MR. RENNIE ON THE FRICTION AND RESISTANCE OF FLUIDS. 
42 O 
diameters; and Couplet (1733), Mariotte, and Deparcieux, estimated the 
ditference between the real and calculated expenditures of glass tubes and 
pipes. 
Chezy (in 1771 and 1786) was the first engineer who endeavoured to esta- 
blish the relation subsisting between the inclination of an aqueduct and the 
transverse section of the volume of water it ought to carry, — on the supposition 
that the accelerating force, due to the inclination of the bed of the conduit, is 
counterbalanced by the resistances of the channel in the ratio of the surface, 
and increasing in proportion to the square of the velocity. What Chezy had 
remarked was concluded by Bossut, who cleared the investigation of most of 
its difficulties, and demonstrated it to be in accordance with theory. He found 
that small orifices discharged less water in proportion than great ones, on 
account of friction ; that the vena contracta, and consequent expenditure, 
diminished with the height of the reservoir : he pointed out the law by which 
the discharge diminishes according to the inclination and number of bends in 
a pipe, and the influence of friction in retarding the velocity of waters moving- 
in canals and pipes, in which he made the square of the velocity to be in the 
inverse ratio of the length of the pipe : he determined the co-efficients by expe- 
riment, and thus obtained a formula expressive of the conditions of the uniform 
motion of water in open canals. The greater part of these hypotheses may be 
said to have been removed by the more extensive researches of Dubuat. His 
great hydraulic work, published in 1779 and 1786, contains a series of the most 
valuable observations, whose results accord very nearly with the new formula 
of the motion of water in pipes and open conduits ; and his experiments, with 
pipes inclined in various angles from the 40,000th part of a right angle to 90 
degrees, and in channels which varied from a line and a half in diameter to 
areas of seven or eight square toises, seem to comprehend every case of in- 
clination ; so that by collecting a prodigious number of facts, both with com- 
pressible and incompressible fluids, he obtained a general expression for all 
cases relative to the friction and cohesion of fluids : but a logarithmic function 
which he introduces in it, by a sort of approximation, gives it a character of 
uncertainty, which restrains its use, and shows the necessity of fresh researches. 
Venturi, in 1798, £C Sur la Communication laterale du Mouvements dans les 
Fluides,” repeated and added many new facts to the experiments of Bossut, on 
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