In this formula i_{t} means the strength of the current after the lapse of a short time t; E is the electromotive force; R, the resistance of the whole circuit; L, its coefficient of self-induction; and _e_ the number 2.7183, 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: ________________________________________ | | | | | t_{(sec.)} | e^{+(R/L)t} | i_{t} | --------------+--------------+---------| | 0 | 1 | 0 | | 1 | 1.105 | 0.950 | | 2 | 1.221 | 1.810 | | 5 | 1.649 | 3.936 | | 10 | 2.718 | 6.343 | | 20 | 7.389 | 8.646 | | 30 | 20.08 | 9.501 | | 60 | 403.4 | 9.975 | | 120 | 16200.0 | 9.999 | ----------------------------------------