Mr. Hopkins o?i the Mechajiism of Glacial Motion. 161 



vary in passing from one point to another, provided it be the 

 same at each point for every direction through that point. 

 This is equivalent to there being no surface of less cohesion 

 through any proposed point; for, in such case, it is manifest 

 that the direction in which a fracture would begin or be con- 

 tinued through any point, could not be influenced by a cohe- 

 sion which should be the same for all directions. If, however, 

 surfaces of less cohesion exist in the mass {i. e. if its cohesion 

 vary according to any discontinuous law), they may evidently 

 affect the directions of fracture. This case I shall reserve for 

 subsequent consideration, restricting myself in the first instance 

 to cases in which the variation of cohesion is continuous. 



20. Let us first consider the formation of open fissures. 



It has been proved (art. 13.) that whatever forces may act 

 at any point of the mass in its state of constraint, they must 

 be equivalent to two systems of tensions whose intensities are 

 (R) and (r), and whose directions are perpendicular to each 

 other. If, therefore, an open fissure commence at any pro- 

 posed point, it must clearly be in a direction perpendicular to 

 that of the greater of these tensions, or the maximum tension 

 at that point. The directions in which the fissure v/ili be sub- 

 sequently propagated through other points may be, in some 

 degree, affected by other circumstances, into the explanation 

 of which it would be useless to enter here*; but those direc- 

 tions will be determined approximately by the same rule as 

 at the first point. Hence, then, the normal to a fissure at 

 any proposed point may be considered to coincide approxi- 

 mately with the direction of maximum tension at that point 

 just previous to the fracture. 



Let us first suppose the glacial valley to become narrower 

 in descending, as is very commonly the case; there will doubt- 

 less be a transversal cojnpression, or Yj in equation (1.) must 

 be negative. Also, it is probable that X| will more frequently 

 be a tension, or, if it be a pressure, it will probably be much 

 less than Yj. We shall thus have 



tan ^ 9 — ^'^' 



the denominator being positive. Yj and Xj may be taken as 

 nearly constant for the same transversal section of the glacier, 

 while/j will vary from its greatest value near the sides, where 

 the tendency to twist each element of the mass is greatest, to 

 zero at the centre, where there is no such tendency at all. 

 Consequently 6 will be the greatest at the sides of the glacier, 

 and will diminish for points nearer to the centre, or the line 



* See my memoir on Physical Geology, in the Transactions of the Cam- 

 bridge Philosophical Society, vol. vi. pavt 1. 



