THE FLOW OF GASES. 167 



2. On examining the equations, it appears that they 

 contain one assumption which is not part of the laws of 

 thermodynamics or of the general theory of fluid motion. 

 And although commonly made and found to agree with 

 experiments in applying the laws of hydrodynamics, it 

 has no foundation as generally true. To avoid this 

 assumption, it is necessary to perform for gases inte- 

 grations of the fundamental equations of fluid motion 

 which have already been accomplished for liquids. These 

 integrations being effected, it appears that the assumption 

 above referred to has been the cause of the discrepancy 

 between the theoretical and experimental results, which 

 are brought into complete agreement, both as regards the 

 law of discharge and the actual quantity discharged. The 

 integrations also show certain facts of general interest as 

 regards the motion of gases. 



When gas flows from a reservoir sufficiently large, and 

 initially (before flow commences) at the same pressure 

 and temperature, then, gas being a nonconductor of heat 

 when the flow is steady, a first integration of the equation 

 of motion shows that the energy of equal elementary 

 weights of the gas is constant. This energy is made up 

 of two parts, the energy of motion and the intrinsic 

 energy. As the gas acquires energy of motion, it loses 

 intrinsic energy to exactly the same extent. Hence we 

 have an equation between the energy of motion, i. e. the 

 velocity of the gas, and. its intrinsic energy. The laws of 

 thermodynamics afi'ord relations between the pressure, 

 temperature, density, and intrinsic energy of the gas at 

 any point. Substituting in the equation of energy, we 

 obtain equations between the velocity and either pressure, 

 temperature, or density of the gas. 



The equation thus obtained between the velocity and 

 pressure is that given by Thomson and Joule ; this equation 



