THE SIZE OF THE EARTH. 19 



ever, be expected on the completion of the Russian geodetic 

 measurements, which are now nearly finished, and which, as 

 they extend almost from the North Cape to the Blaek Sea, 

 will afford a good basis of comparison for testing the accu- 

 racy of the results of the Indian survey. 



According to the determinations published by Bessel in 

 the year 18-11, the mean value of the dimensions of our 

 planet was, according to a careful investigation* of ten 



* The first accurate comparison of a large number of geodetic meas- 

 urements (including those made in the elevated plateau of Quito, two 

 East Indian measurements, together with the French, English, and 

 recent Lapland observations) was successfully effected by Walbeck, at 

 Abo, in 1819. He found the mean value for the earth's ellipticity to 

 k e TnnrVgT> an< ^ tnat of a meridian degree 57009-758 toises, or 324, G28 

 feet. Unfortunately his work, entitled De Forma et Magnitudine Tel- 

 hrris, has not been published in a complete form. Excited by the en- 

 couragement of Gauss, Eduard Schmidt was led to repeat and correct 

 his results in his admirable Hand-book of Mathematical Geography, 

 in which he took into account both the higher powers given for the 

 ellipticity, and the latitudes observed at the intermediate points, as 

 well as the Hanoverian measurements, and those which had been ex- 

 tended as far as Formentera by Biot and Arago. The results of this 

 comparison have appeared in three forms, after undergoing a gradual 

 correction, namely, in Gauss's Bestimmung dcr Breitenunterschiecle von 

 Gottingen unci Altona, 1828, s. 82 ; in Eduard Schmidt's Lehrbuch der 

 Mathcm. undPhys. Geographie, 1829, Th. 1, s. 183, 194-199 ; and, last- 

 ly, in the preface to the latter work (s. 5). The last result is, for a 

 meridian degree, 57008 # 655 toises, or 324,261 feet ; for the ellipticity, 

 YoT^TTW' Vessel's first work of 1830 had been immediately preceded 

 by Airy's treatise on the Figure of the Earth, in the Encyclopaedia 

 Metropolitana, ed. of 1849, p. 220-239. (Here the semi-polar axis 

 was given at 20,853,810 feet=3949 - 585 miles ; the semi-equatorial 

 axis at 20,923,713 feet=3962'824 miles; the meridian quadrant at 

 32,811,980 feet, and the ellipticity at -jiTF-nir)- The g reat astronomer 

 of Konigsberg was uninterruptedly engaged, from 1836 to 1842, in cal- 

 culations regarding the figure of the earth ; and, as his earlier works 

 were amended by subsequent corrections, the admixture of results of 

 investigations at different periods of time has, in many works, proved 

 a source of great confusion. In numbers, which, from their very na- 

 ture, are dependent on one another, this admixture is rendered still 

 more confusing from the erroneous reduction of measurements ; as, 

 for instance, toises, metres, English feet, and miles of 60 and 69 to 

 the equatorial degree ; and this is the more to be regretted, since 

 many works, which have cost a very large amount of time and labor, 

 are thus rendered of much less value than they otherwise would be. 

 In the summer of 1837 Bessel published two treatises, one of which 

 was devoted to the consideration of the influence of the irregularity 

 of the earth's figure upon geodetic measurements, and their compar- 

 ison with astronomical determinations, while the other gave the axes 

 of the oblate spheroid, which seemed to correspond most closely to 

 existing measurements of meridian arcs (Schum., Astr, Nachr., bd. 

 xiv., No. 329, s. 269, No. 333, s. 345). The results of his calculation 



