ME. HOPKINS ON THE THEOET OF THE MiOTION OF GLACIEES. 
725 
maximum, and will consequently have a maximum tendency to separate from each other 
by their differential motion. I have spoken here of physical points as perhaps conveying 
more distinctly the idea of the intervening distance denoted by g-. I might have equally 
spoken of indefinitely small elements of determinate forms, considering § as the distance 
between their centres of gravity. These are only different kinds of phraseology by 
means of which we reason on the ultimate elements of which a continuous mass must 
be constituted. 
In the above investigation the velocity of each particle has been assumed to be the 
same at every point along its line of motion. Consequently whatever holds for the 
motions with which these particles pass through one transverse plane, will hold with 
respect to any other such plane. Consequently there will be two contiguous cylindrical 
surfaces generated by lines parallel to those of the motion of the glacier, and having 
for their directors the two contiguous curves above described on the plane of yz ; and 
the motion of the particles in these cylindrical surfaces will have the same dynamical 
characters as those above enunciated for the particles in the two guiding curves. There 
will be an indefinite number of such surfaces following the same law. A section of the 
mass, made by a transverse vertical plane parallel to that of yz, will be represented by 
fig. 16. Each surface will be perpendicular to this transverse plane. 
Fig. 16. 
This system of surfaces would necessarily result from the differential motion in the sense 
in which I regard it ; nor can I conceive how the veined structure can originate in that 
motion, in the way in which the author of the theory appears to consider it to originate, 
unless the veins should coincide with the surfaces here investigated. In such case every 
line of structure on the surface of the glacier, in the typical case above considered, 
would coincide with a line of motion, and would therefore be parallel to the axis and 
sides of the glacier. In the central parts of the glacier, where the variation of V for 
different points situated on a transverse horizontal line is usually very slow, will be 
very small, and therefore ^ nearly equal 90°. Consequently the struc- 
tural surfaces will be very nearly horizontal. In the marginal portions of the glacier 
these surfaces will meet the superficial surface of the mass at angles 
=90°-^=90°- tan-^^, 
which "will be nearly = 90°, since a' will be usually small near the upper surface, and ^ 
MDCCCLXII. 5 G 
