﻿364 Canon Moseley On the Mechanical Impossibility of 



rallel to Aad~D, and equidistant from one another, and let 

 Vp q Q be one of these planes. Imagine it, too, to be similarly 

 intersected by planes parallel to ABCD. Let the intersections 

 of these planes m nhe the edge of one of the rectangular strips 

 into which the solid will thus be divided. If we suppose the 

 strip mn to be prolonged indefinitely both ways, every particle 

 of ice in it will be moving with the same velocity, the glacier 

 being supposed to be of indefinite length and uniform dimen- 

 sions and slope. The strip mn will therefore sustain no pres- 

 sure downwards from its upward prolongation, nor resistance 

 upwards from its downward prolongation; and supposing the 

 weight of the glacier to be the only force tending to bring it 

 down, the work of the weight of every particle of ice in mn must 

 be equal to the work of the resistances which oppose themselves 

 to its uniform descent ; and since all the particles of mn may be 

 assumed to have equal weights and to sustain equal resistances, 

 what is true of a single particle is true of the whole elementary 

 strip of ice mn. The resistances to the descent of mn&re, first, 

 the shear of its surfaces on the surfaces of similar contiguous 

 strips above and below and on each side of it, and, secondly, its 

 friction on the strips below and above it. Besides these resist- 

 ances, to which its elements, such as m n y are subjected by reason 

 of the different velocities with which its parts move, and which 

 consume the work of its weight internally, there is the work ne- 

 cessary to move the whole solid A c over its floor abed, and to 

 overcome its adhesion to its side B&cC. Let it be supposed 

 that the floor and sides of the channel of, the glacier are so 

 rough that it is necessary to shear the ice over them. 



Let jju — the shear of the ice in lbs. per unit of surface. 

 i = inclination of floor of glacier to horizon. 

 f = coefficient of friction of ice upon ice. 

 w = weight of ice per solid unit. 



AB = #, A« = 6, bp = oc } pm = y, 

 AD = «, BC=/3, bc=zy, ad= ^- 



U sin i = whole work of the weight of solid A c in unit of time. 

 Uj fju — whole work of internal shear of solid A c in unit of time. 

 U 2 jju = work of external shear of bottom ab c din unit of time. 

 U 3 /a = work of external shear of side B b c C in unit of time. 

 U 4 /cos£= work of internal friction of solid A c in unit of time. 

 TJ 5 fcosi = work of friction on floor of channel in do. 



Then, by the principle of virtual velocities, 



U sin i — U j/x + U 2/ u- + Ugf6 + U 4 /cos i + U 5 /cos l, . (I') 



