62 . Mr. HOPKINS, ON THE MOTION OF GLACIERS. 



necessarily separate, if the surface intersect the lines of motion of the particles through which it 

 passes, and the internal state of pressure and tension will be altered. But, again, let us suppose 

 this surface to coincide with the line of motion of every particle situated in it, and while the 

 normal cohesion is destroyed, conceive the tangential force between contiguous particles to be 

 still maintained by friction. Since, by hypothesis, the mass is in a state of transverse com- 

 pression, it is manifest that the destruction of the cohesion along the internal surface in the 

 position now supposed will cause no separation of the two portions into which the mass is 

 thus divided, or any modification of the previous motion, or of the internal pressures and tensions 

 due to it. The same will be true if another such surface existed as near as we please to the 

 former. But in this case, it is manifest that the direction of greatest tension at any point be- 

 tween these two surfaces must be in the direction of these surfaces, i.e. in the direction of 

 motion ; for since by hypothesis no cohesion exists between the portion of the mass included 

 by those surfaces and the contiguous portions, it is impossible that any tensions should be 

 impressed upon it in directions transverse to its bounding surfaces of no cohesion. Consequently, 

 the same must hold when the cohesion of the mass is unbroken, since it has been shewn that 

 the destruction of the cohesion would not affect the state of internal pressure or tension. 



13. From the former part of the preceding paragraph, it follows that if any surface be 

 described within the mass, perpendicular at every point to the direction of motion, there will 

 be a maximum tendency to destroy the cohesion along such surfaces, so far as that tendency 

 depends on the relative motions of the portions of the mass near the upper and lower extremities 

 respectively. 



14. Again, if our imaginary surface be longitudinal, and coincide with the direction of 

 motion of the particles through which it passes, it is manifest that the greater motion of the 

 central parts will cause an action of the particles on one side of the surface, on those on the 

 opposite side of it, and in directions tangential to it. This force will depend on the tendency 

 of the one set of particles to move faster than the other, and will evidently be greatest in the 

 direction in which that tendency is greatest, i.e. in the direction of the motion. If it be 

 sufficiently great the cohesion will be destroyed. There will be no tendency to produce open 

 fissures in the case we are considering, on account of the lateral compression to which the mass 

 is assumed to be subjected, but there will be a tendency to produce longitudinal surfaces of 

 discontinuity. To investigate the effects of the internal forces thus called into action, let the 

 following diagram represent a portion of a glacier bounded by the transverse sections AA' and 

 BB\ originally plane, but brought into the positions there represented by the relative motions 

 of the center and sides of the mass. Let uh, cd, &c. be any longitudinal surfaces along which 

 the tangential forces are called into action, and thei'efore in the direction of motion ; and for the 

 greater simplicity suppose every thing approximately symmetrical with respect to the axis 00'. 



Also let ?<;, w., w„ w, be the weights of these longitudinal portions into which the mass 



is thus divided; V^ V^ V„ F, the velocities with which they would respectively move, in- 

 dependently of the action of adjoining portions on each other ; they may be supposed to diminish 

 from the center to the side ; i>, v.^ u„ «, their actual velocities; f^f.^ ./, ./, the tan- 

 gential longitudinal forces of contiguous portions on each other. 



Now if W denote the weight of a mass of ice moving down an inclined plane, of which 

 the inclination = a, in the manner described in ray experiments, the moving force of gravity 

 along the plane will be W sin a. Let a retarding force (/) be applied to the mass, and let 

 the velocity of descent then = v. Then, if V be the velocity when / does not act, we shall 

 have, by the second observed law of motion in such cases (Art. 2), 



V PFsin a — / 

 r" W sin a ' 



