Changes in. the Sea-level. 203 



It. is to be observed that the whole mass of the sea may be 

 TsVo" or Woo °f ^at of the earth ; and of course the mass of 

 ice is much less. And the disturbance of the sea-level, and the 

 displacement (if any) of the centre of gravity of the solid nucleus 

 with reference to the centre of figure or centre of gravity of the 

 earth, can at most be of the like order of magnitude. Whenever, 

 then, the mass of the ice, or a portion of it, or the amount of 

 disturbance of the surface above or below the mean level, enters 

 as a factor into any term of our expressions, we may take the 

 other factors approximately, if we keep to this order of small 

 magnitudes. 



When the system has assumed its position of equilibrium, it 

 is clear that the sea will form a surface of revolution round the 

 polar axis. 



The ice, and each element of it, will be tending to draw the 

 earth towards it, as if it were a solid body, by its attraction, and 

 will be counteracting that tendency by its pressure at the points 

 where the two masses are in contact. It will also, by virtue of 

 the difference of the amounts of its attraction on the different 

 fluid particles, tend to produce relative motion among them ; and 

 this tendency must be counteracted by the mutual pressures and 

 attractions of the parts of the earth, as determined by the figure 

 it assumes. 



The earth being nearly spherical, the action and reaction of 

 attraction between it and each element of ice will be approxi- 

 mately the same as if its mass were collected at its centre of 

 gravity; or as if the accelerating force due to the action of the 

 element of ice on a particle of the earth at the centre of gravity 

 were exerted equally, and in the same direction, on every par- 

 ticle of the eartn. The effect, therefore, of the pressure of the 

 ice on the earth, which counteracts this force, may be repre- 

 sented by its reverse ; i. e. by applying to each particle of the 

 earth an accelerating force equal, parallel, and opposite to that 

 exerted by each element of ice at the centre of gravity, or ap- 

 proximately, according to the observation made above, at the 

 centre of figure. And this mode of representation will obvi- 

 ously introduce no new pressure into the system, nor alter any 

 existing tendency to relative motion among its particles. 



We have then to consider what shape and relative position 

 the solid and fluid parts of the earth must assume in order to 

 equilibrium between their mutual pressures and impressed forces, 

 each particle being taken to be solicited by (1) the direct attrac- 

 tion of each element of the ice upon it; (2) a force equal and 

 opposite to that which the element of ice exerts at the centre of 

 figure; and (3) the attraction of the whole earth. 



The well-known condition of equilibrium is, that at the sur- 



