732 
ME. HOPKINS ON THE THEOET OF THE MOTION OF GLACIERS. 
61. The author of the preceding extracts would appear, I think, to have somewhat 
mistaken the nature of the problem to be solved. He asserts that if a glacier were 
traversed by a great number of small tubes or ducts filled with water, an enormous hydro- 
static pressure would be the consequence. Now it is absolutely necessary for me to 
examine strictly the correctness of this conclusion ; for, if it be true, it would be useless 
to seek for any cause which should give efficiency to the internal pressures, besides the 
hydrostatic pressure to which it is here attributed. I shall show, however, that this 
conclusion is not correct, and that the efficiency of the dislocating forces is derived, as 
above intimated, from the sliding movement of the glacier. The existence of the above 
assumed capillary ducts, as pervading the more compact parts of a glacial mass, appears 
to be rendered doubtful by the experiments of Professor Hctxlet*, though the observa- 
tions of M. Agassiz undoubtedly prove their existence in certain superficial portions of 
the glacier of the Aar. But waiving any doubt of this kind, let us suppose the interior 
of a glacier completely pervaded by these tubes or ducts, extremely small, but sufficient 
to allow fluid pressure to be communicated freely through them, as Principal Fokbes 
has assumed. When the supply at the upper surface of the mass is regular, the motion 
of the fluid will become steady ; and such I shall suppose it to be in the typical case I 
propose to analyse. We may first confine our attention to a single tube. Suppose the 
area (&>) of its transverse section at any point P to be variable, but always very small, 
and ^5 to denote the length of a small element of the tube ; then will be the volume 
of the element, and, if the density of the water be denoted by unity, it will also repre- 
sent the mass of the water in the element h of the tube. Let the velocity at P, any 
point in the tube, be v, which I shall assume to be the same for each particle in the sec- 
tion (a). The motion will be retarded by i\ie friction of the sides of the tube; letyiySs 
be the retarding force on the element at P. Also let p be the fluid pressure at P ; and 
let the coordinates y, z of that point be taken as heretofore ; then will z be very 
nearly vertical, and we shall have, resolving gravity in the direction of the tube, 
ulp=:g —f. coh—^. 
or 
lp=:ghz—fh— 
or, since the motion, by hypothesis, is steady, 
d'^s. 
d'^s dv 
dt^ ^ ds^ 
and therefore we have 
Jd-\-^=9z-J'fds—lv^, 
Let ^ 1 , Zi, Si and be the values of p, z, s, and v at the point where the tube meets 
the surface of the mass. Then 
( 1 .) 
where p^ is the atmospheric pressure. 
See Dr, Tyndall’s ‘ Glaciers of the Alps.’ 
