392 On the Stratification of the Antarctic Ice. 



assumed value of a on the right of the origin, and, as before, is 



positive unless a is greater than ^ — 



Now take other values of p and iv nearer to the pole. Then 

 p is diminished, while w is increased. On account of the di- 

 minution of p and increase of w, the vertex of the parabola 

 will be brought nearer to the origin, and raised (but more so 

 than in the previous case, when the rings diminished). And 



vp" 

 because — is increased, the point at which the curve cuts the 



m L 



axis of /3 will be raised (compare curves 1 and 3), and the or- 

 dinate corresponding to the former positive value of a will be 

 greater than it was before ; and for a slightly greater value of 

 a, such as we may presume belongs to the next pair of annual 

 rings towards the pole, it will be still greater ; and so on for 

 the next position of the curve. Consequently in this case the 

 difference between the thicknesses of the annual strata will 

 for large values of p be at first small, and will become larger 

 in descending. But should the value of a increase rapidly, as 

 it may possibly do on approaching the pole, then the difference 

 would begin to decrease. 



But the strata which are visible above the water-level must 

 certainly be derived from rings distant from the pole, for 

 which the values of p are large. Hence, on the whole, we may 

 conclude that in the visible ice-cliff the differences of thick- 

 ness in the strata in descending (1) would be constant if 

 the rings from which they are derived were of uniform width, 

 (2) the difference would diminish if the rings diminished in 

 width, and (3) it would increase if they increased in width. 



It does not appear that any sufficiently close observations 

 have been, or perhaps could be, made to determine the rate of 

 decrease in the thickness of the successive strata. In the ad- 

 dress referred to, Sir Wyville Thomson tells us that the ice- 

 cliff of a berg was on an average about 200 feet high, that 

 at about 80 feet below the top the strata were about a foot 

 thick, and near the water-line about three inches. These data 

 are not sufficient to warrant any conclusion beyond the mere 

 fact of the diminution in thickness. 



Let the points r and q be so taken, in fig. 1, that the time 

 which a particle of ice takes to travel from N to K is equal to 

 that which it takes a particle to travel from r to L ; and simi- 

 larly from M to L and from q to E; then, if N M and M Q 

 supply annual strata at A B, it will take one year for a particle 

 to travel from M to r, and the same period for one to travel 

 from Q to q. Hence the mean velocity through M r : mean 

 velocity through Qq : : Mr : Q q. 



