The critical exponent becomes ν ν ¯ ¯ = 0,369 63 … … for the diverging translational correlation length at the hexatic – crystalline transition. D. Nelson and B. Halperin predicted, that Frank's constant diverges exponentially with ν ν ¯ ¯ at T i , too. The red curve shows a fit of experimental data covering the critical behaviour; the critical exponent is measured to be ν ν ¯ ¯ = 0 , 35 ± ± 0 , 02 . This value is compatible with the prediction of KTHNY theory within the error bars. The orientational correlation length at the hexatic – isotropic transition is predicted to diverge with an exponent ν ν = 0 , 5 . This rational value is compatible with mean-field-theories and implies that a renormalization of Frank's constant is not necessary. The increasing shielding of orientational stiffness due to disclinations has not to be taken into account – this is already done by dislocations which are frequently present at T i . Experiments measured a critical exponent of ν ν = 0 , 5 ± ± 0 , 03 . KTHNY-theory has been tested in experiment and in computer simulations. For short range particle interaction (hard discs), simulations found a weakly first order transition for the hexatic – isotropic transition, slightly beyond KTHNY-theory.