340 B. S. Woodward— Mathematical Theories of the Earth. 



tive whether specially applicable to this particular case or not. 

 It seems not improbable that the close agreement of the values 

 of Airy and Bessel, computed independently and by different 

 methods — the greatest discrepancy being about one hundred 

 and fifty feet, — may have been incautiously interpreted as a 

 comfirmation of Bessel's dimensions, and hence led to their too 

 ready adoption. 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 progress. We cannot do less than ac- 

 cord to Bessel the first place among the astronomers and 

 geodesists of his day, but this is no adequate justification 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.* His new values showed an increase over Bes- 

 sel's of about half a mile in the equatorial semi-axis and about 

 three-tenths of a mile in the polar semi-axis. Since 1866, 

 General Clarke has kept pace with the accumulating data and 

 given us so many different elements for our spheroid that it is 

 necessary to affix a date to any of his values we may use. The 

 later values, however, differ but slightly from the earlier ones, 

 so that the spheroid of 1866, which has- come to be pretty gen- 

 erally adopted, seems likely to enjoy a justly greater celebrity 

 than that of its immediate predecessor. The probable error of 

 the axes of this spheroid is not much greater than the hundred 

 thousandth part,f and it is not likely that new data will change 

 their lengths by more than a few hundred feet. 



In the present state of science, therefore, it may be said that 

 the first order of approximation to the form and dimensions of 

 the earth has been successfully attained. The question which 

 follows naturally and immediately is, how much further can 

 the approximation be carried ? The answer to this question is 

 not yet written, and the indications are not favorable for its 

 speedy announcement. The first approximation, as we have 

 seen, requires no knowledge of the interior density and arrange- 

 ment of the earth's mass ; it proceeds on the simple assump- 

 tion that the sea surface is closely spheroidal. The second 

 approximation, if it be more than a mere interpolation formula, 

 requires a knowledge of both the density and arrangement of 

 the constituents of the earth's mass, and especially of that part 

 called the crust. " All astronomy," says Laj^lace, " rests on the 



* Comparisons of Standards of Length, Made at the Ordinance Office, Southamp- 

 ton, England, by Capt. A. R. Clarke, R. E. Published by order of the Secretary of 

 State for War, 1866. 



f Clarke, Col. A. R., Geodesy, Oxford, 1880, p. 319. 



