722 
ME. HOPKINS ON THE THEOEY OE THE MOTION OE GLACIEES. 
The axial section of the surface of structure may be represented by Q E in fig. 13, vary ing 
in its inclination to the nearly vertical axis of z from zero to less than 45°. A similar 
conclusion will hold, as above stated, for all the central portion of the glacier. 
The structure here considered is manifestly a transverse structm’e, and is probably 
only formed where there is a sudden change of inclination in the bed of the glacier, 
like that at the foot of an ice-fall. The intensity of the longitudinal pressm’e to which 
it is there due, may possibly diminish rapidly in receding from the fall ; and so far it 
would follow that, where the structure is continued to any considerable distance from 
the locality in which it was formed, it must be due in a great degree to transmission. 
But this is a question which I reserve for further discussion. 
54. Differential Theory of the Veined Structure . — The idea on which this theory is 
founded has already been stated at the beginning of this section (art. 40) ; and the modes 
in which dislocation may take place so as to admit of the more rapid motion of the 
central portion of a glacier, have been explained. It has also been pointed out (art. 36) 
that the real differential or relative motion of two contiguous particles of the mass must 
necessarily be in the common direction in which the particles are constrained to move, 
by virtue of the external conditions to which the whole glacier is subjected. This, in 
fact, belongs to the definition of “ differential motion ” as I understand the term ; nor 
can I conceive how any mechanical effects, such as dislocation or bruising, can be attri- 
buted to a “differential motion ” in any arbitrary or conventional sense, rather than to 
the real relative motion which I understand to be meant by the expression. If so, it 
appears to me impossible to accept this theory of the veined structure -without a far more 
explicit explanation than any which has yet been given of it. Assuming, then, what I 
conceive to be the only intelligible and determinate meaning of the above expression, I 
shall proceed to investigate certain geometrical results which flow from it. Since the 
investigation is entirely geometrical, we may suppose the surface of the glacier and its 
longitudinal axis to be horizontal. I shall also suppose the line of motion of every 
particle to be parallel to that axis, and the velocity to be invariable along each such line, 
but difierent for different lines, (I) because the velocity of the central is supposed to be 
greater than that of the marginal portions of the mass, and (2) because the velocity of 
its upper is greater than that of its lower surface, 
55, Let P (fig. 14) be any particle of the glacier, and let the plane of the paper 
represent a transverse plane perpendicular to the common direction of all the lines of 
motion of the component particles of the mass. Also let jy be any other particle like- 
"wise in the plane of the paper, its distance from P being very small and equal to f ; 
i. e, ly must lie in the circumference of a circle in the plane of the paper, whose centre 
is P, and whose radius § is extremely small. Our first object will be to determine the 
relative velocity, or differential motion of P and jy, and the positions of jy in the small 
circle when that relative velocity is a maximum, and when it is zero. 
For this purpose let the horizontal plane of the base of the glacier be made the plane 
of xy., and the vertical plane parallel to the longitudinal axis of the glacier, and along its 
