ME. HOPKINS ON THE THEOET OF THE MOTION OF G-LACIEES. 
703 
the form of the bed of the valley; B will be small. If the sides be convergent in descend- 
ing the valley, A will almost necessarily be a pressure, on account of the resistance 
which the sides will oppose, by their convergency, to the onward progress of the glacier. 
B will become a great pressure, greater than A, to which it will bear somewhat the 
same relation as the pressure on the side of a wedge bears to that applied to its back. If 
the valley be divergent, and if when it becomes so, its inclination is very much dimi- 
nished (as at the lower end of the Rhone glacier) A may become an enormous pressure, 
while B may become a tension on account of the lateral expansion which will be given 
to the mass by the great pressure a ter go. C will be best considered in conjunction with 
E. D, as above stated, will always =0. F will have different values for different points 
in the same vertical transverse section of the glacier. It will manifestly be greatest in 
the marginal portions, where the angular distortion represented in fig. 2 is greatest ; in 
the central portions, the motion of the glacier will produce very little of this angular 
distortion about an axis parallel to that of z, and F will be proportionally small. 
27. The forces C and E are more de- 
pendent on each other than A, B, and F. 
I proceed to investigate expressions for 
them. For this purpose let fig. 4 repre- 
sent a vertical section of the glacier paral- 
lel to (a:z) and not too remote from its 
axis ; then will F, as above stated, be very 
small, and may be neglected. Also D = 0, 
and B acts perpendicular to the plane (^ 0 ), 
and will therefore not affect the relations 
between the forces acting parallel to that 
Let g, z be the coordinates of the point Q. We shall have NM=ar, the distance 
of the plane NMQ from that of xz=y, and MQ=^. We might obtain the results 
required by considering the conditions of equilibrium of the element represented 
by Q r S ; but it will be more convenient to take an element represented by M Q g- m, of 
which the volume will be zlxhy. I suppose here the existence of a longitudinal pressure 
parallel to the axis of x, and represented in our general formulae by A. If we draw a 
plane through M Q perpendicular to the axis of x, A may represent the intensity of the 
longitudinal pressure at any point on that plane, referred to a mit of surface. For 
different points in this plane x will be constant, and the pressure may vary generally 
with y and z ; but it will answer our immediate purpose, and much simplify our pro- 
blem, if we suppose A constant for every point in M Q, or independent of y and z. It 
will then vary only in passing from any plane M Q to a consecutive and parallel plane, 
i. e. A will be a function x alone. Hence we shall have 
plane. 
Fig. 4. 
Pressure on one of the sides of the element M q perpendicular to the plane of ^ 2 = A . zly. 
Pressure on the opposite side = — 
5 D 2 
