11 NOTES. 



1818, S. 29.' " The weight of the Earth expressed in pounds = 9933 x 10 21 , 

 and the supposed displaced mass = 947 x 10 1 V 



( 6 ) p. 20. The theoretical investigations of that period were followed by 

 those of Maclaurin, Clairaut, D'Alembert, Legendre, and Laplace; to tfiese 

 should be added the theorem propounded in 1834 by Jacobi: that ellipsoids 

 having three unequal axes may, under certain conditions, be as good " figures 

 of equilibrium as the two earlier assigned ellipsoids of revolution." See, in Pog- 

 gendorffs Annalen der Physik und Chemie, Bd. xxxiiL 1834, S. 229 233, 

 the memoir of Jacobi, removed by an early death from his friends and ad- 

 mirers. 



( 7 ) p. 21. The first exact comparison of a considerable number of measure- 

 ments of arcs (i. e. the Quito, two Indian, French, English, and recent 

 Lapland arcs) was undertaken, with much success, in 1819, by Walbeck at 

 Abo. He found the mean values of ^ for the ellipticity, and 57009*,? 58 

 for the length of a mean degree of the meridian. This memoir, entitled " De 

 Forma et Magnitudine Telluris," has not, unfortunately, been published entire. At 

 the recommendation of Gauss, Eduard Schmidt, in his valuable " Lehrbuch" of 

 mathematical geography, has repeated the investigation with improvements, 

 taking into account the higher powers of the ellipticity as well as the latitudes 

 observed at intermediate points ; and adding the Hanoverian arc, and the prolon- 

 gation by Biot and Arago of the French arc to Formentera. The results, made 

 successively more perfect, were published in three forms : in Gauss's " Bestim- 

 mung der Breitenunterschiede von Gottingen und Altona," 1828, S. 82; in 

 Eduard Schmidt's " Lehrbuch der mathem. und phys. Geographic," 1829, Th. i. 

 S. 183 and 194199; and lastly, in the Preface to the same book, S. v. The 

 final result is: Degree of the meridian, 57008 t> 655; ellipticity, ~^. Bessel's 

 first investigation was immediately preceded (1830) by Airy's important Me- 

 moir on the Figure of the Earth in the Encyclopaedia Metropolitana, pp. 220 and 

 239, in the edition of 1849 (Semi-polar axis, 20853810 feet = 32611637 

 toises ; semi-equatorial axis, 20923713 feet = 3272095'2 toises ; meridian 

 quadrant, 32811980 feet = 5131208-0 toises; ellipticity, ~^)- Our 

 great Konigsberg astronomer, Bessel, was constantly occupied from 1836 to 

 1842 with calculations on the figure of the Earth, and as his earlier investiga- 

 tions were amended and improved by later ones, the mixture of results obtained 

 at different times has become a fertile source of error in many writings. In the 

 case of numbers, which are, by their nature, mutually dependent on each other, 

 this kind of confusion, sometimes made worse by incorrect reduction of measures, 

 (toises, metres, English feet, and miles 60 or 69 to an equatorial degree), is the 

 more to be regretted as it causes enquiries which have cost much labour and 



