10 Mr. Hopkins on the Motion of Glaciers. 



of the periodical terms becomes insensible, on account of the 

 exponential involved in them. Let .r, be the least value of ^ 

 for which we may neglect these terms. Then, if w, be the 

 temperature at that depth, 



V C , 1 



^ L. . . . (2.) 



V C i 



2 It ' ^ 



neglecting the small quantity Vq. Consequently the tempera- 

 ture at a certain depth is independent of annual variations, 



C V . 



and lower by 1 than it would be if the exterior shell 



were composed of rock instead of ice ; for in that case the 

 value of the constant term would be the mean external tem- 



j rV C 

 perature V, instead or — . 



* 2 TT 



If jTg be the depth for which the temperature = 0, we shall 

 have 



V C 



= — -— + ya:2, 



which, if we give to y the value above stated, will be the nu- 

 merical value of .r^ in metres. 



\^ x\ be less than the thickness of the glacier, the formula 

 (1.), and therefore (3.)> will be no longer applicable; for (1.) 

 would give the temperature of the ice at depths greater than 

 .Tg, higher than zero, which, from the nature of the ice, is im- 

 possible. In such cases, the lower surface of the ice, at what- 

 ever depth it might be, would be necessarily at zero, because 

 the heat which, if the superficial crust were not ice, would ele- 

 vate its temperature, will be employed in melting the ice at its 

 lower surface, which will thus be kept at the zero temperature. 



With the value of y above given, equation (3.) gives the 

 value of OTg, supposing the ratio of the conductive power of ice 

 to its specific heat to be the same as for the rocky crust of the 

 earth. If this be not the case, the equation (3.) will still give 

 the depth at which the temperature = zero, by assigning the 

 proper value to y as depending on the ratio just mentioned 

 lor ice. 



As a numerical example, suppose V = 0, and C= 15° (cent.). 

 We shall have at the depth x-^ 



u^ = — 5^ nearly ; 



