168 Mr. Hopkins on the Mechanisin of Glacial Motion. 



in the case before us, the extension would increase forty times 

 faster between the first and second stations than for a con- 

 siderable space near the centre of the glacier; and if the ex- 

 treme flanks were taken, the ratio would probably be still 

 considerably greater. Thus, if the glacier at the present 

 time were perfectly continuous, the flanks would probably be 

 dislocated by transverse fissures in a few months, while the 

 continuity of the central portion, independently of the action 

 of local causes, might be preserved for many years, even if it 

 should break with an extension no greater than that required 

 to fracture the flanks. If also it be allowed that the extensi- 

 bility becomes greater as the extension is produced more 

 slowly, the glacier might move on for a still greater number 

 of years without central dislocations due to the more rapid 

 progression of its centre. 



If this greater extensibility of glacial ice during a long 

 period, or what may be called its secular extensibility, be al- 

 lowed, we must also allow it to possess the property o^ secular 

 plasticity, by which I mean that plasticity which shall require 

 for its development the continuous application of force, possi- 

 bly of great force, for a long period of time, in contradistinc- 

 tion to that plasticity by which a mass submits to an immediate 

 and considerable change of form by the application of forces 

 of comparatively small intensity. This latter kind of plasti- 

 city, when sufficiently great, becomes semijluidity \ and if the 

 observed phaenomena of motion in a case like that of a glacier 

 should justify the conclusion that the mass possesses this high 

 degree of plasticity, we might be justified in asserting that the 

 effectiveness of gravity to put the mass in motion was due to 

 that property. But if, on the contrary, the observed circum- 

 stances of the motion only establish the existence of secular 

 plasticity, and when, moreover, the motion is aKvays accom- 

 panied by numerous and repeated fractures, we have no right 

 thence to conclude that the motion is effectively due to the 

 plasticity of the mass. I shall recur again to this point in the 

 sequel. 



28. With respect to the conclusions I have drawn from the 

 preceding analysis of the problem of glacial motion, it is im- 

 portant to remark how entirely they are independent of the 

 experimental determination of the values of the constants which 

 afford us measures of such properties, for instance, as the 

 elasticity, the extensibility, &c. of glacial ice; and also of all 

 arbitrary constants and functions introduced into analytical 

 results by the integration of the fundamental differential equa- 

 tions of the problem, and requiring for their determination a 

 knowledge of the conditions of each particular problem. My 



