166 THIRD REPORT 1833. 



and for conduit pipes, 



calling U = the mean velocity, 



Z = the head of water in the inferior orifice of the pipe, 

 L = the length of the pipe in metres, 

 D = the diameter of the pipe, 



we shall have 



U = - 0-0248829 + ^0-000619159 + 717857 DZ 

 or, where the velocity is small, 



U = 26-79 \/BZ; 

 L 



that is, the mean velocities approximate to a direct ratio com- 

 pounded of the squares of the diameters and heads of water, 

 and inversely as the square root of the length of the pipes : 

 and by experiments made with great care, M. Prony has found 

 that the formula 



U = - 0-0248829 + -/ 0-000619 159 + 717-857 D^ 



L 

 scarcely differs more or less from experiments than -^^ or -^j. 

 The preceding formulae suppose that the horizontal sections, 

 both of the reservoir and the recipient, are great in relation 

 to the transverse section of the pipe, and that the pipe is kept 

 constantly full *. 



In comparing the formulae given for open and close canals, 

 M. Prony has remarked that these formulae are not only similar, 

 but the constants which enter into their composition are nearly 

 the same ; so that either of them may represent the two series 

 of phaenomena with sufficient exactness. 



The following formula applies equally to open or close canals : 



U = 



0-0469734 + -/ (o-0022065 + 3041-47 ^V 



But the most useful of the numerous formulae given by M. Prony 

 for open canals is the following : 



* According to Mr. Jardine's experiments on the quantity of water delivered 

 by the Coniston Main from Coniston to Edinburgh, the following is a compa- 

 rison : Scots Pints. 



Actual delivery of Coniston Main 189-4 



Ditto by Eytelwein's formula 189-77 



Ditto by Girard's formula 188-26 



Ditto by Dubuat's formula 188-13 



Ditto by Prony 's simple formula 192-32 



Ditto by Prony's tables 1807 



