Thermocouples involve two wires, each of a different material, that are electrically joined in a region of unknown temperature. The loose ends are measured in an open-circuit state (without any current, J = 0 ). Although the materials' Seebeck coefficients S are nonlinearly temperature dependent and different for the two materials, the open-circuit condition means that ∇ ∇ V = − − S ∇ ∇ T everywhere. Therefore (see the thermocouple article for more details) the voltage measured at the loose ends of the wires is directly dependent on the unknown temperature, and yet totally independent of other details such as the exact geometry of the wires. This direct relationship allows the thermocouple arrangement to be used as a straightforward uncalibrated thermometer, provided knowledge of the difference in S -vs- T curves of the two materials, and of the reference temperature at the measured loose wire ends.