1876.] On the Windings of Rivers in Alluvial Plains. 5 



V. On the Origin of Windings of Rivers in Alluvial Plains,, with 

 Remarks on the Flow of Water round Bends in Pipes/'' By 

 Professor James Thomson^ LL.D.^ F.R.S.E. Communicated 

 by Prof. Sir William Thomson, F.R.S. Received March 14^ 

 1876. 



In respect to the origin of the windings of rivers flowing through al- 

 luvial plains, people have usualty taken the rough notion that when there 

 is a bend in any way commenced, the water just rushes out against the 

 outer bank of the river at the bend, and so washes that bank away, and 

 allows deposition to occur on the inner bank, and thus makes the sinu- 

 osity increase. But in this they overlook the hydraulic principle, not 

 generally known, that a stream flowing along a straight channel and 

 thence into a curve must flow with a diminished velocity along the outer 

 bank, and an increased velocity along the inner bank, if we regard the 



flow as that of a perfect fluid. In view of this principle, the question 

 arose to me some years ago: — Why does not the inner hanh wear away 

 more than the outer one ? We know by general experience and obser- 

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

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



The explanation occurred to me in the year 1872, mainly as follows : — 

 For any lines of particles taken across the stream at different places, as 



