the Flow of Gases. 187 



with the experiments. This is in the limit at which diminu- 

 tion of pressure in the receiving vessel ceases to increase the 

 flow, which limit by the equations is reached when the pressure 

 in the receiving vessel is *527 of the pressure in the discharging 

 vessel. 



The equations referred to are based on the laws of thermo- 

 dynamics, or the laws of Boyle, Charles, and that of the 

 mechanical equivalence of heat. They were investigated by 

 Thomson and Joule (see Proc. Roy. Soc, May 1856), and by 

 Prof. Julius Weisbach (see Civilinc/enieur, 1856); they were 

 given by Rankine (articles 637, 637a, Applied Mechanics), 

 and have since been adopted in all works on the theory of 

 motion of fluids. 



Although discussed by the various writers, the theory 

 appears to have stood the discussion without having revealed 

 the cause of its failure ; indeed, Hirn, in a late work, has 

 described the theory as mathematically satisfactory. 



Having passed such an ordeal, it was certain that if there 

 were a fault, it would not be on the surface. But that by 

 diminishing the pressure on the receiving side of the orifice 

 the flow should be reduced and eventually stopped, is a con- 

 clusion too contrary to common sense to be allowed to pass 

 when once it is realized ; even without the direct experimental 

 evidence in contradiction, and in consequence of Mr. Wilde's 

 experiments, the author was lead to reexamine the theory. 



2. On examining the equations, it appears that they con- 

 tain one assumption which is not part of the laws of thermo- 

 dynamics 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 integrations 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 discre- 

 pancy 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 inte- 

 grations 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 



