20 COSMOS. 



measurements of degrees, as follows : The semi-axis major 

 of a rotating spheroid, a form that approximates most close- 

 ly to the irregular figure of our earth, was 3272077*14 

 toises, or 20,924,774 feet ; the semi-axis minor, 3261139-33 

 toises, or 20,854,821 feet; the length of the earth's quad- 

 rant, 5131179-81 toises, or 32,811,799 feet; the length of 

 a mean meridian degree, 57013*109 toises, or 364,596 feet; 

 the length of a parallel degree at latitude, and conse- 

 quently that of an equatorial degree, 57108-52 toises, or 

 365,186 feet; the length of a parallel degree at 45, 40449*371 

 toises, or 258,657 feet; the ellipticity of the earth, -^-^y^- ; 

 and the length of a geographical mile, of which sixty go to 

 an equatorial degree, 951-8 toises, or 6086*5 feet. 



The table on page 21 shows the increase of the length of 

 the meridian degree from the equator to the pole, as it has 

 been found from observations, and therefore modified by the 

 local disturbances of attraction : 



were, 3271953-854: toises for the semi-axis major; 3261072-900 toises 

 for the semi-axis minor ; and for the length of a mean meridian de- 

 gree that is to say, for the ninetieth part of the earth's quadrant 

 (vertically to the equator) 57011-453 toises. An error of 68 toises, 

 or 44:0-8 feet, which was detected by Puissant, in the mode of calcula- 

 tion that had been adopted, in 1 808, by a Commission of the Nation- 

 al Institute for determining the distance of the parallels of Montjouy, 

 near Barcelona, and Mola, in Formentera, led Bessel, in the year 

 1841, to submit his previous calculations regarding the dimensions of 

 the earth to a new revision. (Schum., Astr. Nachr., bd. xix., No. 438, 

 s. 97-116). This correction yielded for the length of the earth's quad- 

 rant 5131179-81 toises, instead of 5130740 toises, which had been ob- 

 tained in accordance with the first determination of the metre ; and 

 for the mean length of a meridian degree, 57013-109 toises, which 

 is about 0-611 of a toise more than a meridian degree at 45 lat. 

 The numbers given in the text are the result of Bessel's latest calcu- 

 lations. The length of the meridian quadrant, 5131180 toises, with a 

 mean error of 255-63 toises, is therefore = 10000856 metres, which 

 would therefore give 40003423 metres, or 21563-92 geographical miles, 

 for the entire circumference of the earth. The difference between the 

 original assumption of the Commission des Poids et Mcsures, according 

 to which the metre was the forty-millionth part of the earth's circum- 

 ference, amounts, for the entire circumference, to 3423 metres, or 

 1756-27 toises, which is almost two geographical miles, or, more ac- 

 curately speaking, 1-84. According to the earliest determinations, 

 the length of the metre was determined at 0-5130740 of a toise, while 

 according to Bessel's last determination it ought to be 0-5131180 of a 

 toise. The difference for the length of the metre is, therefore, 0-038 

 of a French line. The metre has, therefore, been established by Bes- 

 sel as equal to 443*334 French lines, instead of 443-296, which is its 

 present legal value. (Compare also, on this so-called natural stand- 

 ard, Faye, Lerons de Cosinographie, 1852, p. 93.) 



