742 
ME. HOPKINS ON THE THEOEY OF THE MOTION OF GLACIEES. 
lateral vertical planes, ■which could be produced under our assumed conditions. If the 
cohesion were less than this, the mass would necessarily be ruptured in some way or 
other in its marginal regions. The above, however, is only the lowest limit to which 
the force Fj would attain. For let a represent the length of a given portion only of a 
glacier, such that at the lower transverse vertical section of that portion, the longitudinal 
tension shall be greater than at the higher bounding transverse section, instead of being 
equal to it as above supposed. It is manifest that Fj will be increased along the lateral 
vertical planes of that portion of the glacier. Such will also be the case if the same 
portion of the glacier be acted on by a longitudinal pressure on its higher transverse 
bounding section, greater than that on its lower one. There would generally, in such 
cases, be a much greater effort to overcome the cohesion (F) of the mass along the 
lateral vertical planes than in the case previously considered. If the valley of the glacier 
contract somewhat rapidly, the longitudinal pressure may be enormously increased on a 
given portion of the glacier by the action of the mass behind it, and this increased action 
will manifestly depend very much on the facility with which the mass behind slides over 
its bed. 
It may be well to take another numerical example in which the conditions are similar 
to those of the example given above. Let the glacier be something less than half a mile 
broad, and its inclination about 3°. Then it appears, from the above expression for Fj, 
that dislocation would not take place, provided the cohesion of the mass were not less 
than the weight of a column of ice of about 60 feet long, instead of 200 as in the former 
example. This supposes the mass to slide freely over its bed, and the longitudinal 
pressure or tension to be the same behind as before; but if we suppose the mass to 
adhere to its bed, that adherence will help the tangential action along the lateral vertical 
planes to support the mass. Consequently the force F, called into play might be much 
less than the weight of a column 60 feet long, and might not be sufficient to overcome 
the cohesion F, in which case the motion of the mass would be arrested. This conclu- 
sion would be strictly applicable only to our typical glacier, but is sufficient to explain 
how, in the actual case of a glacier, the facility of its sliding may increase its power to 
overcome the obstacles to its motion by the fracturing of its mass. 
I have chosen the simplest cases for the purpose of more easily explaining the manner 
in which the sliding of a glacier increases the dislocating power of the forces acting upon 
it. In the more complicated cases, in which C and E are taken into account at consider- 
able depths, we shall obtain greater values of the tearing and crushing forces and 
It is the latter which will be principally increased at greater depths. Still it must not 
be supposed that the mere increase of weight can explain the apparent difficulty ah’eady 
suggested (art. 60), viz,. Why, when the mass has been crushed and then immediately 
regealed under the existing conditions at any proposed point, it should again be crushed 
at the same point. This second crushing does not, in fact, take place under the same 
pressure as that under which the regelation took place. This latter process occurs when 
the pressure depending on the angular distortion of the element, or on the force F, has 
