o' the Theory of Barker's Mill. 427 



efflux commences, and while the fluid is at rest, the weight 

 a k is sufficient to counteract the tendency to begin motion. 



IV. Computation of the Moving Force of Barker's Mill, or of 

 the impulse produced by the Reaction of the projected Wa- 

 ter; supposing that h is the length of the upright Tube 

 kept constantly fully and v the absolute Velocity of the 

 Orifices in the horizontal Arms. 



This machine has generally two horizontal arms diametri- 

 cally opposite ; but it may have any number of such arms with 

 an orifice in each. Whatever be the number of the arms, I 

 shall suppose that all the orifices are at the same distance, r, 

 from the axis ; and I shall use the symbol a to denote the sum 

 of the areas of all the orifices. 



The velocity V with which the water issues from the ori- 

 fices is known by the formula, 



And, since the water is propelled from the orifices with the 

 velocity V, and has acquired from the machine the velocity v 

 in the opposite direction, the velocity with which it is pro- 

 jected from the arms, is equal to V— v: but cV is the quantity 

 of water so projected in a second ; wherefore the momentum 

 of the projected water is equal to aVx(V-i)); and the same 

 expression is equal to the impulse communicated to the ma- 

 chine by reaction. Wherefore, since the impulse is exerted 

 at the end of the lever r 9 its effect to turn the machine, or the 

 motive force, is equal to 



r XflVx(V-w). (1) 



We may likewise measure the motive force by the momentary 

 impulse multiplied by the space through which it acts ; and 

 the force accelerating the machine will be, 



v xaV x (V-v). (2) 



These two formulae seem to be the most elementary expres- 

 sions of the motive force of this machine. 



. - 



Mr. Ewarfs Formula. 



T I aVx(V-„) n 



Let us put ^ = P ; 



then, aV x(V-p)ssP x 2g; wherefore the reaction is 

 equal to the momentum which the weight P acquires in a se- 

 cond by falling; in other words, the momentary impulse of 

 reaction is equal to the pressure of the weight P. The mo- 



3 I 2 tive 



