of Windings of Rivers in Alluvial Pic 



229 



the outer one ? We know by general experience and observation 

 that in fact the outer one does wear away, and that deposits are 

 often made along the inner one. How does this arise ? 



The explanation occurred to me m tne year 1&Y2, mainly as 

 follows : — For any lines of particles taken across the stream at 

 different places, as A 1 B l , A 2 B,,, &c. in fig. 2, and which may be 

 designated in general as AB, if the line be level, the water-pressure 

 must be increasing from A to B, on account of the centrifugal 

 force of the particles composing that line or bar of water; or, 

 what comes to the same thing, the water-surface of the river 

 will have a transverse inclination rising from A to B. The water 

 in any stream-line CD E* at or near the surface, or in any case 

 not close to the bottom, and flowing nearly along the inner bank, 

 will not accelerate itself in entering on the bend, except in con- 

 sequence of its having a fall of free level in passing along that stream- 

 line t. 



But the layer of water along the bottom, being by friction much 

 retarded, has much less centrifugal force in any bar of its particles 

 extending across the river ; and consequently it will flow sidewise 

 along the bottom towards the inner bank, and will, part of it at 

 least, rise up between the stream-line and the inner bank, and will 

 protect the bank from the rapid scour of that stream-line and of 

 other adjacent parts of the rapidly flowing current; and as the 

 sand and mud in motion at the bottom are carried in that bottom 

 layer, they will be in some degree brought in to that inner bank, 

 and may have a tendency to be deposited there. 



* This, although here conveniently spoken of as a stream-line, is not to be 

 supposed as having really a steady flow. It may be conceived of as an average 

 stream -line in a place where the flow is disturbed with eddies or by the sur- 

 rounding water commingling with it. 



t It must be here explained that by the free level for any particle is to be under- 

 stood the level of the atmospheric end of a column, or of any bar, straight or 

 curved, of particles of statical water, having one end situated at the level of the 

 particle, and having at that end the same pressure as the particle has, and hav- 

 ing the other end consisting of a level surface of water freely exposed to the 

 atmosphere, or else having otherwise atmospheric pressure there ; or, briefly, 

 we may say that the free level for any particle of water is the level of the atmo- 

 spheric end of its pressure column, or of an equivalent ideal pressure-column. 



