A supporting magnetic force leaves an unknown factor
Picture a circular copper coil in an annular gap. The magnetic field points radially across the wire. Current flows around the circle, and the forces on the wire add to a vertical force. A feedback system adjusts the current to hold the coil at a prescribed height, called the null position. A greater mass generally needs a greater supporting current.
Current alone does not reveal the mass. The force also depends on the magnetic field and the effective length of wire inside it. Their combined effect is called the magnetic factor. A real field varies across its gap, and a real winding has dimensions. Measuring these details separately with very high precision is difficult.
Motion measures the factor that weighing needs
A moving coil also develops an induced voltage, the same basic effect used in a generator. The balance removes the mass and leaves the coil circuit open while measuring that voltage. For the same coil shape and magnetic field, a faster motion gives a larger voltage. Dividing voltage by speed measures the magnetic factor needed for weighing.
This changes which quantities must be measured. Instead of separately mapping the field and every part of the winding, the experiment measures voltage and velocity. An interferometer usually follows a reflector attached to the moving assembly. Light travels between that reflector and fixed optics; motion changes the optical path. The angle of the optical axis matters because the instrument measures the component of velocity along its beam.
Bryan Kibble proposed the idea at the UK National Physical Laboratory in 1975 and published it later. Its original purpose concerned the electrical current unit. Stable Josephson and quantum Hall electrical references subsequently helped turn the mechanical and electrical comparison into a route for mass metrology.
The two measurements yield one mass
The moving experiment measures the magnetic factor. The weighing experiment measures the current needed for support. Together with local gravitational acceleration, these quantities determine mass. The shared factor disappears when the relations are combined, leaving voltage, current, velocity and gravity. A familiar arrangement of the relation has power units on both sides.
The term virtual power describes products formed from separate measurements. During weighing the coil is stationary, so gravity supplies no continuing mechanical power. During open-circuit motion no electrical power is delivered to a load. Current and induced voltage are measured in different modes. The instrument can therefore compare the quantities without converting mechanical power into electrical power at the same instant.
Cancellation depends on matching magnetic conditions
Suppose weighing occurs high in the gap but the velocity result comes from lower down. If the field changes with height, the two magnetic factors differ. Giving them the same symbol cannot remove that difference. A velocity scan can instead pass through the weighing height, measuring voltage divided by velocity along its path. Interpolation within that measured range then supplies the local factor. A height beyond the range needs another measurement.
Equal positions also need compatible magnetic states. Weighing current produces a magnetic field and heating; magnetic material can retain a memory of earlier currents. The factor may therefore change between modes. A separate known-mass measurement can test whether their comparison still agrees. A failed check calls for investigating the field change before using a mass result.
Electrical references connect the comparison to the kilogram
A metrology instrument must also establish its voltage and current scales. Josephson voltage standards connect voltage to frequency. Quantum Hall standards supply a stable resistance reference, and calibrated voltage and resistance determine current. These electrical relationships involve the fixed Planck constant, providing a route from a macroscopic mass to fundamental constants.
Length, time, local gravity and electrical standards must all work together. The magnet and the comparison between modes remain central parts of that work. The factor disappears from the final relation because the two experiments share it under checked conditions.