  The energy spectrum of electrons produced in molecular gas by interstellar
cosmic rays (CRs) is rigorously calculated as a function of gas column density
$N$ traversed by the CRs. This allows us to accurately compute the local value
of the secondary ionization rate of molecular hydrogen, $\zeta_{\rm sec}(N)$,
as a function of the local primary ionization rate, $\zeta_p(N)$. The ratio
$\zeta_{\rm sec}/\zeta_p$ increases monotonically with $N$, and can
considerably exceed the value of $\approx0.67$ commonly adopted in the
literature. For sufficiently soft interstellar spectra, the dependence
$\zeta_{\rm sec}/\zeta_p$ versus $N$ is practically insensitive to their
particular shape and thus is a general characteristic of the secondary CR
ionization in dense gas.
