476
OHM ON THE GALVANIC CIRCUIT.
the present case gives, when designates the length of the circuit, and the origin of the abscissæ is placed in its centre[1],
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where the sums must be taken from to , and the integrals from to . If we now substitute in this equation for its value , whereby according to our supposition in the preceding paragraph, if a represents the tension at the place of contact,
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and then integrate, we obtain, since between the indicated limits
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and
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for the determination of the equation
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and, lastly, since
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which equation, for , i. e. when it is not intended to take into consideration the influence of the atmosphere, passes into
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It is easily perceived that the value of the second member to the right in the equations which have been found for the determination of , becomes smaller and smaller as the time increases,
- ↑ See Journal de l'Ecole Polytechnique, cap. xix. p. 53.