ninety-fix thoufundth parts of a line of the toife of Peru, this lafl being conftantly 

 /uppofed to have the temperature of fixteen degrees and a quarter. This laft correiljon be- 

 came necefliury, on account «f the differeHce of expanfion in the two metals. 



(Tt li (Qntinutd.) 



