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Report oil the Progress and present State of our Knowledge 

 of Hydraulics as a Branch of Engineering. Part II. By 

 George Rennie, Esq., F.R.S., Acad. Reg. Sc. Turin. 

 Corresp., 8^c. 8fc. 



My former paper was confined to a brief elucidation of the pro- 

 gress and present state of that branch of hydrodynamics which 

 relates to the motions of fluids through orifices, tubes, and arti- 

 ficial channels. My object was to combine together the expe- 

 riments which had been made by different philosophers (from 

 Castelli and Galileo down to Lesbros and Poncelet,) to deter- 

 mine the effective expenditures from orifices of different kinds, 

 as well as the remarkable phaenomena exhibited by the motions 

 of fluid veins. In the first instance, with regard to orifices, it 

 was shown, That the law of Torricelli relative to bodies gravi- 

 tating in free space, (and which applies to all fluids,) requires 

 certain modifications which diminishes their expenditure as 

 compared with the areas of the orifices nearly one half, and the 

 diameter of the fluid vein after it issued from the orifice nearly 

 three fourths ; — That the form of the orifice (with equal areas) 

 had little influence over the expenditure : 



2ndly, That although an increase of expenditure (considerably 

 above the expenditures by simple orifices of equal magnitude,) 

 is found to take place through additional or cylindrical tubes, 

 equal in length to three times the diameter of the orifice, yet 

 very little variation exists in their coefficients ; — That the same 

 is true of conical or divergent ajutages, but with greater expen- 

 ditures : 



3rdly, That the expenditures by incomplete orifices, i.e. 

 through rectangular notches in dams, (and which form a particu- 

 lar case of simple orifices,) follow the parabolic law, with a co- 

 efficient of two thirds of the orifice : 



4thly, That the expenditures by rectilinear and curvilinear 

 pipes follow more complicated laws, which can only be re- 

 presented by a certain portion of the height or inclination of 

 the column ; and that the various formulae which have been ap- 

 plied to the determination of these questions approximate very 

 nearly. 



The same may be said of the formulae made applicable to the 

 motions of fluids in artificial and natural channels; and to other 

 cases of orifices when influenced by variable pressures, as in 



