4- Mr. Ivory on the Elliptic ily of the Earth 



to stratum, there must be a small central body which may be 

 considered as of uniform density, and which, like a nucleus, 

 will mould the figure of the rest of the mass. This case there- 

 fore is in no respect different from a nucleus, except that it is 

 requisite to know previously the figures of equilibrium of a 

 homogeneous fluid. 



There is an essential distinction between the equilibrium of 

 a fluid of variable density, covering a nucleus, and that of a 

 homogeneous fluid, which takes place when the particles of 

 the fluid attract one another, as happens in the planets. In 

 the first case the conditions of equilibrium bind together the 

 whole fluid mass between the outer surface and the nucleus. 

 If an additional stratum be spread over the external surface, 

 the conditions of equilibrium cannot be adjusted unless the 

 whole fluid mass to which the stratum is added, undergo a 

 modification of its figure. And if an external stratum of equal 

 pressure be taken away, the remaining fluid must change the 

 figure of its surface in order to restore the equilibrium. The 

 thickness of the fluid above the nucleus, or the dimensions of 

 the whole body, is a necessary element of the equilibrium. 



But it is otherwise with respect to the equilibrium of a ho- 

 mogeneous fluid. Supposing a body of this description having 

 any given dimensions to be in equilibrio, we must conceive that 

 there do exist bodies of less and less dimensions that would be 

 in equilibrio if subjected to the action of similar forces. Hence 

 we must infer, that if a homogeneous fluid in equilibrio be di- 

 vided by level surfaces into strata of equal pressure, every in- 

 ternal body bounded by a level surface will be in equilibrio 

 separately and independently of the exterior fluid. If a level 

 stratum be taken away, the remaining fluid will be merely 

 lightened of a pressure, but its equilibrium will not be dis- 

 turbed. On the other hand, if a like stratum be added, the 

 new body will be in equilibrio without any change of the sur- 

 face upon which the stratum is laid. Now the pressure which 

 any thin exterior stratum exerts upon the fluid below it, is the 

 joint effect of two causes ; of the gravitation at the separating 

 surfaces which acts upon the matter of the stratum, and of the 

 attraction of the stratum upon the interior fluid; and it is 

 manifest that the interior fluid body cannot be in equilibrio 

 independently of the stratum, unless there be a separate equi- 

 librium for each of the two forces. But if the action of the 

 exterior stratum does not disturb the equilibrium of the in- 

 terior fluid body, this can happen only because the resultant 

 of the attractions of the exterior matter upon any particle 

 within the stratum, is evanescent. This law, therefore, must 



actually 



