  We use well-established observational evidence to draw conclusions about the
fundamental nature of the viscosity in accretion discs. To do this, we first
summarise the observational evidence for the value of the dimensionless
accretion disc viscosity parameter $\alpha$, defined by Shakura & Sunyaev
(1973, 1976). We find that, for fully ionized discs, the value of $\alpha$ is
readily amenable to reliable estimation and that the observations are
consistent with the hypothesis that $\alpha \sim 0.2 - 0.3$. In contrast in
discs that are not fully ionized, estimates of the value of $\alpha$ are
generally less direct and the values obtained are generally $ < 0.01$ and often
$ \ll 0.01$. We conclude that this gives us crucial information about the
nature of viscosity in accretion discs. First, in fully ionized discs the
strength of the turbulence is always limited by being at most trans-sonic. This
implies that it is necessary that credible models of the turbulence reflect
this fact. Second, the smaller values of $\alpha$ found for less ionized, and
therefore less strongly conducting, discs imply that magnetism plays a dominant
role. This provides important observational support for the concept of
magneto-rotational instability (MRI) driven hydromagnetic turbulence.
