a very slow unaccelerated motion down an inclined plane, presenting 

 a surface like that of a common slab of paving-stone, at an angle 

 scarcely exceeding half a degree (and probably also at still smaller 

 angles), provided the lower surface of the ice in immediate contact 

 with the inclined plane be in a state of constant but slow disintegra- 

 tion. This experimental conclusion was brought forward in support 

 of the sliding theory of De Saussure, and the author endeavoured to 

 explain, according to that theory, different phenomena connected 

 with the motion of glaciers. He there considered glacial ice as a 

 solid substance, having a certain degree of plasticity and flexibility, 

 and the general mass of the glacier as a dislocated mass, the greater 

 motion of the central portion of the glacier being much facilitated by 

 these dislocations, though due partly, but in a comparatively small 

 degree, to the plasticity of the general mass. In the present memoir 

 Mr. Hopkins considers what would be the nature of the motion under 

 other hypotheses respecting the constitution of glaciers. (1.) The 

 lower part of a glacier may be conceived to be crushed, and conse- 

 quently disintegrated, by the superincumbent weight, each compo- 

 nent particle still retaining its solidity; or (2.) the whole mass may 

 be conceived to be plastic, and to move by a change of form, pro- 

 duced by gravity, in each component element. The author contends, 

 if either of these hypotheses were true, that, c ceteris paribus, the more 

 superficial portion of the mass must tend to move the faster as the 

 depth of the glacier should be greater ; and that, consequently, the 

 part of the glacier near the upper extremity must generally tend to 

 move much faster than that near the lower extremity, assuming 

 always the whole, or much the greater part of glacial motion, to be 

 due to the plasticity of the mass, and to be independent of sliding 

 over its bed. But in such case it is manifest that the general state 

 of a glacier must be one of longitudinal compression, more particu- 

 larly during the summer months, when the motion is greatest. Now 

 the author contends that the general existence of transverse fissures 

 (at least during summer) is a conclusive proof against the existence 

 of general longitudinal compression ; and he observes that no ob- 

 server ventured to assert the fact of such compression to be dedu- 

 cible from actual observation. He conceives this to be a serious ob- 

 jection to the hypothesis here considered. 



In this memoir Mr. Hopkins has also investigated the directions 

 in which transverse fissures must be formed when referrible to the 

 internal tensions superinduced by the conditions to which glaciers in 

 general are subjected, and more especially by the more rapid motion 

 of their central portions. 



Assuming the velocity of each particle of the glacier to be the 

 same in any vertical line (which is at least true at points not remote 

 from the surface), the glacier may, in this investigation, be consi- 

 dered as a lamina. In this lamina take a rectangular element having 

 two of its sides parallel to the axis of the glacier, and, therefore, the 

 remaining sides perpendicular to it. Let X denote the intensity of 

 the force acting normally to these latter sides of the element, Y that 

 of the force acting normally to the two former sides. Also let/de- 



