1878.] Uniform Kegime in Rivers and other Open Channels. 123 



a fall of free level, in consequence of the surface declivity. It is thus 

 receiving forward acceleration in the downhill direction, and its 

 velocity goes on increasing until at some depth from the surface it 

 reaches a maximum, from whence, during further lapse of time and 

 further descent of this water towards the bottom, the retarding 

 influences imparted to it from the bottom are predominant over the 

 downhill accelerating influence of gravity. These retarding influences, 

 chiefly acting through transverse rushes of water from the bottom 

 commingling more numerously and more briskly with the descending 

 water under consideration the more it gets into the neighbourhood of 

 the bottom, bring about the result that the water goes forward with 

 less and less velocity as it approaches nearer and nearer to the bottom. 



I have now to offer, by consideration of an imaginable case different 

 from that of an ordinary river, an illustration which will aid in the 

 forming of clear ideas on what I have been presenting as a true theory 

 of the real behaviour of the water in rivers. 



Let us imagine a flowing river composed mostly of water, but with 

 a layer of oil floating on the top, the oil being of some such depth as a 

 tenth or a twentieth part of the whole depth of the river. Let us 

 suppose the width of the river to be so very great relatively to the 

 depth as that in considering the flow in a middle portion of the river, 

 we may regard it as experiencing no sensible retarding influences, 

 either through the water or the oil, from the sides of the river ; and 

 let the flow to be kept under consideration be only that middle portion 

 without the lateral portions which would be sensibly affected by 

 retarding influences from the sides. Here we have a case differing- 

 from that of an ordinary river of water in this important respect, 

 that, while in the ordinary river the superficial stratum of fluid is per- 

 petually changing its substance, and is, as I suppose, perpetually 

 receiving new supplies of deadened water from the bottom, in the 

 imagined case now adduced the substance of the superficial layer being 

 of oil floating at top, does not undergo any such change. The oil then, 

 it seems very certain, would really rush down what we may call the in- 

 clined plane of water on which it lies, and would go on accelerating its 

 motion until, by advancing very much faster than the water, it would 

 introduce a frictional drag between itself and the water sufficient to 

 hinder its further acceleration ;* ' or rather until, without attaining to 



* Postscript note, 1st November, 1878. — An observed phenomenon, which, if duly 

 taken into consideration, must doubtless be found to be closely allied in its nature to 

 the supposed bebaviour of the imagined layer of oil on a flowing river of water above 

 adduced, and which is certainly of much interest, both for its own sake and in refe- 

 rence to theoretical views which have been held as to its origin and its indications, 

 has come under my notice since the time when the present paper in manuscript was 

 presented to the Royal Society. The book by Bazin, which may be briefly named as 

 Darcy et Bazin "Eecherches Hydrauliques," Paris, 1865 (see a previous foot-note in 

 this paper), contains prefixed to it a report, dated 1863, of a committee of the 



