164 Mr. Hopkins on the Mechanism of Glacial Motion. 



be destroyed at all points not remote from each fissure, while 

 the minimum tension or maximum pressure (r) will remain 

 the same. Hence, if at any such points we would find the 

 values of the internal forces, we must refer to the equations at 

 the end of article 13, which become, if we write F for X, and 

 — (r) for (r) (since the transverse force is here a pressnre)^ 

 F= (R)cos2 5-(r)sin2 9, 



/=Y{(R) + W}sm2$, 



where F denotes the normal and y the tangential force before 

 the continuity of the mass is broken, on a line the normal to 

 which makes an angle Q with the direction of maximum tension. 

 In applying these equations after the formation of the fissure 

 we must put (R) = 0, which gives 

 F= - (r)sin2 5, 



/=-i(r)sin2 9. 



Consequently, if we take a portion of the mass between two 

 fissures not remote from each other, it will be in a state of 

 pressure (since F is negative) in every direction except that 

 perpendicular to the fissures, in which there will be neither 

 pressure nor tension. Such portion of the mass may therefore 

 be said to be entirely relieved from its state of tetision. The 

 tangential force /' will remain, but diminished in a ratio de- 

 pending on that which (r) bears to (R). 



When the different portions of the mass are thus far relieved 

 from internal constraint, the motion originally producing that 

 constraint may be continued without causing immediately any 

 further fracture ; but by the continuance of the motion, the 

 constraint must necessarily be again increased as at first, till 

 the tension shall again become greater than the cohesion, 

 when new fissures will be formed in the same manner as before, 

 while the old ones, as they become transverse to the lines of 

 greatest pressure by the more rapid motion of the centre of 

 the glacier, will be gradually closed; and thus this opening of 

 new fissures and closing of old ones may be conceived to go 

 on for any length of time, independently of local causes con- 

 stantly acting at particular points, and which, acting in con- 

 junction with the general cause above considered, continually 

 produce systems of fissures originating at those points, and 

 deviating more or less from the general type which would be 

 impressed on them if they were due solely to the more rapid 

 motion of the centre of the glacier. 



Hence we may understand how the centre of a glacier may 

 move more rapidly than its sides, without actually producing 



