This answer was provided by Robert L. Heider, Lecturer and Adjunct Professor for the Department of Energy, Environmental & Chemical Engineering at Washington University in St. Louis.

The use of either 3- or 4-wire elements depends on the input circuit used. Three leads are used where the element is one leg of a bridge circuit. One of the common leads is connected to the voltage source. This balances the lead resistance, assuming the wires are of the same resistance. Four-wire elements are used where the source is a constant current generator. Two of the leads are used to power the element and the remaining two are used to measure the voltage drop across the element. The lead wire resistances are much lower than the input impedance of the voltage measuring input circuit. Two-wire element creates error in the measurement, the lead wires are not balanced. In the absence of any information from the transmitter specifications, refer to the following table:

Deflection type instruments
Length, feet Wire Size B&S Gage
250 or less 20 or larger
400 or less 18 or larger
625 or less 16 or larger
1000 or less 14 or larger
Null bridge
1500 or less 16 or larger

References

McMillan, G. K., Process/Industrial Instruments and Controls Handbook, New York, McGraw-Hill, 1999, Section 4-24

Considine, D. K., Process/Industrial Instruments and Controls Handbook, New York, McGraw-Hill, 1957, Section 2-57