Reasons are given why the axial dispersion in a gas flowing through a packed bed may be influenced by the elasticity - or compressibility - of the fluid. To support this hypothesis, experiments have been done in a packed column at pressures from 0.13 to 2.0 MPa. The elasticity E of a gas is proportional to the pressure P and the compressibility to 1/P. The axial dispersion coefficients as determined were found to be a function of the pressure in the packed bed in the turbulent flow region of 3 < Re-p < 150 if the Bodenstein number is plotted as a function of the particle Reynolds number. This is shown to be an artifact. The pressure influence is eliminated, if Bo(m,ax) is plotted versus the ratio of the kinetic forces over the elastic forces rho u(2)/E. Regrettably, Bo(m,ax) seems to be independent of rho u(2)/E. For the moment we only can conclude that Bo(m,ax) in the turbulent region is a unique function of the velocity of the gas which flows through the packed bed. Although the fact that a constant Bo value is obtained when plotted against rho u(2)/E, the experimental results are so intriguing we wanted to make them public already now. The experimental work proceeds.