on the Stratification of the Antarctic Ice. 383 



It is evident that this result will be independent of the 

 cause which maintains the temperature of the surface (say) 

 below the average, whether it be a cold climate or an ice- 

 sheet. We may therefore assume that the rate of increase in 

 the earth beneath the ice-sheet is ^ of a degree Fahr. per foot 

 of descent. 



Let us now suppose that our sheet of ice is throughout 

 below the melting-temperature, so that the level of that cru- 

 cial temperature is situated within the rock. In this case the 

 flow of heat from the earth will pass into the ice unaltered in 

 amount, because none of it will be arrested and consumed in 

 melting ice at the junction. The ice will then be under con- 

 ditions which will render it sufficiently amenable to the fol- 

 lowing statement of Fourier: — 



" The thermometric state of a solid enclosed between two 

 parallel infinite planes, whose perpendicular distance is e, and 

 which are maintained at fixed temperatures, a and 6, is repre- 

 sented by the two equations " 



V=a e~ ( € ~ z ^ ( X ) 



dz 7 



) 



where, for convenience in the present instance, we have taken 

 the origin of z (the depth) at the surface. 



v is the temperature at the depth z, 

 a „ „ of the lower surface, 



b „ „ of the upper surface, 



k the conductivity, 



and F is the flow of heat upwards through the solid. 



The last of these equations will be applicable to the rock if 

 the proper value be assigned to k. 



Let K be the conductivity of rock, 

 k „ „ ice. 



dv 

 Now -=- represents the rate at which the temperature in- 

 creases in descending. We know that for rock this is ^, the 

 units being the foot and degree Fahr. Suppose /3 to be the 



dv 

 value of -T- for the ice ; F will be, under the circumstances 



2G2 



