The quantitative experimental study of the Eckhaus instability in one-dimensional systems is carried out, employing electrohydrodynamic convection in a nematic layer. The obtained Busse balloon is in good agreement with that predicted by the Eckhaus theory. However, the observed changes of the wavenumber for unstable roll patterns, caused by the Eckhaus instability, as well as the growth rates for the corresponding spatial modes differ dramatically from those the theory yields for the most unstable Eckhaus modes. Possible reasons for the disagreement are discussed.