Originally Posted by jdlev
so what would be the purpose of the 3rd connection?
Short answer: Greater accuracy.
Long answer (stolen from elsewhere): In a three wire RTD one of the wires is connected to one side of the temperature element and the remaining two wires are connected to the other side of the element. The purpose of the third wire is to allow the temperature transducer to compensate for the resistance that the field cable adds to the total resistance in the RTD circuit. A typical transducer uses a Wheatstone bridge arrangement for the measurement circuitry.
Without lead length compensation, the temperature measurement would be off by the amount of resistance added to the RTD's resistance, and given that a typical industrial RTD is only 100 ohms at 0 deg C, the error can be significant depending on the length of the field cable.
By using two signal wires it provides greater accuracy by eliminating any wiring influences/errors.