on the Stratification of the Antarctic Ice. 385 



for each additional atmosphere of pressure, it will be lowered 



e 



^= x -0137° for the thickness e of ice. 

 61 



Hence we shall have, to determine the limiting thickness of 

 the ice at which its lower surface will begin to liquefy, 



32- ^x -0137 



— x '04441; 



e 



.-. e= 714 feet. 



(2) No certain limit can be imposed upon the thickness to 

 which the ice might accumulate, provided the snowfall be more 

 than sufficient to counterbalance the melting at the bottom. 



We have found the critical value of the thickness of the ice so 

 that melting should just not take place. Suppose the ice thicker 

 than this ; then the bottom of it will begin to melt, and con- 

 sequently must be at the melting-temperature corresponding 

 to the pressure. The flow of heat out of the earth will melt 

 off a layer of it annually. But the whole of this flow of heat 

 will not be so employed, because, the ice being maintained 

 in a condition in which its upper and lower surfaces are at 

 different temperatures, there must ensue a flow of heat through 

 it. This flow of heat will be expressed by the equation 



J e 



Or if, as before, we assume the temperature of the upper sur- 

 face of the ice to be zero, and allow for the lowering of the 

 melting-point by pressure, 



32 -ix -00037 

 ^ ~~ e 



Now it is obvious that there is no source from which this 

 flow can be derived, except the flow out of the earth. Hence 

 F, which is the flow out of the earth, must be split up into two 

 portions, F— /and/; of which F— /goes to melt the ice at 

 the bottom, while / is conducted away through the ice into 

 space beyond. Now 



, ,32-£X -00037 



= *(^- -00037). 



We see, then, that as the thickness of the ice is increased, /is 

 diminished, and the less heat escapes through the ice ; and 



