NOTES. Ill 



time to appear in a disadvantageous light. In the summer of 1837, Bessel 

 published two memoirs ; one on the influence of the irregularities of the Earth's 

 figure on geodesical measurements, and their comparison with astronomical de- 

 terminations ; and the other on the axes of the elliptic spheroid of rotation which 

 would correspond best with the existing measurements of arcs of meridians. 

 (Schum. Astr. Nachr., Bd. xiv. No. 329, S. 269, and No. 333, S. 345.) The 

 results of the calculation were: Semi-major axis, 3271953*'854 ; semi-minor 

 axis, 3261072 t -900; length of a mean degree of the meridian, i. e. the ninetieth 

 part of a quadrant of the Earth, in the direction perpendicular to the equator, 

 57011 tg 453. An error of 68 toises, discovered by Puissant, in the mode of 

 calculation employed by a commission of the French National Institut, 1808, 

 in determining the distance of the parallels of Monljouy, near Barcelona, 

 and Mola, in Formentera, occasioned Bessel to subject his first work on the 

 dimensions of the Earth to a fresh revision, in 1841. (Schum. Astr. Nachr., 

 Bd. six. No. 438, S. 971 1 6.) The revision gave for the length of the Earth's 

 quadrant 513 11 79 f -81, (5130740 toises had been supposed in the first de- 

 termination of the metre), and for the mean length of a degree of the meridian 

 57013 { -109 (being 0*-611 more than the degree of the meridian in 45 lat.). 

 The numbers given in the text are the results of this, Bessel's last determina- 

 tion. The length of 5131180 toises as the quadrant of the meridian (with a 

 mean error of 255 t< 63), is equivalent to 10000856 metres; making the entire 

 circumference of the Earth 40003423 metres (or 5390'98 German, or 21563*92 

 English geographical miles). The difference from the original assumption of 

 the Commission des Poids et Mesures, according to which the metre should be 

 the 40-millioneth part of the Earth's circumference, amounts, therefore, for the 

 circumference, to 3423 met , or 1756 t -27, i. e. 0'46 of a German, or 1'84 of an En- 

 glish geographical mile. According to the earliest determinations, the length of 

 the metre was fixed atO t '5130740; according to Bessel's latest determination, it 

 should be O'-SISIISO. The difference for the length of the metre is therefore 

 0-038 Paris lines, making it, according to Bessel, 443334, instead of 443296 

 Paris lines, which is its present legal value. Compare also on this so-called 

 " natural standard," Faye, Le9ons de Cosmographie, 1852, p. 93. 



( 8 ) p. 23. Airy, Figure of the Earth, in the Encycl. Metrop. 1849, p. 214 

 216. 



( 9 ) p. 23. Biot, Astr. physique, t. ii. p. 482 and t. iii. p. 482. A very ex- 

 act measurement of a parallel arc has been made by Corabceuf, Delcros, and 

 Peytier, on the " Parallel of the Chain of the Pyrenees ;" a work of the greater 

 importance because it has led to the comparison of the levels of the Mediterra- 

 nean and the Atlantic. 



a 2 



