  The precision measurement of the hyperfine splitting $\Delta_{\rm HF} (1P,
c\bar c)=M_{\rm cog} (\chi_{cJ}) - M(h_c) = -0.5 \pm 0.4$ MeV in the
Fermilab--E835 experiment allows to determine the gluonic condensate $G_2$ with
high accuracy if the gluonic correlation length $T_g$ is fixed. In our
calculations the negative value of $\Delta_{\rm HF} = -0.3 \pm 0.4$ MeV is
obtained only if the relatively small $T_g = 0.16$ fm and $G_2 = 0.065 (3)$
GeV${}^4$ are taken. These values correspond to the ``physical'' string tension
$(\sigma \approx 0.18 $ GeV$^2$). For $T_g \ge 0.2$ fm the hyperfine splitting
is positive and grows for increasing $T_g$. In particular for $T_g = 0.2$ fm
and $G_2 = 0.041 (2)$ GeV${}^4$ the splitting $\Delta_{\rm HF} = 1.4 (2)$ MeV
is obtained, which is in accord with the recent CLEO result.
