VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 24/ 



great. Until triangles shall have been extended beyond the Pyrenees, and the 

 sector placed on the south side of the range, the quantity of this attraction, by 

 its double or counter-effect, cannot possibly be ascertained. I will however only 

 suppose it to have been 10" 8"', to be deducted from the latitude of Perpignan, 

 which will then become 42° 41' 52', only 3'' less than that assigned to it in M. 

 Cassini's two books before mentioned. Thus the arc between Rodes and Per- 

 pignan will be 1° 39' 21'' 36''', and the total celestial arc between Greenwich 

 and Perpignan will be 8° 4& 48". 



With regard to the corresponding terrestrial arc, it is to be observed, that 

 various measurements have at different times been made, in different latitudes, 

 of the lengths of the degrees of the meridian, for the purpose of obtaining, 

 within certain limits at least, the true figure and dimensions of the earth. The 

 most essential operations of this sort, are those in Peru under the equator, in 

 middle latitudes in France and Italy, and in Lapland near the polar circle. The 

 attraction of mountains, and unavoidable errors in the execution, will ever pre- 

 vent just conclusions from being drawn from the comparison of measurements 

 made too near each other. These last will always be found to differ more or less 

 among themselves. Sometimes even the results may become absurd or contra- 

 dictory. In cases of this sort, a mean of several should doubtless be taken for 

 a mean latitude. Hence it is, that philosophers are not yet agreed in opinion 

 with regard to the figure of the earth ; some contending, that it has no regular 

 figure, that is, not such as would be generated by the revolution of a curve 

 around its axis. Others have supposed it to be an ellipsoid ; regular, if both 

 polar sides should have the same degree of flatness ; but irregular, if one should 

 be flatter than the other. And lastly, some suppose it to be a spheroid differing 

 from the ellipsoid, but yet such as would be formed by the revolution of a curve 

 around its axis. 



In order therefore to set this matter in its true light, and to enable every one 

 to judge, by simple inspection only, which of the theories agrees best with 

 actual measurement. Gen. R. has computed on 10 different hypotheses, and ar- 

 ranged in their order, the lengths of the arc between Greenwich and Perpignan ; 

 as also some other chief properties of each figure. The first of the 1 1 columns, 

 or that which comes next to the celestial arc, contains the measured portions of 

 the corresponding terrestrial arc, as far as they have yet been executed. In the 

 2d column are arranged the computed dimensions appertaining to the earth as a 

 sphere, supposing its semi-diameter to be a mean between the longest and 

 shortest of M. Bouguer's 2d spheroid. After the sphere follow 7 ellipsoids of 

 different degrees of oblateness, from the first, whose semi-diameters have to 

 each other the ratio of 1 79-047 to 178.047, to the 7th, where it is only that of 

 640 to 539. 



