296" On the Prindples of Pitmp-H'drk, 



of pallets AC, pai^sing over two wheels at the top atrd 

 bottom of the pipe AG, and put in motion by the force of 

 men instead of the weight HNI *. 



57. If instead of the wheel CED a lever GM be used, 

 then a weight R at the end JVJ of the lever would have the 

 same force and produce the same efl'ect with the weight 

 NHI, if it be in proportion thereto, as the distance FG to 

 the distance FM. 



58. Let now the plane AC represent the sucker, bucket, 

 or piston of a common sucking-pump, placed at the bottom 

 of the pipe, and the rod AG connected with the lever or 

 h.tndle Gx\I. And let FG : FM : : 1 : 6. Then, since the 

 column of water A BCD (fig. 5.) 13 feet high, weighs 

 58y-lb., it will be sustained in cquilibrio by somewhat 

 less than 100 lb. = R, at the end of the lever GM. 



."JO. If we suppose the nmscular force of a man's arm 

 equal to 100 lb. it would, acting at M, sustain the same 

 column of water ; therefore two such men would sustain a 

 column of water 54 feet high = AW: which weniay there- 

 fore call a maximum force. 



60. If now it be required to raise water in a sucking- 

 pump, it is evident that given maxinuim force will produce 

 the greatest eflect when the altitude of the water to be raised 

 is A"G = If) feet. 



61. In this case also the lever acts to the greatest advan- 

 tage; for now the force which acts at M being 200 lb., is 

 one-half more than the force 134 lb., which is nearly equi- 

 valent at M to the weiaht of the colunm of water AC 10 

 feet high. And this* is a third maximum in pump-work, 

 and follows immediately from the second. 



62. In all mechanism, what is gained in power is lost in 

 time ; for now the motion of the point G, and consequently 

 of the piston AC, is six times slower than the point M, 

 the motion of which is determined bv considering the lever 

 G M as a pendulum vibrating about the point F, and being 

 charged. with two weights, one at G, the other at M, which 

 are to each other as "785-6 to 200, or as G to 1^; the di- 

 stance of the centre of oscillation will thereby be found, and 

 from thence the time of an oscillation, or motion through 

 the arch dMc, will be known, and is 40'",- then if the said 

 arch cMd be six feet, the arch aGl> will be one foot. 



63. Therefore the velocity of the piston AC is 12 inches 



* Thib is upon sujipositicu that in the cb.nln-pump there !•; no fiiction, 

 and that the pallets lose no water ; but as one or the othti" of these cases 

 must take place jn that machine, it deservts no furtlier consideration. 



in 



