  We have evaluated a universal ratio between diffusion constants of the ring
polymer with a given knot $K$ and a linear polymer with the same molecular
weight in solution through the Brownian dynamics under hydrodynamic
interaction. The ratio is found to be constant with respect to the number of
monomers, $N$, and hence the estimate at some $N$ should be valid practically
over a wide range of $N$ for various polymer models. Interestingly, the ratio
is determined by the average crossing number ($N_{AC}$) of an ideal
conformation of knotted curve $K$, i.e. that of the ideal knot. The $N_{AC}$ of
ideal knots should therefore be fundamental in the dynamics of knots.
