REPORT ON HYDRAULICS. PART TI. 425 



but thinks that in practice u = 0*8V may be adopted, that is, that 

 the mean velocity of a current of water may be found by taking 

 ^ths of the superficial velocity. In conclusion, we may say that 

 the resistance which water experiences in moving in a canal or 

 channel, is proportional to the wetted perimeter, and to the 

 square of the velocity plus a fraction of the velocity, and is in 

 the inverse ratio of the section. This is in accordance with 

 the experiments of Eytelwein, Funk, and Briinings, &c. And 

 with regard to the natural phsenomena of water running in re- 

 gular channels, we have observed, that with the same inclina- 

 tion throughout the length, the water preserves the same breadth; 

 that the section of its surface is composed of curved lines, result- 

 ing from the adhesion of the water to the sides of the channel, 

 and the mutual reaction of each half of the section, by which 

 a swell is produced in the middle ; and, finally, that over the 

 whole surface a series of diagonal lines, crossing each other 

 from side to side like network, is formed, of which the obliquity 

 or resultant of the lateral impulsion is proportional to the velo- 

 city of the water in the channel. 



On the Progress and present State of our Knoivledge of Rivers. 



Hitherto we have confined our attention to the motions of a 

 fluid in pipes and artificial conduits : the motions of rivers follow 

 more complicated laws. So long as philosophers were contented 

 to reason from experiments made under given and determined 

 conditions, the problem was comparatively easy of solution j 

 but the question was very much altered when they attempted to 

 apply the results to rivers. In the former case, they could regu- 

 late the inclination and velocity of the fluid, and, by comparing 

 the effective with the calculated expenditures, could analyse 

 the resistances with approximate accuracy. In the latter case, 

 they had to contend with an infinity of resistances, which were 

 augmented or diminished at every instant of time. 



These natural phsenomena depend upon the physical constitu- 

 tion of the country and soil in which rivers derive their origin 

 and formation. For whether we trace them to their sources 

 among mountains, or follow their directions through the valleys, 

 to the plains, and thence into the sea, we shall find them (al- 

 though actually governed by well-defined laws,) subject to new 

 conditions from every inequality of soil and country. In ana- 

 lysing, therefore, the motions of rivers, it is necessary that we 

 should investigate not only the mechanical properties of the 

 fluid, but the elements of resistance with which these proper- 

 ties arc combined ) that we should prove by comparison how the 



