162 Mr. Hopkins on the Mechanistn of Glacial Motion. 



of fracture will be a curve line. Also its convexity will be 

 turned towards the upper extremity of the glacier ; for, by re- 

 ferring to fig. 5, it will be seen that the point in which the 

 normal to the curve of fracture meets the axis of the glacier, 

 lies towards the loixer extremity of the glacier. The greatest 

 value of d, in the case before us, must be less than 4'5°, what- 

 ever may be the value of _/y, and may be much less than that 

 quantity, if Yj + Xj be considerable. The general form of 

 the curve of fracture is represented by M N (fig. 6), supposing 

 the fissure continued across the glacier. 



It is here deserving of remark, that the force (R) may be 

 sufficient to produce transverse fissures, though there may be 

 no longitudinal tension such as that denoted by Xj, provided 

 y) be great enough ; for, if we put Xj = in the expression 

 for (R) (art. 10.), we have 



(R) = -^{^Y,2 + 4/^-YJ. 



Consequently there may still be fissures due to (R) near the 

 flanks of the glacier, but there can be no transverse fissures in 

 the central portion, where f^ must necessarily be very small. 

 The existence of transverse fissures in this latter portion is as 

 distinctly indicative of longitudinal tension as the absence of 

 longitudinal fissures is indicative of transverse compression. 



21. If the width of the valley should increase instead of de- 

 creasing, at any part, we shall obtain a different result, as- 

 suming what I conceive to be almost universally true, — that 

 when the width of valley increases, its fall diminishes. In 

 such case the portion of the glacier in the more expanded part 

 of the valley will be pressed upon by the mass immediately 

 behind it, tending to descend with greater rapidity. The lon- 

 gitudinal action will then become a pressure instead of a ten- 

 sion, or X^ will become negative, and may be great. We 

 shall then have 



Hence, assuming Y, to be a tension, or, if a pressure, smaller 

 than Xj, tan 2 9 will be small and negative at points not re- 

 mote from the centre of the glacier; and, therefore, 9 will be 

 either a very little less than 90°, or will be very small and 

 negative. The former value will in this case manifestly cor- 

 respond to the direction of greatest tension, and consequently, 

 if a fissure be formed, it will tend to parallelisin with the axis 

 as it approaches the centre of the glacier, making a larger 

 angle with the axis at points more remote from it, since/) will 

 then be greater. Thus the fissure will become longitudinal 



