Submergence and Emergence in the Glacial Epoch. 305 



had no real foundation. For during a glacial period, say on 

 the northern hemisphere, the entire mass of ice which presently 

 exists on the southern hemisphere would be transferred to the 

 northern, leaving the quantity of liquid water unchanged. 



Note on the preceding Paper. By Professor W. Thomson, F.R.S. 



Mr. Croll' s estimate of the influence of a cap of ice on the 

 sea-level is very remarkable in its relation to Laplace's celebrated 

 analysis, as being founded on that law of thickness which leads 

 to expressions involving only the first term of the series of 

 " Laplace's functions," or " spherical harmonics." The equation 

 of the level surface, as altered by any given transference of solid 

 matter, is expressed by equating the altered potential function 

 to a constant. This function, when expanded in the series of 

 spherical harmonics, has for its first term the potential due to 

 the whole mass supposed collected at its altered centre of gravity. 

 Hence a spherical surface round the altered centre of gravity is 

 the first approximation in Laplace's method of solution for the 

 altered level surface. Mr. Croll has with admirable tact chosen, 

 of all the arbitrary suppositions that may be made foundations 

 for rough estimates of the change of sea-level due to variations 

 in the polar ice-crusts, the one which reduces to zero all terms 

 after the first in the harmonic series, and renders that first ap- 

 proximation (which always expresses the essence of the result) 

 the whole solution, undisturbed by terms irrelevant to the great 

 physical question. 



Mr. Croll, in the preceding paper, has alluded with remark- 

 able clearness to the effect of the change in the distribution of 

 the water in increasing, by its own attraction, the deviation of 

 the level surface above that which is due to the given change in 

 the distribution of solid matter. The remark he makes, that it 

 is round the centre of gravity of the altered solid and altered 

 liquid that the altering liquid surface adjusts itself, expresses the 

 essence of Laplace's celebrated demonstration of the stability of 

 the ocean, and suggests the proper elementary solution of the 

 problem to find the true alteration of sea-level produced by a 

 given alteration of the solid. As an assumption leading to a 

 simple calculation, let us suppose the solid earth to rise out of 

 the water in a vast number of small flat-topped islands, each 

 bounded by a perpendicular cliff, and let the proportion of water- 

 area to the whole be equal in all quarters. Let all of these 

 islands in one hemisphere be covered with ice, of thickness ac- 

 cording to the law assumed by Mr. Croll — that is, varying in 

 simple proportion to the latitude. Let this ice be removed from 

 the first hemisphere and similarly distributed over the islands of 



