6 Mr. Hopkins on the Motion of Glaciers. 



I have staled above that there was very appreciable motion 

 on a smooth unpolished slab, when the inclination did not ex- 

 ceed 40', and that I have no reason to suppose that a similar 

 result would not be obtained at still smaller angles. Perhaps 

 one of the best tests of the correctness of this conclusion is 

 afforded by the second of the laws of the observed motion, viz. 

 that the velocity, at small inclinations, is nearly proportional 

 to the inclination. If the law were accurately true, there would 

 be appreciable motion for the smallest appreciable inclination. 



3. By means of this law we easily establish the relation be- 

 tween the intensity of any additional retarding force and the 

 retardation produced by it. 'Leif— the retarding force, ?;= 

 the velocity of descent when that force is applied, V being the 

 velocity when the mass descends by its own weight. The re- 

 tardation will be N — V. Also let W= the weight of the mass, 

 and a the inclination of the plane. Then, if/act in a direc- 

 tion parallel to the plane, the moving force will =W sin a— yi 

 and we shall have, by the law referred to, 



V _ W sin « — y 



V ~ W sin « ' 

 and therefore the retardation, which 



= V — t? = - —. . V. 



Wsin a 



In order that the whole velocity may be destroyed by the 

 retarding force, that force must = Wsin «. This, in the case 

 of a glacier, in which a may vary from 3° or 4° to 10° or 15°, 

 becomes enormous. 



4. It should be observed that the velocities (Vu) here spoken 

 of, are the constant velocities of descent. In the experiments the 

 motion appeared to begin with the uniform velocity with which 

 the mass continued to descend ; but this velocity is manifestly 

 a tenninal velocity, like that to which a body acted on by a 

 constant force will rapidly approximate when moving in a re- 

 sisting medium ; and in the experiments the approximation to 

 the terminal velocity must have been too rapid to admit of my 

 observing, by the means I made use of, the variation of velocity 

 in the first stage of the motion. The whole action of the plane 

 retarding the motion must be some function of the velocity 

 <^ ill), so that the equation of motion will be 



jj==gsma-4>{u), 



where u denotes the velocity at any time /, before the mass 

 has acquired the terminal velocity v; and since, in a small 

 time, u becomes = v, <p {u) soon becomes =o-sin«. Also, as- 



