Mr. Hopkins ofi the Moitofi of Glaciers. 7 



suming the approximate truth of the second of the laws above 

 stated, there will be motion for very small values of a, or when 

 ^sin« is extremely small; consequently <p (u) will become 

 nearly = zero when u = 0. Hence at the instant the motion 

 begins from rest, the tangential action of the plane on the mass, 

 or conversely that of the mass on the plane, is approximately 

 = 0; but in a very short time that action (estimated as a 

 moving force) becomes = weight of the mass resolved in the 

 direction of the plane. I have entered into this explanation 

 to point out the distinction between the action of the retarding 

 force in the motion we are considering, and that of friction in 

 the common and established acceptation of the term. 



5. Temperature of the Lo'wer Surface of a Glacier. — The 

 essential condition under which gravity becomes eifective in 

 putting the loaded ice in motion in the experiments above de- 

 scribed, is that the lower surface of the ice shall be in a state 

 of disintegration, or that its temperature shall be that of zero 

 of the centigrade thermometer. In order, therefore, that our 

 results may be applicable to any proposed glacier, we must 

 show that the temperature of its lower surface must be zero. 

 For this purpose let us conceive the earth to be covered with 

 a superficial crust of ice. The temperature of the ice to a 

 certain depth will be subject to sensible annual variations ; at 

 that depth the temperature will be constant, and at greater 

 depths will increase. The rate of increase will depend on that 

 which obtains within the earthy nucleus, the conductive power 

 of ice, and the external temperature, supposing the thickness 

 of the icy crust to be so small that the temperature shall not rise 

 to zero before we reach the earthy nucleus. Assuming this 

 condition to hold, we are able to determine the greatest thick- 

 ness of the icy crust compatible with it. If the actual thick- 

 ness of the crust be greater than that thus determined, it is 

 manifest that the lower surface of the ice will be kept in a con- 

 stant state of liquefaction by the flow of heat from the earthy 

 nucleus. 



The numerical determination of the greatest depth at which 

 the ice could retain its perfect solidity at its lower surface de- 

 pends partly, as just remarked, on the conductive power of ice, 

 of which we have no exact knowledge. It is quite sufficient 

 however for our purpose to know that it is small. I shall sup- 

 pose it (for the greater simplicity of investigation) to be the 

 same as that of the earthy matter supposed to constitute the 

 nucleus of the sphere; and for the same reason I shall also 

 suppose the conductive power from the nucleus to the icy en- 

 velope to be the same as in the interior of the nucleus, or in that 

 of the icy crust. I shall also assume the external temperature 



