ME. HOPKINS ON THE THEOEY OE THE MOTION OF GLACIEES. 
691 
only tend to preserve the particles on opposite sides of s in contact, but if it be a tension^ 
it will tend to separate those particles by motions parallel to the normal. Also the 
tangential forces sin ^ and —/’sin ^ will always tend to separate two particles on oppo- 
site sides of s and in contact, by making them move in opposite directions parallel to 
the plane. If we conceive s to revolve about P as a fixed point, and thus to assume all 
possible angular positions, the forces/' cos § and /“sin ^ will vary with the angular posi- 
tion of the plane, - in certain positions of which they will assume their maximum and 
minimum values. The determination of these positions is one immediate object of the 
problem, with the view of determining the eflFect of the distorting forces on the form of 
each element of the mass, and thence, if the problem were completely soluble, the dis- 
tortion of the whole mass. But before proceeding further, we may explain more 
explicitly what will be the kind of distortion to which every element of any solid body 
will be subjected under the action of distorting forces. Let us take a small rectangular 
parallelepiped as the element of the body while unconstrained by such forces. The 
normal forces acting on opposite sides of the element will manifestly form three pairs ot 
equal* and opposite forces, each force of each pair acting in a direction opposite to the 
other force of that same pair, and thus producing compression or extension of the 
element according to the directions in which they act. Again, it is manifest, from what 
has been said respecting the small plane 5 , that the tangential force on any one side of 
the elementary parallelepiped will be equal to that on the opposite side, but will act in 
the opposite direction, thus tending to twist the element from its original rectangular 
form into an oblique-angled parallelepiped. Hence the primitive undistorted element 
will be compressed or extended according to circumstances, and will always (unless the 
forces acting on it be entirely normal) be twisted so as to destroy its rectangularity. In 
the final application of the results obtained from this our typical problem, we shall have 
to deduce the manner in which the continuity of the glacial mass will be destroyed 
when the power of resistance of the ice is no longer sufficient to equilibrate the distort- 
ing forces acting on it, and also to consider the phenomena which may result from such 
breach of continuity. 
With respect to the solution of our abstract problem, I have little to add to that 
which I gave in the Transactions of the Cambridge Philosophical Society for the year 
1847, and I might be content merely to refer to that solution for the results. In doing 
so, however, it would be necessary to give a somewhat complicated notation, and certain 
explanations in such detail that the space thus occupied would not differ materially from 
that required for the mathematical analysis of the first part of the general problem. ^By 
giving this analysis here, considerable trouble of reference will be avoided. I would 
request permission, therefore, to repeat a part of what appeared in the Transactions 
above referred to. The quotation includes the following articles, from the 1 4th to the 
1 7th inclusive: — 
* Omitting small quantities of a certain order, which it is not necessary in this general explanation to 
take into account. 
