REPORT ON HYDRAULICS. PART II. 417 



3rdly, That when the mean velocity of a current is uniform, 

 the accelerating force is equal to the retardations ; 



4thly, That as the particles of the fluid fill up the cavities of 

 the surface and form their own fluid bed, the nature of the sur- 

 face makes very little diiference in the retardation. 



The inclination of the surface, or the force of gravity, being 

 the cause of motion in the whole mass, it follows that when the 

 motion has become uniform there pass equal quantities of water 

 through each section in equal times and velocities ; hence the 

 depth of the water will be the same in every part of the sec- 

 tion, and the surface will be parallel to the bottom of the 

 channel. 



But the motion would never be uniform if the fluid were per- 

 fect and there were no resistance in the channel : on the con- 

 trary, it would follow the laws of acceleration. But experiment 

 proves, even with very great inclinations, that the motion soon 

 becomes uniform : hence the conclusion as a general principle, 

 that when water moves uniformly in any channel or conduit, 

 *' the resistance which it experiences is equal to the force of acce- 

 leration*." 



If we examine the motion of a stream of water running in an 

 open channel, we shall find that the instant the water enters 

 into the channel, it spreads along the bed in filaments, which 

 continue to precede the general mass until they are retarded by 

 the resistances of the bed and overtaken by the superior fila- 

 ments as they reach the termination of the channel, and being 

 no longer retarded by the friction of the bottom and sides, they 

 acquire a greater velocity, and thus produce inequalities in the 

 motions of different parts of the section of the stream ; and ex- 

 periment teaches us that every mass of water, whether it moves 

 in a pipe, open channel, or river, follows more or less the same 

 law ; and since the resistance is caused by the surface of the 

 channel, the greater the extent of surface, the greater will be 

 the resistance t, and vice versa. Hence the effect of the re- 

 sistance will be in the inverse ratio of the section ; and as adhe- 

 sion forms a certain portion of the resistance, and has been 

 proved by Coulomb to be simply proportional to the velocity, 

 it follows that the resistance which water experiences in moving 

 in an artificial channel is proportional to the quantity of wetted 



• Bossut found that when an artificial canal of wood 200 metres in length 

 was inclined in the proportion of one decimetre per metre, or one in ten, and 

 divided the length into 33 metres, each of the spaces, with the exception of the 

 first, was run over in the same numher of seconds. 



t This has been found by me to be very partial. 

 1834. 2 E 



