We already can set limits on the drift over a long period by looking at the values obtained for fundamental constants that depend critically on mass. Thus setting an upper limit of < 0.1 mg per decade sets a limit of < 0.01 mg per year. These limits are being set more tightly as progress is made in such measurements. NPL has pioneered a promising method of monitoring this based on an improved realization of the watt, which can be monitored in terms of the Josephson and von Klitzing effects.