Fundamental limits to mass comparison by means of a beam balance

Abstract

An attempt is made at an estimate of the ultimate limitations to the precision of mass comparison by means of a beam balance. Systematic effects due to imperfections of the balance suspensions, air buoyancy, humidity and load decentring are not considered. Mathematical models of knife-edge balances and flexure-strip balances are used to derive balance sensitivity and susceptibilities to tilt and horizontal ground vibration. It is shown that optimum designs exist and the magnitude of ground vibration perturbation is calculated. A rigorous treatment of thermal noise is given and the magnitude of the fluctuating torques due to viscous damping is calculated. The principal conclusion is that the precision of weighing is at present probably limited by ground vibration noise. Nevertheless, knife-edge balances should be capable of a resolution of tens of nanograms.