120 Mr. W. M. Bucuanan's Theory of the Reaction Water-Wheel. 



not at the same time be causing pressure. The orifice of issue being 

 formed in the bottom of a vessel containing water, a column of the fluid 

 will descend through it, and expend, during its descent, a quantity of 

 pressure equal to that of its own volume. Now admitting the velocity of 

 the effluent particles at the orifice to bo the same that they would acquire 

 by falling freely from the height of the water-level, which, for simplicity, 

 we shall suppose to bo 16 feet above the orifice, the velocity of issue will 

 be at the rate of 32 feet in a second ; and, therefore, a column of 32 feet 

 in length will pass through the orifice every second with the whole velo- 

 city derivable from its weight. It is therefore clear that an amount of 

 gravitation sufficient to generate that velocity in the volume of fluid dis- 

 charged must have been expended, and consequently falls to be deducted 

 from the pressure exerted by the fluid upon the bottom of the vessel. In 

 like manner, if the jet issue from a lateral orifice at the same depth below 

 the water-level, the pressure upon that side will be diminished by a quan- 

 tity equal to the gravitation employed in producing the motion of the fluid. 

 But the amount of gravitation thus expended is equivalent to a column 

 of the fluid of twice the head, and therefore the effect upon the vessel 

 will be the same as if it were subjected to an equal pressure of any other 

 kind in an opposite direction. And moreover, the pressure being lateral, 

 and therefore perpendicular to the only direction in which a vertical force 

 like that of gravity can itself act, it must be derived by reaction of the 

 moving particles on the opposite surface of the vessel, and may be assi- 

 milated to the constant pressure of a spring, interposed between the par- 

 ticles of fluid and the unit of surface immediately opposite to the orifice. In 

 this position the spring must needs act in a direction exactly contrary to 

 that of the movement impressed upon the issuing fluid, and with an inten- 

 sity exactly equal to the hydraulic pressure of the jet. 



This principle of reaction equal and contrary to action, as applied in 

 hydraulics, has been acknowledged upwards of a century. Daniel Ber- 

 nouilli, in his Hydrodynamica, (Strasbourg, 1738,) among other proposi- 

 tions, then new to science, announced that " the reaction of a jet of water 

 is equal to the weight of a column of the fluid of double the height due 

 to the velocity of efflux, and having for its base the area of the orifice." 

 This proposition was afterwards submitted to the test of experiment, and 

 partially confirmed ; but I cannot find that it at any time received that 

 rigorous investigation which was necessary to secure confidence in the 

 result, and justify an unqualified acceptance of the literal terms of the 

 proposition as the basis of a practical theory of the Reaction Water-Mill. 

 Under this feeling of doubt, and impressed with the necessity that existed 

 of obtaining accurate data for the calculation and construction of those 

 machines, a very extensive series of experiments was undertaken and con- 

 ducted by Mr. C. Randolph and myself, with every opportunity and inten- 

 tion of obtaining a quantative result upon whicli we could rely. The 

 apparatus employed was that depicted in the accompanying drawing. 

 (Plate IV.) It consisted of a small reaction machine, capable of passing 



