jVCR. HOPKINS ON THE THEOET OE THE MOTION OE OLACIEES. 
705 
solutions it has been assumed that C, D, and E are so small as to be neglected. D always 
= 0, and it follows from the preceding expressions for C and E that, generally, they are 
relatively small for all those more superficial portions of a glacier to which our observa- 
tions can extend. Hence, for the same portions, our first solutions will be approxi- 
mately true and practically applicable. 
Sectiojv IV. — On the manner in which Dislocations in the Mass of a Glacier^ or in its 
Structure, may he produced ; and on the resulting Phenomena. 
28. It will be recollected that the internal pressures and tensions which have been 
investigated in the preceding pages, are those which would exist in a continuous solid 
mass acted on by certain external forces, previous to the dislocation which must result 
from such forces if the intensity of the internal tensions should be sufficient to over- 
come the cohesion of the mass, or the pressures to overcome its resisting-power. We 
may, however, carry our geometrical and mechanical analysis of the problem somewhat 
further, and consider how the dislocation wfill take place when the forces are sufficient 
to produce it. It has already been remarked (art. 2) that there are three ways in 
which this may occur. In the first place, the cohesion may give way to the greatest 
normal tension, p ^ ; open fissures will then be formed. Again, when the maximum 
compression [p.^^ becomes very great, it may be easily conceived how the primitive 
structure may break down, as it were, especially if the mass be of a crystalline structure 
like ice. The third kind of dislocation is that produced by the tangential action between 
two contiguous elements, which obviously tends to make one element slide past the 
other, and thus to produce what Principal Forbes has called a “ differential motion.” I 
shall consider successively these different kinds of dislocation, and the phenomena which 
respectively result from them, with reference, in the first place, to the more superficial 
portions of the glacier, in which our first approximate formulae are applicable; and 
secondly, the possible formation of similar phenomena in the deeper parts of the glacial 
mass. 
From the equations (<Z'.), art. 20, we have 
i<,=i{A+B+y(A-B)’+4P}, 
^),=i{A+B-v'(A-Bf+4P}, 
2F 
tan 2 c£:^^ jg. 
The last equation gives two values and of a, which determine the directions of 
and p^ with respect to the axis of the glacier. A, B, C, and F, in the application of 
the formulae to an actual canal-shaped glacier, are such as described in arts. 25 and 26. 
We have also the result that the lines of maximum tangential action at any point bisect 
the right angles between the directions of maximum tension and maximum pressure. 
Of the values and oc,^ of a, one will be greater and the other less than 90° ; and we 
must determine, in each problem, which gives the maximum and which the minimum 
