1869.] of the Descent of Glaciers by their Weight only. 205 



and the sides, is supposed to obtain throughout the mass of the glaciers. 

 Any deviation from it, possible under the circumstances, will hereafter be 

 shown to be such as would not sensibly affect the result. 



The trapezoidal mass of ice thus passing through a transverse section 

 in a day is conceived to be divided by an infinite number of equi- 

 distant vertical planes, parallel to the central line, or axis of the glacier, 

 and also by an infinite number of other equidistant planes parallel to the 

 bed of the glacier. It is thus cut into rectangular prisms or strips lying 

 side by side and above one another. If any one of these strips be sup- 

 posed to be prolonged through the whole length of the glacier, every part 

 of it will be moving with the same velocity, and it will be continually 

 shearing over two of the similar adjacent strips, and being sheared over by 

 two others. The position of each of these elementary prisms in the trans- 

 verse section of the glacier is determined by rectangular coordinates ; and 

 in terms of these, its length, included in the trapezoid. The work of its 

 weight, while it passes through the transverse section into its actual posi- 

 tion, is then determined, and the work of its shear, and the work of its 

 friction. A double integration of each of the functions, thus representing 

 the internal work in respect to a given elementary prism, determines the 

 whole internal work of the trapezoid, in terms of the space traversed by 

 the middle of the surface in one day, the spaces traversed by the upper 

 and lower edges of the side, and a symbol representing the unit of shear. 

 Well-known theorems serve to determine the work of the shear and the 

 friction of the bottom and side in terms of the same quantities. All the 

 terms of the equation above referred to are thus arrived at in terms of 

 known quantities, except the unit of shear, which the equation thus deter- 

 mines. The comparison of this unit of shear (which is the greatest pos- 

 sible, in order that the glacier may descend by its weight alone) with the 

 actual unit of shear of glacier ice {determined by experiment), shows that 

 a glacier cannot descend by its weight only ; its shearing force is too great. 

 The true unit of shear being then substituted for its symbol in the equation 

 of condition, the work of the force, which must come in aid of its weight 

 to effect the descent of the glacier, is ascertained. 



The imaginary case to which these computations apply, differs from that 

 of an actual glacier in the following respects. The actual glacier is not 

 straight, or of a uniform section and slope, and its channel is not of uni- 

 form roughness. In all these respects the resistance to the descent of the 

 actual glacier is greater than to the supposed one. But this being the 

 case, the resistance to shearing must be less, in order that the same force, 

 viz. the weight, may be just sufficient to bring down the glacier in the one 

 case, as it does in the other. The ice in the natural channel must shear 

 more easily than that in the artificial channel, if both descend by their 

 weight only ; so that if we determine the unit of shear necessary to the 

 descent of the glacier in the artificial channel, we know that the unit of 



