  Using the recently observed torsional Alfv\'en waves in solar prominences, we
determine the ionisation state of the plasma by taking into account that
Alfv\'en waves propagate in a partially ionised prominence plasma. We derive
the evolutionary equation of waves and compare the analytical solutions to
observations to determine the number density of neutrals. Using a single fluid
plasma approximation, where the wave damping is provided by the Cowling
resistivity, we study the temporal evolution of waves. By comparing the
solution of equations with observational data (period, amplitude, propagation
speed), we determined the value of the Cowling resistivity that led us to draw
a conclusion on the amount of neutrals in the partially ionised plasma, a
quantity that cannot be measured directly or indirectly. Our results show that
damped torsional Alfv\'en waves are an ideal diagnostic tool for the ionisation
state of the plasma. Using a simple model, we find that at the observational
temperature of torsional Alfv\'en waves, the number of neutrals is of the order
of $5\times 10^{10}$ cm$^{-3}$.
