Mr. W. Hopkins on the Theory of the Motion of Glaciers. 231 



also two other directions through P characterized by a peculiar pro- 

 perty. If we take two adjoining particles, P and P', in the line of 

 maximum tension, that tension will exert a greater effort than there 

 will be in any other direction to separate those particles; or if the 

 internal force be the maximum pressure, those points will be more 

 compressed together than in any other direction. In the two direc- 

 tions (now to be denned) the forces on P and P', acting perpendicu- 

 larly to the hue joining those particles, will exert a greater tendency 

 than is exerted in any other direction, to separate them by making 

 one slide tangentially past the other, and then to twist and contort 

 any internal elementary portion of the mass. These two directions 

 are perpendicular to each other, and bisect the angles between the 

 directions of maximum tension and maximum pressure. This problem 

 is treated entirely mathematically ; it is the typical problem of this 

 part of the subject. The results are applied to a real glacier by the 

 analogy which it bears to the typical one. 



For the application of these analytical results, the author then 

 considers the nature of the forces called into action by the two pri- 

 mary characteristics of the motion of a glacier — that its central move 

 faster than its marginal portions, and the portions near the upper 

 faster than those near the lower surface of the mass. He also takes 

 account of the modifications to which these forces may be subjected 

 by changes of form and inclination in the containing valley. He 

 likewise explains the different modes in which the mass may be 

 fractured when the forces become such as to overpower its powers of 

 cohesion or resistance. If the cohesion give way to the maximum 

 tension, an open fissure must be formed in a direction perpen- 

 dicular to that tension. If the resisting power of the ice give way to 

 the maximum pressure at any point, the mass will be crushed at that 

 point, but its continuity will be immediately restored by regelation, 

 the internal constraint will be momentarily removed, and the mass 

 will move on. By a repetition of this process the glacier is enabled 

 to move forward, preserving at once the continuity of its motion, of 

 its mass, and of its structure. 



The veined structure of glacial ice is then examined, and it is shown 

 that, so far as Professor TyndaXY s pressure theory of that structure 

 involves the condition of the structural surfaces being perpendicular 

 at each point to the maximum pressure there, it is perfectly accordant 

 with the theoretical results of this paper. Whether the structure be 

 .marginal, longitudinal and central, or transversal, this is equally true, 

 assuming always that the structure in each locality is the direct and 

 immediate consequence of the forces acting there and tending to pro- 

 duce it. Probably, however, the veined structure in one locality 

 may have originated in another from which it has been transmitted 

 by the motion of the glacier. Supposing this to be so entirely, the 

 author examines how this motion of transmission would modify the 

 forms of the transmitted structure. Practically, and within the 

 limits to which observation has yet extended, these modifications 

 would produce forms sensibly coincident with those which would 

 result, as in the previous case considered, from the immediate action 



