740 
ME. HOPKINS ON THE THEOET OF THE MOTION OF GLACIEES. 
E=0, as well as D=0. We shall thus have (art. 29 (1.)), 
tan 2a=oo . 
F will vanish along the axis of the glacier, as we have seen, and will have its greatest 
value along the imaginary vertical planes by which we here consider the moving mass 
as effectively bounded along its lateral margins. Let its value along these planes be Fj. 
If we suppose, as we may in this approximation, that every particle in the same vertical 
line moves with the same velocity, Fj will be the same for every point of the bounding 
lateral planes. Moreover, let the tangential action exercised by the bed of the glacier 
on its lower surface be denoted by^i. Let us now conceive the mass to be placed in a 
position of no constraint. It will immediately assume a position of constraint by virtue 
of its small extensibility, and, provided the internal forces and F are insufficient 
to dislocate the mass along the lateral vertical planes (where their magnitudes will be 
the greatest), the glacier will be held at rest in its state of constraint by the external 
forces acting upon it. Now Fj and being referred to a unit of smrface, if a, 5, c be 
the length, breadth, and depth of the glacier, we shall have 
The tangential force on each flank = F^ac, 
The tangential force on the bottom —f^ab, 
and these must be in equilibrium with the weight of the mass on the plane whose incli- 
nation is /. Hence if &> be the weight of a unit of volume of glacial ice, we shall have 
2F^ac-\-fiai=i<>a^c sin /, 
and r , 
Fi=i|^y5 sin/— 
Suppose F to denote the tangential cohesive power of the mass. Then, if 
F,=F, 
the glacier will be just on the point of dislocation ; and if Fj exceed F in the smallest 
degree, the mass will be dislocated along the lateral planes and move onwards. 
We have shown (art. 8) that the effect off^ to hold the mass of the glacier at rest is 
extremely small ; consequently it may be neglected in the above equation, and we shall 
then have 
F,=|-/y5 sin/. 
If the lower surface of the glacier were firmly frozen to its bed, we might have/’i=Fi, 
and therefore 
mb sin ^ 
-Cl— j . 
2 + - 
c 
c is properly the depth of the glacier along its flanks, so that ^ may be large. 
Hence we see that Fj may become much greater whenyi is very small, than if it were 
