Mr. HOPKINS, ON THE MOTION OF GLACIERS. 65 



15. If we add together the two sides respectively of the first n of the above equations, 

 we have 



/„ = (l - ^j Wi sin a + + y- y] '"" ^^""' 



But u, = Dj = = i)„ nearly; and if we suppose T, V.^ V„ not to differ much from each 



other (as will probably be the case in most glaciers), we may substitute for each a mean value 

 V. Then we have 



(j> =f„ = [^ ~ y) (""> + "^2 + M*") sin a. 



where v is the common velocity of the central portion ; or, if 



M'l + W2+ + W„ = IF,,, 



(p= (l -^ W„ sin a. 



If the whole mass be very wide, like that of a glacier, and a be equal to the ordinary incli- 

 nation of a glacier (from 3° to 10° or 12"), and if the retardation V- v be considerable, (p may 

 become a force of enormous magnitude. In order that the motion of the mass may be entirely 

 destroyed, cd must coincide with AB, and we shall have 



(p = W sin a, 

 where W = weight of the whole mass. 



This explains the prodigious power which large glaciers are capable of exerting to overcome 

 local obstacles to their motion, arising from irregularities along the sides or bottoms of the valley 

 down which they move. 



16. If the tangential action along gh, instead of being equal to (p, be equal to (p' less 

 than (p, the portion eh will be accelerated by the difference of the lateral actions, (p and (p', 

 and similarly for any other portion ; but it will be observed that the portion cf, the nearest to the 

 center of those against which sliding takes place, will be neither accelerated nor retarded by 

 these lateral actions. Hence, if, in any proposed glacier, the velocity is nearly the same for the 

 central portion (dd'), but diminishes with considerable rapidity on approaching the sides, we 

 shall have two points (d, d') which may be determined approximately, in any transverse section, 

 at which the velocity will be the same as that of a glacier whose thickness should be the same 

 as the depth at these points, and in which the conditions at its lower surface should be the 

 same as for the longitudinal portions through d and d', but whose motion should be unimpeded 

 by any lateral obstacles. This conclusion is not unimportant as shewing that the slowness of 

 glacial motion does not result from lateral or local impediments, but is a necessary consequence 

 of the action of the bed of the glacier on the lower surface of the mass, as in the experiments 

 above detailed. It is this unimpeded or mean motion which ought in strictness to be compared 

 with the motion in these experiments. 



17. In the preceding investigations the mass has been supposed to be continuous, but it 

 is easily seen that similar reasoning will apply if the mass be more or less dislocated. In 

 such case its cohesion will oppose comparatively little resistance to the formation of transverse 

 fissures ; and the greatest tangential force (<i) which can be exerted will be much less than 

 when the cohesion is continuous. The sliding of one longitudinal portion past another, and the 

 more rapid motion of the central portions, will thus, as already remarked, be much facilitated. 



18. Formation of Crevasses. — It has been shewn (Art. 1."?), that if the mass of a glacier 

 were continuous, there would be the greatest tendency to form fissures in directions perpendicular 

 to those of motion, when the lower extremity of the glacier moves faster than the upper one. 

 Hence, if the tension becomes sufficient to overcome the cohesion, fissures would be formed in 



Vol. VIII. Part I. I 



