Length of a Degree of the Terrestrial Meridian. 229 
of, 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 “i them 
upon the principle of the least squares, has obtained « = oa ; and 
combining the same number, according to the method of Boscovicb, 
has found “= 969)? using a formula for the length of the pendulum, 
in which the second and higher powers of « 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 305.05" 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 _ — 
this measure is contained, and which are found to be 5=; ia and >= Bee 
