734 ME. E. D. OLDHAM ON" THE LAW THAT GOYEENS 



conditions and combinations of no little complexity. Mr. Greenwood 



has explained how the tendency of a river to preserve a uniform 

 velocity throughout its course leads to the parabolic section presented 

 by the channel from source to mouth ; but, owing to his having 

 overlooked the very different nature of the solid burden carried by 

 the river in different parts of its course, his explanation lacks com- 

 pleteness. As it seems to me, the law is not that the river tends to 

 preserve or obtain a constant velocity, but that at any point of its 

 course the velocity of current will tend to become such that the 

 stream can just carry its solid burden. With regard to the appli- 

 cation of this law, it is necessary to observe that it is the coarsest 

 debris borne by the stream which will determine its velocity ; thus, 

 in a stream carrying shingle, sand, and mud, the velocity will be 

 controlled by the shingle, after that has been deposited, by the sand, 

 and finally by the mud. 



But this must not be taken to mean that the current is directly 

 governed by the nature of the burden cast upon the stream. Gra- 

 dient and shape of channel are of course the two principal factors 

 which govern the velocity of current, and in a subsidiary degree the 

 nature of the sides of the channel ; of these the two former frequently, 

 the last generally, are to a greater or less degree the product of the 

 stream itself, and by deposition or erosion they tend to become such 

 that, when equilibrium has been established, the stream is just able 

 to transport its solid burden. 



The law, as stated above, I hold to be obeyed by every stream 

 throughout its length, though its action is often controlled and 

 obscured by interfering causes, such as unequal hardness of the bed 

 where the stream flows over rock. Where a stream enters on an 

 alluvial plain, the law can be seen to prevail, and is moreover, on 

 slight consideration, seen to be almost axiomatic in its nature ; for, 

 suppose the velocity of current to be greater than that due to the 

 law propounded, the immediate consequence would be erosion of 

 the channel and transport of debris : when the stream reached the 

 sea, if not sooner, the velocity would be checked and the transported 

 debris would be deposited. In this way the lower end of the reach 

 would be raised, the upper lowered, and the gradient diminished ; 

 this, leaving out of consideration the effect of the shape of the 

 channel, would result in a diminished velocity and equilibrium 

 when the stream could just transport its solid burden. Similarly, 

 if the velocity were less than that demanded, deposition would 

 commence, and the gradient below the deposit would increase 

 until the velocity of the stream reached the required limit. 



But it is not only by an alteration of gradients that the stream 

 can adjust its velocity, for, with the same slope and sectional area 

 of channel, the velocity varies with the square root of the hydraulic 

 mean depth, or of the sectional area divided by the wetted perimeter. 

 From this it follows that the gradient required to produce a given 

 velocity will vary with the shape of the channel, being greater 

 where this is broad and shallow, and less where it is narrow and 

 deep. 



