7183, which is the base of the Napierian
logarithms. Let us look at this formula; in its general form it
resembles Ohm's law, but with a new factor, namely, the expression
contained within the brackets. The factor is necessarily a fractional
quantity, for it consists of unity less a certain negative
exponential, which we will presently further consider. If the factor
within brackets is a quantity less than unity, that signifies that
i_{t} will be less than E / R. Now the exponential of negative sign,
and with negative fractional index, is rather a troublesome thing to
deal with in a popular lecture. Our best way is to calculate some
values, and then plot it out as a curve. When once you have got it
into the form of a curve, you can begin to think about it, for the
curve gives you a mental picture of the facts that the long formula
expresses in the abstract. Accordingly we will take the following
case. Let E = 2 volts; R = 1 ohm; and let us take a relatively large
self-induction, so as to exaggerate the effect; say let L = 10 quads.
This gives us the following:
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