PNEUMATICS. 



25 



to depress the piston will be expressed 

 in pounds by 



h'x r x r x 3.14 x 62.5 P. 



From these observations, it appears 

 that the weight of the piston and its 

 rods assist the forcing-power of the 

 machine, but oppose its suction-power. 

 These effects, therefore, on the whole, 

 neutralize each other. 



The entire force used in raising the 

 water will be found by adding the force 

 necessary to elevate the piston to that 

 which is necessary to depress it. As in 

 this case the weight of the piston and 

 rods increases the one by as much as it 

 diminishes the other, the entire force 

 will be the weight of a column of water 

 whose base is the section of the piston, 

 and whose height is P C + M N, that is 

 the height of the level of the water 

 in the forcing-pipe above the level of 

 the water in the reservoir, and expressed 

 in pounds, this is 



(h+ h') x rx rx 3.14 x 62.5. 



(47.) It appears, therefore, that other 

 circumstances being the same, the power 

 of the forcing-pump has the advantage 

 over that of the suction-pump by the 

 weight of the piston and its rods. 



In the suction-pump the elevation of 

 the water is entirely effected by the as- 

 cent of the piston : during its descent the 

 engine, mechanically speaking, is inac- 

 tive. It would, therefore, require that 

 the power applied to the piston-rod 

 should be an intermitting one, for other- 

 Elevating force . . . 

 Depressing force . . 



Difference . . . 



Or (2P+/ixrxrx3, 

 This difference will evidently be 

 nothing, and the elevating and depress- 

 ing forces will be equal when 



2P=(^' A)x rxrx3. 14x62.5 

 that is, when the weight of the column 

 M N exceeds that of the column P C 

 by twice the weight of the piston and 

 rods. The position of the spout should, 

 therefore, be regulated by these consi- 

 derations ; and it is evident that, in order 

 to an uniformity of action, if P C is 

 nearly thirty-four feet, the piston rods 

 should always be loaded with a sufficient 

 weight to balance a column of water, 

 whose base is the section of the pis- 

 ton, and whose height is the excess of 

 the height of the spout from the level of 

 the \vater in the cistern above sixty- 

 eight feet. 



It must be evident from this account 

 of the forcing-pump, that the discharge 



wise a waste would take place on every 

 descent of the piston. On the other 

 hand, in the forcing-pump, the elevation 

 is partly produced in the ascent and 

 partly in the descent of the piston, and 

 the power must be continued, but pro- 

 portionally less intense. Thus a single- 

 acting steam-engine, or an atmospheric 

 engine, would be suitably applied to raise 

 water by the suction-pump, and a 

 double-acting engine by the forcing- 

 pump. 



In the forcing-pump, however, the 

 forces required to effect the elevation 

 and depression of the piston are not 

 always equal, and it is in many cases 

 desirable that they should be so"; for it 

 generally happens that the pow r er ap- 

 plied to elevate and depress is uniform, 

 as for example, in the steam-engine. 

 Let us consider how the powers of ele- 

 vation and depression could be equal- 

 ized. 



We have proved that the power of 

 elevation is equal to the weight P, to- 

 gether with that of the column of the 

 height h, and with a base equal to the 

 section of the piston. The power of 

 depression is equal to the weight of a 

 column whose height is h', diminished by 

 the weight P. Now the difference of 

 these two forces is twice the weight P, 

 together with the weight of the column 

 h diminished by the w r eightof the column 

 h'. This, expressed algebraically, is 



, Axrxrx3.14x62. 



, A'xrxrx3.14x62.5 P 



> (h A')xrxrx3.14x62.5 

 14x62.5) h'xrxrx 3. 14x62.5 

 from the spout can only take place on 

 the descent of the piston, and is there- 

 fore intermitting. One method of re- 

 medying this is the application of an 

 air-vessel to the apparatus. At the top 

 of the forcing-pipe D E (Jig. 26.) instead 

 of a spout place a close vessel E F com- 

 municating with the force-pipe by a 

 valve in the bottom opening upwards 

 at E. A tube T T is introduced at the 

 top of this vessel, and fitted so as to be 

 air-tight, and extending nearly to the 

 bottom, furnished with a stop-cock G. 

 The stop-cock being closed and water 

 forced in through the valve, the air con- 

 tained in the vessel will be condensed. 

 and will exert a proportionate pressure 

 on the surface of the water in the vessel, 

 so as to force it up in the tube which is 

 terminated with the stop-cock G. If 

 then the stop-cock be opened, the water 



