442 HENRY M. EAKIN 



is practically constant, at some point the two must coincide, and no 

 vertical movement will occur. And so, for each stratum of equal 

 pressure we will have a zone {nn' , Fig. i) without vertical movement. 

 To the right all particles will have a downward component of motion, 

 to the left, an upward component. At the point of intersection of 

 mm' and nn' all impulses are balanced save Fg acting down the 

 stream gradient. 



The stream has, then, a central axis about which a sort of revolu- 

 tion takes place. Under the influence of either F^ or F^ or of both, 

 the stream progresses with a boring movement. 



Fig. 2 



Being the last factor that can be closely approximated, we may take 

 the potential lateral gradient of the stratum of maximum velocities 

 on the right and left curves of a meandering stream as a measure of 

 the relative tendency of lateral erosion. 



On the right curves F^ and F^ will combine. . This condition is 

 expressed graphically in Fig. 2, in which aa' represents the gradient 

 arising from F^^ bb', that from F^ and cc', the resultant. 



The condition of left curves is illustrated in Fig. 3, aa' represent- 

 ing the potential gradient due to F^^ bb', the potential gradient due 

 to Fj with the inclination to the right, and cc', the resultant potential 

 gradient, being the mean. 



Mathematically the potential lateral gradients on right and left 

 curves may be computed and compared. 



Using Ferrel's formulae for F^ and F^ and the data of Humphreys 

 and Abbot on the Mississippi at Columbus, Ky., the potential lateral 

 gradient would be 18 per cent stronger on the right curves. In this 



