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Report on the Progress and Present Stale of our Knowledge 

 of Hydraulics as a Branch of Engifieering. By George 

 Rennie, Esq., F.R.S., §-c. ^-c. 



Part I. 



The paper now communicated to the British Association for 

 the Advancement of Science comprises a Report on the pro- 

 gress and present state of our knowledge of Hydrauhcs as a 

 branch of Engineering, with reference to the principles already 

 established on that subject. 



Technically speaking, the term hydraulics signifies that 

 branch of the science of hydrodynamics which treats of the 

 motion of fluids issuing from orifices and tubes in reservoirs, 

 or moving in pipes, canals or rivers, oscillating in waves, or 

 opposing a resistance to the progress of solid bodies at rest. 



We can readily imagine that if a hole of given dimensions be 

 pierced in the sides or bottom of a vessel kept constantly full, 

 the expenditure ought to be measured by the amplitude of the 

 opening, and the height of the liquid column. 



If we isolate the column above the orifice by a tube, it ap- 

 pears evident that the fluid will fall freely, and follow the laws 

 of gravity. But experiment proves that this is not exactly the 

 case, on account of the resistances and forces which act in a 

 contrary direction, and destroy part of, or the whole, effect. 

 The development of these forces is so extremely complicated 

 that it becomes necessary to adopt some auxiliary hypothesis 

 or abbreviation in order to obtain approximate results. Hence 

 the science of hydrodynamics is entirely indebted to experi- 

 ment. The fundamental problem of it is to determine the efflux 

 of a vein of water or any other fluid issuing from an aperture 

 made in the sides or bottom of a vessel kept constantly full, or 

 allowed to empty itself. Torricelli had demonstrated that, 

 abstracting the resistances, the velocities of fluids issuing from 

 very small orifices followed the subduplicate ratio of the pres- 

 sures. This law had been, in a measure, confused by sub- 

 sequent writers, in consequence of the discrepancies which 

 appeared to exist between the theory and experiment ; until 

 Varignon remarked, that when water escaped from a small 

 opening made in the bottom of a cylindrical vessel, there ap- 

 peared to be very little, or scarcely any, sensible motion in the 



