276 On the Solidity and Fluidity of the Mass of the Earth. 
and solid parts are different. But it will not be the case at the 
bounding surface between the solid and fluid parts, unless the 
values of ese derived from the law of the fluid and from the law 
of the solid layers, are the same at this bounding surface. Asp 
is some function of a, e is some function of a (as equation (13) 
shows) ; hence p& is some function of p only. Hence, then, 
the laws of density of the solid and fluid layers may be different, as 
far as the reasoning at present has carried us; but the two laws 
must give the same amount of density at the bounding surface, 
otherwise equation (13) does not follow from equation (12). 
6. Thus far, then, this is the result we are come to. The 
mass consists of solid layers following a certain law of density, 
and of fluid layers following the same or another law of density ; 
but at the surface where they meet the density is the same. 
Also the resultant force acting at any point of any layer, solid 
or fluid, is at right angles to that layer. 
7. Now the equilibrium of this mass will not be disturbed if 
the first solid layer, reckoning from the inner surface towards 
the outer one, become fluid, retaining its density. For the den- 
sity of that one layer accords with the fluid law, and the forces 
acting on the layer are perpendicular to its surface. 
Equation (13), therefore, holds for the bounding surface be- 
tween the first and second solid layers only on the same terms 
that it holds for the bounding surface between the solid and 
fluid portions. From this it follows that the density of the second 
solid layer must follow the fluid law, and so in succession with 
all the rest ; and therefore the law of density of the solid and 
fluid portions must be the same throughout the whole mass, if 
equation (13) is a correct inference from equation (12). 
8. This result appears to me to be a priori evident without 
this proof. For Professor Haughton will acknowledge that the 
equilibrium of the fluid parts will hold, if the solid parts do fol- 
low the law of the fluid parts. But if any different distribution 
of the solid parts take place, their resultant attraction on the 
fluid cannot possibly be the same as before on every particle of 
the fluid. The conditions of equilibrium would therefore not 
hold, and the equilibrium would become impossible without a 
change. 
9. With regard to the other subject touched upon in Professor 
Haughton’s last paper—the argument drawn from the Himma- 
laya Mountains, and the Ocean south of India, in my paper in 
your Number for November—I will simply make the following 
observations. 
