170 TIURD REPORT — 1833. 



In the year 1801, M. Eytelwein, a gentleman well known to 

 the public by his translation of M. Dubuat's work into German, 

 (with important additions of his own,) published a valuable 

 compendium of hydraulics, entitled Handbuch der Mechanik 

 und der Hydraidik, in which he lays down the following rules. 



1 . That when water flows from a notch made in the side of 



a dam, its velocity is as the square of the height of 

 the head of the water ; that is, that the pressure and 

 consequent height are as the square of the velocity, the 

 proportional velocities being nearly the same as those 

 of Bossut. 



2. That the contraction of the fluid vein from a simple orifice 



in a thin plate is reduced to 0*64. 



3. For additional pipes the coefiicient is 0*65. 



4. For a conical tube similar to the curve of contraction 0*98. 



5. For the whole velocity due to the height, the coefficient 



by its square must be multiplied by 8 "0458. 



6. For an orifice the coefficient must be multiplied by 7 "8. 



7. For wide openings in bridges, sluices, &c., by 6*9. 



8. For short pipes 6*6. 



9. For openings in sluices without side walls 5*1. 



Of the twenty-four chapters into which M. Eytelwein's * work 

 is divided, the seventh is the most important. The late Dr. 

 Thomas Young, in commenting upon this chapter, says : 



. " The simple theorem by which the velocity of a river is de- 

 termined, appears to be the most valuable of M. Eytelwein's 

 improvements, although the reasoning from which it is deduced 

 is somewhat exceptionable. The friction is nearly as the square 

 of the velocity, not because a number of particles proportional 

 to the velocity is torn asunder in a time proportionally short, — 

 for, according to the analogy of solid bodies, no more force is 

 destroyed by friction when the motion is rapid than when slow, 

 — but because when a body is moving in lines of a given curva- 

 ture, the deflecting forces are as the squares of the velocities ; 

 and the particles of water in contact with the sides and bottom 

 must be deflected, in consequence of the minute irregularities 

 of the surfaces on which they slide, nearly in the same curvi- 

 linear path, whatever their velocity may be. At any rate (he 

 continues) we may safely set out with this hypothesis, that the 

 principal part of the friction is as the square of the velocity, 

 and the friction is nearly the same at all depths f; for Professor 

 Robison found that the time of oscillation of the fluid in a bent 



• See Nicholson's translation of Eytelwein's work. 



t See my "Experiments on the Friction and Resistance of Fluids," Philo- 

 sophical Transactions for 1831. 



