160 THIRD REPORT — 1833. 



and by the application of its principles to the solution of a gi'eat 

 many cases in practice, Dubuat' was convinced that the motion 

 of water in a conduit pipe was analogous to the uniform motion 

 of a river, since in both cases gravity was the cause of motion, 

 and the resistance of the channel or perimeter of the pipes the 

 modifiers. He then availed himself of the experiments of Bossut 

 on conduit pipes and artificial channels to explain his theory : 

 the results of which investigations were published in the year 

 1779. M. Dubuat was, however, sensible that a theory of so 

 much novelty, and at variance with the then received theory, 

 required to be supported by experiments more numerous and 

 direct than those formerly undertaken, as he was constrained 

 to suppose that the friction of the water did not depend upon 

 the pressure, but on the surface and square of the velocity. 

 Accordingly, he devoted three years to making fresh experi- 

 ments, and, with ample funds and assistance provided by the 

 French Government, was enabled to publish his great work, 

 entitled Principes d' Hydraidique verifies par un grand nombre 

 d' Experiences, faittis par Ordre du Gouvernement, 2 vols. 1786, 

 (a third volume, entitled Principes dHydrauUque et Hydro^ 

 namique, appeared in 1816); — in the first instance, by repeating 

 and enlarging the scale of Bossut's experiments on pipes (with 

 water running in them) of difFei'ent inclinations or angles, of 

 from 90° to iqMj*^ P^'^* ^^ ^ right angle, and in channels of from 

 1 \ line in diameter to 7 and 8 square toises of surface, and sub- 

 sequently to water running in open channels, in which he ex- 

 perienced great difficulties in rendering the motion uniform : 

 but he was amply recompensed by the results he obtained on 

 the diminution of the velocity of the different parts of a uniform 

 current, and of the relation of the velocities at the surface and 

 bottom, by which the water works its own channel, and by the 

 knowledge of the resistances which different kinds of beds pro- 

 duce, such as clay, sand and gravel; and varying the experiments 

 on the effect of sluices, and the piers of bridges, &c., he was ena- 

 bled to obtain a formula applicable to most cases in practice*. 

 Thus, let V = mean velocity per second, in inches. 



d = hydraulic mean depth, or quotient which arises 

 from dividing the area or section of the canal, 

 in square inches, by the perimeter of the part 

 in contact with the water, in linear inches. 

 s = the slope or declivity of the pipe, or the sur- 

 face of the water. 

 g = 16'087, the velocity in inches which a body 

 acquires in fidling one second of time. 



* Edinburgh Encyclopedia, Art. Hydrodynamics, by Brewster. 



