246 Mr. Hopkins on the Mechanism of Glacial Motion. 



letter, that my investigations involve the condition of conti- 

 nuity in the same manner as the common investigations of the 

 motions of fluids. In these latter motions, however, there is 

 one obvious case in which that condition is not satisfied — that 

 in which the motion results from the heating of the lower por- 

 tion of the fluid contained in a vessel, as in the ordinary case 

 of boiling water. It would seem that at every point of the 

 fluid mass, some particles must be ascending and some de- 

 scending, which is inconsistent with the condition of conti- 

 nuity as here understood. In solid bodies we may conceive 

 a case exactly analogous. Suppose a body composed of two 

 parcels of parallel rods, the rods of one parcel being inter- 

 mingled with, and placed parallel to, those of the other; and 

 let us suppose the component rods to be parallelopipeds, and 

 so arranged that each of the four longitudinal faces of any rod 

 in one parcel shall be in contact with a rod of the other par- 

 cel, with the exception of those faces which form the exterior 

 surface of the whole body. This particular arrangement is 

 not essential for our purpose; it is merely assumed for the 

 greater clearness of conception. Also conceive the whole 

 mass thus formed to be terminated by two planes, perpendi- 

 cular to the common direction of the rods, of which one par- 

 cel is fixed to one terminal plane, and the other parcel to the 

 opposite plane. If forces of sufficient magnitude be applied 

 in opposite directions on the terminal planes, the two parcels 

 of component rods may be drawn out from each other, thus 

 producing extension of the mass, by giving motions in oppo- 

 site directions to elements laterally in contact. This relative 

 motion of such elements would be exactly similar to that above 

 mentioned in boiling water, and is inconsistent with our con- 

 dition of continuity. 



I would here observe that this case is not introduced as 

 belonging to Prof. Forbes's theory, for it is one which he does 

 not appear ever to have contemplated in his mechanical rea- 

 soning on this subject; but I notice it as a case in which nu- 

 merous parallel surfaces of discontinuity (such as supposed in 

 Prof. Forbes's theory) might be produced by the sliding of 

 contiguous particles past each other in the directions of the 

 lines of maximum tension. It is not unimportant, therefore, 

 to investigate the conditions under which extension may take 

 place in the manner here supposed. 



Let 6x and di/ be the sides of the section of one of the 

 component rods, made by the plane of .rj/ supposed perpen- 

 dicular to the direction of the rods; then the edges of any 

 element of the rod will be So;, S j/ and 8 z. Let Z be the force 

 parallel to the axis of ^r at the point {xi/z). Z8.«*Sj/ and 



