The general arrangement of the instrument is shown in Fig. 1; Fig. 2 being a diagram of the electrical connections.
FIG. 1.--KIRCHHOFF AND HANSEMANN'S BRIDGE FOR
MEASURING SMALL RESISTANCES.
The piece of metal to be measured, M, is placed in the measuring forks, gg, in such a manner that the movable fork is removed as far as possible from the stationary one; if the weight of the piece be insufficient to secure a good connection, additional weights may be placed upon it. The main circuit includes the battery, B (Fig. 2), consisting of from two to four Bunsen cells, the key, T, the German silver measuring wire, N, and the piece of metal resting on the forks, all being joined in series. The German silver wire, N, is traversed by two movable knife-edge contacts, cc, as shown. Connections are made between these contacts, cc, the resistance box, the prongs, k and l, of the forks, gg, and the reflecting galvanometer, as shown in Fig. 2. A resistance of ten units is inserted at o and n, while at m and p twenty units or one thousand units are inserted. The positions of cc are then varied until the galvanometer shows no deflection when the key, T, is depressed.
FIG. 2.--DIAGRAM SHOWING ELECTTRICAL CONNECTIONS OF BRIDGE.
When such is the case, the ratio of resistances n/m is equal to o/p; letting M equal the resistance of the metal bar between the points, h and i, and N equal to the resistance between the points, cc, on the measuring wire, N, then we shall have
M = N (n/m) = N (o/p).
Knowing the cross section in millimeters, Q, of the bar, and observing the temperature, t, in degrees Centigrade, its conductivity, x, as compared with mercury can be determined. If L be the distance, h l or k i, in meters, then
x = (1/m) (L/Q) (1 + at).