118 Mr. W. M. Buchanan's Theory of the Reaction Water- Wheel 



chance be so ill constructed as completely to nullify the reacting force of 

 the water ; but it is quite possible, without any attempt to produce a mal- 

 formation, to find the machine yielding only forty, instead of eighty per 

 cent., which it ought generally to realize. But although inviting, tho 

 discussion of this part of the general problem must be deferred. At 

 present it will be sufficient that we establish tho theory of the machine — 

 the measure of its efficiency — assuming the technical conditions to be 

 strictly fulfilled. The details submitted are preliminary to this end, and 

 were entered upon only because they appeared necessary to insure a clear 

 conception of the modus operandi of the machine in its practical and most 

 effective form. 



Fundamental Principles. — The characteristic property of fluids — that 

 which essentially distinguishes them from solids — is the remarkable pro- 

 perty they possess of transmitting equally in all directions the pressure 

 applied to their surfaces. From this property it follows, that when a 

 vessel is filled with water to a given depth, the pressure produced by the 

 gravity of the fluid alone upon any unit of the interior surface of the ves- 

 sel, horizontal or lateral, is always equal to the weight of a vertical column 

 of the fluid, having that unit of surface for its base, and the depth from 

 the water level as its length. But the pressure being propagated equally 

 in every direction, motion does not ensue ; the horizontal filaments of the 

 fluid pressing from within outwards, in virtue of the universal principle 

 of action and reaction equally and contrary, mutually counteract each 

 other's effect, pair and pair, over the entire interior of the vessel, and the 

 system of pressures remain in equilibrio. If the vessel be suspended by 

 a cord, it will remain at rest, and the line of suspension will be vertical ; 

 the horizontal components of pressure cannot put it in motion, and the 

 sum of the vertical pressures are neutralized by the tension of the cord. 

 But if a lateral orifice be made in the vessel below the level of the water, 

 the equilibrium will be destroyed ; for, by taking away a portion of the 

 retaining surface, the pressure on that side of the vessel must necessarily 

 be diminished, and will no longer balance the pressure on the surface 

 opposite. In consequence of this difference of pressure on the two sur- 

 faces, the vessel will no longer hang vertically, but will be deflected in a 

 direction opposite to that in which the jet of fluid is projected, in obe- 

 dience to the unbalanced force exerted within it. 



This is immediately evident on the mere statement of the condition of 

 equilibrium ; but it does not follow, because there is no pressure on the 

 part of the surface which is removed, that we have found a measure of 

 the unbalanced pressure or reaction exerted on tho equal portion of the 

 retaining surface immediately opposite. When the orifice is opened, it is 

 no longer a question of hydrostatic, but of hydraulic pressure, which we are 



lli'il upon to consider. In the former case we are required to regard 

 only the weight of the fluid; but in the latter wo have weight and motion 

 combined. 



To determine the amount of this reaction, it will be necessary and suffi- 



