on the Stratification of the Antarctic Ice. 389 



2irrv8h n = irs(2p n w n — w 2 n ). 



s ( w n \ 



This relation expresses the thickness of the layer of ice at A B 

 which is derived from the snowfall on the ring whose section 

 isNM. 



If, then, Bh n be the thickness of a layer derived from one 

 year's snowfall, or an annual stratum of ice at A B, this im- 

 plies that it takes one year more for a particle to travel from 

 M to L than from N to K. 



(4) To account for the downward diminution in thickness of 

 the annual strata of ice. 



For the width of the ring next nearer to the pole we shall 

 have to substitute for p n the value p n —w n ; and if the width of 

 that ring be w n + a, and 8/* n _i the thickness of the correspond- 

 ing stratum at A B, taking s and v as constant for adjoining 

 strata, we shall have 



M„- 1 =^(( P „-,o(-„+«)- ( ^- 2 ), 



whence it appears that 



hh n -U n .^^{wl+^-a(p n -i Wn )). ■ . (A) 



Now we do not know whether the rings which contribute 

 the annual strata diminish or increase in width as they ap- 

 proach the pole. But we may gain a knowledge of the effect 

 which a diminution or increase in the width of the rings would 

 have upon the relative thickness of the successive strata at 

 A B by putting 8h n — SA w _] = /3, and considering it as the ordi- 

 nate of a curve whose abscissa is a. If we suppose A B to be 

 near the free edge of the ice-cap, r will be large ; and we may 

 without much risk of error consider v constant for all depths 

 above the water-level in that position. 



Substituting (3 and suppressing the suffixes, and writing m 



vr 

 for — , which we now take as constant, and observe that it is 

 s 



large, because although v is small, yet r is large and s is 



small, we obtain 



This represents a parabola whose axis is vertical, and which 



