516 



HYDRODYNAMICS. 



Pipi> and 

 Canal 



Motion of In the preceding experiments, Bossut only observed 

 W.uer m the velocity of the first portion of the water that issued 

 from the reservoir. In order to compare this velocity 

 with that of the current after it is completely establish- 

 ed, he made the experiments in the following Table ; 

 the time in which the first portion of the water moved 

 through the spaces in col. 6'. was measured by means 

 of the small wheels already mentioned; and the time in 



which the established current moved through the same 

 spaces, was ascertained by placing gently upon the 

 water four pieces of cork, which followed exactly the 

 current. The first portion of the canal was always run 

 through in less time than any of the other divisions, 

 and the velocity did not become sensibly uniform till 

 the declivity was about the 10th part of the length of 

 the canal. 



Motion of 



Water in 



Pipes and 



Canals. 



TABLE IX. Containing a Comparison between the Velocity of the First Por- 

 tion of Water, and that of the Established Current. 



It will be seen from these results, that the velocity 

 of the first portion of water is always less than that of the 

 established current, and that the one has to the other a 

 ratio which is nearly constant. The difference between 

 these two velocities is obviously owing to friction, and 

 to the viscidity of the fluid. The velocity of the water 

 in contact with the bottom of the canal is not only re- 

 tarded by friction, but the weight of the superincum- 

 bent fluid; and the fluid must obviously have the 

 greatest velocity at the surface at a point equidistant 

 from the sides. 



SECT. II. Account of the Researches and Experiments 

 of the 'Chevalier Du Btiat. 



Account of IN the preceding investigations of Bossut, no attempt 

 Buat's ; s made to deduce any very general principle or formula 

 from which the quantity of water discharged by pipes 

 and canals could be obtained in cases, which are not 

 comprehended in the limits of his tables. His experi- 

 ments, indeed, were neither sufficiently numerous nor 

 varied to lay the foundation of any very general rule ; 



and it is perhaps too much to expect that the same 

 person should have the honour both of laying the foun- 

 dation, and of bringing to perfection one of the most 

 difficult branches of physico-mathematical science. 



In the historical part of this article, we have given a 

 full account of the origin of the labours of the Chevalier 

 Du Buat, and have stated the general formula which 

 he obtained for expressing in all cases the velocity of 

 water, whether it is conveyed in a pipe or canal, or 

 rolls in the beds of rivers. We shall now proceed to 

 give as succinct and perspicuous a view as possible of 

 the principal steps by which this formula was obtained, 

 and shall then point out the method of applying the 

 formula in practice, by means of copious Tables, which 

 have never before been published. 



Considering an inch as the unity of length, and a j| 0( ] e O f 

 second as the unity of time, we may express the decli- expressing 



1 the slope of 



vity of a canal by , on the supposition that upon a pipe or 



the length of the pipe or canal s there is a fall of 

 1 inch. But, in order to find the slope of a conduit 

 pipe when the height of the reservoir and the place of 

 discharge are known, we must subtract from the height 



