324 Mr. Ivory on the Variation oj Density and Pressure 



density from the centre to the surface. The regularity with 

 which gravity is found to vary on the earth's surface would 

 follow fi'om the regular disposition of the fluid strata, and in- 

 deed can hardly be otherwise accounted for ; and this cir- 

 cumstance affords a strong argument in favour of the suppo- 

 sition of primitive fluidity. 



The homogeneity of the etirth is extremely improbable. 

 We are acquainted with no fluid that is perfectly incompressi- 

 ble. Every material substance yields in some degree to a com- 

 pressive force sufficiently great. It is very probable that the 

 increasing densities as we approach the centre of the earth are 

 caused by the weight of the incumbent matter*. But all that 

 we really do know is confined to the external figure of the 

 earth, and to the variation of gravity on its surface. From 

 this knowledge we may be led to form some probable conjec- 

 tui'es concerning the density and pressure in the interior parts. 

 In such an inquiry we must be guided by what is generally 

 true of those qualities in the instances that have fallen under 

 our observation. A law of density, however well it agree 

 with the figure of the earth, must be rejected if it lead to an 

 improbable law of pressure. And it would be futile and a 

 mere waste of words to descant upon a law of density and pres- 

 sure without showing that it is consistent with what is ex- 

 perimentally known of the figure of the earth. 



Clairaut first determined the figure of an elliptical sphe- 

 roid in equilibria, supposing it to be little different from a 

 sphere, to revolve upon its axis, and to consist of strata of 

 variable density. He has given a general equation between the 

 densities and the excentricities. From what has been said, it 

 appears that the variation of density merely modifies the pro- 

 portion between the excentricities and the centrifugal force, 

 this force being always estimated in parts of the gravitation at 

 the surface of every stratum. It therefore occui'red to me that 

 Clairaut's equation might be simplified if, instead of the ex- 

 centricity, we substitute the proportion it bears to the centri- 

 fugal force. Having found my conjecture in some degree 

 verified, I shall now briefly explain the results I have ob- 

 tained. 



Let the radius of the earth's equator be unit , a the equa- 



♦ " Cette hypothese (que les densites de la terre croissent vers le centre) 

 n'est elle pas fort probable d'ailleurs d'elle meme ? L'eau est elle le seul 

 fluide que nous connoissions ? et ne faut-il pas que les fluides plus pe- 

 Eants, soient plus proches du centre de la terre ? le mercure est pres de 

 quatorze fois plus pesant que l'eau : la grande compression que souffrent 

 les parties proches du centre de la terre, ne pourroit-elle pas ccntribuer 

 a rendre la matiere plus compacte et plus dense?" — Traits sur le Flux 

 et Reflux de la Mer, far Daniel Bernoulli, cap. iv. ^ 12. 



toriul 



