36 Mr. D. D. Heath on the Problem of Sea-levels. 



This explains, perhaps, how he came by the proposition to 

 which I have objected. For one of Laplace's theorems is that, 

 when a nearly spherical nucleus is everywhere covered by a fluid 

 envelope, the centres of gravity must coincide. 



But not only is this hypothesis quite irrelevant to the physical 

 facts, but it utterly vitiates the whole reasoning. If we neglect 

 the difference of density between ice, and water, it is perfectly 

 indifferent to equilibrium how much of the sea becomes ground- 

 ice; and if we take it into account, the ground-ice gives buoy- 

 ancy instead of weight to the attached nucleus, and will dis- 

 turb equilibrium in the sense opposite to that assumed by Mr. 

 Croll. In his imaginary case, introduced for illustration, of a 

 nucleus of the same density as ice, no position will be stable but 

 with the solid partly out of water. I need not say that this is 

 not the theory which Professor Thomson has really adopted in 

 his own solution of the problem. And in truth he only throws 

 a student off the scent by directing him to " work according to 

 Mr. CrolPs directions/' What he really does, in substance, is 

 this. 



He borrows from Mr. Croll the conception of an ice-cap ex- 

 tending down to the equator, and substituting (as I and other 

 followers of Laplace have done) density for thickness, he supposes 

 the density to vary as the cosine of the polar distance; which re- 

 presents the law of thickness in Mr. CrolFs meniscus when in 

 its vanishing state. This being so, if we start with a southern 

 glacial epoch, and suppose the hemispherical shell to represent 

 the excess of southern over any then existing northern ice, then 

 a northern epoch, or the exact reversal of this state of things, 

 may be represented by the superposition upon it of a complete 

 spherical shell, following the above law with reversed pole; i. e. 

 having a negative density southward, which will neutralize the 

 southern cap, and a positive density at the north. 



Such a shell will be found to exert on all points within it equal 

 and parallel forces directed northward. It will therefore produce 

 no effect on the contour, but will displace the moveable fluid 

 until the excess of matter in the nucleus balances the northerly, 

 as it formerly balanced the southerly attraction of the hemisphe- 

 rical shell at the centre of figure. 



/3 

 This gives in my notation a displacement T , which in Pro- 



it .P~ l 



fessor Thomson's would be r— . But he introduces the consi- 



i— w 



deration of the supports of the ice-cap as islands equably distri- 

 buted over the globe, on which alone he supposes the ice to rest. 

 This makes the average thickness of ice covering any zone of lati- 

 tude proportional to (1— co)it, and the proportion of fluid matter 



