ON HYDRAULICS AS A BRANCH OF ENGINEERING. 167 



Let g = the velocity of a body falling in one second, 

 11) = the area of the transverse section, 

 p = the perimeter of that section, 

 I = the inclination of the canal, 



Q = the constant volume of water through the section, 

 U = the mean velocity of the water, 

 R = the relation of the area to the perimeter of the section; 



then 1st, 0-000436 U + 0-003034 V^ = gIR=gI-; 



Sndly, U = ^; 



Srdly, R w^ - 0-0000444499 .wj- 0-000309314 y = 0. 



This last equation, containing the quantities 



Q I m; and R = — , 

 p 



shows how to determine one of them, and, knowing the three 

 others, we shall have the following equations : 



^' ^ ~ 0-000436 Qw + 0-003034 Q"^* 

 ^^j^j J _ p (0-0000444499 Qw + 0-000309314 Q^) 



ethly, » = 0-000«6 ± ^[(0-000«6)'+4(0-003034)gRI]Q_ 



These formulae are, however, modified in rivers by circum- 

 stances, such as weeds, vessels and other obstacles in the 

 rivers ; in which case M. Girard has conceived it necessary to 

 introduce into the formulae the coefficient of correction = 1-7 

 as a multiplier of the perimeter, by which the equations will be, 



• p - 1-7 (0-000436 U + 0-003034 U^) = ^ I w. 



The preceding are among the principal researches of this 

 distinguished philosopher *. 



In the year 1798, Professor Venturi of Modena published a 

 very interesting memoir, entitled Sur la Communication lat^- 

 rale du Mouvement des Fluides. Sir Isaac Newton was well 

 acquainted with this communication, having deduced from it 

 the propagation of rotary motion from the interior to the exte- 

 rior of a whirlpool ; and had affirmed that when motion is pro- 

 pagated in a fluid, and has passed beyond the aperture, the 



• Recherches Physico-mathematiques sur la Theorie des Eatix courantes, 

 par M. Prony. 



