56.] RECTILINEAR MOTION. 29 



At the beginning of the stroke, steam is admitted and acts with nearly 

 constant pressure on the piston; the line 

 AB (Fig. 10) traced by the indicator will 

 therefore be nearly parallel to the axis of s. 

 As soon as the steam is shut off by the slide- 

 valve, the steam, being now confined within 

 the cylinder, begins to expand nearly accord- 

 ing to the law pv = const., or Fs = const. ; 

 the curve traced by the indicator is therefore 

 approximately an equilateral hyperbola BC, Fig. 10. 



having the axes as asymptotes. When the 



slide-valve connects the cylinder with the condenser, a partial vacuum is 

 established behind the piston, and the pressure curve is approximately 

 a line CD, parallel to the axis of F. 



54. The area ABCDO evidently represents approximately the 

 work of the pressure on the inside of the piston in one complete (for- 

 ward and backward) stroke. In reality, a large number of circum- 

 stances produce deviations from the regular shape ABCDO, and the 

 actual trace, obtained by means of an indicator for one (forward and 

 backward) stroke, usually called the indicator diagram, forms a loop 

 somewhat like that indicated by the dotted curve in Fig. 10. The area 

 of this loop, which represents the work in question, can readily be found 

 by dividing it up into narrow rectangular strips, or with the aid of a 

 planimeter. 



55. The effective piston pressure is of course the difference between 

 the pressures on the two sides of the piston. A diagram should there- 

 fore be obtained for each side of the piston ; from these two diagrams 

 the curve of effective piston pressure is then derived by constructing the 

 curve whose ordinates are the differences of the corresponding pressures 

 on the two sides. By dividing the area contained between this curve 

 and the axes by the length of the stroke, the average, or mean, piston 

 pressure is finally found. 



For details the student is referred to special works on the steam 

 engine, such as G. C. V. HOLMES, The steam engine, New York, Apple- 

 ton, 1887, pp. 317-345. 



56. Attractive and Repulsive Forces. Let us consider the 

 motion of a particle acted upon by a so-called central force, i.e. 



