THE LATERAL EROSION OF STREAMS 441 



Each particle in motion feeling a lateral impulse, whether from 

 F^ or F^, will tend to move in that direction. For simplicity, we 

 may take the case of a stream acted upon by F^ only. The lateral 

 impulse will be transmitted to the right, so that each particle will 

 feel the combined impulse of all those to the left in strata of equal 

 pressure. The tendency will be for all to move to the right until a 

 lateral gradient is established that will furnish at each point an equal 

 impulse in the opposite direction. In a stream with velocities in 

 each stratum of equal pressure arranged symmetrically with respect 

 to the center, this gradient would be a compound curve with a general 

 inclination to the left (see aa, Fig. i). 



Fig. I 



But this potential gradient is never established. The velocities 

 of the particles at x', y', z' (Fig. i), being less than those at x, y, z, are 

 unable to support the same lateral gradient, so that, before the poten- 

 tial lateral gradient for x, y, z, is established, some lesser gradient will 

 cause a movement of x\ y', z' to the left. This actual gradient would 

 be constant for any set of conditions and would also be a compound 

 curve (see hh, Fig. i). 



At some point between x and x' , the force of F^ will just equal 

 the opposing impulse from the actual lateral gradient. At this point 

 no lateral movement will take place. Above it movement to the 

 right will occur, below it, movement to the left. Between other 

 points similarly related, like conditions will hold, giving a zone in 

 which lateral movement is absent {mm' , Fig. i). 



Since the curve representing the potential gradient is stronger 

 than that of the actual and the area of the cross-section of the stream 



