ON HYDRAULICS AS A BRANCH OF ENGINEERING. 165 



The fifth and last section investigates the diflferent circum- 

 stances (such as friction, adhesion and rigidity,) which influence 

 the motions of machines. 



A second volume, published in the year 1796, is devoted to 

 the theory and. practice of the steam-engine. Previously to the 

 memoir of M. Prony, Sur le Jatcgeage des Ectux courantes, in 

 the year 1802, no attempt had been made to establish v^ith cer- 

 tainty the correction to be applied to the theoretical expendi- 

 tures of fluids through orifices and additional tubes. The phas- 

 nomenon had been long noticed by Sir Isaac Newton, and illus- 

 trated by Michelotti by a magnificent series of experiments, 

 which, although involving some intricacies, have certainly 

 formed the groundwork of all the subsequent experiments upon 

 this particular subject. 



By the method of interpolation, M. Prony has succeeded in 

 discovering a series of formulae applicable to the expenditures 

 of currents out of vertical and horizontal orifices, and to the con- 

 traction of the fluid vein ; and in a subsequent work, entitled 

 Recherches sur le Mouvemens des Eaux courantes, he establishes 

 the following formulae for the mean velocities of rivers. 



When V = velocity at the surface, 

 and U = mean velocity, 



U = 0-816458 V, 

 which is about y V. 



These velocities are determined by two methods. 1st, By a 

 small water-wheel for the velocity at the surface, and the im- 

 proved tube of Pitot for the velocities at different depths below 

 the surface. 



If h = the height of the water in the vertical tube above the 

 level of the current, the velocity due to this height will be deter- 



/ metres 



mined by the formula V = V^gh=\/ 19-606^ = 4-429 Vh. 

 When water runs in channels, the inclination usually given 

 amounts to between ^^^q*^ ^^^ OTo^h V^^^ <^f ^^^ length, which 

 will give a velocity of nearly 1| mile per hour, sufficient to 

 allow the water to run freely in earth. We have seen the incli- 

 nation very conveniently applied in cases of drainage at Tg'oijt^ 

 and y^^th, and some rivers are said to have ^p'^o*^ only. 



M. Prony gives the following formulae, from a great number 

 of observations : 



If U = mean velocity of the water in the canal, 

 I = the inclination of the canal per metre, 

 R = the relation of the area to the profile of its perimeter, 

 we shall have 



U = - 0-07 + v'0-005-h3233.R.r; 



