A hot-wire movement is a historical movement in which the expansion of a wire provides the pointer deflection. The hot-wire movement consists of a hot wire tensioned by a coil spring, to which the instrument pointer is attached via a small roller.
When current flows through the hot wire, it expands and the coil spring moves the instrument pointer. The more current flows through the hot-wire, the greater its expansion and the associated pointer deflection.
The expansion of the hot-wire depends on the power dropped across the hot-wire, regardless of whether it is AC or DC. Since the expansion of the hot-wire depends on the power, resp. on the current flowing through as `I^2*R, there is a quadratic relationship between the expansion and the rms current, which is indicated via the non-linear instrument scale.