1 48 Mr. Hopkins on the Mechanism of Glacial Motion. 



siderable portion of it, remains unbroken. In the second 

 place, I shall show how the continuity will be broken when 

 the internal tensions become greater than the cohesive power 

 of the ice, and shall investigate the forms and positions of the 

 lines or curves of fracture ; and thence I shall explain how the 

 progressive motion of the glacier may take place by a constant 

 repetition of such dislocations. 



It has been already stated that no conclusive observations 

 have been made respecting the difference between the veloci- 

 ties of the upper and lower surfaces of a glacier. In the fol- 

 lowing investigations I shall assume these velocities to be the 

 same as they will be approximately, if the general motion be 

 due to sliding. There would be no difficulty introduced into 

 our investigations by the adoption of the contrary hypothesis 

 — that the lower surface moves much slower than the upper 

 one — but the resulting formulae would be of much greater 

 complexity. For the sake of simplicity I have therefore 

 adopted the first hypothesis. Any one wishing to pursue the 

 subject under the latter hypothesis will find no difficulty in 

 doing so. This, however, will not be necessary for our imme- 

 diate purpose. 



4. Directions of Maximum Tension and Pressure. — Of the 

 above laws the first and second are those with which we shall be 

 first more immediately concerned. Let ja'g'' be the line of motion 



Fig, 1. 



7^'' ^' n^ :u 7 T sf 77. 



7*^ M 



of one set of particles of the glacier, and /s' that for another 

 set, the distance between them being small ; these lines will be 

 parallel to each other and approximately so to the axis of the 

 glacier. Let M and N be particles in /' s' and p' q' respect- 

 ively. Assuming 7-' s' to be nearer the side of the glacier than 

 y^', N will move faster than M, by the second law. If they 

 moved with the same velocity, the physical line M N would 

 neither be lengthened nor shortened by the motion we are 

 considering; and therefore it will be to the difference of motion 

 of M and N that extension or compression will be due. Con- 

 sequently we may suppose M to be at rest, and N to move 



