R. M. Deeley — Viscous Flow of Glacier-Ice. 415 



Also the volume Vi swept througli by any cross-section in unit of time 

 = 4 F&»- 



o - • . (12) 



o a /I 



So the volume passed is directly proportional to the pressure P, and 

 to the cube of the thickness r^ in the case of the central portion of 

 a vei'y wide glacier. 



If the bed be semicircular we obtain in a similar way 



F. = ^ . Z^ . . . (IS) 

 lb a /I 



No account is taken of the volume passed owing to slipping at 

 the boundary. It, however, is only a fraction of that passed owing 

 to the viscosity of the ice. 



Experiments employed to ascertain the conditions of motion of 

 existing glaciers have proved that velocity curves drawn across the 

 glacier are parabolas, distorted somewhat where the ice-river is 

 caused to make a bend, much in the same way as are the curves 

 illustrating the flow of a river by the momentum of the water. 



Above Montanvert the Mer-de-Glace is fractured across at one 

 point, and into the crevasses so formed the surface moraine falls 

 and forms imbedded strings of stone and mud. Lower down the 

 melting of the ice at the surface again exposes the debris. But 

 instead of running as straight lines across the glacier, the lines of 

 debris sweep across as great parabolic curves having their apices 

 pointing down-stream. No finer illustration of the fact that glacier- 

 flow is a strictly viscous phenomenon could be conceived than is 

 here presented. Proofs have also been given that a glacier moves 

 more rapidly at the surface than it does at the bottom. 



We also find that the rate of distortion at the bounding surface, 

 where it rests upon rock, is greater than at any other point, and 

 that there the abrading action is most energetic. Indeed, at the 

 bottom of a hollow which might form the bed of a lake, even if 

 the motion of the ice be slow, the pressure is very great, the ice 

 going down into it at one end and rising from it at the other. 

 Even at the bottom of such a hollow the maximum rate of distortion 

 is located and a powerful grinding action maintained. 



Throughout its course a glacier is urged along, not by a pressure 

 from above but by gravity acting upon each molecule of ice during 

 its whole course from the cold snow-fields above to the poi^lt where 

 it melts in the warm valley below. No doubt thrust does play some 

 part in the movement, just as does the momentum of the water in 

 the flow of a river ; but it is quite a subordinate feature and only 

 produces local effects. 



I am much indebted to Mr. C. E. Wolflf, B.Sc, for the assistance 

 he has rendered in the mathematical treatment of the subject. 



