Mr. HOPKINS, ON THE MOTION OF GLACIERS. 59 



To take a miraerical example, let us suppose PN to be 2000 feet, where the relative velocity 

 (w) is ,3 feet*, the unit of time being one day ; we shall then have 



'-(k)' 



0" = 0; 



nearly. Consequently it would in this case require nearly two months to diminish the angle 

 9 by one degree. If 6^ = 8' or 10°, the change of curvature during a whole summer will 

 scarcely, be sensible to the eye. 



AVhen the whole curvature is destroyed we must have 6—0, or 



180 2 u 

 6 .—< = 0; 



= 58 0, 



nearly with the above values of v and 6, 



If 6^ = lo", t = 580 days, supposing the relative motion to be ,3 feet each day. 



If the central part of the glacier move through a foot each day, the curvature in the 

 above case would be destroyed after the highest point (iV) of the fissure should have moved 

 through 580 feet. 



9. Professor Forbes has shewn by his observations on the Mer de Glace, that there is 

 little variation of velocity except at points near the sides of the glacier. Consequently, if 

 we take a fissure of which the extremities do not approach too near the sides, the relative 

 velocities of different points of it may be much less than supposed in the above example, and 

 a fissure might remain for several years without losing its convexity. The period during 

 which these crevasses preserve their identity as open fissures, has not yet been made suf- 

 ciently a matter of observation. Whatever this period, however, may be, it is manifest, that 

 since it is too short for the convexity above described to be destroyed, the crevasses must 

 generally close after moving with the general mass of ice through a space extremely small com- 

 pared with the length of the glacier. After being closed they will form surfaces of discon- 

 tmuity within the glacier, i.e. surfaces along which there is a discontinuity in the cohesive 

 power of the ice. There will, in fact, be no cohesion along such a surface when the crevasse 

 first closes, though it inay be afterwards partially restored. As the existence of these surfaces 

 may exercise an important influence on the relative motions of different parts of the glacier, 

 it may be well to examine more particularly the positions they will assume in consequence of 

 the observed relative motions of the center and sides of a glacier. 



10. Surfaces of Discontmuity. — Let AA' in the annexed diagram represent a fissure im- 

 mediately after its first formation. For the greater distinctness of explanation it is supposed to 

 extend from one side of the glacier to the other. Suppose it to move to BB' before it closes. 

 During that time other fissures will have been successively formed at AA', and will in like manner 

 have moved forward ; so that between AA' where the fissures are formed and BB' where they 

 finally close, there will be a system of open fissures as represented in the figure. Below BB' the fis- 

 sures will no longer be open, but will form surfaces of discontmuity, as above described. The 



• If the central velocity be reprcBcnted by unity, the velocity of the sides will ]>robal)ly Ije vtry frequently between ^t! and .11, and 

 therefore the relative velocity of the center between ,2 and ,4. 



