168 THIRD REPORT — 1833. 



motion diverges from that opening, as from a centre, and is 

 propagated in right Hnes towards the lateral parts. The sim- 

 ple and immediate application of this theorem cannot be made 

 to a jet or aperture at the surface of still water. Circumstances 

 enter into this case which transform the results of the principle 

 into particular motions. It is nevertheless true that the jet 

 communicates its motion to the lateral parts without the orifice, 

 but does not repel it in a radial divergency. M. Venturi illus- 

 trates his theory by experiments on the form and expenditure 

 of fluid veins issuing from orifices, and shows how the velocity 

 and expenditure are increased by the application of additional 

 tubes; and that in descending cylindrical tubes, the upper ends 

 of which possess the form of the contracted vein, the expense 

 is such as corresponds with the height of the fluid above the 

 inferior extremity of the tube. The ancients remarked that a 

 descending tube applied to a reservoir increased the expendi- 

 ture*. D'Alembert, Euler and Bernoulli attributed it to the 

 pressure of the atmosphere. Gravesend, Guglielmini and others 

 sought for the cause of this augmentation in the weight of the 

 atmosphere, and determined the velocity at the bottom of the 

 tube to be the same as would arise from the whole height of 

 the column, including the height of the reservoir. Guglielmini 

 supposed that the pressure at the orifice below is the same for 

 a state of motion as for that of rest, which is not true. In the 

 experiments he made for that purpose, he paid no regard either 

 to the diminution of expenditure produced by the irregularity 

 of the inner surface of the tubes, or the augmentation occa- 

 sioned by the form of the tubes themselves. But Venturi esta- 

 blished the proposition upon the principle of vertical ascension 

 combined with the pressure of the atmosphere, as follows : 



1st, That in additional conical tubes the pressure of the at- 

 mosphere increases the expenditure in the proportion of the 

 exterior section of the tube to the section of the contracted 

 vein, whatever be the position of the tube. 



Sndly, That in cylindrical pipes the expenditure is less than 

 through conical pipes, which diverge from the contracted vein, 

 and have the same exterior diameter. This is illustrated by 

 experiments with differently formed tubes, as compared with a 

 plate orifice and a cylindrical tube, by which the ratios in point 

 of time were found to be 41", 31" and 27", showing the advan- 

 tage of the conical tube. 



3rdly, That the expenditure may be still further increased, 



* "Calix devBxus amplius rapit." — Frontinus de Aqueductibus. See also 

 Pneumatics of Hero. 



