We have investigated the damping of a tightly stretched circular nickel grid vibrating at a few kHz in air, in gaseous 4He, in liquid He1 and in liquid HeII. Within experimental error, all the data can be plotted on a universal curve of Delta omega/omega0rho1 against lambdan, where Delta omega and omega0 are respectively the width and centre frequency of the resonance, rho1 is the density of the medium and lambda is the viscous penetration depth. The nuisance damping is small. It appears feasible to develop a vibrating grid viscometer which could with advantage be applied to certain specialised situations and, in particular, to the superfluid phases of liquid 3He.