OOi Cambridge Philosophical Society. 



of general longitudinal compression ; and he observes that no ob- 

 server ventured to assert the fact of such compression to be dedu- 

 cible from actual observation. He conceives this to be a serious ob- 

 jection to the hypothesis here considered. 



In this memoir Mr. Hopkins has also investigated the directions 

 in which transverse fissures must be formed when referrible to the 

 internal tensions superinduced by the conditions to which glaciers in 

 general are subjected, and more especially by the more rapid motion 

 of their central portions. 



Assuming the velocity of each particle of the glacier to be the 

 same in any vertical line (which is at least true at points not remote 

 from the surface), the glacier may, in this investigation, be consi- 

 dered as a lamina. In this lamina take a rectangular element having 

 two of its sides parallel to the axis of the glacier, and, therefore, the 

 remaining sides perpeirdicular to it. Let X denote the intensity of 

 the force acting normally to these latter sides of the element, Y that 

 of the force acting normally to the two former sides. Also let/ de- 

 note the intensity of the force acting tangentially on the sides on 

 which X acts normally. It is proved that/ will also be the inten- 

 sity of the tangential force on the other two sides. Then, if 6 be 

 the angle which the line of maximum tension through the proposed 

 element makes with the axis of the glacier, it is proved that 



tan 2 9 



2/ 



X-Y' 



where X and Y are tensions. If either be a pressure, it must be 

 made negative. 



If the maximum tension become greater than the cohesion of the 

 ice, a fissure will be formed in a direction perpendicular to that of 

 the tension at each point, or at least approximately so. Conse- 

 quently, the line whose direction is defined by the angle 9, will be a 

 normal to the curve of fracture. Now, taking the case in which 

 the glacial valley contracts in descending (which is the more frequent 

 case), Y is doubtless most frequently a pressure, in which case 



tan 2 9 



2/ 



X + Y' 



also/ will be greatest at the sides (where the velocities of particles 

 in a transverse line vary most rapidly), and will vanish at the centre. 

 Hence S will vanish at the centre of the glacier, and will increase 

 towards the sides, since the change in the value of the denominator 

 cannot be great. Consequently, if a fissure were continued across 

 the glacier it would form a curve, meeting the axis of the glacier at 

 right angles ; and its convexity will be turned towards the upper ex- 

 tremity of the glacier, for the line defined. by the angle 9, or the 

 normal to the curve, meets the axis of the glacier when produced 

 towards its lower extremity. This is the well-known character of 

 transverse fissures, which the author conceives to be thus completely 

 accounted for. In the previous memoir above referred to, this cu- 

 rious character had been very imperfectly explained by referring it 

 to the action of the longitudinal tension (X) alone. 



