  The energy dependence of the rate coefficient of the H$_2^+\ + {\rm H}_2
\rightarrow {\rm H}_3^+ + {\rm H}$ reaction has been measured in the range of
collision energies between $k_\mathrm{B}\cdot 10$ K and $k_\mathrm{B}\cdot 300$
mK. A clear deviation of the rate coefficient from the value expected on the
basis of the classical Langevin-capture behavior has been observed at collision
energies below $k_\mathrm{B}\cdot 1$ K, which is attributed to the joint
effects of the ion-quadrupole and Coriolis interactions in collisions involving
ortho-H$_2$ molecules in the $j = 1$ rotational level, which make up 75% of the
population of the neutral H$_2$ molecules in the experiments. The experimental
results are compared to very recent predictions by Dashevskaya, Litvin, Nikitin
and Troe (J. Chem. Phys., in press), with which they are in agreement.
