Length of a Degree of the Terrestrial Meridian. 229 



of a, resulting from this process, is less liable to inaccuracy than the 

 value resulting from the measured degrees of the meridian. Dr. 

 Bowditch has collected and recorded about fifty observed lengths of 

 the seconds pendulum ; and, combining the best forty four of them 



.1 



upon the principle of the least squares, has obtained a = ^^^ ; and 



combining the same number, according to the method of Boscovich, 



1 



has found °^=^or\^^ using a formula for the length of the pendulum, 



in which the second and higher powers of a are neglected. 



12. The third method for determining the measure of the earth's 

 oblateness, is less direct than either of those before mentioned, but is 

 one of the most striking results, that the application of analysis to 

 the great law of universal gravitation, has produced ; and is worthy 

 of an important rank in the history of the progress and powers of the 

 human mind. This method consists in recognizing among; the nu- 

 merous inequalities of the moon's motion, those which depend upon 

 the non-sphericity of the earth ; and in comparing their values, as 

 given by observations, with those resulting from calculations founded 

 upon the hypothesis of a spheroidal form for the earth, and that the 

 protuberance at the equator would sensibly affect the moon's mo- 

 tion. Laplace, to whom the idea of the method now being consid- 

 ered, is due, found, by using the observations of Burg, upon the ir- 

 regularities of the moon's motion, that the oblateness of the earth, 



1 . 



resulting from these phenomena, was oTTFTjc:' Doubtless this meth- 

 od of determining a is susceptible of greater accuracy than any other 

 which is founded upon observation, since the other two methods in- 

 volve observations peculiarly liable to be affected by local irregulari- 

 ties and causes necessarily encountered on the earth's surface; whilst 

 on the contrary, these same irregularities and local causes, owing to 

 the distance of the moon, would not sensibly disturb the circumstan- 

 ces of the moon's motion, which depend upon the oblateness of the 

 earth. 



13. Finally, the phenomena of nutation and precession of the 

 equinoxes, furnish valuable ideas upon the figure of the earth". These 

 phenomena do not, it is true, give the absolute value of the measure 

 of its oblateness, but they make known two limits between which 



1 1 



this measure is contained, and which are found to be ^^=7?^ and ;r;^>,. 



»<y 578 



