ME. HOPKINS ON THE THEOET OE THE M;0TI0N OF GLACIEES. 
721 
fall. The dotted lines are moraines, and indicate the course of the ice-current. It is 
manifest that the mass, in approaching the fall, must sulFer immense transverse com- 
pression, which accounts for the longitudinal structure in that part of the glacier. 
53. Formation of the Veined Structure in the deeper portions of a Glacier. — We cannot 
determine completely the direction of the greatest pressure at any proposed point at a 
great depth in a glacier, for the reason above assigned (art. 34). That direction would 
give us the normal to the surface of greatest pressure, and therefore, also, to the surface 
of structure through that point, whence the differential equation to the surface would 
be known. In our practical inability to follow this method, we may proceed, as in 
art. 34, to determine the section of the required surface made by a vertical plane through 
the axis of the glacier. In a glacier of considerable width, the sections of this surface 
made by planes parallel to the one just mentioned, will be very similar to the axial 
section ; because the velocities will be very nearly the same for all points in a transverse 
line on the surface of the glacier, "within considerable distances of the axis* ; and the 
same therefore must also hold for points at greater depths. The most important case 
is that which occurs at the base of an ice-fall in which A becomes very large and a 
pressure. Also B, the transverse force, may p-g X 3 . 
be considered much smaller than A, and a 
pressure. Our general formulse will become 
^.=-i{A+C-v'(A-C)»+4E>), 
p^~ — -KA+C+v^ (A — C/+4E'^}, 
i>3=— B; 
and we shall have, also, 
cos/3 = 0, tan 2a = 
the plane of a being now that of xz. Now B being supposed small compared with A, 
p^ will be the maximum pressure and p^ the minimum pressure, or algebraically the 
maximum tension. The above equation gives two values of a. Now 2a must be nega- 
tive and less than 90°, or positive and between 90° and 180°; and therefore a must be 
negative and less than 45°, or positive and between 45° and 90°. The negative value 
will evidently here correspond to p^ the greatest pressure. A may possibly be much the 
same at different depths, in our present case, and E (art. 34) will be zero at the surface, 
and will increase with the depth. C also increases with the depth, as does, therefore, 
costexis paribus, the negative angle a^. It must always, however, be less than 45°, so 
long as C is less than A, whatever may be the depth ; and near the surface it will vanish. 
* M. Agassiz has best exemplified this in his admirable map and diagrams of the glacier of the Aar 
already referred to. He there delineates (Atlas, pi. 4) the forms assumed by an orig inall y straight trans- 
verse physical line on the glacier near the junction of its two great tributaries in three successive years. 
The motion of different points on the central portion of the mass do not differ much throughout a breadth 
of nearly one-half of the glacier. 
