202 ON TIIK I'llYSTOAL STRUCTURE OF TTIE KAKTII. 



of its inntorinls wliicli come mi(l(>r our iiotico. Of tlioso ]>roi)ortio.s the 

 most important arcdoiisity, compressibility, aud contraction or dilation 

 from changes of temperature. Newton and other philosophers have 

 already adoi)tcd the same ])rinoiple to a limited extent, when assuming 

 for the mass of tlnid comj)osin<»: the Earth in its primitive condition 

 those specific properties which have been assigned to all kinds of fluids 

 observed at the surface. Tt is impossible to frame any statement more 

 erroneous and misleading than that I have endeavoied to render the 

 question more hypothetical than it was. On the contrary, I have dis- 

 carded the invariable assum])tion of mathematicians who treated the 

 question, namely, the hypothesis of the invariability of positions of the 

 particles composing the solidifying earth. The speculations of all 

 rational inquirers upon the Earth's internal structure must necessarily 

 start from the same general principle as above. Some investigators 

 have disregarded that principle and made the problem thereby a purely 

 mathematical exercise. 



In order to reason upon the Earth's figure, we must assume that the 

 laws of fluid equilibrium apply to the inner portions of the fluid as well 

 as the outer. There is nothing hypothetical in reasonings as to the 

 formation of the solid shell and the law of increase of ellipticity of its 

 inner surface as a result of the transition of the formerly fluid matter to 

 the state of solidity. On the contrary, the assumi)tions of Mr. Uopkins 

 and other mathematicians, that this transition created no change in the 

 law of density of the matter composing the Earth and in the ellipticity 

 of the strata of equal pressure, are not merely hypothetical; they are 

 directly opposed to well-established physical and mechanical laws. 



On the other hand, those who have concluded that nothing can be 

 known of the form of the fluid nucleus seem to deny that the recognized 

 laws of matter api)ly to the internal condition of the Earth. The shape 

 of the nucleus and the figures of its stiata of equal density follow from 

 physical and mechanical laws, just as the forms of the isothermal sur- 

 faces within the si)heroid follow from the known laws of conduction of 

 heat. Some of the mechanical reasonings regarding the strata of the 

 nucleus and the structure of the solid shell can be presented without 

 employing mathematical symbols, and in what follows I have, as far as 

 possible, avoided the use of such symbols. 



This course, moreover, possesses the advantage of making many 

 parts of reasonings more clear to geologists aud observers of the strati- 

 grajihical featnr( s of tiie Earth, who are in reality the ultimate judges 

 of the matter, and not mathematicians. The necessity under which 

 the latter are constrained when dealing with problems, of throwing the 

 I)reliminary i)ropositions into simple, welldefined sha))es, admitting of 

 definite deductions, obliges them to overlook the most essential condi- 

 tions of the very questions at issue, and they thus arrive at results 

 which may be precise, but which are totally inconclusive with reference 

 to the Earth's structure. 



