446 The Rev. S. Haughton on the Thickness of 
known, because they depend on its mass, and moments of inertia, 
If we assume the law of density, they will both become known, 
or at least capable of evaluation, because the ellipticity is a 
function of the density, by virtue of equation (B), which belongs 
to the fluid nucleus, and to it only. 
a de 
III. {° 7a’ 
This integral extends through the crust, and is unknown. It 
can only become known by our being acquainted with the law 
of density, and also the law of ellipticity of the layers of the crust, 
which are not connected with each other by an equation, as is 
the case in the fluid portion of the earth. : 
If these preliminary difficulties were overcome, and the values 
of the definite integrals known in terms of a, and known 
numbers, since ¢, is also a function of a, (because it is included 
in equation (B) as part of the fluid nucleus), the equation (Ag) 
would become simply a function of a, and this unknown 
quantity, the radius of the fluid nucleus, might be easily found. 
The hypotheses requisite are the followmg :-— 
1st. The law of density of the fluid portions of the earth. 
2nd. The law of density of the solid portions. 
3rd. The law of ellipticity of the solid portions. 
Of these three essential laws, I maintain that we are in igno- 
rance, and must be content to remain so; and I challenge 
Archdeacon Pratt, or any other person possessed of “ positive” 
knowledge of the interior of the earth, to state what these laws 
are. 1am, indeed, well aware that a chance guess of Laplace’s as 
to the first law, has been considered by some almost an established 
law of nature, and I would therefore offer a few observations 
upon it, to show how improbable it is that it should be even 
an approximation to the real law of density that prevailed in 
the layers of earth when altogether fluid, or in the layers of it 
that are still fluid, if there be any such. 
Legendre first applied the following law of density to the 
determination of the earth’s figure, 
sane sin na 
where— iy ‘ 
p = density of any layer, 
a = the equicapacious radius, and 
A, 7 are constants to be determined. 
Laplace knew well what the meaning of this law was; for in 
discussing it in the Eleventh Book of the Mécanique Ceéleste, 
he says, “Je vais présentement considérer la figure de la terre, 
en la supposant formée dun seul fluide compressible” (Méc. Cél. 
