549 
Mr. Airy on the figure of the earth. 
the figure of the earth to differ from an ellipsoid ; and there 
was no reason to think that the first approximation to that 
figure was more accurate, than the first approximation to the 
motion of the moon’s perigee. The result of my investiga- 
tion does not at all serve to reconcile the pendulum observa- 
tions made by Captain Sabine with the measures of degrees : 
and with respect to one object, which I hoped to obtain, I am 
therefore completely unsuccessful. The theory shows, how- 
ever, that the earth’s figure, on the usual suppositions as to 
its constitution, is not an elliptic spheroid ; and the formulas 
which I have obtained will give the means of determining 
very exactly the figure of the earth, when the experiments 
on the variation of gravity, or the measures of arcs on the 
earth’s surface, shall be thought sufficiently accurate. As 
the subject is one whose interest is not confined to the present 
time, I have ventured to offer my investigations to the Royal 
Society. 
The first part of the following sheets contains the theory 
of the heterogeneous earth, pushed so far as to include all the 
terms of the second order : it is succeeded by a comparison 
of this theory with Captain Sabine’s results, and with the 
best arcs of the meridian that have been measured : and in 
the conclusion, I have offered some suggestions on the pro- 
priety of repeating some of these measures. 
(l.) To ascertain the form of equilibrium of a fluid, it is 
first necessary to find the sum of the products of each par- 
ticle by the reciprocal of its distance from any point of the 
fluid (Laplace, Mecanique Celeste , livre iii. n°. 23). This can 
be done only by assuming a function with indeterminate 
constants to represent the form of each stratum of equal 
mdcccxxvi. 4 B 
