of a steady stream, the theory is still applicable because the flow 

 around the particle has not yet been modified by viscosity. This may be 

 true, but even if we accepted the validity of the argument, still we are 

 faced with a phase of our problem which Jeffreys' model does not seem to 

 recognize; this is the erratic fashion by which particles move on the bed. 

 According to his theory the flow which is responsible for the forces 

 induced on the particle is uniform and steady everywhere on the bed, re- 

 sulting in a uniform force field very similar in character to the one 

 associated with the tractive force theory described above. Therefore a 

 particle that starts moving at some point of the bed will never have a 

 chance to come back to rest at some other point on the bed, a mode which 

 is inconsistent with the actually observed form of motion. 



The more modern theories go a step further ; they concern themselves 

 again with the stability of the individual particle, but they recognize 

 the fact that the hydrodynamic forces acting upon it vary rapidly with 

 time, a phenomenon strongly associated with turbulence. Moreover, they 

 use some elementary concepts concerning the structure of turbulence to 

 explain the mechanism of suspension. Accordingly, the particles are being 

 moved upwards from lower layers of high concentration to higher ones of 

 lower concentration by the vertical velocity fluctuations. Equations have 

 been derived based on the concept of momentum transfer by turbulence which 

 describe the distribution of concentration of sediment in suspension re- 

 lative to a specified value at a reference level. If there were a way of 

 predicting this value the rate of sediment moving in suspension would be 

 readily obtained by multiplying corresponding values of local mean velocity 

 and concentration and integrating over the entire depth. One method to 

 predict the concentration at some point in the flow has been proposed by 

 Lane and Kalinske (1939). These authors claimed that the bed itself may 

 be taken as the reference level. The corresponding concentration can be 

 obtained by making use of the statistical properties of turbulence close 

 to the bed. This implies direct exchange of particles between the sus- 

 pension load and the bed. 



Another method proposed by Einstein (1950) interposes a thin layer 

 between the suspension load and the fixed bed. The reasoning behind this 

 model is that very close to the bed the scale of turbulence is so small 

 that the eddies are of about the same order of magnitude as the particles 

 on which they act and, consequently, they are unable to move them away 

 from the bed. Within this thin layer adjacent to the bed and called the 

 "bed layer" the particles move by sliding and rolling, in a fashion much 

 different than the particles in suspension above. The bed layer has been 

 assumed to have a thickness of about two grain diameters, an estimate 

 based on observation. There is a continuous exchange of grains between 

 the bed layer and the bed and between the suspension load and the bed 

 layer. The basic concept of the theory of the bed-load function as it 

 applies in a river flow is that at equilibrium all these exchanges occur 

 at the same rate. The fraction of the total load that is carried within 

 the bed layer is called the bed load. The rate of deposition from the 

 bed layer to the bed is found to be a function of the bed-load rate, 



