Mr, Hopkins on the Mechanism of Glacial Motion. 165 



longitudinal planes of discontinuity, such that the portion of 

 the mass immediately on one side of such plane shall slide past 

 the contiguous portion on the opposite side without forming 

 open fissures like those above considered. But though this 

 is not a necessary consequence of the state of constraint of 

 the mass, it is one of the ways, as already stated, in which the 

 constraint may be destroyed. I proceed to consider the con- 

 ditions under which this will take place. 



25. If we take a geometrical line along the surface of a 

 continuous portion of a glacier, the tendency to form an open 

 fissure along that line will be measured by the intensity of the 

 force which is normal to it; and in like manner the tendency 

 to form a vertical plane or surface of discontinuity along the 

 line will be measured by the tangential forced. If/'= along 

 the proposed line, there can be no tendency in contiguous par- 

 ticles on opposite sides of this geometrical line to separate 

 from each other by different velocities estimated along the line, 

 since such a tendency must necessarily generate the tangential 

 force {f) in question, and the greater the tendency the greater 

 will be the force. Consequently there must be the greatest 

 tendency to form these planes of discontinuity in those direc- 

 tions in which the force^is a maximum or minimum*. These 

 directions are given by equation (4.) (art. 11), and are repre- 

 sented in diagram 3 of the same article. They are perpendi- 

 cular to each other, and, in all cases, make angles of 45° with 

 the directions of (R) and (?), those of maximum and minimum 

 tensions. In these latter directions the values ofyare always 

 zero. 



Hence, if there be no planes of less cohesion in the mass:, 

 and its cohesion should give way to the tangential force, before 

 it yields to the normal tension, it must be along one of the 

 lines for whichy is a maximum or minimum, /. e. along a line 

 inclined at an angle of 45° to the direction in which an open 

 fissure would be formed, if formed at all, by the normal ten- 

 sion (11). If Xi= and Y| = 0, one of these directions will 

 coincide with that of the axis of the glacier, to which the other 

 will be perpendicular. Consequently there will be an equal 

 tendency to fracture the mass in the way we are now consider- 

 ing, longitudinally and transversely. If the mass, instead of 

 being constituted as just supposed, have a system of parallel 

 planes of less cohesion, each fracture will take place along 

 some one of such planes, provided they approximate suffi- 

 ciently to those directions in which the fractures would take 



* It must be recollected that the minimum only differs from the maxi- 

 mum value ofy" in sign and not in magnitude. Consequently there will be 

 the same effort in both cases to overcome the cohesion of the mass. 



