1888.] 



On the Plasticity of Glacier and other Ice. 



339 



It will be interesting to make some numerical comparison between 

 the figures we have given and the plasticity actually observed in the 

 motion of glaciers. Perhaps the most striking proof of the existence 

 of plasticity is the great increase of velocity from the side to the 

 centre of a glacier. A number of measurements on this point have 

 been collected by Heim (' Gletscherkunde,' p. 147). The most rapid 

 increase he mentions among the glaciers of the Alps is on the Rhone 

 glacier, on a line 2300 metres above the top of the icefall. At 

 100 metres from the western bank the mean yearly motion, 1874 to 

 1880, was 12'9 metres; at 160 metres from the bank it was 

 43" 25 metres. This gives an increase of velocity in each metre 

 across the glacier of 0*000058 metre per hour. 



Let us consider what rate of extension this involves. 



Fig. 1. 



Let AB (fig. 1) be two points on a glacier moving in parallel direc- 

 tions, of which B is moving faster. In the small time H ( whose 

 square we may neglect) let A move to A' and B to B'. Draw AN, A'N' 

 perpendicular to B'B produced. Let AN" = A'N' = a, BX = x, B'N' 

 = x', AB = r, A'B' = and let the velocities be v a and Vb. 



Then AA = v a ct, B'B = v h ct, 



r 2 = a 2 -fa; 2 , 



r ,2 = a 2 + z' 2 = a*+{x+ (v b -v a )U}* 

 = a 2 -|-a,' 2 + 2z (vb-Va) to 



