176 On tlie Hintereis Glacier. 



Appendix. 

 The distribution of shear force in a viscous fluid flowing 



along Parr's channel. 



As explained in our previous paper *, the equation to 

 Parr's curves is 



= C - ^ - fif + ryx+ <5u- - dxf) 



+ g(.t*-6«y +tf) + K^-lOaV + 5j#*J, 



■where C = 1 — T v . w being the velocity parallel to the axis 

 K c 



of c. K the central surface velocity, the channel being 

 given M?=0, or 0=1. Also, for a channel approximating 

 to a natural valley, the equation must be of the form 



+ a 2 ) O - a) 2 (x + c) when y = 0. 

 The shear force at any point is equal to fi ^— , where ytx is 



the coefficient of viscosity, and "fan is an element of "he 

 normal to the curve w=const. passing through the point. 

 Also 



_1_ 



d ?/; df . / (~d.fY , fdf\ 2 



w = 2Z /tqiv ion 



~bn ^icV Vbccl ^Xdy) 



where /represents Parr's function as above. 

 Differentiating, 



|/=5fe 4 + 4e^-3(10^ 2 -o> 2 



2(6ey 2 + oC) x + (5£r — 35V + 7 

 .3_ 1 9 e ^ + (2( 

 + (4ey 2 -2#)} : 



|^{_20^-12e^+(20^-6o> 



-dic~ K" 



These values do not lend themselves to an easy direct 

 determination of the curves of equal shear force, but the 

 values of the shear force along radial lines y=px are easily 

 founds and the curves being plotted, the equal shear curves 

 may then be drawn easily. The result for the section 

 approximating to the valley of the Hintereis Glacier is 

 given in the preceding paper, fig. 4; the curve d is the shear 

 on the bed. and the curve e is the transverse surface shear. 



* Phil. Mag. July 1913, p. 109. 



