in the interior Parts of the Earth. 329 



sistance, it is reasonable to suppose, will be made to further 

 compression. But in one respect the hypothetical law seems 

 to be at variance with experiment. In all small pressures it 

 is found that the increments of pressure and density are nearly 

 proportional to one another. We should therefore expect 



that the quantity -^ must be nearly constant at the earth's 



surface, then increase slowly, and afterwards more rapidly 

 near the centre. But the assumed formula is just the opposite 

 of all this. For it varies most rapidly near the surface, while 

 the arc a n decreases to 90° ; it then increases more slowly,, 

 and near the centre it is almost constant. 



It may likewise be observed that the solution is not com-! 

 mensurate with the nature of the problem. For there are two 

 phjenoraena to be deduced from the law of pressure ; namely, 

 the ellipticity, and the proportion of the superficial, to the 

 mean, density. These quantities are no doubt connected; but 

 as their relation must vary with the law of pressure, the defi- 

 nitive formulae, instead of one indeterminate quantity, should 

 contain two, in order to represent the values of the ellipticity 

 and the superficial density determined by observation. 



But it was never intended by the illustrious author who 

 has treated of this problem, to substitute a hypothetical assump- 

 tion in the place of a law of nature. The particular law of 

 densities was adopted by Legendre, and the law of pressure 

 by Laplace, because in both cases an exact solution was ob- 

 tained by means of formulae of easy calculation. This is an ad- 

 vantage not to be altogether disregarded in cases where, from 

 a want of knowledge, we are reduced to make hypotheses the" 

 foundation of our reasonmg. From the calculations that have 

 been made no inference can be drawn with regard to the el- 

 lipticity or the superficial density ; but we may conclude legi- 

 timately, that the compression produced by the weight of 

 the incumbent matter is sufficient to account for the increas- 

 ing density in the interior parts of the earth, and for the de- 

 viation of its actual figm-e from that which it would possess on 

 the supposition of a homogeneous fluid assumed by Newton. 



^•^'•^'^SSS. James Ivory. 



Vol. 66. No. 331. ATw. 1825. Tt LIV. 0« 



