114 Prof. J. Thomson on the Floiv of Water in [Dec. 12, 



T. " On the Flow of Water in Uniform Regime in Rivers and 

 other Open Channels." By James Thomson, LL.D., D.Sc, 

 F.R.S., and F.R.S.E., Professor of Civil Engineering and 

 Mechanics in the University of Glasgow. Received Au- 

 gust 15, 1878. 



In respect to the mode of flow of water in rivers, a supposition 

 which has been very perplexing in attempts to form a rational theory 

 for its explanation, has during many years past, during at least a great 

 part of the present century, been put forward as a result from experi- 

 mental observations on the flow of water in various rivers, and in 

 artificially constructed channels. It was, I presume, put forward in 

 the earlier times only as a vague and doubtful supposition ; but, in 

 later times it has, in virtue of more numerous aud more elaborately 

 conducted experimental observations, advanced to the rank of a con- 

 firmed supposition, or even of an experimentally established fact. 

 This experimentally derived and gradually growing supposition was 

 perplexing, because it was in conflict with a very generally adopted 

 theory of the flow of water in rivers which appeared to be well 

 founded and well reasoned out. 



That commonly received theory, which for brevity we may call the 

 laminar theory, was one in which the frictional resistance applied by 

 the bottom or bed of the river against the forward motion of the 

 water was recognized as the main or the only important drag hinder- 

 ing the water, in its downhill course under the influence of gravity, 

 from advancing with a continually increasing velocity ; and in which 

 it was assumed that if the entire current is imagined as divided into 

 numerous layers approximately horizontal across the stream, or else 

 trough- shaped so as to have a general conformity with the bed of the 

 river, each of these layers should be imagined as flowing forward 

 quicker than the one next below it, with such a differential motion as 

 would generate through fluid friction or viscosity, or perhaps jointly 

 with that, also through some slight commingling of the waters of con- 

 tiguous layers, the tangential drag which would just suffice to prevent 

 further acceleration of any layer relatively to the one next below it. 

 Under this prevailing view it came to be supposed that for points at 

 various depths along any vertical line imagined as extending from the 

 surface of a river to the bottom, the velocity of the water passing that 

 line would diminish for every portion of the descent from the surface 

 to the bottom. 



The experimentally derived and perplexing supposition for which no 

 tenable theory appears to have been proposed, though the want of 

 such a theory has been extensively felt as leaving the science of the 

 flow of water in rivers in a state of general bewilderment, is, that 

 inconsistently with the imagination of the water's motion conceived 



