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XXXIII. On the figure of the earth. By George Biddell 
Airy, M. A. Fellow of Trinity College , Cambridge. Com- 
municated by J. F. W. Herschel, Esq. Sec. R. S. 
Read June 15, 1826. 
The ellipticity of the earth, deduced by Captain Sabine 
from a series of pendulum experiments the most extensive, 
and apparently the most deserving of confidence, that has 
ever been made, differs considerably from that which, as is 
generally believed, is indicated by geodetic measures. The 
difference can only be explained by errors of observation, by 
peculiarities of local circumstances, or by some defect in the 
theory which connects the figure of the earth with the vari- 
ation of gravity on its surface : under the last head may be 
placed defects in the mathematical part of the theory, and 
errors in the assumptions of the original constitution and 
present state of the earth. It was with a view to ascertain 
the sufficiency of the mathematical theory, that I undertook 
the investigations contained in this paper. The celebrated 
proposition called Clairaut’s theorem, by which the earth's 
ellipticity is inferred from the variation of gravity on its sur- 
face, is obtained only by the rejection of the squares and 
higher powers of the ellipticity. It is by the same rejection 
that the figure of the earth, supposed a heterogeneous fluid, 
is proved to be an elliptic spheroid. It appeared therefore 
probable, that a more accurate theory might introduce some 
modification into Clairaut's theorem, and might also show 
