the Crust of the Earth. 195 



1859, p. 259), viz. that his investigation does not concern the 

 question of fluidity and solidity, but only of densities. 



Even if Professor Haughton knew the law of density of the 

 fluid nucleus, and also knew every circumstance regarding the 

 solid portions of which the crust is composed, excepting only the 

 total thickness, his equations would not give any information 

 regarding that thickness. The constants involved in the ex- 

 pression for the law of the fluid density (which must be two at 

 least, except in the impossible case of homogeneity) would still 

 be arbitrary ; and his three equations (the two appertaining to 

 the outer and inner surfaces of the crust, and the third given by 

 the value of the mean density) would involve at least four un- 

 known quantities. The expression for the thickness would 

 thus come out a function of one or more arbitrary constants, on 

 which the density of the fluid nucleus depends. The greater this 

 density the greater must be the thickness, and vice versa. The 

 problem, in fact, which Professor Haughton' s equations would 

 solve is this : if the materials of the earth follow one or more 

 known laws of density (for the density of the crust may be dis- 

 continuous) down to a certain depth, and another known law 

 below that to the centre, what must that depth be that the total 

 mass may be what we know the earth's mass and dimensions to 

 be ? He introduces no physical principle into the problem 

 characteristic of the different properties of a solid and fluid 

 mass, such a principle as that which Mr. Hopkins introduces, 

 viz. that the fluid parts pressing against the solid shell give it a 

 precessional motion, which is a matter for external observation 

 and measurement; or such a principle as this (which would 

 suffice if experiment had determined the law), viz. the relation 

 between pressure and temperature which serve just to produce 

 solidity. Professor Haughton treats the question more mathe- 

 matically than physically. He shows that without an exact 

 knowledge of the laws we cannot have an exact solution. But 

 this we knew before as a matter of course, and it did not require 

 Laplace's analysis to prove it. 



Our ignorance of the exact laws does not preclude our approxi- 

 mating to a solution. We may use laws which a priori con- 

 siderations may show to be highly probable, and the probability 

 of which may be still further increased by the results they lead to. 



For example, the law of density, — , is a highly probable 



law for the fluid portion. On the hypothesis that the earth 

 took its form from being in a fluid state, the same law, both of 

 density and ellipticity, is highly probable for the solid parts as 

 well as for the fluid. I think that the Table of Deflections of 

 the plumb-line caused by variations of density from the fluid 



