160 Mr. HOPKINS, ON THE MOTION OF GLACIERS. 



(3 ) The facial mass may be conceived to have the property of great plasticity, and to move 

 by a change of form in the elomentry particles composing it, tlie continuity of the mass, in the sense 

 above defined, being strictly preserved. It is in this sense that the continuity of a fluid is assumed 

 to be preserved in those cases of fluid motion which have been subjected to mathematical analysis. 



(i) The mass may be supposed to be viscous, and the motion to take place partly by a change 

 of form in the elementary portions of the mass, and partly by the destruction of the continuity sup- 

 posed to be strictly preserved in the preceding hypothesis. . . ,, 



My immediate purpose in this communication is to investigate certain properties ol the motion 

 which would exist in glaciers constituted according to these several hypotheses, and to examine 

 somewhat more in detail than in my former memoir, the state of internal pressure and tension super- 

 induced by the unequal velocities of the central and lateral portions of a glacier. i he explanation 

 of this inequality of motion given in my former memoir, will apply with little alteration if we should 

 adopt any of the preceding hypotheses; it will not therefore be necessary to recur to that part ot 

 our problem. We shall have" to examine more especially the relative motions of the superficial and 

 inferior portions of the mass, to ascertain how far they may be consistent with observed phenomena, 

 and thus to test the truth of our hypotheses. 



2. Let us first suppose the glacier stratified as in (1). 



Fig. 1. 



Let JBCD represent the vertical section of a mass reposing on the inclined plane JB, 

 makino- an anfle a with the horizon ; and let MN represent the surface of one of the strata of 

 which we here suppose the mass to consist. We have first to consider under what condition the 

 upper part CDMN would slide over that on which it is superincumbent. Assuming the absence 

 of all cohesion between contiguous strata, the only force opposing the sliding motion will be 

 the friction along tiie plane MN. Now so long as the original texture of the lower surface of 

 the sliding body and that of the surface on which the motion takes place, remain unaltered by the 

 weight of the sliding mass or other cause, it is well known that the inclination at which the 

 sliding will begin is independent of the weight of the sliding body, and that, if the inclination 



be a, we must have 



tan a = fjL, 



where a is the constant ratio which friction bears to the normal pressure. If tan a were greater 

 than u, the whole mass would begin to move ; and (supposing the friction the same throughout) 

 in such a manner that the relative motion of each stratum to the one immediately subjacent to 

 it would be the same for all the strata. Consequently, if we could ascertain from observation 

 that no such relative motion existed in the upper strata, we should be certain that none existed 

 amono- the inferior strata, unless at depths at which the assumed condition that the texture of 

 the sliding surfaces shall remain unaltered, may be no longer satisfied. 



Now iud^ino- from the observations I have made on the descent of ice down inclined planes, 

 I much doubt whether it be possible that two surfaces of ice at a temperature below that of 

 freezing could, under any circumstances, be so smooth as to admit of the sliding motion above 

 contemplated at an inclination so small as that of some observed glaciers ; and therefore I believe 



