  The Be stars display variable optical emission lines originating in the
circumstellar disc. Here we analyse high resolution spectroscopic observations
of Be stars and the distance between the peaks of H-alpha, H-beta, and H-gamma
emission lines ($\Delta V_\alpha$, $\Delta V_\beta$, and $\Delta V_\gamma$
respectively). Combining published data, spectra from the ELODIE archive
(obtained in the period 1998 -- 2003) and Rozhen spectra (obtained 2015 --
2023) of 93 Be stars, we find a set of relations connecting $\Delta V_\alpha$,
$\Delta V_\beta$ and $\Delta V_\gamma$. They are effective for $30 \le \Delta
V_\alpha \le 500$ km s$^{-1}$, $80 \le \Delta V_\beta \le 600$ km s$^{-1}$, and
$40 \le \Delta V_\gamma \le 300$ km s$^{-1}$. The new equations are in the form
$y=ax + b$ and are valid for a wider velocity range than in previous studies.
