422 Mr. Ewart on the Reaction of efflnmt IVater, 



The theory of this machine has occasionally occupied the 

 attention of many distinguished mathematicians, and M. Euler 

 has given two elaborate treatises on its principles in the Me- 

 moirs of the Berlin Academy for 1750, p. 311 ; and for 1751, 

 p. 271. His demonstrations relating to this subject are very 

 complicated, and they do not appear to have been adopted by 

 succeeding authors*. 



Mr. Waring, of America, has given quite a different theory, 

 which has been approved of by several good writers on hy- 

 draulics. He concludes that the greatest effect will be produced 

 when the velocity of the orifice is half that of the issuing water ; 

 and that this effect will be nearly the same as that of a well- 

 constructed undershot water-wheel f. 



The explanation which I have offered of the action of the 

 water on this machine is different from any other that I have 

 had an opportunity of consulting. I offer it, therefore, merely 

 as an attempt to solve an intricate problem. 



If it were possible for the water to issue with the velocity due 

 to the pressure, it is obvious, if my explanation be right, that al- 

 though a very large proportion of the moving force of the water 

 may be communicated to the machine, moving with a moderate 

 velocity, the maximum of effect can only be obtained by an in- 

 finite velocity. But when the water issues with a velocity which 

 is less than what is due to the pressure, as must always be the 

 case in practice, the velocity at which the maximum of effect is 

 produced, may be found as follows. It should first be ascer- 

 tained by experiment how near the issuing velocity can be 

 brought to that which is due to the pressure. From the ex- 

 periments which I have made, I have been led to conclude 

 that no greater issuing velocity can possibly be obtained from 

 a machine of this kind than what is due to *8 of the pressure. 

 If this conclusion be correct, it follows, that, whatever may be 

 the issuing velocity of the water, a moving force, equal to \ of 

 the moving force which is necessary to generate that velocity 

 in the water, when falling freely, is expended in producing 

 change of figure; that is, in forcing the water through the 

 tubes and through the orifice C ; and if the velocity of the ma- 

 chine be such that PC = 5 AB, the issuing velocity will be 

 equal to the velocity of the orifice, and the whole moving force 

 of the water in descending from A to B will be expended in 

 producing change of figure. 



For, the head due to V, the issuing velocity, will in this case 



* M. Euler says, " In employing the same quantity of water, and the 

 same fall, this machine will produce an effect nearly four times greater than 

 the ordinary machines." 



f American Philos. Trans, vol. Hi. |Cl91 and 192. 



be 



