ME, HOPKINS ON THE THEOET OE THE MOTION OE GLACIEES. 
715 
the fii’st approximate solutions of our equations, as applicable to all usually accessible 
depths. 
41. Pressure Theory of the Laminated Structure. — We have generally, 
^,=i{A+B+v/(A-Bf+4P}, 
^,=i{A+B-V(A-B)-+4P}, 
. o 2F 
tan 2o;= ^ - _g - 
In the formation of crevasses, we have been principally concerned with and its 
direction, we shall now be more especially concerned with when a pressure, and the 
corresponding value of a ; but it will be convenient to bear in mind that, according to 
the fundamental principle of this theory, the curve of structure through any point will 
always coincide with the dii’ection of ^i, the maximum tension or minimum pressure at 
that point, being always the maximum pressure there. Also, since the direction of 
^2 is horizontal (neglecting C and E as in our first approximation), each laminar surface 
must be vertical, and will therefore be completely determined by the line of structure 
corresponding to it. 
42. Formation of the Marginal Structure. — I have stated that this is frequently found 
in canal-shaped glaciers. Suppose the glacial valley to be more or less convergent, so 
that the transverse force B may become a pressure ; and suppose its magnitude to be 
greater than that of A, as it probably will be generally in such a valley. We may also 
suppose A to be a pressure, though this is not essential for the production of the laminar 
structure in the case before us. The preceding formulae now become 
i),=i{-A-BW(B=^A)q:4F*}, 
;),=*{ -A-B-y(B-A)»+4F'}, 
tan Za= 
^2 will be the maximum pressure, and the structural curve at any proposed point will 
be perpendicular to the direction of ^2 5 it will therefore coincide with that ofpj, which 
will be determined by the above expression for tan 2a. Let a, be the value of a which 
gives the direction of^,, or that of the curv^e of structure at any proposed point. Then 
will lie between 0 and 45°. At points near the axis of the glacier, the twisting 
tendency, and therefore F also, will be very small, and may be neglected. We shall 
then have 
y)2=— B. 
Let us first suppose B too small to produce the veined structure. It will not, in such 
case, exist at all in the central portion of the glacier. At any point more remote from 
the axis, will be increased by the increase of F, and may become sufiicient to produce 
the structure, a, will be greatest when F is so, i. e. at the sides of the glacier, supposing 
A and B to remain constant. Should B be much larger than F, as we should antici- 
