712 
ME. HOPKINS ON THE THEOET OE THE MOTION OE GLACIEES. 
section of a small elementary rectangular parallelepiped (lx, ly, made by the plane 
of the paper (that of xy)\ and let^ s be in the direction ('pp') of the motion of^; it will 
be parallel to x, and the transverse line q N, perpendicular to pp’, will be parallel to 
y. Now the physical line M N will, in a short time, come into the position M' N', by the 
assumed motion of the glacier, and the greater velocity of its axial portion. The 
element^ qrs will then come into the position s', and will be angularly distorted. It 
will be acted on by the tangential force (F), forming two equal and opposite couples, with 
a common axis parallel to z (art. 29, (1)), and tending to destroy the continuity on every 
side of the element, by overcoming the tangential cohesion. The force F will be diffe- 
rent for different angular positions of the element, and will always be greatest when the 
sides of the element bisect the two right angles between^! and ^ 2 ? flie greatest tension 
and the greatest pressure (art. 18). In the present case the directions oi p^ and ^2 
each be inclined at an angle of 45'’ to the axes of x and y (art. 29, (1)) ; and there- 
fore the intensity of the forces (F) of the two couples will be greatest when they act 
respectively parallel to x and y, i. e. when the element is in the angular position repre- 
sented in the figure. 
Now if tangential dislocation take place, it must necessarily do so in those dhections 
in which the tendency of the forces F to produce it is greatest, or, in the case before 
us, in directions parallel and perpendicular to the axis of the glacier, the tendencies 
being the same in both those directions. Let us suppose, then, a complete tangential 
rupture to take place, and simultaneously, on each side of the element p qrs, as well as 
in the surrounding elements. Each element, represented hj p' q[ 7 ^ s', will then regain its 
original rectangular form by its elasticity, but so moving that its centre of gra\ity (g') 
shall remain at rest, since the elastic force of restitution acts entirely within the element. 
Thus pqr s will return to its original rectangular form p"q'’r"s" ; and if we take two con- 
secutive elements whose centres of gravity are G and G', they will be brought into the 
relative positions represented in the figure, in which G' is slightly in advance of G, as 
much, in fact, as is necessitated by the more rapid motion of the central parts of the 
glacier. After the rupture, if we suppose the continuity to be instantaneously restored 
(as it will be by regelation according to our theory), the glacier will again be brought 
as a continuous mass into a position of no constraint by its general motion. By a repe- 
tition of this process, the continuity of the mass will be constantly destroyed and as 
constantly restored; and we thus see the modus operandi by which, taking any two 
elements situated like G and Gr^, the one nearest the axis of the glacier gets gradually 
in advance of the other, as it must do, in accordance with the general law of the 
glacier’s motion. 
37. But, it may be asked, if the dislocation takes place on the two sides of the 
element whose directions are transverse to the glacier, simultaneously with the rupture 
along the sides whose directions are longitudinal, why is it that the subsequent relative 
or differential motion of two contiguous elements, such as G and G', should not be 
transversal as well as longitudinal % The reason is obvious. The motion which instan- 
