348.]
WHEATSTONE'S BRIDGE.
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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
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with the equations of continuity
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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
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Hence, if we put
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we find |
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and |
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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
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If the electromotive force were made to act along the resistance of being still , and if the galvanometer were placed