Carey Foster bridge

In electronics, the Carey Foster bridge is a bridge circuit used to measure medium resistances, or to measure small differences between two large resistances. It was invented by Carey Foster as a variant on the Wheatstone bridge. He first described it in his 1872 paper "On a Modified Form of Wheatstone's Bridge, and Methods of Measuring Small Resistances" ("Telegraph Engineer's Journal", 1872–1873, 1, 196).
Use.
In the adjacent diagram, X and Y are resistances to be compared. P and Q are nearly equal resistances, forming the other half of the bridge. The bridge wire EF has a jockey contact D placed along it and is slid until the galvanometer G measures zero. The thick-bordered areas are thick copper busbars of almost zero resistance.
To measure a low unknown resistance "X", replace "Y" with a copper busbar that can be assumed to be of zero resistance.
In practical use, when the bridge is unbalanced, the galvanometer is shunted with a low resistance to avoid burning it out. It is only used at full sensitivity when the anticipated 
measurement is close to the null point.
To measure σ.
To measure the unit resistance of the bridge wire EF, put a known resistance (e.g., a standard 1 ohm resistance) that is less than that of the wire as X, and a copper busbar of assumed zero resistance as Y.
Theory.
Two resistances to be compared, X and Y, are connected in series with the bridge wire. Thus, considered as a Wheatstone bridge, the two resistances are X plus a length of bridge wire, and Y plus the remaining bridge wire. The two remaining arms are the nearly equal resistances P and Q, connected in the inner gaps of the bridge.
Let be the null point D on the bridge wire EF in percent. is the unknown left-side extra resistance EX and is the unknown right-side extra resistance FY, and is the resistance per percent length of the bridge wire:
and add 1 to each side:
Now swap X and Y. is the new null point reading in percent:
and add 1 to each side:
Equations 1 and 2 have the same left-hand side and the same numerator on the right-hand side, meaning the denominator on the right-hand side must also be equal:
Thus: the difference between X and Y is the resistance of the bridge wire between and .
The bridge is most sensitive when P, Q, X and Y are all of comparable magnitude.