322 Mr. Ivory on the Variation of Density and Pressure 



ridian. But there is one thing indispensable to the success of 

 both methods. A degree of the meridian and the length of a 

 pendulum vibrating in a given portion of time, both vary with 

 extreme slowness in advancing from the equator to the pole. 

 A pendulum that vibrates in a second at the equator, requires 

 to be lengthened only about yjjths of an inch in order to oscil- 

 late in the same time at the pole. The experiments to be 

 compared must therefore be made at places as distant from 

 one another as possible. Unless this precaution is used, the 

 imavoidable errors of observation will bear a considerable 

 proportion to the minute quantities to be found, and conse- 

 quently the results will be uncertain and irregular. 



Besides the two methods of investigating the figure of the 

 earth by terrestrial experiments, there is another derived from 

 astronomical observation. If the earth and the moon were 

 both spherical, the attractive forces which they exert upon one 

 another would depend only on their quantities of matter and 

 their distance. But as the earth has an oblate figure, the 

 moon acts upon the protuberant matter at the equator, and 

 causes a nutation of the axis, the theory of which is well 

 known. Now if the moon displace the axis of the earth, that 

 luminary must itself be re-acted on, and must imdergo some 

 change of position in the heavens. Astronomers have disco- 

 vered two inequalities of the moon, — one in longitude and one 

 in latitude, — which, being determined by actual observation, 

 lead dii'ectly to a determination of the earth's ellipticity by 

 which they are caused. 



When the results obtained from all the degrees that have 

 been measured are combined with the pendulum experiments 

 made in England and France, and with the determination de- 

 rived from astronomical observation, the terrestrial ellipticity 

 has been fixed at ^i^. But this is only the most probable 

 quantity ; for the discrepancies are so great as to prove either 

 some imperfection in the methods employed, or considerable 

 irregularities in the figure of the earth. 



Captain Sabine, in the employ of the British government, 

 has, in the course of two voyages, made experiments with the 

 pendulum at thirteen different stations from the equator to 

 Spitzbergen in 80° of north latitude. The distance of the 

 extreme stations is nearly the greatest possible ; and this mode 

 of experimenting has, therefore, been carried into execution 

 in circumstances the most advantageous that can be chosen. 

 The ellipticity deduced from these experiments is ■^^. But 

 the most important consideration attending them is the almost 

 exact agreement of the results obtained by combining them 

 with one another, and with the experiments made in England 



and 



