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 . 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 .