﻿230 Royal Society : — 



force of cast iron, for instance, is so great that, although its weight 

 is also very great, it is highly improbable a mass of cast iron would 

 descend if it were made to fill the channel of the Mer de Glace, as 

 the glacier does, because its weight would be found insufficient to 

 overcome its resistance to shearing, and thus to supply the work 

 necessary to those internal displacements, of which a glacier is the 

 subject, or even to shear over the irregularities of .the rocky channel. 

 The same is probably true of any other metal. 



I can find no discussion which has for its object to determine this 

 mechanical relation between what is assumed to be the cause of the 

 descent of a glacier, and the effect produced — to show that the work 

 of its weight (supposing that alone to cause it to descend) is equal 

 to the works of the several resistances, internal and external, which 

 are actually overcome in its descent. It is my obiect to establish such 

 a relation. 



The forces which oppose themselves to the descent of a glacier 

 are :— -1st. The resistance to the sliding motion of one part of a piece 

 of solid ice on the surface of another, which is taking place continu- 

 ally throughout the mass of the glacier, bv reason of the different 

 velocities with which its different parts move. This kind of resist- 

 ance will be called in this paper (for shortness) shear, the unit of 

 shear being the pressure in lbs. necessary to overcome the resistance 

 to shearing of one square inch, which may be presumed to be con- 

 stant throughout the mass of the glacier. 



2ndly. The friction of the superimposed laminae of the glacier 

 (which move with different velocities) on one another, which is 

 greater in the lower ones than the upper. 



3rdly. The resistance to abrasion, or shearing of the ice, at the 

 bottom of the glacier, and on the sides of its channel, caused by the 

 roughnesses of the rock, the projections of which insert themselves 

 into its mass, and into the cavities of which it moulds itself. 

 i 4thly. The friction of the ice in contact with the bottom and 

 sides so sheared over or abraded. 



If the whole mechanical work of these several resistances in a 

 glacier could be determined, as it regards its descent, for any rela- 

 tively small time, one day for instance, and also the work of its 

 weight in favour of its descent during that day, then, by the prin- 

 ciple of "virtual velocities" (supposing the glacier to descend by its 

 weight only), the aggregate of the work of these resistances, opposed 

 to its descent, would be equal to the work of its weight, in favour of 

 it. It is, of course, impossible to represent this equality mathema- 

 tically, in respect to a glacier having a variable direction and an 

 irregular channel and slope ; but in respect to an imaginary one, 

 having a constant direction and a uniform channel and slope, it is 

 possible. 



Let such a glacier be imagined, of unlimited length, lying on an 

 even slope, and having a uniform rectangular channel, to which it fits 

 accurately, and which is of a uniform roughness sufficient to tear 

 ott the surface of the glacier as it advances. Such a glacier would 



