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



And from this he infers that the " whole elevation of the sea- 

 level," i. e. the value of r — R, is the integral - fTOw "between 



the proper limits." (Phil. Mag. p. 174.) 



But for these " proper limits " he, without reason or warrant, 

 takes the equator and the latitude where he wants to ascertain 

 the submergence ; whereas he ought to take it from the point 

 where the disturbed and undisturbed surfaces coincide, which 

 he has never determined. 



If I may venture on a conjecture, it is from mistrust of the 

 assumption "that the attraction of an elementary prism of the 

 superficial matter may be treated as concentrated in one point 

 of its length" — the same, approximately, whether the attracted 

 particle is under, near, or distant from it — that Archdeacon 

 Pratt has adopted his peculiar method and got hold of his dis- 

 continuous formulas. This may require a closer investigation ; 

 but I believe the objection is unfounded as applying to the de- 

 termination of the general figure of the ocean. It may be valid 

 as regards a small margin on either side of the latitude at which 

 the capping terminates abruptly; but not, I think, as regards 

 points fairly under the capping or fairly away from it. I will 

 not attempt here to go further into the question. If that as- 

 sumption (which I have distinctly made) must be abandoned, 

 we must hope that Archdeacon Pratt will be able to remove ob- 

 jections and complete his own theory. 



I will conclude with an observation of a physical character, 

 though I have hitherto kept entirely to the mathematical theory 

 of attractions. 



I have taken a uniform thickness of ice : others have supposed 

 it to thin out in lower latitudes, according to whatever law they 

 found convenient for their calculations. T think it essential that 

 those calculations should not depend for their validity on the 

 cap reaching down to the equator. But, this once secured, it 

 may at first sight appear that a law of thinning out must be 

 nearer to the case of nature than that of uniform thickness. 

 But I doubt whether it is so. Within certain limits of climate, 

 I apprehend the real cause determining the thickness will be the 

 distribution of land and shallow seas; and that you cannot have 

 more than a certain depth of ice heaped up on a given area, island 

 or shoal. It will crack away, or ultimately be crushed by its 

 own weight, and float away in powder, flakes, or icebergs, into 

 seas of lower latitudes. 



Kitlands, Dorking. 



