Mn. HOPKINS, ON THE MOTION OF GLACIERS. . 61 



SECTION IV. 

 Explanation of Phenomena depending on the Motion of Glaciers. 



11. Relative Velocities of different parts of a Glacier. — According to our theory, the velocity 

 of any portion of a glacier will depend (1) on the inclination of its bed, (2) the disintegration 

 of its lower surface by the internal heat of the earth, (3) on subglacial currents, (4) the 

 depth of the mass, and (5) local and lateral obstacles. The first and second causes will generally 

 have nearly the same effect both in the central and lateral portions ; but the third cause will 

 manifestly pi-oduce in general the greatest acceleration in the central parts, and the fourth 

 cause will produce a similar effect, if the glacier be deeper in the center than at its sides 

 [Art. 2 (3)], while the greatest retardation will be produced on the lateral portions by the last 

 of the above-mentoned causes. These causes sufficiently account for the greater velocity of the 

 center of the glacier. 



Again, the second of the above causes will probably act with approximate uniformity through- 

 out the whole length of the glacier, but the third cause will act with the greatest energy at 

 the lower extremity, because the subglacial currents will be increased by innumerable tributaries 

 as they descend. This cause, therefore, will tend to make the velocity greater, as we approach 

 the lower end of the glacier, while the greater depth of the mass at the upper extremity will 

 tend to give the greater velocity to that part of the glacier [Art. 2 (3)]. In winter the effect 

 of the currents must be very inconsiderable, and we should consequently expect that there would 

 be a tendency in the portions of the glacier in the higher regions to move faster than those in 

 the lower, in which case there must be a longitudinal compression, and consequent closing up 

 of transverse fissures in a greater or less degree. During the summer, on the contrary, the sub- 

 glacial currents will be most efficient, and we should expect that they would give the greater 

 velocity to the lower extremity of the glacier, in which case the mass would be brought into 

 a state of longitudinal tension, by which new transverse fissures would be formed, or old ones 

 reopened. 



12. Internal Tensions and Compressions arising" from the unequable Motion of the Glacier 



The mathematical determination of the internal state of tension or pressure of a solid, but 

 extensible and compressible body, acted on by external forces, presents difficulties which are 

 at present insuperable, except in the most simple cases ; nor can demonstrable conclusions of 

 a less determinate character be arrived at except by an exact knowledge and careful application 

 of mechanical principles. The cases I shall consider are the simplest of the kind, and admit 

 of simple and conclusive reasoning. Let us first suppose a glacier to be a continuous mass, and 

 to descend down a gradually contracting valley, so that the mass may be everywhere sub- 

 jected to lateral compression ; and let us also suppose that points near the upper extremity 

 of the glacier tend to move with a smaller velocity than those more remote from it, and the 

 central with a greater velocity than the lateral portions, from the causes above explained. Our first 

 object is to determine the direction of greatest tension at any proposed point. 



Conceive the mass divided into two portions by an imaginary surface, which, for the greater 

 distinctness, may be supposed vertical or nearly so at every point. The mechanical action 

 between any two contiguous particles, situated on opposite sides of this geometrical surface, may 

 be resolved into two forces, the one normal and the other tangential to it. Tlie normal force 

 may be either a pressure or tension ; in the latter case there must be cohesion between the 

 particles. The tangential force may arise from cohesion, or may be of the nature of friction, 

 and indej)endeiit of the existence of cohesive power. Now let us conceive the normal cohesion 

 at every j)oint of our imaginary surface to be destroyed. Tiicn, since the part of the mass 

 near the lower extremity tends to move faster than the other part, these two portions will 



