22 



PNEUMATICS. 



ance, that the height of the valve V, at 

 the top of the suction-pipe, above the 

 level of the water in the reservoir, 

 must always be less than thirty-four 

 feet*. 



Let us then suppose that the height 

 B C is less than thirty-four feet, and 

 that the exhaustion has been carried so 

 Tar, that the water has risen in the suc- 

 tion-pipe, and that a portion of it, B H", 

 Jhas been forced by the atmospheric 

 pressure through the valve V. Upon 

 the next descent of the piston, the water 

 in H" B will be forced through the valve 

 in the piston, and will be above the 

 valve when the piston has reached V. 

 Since the piston-valve opens upwards, 

 this water cannot return through it ; and 

 upon the next ascent of the piston, the 

 atmospheric pressure forces more water 

 through V. The next descent and ascent 

 are attended with like effects. By con- 

 tinuing this process, a column of water 

 is collected above the piston, which is 

 lifted ever} r ascent, and receives an ad- 

 dition to its quantity every descent. 

 Near the top of the pump-barrel a spout 

 S is provided for the discharge of the 

 water, and when the elevation of the 

 column of water on the piston reaches 

 the level of this spout, it ceases to accu- 

 mulate ; whatever addition of water is 

 received through the 1 piston-valve on 

 the descent, being discharged at the 

 spout S on the ascent. 



It should be observed, that if the 

 piston in its descent do not reach the 

 bottom of the barrel B, the space be- 

 tween it and the bottom B will never be 

 reduced to a vacuum, and can only be 

 rarefied to a certain extent. In this case 

 the suction-pipe B C should be. much 

 less than thirty-four feet, for, otherwise 

 the water can never rise to the valve V, 

 since it has the elastic force of the air 

 in P B to oppose its ascent. 



(41.) From this description of the 

 common pump, it appears that two dis- 

 tinct forces are engaged in the elevation 

 of the water. The pressure of the at- 

 mosphere, acting on the surface of the 

 water in the well, raises it through the 

 valve V. After what has thus been 

 lodged in the chamber above V, has 



* Thirty-four feet is here used as the height of a 

 column of water equal to the atmospheric pressure. 

 i his pressure, as we have already stated, is van- 

 able, and its lowest value in these countries is about 

 141bs. to the square inch. This is equal to the 

 pressure of a column of water of about 32$ feet high. 

 When the barometer is at 28 inches this is the pres- 

 sure. When it is at 30 inches the pressure is equal 

 to. a column of water 3*J feet high, 



pnssed through the piston-valve, it is 

 then lifted by the mechanical force, 

 whatever that be, which works the 

 pump-rods. 



(42.) Let us now consider the force 

 which is required in each stage of the 

 process, to elevate the piston, exclusive 

 of the weight of the piston-rods and the 

 effects of friction. 



Let the piston be at V, and the level 

 of the water in the suction-pipe at H. 

 Let the number of feet in C H be called 

 h. The elastic force of the air in B H 

 will then be such as to exert a pressure 

 on every square inch, equal to the 

 weight of a column of water, whose base 

 is a square inch, and whose height, ex- 

 pressed in feet, is 34 h*. In its 

 ascent, therefore, each square inch of 

 the section of the piston is pressed up 

 by this -force. It is, on the other hand, 

 pressed down by the whole force of the 

 atmosphere, which is equal to the 

 weight of thirty-four feet of water on 

 each square inch. The effective force 

 then which resists the ascent of the pis- 

 ton, for each square inch, is the weight 

 of a column of water, whose base is a 

 square inch and whose height is the 

 difference between thirty-four feet and 

 34 h feet ; that is, h feet. Thus it 

 appears, that it requires a force to lift 

 the piston exactly equal to the weight 

 of a column of water, whose base" is 

 equal to the section of the piston, and 

 whose height is that of the water in the 

 suction-pipe, above the level of the wa- 

 ter in the well. 



It follows, therefore, that as the water 

 rises in the suction-pipe, the force re- 

 quired to lift the piston is proportionally 

 increased. 



Let us next consider the force requi- 

 site to lift the piston, in the second part 

 of the process ; viz. when the water 

 raised has passed through the piston 

 valve. 



Let the piston be at V, and the level 

 of the water at H" ; the downward 

 pressure sustained by the piston in this 

 case, is evidently the weight of the in- 

 cumbent water B H", together with the 

 weight of the atmosphere. Let h be the 

 number of feet in the height B H", and 

 34 + h } will express the number of feet 

 in a column of water, whose base is 

 equal to the section of the piston, and 

 whose weight is equal to the whole 



* 34 h means the remainder, obtained by sub- 

 tracting the number which h represents from 3k 



f 34 -f h moans the svun obtained by adding the 

 number expressed by /* to 34. 



