on the Stratification of the Antarctic Ice. 



391 



be constant ; or, in other words, their thicknesses would form 

 a decreasing arithmetical progression, whose common differ- 



10 



ence would be — 

 m 



Let curve 1 in fig. 2 be drawn with any assumed values 



Fig. 2, 



of p and a. And, first, suppose the rings to decrease in width 

 as they approach the pole. Then the difference in thickness 

 between the ring under consideration and the next nearer to 

 the pole is given by the ordinate corresponding to the assumed 

 value of a on the left of the origin. We observe these ordi- 

 nates to be all positive. Hence the strata decrease in thick- 

 ness. 



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

 both p and iv will be diminished. On account of the diminu- 

 tion of p, which we suppose much greater than w, the vertex 



of the parabola will be raised ; and because — is diminished, 

 1 m 



the point at which it cuts the axis of /3 will be lowered (com- 

 pare curves 1 and 2), and the ordinate corresponding to 

 the former negative value of a will be less than it was before, 

 and less still for the probably smaller value of a which corre- 

 sponds to the diminished value of p. Hence the difference in 

 the thickness of the strata will become less and less for the 

 lower ones. 



Next suppose the width of the rings which supply the an- 

 nual strata at AB to increase as they approach the pole. 

 Then the difference in thickness between the stratum derived 

 from the ring under consideration and the next to it nearer 

 to the pole is given by the ordinate corresponding to the 



