1878.] Uniform Regime in Rivers and other Open Channels. 121 



the interior of the current, and have been gaining forward acceleration 

 there are gradually expelled, or do gradually flow from that region, and 

 come themselves into close proximity to the resisting channel face ; 

 and so, in their turn, do receive very directly backward forces from 

 the face, because in proximity to it processes of fluid distortion subject 

 to viscid resistance are going on with great activity and intensity. 



The transverse motions have their origin primarily in the rush of 

 the water along the wetted channel face. When that face is rough or 

 irregular with lumps and hollows or other asperities, reasons for the 

 origination of transverse currents may be sufficiently obvious. But 

 even if the channel face is extremely smooth, so as to present no 

 sensible asperities, still there is good reason to assert that transverse 

 flows will come to be instituted in consequence of the rapid flow of 

 the main body of the current along a lamina, very thin it may be, of 

 water greatly deadened as to forward motion by viscid cohesion with 

 the channel face, and throughout and across which, if regarded as only 

 very thin, in virtue of its thinness, the backward force applied by the 

 face can be transmitted by mere viscosity. The thin lamina of 

 deadened water will tend by the scour of the quicker going water 

 always moving subject to variations both of velocity and of direction 

 of motion to be driven into irregularly distributed masses ; and these, 

 acted on by the quicker moving water scouring past them, will force 

 that water sidewise, and will be entangled with it and will pass away 

 with some transverse motion to commingle with other parts of the 

 current.* 



If we watch the surfaces of flowing rivers, or of tidal currents 

 flowing in narrows or hyles, we may often have opportunity to observe 

 very prevalent indications of rushes of water coming up to the surface 

 and spreading out there. These rushes often may be seen to keep 

 rising in quick succession in numerous neighbouring parts of the 



* This principle I noticed myself in the connexion in which it is here adduced ; 

 and the idea has since been confirmed to me and rendered more definite through 

 additional considerations mentioned to me lately by my brother, Sir William Thomson, 

 which have originated with him in some of his theoretical investigations in quite 

 another branch of hydraulic science, and which relate to finite slip in a frictionless 

 fluid. He pointed out that if, for water theoretically regarded as frictionless, or 

 devoid of viscosity, we imagine a long smoothly formed straight trough or channel 

 with a thin vertical longitudinal plane septum dividing it into two parts each uniform 

 in cross-section throughout its length, and if we imagine the space on one side of the 

 septum to be occupied by still water, and a current to be flowing along on the other 

 side ; and if, while this is in progress, we imagine the vertical partition to be with- 

 drawn so as to leave the current flowing along a plane face of still water, the motion 

 with the finite slip thus instituted will be essentially unstable. Reasons for this, 

 when once it is brought under notice, are very obvious from consideration of the 

 centrifugal forces, or centrifugal actions, which would be introduced on the slightest 

 beginning being made of any protuberance or hollow in the originally plane interface 

 between the still water and the current. 



