Mr. Hopkins on the Mechanism of Glacial Motion. 151 



line A' A parallel to the axis of ^, and let pqhe b. portion of 

 it so small that the actions on every point of p q may be consi- 

 dered equal. Let Yj .pq denote the normal force exerted by 



the particles immediately above pq in the annexed figure, on 

 those immediately below it, estimated in the direction q B ; 

 and letfi.pq represent the tangential action on pq. Again, 

 let the line of separation coincide with B' B, parallel to the 

 axis of 1/, and perpendicular to A' A ; and let X^ .qs denote 

 the normal force exerted by the particles immediately on the 

 right of 5' 5 on the contiguous particles immediately on the left 

 of it, and//, q s the tangential action. Join p and s, and let a 

 perpendicular to p s make an angle 9 with A' A or the axis of 

 X. Then if X.^J^and Y .ps be the resolved parts of the 

 forces which the particles on one side o^ps exert on those on 

 the opposite side, estimated in the direction q A and q B re- 

 spectively, we shall have 



X = Xj cos & +yjsin Q, 

 Y = Yisinfl -h/i'cosQ. 



To prove these formula?, we have only to observe that the 

 forces acting on the sides p q and q s of the triangular element 

 pq s must be in equilibrium with the forces — X and — Y 

 acting externally on the side ps, neglecdng small quantities of 

 the third order. Hence we have 



-X.ps-{-Xi.qs+fi.pq = 0, 

 -Y.ps + Y,.pq+fl.qs = 0, 



