THE MATHEMATICAL THEORIES OF THE EARTH. 185 



ments conducted ou the surface quite iudepeiulently of any knowledge 

 of the interior constitution of the earth. It is evident in fact, without 

 recourse to mathematical details, that the length of any arc, as a degree 

 of latitude or longitude ou the earth's surface, must depend ou the 

 lerigths of those axes. Conversely, it is plain that the measurement of 

 such an arc and the determination of its geographical position consti- 

 tute an indirect measurement of the axes. Hence it has happened 

 that scientific as distinguished from practical geodesy has been con- 

 cerned chiefly with such linear and astronomical measurements, and 

 the zeal with which the work has been pursued is attested by triangu- 

 lations on every continent. Passing over the earlier determinations as 

 of historical interest only, all of the really trustworthy approximations 

 to the lengths of the axes have been made within the half century just 

 passed. The first to appear of these approximations were the well- 

 founded values of Airy,* published in 1S30. These, however, were 

 almost wholly overshadowed and supplanted eleven years later by the 

 values of Bessel,t whose spheroid cauie to occupy a most conspicuous 

 place in geodesy for more than a quarter of a century. Knowing as 

 we now do thatBessel's values were considerably in error, it seems not 

 a little remarkable that they should have been so long acce])ted with- 

 out serious question. One obvious reason is found in the fact that a 

 considerable lapse of time was essential for the accumulation of new 

 data, but two other possible reasons of a different character are 

 worthy of notice because they are interesting and instructive, whether 

 specially applicable to this i)articular case or not. It seems not im- 

 probable that the close agreement of the values of Airy and Bessel, 

 computed independently and by different methods — the greatest dis- 

 crei)ancy being about 150 feet — may have been incautiously inter- 

 preted as a confirmation of Bessel's dimensions, and hence led to their 

 too roady adoi)tion. It seems also not improbable that the weight of 

 Bessel's great name may have been too closely associated in the minds 

 of his followers with the weights of his observations and results. The 

 sanction of eminent authority, especially if there is added to it the 

 stamp of an official seal, is sometimes a serious obstacle to real prog, 

 ress. We can not do less than accord to Bessel the first place amongst 

 the astronomers and geodesists of his day, but this is no adequate jus- 

 tification for the exaggerated estimate long entertained of the precision 

 of the elements of his spheroid. 



The next step in the approximation was the important one of Clarke]: 

 in 1866. Bis new values showed an increase over Bessel's of about 

 half a mile in the equatorial semi-axis and about three-tenths of a mile 



* Encuclopcdia MetropoUtana. 



t AHtronomhphe Nachrichlen No. 438, 1841. 



t Comparison of Staii'larda of Length, made at the ordnance oflice, SouHiampton, 

 England, by Capt. A. R. Clarke, R. E. Published by order of the secretary of state 

 for war, 1866. 



