Let us make use of the fact that any "black box" circuit consisting of resistors can be reduced

to a form (Fig. 217), where the quantities R_{1}, R_{2}, . ., R_{5} are expressed in terms of the resistances of the initial resistors of the "black box" circuit (this can be verified by using in the initial circuit the transformations of the star-delta type and reverse transformations). By hypothesis, equal currents pass each time through resistors of resistance R_{1} and R_{4} and also through R_{3} and R_{5} (or there is no current through them when the clamps are disconnected). Using this circumstance, we can simplify the circuit as shown in Fig. 218. Then, by hypothesis,

It can easily be verified that