160 Mr. Hopkins on the Mechanism of Glacial Motion. 



18. Let us now take the annexed diagram (fig. 6) to repre- 

 sent a glacier, or rather a horizontal section of it. Any trans- 

 Fig. 6. 



verse element P Q will, by the more rapid motion of the centre, 

 be brought into the position P' Q', and the rectangular ele- 

 ment ^V j' 5' r' will assume the form PiqtS^rp the continuity of 

 the mass still remaining unbroken. This distortion is pro- 

 duced by the tangential force (_/,') impressed on the element in 

 the directions p^q, along that side, and s^r^ along the opposite 

 side, together with equal tangential forces called into action 

 along the other sides in the directions p^ r^ and s^ q^ respect- 

 ively. The longitudinal tension will be represented by Xj 

 in the previous formulae, and the transversal tension by Yj, 

 these quantities being negative whenever we have pressures 

 instead of tensions. Hence, if at any point q we take pqr m. 

 the direction of motion, and take /§'/' = to fl as determined by 

 equation (1.), g^will be the direction of maximum tension, 

 and a line perpendicular to qt, that of maximum pressure at 

 the point q. They will also be the lines of no tangential 

 force. 



19. Formation of Surfaces of Discontinuity in the Mass of 

 the Glacier. — In the previous investigations the continuity of 

 the mass has been supposed to remain unbroken ; let us now 

 suppose the internal actions to become greater than the cohe- 

 sion, and the continuity, consequently, to be broken. This 

 breach of continuity may be produced in two ways; by the 

 normal fof)-ce (R), which measures what is properly called the 

 tension^ or by the tangential force [f). Open fissures will 

 result in the first case, and merely surfaces of discontinuity in 

 the latter. The directions of fracture may depend on the co- 

 hesion of the mass as well as on the internal forces to which 

 it is subjected, but it is important to observe that they will 

 depend on the internal forces alone, however the cohesion may 



