216 Mr. Airy on the Figure of a Fluid Mass, &c. 
Making this substitution in the expression for x(c) we find 
862.149 fet 087 ct Ol 2 
2 ne ae 2 = 
@=r—c+y(c)=(7 -e)f1.415 cas an ane 57 
an approximate equation to the generating curve of Saturn sup- 
posing him homogeneous. 
(27.) This gives an ellipticity = .185, independently of that 
produced by the attraction of the ring. This is so large a quantity, 
that the neglect of its square and higher powers must produce 
sensible errors; those terms, however, which arise from the attrac- 
tion of the ring, and which it is our more immediate object to 
investigate, will be little affected by their rejection. And though 
our supposition of Saturn’s homogeneity is highly improbable, 
yet if his density be variable, the aberration. from the elliptic 
figure produced by the attraction of his ring, will be the same 
in kind (though differing in quantity) as that which would exist, 
were his density uniform. 
(28.) An inspection of the equation at the end of (26) will shew, 
that the theoretical figure of Saturn is flattened between the 
poles and the equator. It is remarkable, that this deviation from 
the elliptic form, is exactly the opposite to that given by the obser- 
vations of Dr. Herschel. This accurate observer, in the Philo- 
sophical Transactions for 1805 and 1806, has given a great number 
of his observations, which shew, that Saturn is protuberant between 
the poles and the equator, and that his longest diameter makes 
an angle of 43° with the plane of his equator. Here then is a com- 
plete discordance between theory and observation ; nor is it easy, 
with our present knowledge of the planet, to suggest any thing 
by which they can be reconciled. 
G. B. AIRY. 
Trinity CoLueceE, 
March 15, 1824. 
