the Crust of the Earth. 329 



his conclusion can hardly be received in opposition to the more 

 sure results of Mr. Hopkins. 



4. "With regard to Mr. Haughton's investigations, it appears 

 to me that, owing to a fallacy in the reasoning, his conclusions 

 do not prove anything whatever regarding the proportion of the 

 solid to the fluid parts. He obtains the following equation of 

 the surface of any stratum : 



e T" , ,o , , 1 T"" ,d.a!h' , , eV ids' j i ^^^ f^ \ ha \ n n ^ 

 and by differentiation deduces (\i we put 3 j p'tt'W=^(rt)^ 



di^^'^ ,^{a) da aA <^(«)/ "• ' • ' W 



It is in the next five lines (p. 265) that the fallacy lies : — 

 " This equation [viz. (2)] is identical with that derived from the 

 supposition that the earth is completely fluid, and is therefore 

 independent of the law of density and ellipticity of the solid 

 parts of the earth : it determines the relation which necessarily 

 exists between the law of density and ellipticity of the fluid por- 

 tions of the earth." But this is not the case. If in equation (1) 

 we assign different laws of density and ellipticity to the solid 

 parts and to the fluid parts, the integrals will be discontinuous, 

 the break being at the bounding surface. Thus the p in the 

 second and third integrals not being the same function, equa- 

 tion (2) does not follow from equation (1) by differentiation. In 

 fact equation (2) assumes that the law of density and ellipticity 

 is continuous throughout the whole mass, solid and fluid, the 

 solid parts lying in strata of the form and density they would 

 have if they were wholly fluid. The question is, in fact, treated 

 by Mr. Haughton purely in a mathematical, and not in a phy- 

 sical manner. There is no condition or datura introduced to 

 show what is fluid and what solid. The reasoning therefore 

 which follows falls to the ground. The application to the case 

 of a homogeneous body (in p. 267) proves nothing regarding 

 solidity or fluidity. It is merely an algebraical, not a physical, 

 problem of densities, and is this : — " If the earth consist of two 

 liomogcneous portions (solid or fluid, in part or in whole) 

 bounded by a surface of equilibrium; and the outer portion 

 have the density of superficial rock, and the nucleus such a den- 

 sity as to make up the whole mass of the earth; how thick is 

 the outer portion ? " The answer is 768 miles, a result which 

 proves nothing regarding the thickness of the solid crust of the 

 earth. The result which follows if the nucleus be not homoge- 

 ^ Phil. Mag. S. 4. Vol. 17. No. 115. May 1859. Z 



