Mr. HOPKINS, ON THE MOTION OP GLACIERS. 5.5 



2. In the experiment above detailed we have these results : — 



(1). For all angles less than that just mentioned the motion was not an accelerated motion. 

 This result was verified in every experiment I made. 



(2). For inclinations not exceeding 9 or 10 degrees, the velocity, ccBteris paribus, was 

 approximately proportional to the inclination. This, I doubt not, would hold in all cases in 

 which the inclinations should be sufficiently small compared with the angle of accelerated motion. 

 It is manifestly equivalent to the assertion, that the velocity is proportional to the moving 

 force. 



(3). The velocit}' of the mass was increased bj' an increase of weight. 



3. It is not very difficult to give a general explanation of the mechanism of this motion. Con- 

 ceive a very thin slice of the sliding body in contact with the inclined plane on which the motion 

 takes place to become instantaneously fluid: an indefinite!}' small motion would necessarily take place, 

 by which the lower surface of the portion of the mass retaining its solidity would be brought in con- 

 tact with the plane. If the plane were horizontal, it is manifest that this indefinitely small motion 

 would be vertical ; but it appears sufficiently evident, that if the plane be inclined the motion will 

 be compounded of a vertical motion by the action of gravit}', with a motion parallel to the plane 

 arising from what may be termed a momentary gating of the solid body on the small portion 

 which has been supposed to become fluid or disintegrated, and depending partly on the inclina- 

 tion of the plane. The instant the solid portion of the body comes in contact with the plane, 

 the motion will be arrested. At that instant, suppose another thin slice of the body to become fluid ; 

 the same motion will be repeated, and so on. A discontinuous motion would be thus produced ; 

 but if the successive slices which become disintegrated be indefinitelj^ thin, i. e. if the liquefaction 

 or disintegration be continuous, the resulting motion will be continuous, and it will, moreover, 

 be uniform if the disintegration be so. 



The fact that motion takes place down planes of such small inclination compared with that 

 necessary to make the ice slide independently of its disintegration at the lower surface, may simply 

 be stated as due to this circumstance — that, whereas the particles of ice in contact with the plane 

 are capable, so long as thej' remain a part of the solid mass, of exerting a considerable force to 

 prevent sliding, they are incapable of exerting anj' sensible force when thej' become detached 

 from the mass by the liquefaction or disintegration of its lower surface. 



When the sliding mass is small (as in the experiments above described) the exact uniformity 

 of the motion will be destroyed by local irregularities in different parts of the inclined plane down 

 which it takes place, or temporary irregularities in the disintegration ; but where the whole in- 

 clined surface on which the motion takes place is always the same (as in the case of a glacier), 

 and the mass is sufficiently large, all local or temporary irregularities will, in a great measure, 

 counteract each other, and will therefore not materially disturb the uniformity of the motion, 

 which will be preserved so long as the intensity of tlie causes of disintegration remains unaltered. 



4. Temperature of the Lower Surface of a Glacier The essential condition under which 



gravity becomes effective in putting the loaded ice in motion in the experiments above described, 

 is that the lower surface of the ice shall be in a state of disintegration, or that its temperature 

 shall be tiiat of zero of the centigrade thermometer. In order, therefore, that our results may 

 be applicable to any proposed glacier, we must shew 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, and, for the greater simplicity of explanation, let us suppose the conducting power for heat 

 within the icy shell, and in passing into it from the earthy nucleus, to be the same as in the 

 interior of the nucleus. The temperature of the ice, to a certain depth beneath the external 

 surface, would be subject to sensible annual variations of temperature, which would become 

 insensible at a certain depth (<»,), where the temperature (/e,) would be constant. The mathe- 

 matical determination of a;^ and Mi will be given in the concluding section. The temperature m, 

 would necessarily be less than zero (centigrade) and at greater depths than >r?,, the increase of 



