204 On the Principles of Pump-tVork. 



bore, the -Aeight of the water which fills it is 589'2lb., and 

 equal to the weight HGI. 



37. The weight on the plane AC will always be the 

 same while the fluid stands at the same height A B, what- 

 ever be the form or capacity of the pipe ABDC above it. 



38. If the top BD be covered close, and in the cover be 

 made a small hole; then if a weight HI KL be appended 

 to the former, it will cause the water of the tube to rise 

 through that hole in form of a jet d'eaii) and with a velocity 

 that will carry it to a certain perpendicular height DO. 



39. This height will be such, that a body B VOD of the 

 fluid, of the same diameter with the pipe AB, will be equal 

 in weight to the superadded weight H L. 



40. The velocity with which it rises from the hole at D, 

 is the same as a heavy body acquires in descending through 

 the same height VB. 



41. The space through which any body descends in a 

 second of time is 1 6^ feet ; in two seconds it descends 

 through four times that space ; in three seconds, through 

 nine times that space j and so on : the descent is therefore 

 known for any given time. 



42. If a third weight KLMN be added to the two former 

 it w ill cause the jet to rise higher still, viz. from B to W. 



43. If upon the axis of the pipe continued out, be de- 

 scribed the parabola DPRS, and through V and W be 

 drawn the right lines VP, WR, to the parabola (in the 

 points P and R), and parallel to the horizon. Then these 

 lines VP, WR, will be as the square roots of BV and BW 

 (the heights of the jets), and therefore as the velocities of 

 the water at D, which produce those jets, respectively. 



44. These lines VP, WR, will therefore, when compared 

 with AV and AW, express the velocities of the jets com- 

 pared with the weight KGL and MGN which produce 

 them. 



45. But the ratio of VP to AV is expressed by the angle 

 VCP made by drawing the line CP. Now this angle will 

 be greatest of all when the right line CP touches the curve, 

 but does not cut it ; which suppose to be at the point R- 



46. Then in that case we have BW equal to BA, and 

 consequently the weight HN equal to the weight HGI. 



47. Therefore the velocity of a fluid at D will be greatest 

 in proportion to the force which produces it when that force 

 is double of ;he force that will just sustain a column of 

 water to the given height AB. And this is the first maxi- 

 nuim in pump-work. 



49. Hence if 58C)*'- lb. sustains a column of water in the 

 5 pipe 



