310 Prof. Stokes's Examination of the possible effect of 



sure of the air in the cylinder as it had been opposed in its for- 

 ward motion. Sunilarly, as the piston continues its backward 

 motion, rarefying the air, the temperature falls, the pi'essure 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 fi'om 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 pis- 

 ton to oscillate mth 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 pressiu-es 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 consimiption 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 prodiiced by rarefaction, the force 

 urging the piston towards its position of equilibrium, on which- 

 ever side of that position the piston may happen to be, is greater 

 than it would have been had the temperature remained unaltered. 

 Now the first case is analogous to that of the sonorous vibra- 

 tions of air when the heat and cold produced by sudden conden- 

 sation and rarefaction are supposed to pass away with great 

 rapidity. For we are evidently concerued only with the relative 

 rates at which the phase of vibration changes, and the heat 

 causing the excess of temperature 6 passes away, so that it is 

 perfectly immaterial whether Ave suppose the change of motion 

 to be very slow, or the cooling of heated air to be very I'apid. 

 The second case is analogous to that of so^^nd, when we suppose 

 the constants q and 7i comparable with each other ; and we thus 

 see how it is, that, on such a supposition, labouring force would 

 be so rapidly consumed, and the sound so rapidly stifled. The 

 third case is analogous to that of sound when we make the usual 

 supposition, that the alternations of condensation and rarefaction 

 take place with too great rapidity to allow a given portion of air 

 to acquire or lose any sensible portifm of heat by radiation. The 



