Mr. HOPKINS, ON THE MOTION OF GLACIERS. 167 



frequently large, and in the preceding formulae must be made negative, because it will generally be a 

 pressure, and not a tension. Equation (l) thus becomes 



If Xx = 0, and F, = 0, = 45" or 135". In the case before us it is easily seen that the former 

 of these values corresponds to the maximum and the latter to the minimum value of R ; and, there- 

 fore, the direction of greatest tension at ]}' will bisect the angle rpq , that angle being supposed, 

 as in the previous reasoning, to differ but little from a right angle. Consequently the greatest 

 tendency to form a fissure will be along a line bisecting the exterior angle rp'q. If the value of 

 Xx+ F| be finite, that of 9 will be less than 45°, and the direction of the fissure will so deviate 

 from the above-mentioned position as to approximate more nearly to perpendicularity to the sides 

 and axis of the glacier. 



If the angle q p r' should deviate from a right angle by a finite quantity before the fissure 

 should be formed, it would not be difficult, to shew that the line of greatest tension might be still 

 considered to bisect that angle. This would cause a still further deviation in the direction of the 

 fissure towards perpendicularity to the sides. 



Since the relative motion of particles situated in a transverse line varies most rapidly in tlie 

 lateral portions, the value of / will be greatest near the sides, and vanish along the axis of the 

 glacier ; while the value of X-^ + I', will be approximately the same at the sides and center. Conse- 

 quently, the value of Q will diminish as the distance from the sides increases, and the fissures will 

 be curved ; the curvature being most rapid near the sides of the glacier, and the convexity being 

 turned towards the upper extremity of the glacier. The force / will probably be much more 

 effective than X^ in producing the fissures near the sides of the glacier, while X-^ will possibly be 

 the more effective in the central portion. The incompleteness of my former explanation consisted 

 in ascribing the phenomena to the latter force only, to which alone the reasoning there applied 

 is applicable. The above investigation appears to me to offer the complete solution of the 

 problem. 



11. Riband or Laminated Structure. — I have made no attempt to account for this curious 

 structure in glacial ice ; but I would observe that it appears to me impossible that it should be 

 due, as some persons, I think, have supposed, to internal tensions or pressures, producing, as their 

 direct and immediate effect, an almost infinite number of parallel fissures, into which water percolates, 

 and forms, when frozen, the bands of blue ice. It is conceivable, as an abstract hypothesis, that 

 a mass should be accurately homogeneous, and that the external and internal forces should be such 

 as to have exactly the same tendency to produce a fissure at one point of the mass as at another ; 

 but practically, this state is no more possible than that a body should rest in a position of unstable 

 equilibrium — that a cone should rest permanently on its vertex, or a needle on its point. Allowing 

 the nearest practical approximation to this state of the mass, fissures would necessarily begin to be 

 formed, first at particular points, after which the uniformity of condition throughout would be 

 instantly destroyed, and irregular fissures at intervals, large, compared with those between con- 

 secutive bands of blue ice in the riband structure, would be the necessary consequence. I repeat, 

 that the formation of a system of parallel fissures, of sensible or insensible width, at distances not 

 exceeding a few inches, in the mass of a glacier, is no more possible than that the mass should 

 permanently maintain a position of unstable equilibrium. 



The internal pressures and tensions here spoken of are the consequences of external forces acting 

 on the mass, such as gravity and the resistances of the rocks with which the glacial mass may be in 

 contact. There is, however, another class of internal forces, the molecular forces, the existence and 

 nature of wliich may be considered independent of the external conditions to which the mass is 

 subjected, though their action and effects may very probably be modified by those conditions. I 

 have investigated the effects of the first kind of forces, and have explained how transverse and 



