6 1 Mr. HOPKINS, ON THE MOTION OF GLACIERS. 



/.4 1 -/, = (l - ;'—)»„ + , sin a, 



/s -/«-i = ( ' "" y) ««sSinn, 



Suppose (^ to be the greatest value of the tangential forces (/) which one portion of the 

 mass, on account of its nature and structure, is capable of exerting on a contiguous por- 

 tion, without destroying their cohesion, and the one sliding past the other. The above equations 



shew that /, /j, &c. are in ascending order of magnitude. Let/„ = <^; then will /, /j ./„_, 



be less than <p, which will also be the limiting value of /],+, y"„+2 ./, , and will be their 



actual values if we suppose <p to be the same for every two contiguous portions. In this case, 

 we shall have 



/„.. -/„ =0, 



and therefore 



Hence if erf, c'd' represent the boundaries of the w"' portions on each side of the axis, the por- 

 tions between these lines and the boundaries, AB, A'B' respectively of the glacier will move with 

 the same velocities as if they were not affected on the one hand by the lateral action of the central 

 ))ortion, and on the other by that of the side of the containing valley, assuming this latter action 

 also = (p. If each longitudinal portion of the mass were perfectly rigid, the central portion cdd'c 

 would remain unbroken (since/,/,. ..y;,_, are less than <p), and would move with a common velocity, 

 sliding past the adjoining portions, as these portions would again slide past those contiguous to 

 them. The central part would thus be brought into the position represented in the diagram 

 l)y the dotted lines at its upper and lower boundaries; but if the mass have some degree of 

 plasticity (as is doubtless the case with ice), it will be brought into the position defined by the dark 

 transverse lines ; for any such portion as cf will be acted on by a tangential longitudinal force (p 

 on one side in the direction cd, and on the other by an equal force in the direction /e; and these 

 forces, while they counteract each other with respect to the progressive motion, will twist the mass 

 from the form of a rectangular into that of an oblique-angled parallelopiped. The forces/,/, &c. 

 will in like manner twist the component portions of the central mass cdd'c in a degree propor- 

 tional to their intensitie.s, and therefore in the least degree those parts nearest the axis; so that 

 the central parts of cc and dd' will have little curvature. A small additional motion, however, will 

 thus be given to the middle of the central portion, but with the degree of plasticity here supposed, 

 it may be considered as much less than that due to the sliding of one portion past another. 



If (p be considerably smaller near the sides than at points more remote from them, the 

 width cc will be large, and there will be little variation in the velocity of the glacier except 

 at points near its edges, as stated by Professor Forbes to be generally the case. 



