270 R. Russell — On the Flow of Rivers, ^c. 



float ought to be of such weight as barely to reach the surface of the 

 Tvater, so as not to be affected by the wind, by this means the velo- 

 city of the swiftest part, or the centre of the stream, can be obtained, 

 and the mean velocity may be calculated from the greatest velocity 

 by an empirical formula, which I give on the authority of Prony. 

 Let Y = mean velocity. 



V. = greatest velocity. Then | = ^^g^i^^^,. 



By the use, however, of a current metre, the velocity can be 

 measured at any point, and at any depth, in the cross section of the 

 river under consideration. Professor Eankine recommends, as the 

 most convenient instrument for this purpose, "a small light re- 

 volving fan, on whose axis there is a screw, which drives a train of 

 wheel-work, carrying an index that records the number of revolu- 

 tions in a given time. The whole apparatus is fixed at the end of a 

 pole so that it can be immersed to different depths in different parts 

 of the stream."^ Whence the mean velocity can be obtained. 



With regard to the rate at which the materials forming the bed of the 

 river are carried along and worn down, it depends on the velocity and 

 flow, and what the nature of the bed of the stream really is, since the bed 

 of a river may be stable as when it is composed of rock, unless when 

 exposed to a very strong current, or it may be stable in the ordinary 

 state of the river, and unstable during floods, as when it is com- 

 posed of stones and gravel ; or it may be permanently unstable, as 

 in the case of a muddy bottom. This last arises from the fact of 

 the stream carrying matter in suspension, and which is just heavy 

 enough to subside ; but the least increase in velocity once more 

 carries it forward. Du Buat states that the bed of a stream in a 

 permanent condition of instability exhibits a number of transverse 

 ridges, each with a gentle slope at the up-stream side, and a steep 

 slope at the down-stream side. The particles of the bed are rolled 

 by the current up the gentle slope till they come to the crest of the 

 ridge and eventually drop down the steep slope to the bottom of the 

 furrow, where they become covered up, and remain till the gradual 

 removal of the whole ridge leaves them again exposed.^ An exact 

 counterpart of the sand blown into ridges by the wind, as described 

 by Sir Charles Lyell, when speaking of the ripple mark,^ 



Observation alone could determine with certainty the size of 

 pebbles and shingle which a known velocity of current would 

 propel, and it would be easy to make a series of experiments by 

 exposing sand, clay, pebbles of various sizes, shingle, rock, etc., 

 to known velocities, and noting that velocity which just carries 

 them along. The requisite velocity of current can always be 

 obtained from a given head of water, taking into consideration the 

 friction of the orifice through which the stream issues from the 

 reservoir, and flows into the channel where the material to be 

 tested is situated. A table, given by Du Buat, shows the greatest 

 velocity of the current close to the bottom of the river, so as 

 not to interfere with the stability of the substances of which it 

 is composed.* 



