GEOGRAPHICAL LATITUDE. 787 



ply the telescope to the quadrant, he was enabled to make more accu- 

 rate observations than his predecessors ; but it is not to be wondered 

 at that he committed an error of a few geconds. He acknowledged 

 himself that he could not be responsible for errors of 2 seconds, not- 

 withstanding his exactitude, which error would make a difference of 32 

 toises on each observation,^ This error however was happily com- 

 pensated by his toise being about one thousandth shorter than the 

 standard.^ Kecent authorities tind the length of a degree at this 

 latitude to be 57,011.825 toises,^ so that Picard's error amounted to 

 45.175 toises, or 0.79 per cent. 



To settle a point of such importance Louis xiv ordered (1700) a 

 survey of a meridian line stretching throughout the entire length of 

 France. As early as 1680 a survey had been commenced with the 

 idea of giving it this extent, but had been discontinued without coming 

 to any result. Now the line was divided into two j^arts, the one ex- 

 tending from Paris north to Dunkerque, the other from Paris south to 

 Collioure. Th(j survey of the first was intrusted to La Hire, and was 

 found to have an amplitude of 2° 12' 9" SO""* and a length of 125,454 

 toises, which, reduced to sea-level and calculating on the basis of the 

 sphericity of the earth, gives to the degree 56,960 toises. Jacques 

 Cassini conducted the survey of the second and much longer line, found 

 its amplitude to be 0^ 18' 57" and its length 360,614 toises, which gives 

 for the degree 57,097 toises.* Combining the two surveys, one has a line 

 with an amplitude of 8° 31' 11"|, with a length of 486,156 toises ; this 

 gives as the mean length of a degree 57 ,061 toises, which approaches so 

 nearly to that determined by M. Picard that it was thought it should 

 conform to it.*' A base of 7,246 toises 2 feet was measured ''^ for the 

 southern division, which varied 3 toises from "the calculated length con- 

 tinued from Paris," in consequence of which various corrections in the 

 observed angles were made, by which the result was brought very near 

 {k tres pen pr^s) to that measured on the ground.^ For the northern 

 division, Picard's old base-line from Villejuive to Juvisy was adopted 

 without re-measuring, and a second base-line near Dunkerque was 

 measured for purposes of verification. This had a length of 5,464 

 toises 3 feet,^ which was within almost 1 toise of the length found by 

 calculating the line from Picard's base. All the angles of each tri- 

 angle of the entire survey were actually observed,^" and, for purposes of 



1 Cassini, Grandeur de la terre, 183. 

 *Mechain, et Delambre, Base du systfeme, etc., i, 7. 

 ^Bessel's calculations in H. Struve, Landkarten, p. 61. 

 ■• Cassini, Grandeur de la terre, 292. 



^Ibid., 178-181. Quoted all together in Maupertuis, CEnvres, IV, 327, with 9" 30" 

 false. 

 ^Ibid., 302. 

 ''Ihid., 123. 

 ^Ihid., 125,126. 



'*Ihid., 270, p. 237. He gives 5,564 toises. 

 '° lUd., 331. 



