Mr. W. M. Buchanan's Theory of the Reaction Water- Wheel. 125 



But betwixt this the least contraction of the fluid vein, and that which 

 takes place when the orifice is formed in a thin plate, we may evi- 

 dently have a series of any number of terms expressing successive degrees 

 of approximation of the ajutage to the theoretical form of least con- 

 traction. This is obvious, as regards the discharge from a fixed aju- 

 tage, and it is equally obvious, that if an ajutage be constructed to 

 fulfil the conditions of least contraction when the vessel is at rest, it 

 will no longer answer that condition when it moves in the line of the 

 jet with any given velocity. If its motion be in the direction of the 

 jet, its length will manifestly bo virtually increased, and the contrac- 

 tion will approach to that of a jet issuing from a parallel pipe, the 

 coefficient for which is *8 ; and if the movement be in the contrary direction, 

 the length of the ajutage will be in effect diminished, and the con- 

 traction will approach that from an orifice in a thin plate. This last 

 is the actual case which falls to be considered in the reaction machine ; 

 the ajutages have a determinate velocity, in an opposite direction to 

 that in which the fluid issues, and accordingly have their length virtually 

 reduced. This must necessarily be provided against in the construction 

 of the machine, and a length and form of the ajutages determined, 

 which shall exactly correspond, at the given angular velocity of the 

 machine, to the proper dimensions at which, if stationary, they would 

 yield their maximum discharge. This is a problem which requires to be 

 resolved for every machine. 



But with a machine thus constructed, it is easy to perceive that the 

 contraction of the jets will greatly exceed the minimum just assigned, 

 when motion is prevented; and, therefore, in those experiments made 

 for the purpose of determining the measure of the reaction, it might be 

 predicted that the coefficient of discharge would fall considerably below 

 •975. By calculation of the valves of *, /3, y, and, taking into account 

 the difference of the atmospheric pressure at the higher and lower levels 

 of the water-surfaces, it was found that k = *942, and that the loss of head 

 due to the contraction of the jets, measured by the discharge, was there- 

 fore 112636 IT, instead of the minimum, -049375 H. 



If to those absorbing influences we add « — comprehending the loss of 



atmospheric pressure duo to the head H, and the effect of the cohesion of 

 the water to the perimeter of the orifices, (not valued,) we shall have 

 as the total calculated loss 



O + + y + 5 + «) ^!=01421 H, 



and, therefore, upon the moan head of 10 feet employed in these experi- 

 ments, the loss ss 1421 feet. This result is sufficiently near the actual 

 quantity to warrant us in assuming the measure of the reaction assigned 

 to be practically correct for the particular case ; and, therefore, we may 

 assume that wherever the values of the coefficients can be determined 



