On the Comparison of Resistances.
345.] If is the electromotive force of a battery, and the resistance of the battery and its connexions, including the galvanometer used in measuring the current, and if the strength of the current is when the battery connexions are closed, and when additional resistances are introduced into the circuit, then, by Ohm's Law,
Eliminating the electromotive force of the battery, and the resistance of the battery and its connexions, we get Ohm's formula
This method requires a measurement of the ratios of and and this implies a galvanometer graduated for absolute measurements.
If the resistances and are equal, then and are equal, and we can test the equality of currents by a galvanometer which is not capable of determining their ratios.
But this is rather to be taken as an example of a faulty method than as a practical method of determining resistance. The electromotive force cannot be maintained rigorously constant, and the internal resistance of the battery is also exceedingly variable, so that any methods in which these are assumed to be even for a short time constant are not to be depended on.
346.] The comparison of resistances can be made with extreme
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accuracy by either of two methods, in which the result is in dependent of variations of and .