Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/441

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348.]
WHEATSTONE'S BRIDGE.
399

conductors Let the currents along be and the resistances Let an electromotive force act along Required the current along

Let the potentials at the points be denoted by the symbols The equations of conduction are


with the equations of continuity



By considering the system as made up of three circuits in which the currents are respectively, and applying Kirchhoff's rule to each cycle, we eliminate the values of the potentials and the currents and obtain the following equations for



Hence, if we put


we find
and


348.] The value of may be expressed in the symmetrical form, or, since we suppose the battery in the conductor and the galvanometer in , we may put the battery resistance for and the galvanometer resistance for . We then find



If the electromotive force were made to act along the resistance of being still , and if the galvanometer were placed