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



But even if this were otherwise, I apprehend the question 

 which geologists are now putting is not to be answered by merely 

 calculating the difference between two approximately similar and 

 opposite states. They want to know whether any conceivable 

 glaciation in the northern hemisphere would raise the sea in the 

 latitude of North Wales by 1 000 or 2000 feet above its now ex- 

 isting level. Surely, with the excentricity of our orbit, I believe, 

 near its minimum, we are not now in a state of extreme southern 

 glaciation !, If we are, the whole astronomical theory of glacial 

 epochs falls to the ground ; and, moreover, though I suppose 

 there may be sensibly more ice now in the south than in the 

 north, no one can imagine that the difference is enough to pro- 

 duce any sensible change of level. 



My investigation has the disadvantage of resulting in a series, 

 whence it is not easy to deduce general propositions; but it is 

 addressed to the actual question. 



Archdeacon Pratt has also given a solution of the problem in 

 the March Number of the Magazine. If it could be accepted 

 as it stands, or if it admits of correction, it possesses the advan- 

 tage of being expressed in few terms, though it is liable to the 

 objection that, like Professor Thomson's, it supposes the cap- 

 ping to reach to the equator. 



But I must confess, with some diffidence, that it appears to 

 me radically erroneous. 



It is a corollary from his ' Figure of the Earth/ with which I 

 have only become acquainted in consequence of the paper's refer- 

 ences ; and I must admit that the objections I have to urge 

 against the paper are equally applicable to a large section of the 

 more permanent work, I will, however, endeavour to make them 

 intelligible to those who have only the Magazine before them. 



The fundamental equation (1), p. 173, is an empirical for- 

 mula, the coefficients being determined by making it approxi- 

 mately represent the attractions on points in four latitudes, 0° 

 and 30°, 45° and 60° south, which four attractions are to be 

 previously computed "by the reader" with the help of certain 

 Tables. I have not had the courage to verify the calculations ; 

 but taking them as data, I find that the formula (1) is made to 

 represent three of them exactly ; and then the remaining one 

 comes out *422 instead of *412, which is perhaps near enough 

 to give us confidence in applying it to other southern latitudes. 



But it fails in the northern hemisphere. The Archdeacon 

 has, if 1 am not mistaken, exaggerated the divergence. For the 

 expression 0*6 sin 2(/> . e. g. (p. 173) seems to be that for the 

 attraction of a homogeneous spheroid of the same density with 

 the earth ; whereas he uses it for one of the density 2*75, or 

 about half that of the earth. 



