GRAPHICAL REPRESENTATION OF WORK 151 



The area of this figure is clearly equal to AB multiplied by the ordinate 

 at the middle point of AB. This ordinate represents the tension of the 

 string when its length is equal to \(OA + OB), so that we again obtain the 

 result of 113, namely 



(work done) = (range of stretching, 



x (tension at halfway stage of stretching). 



116. The indicator diagram. The graphical representation of 

 work explained in 114 is made use of in practical engineering. 

 Suppose that 00' is the distance traveled by a piston inside a 

 cylinder. When the piston is in any position P, let the pressure 

 acting on the piston be measured, 

 and let a line PP f be drawn at 

 right angles to 00' to represent it 

 on any assigned scale. As the 

 piston moves along the range 00 r 

 and then back along the range 

 O'O, the point P r will describe a 

 closed curve AP'BP"A, which is 

 called the indicator diagram of the 

 motion of the piston. 



The work done by the steam on 

 the piston in its forward motion is, 

 as we have seen, represented by the area AP'BO'POA inclosed be- 

 tween the curve AP'B and the axis 00 r . This work is expended in 

 moving the piston forward in opposition to the thrust in the piston 

 rod. Similarly the work done by the steam on the piston in its back- 

 ward motion is represented by the curve BO'POAP n B inclosed be- 

 tween BP"A and the axis O0' } this area being taken negatively, since 

 the piston is now moving in opposition to the pressure at work on it. 



Thus the whole work done on the piston is represented by the 

 difference of these two areas, and this is easily seen to be the area 

 AP'BP"A of the indicator diagram itself. Hence, to find the rate 

 at which an engine is performing work, it is only necessary to 

 measure the area of its indicator diagram and the number of 

 revolutions per unit time. 



FIG. 86 



