58 
tain one assumption wliich 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 experi- 
ments in applying the laws of hydro-dynamics, it has no 
foundation as generally true. To avoid this assumption it 
is necessary to perform for gases integrations of the funda- 
mental equations of fluid motion which have already been 
accomplished for liquids. These integrations being affected, 
it appears that the assumption above referred to has been the 
cause of the discrepancy between the theoretical and experi-. 
mental 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 non-conductor 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 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.6., the velocity of the gas, and its intrin- 
sic energy. The laws of thermo-dynamics afford 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 J oule ; this equa- 
tion holds at all points in the vessel or the effluent stream. 
If then the pressure at the orifice is known as well as the 
pressure well within the vessel where the gas has no energy 
of motion we have the velocity of gas at the orifice, and 
