350 Don J. Rodriguez's Observations on the 
importance, The oblateness of the earth is a quantity which 
varies considerably, by the least difference in the elements on 
which it depends. Accordingly it is not surprising, that its 
value fluctuates between two proportions which differ sensibly 
from each other. To illustrate this, let p be the function 
which serves to determine the oblateness of the earth, so that 
~ — p. When this equation varies — Ss == s* . $p. 
Now the coefficient e being very great, we see why the 
least variation in the elements of the function y>, occasions so 
considerable a variation in the denominator of the oblateness. 
This is precisely what happens in the lunar equations depen- 
dent on the figure of the earth, and which M. Laplace has 
deduced from his beautiful theory. Thus, for example, in the 
inequality that depends on the longitude of the moon’s node, 
which he has determined analytically with so much precision, 
the numerical coefficient found by Burg gives for the 
oblateness ; but if this coefficient be diminished by o ",665, 
then the oblateness becomes so that a variation even' to 
this small amount in the coefficient augments the denominator 
of the oblateness nearly - 1 - part. 
The same happens with regard to the pendulum vibrating 
seconds ; for, supposing its length at 45 0 to have been cor- 
rectly ascertained by M M. Biot and Mathieu, if we wish 
to know the length of a second’s pendulum at the equator, 
corresponding to an oblateness of -H~o , we find it to be 439, 1810 
lines. Now this length differs from that determined by Bou- 
guer only by 0,029 of a line, and M. Laplace even thinks 
that the result of Bouguer should be diminished by about 
double this quantity. We see from hence how much these 
little differences, whether produced by errors of observation. 
