On tlw Principles of Pump-JVork. 295 



pipe AB = 12 feet high, in equilibrio; twice that weigh t 

 will produce a jet 12 feet above it, or a velocity of water 

 at D greater in proportion to the height than any other 

 weight can do. 



49. But this velocity and altitude of 12 feet i.^ not the 

 greatest effect that this maximum force of 1 1 ra-l lb. will 



f)roduce; but some other altitude AG, and some other ve- 

 ocity acquired by a descent through \VG, will be the maxi- 

 mum effect produced by the said given weight. See 



Fig. 6. 



50. For, since the weight 1 1 78-4 lb. will sustain in equi- 

 librio a column of water in the pipe to the height AW = 

 24 feet, it will produce a jet of water at any less height AG; 

 and its effect will be proportional to that altitude AG, and 

 the velocity of the jet at G conjointly. 



51. Therefore let WPS be a parabola, passing through 

 the point P such, that G P may every where be as the ve- 

 locity acquired at G in descending through WG. Then it 

 is plain, if we complete the parallelogram AGPO, the effect 

 of this force will be every where as the area of that figurft 

 inscribed in the parabola, viz. AG x PG, 



52. But the area of that figure is greatest of all when 

 GW is one-third part of the altiiude AW; and conse- 

 quently when AG is equal to 16 feet, then the effect of the 

 weight NHI = 1178*4 lb. will be a maximum, or greatest 

 possible. And this is the second maximum of pump-work. 



53. If the orifice of the pipe at G were quite open, the 

 whole body of the fluid would rise to W in the same time 

 with the jet, and the velocity of the plane or pallet AC 

 would be the same in both cases by the action of the weight 

 NHI. 



54. Therefore, if the said weight was connected with a 

 chain AG with many pallets AC fixed upon it, and passing 

 over the wheel GEE), moving on its centre F, it would, 

 by a continual descent, cause a constant column of water 

 to rise from G to W of 8 feet in length. 



55. The velocity of the rising water, and consequently 

 of the pallets AC, will be at the rate of 23-6 feet per se- 

 cond; and every such foot will contain 4-8 gallons; there- 

 fore the whole quantity of water raised by this maximum 

 force will be 108 gallons per second, at the height of 16 

 feet. 



5C. Hence the nature of a chain-pump appears ; and its 



utmost force (with a tube or pipe of any given bore) may 



be estinidtcd ; for that pump is only a constant succession 



T4 t>f 



