28 



KINETICS OF A PARTICLE. 



[52. 



volume v occupied by the gas. This volume being in the 

 present case proportional to the distance s of the piston from 



the fixed base of the cylinder, the 

 force F is a function of s. The 

 variation of F can therefore be rep- 

 resented graphically by a curve hav- 

 ing s for abscissa and F for ordinate 

 (Fig. 9) ; and the area of this curve, 

 i.e. the area contained between the 

 curve, the axis of s, and two ordi- 

 nates whose abscissas are s and s, 



being given by the integral j Fds, 



represents the work done on the piston 

 when ptished through the distance 

 s-s . 



Fig. 9. 



52, In the case of a perfect gas, Boyle's law gives the rela- 

 tion pv = k, where k is constant if the temperature remains con- 

 stant. Hence, 



where K and P Q are constants. This equation represents an 

 equilateral hyperbola, whose asymptotes are the axis of F and a 

 line parallel to the axis of s. For steam, the law connecting 

 pressure and volume is more complicated, but the curve may 

 be taken as very nearly hyperbolic. 



53. The Steam-engine Indicator is an apparatus for measuring the 

 pressure of the steam in the cylinder and at the same time recording it 

 automatically on a drum revolving as the piston moves. Thus, if the 

 indicator be put in connection with the interior of the cylinder, the 

 curve traced by the indicator has for its abscissas the distances s of the 

 piston from this end, and for its ordinates the corresponding pressures 

 F of the steam on the inside of the piston. 



