354 THE JOURNAL OF GEOLOGY. 



Then, denoting the three elements by their initials : 



„ wvx 



/'= ; and 



s 



E^U-z) — ' 



uo 



Obviously, these elements are of unlike value in different 

 parts of the cross-section of a glacial valley, and the rate of 

 erosion is hence differential ; but since important unknown factors 

 are involved, no reliable expression either for the absolute rate 

 of erosion at any point, or for the ultimate form of the glacial 

 bed, can be directly deduced. The general tendency of glacial 

 action may, however, be learned from separate consideration of 

 the individual tendencies of the several agencies comprehended. 



' In the above statement, it has been the purpose to eliminate what is thought to 

 be an element of uncertainty in the extension of the customary formula for friction to 

 quantities so great and so peculiarly conditioned as those involved in the move- 

 ments of great glaciers. It might be simpler also, as Dr. Hendricks points out, 

 to reduce the determinants of glacier motion to those of positive action — viz., 

 (l), the weight of the ice, (2), the declivity of the channel, and (3), the potential 

 energy available in producing mass motion — by excluding the negative determinant, 

 friction. The down-stream impulse might also be represented by nw sin^, n being 

 an unknown factor depending on molecular force, and hence involving temperature, 

 etc. Then, making x the co-efhcent of friction, the equations would become : 



I=^w X nw sin^.' 



F^w X cosO; and 



V + F 



E={i-z) X 



7V X COsO 



Or, introducing the factor / (v) to represent the influence of velocity of flow in 

 determining the friction ; the last two equations would become : 



F=:w X cos^ X / (v); and 

 _ V -\- F 



~^^~^> w X cosO X / {v) 



It will be observed that this modification of the equations for intensity, friction, and 

 efficiency do not materially affect the discussion, and do not in any way detract from 

 the conclusions reached. The original equations are retained, however, in the opinion 

 that they suggest, if they do not actually present, the more direct and serviceable mode 

 of analysis. 



It is a pleasure to acknowledge obligation to Dr. J. E. Hendricks, of Des Moines 

 for working out the expressions in this note (January 25, 1885). 



I! 



