154 HISTORY OF PHYSICAL ASTRONOMY. 



As soon as the result of these measurements was known, there was 

 no longer any doubt as to the fact of the earth's oblateness, and the 

 question only turned upon its quantity. Even before the return of the 

 academicians, the Cassinis and Lacaille had measured the French arc, 

 and found errors which subverted the former result, making the earth 

 oblate to the amount of l-168th of its diameter. The expeditions to 

 Peru and to Lapland had to struggle with difficulties in the execution of 

 their design, which make their narratives resemble some romantic his- 

 tory of irregular warfare, rather than the monotonous records of mere 

 measurements. The equatorial degree employed the observers not 

 less than eight years. When they did return, and the results were 

 compared, their discrepancy, as to quantity, was considerable. The 

 comparison of the Peruvian and French arcs gave an ellipticity of 

 nearly l-314th, that of the Peruvian and Swedish arcs gave l-213th 

 for its value. 



Newton had deduced from his theory, by reasonings of singular in- 

 genuity, an ellipticity of l-230th ; but this result had been obtained by 

 supposing the earth homogeneous. If the earth be, as we should most 

 readily conjecture it to be, more dense in its interior than at its exterior, 

 its ellipticity will be less than that of a homogeneous spheroid revolving 

 in the same time. It does not appear that Newton was aware of this ; 

 but Clairaut, in 1743, in his Figure of the Earth, proved this and 

 many other important results of the attraction of the particles. Espe- 

 cially he established that, in proportion as the fraction expressing the 

 Ellipticity becomes smaller, that expressing the Excess of the polar 

 over the equatorial gravity becomes larger ; and he thus connected the 

 measures of the ellipticity obtained by means of Degrees, with those 

 obtained by means of Pendulums in different latitudes. 



The altered rate of a Pendulum when carried towards the equator, 

 had been long ago observed by Richer and Halley, and had been 

 quoted by Newton as confirmatory of his theory. Pendulums were 

 swung by the academicians who measured the degrees, and confirmed 

 the general character of the results. 



But having reached this point of the verification of the Newtonian 

 theory, any additional step becomes more difficult. Many excellent 

 measures, both of Degrees and of Pendulums, have been made since those 

 just mentioned. The results of the Arcs'" is an Ellipticity of l-298th ; 

 of the Pendulums, an Ellipticity of about l-285th. This difference 



Airy, Fig. Earth, p. 230. 



