208 Mr. D. D. Heath on Secular Local 



the ultimate limit ^ or 2, for this divisor as soon as I reached 



the first set of negative terms in the series. With these data I 

 give the approximate results for the disturbance : 1st, at the north 

 pole, where 0^=1; 2ndly, at the south pole, where Q»=±l 

 alternately; 3rdly, at N.P.D.35 ; and 4thly, at the corresponding 

 southern latitude, at which the values of Q w are also the same in 

 magnitude as in the north, but with the alternate signs changed. 



1 . At the north pole, summing together each set of positive 

 and negative terms, we have the elevation 



£{•13132 + -00623 + -00176 + -00101 + -00036}, 



or ft x -07034. If we suppose such a mass as two miles thickness 

 of ice, or say 10,000 feet of the density of water, this would give 

 an elevation over the mean level of some 700 feet. But it is to 

 be borne in mind that, to obtain such a mass, we must rob the ex- 

 isting sea of the greater part of it. In our ideal case of an ocean 

 covering the whole surface, each mile of ice taken from it would 

 lower the mean level by about ^^ths, or 332 feet. 



2. At the south pole we have also a relative elevation, but 

 the amount is only 



| {-03128 + -00128 + -00045 + -00042 + -00035}, 



or ft x -01689, less than one-fourth of that at the north pole. 



3. At north polar distance 35°, as might be expected, the 

 series is much less regular. Grouping positive and negative 

 terms separately, it gives 



|{-03719--01485 + -00112--00559 + -00003--00456 



+ -00001 - -00079 + -00008 - -00035 + -00019 - -00012 



+ -00024- -00004+ -00027}, or (3 x -00642. 



It will be seen that the positive terms by themselves descend 

 and then rise again, and the negative terms rise and then fall by 

 themselves ; but it is certain that the maxima in each group will 

 grow less and less ; and though a hundred terms would have been 

 more satisfactory than fifty, we may feel very confident that the 

 elevation over the mean level for two miles of ice will not exceed 

 80 feet, which is really a considerable depression from the 

 existing level. 



4. At south polar distance 35° the series has for its principal 



