PLANE WAVES OF SOUND 189 



the motion would go on without any permanent consumption 

 of labouring force. Next, suppose the motion of the piston 

 somewhat quicker, so that there is a sensible change of tempera- 

 ture produced by condensation and rarefaction. As the piston 

 moves forward in condensing the air, the temperature rises, and 

 therefore the piston has to work against a pressure greater than 

 if there had been no variation of temperature. By the time 

 the piston returns, a good portion of the heat developed by 

 compression has passed off, and therefore the piston is not 

 helped as much in its backward motion by the pressure of the 

 air in the cylinder as it had been opposed in its forward motion. 

 Similarly, as the piston continues its backward motion, rarefying 

 the air, the temperature falls, the pressure of the air in the 

 cylinder is diminished more than corresponds merely to the 

 change of density, and therefore the piston is less helped in 

 opposing the atmospheric pressure than it would have been had 

 the temperature remained constant. But by the time the 

 piston is returning towards its position of equilibrium, the cold 

 has diminished in consequence of the supply of heat from the 

 sides of the cylinder, and therefore the force urging the piston 

 forward, arising, as it does, from the excess of the external over 

 the internal pressure, is less than that which opposed the piston 

 in moving from its position of equilibrium. Hence in this case 

 the motion of the piston could not be kept up without a 

 continual supply of labouring force. Lastly, suppose the piston 

 to oscillate with great rapidity, so that there is not time for any 

 sensible quantity of heat to pass and repass between the air and 

 the sides of the cylinder. In this case the pressures would be 

 equal when the piston was at a given point of the cylinder, 

 whether it were going or returning, and consequently there 

 would be no permanent consumption of labouring force. I do 

 not speak of the disturbance of the external air, because I am 

 not now taking into account the inertia of the air either within 

 or without the cylinder. The third case, then, is similar to the 

 first, so far as regards the permanence of the motion; but there 

 is this difference ; that, in consequence of the heat produced by 

 compression and the cold produced by rarefaction, the force 

 urging the piston towards its position of equilibrium, on 



